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Frosting and Defrosting of Air-Coils- Results from Laboratory Testing

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Swedish National Testing and Research Institute Energy TechnologyOP DCDfiDT -4 nnc oo

Per Fahlen

Frosting and Defrosting of Air-Coils - Results from Laboratory Testing

This report pertains to research grant No. 950203-6 from the Swedish Council for Building Research and the annual grant from the Ministry of Industry and Commerce to the Department of Energy Technology of the Swedish National Testing and Research Institute.

SPSwedish National Testing and Research Institute Energy TechnologyQP RPPDRT 1QQR-9Q

2

AbstractFrosting of air-coils is an important factor in the design and operation of air-source heat pumps, heat recovery ventilators, cooling and refrigeration equipment etc. This report presents results from laboratory testing of two brine-cooled air-coils under frosting conditions. The coils have the same number of plane, continues fins, 4 tube rows with 12 tubes in each row, tube spacing of 50 mm and fin spacing of 3 and 6 mm respectively.

The original purpose of the test program was to compare various possible indicators of coil frosting and to analyze the possible effects of different control strategies on coil capacity and the COP of the system (the analysis will be presented in a separate report). Tests involved inlet air temperatures of -7 and +2 °C, variation of humidity between 70 and 100 % RH (including simulated rain), velocities in the range 1 to 4 m/s, and specific cooling loads from 50 to 150 W/m2.

Test results include variations due to frosting of e.g. cooling capacity, COP, air flow and pressure drop, fan power, air outlet temperature and humidity, coil temperature, frost mass, and frosting time. Results also include the subsequently required defrost time, defrost energy and collected mass of defrost water. The frosting process was interrupted when the air flow had decreased to 30 % of the original value with a non- frosted coil. The results clearly show the advantage of demand controlled defrosting with variations in frosting time between 2 h with high humidity/high specific cooling load up to, for practical purposes, infinite frosting times with low humidity/low specific cooling load. The accumulated frost mass during one frosting cycle varied from less than 0.02 kg/m2 up to approximately 0.4 kg/m2.

Key words: air-coil, defrost, experimental, frost, heat pump.

Swedish National Testing and Research Institute

SP RAPPORT 1996:29 SP REPORT 1996:29ISBN 91-7848-634-3 ISSN 0284-5172 Boras 1996

Postal address:Box 857, S-501 15 BORAS, SwedenTelephone + 46 33 16 50 00 Telex 36252 Testing S Telefax+ 46 33 13 55 02

DISCLAIMER

Portions of this document may be illegible in electronic image products. Images are produced from the best available original document

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- Contents Page"Abstract 2

List of symbols and abbreviations 4Symbols 4Subscripts and superscripts 11Abbreviations 12Dimensionless numbers 13

1 Introduction 141.1 Background 141.2 Project description 141.3 Test coils 151.4 Test program 161.5 Test equipment 21

2 Measurands and defrost indicators 312.1 Alternative defrost indicators 312.2 Selected defrost indicators 36

3 Test coils 413.1 Coil design 413.2 Coil data 483.3 Dry coil tests 53

4 Results with a frosting coil 654.1 +2 °C: Variation of specific cooling load 654.2 +2 °C: Variation of humidity 854.3 +2 °C: Variation of air velocity 1054.4 -7 °C: Variation of air velocity 1254.5 -7 °C: Variation of specific cooling load 1444.6 Simulated rain - coil A 1554.7 Simulated rain - coil B 1754.8 Commercial defrost controller 194

5 Discussion and presentation of final results 1955.1 Defrost indicators 1955.2 Optimized defrost control 1965.3 Defrost time and energy 1975.4 Frost mass, defrost water and some characteristics 198

of the frost5.5 Use of the Lewis equation 1995.6 Quality of results 200

6 References 201

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Appendices

A Uncertainty budgets of measured quantities 203B Uncertainty budgets of derived quantities 221C List of measurands and measuring channels 233D List of data files 237E Mass flux of water vapour 239F Equations for pressure drop 243G Equations for heat transfer 246

List of symbols and abbreviationsSymbolsLatin letters

A Area; m2Aa Total air-side effective surface area of coil;Ay Total brine-side surface area of coil;Afin Surface area of fins;Afront Frontal area of coil;Ar Total, refrigerant-side surface area of coil;A0 Total air-side surface area of coil;Ad Inside surface area of tubes with diameter d;Ad Outside surface area of tubes with diameter D;

a Thermal diffusivity; m2/s

COP Coefficient of performanceCOPj Coefficient of performance in the heating modeCOPim Coefficient of performance in the heating mode; integrated mean valueCOP2 Coefficient of performance in the cooling modeCOP2m Coefficient of performance in the cooling mode; integrated mean value

C Heat capacity flowrate (C = M -cp);Wor kW

cp Specific: heat capacity at constant pressure; J/kg/K or kJ/kg/Kcpa Specific heat capacity; dry air;cpa. Specific heat capacity; humid air;cpb Specific heat capacity; brine;cpw Specific heat capacity; liquid water;cpw. Specific heat capacity; water vapour;

D Binary diffusion coefficient; m2/sDjr Effective diffusion coefficient of water vapour in frost; m2/s

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D, d Diameter; m or mmD Outside diameter of tubes;d Inside diameter of tubes;dh Hydraulic diameter;

H Height; m or mmH Height of a coil;

h Specific height; m or mmh Specific height of a fin (h = H/nJ;

h Specific enthalpy; J/kg/K or kJ/kghal Specific enthalpy; dry air; inlet of coil; J/kg/K or kJ/kgha.j Specific enthalpy; humid air; inlet of coil; J/kg/K or kJ/kgh^ Specific enthalpy; dry air; outlet of coil; J/kg/K or kJ/kgha-2 Specific enthalpy; humid air; outlet of coil; J/kg/K or kJ/kg

I Electric current; A

L Length; m or mmL Length of the coil in the direction of air flow;Lfin Length of a fin in the direction of air flow;

l Specific length; m or mml Specific length of a fin ((= Lfm/n( = pj)\l Characteristic length (e.g. in the definition of Reynolds number);

M Mass; kgMa Mass; dry air;Ma. Mass; humid air;Mdw Mass; collected defrost water;Mfr Mass; frost on coil surface;Mw. Mass; water vapour in air;Ma Mass; molar mass of dry air; kg/kmol

Mw Mass; molar mass of water; kg/kmol

M Mass flowrate; kg/s or kg/hMa Mass flowrate; dry air through coil;Ma> Mass flowrate; humid air through coil;Mb Mass flowrate; brine;M fr Mass growth rate; frost on coil surface;

Mw Mass flowrate; water;

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m Surface mass; kg/m2mfr Specific frost load (referenced to the air-side surface area of a coil);

m Mass flux or mass velocity; kg/s/m2 or kg/h/m2rhj-r Mass flux of frost (referenced to the air-side surface area of a coil);ma Mass velocity of air;ma< Mass velocity of humid air;mb Mass velocity of brine;

N NumberNfm Total number of finsNrow Total number of tube rows (see nj)Nmbe Total number of tubes

n Specific numbern[ Number of tubes in the direction of air flow (longitudinally; n; = Nrow)nt Number of tubes orthogonal to the direction of air flow (transversely)

n Moisture content (absolute humidity); kg water vapour/kg humid airn' Actual moisture content of air;n" Saturated moisture content of air;n"w Saturated moisture content of air at wall temperature;

p Pitch; m or mmPfin Fin Pitch;Pl Longitudinal tube pitch;pt Transverse tube pitch;

p Pressure; Pa, hPa or kPa (pressure difference is designated Ap)pa Absolute pressure in the air flow; ,p' Actual vapour pressure of water in air;p" Saturated vapour pressure of water in air;p"w Saturated vapour pressure of water in air at wall temperature;p0 Absolute atmospheric pressure;

Q Thermal energy; J or kJQd Heat input to coil during defrosting;

Q Thermal capacity; W or kW

Q j Heating capacity (at the condenser of a heat pump);

Q 2 Cooling capacity (at the evaporator of a heat pump);

Q a Cooling capacity (on the air side of a coil);

Q b Cooling capacity (on the brine side of a coil);

Q d Defrosting capacity (on the brine side of a coil);

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q Specific heat load; W/m2 or kW/m2q a Specific cooling load (cooling capacity referenced to the

total air-side surface area of a coil);

R Gas constant;R Universal gas constant; 8134 J/kmol/KRa Gas constant of air; kJ/kg (Ra = R / Ma)

Rw Gas constant of water vapour; kJ/kg (Rw = R / Mw)

r Specific enthalpy of phase change; J/kg or kJ/kgrgs Specific enthalpy of sublimation, gas—>solid

(add index 0 to indicate at 0 °C); rgl Specific enthalpy of vaporization, gas—^liquid;

(add index 0 to indicate at 0 °C); rIs Specific enthalpy of freezing, liquid->solid;

(add index 0 to indicate at 0 °C);

s Spacing; m or mms0 or sfin Unfrosted fin spacing;s or Sfr Spacing between frost surfaces of adjacent fins; s( Longitudinal tube spacing;st Transverse tube spacing;

t Temperature; °Ctj Temperature; condensing temperature;t% Temperature; evaporating temperature;tal Temperature; air inlet to a coil; dry bulb;ta2 Temperature; air outlet from a coil; dry bulb;tdp j Temperatore; air inlet to a coil; dew point;tdp2 Temperature; air outlet from a coil; dew point;tbl Temperature; brine inlet to a coil;tb2 Temperature; brine outlet from a coil;tbi Temperature; brine inlet (cold side) to a heat pump evaporator;tbo Temperature; brine outlet (cold side) from a heat pump evaporator;tfin Temperature; fin surface;tr Temperature; refrigerant temperature;ts Temperature; frost surface;tw Temperature; wall temperature;twb Temperature; wet bulb;twi Temperature; heating water inlet to a heat pump condenser;two Temperature; heating water outlet from a heat pump condenser;

T Thermodynamic (absolute) temperature; K

U Thermal transmittance (total coefficient of heat transfer);W/(m2-K) or kW/(m2-K)

U Defrost indicator signal; V or normalized (non-dimensional)

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u Velocity; m/sua Velocity of approach; mean value based on the air flowrate and the

frontal area of a coil; m/s

V Volume; m3 or dm3Vdw Volume of water collected after defrosting of a coil; m3 or dm3

v Specific volume; m3/kg or dm3/kg

V Volume flowrate; m3/s or m3/hVa Volume flowrate; air through coil;Va< Volume flowrate; humid air through coil;

Vb Volume flowrate; brine (cold) side of a heat pump;Vw Volume flowrate; water (hot) side of a heat pump;

W Width; m or mmW Width of a coil;

w Specific width; m or mmw Specific width of a coil, i.e. the fin pitch (w = W/(Nfin - 1) =

= Sfm + Sfin = Pfin); m or mm

W Work (mechanical or electric); J or kJWef Electric energy input to fan;Wem Electric energy input to compressor motor;We0 Total electric energy input to heat pump (excluding defrost);Wd Electric energy input to defrost system;Wd* Energy released during a defrost;

W Power (mechanical or electric); W or kWWef Electric power input to fan;

Wem Electric power input to compressor motor;WeQ Total electric power input to heat pump (excluding defrost);

Wed Electric power input to defrost system;

Wd Mean electric power input to defrost system;

Wd Mean defrost power with total cycle input concentrated to a defrost;

x Vapour ratio (specific humidity); kg water vapour/kg dry airx' Actual vapour ratio;x" Saturated vapour ratio;x"s Saturated vapour ratio at frost surface temperature;x"w Saturated vapour ratio at wall temperature;

z Concentration; kg/kg or %zb Concentration; brine; kg glycol/kg aqueous glycol solution or %

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Greek letters

a Film coefficient of heat transfer; W/m2/K or kW/m2/Kaa Film coefficient of heat transfer; air side;<xb Film coefficient of heat transfer; brine side;

Ap Pressure difference; Pa or kPaApa Pressure difference; air side of coil;Apb Pressure difference; brine side of coil;

8 Thickness; m or mm8fm Fin thickness;8fr Thickness of the frost layer;8W Wall thickness;

ew Porosity;Lewis coefficient = (3-Cp/a = Le""1 (n = 0.33 or 0.67);

<p Relative humidity; Pa/Pa" or %(pal Relative humidity; air inlet of coil;(pa2 Relative humidity; air outlet of coil;

(p Phase angle (between current and voltage); ° or radians

X Thermal conductivity; W/m/KXa Thermal conductivity of air;Xh Thermal conductivity of brine;Xfin Thermal conductivity of fin;X^bg Thermal conductivity of tube;

fl Viscosity (dynamic); Pa-s or mPa-sp.a Viscosity of air;|Xb Viscosity of brine;

Tj Efficiency; -ri A Area efficiency; -rifin Fin efficiency; -rid Defrosting efficiency; -

V Viscosity (kinematic); m2/s or mm2/sva Viscosity of air;vb Viscosity of brine;

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9 Temperature difference; K0j Inlet temperature difference of coil (taj - tb2);______Ogjn Geometric mean temperature difference (= «Jdi ■ % );0jn Logarithmic mean temperature difference (= — %)/ ln(0j / 62))',0O Outlet temperature difference of coil (t^ - tbl);

p Density; kg/m3pa Density of air;pa- Density of humid air;pb Density of brine;pw Density of water;p' Density of water vapour;p" Density of saturated water vapour;

T Time; s, min or hXc Time; duration of a full frosting - defrosting cycle;Xd Time; duration of the operation in the defrost mode;Tyr Time; duration of the operation in the frosting mode;

T Tortuosity; -

Dimensionless numbers£tube Pressure-loss coefficient related to the tube arrangement

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Subscripts and superscripts

A Area 0 Outleta Air (dry)* row Number of tube rowsa' Moist air* t Transversea" Saturated moist air tube TubeB Bulk tot Totalb Brine** w Wallc Coil w Waterc Cold side w Weightc Condensate S Sensible (heat)c Cycle s Solidd Defrost s Surfacedw Defrost water stab Stabilizationdp Dew point wb Wet bulbe Evaporating X Variable xe Electricf Fan 0 Non-frosted conditionfin Fin 0 Total (e.g. total air pressure)fr Frost 0 0°Cfront Frontal (area) 1 Hot (condenser) sideg Gas 1 Inlet sideh Hot side 2 Cold (evaporator) sideh Hydraulic 2 Outlet sideI Currenti Inlet Vapour phaseL Latent (heat) Saturated vapour( Liquid Infinity (far from the wall)( Longitudinalmax Maximummin Minimum

*As the physical properties of moist and dry air differ only marginally, the distinction between index a and a' is not always observed in the report.

**EN 255(2) denotes any secondary coolant based on water with an anti-freeze additive as a 'brine'.

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Defrostheater pump

Figure 0.1. Designations used in the present research work on the frosting of coils.

References

Reference to literature is made by superscripts within brackets, e.g.:I

'....Swedish standard 2095(22)...... 1

Abbreviations

DAS Data Acquisition SystemDBT Dry Bulb TemperatureDPT Dew Point TemperatureFITT Fixed Interval Time-Temperature defrostLHR Latent Heat RatioLMED Logarithmic Mean Enthalpy DifferenceLMTD Logarithmic Mean Temperature DifferenceNTU Number of Transfer UnitsPRT Platinum Resistance ThermometerRE Relative HumiditySHR Sensible Heat RatioSP Swedish National Testing and Research InstituteVITT Variable Interval Time-Temperature defrostWBT Wet Bulb Temperature

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Dimensionless numbers

Eu

Fr

J

La

LHR

NTU

Nu

Pe

Pr

Re

Sc

Sh

St

SHR

A

Euler number; Eu = ■2 Ap

Froude number; Fr =

Colburn J-factor; J =

nl 'P'umax u

NuRe- Pr1/3

= Sf-Pr2/3= — 8

, , Pr D Sc a .Lewis number; Le = — = — (or Le = — = — in some references)

Sc a Pr D

Latent Heat Ratio; LHR = Ql Qs

Qtot Ql+QsU-A

Number of Transfer Units; NTU = ~zUA

(-min (Af • C„)p/mm

Nusselt number; Nu ■a-lX

H • lPeclet number; Pe =----

aV

Prandtl number; Pr = — a

H * lReynolds number; Re =-----

VV

Schmidt number; Sc = -~

, BlSherwood number; Sh — —g-

Stanton number; St = NuRe Pr

Qc QcSensible Heat Ratio; SHR = — = -t-----%—

Q,ot Ql+Qs

Analogy number; A = —y ~ Pr-2/3

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1 IntroductionThis report provides detailed data from measurements on two cooling coils under frosting conditions. The data include temporal variations of thermal capacities, flowrates, pressure drops, temperatures, humidities, and frost mass. Analysis and detailed discussions of these data will be conducted in subsequent reports. However, some derived results have already been presented at international conferences (Fahlen(7,9)).

1.1 Background

Frosting is a well-known phenomenon in air-source heat pumps, refrigeration coils and heat recovery ventilators. Current scientific literature reflects this by providing numerous articles and reports connected to this topic. O'Neal^20) and FahlenC10), for instance, provide in depth reviews and surveys of this literature. The practical importance notwithstanding, there is a shortage of measured data regarding real-world air-coils. Most theoretical and experimental work concern simple geometries such as flat plates or circular tubes and O'Neal^20) points to the importance of further work regarding actual coils. In particular, there is scant information on frosting in the regime of low Reynolds numbers. As practical coils often operate in the transitional or even pure laminar regime, this is indeed an important area for continued research.

Malhammart18) and Sanders^21) provide the most extensive investigations previously reported on finned-tube coils. Malhammart18) in particular, has. tested a number of different direct-expansion refrigerant-cooled air-coils. These data form the basis for some thorough theoretical work resulting in a reasonably simple proposal for the description of the frosting process in terms of non-dimensional characteristic numbers. Sanders also discusses defrosting and its control in some detail.

Defrost control poses many practical problems that often find unsatisfactory solutions in every-day installations. Indeed, Fahlen^5- Q discloses that this is one of the most frequent problem areas regarding air-source heat pumps and heat recovery ventilators and this very fact was the origin of the present investigation. This has been further highlighted by Bergstrom^) et al during field investigations of air-source heat pumps. Finally, several researchers propose various methods of optimizing defrost control, e.g. Granryd(lS), Young(23) et al and Fahlen(4X

1.2 Project description

The problem of defrost control initiated a series of projects on the topic of 'Frosted air-coolers' conducted in co-operation between the Swedish Council for Building Research and SP. In this series of investigations our main objective has been to survey existing literature, to look at the performance of current equipment in field tests as well as in laboratory situations, and finally to investigate the detailed behaviour of real coils under frosting conditions, in particular with respect to defrost control. The projects did not, however, purport to investigate the mechanisms of frost formation as such.

1 Introduction

15

In retrospect this is a pity since the laboratory results in particular could have yielded highly interesting information regarding the actual frost growth. Some measurands were regarded merely as indicators in the study of defrost control, where absolute accuracy was not of great concern. However, for the study of processes involved in the heat and mass transfer during frosting, some parameters must be measured with high accuracy, notably surface temperatures in the coil and the humidity and flow conditions. Fahlen® discusses this in great detail. With a judicious choice of some of the measuring equipment, accuracy could have been much improved if this had been of concern at the time the project was conceived.

To summarize, the measurements and calculations that were planned for the present project had the following main objectives:

• To compare different criteria for the initiation of a defrost,• To investigate the potential for some kind of optimized defrost control,• To investigate the time and energy requirement of a defrost,• To study the frosting process and compare the mass of frost and defrost water,• To validate using the Lewis equation in the calculation of frost growth.

For this purpose, we commissioned two brine-cooled air-coils (see 1.3 and 3.1-3.2) to act as test beds for our frosting - defrosting tests.

1.3 Test coils

We chose brine-cooled coils in order to have a high degree of flexibility regarding the choice of temperature profile through the coil. A more important reason, however, was a recognition of the fact that very few previous investigations concern indirect air-cooling systems. There has also been a clear trend in Sweden since the early 1980s towards indirect systems, both regarding refrigeration applications and regarding large exhaust and outdoor air heat pumps.

As a starting point we opted for a coil with a nominal fin spacing of 3 mm and this, combined with the values of specific cooling load and air velocity, gave the design specifications of the coil. Sections 3.1-3.2 detail the coil design. To investigate the influence of fin spacing we designed a second coil, identical to the first except for a fin spacing of 6 mm. Both coils had the same fin thickness and the same arrangement of tubing (in-line arrangement, transverse and longitudinal pitch of 50 mm, 12 tube rows high and 4 tube rows deep). The coils were also equipped with plexi-glass windows on the top and bottom to facilitate visual observation of the frost growth. Defrost water dripped into a an inclined pan below the coil and drained through a pipe at the front. Table 3.2.1 in section 3.2 summarizes the most important coil data.

1 Introduction

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1.4 Test program

As stated in section 1.2, the project focuses on the study of defrost control. This necessitates investigations of coil behaviour under a variety of operating conditions. The available economic resources enabled us to perform approximately 30 different tests. Therefore we had to limit the number of tests and in the planning of the test program the following parameters were considered to be the most important influence factors on the frosting process of a coil:

• Air temperature and humidity at the inlet of the coil• Air velocity at the inlet of the coil (flowrate divided by facial area of the coil)• Specific cooling load (initial coil capacity divided by total air-side heat transfer

area)• Coil specifications (fin separation, fin thickness, type of fins, tubing and its

arrangement, number of rows transversely and longitudinally, etc.)

Obviously the resources were not sufficient to investigate all the influence factors mentioned above. It was decided to concentrate on the two most severe test conditions for air source heat pumps according to the Swedish standard SS 2095(22X These rating conditions also closely resemble those of the coming European standard EN 255-2(2X We considered 2 m/s to be a fairly typical velocity of approach for the air entering the coil and that 100 W/m2 was a suitable starting point for the specific cooling load. These basic assumptions gave a set of nominal test conditions around which the important parameters were varied one at a time. Hence a test program, as described in table 1.1, evolved.

During the tests, the condenser flowrate and inlet temperature were kept constant, as stipulated by SS 2095. The brine flowrate was also kept constant but the brine temperature was allowed to drop as the coil frosted up, just as it would in a real air- source heat pump. The air flow rate was adjusted to give the nominal inlet air velocity with a dry coil, but was then left to decrease as a result of the combination of the fan characteristics and the changing load-line due to coil frosting. The test program was repeated for yet another coil, identical to the first coil except for a fin spacing of 6 mm. In both cases the flow arrangement was cross-counterflow with two parallel circuits, (see figure 3.2.1. in section 3.2). Table 1.4.1 below gives the operating conditions of the test program.

1 Introduction

Table 1.4.1. Operating conditions during tests of air coils in frosting situations.A and B designate the coils with 3.5 and 6.1 mm fin spacing respectively (nominal spacing of 3 and 6 mm).

Test no. Temperature(°C)

Relative humidity (%)

Air velocity (m/s)

Specific cooling load (W/m2)

Al.Bl +2* 85* 2* 100*A2, B2 +2 85 2 50A3, B3 +2 85 2 150A4,B4 +2 70 2 100A5, B5 +2 95 2 100A6, B6 +2 85 1 100A7, B7 +2 85 4 100AS, B8 7** 85** 2** 100**A9, B9 -7 85 1 100

A10.B10 -7 85 4 100All, Bll -7 85 2 50A12.B12 -7 85 2 150

Extreme testsA13.B13 +2 Rain 2 100A14.B14 +2 Rain 1 100A15.B15 +2 Rain 4 100

Dry testsA16.B16 +20 Dry coil 0.5 50-250

(5<f*,<15 °C)A17.B17 +20 Dry coil 1.0 50-250

(5<fM<15 °C)A18.B18 +20 Dry coil 1.5 50-250

(5<t„<15 °C)A19.B19 +20 Dry coil 2.0 50-250

(5<fM<15 °C)A20, B20 +20 Dry coil 3.0 50-250

(5<fH<15 °C)A21, B21 +20 Dry coil 4.0 50-250

(5<f„<15 °C)

^Nominal test conditions, +2 °C.**Nominal test conditions, -7 °C.Figures in bold type indicate variables that were changed from the nominal conditions.

1 Introduction

18

1.4.1 Defrost indicators

There is a proliferation of different defrost indicators in actual installations and in theoretical presentations. Sections 2.1 - 2.2 discuss some of these possible indicators. To compare the most common of these indicators, without installing all the actual controllers, some basic variables were measured. In the tests, frosting was permitted to pass the point of defrost initiation normally indicated by any of the variables, thus permitting a comparison of all variables at the same time. Some of the variables below were calculated from the measured operating parameters (see 1.4.6) whereas others had to measured separately.

tal - lb2 :

{al ~ tfin •

APac:Apf:va or ual :Wef or Ijjn .costp:%d and xfr:ur.

U2-

Air inlet temperature difference (referred to the brine outlet)Air inlet temperature difference (referred to the coil surface)Coil pressure drop Fan pressure difference Air flowrate or air velocity Fan motor power or current input Fan motor phase angleThe time to carry out a defrost compared to the frosting time Output from a commercially available controller (analogue Lidstrom unit)Output from a commercially available controller (digital Lidstrom unit)

The different parameters were measured continuously and compared to see when either of them would have initiated a defrost, had it been in control of the defrost system.

1.4.2 Optimized defrost control

Proposed measurands for optimized defrost control were (see for instance Young(23)

: Instantaneous and integrated mean value of the heating capacity (by means of twi, two, and Vw)

: Instantaneous and integrated mean value of the cooling capacity of the heat pump (by means of tbi, tbo, and Vb )

: Instantaneous and integrated mean value of the cooling capacity of

the coil (by means of tbh tb2, and Vb )Instantaneous and integrated mean value of the coefficient of performance in the heating mode (dividing Q\ by Wem) Instantaneous and integrated mean value of the coefficient of performance in the cooling mode (dividing <22 by Wem)

and FahlenW):

Q\ and Q\m

Q2 and Qlm

Qb and Qbm

COP] and

COP2 and

1 Introduction

19

1.4.3 Defrost time and energy

The air-coil was defrosted by means of warm brine or electric heating elements. In the case of defrosting with brine, the input was estimated from the measured electric input to heat the brine and the time it took to defrost. The following parameters were measured:

Wed : Electric input to the warm brine tank (by an electronic powermeter)

xd: Defrost time, defined as the time the compressor stops due to thedefrosting criteria (measured by the computer time base)

1.4.4 Frost mass, defrost water, and some characteristics of the frost

The frosting process was studied by measuring the mass of frost, ice, and water on the coil as a function of time. Furthermore, the coil pressure difference was measured as a function of time and at certain selected operating conditions special studies were made of the frost distribution and this was documented by photography. An IR- thermography documentation was planned but was never actually carried out.

As an extra check, the defrost water was collected and measured after each defrost and compared with the measured frost mass in the coil. It was also planned to take frost samples for determination of the frost density. The method of measurement, however, was not immediately successful and no further time was spent on this. The following parameters were measured:

Mfr: Frost mass of the coil (1 strain-gauge load-cell)Mdw : Mass of defrost water (1 volume vessel)Apac: Coil pressure drop (1 electronic pressure difference device)

1.4.5 Use of the Lewis equation

The analogy between heat and mass transfer, in terms of the Lewis relation, can provide an estimate of the mass flux of water from humid air to a surface with a temperature below the current dew point. Coil design and air flow determine the heat transfer coefficient. Knowing the dew point temperature of the air and the surface temperature of the coil, the mass flux of water vapour can be estimated. For this purpose the following variables had to be measured:

Air inlet temperature (1 PRT and 6 thermocouples)Air inlet humidity (1 DPT-hygrometer)Air outlet temperature (1 PRT and 6 thermocouples)Air outlet humidity (1 DPT-hygrometer)Air flowrate (1 inverted orifice plate)Fin surface temperature (6 thermocouples)

*al•

^dpl'

ldp2'-Va-tfiiv

1 Introduction

20

1.4.6 Operating conditions

The operating conditions of the combination heat pump - cooling coil during a test are defined by the air temperature and humidity, the air flow through the coil, the specific cooling load of the coil, the temperature and flowrate of the brine, and finally the temperature and flowrate of the condenser water circuit. Therefore the following variables were measured during each test:

taJ\ Air inlet temperature (1 PRT and 6 thermocouples) tdpj: Air inlet humidity (1 DPT-hygrometer)ta2- Air outlet temperature (1 PRT and 6 thermocouples)tdp2- Air outlet humidity (1 DPT-hygrometer)Va : Air flowrate (1 inverted orifice plate)tbi: Brine inlet temperature at the heat pump (1 PRT)tbo: Brine outlet temperature at the heat pump (1 PRT)tbl: Brine inlet temperature at the coil (1 PRT)tb2: Brine outlet temperature at the coil (1 PRT)Vb: Brine flowrate (1 electromagnetic flowmeter)tbi: Water inlet temperature at the heat pump (1 PRT)tbo: Water outlet temperature at the heat pump (1 PRT)Vw: Water flowrate (1 electromagnetic flowmeter)

The specific cooling load defining the test condition is taken as the cooling capacity of the coil just after a defrost divided by the total air-side heat transfer area. This includes the air-exposed tubes and both sides of the fins but does not take fin efficiency into consideration. Flowrate and temperature difference at the coil provide the input to calculate cooling capacity.

1 Introduction

21

1.5 Test equipment

A test installation for air-source heat pumps provided a suitable facility for the testing of frosted air-coils. FahlenC7- U) briefly describes this set-up.

1.5.1 Climate chamber

The main purpose of the climate chamber is to keep the air inlet state at the prescribed temperature and humidity levels. Figure 1.5.1 illustrates the principle of the chamber and Fahlen(H) gives some further technical details. One important feature of this test room is a displacement conditioning system, which makes it possible to have large conditioning air flows and still have a low velocity inside the chamber (12 000 m3/h at less than 0.5 m/s). Another feature is a humidification system based on the principle of humidifying the outlet air until it is close to saturation and then cooling the air to the set dew-point. An SCR-controlled heater then reheats the air to the correct dry bulb temperature.

Test chamber, -20 to +40 °C

Figure 1.5.1. Principle of a test chamber with displacement ventilation and a dew point controlled humidification system.

1.5.2 Heat pump refrigeration system

A number of small unit-chillers acted as the heat pump or refrigeration system (manufactured by Volund, approximately 2.5 kW cooling capacity each). By connecting one or several such units, the cooling load on the coil could be varied in steps. Adjustment of the condenser flow and/or temperature then facilitates fine tuning of the capacity (see 1.5.3). Originally, three such units were intended to produce the three specific cooling loads stated in the test program. The coils, however, turned out to be somewhat oversized, so another Volund unit plus a larger

1 Introduction

22

ground-source heat pump unit were connected to the system (Thermia Module 8, approximately 5 kW cooling capacity). The Volund units operated in parallel and the Thermia unit in series with the battery of Volund units. The brine flowrate was kept constant and a buffer tank moderated any spurious temperature variations. Section 3.1 elucidates the question of coil size and cooling load and figure 1.5.2 below outlines the principle of the chiller system.

Exp. vessel

WarmExp. vessel

Flowmeter

Figure 1.5.2. Principle of the cold side of the chiller system, including a buffer tank and a brine storage tank for warm defrost liquid.

1.5.3 Heat sink (simulated heating system)

The water circuit of a simulated hydronic heating system cooled the condenser of the heat pump system (see figure 1.5.3). A speed-controlled pump kept the flowrate constant in this circuit and a buffer tank, with a volume equivalent to the volume of a radiator system, helped moderate variations of the water temperature. Furthermore, a plate heat exchanger, supplied by a central cooling water system, cooled the radiator/tank system and an SCR-controlled heater ensured that the inlet temperature to the condenser was constant. A computer updated the set value of this temperature after each defrosting cycle to keep the outlet temperature at a predetermined value with a dry coil. The outlet temperature was then permitted to drop, as the capacity dropped due to frosting, to imitate the behaviour of a real air-source heat pump system.

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23

V vvv

Exp. vessel

SP4680

From heat pump

To heat pump

H P4

Figure 1.5.3. Principle of the heatsink/heating system.

1.5.4 Test coils and brine

Sections 1.3 and 3.1-3.2 describe the test coils. To simulate an outdoor air heat pump, the coil was not ducted at the inlet. Since air flowrate was one of the important defrost indicators, a flow measuring system was attached to the outlet of the coil and the nominal flowrate could be adjusted by means of controlling the fan-speed or by using a specially designed damper (see figure 1.5.4). In the test program, flowrate was always adjusted by means of the damper. The flow measuring section also contained measuring points for the air outlet pressure, dry bulb temperature and dew point temperature after the coil. The intention was to have the fan mounted after the flowmeter, but in practice the order was reversed. This caused all sorts of measuring problems, which FahlenW discusses in detail.

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24

o

■ 500 : 540o--------- -------------B>*e- 810 575 255 • 180-[><1—^*<9—B=-

2860

Figure 1.5.4. Principle of the coil air-handling system.

The brine was a 44 %w ethylene glycol - water mixture, corresponding to a freezing point of -27 °C (EN 255 denotes any secondary coolant based on water with an antifreeze additive as a 'brine'). We chose this brine because it has better transport properties than propylene glycols or alcohols, without having the corrosive effect of e.g. calcium chloride. However, determination of the exact composition of the brine and its corresponding thermophysical properties proved to be a fairly complex task. We discovered substantial deviations between data for a pure glycol and the technical glycol that we used, which contained small amounts of various inhibitors. FahlenC8) discusses this in detail.

1.5.5 Defrosting system

We envisaged two main methods of defrosting the coil, firstly by means of warm brine and secondly by means of electric heating rods inserted in the coil. During the test program of section 1.4, we used only the first method.

1.5.5.1 Defrost initiation and termination

Defrosting was initiated when the airflow of an initially dry coil had dropped to 30 % of the initial flow due to frost build-up (in the tests with rain, this value was reduced to 10 %). A temperature criterion regarding the brine or coil surface terminated the defrost process and started the heat pump (see 1.5.5.2 and 1.5.5.3 respectively). For the fan to start, two conditions must be fulfilled. Firstly, there was a minimum delay of 30 seconds between heat pump start and fan start and secondly, the brine temperature must fall below the air inlet temperature.

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1.5.5.2 Defrosting system - Warm brine

Figure 1.5.5 illustrates the basic principle of the warm brine defrost system.

Exp. vessel

WarmExp. vessel

Defrostin

WdefrFrostingFlowmeter

Figure 1.5.5. Principle of the warm brine defrost system.

The warm brine system consisted of a constant speed pump, an electric heater and a tank to store the warm brine. A thermostat controlled the electric heater. When the control system triggered a defrost, the heat pump and the coil-fan stopped and a three- way valve switched the brine flow from the tank charging-circuit to the coil. The warm brine had an outlet temperature of around +70 °C and the defrost was considered completed when the return temperature from the coil exceeded +30 °C. Tests were also made with a return temperature criterion of+15 °C. With this criterion, however, there could still be frost left in the coil.

The defrost was quite rapid and only took 1 to 2 minutes. When the temperature had fulfilled the termination criterion, the three-way valve switched back, cold brine started to circulate through the coil, the heat pump started and the fan followed with the specified delay. The tank in the cold part of the brine circuit enabled the test setup to keep a reasonably low temperature in the system during the heat pump off- period. This method of defrost proved quite successful and the influence on the air inlet state was minimal thanks to the very rapid process.

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1.5.5.3 Defrosting system - Electric heating rods

Three electric heating rods could be inserted in tubes centrally located in the coil and evenly spaced in the vertical direction. After a defrost was initiated, the heaters would operate until the surface temperature of the fins exceeded +8 °C. Restarting of heat pump and fan followed the procedure of 1.5.5.1. Tests showed that this method was nowhere nearly as quick as the warm brine method. Instead of a few minutes, the defrost time was more than half an hour. This also caused practical problems in trying to keep the ambient air state at the prescribed temperature and humidity, and therefore this method was not used in the actual test program.

1.5.6 Measuring system

The following description of the data acquisition system (DAS) comes from a report by Fahlen(8).

1.5.6.1 Data acquisition

The measuring system that was used during the project was based on a central mainframe computer (PDF 11/44), which was used both to control the data acquisition and to control the testing equipment. The computer controlled a digital voltmeter (Solartron Orion 3530) to record analogue signals and to supply PRTs with a constant current. Pulses from flowmeters were counted by a special unit (SP AE-4680), which also served as an interface between the computer and the control equipment in the test rig by means of analogue controllers and relays. Figure 1.5.6 sketches the general layout.

power

Figure 1.5.6. General lay-out of the measuring system.

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To ascertain a reliable and distortion-free transmission of electrical signals a number of measures were taken. Some of these are listed below.

• Computers and measuring equipment had their electric power supplied via magnetic stabilizers to protect the equipment from conducted transients,

• All transmission lines were equipped with external copper-screens and individual screening of the parts to protect the system from electromagnetic interference by capacitive coupling. Furthermore, the transmission lines were installed in sheet-steel ducts to protect the system from interference by inductive coupling,

• The pulse-counter unit was designed only to accept pulses of a specified duration and amplitude (4 ms, 9 V) using a 2-wire open-collector type transducer on each flowmeter,

• The digital voltmeter has a high input impedance (> 1 Gohm, < 1 pF) to avoid electrical loading of the connected sensors. The DVM also has high values of Common Mode Rejection Ratio (CMRR > 160 dB) and Series Mode Rejection Ratio (SMRR > 70 dB) to further reduce the possibility of electromagnetic interference.

Other measures to ascertain the overall quality of measurement included a Measurement Assurance Program. This involved, among other things,

• Calibration of the digital voltmeter by the National Primary Calibration Centre (RMP). Deviations were generally within ±2 (J.V,

• Calibration of each sensor in situ, connected to the measuring system. In this way the entire measuring system, including computer soft-ware, was checked and each sensor was assigned with its own individual calibration factor, traceable to national or international standards,

• The possibility to double-check the DVM and temperature measuring system by means of precision resistors connected to some of the measuring channels. This provided a facility of on-line checking of the stability of the voltmeter and its current-supply for PRTs.

As a result of the measures taken to suppress electromagnetic interference, the selection of data acquisition equipment, and the calibration procedures used, errors introduced by the data acquisition system could generally be neglected.

1.5.6.2 Principles of measurement

The heating and cooling capacities were determined from measurements of flowrate and temperature difference during each measuring cycle. For each measuring cycle, the DAS calculated values of density and specific heating capacity depending on the actual

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temperature and composition of the fluid. The coil capacity could also be determined on the air-side by means of air flowrate and the differences in temperature and humidity.

The liquid flow-measuring sections contained straight lengths of more than 20D. For the air flow, there was only room for a very short straight length, so a flow straightener was installed and the entire coil-flowmeter package was calibrated.

Liquid temperatures were measured by very thin and long sensors inserted counterflow directly in the liquid. Sensors for the air temperature were fitted with radiation shields. To determine surface temperatures, a special arrangement was made to ensure good thermal contact with the fin (see figure 1.5.7 below).

Figure 1.5.7. Principle of the surface temperature measurement.

Air humidity could be measured by sampling the air in front of and behind the coil by means of hoses connected to small fans. By using dew point hygrometers, the humidity measurement is independent of temperature and can be measured outside of the actual air flow (see figure 1.5.8).

Figure 1.5.8. Principle of the humidity measurement.

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Frost mass was measured continuously by suspending the coil in a supporting frame, attached to an electronic load-cell. Figure 1.5.9 out-lines this arrangement. An insulated box protects the load-cell from adverse ambient conditions. A number of measures have been taken to eliminate the effect of undue forces on the load-cell. For instance, the connection between the coil and the subsequent flow measuring section was made of an air- and water-tight elastic fabric, and the inlet and outlet pipes were connected to the headers on the coil via metallic U-shaped bellows. The bellows facilitate any coil movements relative to the pipe-work. Finally, to avoid flow induced vibrations the coil was connected to the supporting frame via thin brass foils. These foils offer little resistance in the vertical, weighing direction, but are very stiff in the horizontal flow direction. Then the entire system was carefully calibrated before the tests commenced.

Loadccll

To the heat pump

Frame

Bellows

Cooling coil

Drip tray

Figure 1.5.9. Principle of the measurement of frost mass.

The defrost water that drains from the coil was collected in a small vessel. A levelsensor operated a pump which pumped the water from the vessel adjacent to the coil to a measuring vessel outside the climate chamber. This quantity could be compared with the measured frost mass.

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Finally, the measuring interval during frosting was 60 seconds. Since the duration of one single test could amount to 3 days and nights, one data file could have up to 4320 successive values for each measurand. On the other hand, the defrost process was so rapid that a different measuring program, with a sampling interval of 3 seconds, had to be triggered by the defrost initiation signal and operated only in the course of a defrost.

1.5.7 Measuring equipment

Fahlen® also provides a detailed description of the sensors used and their respective performance. Appendix C gives a complete list of all measurands, and the following types of sensors were used:

Liquid flowrate:

Air flowrate:

Air velocity:Liquid temperature: Air temperature:

Surface temperature:

Humidity:

Liquid pressure drop: Air pressure drop:

Frost load:Electric power input:

Phase angle:

Electromagnetic flowmeters (Krohne, Fischer & Porter)Inverted orifice plate (SP) with an electronic pressure difference sensor (Furness)AnemometerPlatinum resistance thermometers (Pentronic) Platinum resistance thermometers (Pentronic) for the absolute level and T-type thermocouples (Pentronic) for the spatial temperature distribution T-type thermocouples (Inor/Heraeus) of extra thin gauge wire, inserted in specially designed spacers to ensure a good contact with the fin surface Dew point hygrometers (chilled mirror devices; General Eastern)Electronic pressure difference sensor (Druck) Electronic pressure difference sensor with an automatic zero point setting device (Autotran)Strain gauge load cell (Load Indicator)Electronic power transducers (Cewe; individual measurement of each phase)Electronic phase angle transducer (HC FPPF)

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2 Measurands and defrost indicatorsThere are three major ways of counteracting the effects of frost growth :

• To design the coil in such a way that frosting does not occur (e.g. by surface coating, oversizing the coil etc.)

• To operate the coil in such a way that frosting does not occur (e.g. by capacity control or by changing the air-source inlet condition, for instance through a combination of outdoor or exhaust air and flue gases from a condensing boiler, which may be used as supplementary heat etc.)

• To defrost the coil when frosting is severe (e.g. by stop defrosting when the air temperature is sufficiently high, reverse-cycle or warm gas defrosting of direct expansion evaporators, warm brine defrost of indirect coolers, or by means of electric heaters in the coil etc.)

The main purpose of this project was to study and compare different methods of defrost control, in particular various possible indicators to initiate a defrost. Therefore only the third of the above alternatives will be discussed in the proceeding text. As to the possible alternatives of defrost control, Fehrm#2) lists a large number of possible methods in a literature survey that proceeded the present study. Young#3) gives some further alternatives, and Bergstrom#) et al account for practical experience with various control strategies.

2.1 Alternative defrost indicators

If you operate a system that needs defrosting at regular intervals, it is obvious that such defrosting should only take place when really necessary. When it does occur, the defrost should be as quick as possible to minimize 'production losses' as well as heat losses from the coil. To trigger the defrost activity, there are two principal methods:

• Time control (either a fixed interval time-temperature control, FHT, or a variable interval time-temperature control, V1TT)

• Demand control (direct or indirect sensing of the degree of performance degradation due to frosting)

The proceeding text will present a few different type of defrost controllers.

2.1.1 Time control

In general, time control constitutes a simple, inexpensive, and reliable alternative. The draw-back with such a system is that the margin required to be on the safe side results in a large number of unnecessary defrosts. This is detrimental both to the energy economy and the reliability of the system (even if the defrost controller as such has a high reliability, the large number of defrosts will unnecessarily stress the compressor).

2 Measurands and defrost indicators

32

2.1.2 Fixed time-temperature control (FITT)

A measured ambient temperature makes it possible to avoid defrosting in situations where no frost is forming at all. When the defrost interval is fixed during frosting conditions, i.e. below the set ambient temperature, the system is called fixed interval time-temperature control (HIT). Of course, even if the temperature as such would seem to require defrosting, this may often not be the case in practice since humidity and relative operating time of the compressor may vary greatly.

2.1.3 Variable time-temperature control (VITT)

When the defrost interval varies with the ambient temperature, the system is called a variable time-temperature control (VITT). The interdependence between temperature and defrost interval may be arranged as a continuously variable function or in fixed steps. Even in this case, there will be many unnecessary defrosts since there is no check on the actual status of the coil.

2.1.4 Control by temperature difference

One of the most commonly used demand control defrost indicators is the use of a representative temperature difference. As a result of frosting, the refrigerant or brine temperature will start to drop, given a constant air inlet temperature. Hence the difference between the air inlet temperature and the refrigerant temperature will increase. Measurement of the outlet refrigerant temperature will give the largest change and would therefore appear to be the first choice. As an alternative, the surface temperature somewhere in the coil can be used, but this has the disadvantage of not providing an integrated indication of coil performance, just the change in one particular position.

To account for the variations in temperature difference that derive from capacity variations induced by changes in air inlet temperature, sophisticated systems change the set-value of the difference with changes in air temperature (see for instance 2.1.11). To obtain a good result with such a system, each individual unit normally has to be fine-tuned on-site.

The end of a defrost cycle can be detected from either the refrigerant/brine outlet temperature or the surface temperature, depending on the type of defrost method. In the case of electric defrost, the surface temperature is the most likely candidate. On the other hand, when warm brine or hot or warm gas defrost is used, the refrigerant/brine outlet temperature can be put to good use also as an indicator of defrost termination.

Detection by temperature difference appears to work well for direct systems operating with constant air flowrate. However, in multi-coil systems, with a central supply of constant temperature brine or refrigerant, the inlet temperature to the coil will be constant and the change in outlet temperature may prove to small to detect with reasonable certitude. Furthermore, when sudden changes in air flowrate occur, as in exhaust-air heat pump systems with variable ventilation flows, it may be difficult to distinguish between flow related and frost related changes in the temperature difference.


33

2.1.5 Control by pressure difference

This is one type of demand control which has often been used on exhaust air heat pumps. As the coil frosts up, the pressure drop across the coil will change. How much the flowrate will decrease as a result of the increased pressure drop depends on the fan characteristics in relation to the load-line of the air-handling system. In exhaust air applications there may be complications if the ventilation rate can be varied. Sometimes the change in pressure difference is sensed with an air velocity sensor positioned in a small by-pass tube parallel to the coil. In outdoor coils the pressure sensor may also be exposed to spurious signals due to wind, leaves etc.

2.1.6 Control by flowrate

The change in flowrate partly works along the same line as the pressure difference method. However, this method has the advantage of measuring a parameter that is more directly coupled to coil performance than is the pressure drop. It is the change in flowrate which generally has the single most important effect on coil performance. Furthermore, when you measure flowrate directly you do not depend on fan characteristics in the same way you do with pressure difference methods (unless, of course, there is some form of speed control of the fan or an axial fan enters the 'pumping' region of its characteristic curve).

2.1.7 Control by fan-motor current

As pressure drop and flowrate change during frosting of a coil, so will the power input to the fan. Assuming constant supply voltage, the motor current will change more or less in proportion to the power input and therefore a current sensor is a viable defrost indicator. Detection of changes in fan power has the advantage of being an integrated indicator, not relying on the exact positioning of e.g. a temperature sensor somewhere in the coil. The modifying statement 'more or less' above, regarding current - power proportionality, refers to possible changes in phase-angle.

2.1.8 Control by fan-motor phase-angle

Just as the fan power changes as a result of load variations, so will the phase-angle between current and voltage. Such changes will depend greatly on both the fan and the fan-motor characteristics. For particular types of fan and motor combination, a phase-angle sensor has the potential of being a defrost indicator much as the fan- motor current has.

2.1.9 Control by required defrost time

There is a high degree of correlation between the mass of frost accumulated in an air- coil and the time it takes to defrost the coil. Hence, the defrost time is an indicator of frost accumulation and by monitoring this time the interval between defrosts can be modified accordingly. However, since the blocking effect of the same mass of frost depends on frost density, which in its turn depends on the conditions of its formation, some further considerations are due.


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2.1.10 Optimized control

True optimization of defrosts must consider the overall performance of the installation. Hence, the obvious method is to determine how changes in the defrost interval affects mean performance over a complete frosting-defrosting cycle (for further details, see 2.2). GranrydO5) has analyzed this problem in detail, both regarding optimization of the cooling capacity and optimization of the COP.Young(23) proposes an optimizing criterion in terms of a comparison between the instantaneous and integrated mean value of the COP. The integrated value includes the defrost period. When the instantaneous value falls below the mean value, this is the time to defrost since continued operation will lower the mean value. Finally, FahlenW discusses some possible ways of implementing an optimizing system, e.g. by measuring refrigerant temperatures and pressures.

2.1.11 An example of a commercially available defrost controller (Lidstrom)

We included one example of a commercially available defrost controller in the test program. This particular unit was chosen because it had faired well in the field tests reported by Bergstrom^1) et al, which preceded our laboratory work. The controller is made by K Lidstrom AB(16>17) and uses the temperature difference principle. The company markets two models, one using an analogue electronic unit and the other operating with digital electronics. In both cases the controller uses two temperature sensors of the type Ni-1000. One is installed at the air inlet of the coil and the other is attached to the refrigerant outlet pipe from the coil.

For the analogue unit, the installer sets a curve of the lowest permissible refrigerant outlet temperature, as a function of the air temperature, in accordance with figure 2.1.1. The curve is adjusted on the basis of information regarding a few temperature conditions that warrant a defrost. These temperature conditions should be selected within the expected operating range with defrost control. Lacking the possibility to . test and trim the installation, one can estimate the lowest permissible outlet temperature at a given air inlet temperature on the basis of the compressor-coil specifications.

In this example, an air temperatures of -10 and -17 °C correspond to evaporating temperatures of -23 and -29 °C respectively with a dry coil. To create the defrosting curve one must decide the minimum evaporating temperature at a given inlet air temperature before a defrost is due, in this case -10/-28 °C and -111-33.1 °C. The defrosting curve is a straight line connecting the minimum temperatures. This line is moved in parallel until it intersects the reference air-in curve at 0 °C and minimum evaporating temperature at 0 °C, in this case -20 °C, is set on the controller as Tpj. Finally, the current air inlet temperature and the controller output Tp2 are measured. If, for instance, the air temperature is -14 °C then Tp2 is adjusted to -2.8 °C in accordance with the difference between the air reference curve and the ‘help’ curve in figure 2.1.1.


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Reference curve (air in)

'Help' purve (parallel to the defrosting curve)

-14-(-11.2)=

L__ Compressor |

Defroslcurve

Figure 2.1.1. Principle of how to adjust the Lidstrom controller.

The controller has two basic functions, to initiate a defrost and subsequently to terminate this defrost. Termination is triggered when the outlet refrigerant reaches a predetermined temperature, set with a potentiometer. This temperature is independent of the air temperature. Initiation, on the other hand, is set by means of two other potentiometers. The first gives the lowest permissible refrigerant temperature at an air temperature of 0 °C. This setting (Tpi) decides the level of the defrost temperature curve. The second provides the slope of the curve (Tpi) and is adjusted at a different air temperature.

The digital controller works in a slightly different manner. This device automatically adjusts the defrost temperature curve and in doing this also considers long-term changes due, for instance, to compressor degradation or fouling of the heat exchanger. This controller also modifies the defrost termination temperature by considering the ambient air temperature. To set the controller, three parameters are adjusted. The first sets the maximum air temperature that warrants a defrost (+5 °C is the default value). The second set-point is the duration of the 'cooling-off period until the coil returns to normal operating temperature after a defrost. Finally, the third set-point decides the lowest permissible refrigerant temperature by setting the tolerance on temperature drop before a defrost is initiated. Once set, this tolerance automatically adapts itself to the prevailing air temperature.


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2.2 Selected defrost indicators

The main purpose of this project was to compare possible optimized defrost criteria with commercially available alternatives. Section 2.1 reviewed the viable alternatives and from this review some measurands will be obvious.

2.2.1 Optimizing measurands

Depending on the circumstances, one may wish to optimize the COP in either of the heating or cooling modes or, at other times, one may wish to optimize the heating or cooling capacity. The optimum time of defrost initiation will vary and optimum COP will generally require longer defrost intervals than does optimum capacity. The necessary measurands are:

- Heating and cooling capacity (<2i and <22 )

- Drive power and defrost energy input (We and Wd)- Heating or cooling mode coefficient of performance (CO/j and COPfr- Frosting, defrosting, and total cycle times (T^., Td, and Tc)

Thermal capacities were determined from measured flowrates and temperature differences across the respective heat exchangers (condenser and evaporator of the heat pump and the brine-cooled air-coil). COP was calculated by means of the calculated capacity and measured electric input.

2.2.2 Optimized capacity

If you know simultaneously the instantaneous and integrated mean capacity values, it is possible to optimize heating or cooling capacity according to:

<2(T)<<2m(T)VT<Tcwhere

A defrost starts at time To and during the defrost period useful cooling or heating capacity will be zero (or negative in the case of reverse cycle defrost). Since integration starts at the time of defrost, the integrated mean value will always be burdened with an initial period of zero capacity. It will therefore be lower than the instantaneous capacity until this starts to drop because of frosting. The general appearance of such a sequence will be the same as that illustrated in figure 2.2.2 regarding COP.

Regarding defrost time, there are really two such times with the selected defrost strategy of this project. The first is the actual duration of the defrost and the second is the time until the coil has been cooled below the ambient air temperature. At this point the fan will start and useful capacity will be available. Capacity between the end of the actual defrost and start of the fan is used to recover some of the heat expended


37

in the defrost. Unless stated otherwise, defrost time in this report refers to the time until the fan starts.

Figure 2.2.1. Temporal variation of heating or cooling capacity during a frosting - defrosting cycle using a time-discrete measuring system.

Figure 2.2.1 illustrates how the numerical integration was carried out. If the temporal change is slow, then integration over a short time interval can be approximated by the mean of the values at the start and finish multiplied by the interval, i.e.

t+AtJ Q(r) • dr =T

Q(r) + Q(r+Ar) ^ 2

This facilitates numerical integration by making it possible to easily update current values of the integrated mean at some particular time T;. If the last defrost was actuated at time To, then we have

<2m(Tt-+AT) =1

(t;+At-t0)

t,-+AtjQ(r)-dr =

TO

1(t; + At-t0)

dr +t,-+AtJ <2(t) • dr

\

T; y

i.e.

Qm(?i+Ar)~(Tf-Tp)

(Ti+i -To) (?i-r o)

(Qi + Qj+i)

2


38

This relation illustrates how new values contribute relatively less after some time than at the beginning since At becomes an ever smaller portion of total elapsed time. A more straight forward way is of course to just add incremental energy quanta as you go along,

At,- _«2i-At1+4't ^1 Qt • At,-(T;+l-?o) 2 • (T/+1 -To) ^ (T; - To )

In the end this will be the same but the previous relation is more convenient to use since you are only updating the most recent mean value.

2.2.3 Optimized drive power

By analogy with 2.2.2, the recurring update of the integrated mean value of the electric power input can be expressed as

However, at the start there is a principle difference between capacity and drive power since in the latter case the input to actuate a defrost must be considered. In the case of a reverse cycle or warm gas defrost this will be automatically included as the instantaneous power input to the compressor effects the defrosting (see also figure 2.2.2). In this project, however, warm brine from a storage tank effected the defrost and the input to this tank was distributed over the entire operating cycle. In the optimizing process this energy has to be concentrated to the actual defrosting period so that at t = Tj = T0 + id we have We = W*d (circumflexed times denote time intervals while T denotes clock-time). If we translate this energy to a mean defrosting power input Wj , concentrated to the defrost period, and introduce the total input to

the heat pump WeQ (excluding defrosting), we have

and

If we neglect the small input of controllers etc., then

We0 = Wem + Wepl + Wep2 + Wef


39

Finally, including defrost energy in the expression for time discrete systems we have

(Tz+1 -To) (Tz+1 _To)ATt-

(Tz--T0)

(%+We,M)

2

2.2.4 Optimized COP

Using the same approach as in the case of capacity and drive power, the optimizing criterion regarding COP may be expressed as:

where

COPm

COP(T)<COPm(T)VT<T

W = (^T)-W>^=7^7-|

T0O-T0)

G(T)

t0Xdt

The defrost energy will of course depend on the length of the frosting period, i.e. on %fr, and COP may refer to either the cooling or heating mode.

We can also express the mean value of COP in terms of energy, i.e.

T

COPm^) =<2(t)

Wj +We( T)

Je(T)-dT

TpT

W*d + \we(x)-dx

TO

aWz

(T-T0)+0%)eJm

and use the already calculated values of the integrated mean values for capacity and drive power according to 2.2.2 and 2.2.3. Depending on the type of defrost, the instantaneous and integrated curves may look somewhat different, as figure 2.2.2 illustrates.

COP (electric defrost)COP (reverse cycle defrost)

Figure 2.2.2. Qualitative appearance of instantaneous and integrated COP for two types of defrost.


40

When a heat pump takes energy from the heating system for defrosting purposes, such as the case is for reversible units, then both the heating output and the COP will be negative (fictitiously) during the defrost phase. Similarly, when a refrigeration coil defrosts, the cooling capacity will be negative as heat is emitted to the refrigerated space during the defrost. Furthermore, in a refrigerating application, the fan-motor input will detract from effective cooling capacity and the optimizing strategy will have to consider this.

2.2.4 Conventional measurands

The selected conventional measurands were:

- Temperature difference (ta — tb and ta-tj-in)- Coil pressure drop (Apac)- Air flowrate (Va)- Fan motor current and phase angle (Wej or 7^ and cp)- Defrost time (Td)

In order to be able to more readily compare these indicators, they were all normalized in relation to initial, non-frosted values, e.g.

fel-%2)0 (tb2)0-{tb2)r

with0<[^(T)<1

The spread in normalized values of a conventional indicator at the optimal time of defrost for different operating conditions may serve as a hint as to its usefulness. This would include the required safety margin to avoid a total frost-up and the corresponding trade-off in efficiency.

During the tests, the important environmental parameters were controlled and thus had to be measured. Such variables included the temperature and humidity of the inlet air. In order to check the actual precipitation of frost in the coil, the change in frost mass with time was measured and compared with the rate of dehumidification of the air as well as with the measured defrost water. All-in-all, a large number of parameters were monitored and appendix C gives an overview of these.


41

3 Test coilsThe test program envisaged testing of two coils with fin-spacing of 3 and 6 mm respectively. The intention was to have the possibility to simulate operation both with direct expansion of primary refrigerants and operation with the secondary coolant of an indirect system. Furthermore, tests with different types of defrosting should be possible. For this reason the coils were commissioned to have straight, open-ended tubes without the usual connecting bends. The coils were also equipped with inserts for electric defrosting rods.

3.1 Coil design

3.1.1 Back-ground

The out-lined concept makes it possible to connect the tubes in series or in parallel and to have the flow directions counter-current or in parallel according to the type of system to be simulated. Having a large portion of the tubes connected in parallel will result in a small temperature drop, thus facilitating simulation of refrigerant evaporators. On the other hand, in most dry evaporators there is a noticeable temperature drop caused by the pressure drop in the refrigerant tubes (often several K). This is more in line with the conditions in brine-cooled coils, with a fairly evenly distributed temperature difference through the coil.

The planned tests also included variations of the face velocity with nominal values of 1,2, and 4 m/s. Therefore, the fan was possible to operate with speed-control and the flow measuring section at the outlet of the coil was equipped with a specially designed damper. The specific cooling load was to be varied at 50,100, and 150 W/m2, which was considered to represent a commonly used design range. Hence the coil had to be sized for this capacity range using the capacity of the heat pump chiller available for this project.

The heat pump chiller at hand was a residential ground-source machine of the type Volund 700, containing 3 compressor modules with cooling capacities of 2 to 3 kW per unit. By using 1, 2 or 3 modules the specific cooling load could easily be varied in the three required steps. Fine-tuning of the capacity could be accomplished by adjusting the brine flowrate together with the condenser temperature and/or flowrate. Previous laboratory tests of this type of heat pump yielded cooling capacities for each module of

0.2 = 2.4 + 0,095 • tbi - 0.04 -(two- 45) [kW]

and an approximate power input to the compressor of

Wem = 1.3+0,023 • tbi +0.011- (two - 45) [kW]

These values apply to water and brine flowrates of 0.8 m3/h per module (the nominal test condition was tbiltwo = 0/45 °C).

3 Test coils

42

3.1.2 Sizing

The coil was designed for a specific cooling load of 50 W/m2 at the nominal dry bulb temperature of +2 °C, dry air, and a mean temperature difference of 5 K with a face velocity of 2 m/s. This sizing applies for the cooling capacity of one chiller module. Furthermore, it was decided to opt for a coil which was 4 tube rows deep and with equal transverse and longitudinal tube pitches of 50 mm. The nominal capacity of the coil at these conditions would then be 2.2 kW and the number of tubes per row along with the number of fins have to be determined. Summing the information, we have:

Coil dataTube pitch, transverse: pt = 50 mmTubes per row: nt = mNumber of fins: = nFin flow length: L = 4 50 = 200 mmCoil width: W= (n-l)-3 mmFin material, Al: Xj-m = 218 W/m/KTube inner diameter: d = 14.3 mmCooling capacity: Qb = 2.2 kW

Air dataAir inlet temperature, tal = +2 °C Face velocity: ua = 2 m/s Air density: pa = 1.29 kg/m3 Air side pressure drop: Apa = ... Pa

Tube pitch, longitudinal: p[ = 50 mmTube rows: = 4Fin pitch: pj-in = 3 mm or 6 mmFin height: H = m 50 mmFin thickness: 8pn = 0.5 mmTube material, Cu: \ube = 395 W/m/KTube outer diameter: d = 15.9 mmSpecific cooling load: qa = 50 W/m2

Air outlet temperature, = ••• °C Air flowrate: Va = ua-Ajront m3/s Air spec, heat capacity: cpa = 1006 J/kg

Bn'/ze z/ato (50 % ethylene-glycol/water) Brine inlet temperature, tbl =... °C

Brine flowrate: Vj, = 0.8 m3/h

m/sBrine density: p& = 1080 kg/m3 Brine viscosity: p.b = 8 mPas Reynolds number: Reb = 2644 Brine side pressure drop: Apb =... kPa

Brine outlet temperature, tb2 = ... °C

Tube-side velocity:Vh

ub = 1.37

Brine spec, heat capacity: cpb =3100 J/kg Brine thermal cond.: Xb = 0.43 W/m/K Brine Prandtl number: Prb = 57.6

3.1.2.1 Heat transfer

The cooling capacity is given by

withQb=U-A-F-6l n

%In

(eq. 3.1.1)

(eq. 3.1.2)

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43

F is the correction factor for not having a pure counter-flow arrangement. With the estimated heat capacity flowrates and temperature differences, F > 0.95 and will therefore be neglected in the following discussion.

The overall coefficient of heat transfer can be derived from

- + -°fin

- + -

U • A CCa • (Ay + Tfjfn • Ajfn) Xiube ' ^d,ln &b 'with

Ad,In “ %{D-d)

InD ‘ hube

(eq. 3.1.3)

(eq. 3.1.4)

According to Jiirges, aa can be estimated by the following simple approximation:

aa = 5.8 + 3.9nti = 13.6 W/m2/K (eq. 3.1.5)

This is the lowest value of the air-side heat transfer coefficient obtained by various relations that we considered and was therefore used to avoid undersizing of the coil.

The fin efficiency is a function of (as-Le2)/(>^„-<^n) and Le is an effective fin length that depends on the shape of the fin. Using a nomogram from Glas^13) et al the fin efficiency was estimated as

T\fm = 0.92

This is a very high value, which partly is due to the underestimated coefficient of heat transfer and partly due to the choice of a thick fin.

The heat transfer coefficient on the brine-side was estimated by Hofmann's relation,

Nub = 0.0216-Re°-86-Pr0-23 = 48.1 (eq. 3.1.6)

Hence the film coefficient of heat transfer could be obtained from

OCbNub • Xb

d= 1447 [W/m2/K] (eq. 3.1.7)

The following expression provides the tube-related heat transfer surface on the brine- side:

A<i =ni-m-W-jz-d = 4-m-(n — Y)-iz-d~0.00054m • n [m2] (eq. 3.1.8)

and correspondingly, for the air-side:

AD+rlfin-Afin=nrm-W-K-D + rlfin-2n-L-H =

= 0.00060m(n — 1) + 0.0184m- n~ 0.019m-n[m2] (eq. 3.1.9)

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44

The mean transfer area for heat transfer through the tube wall is:

(D-d)Ad, in = X—7Jy\" Ltube = 0-047%,-m-W =

In

= 0.00057m •(% — !) « 0.00057m •% [m2] (eq. 3.1.10)

Equation 3.1.3 then gives the overall coefficient of heat transfer as

—= —[1.28 + 0.0022 + 3.87] = — (eq. 3.1.11)U - A m-n m-n

This clearly shows that the heat resistance of the tube wall is quite negligible and the overall coefficient of heat transfer can be approximated by:

U- A = 0.194m •% (eq. 3.1.12)

where m is the number of tubes per row and n is the number of fins.

The requirement on specific cooling load of 50 W/m2 results in

Qb = 2200 = 50• (Ay + ) = 50• 0.02-m-n (eq. 3.1.13)and

m • % = 2200 (eq. 3.1.14)

The following relations apply for the cooling capacity:

Qa=Qb=U A'F'0\In (eq. 3.1.15)

Qa = Va ' Pa ’ cpa ’ (*<zl ~ Xa2) (e9- 3.1.16)

Qb~vb'Pb' cpb ■ (4,i - hi) (eq. 3.1.17)

Eq. 3.1.15, 3.1.12 and 3.1.14:

9ln=Q/(U-A-) = 2200 / (0.194 • 2200) = 515K

Eq. 3.1.16:

where

and

hi ~h2--2200 5651

(2m- 0.05% -0.003) -1.29 -1006) m-n

Va=ua- Afront = 2 - (0.05m) • (0.003%)

5651 5651hi-hi-'m ■ n 2200

= 2.57 K

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45

With taj = +2 °C and m-n = 2200 we have:

ra2 = +2 - (5661/2200) = 2 - 2.57 = -0.57 °C and

%2 -/M= 2200 / ((0.8 / 3600) -1080-3100 = 2.96^

Defining the inlet and outlet temperature differences of the heat exchanger as:

and usingei = W - h2 and 60 = ta2 - hi

%=-In

we have

$=<?,*•J

But- 0O = (.hi - hi)' (fa2 ' = (W" W " %7 " hi) = 2-57 -2.96 = -0.39 K

and0Zn = 5.15 K giving 9f = 0^-0-39/5.15 _ 0^.^0.0757 = 6o.0.9271

This gives us0,- = 2- (tbl + 2.96) = 0.9271-(-0.57 - fw)

andfw-(0.9271 - 1) = -0.57-0.9271 -2 + 2.96

Hencetbl = -5.92 °C and tb2 = -5.92 + 2.96 = -2.96 °C

Now, the physical properties of the brine used in the above estimates were taken at a temperature of approximately -5 °C and this would appear a close enough guess. At least the data should be on the conservative side for sizing purposes.

3.1.2.2 Pressure drop

The following approximate relation from Glas(3) et al is used for a first estimate on the air-side:

Apa Pa ■ ua = 1-29 -22 « 34 PaPfin ^

For the tube-side pressure drop, Blasius approximation for the friction factor gives:

0.3164 ' " Re/^

0.3164 2644° *25

0.04412

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46

and

4p* «(£&+/•i

= (38 + 0.04412-48-0.609 1080 0.0143 2

2 _

•1.372 = 130-103Pa

where the sum of the one-time losses of all bends and connections have been included. This means that a pump capable of more than 1.3 bars was needed with a straight series connection of the tubes. Therefore the pumps included in the heat pump unit had to be supported by a large external pump.

3.1.2.3 Design specifications

To summarize the estimates, we have for the air-side:

Air inlet temperature, tal = +2 °C Air outlet temperature, ta2 = -0.57 °CAir flowrate: Va = 0.731 m3/s = 2631 m3/h Air pressure drop: Apa = 34 Pa

and for the brine-side:

Brine inlet temperature, tbl = -5.92 °C Brine outlet temp., tb2 =.-2.96 °G Brine flowrate: Vb = 0.8 m3/h Brine pressure drop: Apb = 260 kPa(minimum flowrate with tubes connected in series)

The coil specifications are:

Tube pitch, transverse: pt = 50 mm Tube pitch, longitudinal: pi = 50 mmTubes per row: nt = 12 Tube rows: «; = 4Number of fins: Njjn = 204 Fin pitch: p^n = 3 mm or 6 mmFin flow length: L = 200 mm Fin height: H = 600 mmCoil width: W = 609 mm Fin thickness: S^n = 0.5 mm

Each coil was planned to have 3 electric defrosting rods, 650 mm long for the 3 mm fin pitch coil and 1400 mm long for the 6 mm pitch coil). This decreases the number of tubes by 3, so one extra longitudinal tube row was included for heat transfer purposes. Therefore the calculated number of fins is based on nt - 1. In the end the defrosting rods were included in a different manner, so all tubes were effective and hence the coil turned out slightly oversized. This had to be compensated for by including an extra chiller unit at times of high specific loads.

The heat exchanger with a 6 mm fin pitch was designed with the same height, depth, and number of fins. This, of course, would make the coil wider with W = 1218 mm and thus for this coil the design air flowrate at 2 m/s would be 1.462 m3/s (5262 m3/h).

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47

-Finally, to select a suitably sized load-cell for the weighing system, the mass of the large coil was estimated as the sum of the masses of copper tubes, aluminium fins, and the brine volume in the coil:

Mean = 4-12-(1.218+0.2)-(tc/4)-(0.01592 - 0.01432>8930 ++ 2040.00050,20.62700 + (rt/4)0.014324 12(1.218+0.2) 1080 == 23.1 +33.0+11.8 = 67.9 kg

Furthermore, the maximum expected frost mass, i.e. with the coil fully blocked by frost, was estimated at 20 kg for the small coil and 40 kg for the large coil (mean frost density of around 300 kg/m3). Thus a load cell with 100 kg capacity, and some overload capability, would be suitable.

Figure 3. /. 1. Photo of a test coil.

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48

3.2 Coil data

The coils as delivered from the manufacturer turned out to have wider fin spacing than commissioned (the spacing was approximately equal to the commissioned fin pitch). Therefore the coil width was also larger and the design air flows had to be increased. In the end the cooling capacities of the unit-chillers were not enough and had to be supported by extra units. Table 3.2.1 gives the coil data as measured on the delivered units. In the calculation of fin and tube surfaces the following relations apply:

i,tube 7t • d-W• Ntufoe

Ao,tube — ft ' D ■ Ntube ' — ^ fin " ^fin )

Am=2Nj,n(,HL-N,ubenD2/4)

Tube side pressure drop turned out to be a problem with all tubes connected in series. On the other hand, with to many tubes in parallel, flow became distinctly laminar and heat transfer became a problem. As a compromise, we chose a flow arrangement that was cross-counterflow with two parallel circuits (see figure 3.2.1. below).

Figure 3.2.1. Flow arrangement of the coils (cross-counterflow with two parallel circuits).

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49

Table 3.2.1. Characteristics of the air-coils. Type of fin: Plane, continuous. Tube arrangement: In line._____________ _________________ ___________ _____Characteristic Designation Coil A Coil B

Measured data

Number of fins in the flow direction zir) 1 1

Number of tube rows per fin in the flow direction

«/(-) 4 4

Number of parallel tube circuits np(r) 2 2

Width W(mm) 808 ±1 1317 ±2

Height H (mm) 600 ±1 600 ±1

Length (in the direction of airflow) L( mm) 200 ±1 200 ±1

Fin thickness 5fin (mm) 0.5 ± 0.05 0.5 ± 0.05

Inside diameter of tubes d (mm) 14.9 ± 0.2 14.9 ± 0.2

Outside diameter of tubes D (mm) 16.6 ± 0.2 16.7 ± 0.2

Number of fins AM-) 204 ±2 200 ±2

Number of tube rows Alrow (") 4 4

Total number of tubes Ntube (") 48 48

Calculated data

Specific number of fins nfin = NfinW (nr1) 252 ±4 152 ±1.5

Number of tubes per row nt = NtubJA/row (”) 12 12

Specific width (i.e. the fin pitch, pjjn) w = WI(Nfin -1) (mm) 3.98 ± 0.04 6.62 ±0.04

Specific height h = H/nt (mm) 50.0 ± 0.1 50.0 ±0.1

Specific length l = L/Nrow (mm) 50 ± 0.2 50 ± 0.2

Fin pitch Pfin (mm) 3.98 ±0.04 6.62 ± 0.04

Transverse tube pitch Pt (mm) 50 ±0.1 50 ±0.1

Longitudinal tube pitch pi (mm) 50 ±0.2 50 ±0.2

Fin spacing (no frost) so (mm) 3.48 ± 0.06 6.12 ±0.06

Transverse tube spacing (pt - D) st (mm) 33.4 ±0.2 33.3 ± 0.2

Longitudinal tube spacing (pi - D) S[ (mm) 33.4 ±0.3 33.3 ± 0.3

Fin-side hydraulic diameter (no frost) dho ~ 2so (mm) 6.96 ±0.1 12.24 ±0.1Tube-side hydraulic diameter dht (mm) 14.9 ± 0.2 14.9 ± 0.2

Total tube length l-'tube (m) 38.78 ± 0.04 63.22 ± 0.04

Inside surface area of tubes Ad (m2) 1.82 ±0.02 2.96 ± 0.04

Outside surface area of tubes Ad (m2) 1.77 ± 0.02 3.07 ±0.04

Surface area of fins Afln (m2) 44.7 ±0.3 43.8 ± 0.3

Total air-side surface area of coil A0 (m2) 46.5 ±0.3 46.9 ±0.3

Frontal area of coil Afront (m2) 0.48 ±0.02 0.79 ±0.03

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50

Figure 3.2.2 shows the tube-side Reynolds number as a function of flowrate with the chosen configuration. It is obvious that the flow regime will be in the transitional region between laminar and turbulent and hence the value of the heat transfer coefficient will be uncertain. In particular at low brine temperatures, heat transfer will suffer.

Similarly, diagram 3.2.3 relates the air-side Reynolds number to the air flowrate. Also in this case the flow regime will be in the transitional region, ranging from laminar conditions at the low face velocity with coil A to turbulent flow with the high velocity and coil B. In this case, however, Granryd's relations cover the entire flow regime and thus the uncertainty regarding heat transfer should be smaller. Furthermore, the change from laminar to turbulent conditions are not at all as distinct on the air-side as on the brine-side, largely due to the combination of tube related turbulence with fin related laminar conditions

Tube-side Reynolds number as a function of brine flowrate

TurbulentLaminar f]

Brine flowrate (m3/h)

Figure 3.2.2. Reynoldsnumber as a function of brine flowrate, Vb, for different brine temperatures, tb.

Diagram 3.2.2 shows that the brine flowrate, in particular at low temperatures, has to be kept above 2 m3/h to ascertain turbulent conditions. In most of the tests, the flowrate has been in the range 1.8 to 2.4 m3/h, and this has generally sufficed in the tests with air inlet temperatures of +2 °C but not in the tests with -7 °C.

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51

Air-side Reynolds number as a function of air inlet velocity

Coil B

Coil A

Coil face air velocity (m/s)

Figure 3.2.3. Reynolds number as a function of air inlet velocity for three inlet air temperatures, ta(dfl = 2s0).

Diagram 3.2.3 gives the air-side Reynolds number, based on the fin-spacing, as a function of the air inlet velocity (also called face velocity or velocity of approach). It is obvious from this diagram that the flow will be mainly laminar in all tests with coil A. With coil B, however, the flow will vary between laminar in the case of 1 m/s over the transitional regime with 2 m/s to mainly turbulent flow with 4 m/s. Finally, diagram 3.2.4 relates the air velocities to the volume flowrate through the coils.

Air-side approach (ua) and fin spacing (us) velocities as a function of air flowrate

Coil A / Coil B

Air flowrate (m3/s)

------- Coil A: ua

------ Coil A: us

-- - - - - - -Coil B: ua

------ Coil B: us

Figure 3.2.4. The approach velocity, ua, and the air velocity between fins, u^ as a function of the air flowrate, Va ,for coils A and B.

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52

Table 3.2.2. Calculated flowrates, velocities and Reynolds numbers for coil A (nominal fin spacing of 3 mm). Index sO indicates that the Reynolds number is based on the hydraulic diameter 2sq of the fin spacing.

Coil A: s0 = 3.5 mm

Va ua us Ream3/s m/s (m/s) ta = -20 °C ta=o°c ta = +20 °C

0,00 0,00 0,00 0 0 00,24 0,50 0,57 339 297 2630,48 1,00 1,14 679 594 5260,72 1,50 1,72 1018 890 7890,96 2,00 2,29 1357 1187 10521,20 2,50 2,86 1697 1484 13151,44 3,00 3,43 2036 1781 15781,68 3,50 4,00 2375 2078 18411,92 4,00 4,57 2714 2374 2104

Tables 3.2.2 and 3.2.3 give the values used as inputs to the diagrams 3.2.2 and 3.2.3 respectively.

Table 3.2.3. Calculated flowrates, velocities and Reynolds numbers for coil A (nominal fin spacing of 6 mm). Index s indicates that the Reynolds number is based on the hydraulic diameter 2sq of the fin spacing.

Coil B: s0 = 6.1 mm

Va ua us Rcso

m3/s m/s (m/s) ta = -20 °C f,=o°c ta = +20 °C0,00 0,00 0,00 0 0 00,40 0,50 0,54 564 494 4380,79 1,00 1,08 1129 987 8751,19 1,50 1,62 1693 1481 13131,58 2,00 2,16 2257 1975 17501,98 2,50 2,70 2822 2468 21882,37 3,00 3,25 3386 2962 26252,77 3,50 3,79 3951 3456 30633,16 4,00 4,33 4515 3949 3500

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3.3 Dry coil tests

Some preliminary tests were made on the coils to check whether the design data were within reach. The main purpose was to ensure that the design specific cooling loads could be attained and that the brine flow could be kept in the turbulent range (which in the end proved not possible). The tests were primarily conducted on coil A.

3.3.1 Pressure drop

3.3.1.1 Air-side pressure drop

The air-side pressure drop was measured simultaneously with the calibration of the air flowmeter. Diagram 3.3.1 compares the measured data with data calculated according to Granryd(14) and GlasC13) for coil A and diagram 3.3.2 does the same for coil B (see also section 3.1).

We had expected the measured pressure drop to exceed the calculated value since, for the purpose of this project, we chose to operate with a non-ducted coil. Therefore, there will be contraction effects at the inlet and this was clearly demonstrated during measurements of the velocity distribution of the inlet air. Fahlen® indicates that the velocity in the peripheral parts of the coil face may be in the range of 10-25 % lower than the mean value. This, of course, will result in higher acceleration as well as total losses causing a larger than calculated pressure drop. Furthermore, subsequent heat and mass balances indicate that the problems regarding air flowrate, already mentioned in 1.5.4, resulted in the flowrate of coil A being underestimated by 10-20 % in the actual testing. Bearing this in mind, measured and calculated pressure drops agree fairly well. Appendix F provides the relations for pressure drop that were used.

Pressure drop as a function of velocity of approach

Velocity of approach (m/s)

Diagram 3.3.1. A comparison between measured and calculated pressure drop for coil A. Measured results derive from the calibration of the air flowmeter, so in this case the airflows will be the correct values of the laboratory standard.

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54

Regarding coil B, accuracy of the measured air flow was much better than for coil A, resulting in better agreement between measured and calculated data.

Pressure drop as a function of velocity of approach

Velocity of approach (m/s)

Granryd

MeasMeasMeas

Diagram 3.3.2. A comparison between measured and calculated pressure drop for coil B. Measured results derive from the calibration of the air flowmeter, so in this case the airflows will be the correct values of the laboratory standard.

3.3.1.2 Brine-side pressure drop

The brine-side pressure drop determines the attainable flowrate with a given pump. Since there is a tremendous difference in heat transfer between laminar and turbulent flow, it was important to ascertain turbulent conditions.

Pressure drop as a function of flowrateLaminar flow (-20 °C)

Laminar flow (-10

Laminar flow (0 0| ])


-20 °C, lam.

-20 °C, turb

°C, lam.

-10 °C, turb

------------0 °C, lam.

------------- 0 oC- turb.

♦ Measured

Diagram 3.3.3. Calculated pressure drop for coil A using relations for laminar and turbulent flow respectively. Arrows mark the transition points at 0, -10 and -20 °C. Measured values relate to a temperature range -5 °C to -10 °C.

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55

However, it proved difficult to maintain turbulent conditions and despite testing different tube arrangements and modifying the distribution system to the coil, it was quite difficult to avoid operating in the transitional to laminar regime. Figure 3.3.3 shows the calculated pressure drops for the selected tube arrangement at temperatures of 0, -10 and -20 °C. Coil A and coil B have the same tube diameters but due to the longer tubing of the wider coil B, the pressure drop will be approximately twice as high in this case.

In the tests the brine flowrate has varied in the range 1 to 2.5 m3/h. The indicated transitions between turbulent and laminar flow show that in most cases the flow has been in the transitional to laminar regime. This, of course has implications for the brine-side heat transfer

3.3.2 Capacity

Table 3.3.1 gives the results from measurements of the dry coil capacity of coil A. During test number 2, with a high specific cooling load, the surface temperature in the coil actually fell below the dew point temperature of the inlet air. Therefore the capacity in case 2 includes some latent cooling, approximately 5 %, but there is hardly any frosting due to the high ambient temperature. However, to infer the air-side heat transfer coefficient, only the sensible cooling capacity should be used.

Table 3.3.2 compares the measured and calculated overall heat transfer coefficients. By means of the calculated air and brine-side heat transfer coefficients, the inlet and outlet coil surface temperatures can be estimated according to:

4 -1 +

f ab'^b (eq. 3.3.1)

where s denotes the coil surface, a the air-side, and b the brine-side. The calculated values can be compared with measured surface temperatures.

From the results of table 3.3.1 it is obvious that something is wrong with the determination of cooling capacity, most likely regarding brine temperature since tbo should be greater than th2. In other tests with the same equipment, power balance was generally within +2 % on the heat pump and +20 % on the coil according to Fahlen(8).

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Table 3.3.1. Results from, tests without frosting.Measurand Symbol Testl Test 2

Temperature (AIfal/A16) (Alfa2/A17)Air inlet (PRT): W°C) 20.11 19.99Air outlet (PRT): (°Q 16.08-1.26* 6.84-1.27*Air inlet (TC): 'a, (°Q 19.59 18.53Air outlet (TC): 'a,(°C) 14.22 3.70Coil surface (TC): W°c) 15.57 11.37Coil surface (TC): W°C) 18.87 16.26Coil surface (TC): W°C) 16.71 9.55Coil surface (TC): W°C) 17.54 11.83Coil surface (TC): 19.46 18.16Coil surface (TC): 17.59 ' 12.81Coil surface (TC): W°c) 17.42 13.00Brine inlet to coil (PRT): (°Q 11.13 -5.69Brine outlet from coil (PRT): WQ 12.46 -1.66Brine inlet to heat pump (PRT): WO 12.91 -1.02Brine outlet from heat pump (PRT): WQ 11.17 -5.71Water inlet to heat pump (PRT): 18.01 18.14Water outlet from heat pump (PRT): WQ 19.81 22.91HumidityDPT: '4,/CC) 9.85 3.89DPT: 4,2 (°Q 8.59 1.08Frost/water: nhv (kg/h) 0.00 0.58FlowrateAir outlet: Va (m3/s) 0.504 0.515

Brine: Vb (m3/h) 2.212 2.096

Water: Pw (m3/h) 2.409 2.439

CapacityHeating capacity of heat pump: <2i (kW) 5.05 13.38

Cooling capacity of heat pump: 02 (kW) 3.85 9.64

Cooling capacity of coil (brine): <2& (kW) 2.95 8.27

Cooling capacity of coil (air):(gs + ql) 6, (kW) 3.29 (3.29) 9.52 (9.98)

Electric power inputCompressor motor: 1.218 3.985

Pump (water) ^i(kW) - -

Pump (brine) (kW) 0.528 0.529

Pump (brine) 0.895 0.652

Fan W^(kW) 0.712 0.736

Energy balanceHeat pump EB (%) +10.8 +5.8Coil EB (%) -11.5 -15.1 (-20.7)^Correction for the heating effect of the fan plus change of calibration constant

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\ %

Table 3.3.2. Comparison of calculated data and data inferred from measurements. The table uses values for the brine-side assuming turbulent or laminar conditions respectively.

Quantity Test 1 (turb./lam.) Test 2 (turb./lam.)Measured Calculated Measured Calculated

U (W/m2/K) 14.0 ■ 19.0/6.61 14.6 18.0/6.0aa (W/m2/K) — 22.3 —

ah (W/m2/K) — 3231/239 — 2328 /208+17.6 +13.5/+17.5 13.0 +2.3/+13.1

ts.OUt (°C) +15.6 11.6/13.3 9.6 -3.9/+1.2ts.mean ( C) +17.3 12.6/15.4 12.5 -0.8/+7.1Res — 570 — 601Red — 8299 — 3879

3.3.2.1 Air-side heat transfer

The air-side heat transfer depends on the flow conditions, the effective area of heat transfer and the thermo-physical properties of air.

Coefficient of heat transfer, Cta

Three alternative methods were used to calculate the air-side coefficient of heat transfer (1. by Granryd, 2. by Glas and 3. by Fahlen, see appendix G). Figure 3.3.4 compares the respective coefficients of heat transfer as a function of the face velocity of coil A.

Air-side heat transfer

air velocity, ua (m/s)

Diagram 3.3.4. Comparison of calculated air-side coefficients of heat transfer.

3 Test coils

58

Effective air-side area of heat transfer, Aa

The effective area relates to the total surface area by means of the area efficiency:

4z = 77a-4) (eq. 3.3.2)with

7?A = 1----J1 = Vfin since Afin = A0 (eq. 3.3.3)A)

This approximation applies in general for air-coils, since the finning factor is large. In the present work, Ayjn/ A0 ~ 0.96 and 0.93 respectively for coils A and B.

Fin efficiency, r\fm

Sanders has derived an expression for the efficiency of frosted fins by adding a term that represents the thermal resistance of frost,

tanh(;7 • L) P-L

with

P =

1

1 1^fr j cpa A'fin' ^ fin

(eq. 3.3.4)

(eq. 3.3.5)

ffr aa •'

and with L = equivalent height of fin,

L = Pt'Plit

— Z)) •

f2i

Pt-Pi'

1 + 0.35 In %D

\ J

(eq. 3.3.6)

where pt and pt are the transverse and longitudinal tube pitches respectively, b is the ratio of the change in enthalpy to the change in temperature for saturated air approximated by h-a0 + b-t. The ratio b/cpa indicates the augmented wet heat transfer in relation to the coefficient of dry heat transfer. Setting 5/r = 0 gives the traditional relation for dry fins.

The test coils have fin efficiencies around 0.9 in most test conditions. The high efficiency derives from a combination of fairly thick fins and low air-side heat transfer coefficient.

Thermo-physical properties of air

The most important thermo-physical properties of air are density (p„), specific heat capacity (cpa), thermal conductivity (ka), dynamic (p.a), and kinematic viscosity (v„),

3 Test coils

59

thermal diffusivity («„), and Prandtl number(Pr„). Fahlen® provides the following relations:

1.2925 p .pa =-------~t— 101^4 kg/m3 (? m °C and p in kPa)

1 +2733

cpa = 1.006 kJ/kg/K

4 = (24.54 + 0.0755? - 0.4375 • KT4 • ?2) • 10“3 W/m/K

jtta = (l7.10+0.0465? - 0.9375 • KT4 • ?2) • 10"6 Pa-s

Va =— m/s Pa

aa =Pa 'cpa

m2/s

The thermo-physical properties should be evaluated at the bulk temperature, ?a-6, or the film temperature, ?„/, according to the advice given with the heat transfer relation. In the present work the following definitions apply:

and

7 fal + fa2 la,b ~ 0

7 _ /q! /fl2 /wl /yv2r«./ “ A

with index b for bulk,/for film and w for wall.

3.3.Z.2 Brine-side heat transfer

Coefficient of heat transfer, 0la

The Hausen or Dittus-Boelter relations were used to calculate the brine-side coefficient of heat transfer (see appendix G). Figures 3.3.5 and 3.3.6 compare the respective coefficients of heat transfer as a function of the coil total flowrate (2.5 m3/h corresponds to a mean brine-velocity in the tubes of 2 m/s).

3 Test coils

60

Brine-side heat transfer


—■— 0 °C. lorn

—■— 0 “C. turb

-io°C,lom

*••<>-• -10 °C, turb

—*- - -20 ”C, lam

— * - -20 °C, turb

Diagram 3.3.5. Comparison of calculated brine-side coefficients of heat transfer for both laminar and turbulent flow.

It is obvious that there is an extremely large difference between the calculated turbulent and laminar coefficients of heat transfer. In the actual work with frosted coils, flow was generally laminar resulting poor heat transfer.

Brine-side heat transfer


—■— 0 °C. lam

-io°C,lam

—*- - -20 °C. lam

Diagram 3.3.6. Comparison of calculated brine-side coefficients of heat transfer assuming laminar flow.

One observation in hind-sight is that enhancement of the inside heat transfer surface should be quite beneficial. It may well be better to accept the fact that flow will be laminar and heat transfer poor and increase the area instead of trying to push the flowrate up with resulting high pressure drops.

3 Test coils

61

Thermo-physical properties of brine

The most important thermo-physical properties of brine are density (p*), specific heat capacity (cpb), thermal conductivity (X6), dynamic (p&), and kinematic viscosity (yb), thermal diffusivity (ab), and Prandtl numberC?^). Fahlen® provides the following relations for the chosen brine (ethylene-glycol).:

pbySP(t°C) = 1004.074461 -25.2639f4r)- 135sf-Ilf ? ^.100, .100, .100,

+ 19.03701 — -11.23961 T^r I +144.4485] — | +.100, iJ .100,

'I5-6feI+4feI-'53-49181r_i_y

Viooj +

-51.32100) 1100

z l + 69| 1ioo; uoo

t \ ( z )3 ______j t \ { z-155.8008

100, vooj + 107.3914 ioo ; uoo;

where t is given in °C and z in % by weight of the aqueous glycol solution.

<>,$/>(<“ C) = 4.182837 + 0.0915^^-0.26^ tlOOy

\2+ 0.2177603

.100,+

+ 0.2215395f t ^

U00y•0.291192

' t ^

Uoo;-03367 ioo; -6.95

U00y+

+9-074786(h)3-3-682002(m)4-a4ti(l55

+6971.15o J' l Too J "9m969 H

(+ 3.741235 ioo; Uoo;

uooj

kl/kg/K

3 Test coils

62

4 = (0.40585 + 0.00075; - (z - 41) • (0.0036 +1 ■ 0.000016) W/m/K

^ = (5.95-0.31725;+0.0082625.;2)-10~3 Pa-s

vb:^-m2/sA,

4

Pa " cpAm2/s

The thermo-physical properties should be evaluated at the bulk temperature, tbib, or the film temperature, tabj, according to the advice given with the heat transfer relation. In the present work the following definitions apply:

and

r lb\ + hi tb,b ~ o

r tb\ + lb2 + fwl + fw2fbJ ~ J

with index b for bulk,/for film and w for wall.

3.3.2.3 Over-all heat transfer

Equation 3.3.7 expresses the over-all heat transfer in a heat exchanger,

(eq. 3.3.7)

where U is the over-all heat transfer coefficient related to the air-side heat transfer area, F is the correction factor for not having pure parallel or counter flow, Aa is the effective air-side heat transfer area (including tubes and fin-efficiency) and 0m is the mean temperature difference between air and brine. U is related to the air and brine side heat transfer coefficients and the associated areas as well as the tube-wall thickness and thermal conductivity

i- = — +fyube . +

U CLa \ube % 4

Am is the mean tube heat flow area, which is given by

(eq. 3.3.8)

Ab

dD-d

(eq. 3.3.9)

3 Test coils

63

Using data for coil A (k,ube = 393 W/m/K, 8= 0.85 mm, Z) = 16.6 mm, d = 14.9 mm, ~T]A ~ 0.9, A/z„ = 48.6 m2, Aa = 45.8 m2, A& = 1.815 m2, Am = 1.92 m2) we have:

J___ 1_ 0,00085 45.8 1 45.8 40 + 0.05 + 8.4U~ 25 + 393 ' 1.92 + 3000 ’ 1.815 “ 1000

and

U ~ 20.6 W/m2/K

In relation to the convective heat transfer resistances, the wall thermal resistance is clearly negligible. On the other hand, even though the brine-side convective resistance is much smaller than that of the air-side in the example above, it will increase by a factor 10 when the brine flow turns laminar. Thus if the flow is laminar, which has been the case in much of the present work, then the brine-side heat transfer is decisive for the over-all heat transfer.

The generally used logarithmic mean temperature difference can often be approximated by the geometric mean temperature difference, which is more practical to use, i.e.

%&2

(eq. 3.3.10)

with the inlet and outlet temperature differences given by

6\=ta\- tb2 and % = ta2 - tbl (eq. 3.3.11)

Finally, the correction factor F is generally close to 1 (0.9-0.95) since the brine-side heat capacity flowrate is much greater than that of the air-side. As an example, data from table 3.1.1 provide the following values of the parameters P (temperature efficiency) and R (ratio of heat capacity flowrates):

p = tal-ta2 =Q # £=(m Cp)a ~0.28

tal-tbl (*n-cp)b

Using a diagram for F with the flow on the brine-side mixed and that of the air-side un-mixed results in F ~ 0.95.

3 Test coils

64

4 Results with a frosting coilTable 1.4.1 describes the test program, which included variations of specific cooling load, air humidity, air inlet velocity, and air temperature. With each variation, results are compared with the nominal test conditions A1 or A8 for +2 and -7°C respectively (most results derive from tests with coil A).

Some of the test equipment was described in 1.5 and figure 4.0 below shows the layout of the coil set-up with a flow measuring section and a supporting frame for the load-cell. The following items are numbered:

1 Test coil2 Drip tray3 Air tight, flexible sheet to connect coil and flow measuring section4 Axial fan5 Pressure connections for the inverted orifice flowmeter6 Reverse cone damper to adjust flowrate7 Load-cell with connecting rod to the coil8 Drain pipe for the collected defrost water9 Brine supply pipe

10 Brine return pipe11 Insulated wall of climate chamber12 Perforated plate for inlet and outlet of the displacement ventilation13 Sampling hose for dew point hygrometer14 Measuring box with fan, dew point hygrometer and PRT15 Pressure connections (piezometer-ring) to measure coil pressure drop

ujiMnjuuiAJU^nnAJUuuuiniuuuuuuuuuuuuuuuuuuuuuuuulnnA.

Figure 4.0. Lay-out of the test section to measure frost growth.

4 Results with a frosting coil

65

4.1 +2 °C: Variation of specific cooling load

Table 4.1 gives an overview of the nominal and actual test conditions during tests with different specific cooling loads. The specific cooling load is based on the brine- side cooling capacity of the coil, Qb, and the total air-side heat transfer area of the coil, Aq. Unfortunately the actual area of the coil turned out to be greater than commissioned and the losses between the heat pump and the coil were substantial so the actual loads were smaller than planned. Mean, max and min values refer to the frosting period (i.e. excluding defrosting).

Table 4.1. Mean, maximum and minimum values of the variables defining the operating condition during the test sequence.

Quantity (°C) Ual (m/s) &,(W/m=)

Nominal: A1 +2 -0.3 (85 %RH) 2 100Mean 1.8 -0.2 1.2 71Max 2.9 2.4 1.9 87Min 1.1 -1.2 0.1 32Quantity WQ tw (°Q Ual (m/s) &,(W/m=)Nominal: A2 +2 -0.3 (85 %RH) 2 50Mean 2.0 -0.1 1.9 48Max 2.7 1.1 1.9 52Min 1.6 -1.5 -0.7 17Quantity WQ Ual (rn/s) &,(W/m=)

Nominal: A3 +2 -0.3 (85 %RH) 2 150Mean 1,6 0,0 1.2 116Max 2,8 2,9 1.9 145Min 1.0 -1,2 0.1 49

Set values correspond to mean values regarding dry bulb and dew point temperatures. For these measurands maximum values normally occur during defrosting. For air velocity, however, set values correspond to maximum values since flow is set with a dry coil and veloeity will drop as soon as frosting begins. During defrosting air velocity may be negative due to natural convection during the fan stop in the defrost period. Set values correspond to maximum values also regarding specific cooling load for the same reason. During defrosting cooling is reversed to heating and hence values may be negative. Table 4.1, however, only includes the frosting period and will therefore not include any negative loads. The negative velocity in A2 comes from the time resolution in defining frosting/defrosting causing a measured value to appear on the wrong side of the time divider. This will frequently happen in all the tables of this section.


66

4.1.1 Heat pump capacity

Figure 4.1.1 shows the time dependent heating and cooling capacity of the heat pump unit during frosting with specific cooling loads of approximately 100, 50 and 150 W/m2. The diagrams also include integrated mean values of the capacities, QIm and Q2m, according to the principles of section 2.2.1. In addition, table 4.1.1.1 gives the mean, maximum and minimum values during an integral number of frosting - defrosting cycles, both for the total cycle and for the frosting and defrosting periods respectively.

Table 4.1.1.1. Mean, maximum and minimum values during frosting and defrosting periods; thermal capacities.

<7a = 100 W/m2 A1 50 W/m2 A2 150 W/m2 A3Period & (kW) &(kW) 6,(kW) &(kW) &(kW) &(kW)Full cyclesMean 8.54 5.74 6.62 4.24 14.66 8.89Max 18.04 41.42 11.72 15.16 24.28 31.24Min 0.61 -9.63 0.92 -14.20 0.50 5.29FrostingMean 8.23 5.41 6.39 4.17 14.51 8.30Max 11.13 6.39 7.40 4.29 21.68 10.53Min 0.91 4.64 6.24 4.10 11.67 6.44DefrostingMean 11.57 8.99 8.45 4.75 16.07 12.14Max 18.04 41.42 11.72 15.16 24.28 28.21Min 0.61 -9.63 0.92 -14.20 0.50 5.29

The table shows that just after a defrost, when the coil is quite warm, heating capacity is extremely high (defrosting terminates when %,2 is +30 °C). During defrosting, cooling capacity is negative (heating instead of cooling).

In the diagrams representing tests A1 and A3, a dashed line indicates the time of the maximum integrated mean value of the heating and cooling capacities, Qlm and Q2m, (the times are virtually the same). In the case of A2, frosting is too slow to warrant a defrost but after 24 h one is carried out anyway. Table 4.1.1.2 below gives the times after a defrost when maximum integrated mean capacity occurs.

Table 4.1.1.2. Time for maximum integrated mean capacity.

9a = 100 W/m2 A1 50 W/m2 A2 150 W/m2 A342, Qi Qi Qi 6, Qi

Time (h) 12.8 12.8 - - 5.0 5.0

The table shows a great diversity in optimum time depending on the operating conditions of the coil.


Ther

mal

capa

city

(kW

) Th

erm

al c

apac

ity (k

W)

Ther

mal

cap

acity

(k\V

)

67

Test condition Al: Thermal capacity

---Q2m

Time (h)

Test condition A2: Thermal capacity

0 12 24 36 48

Time (h)


---- Q2

0 12 24 36 48

Time (h)

Figure 4.1.1. Thermal capacities of heat pump (heating, cooling, integrated mean).

\

'<V


68

4.1.2 Coil capacity

The diagrams of figure 4.1.2 show the time dependent cooling capacity of the coil during frosting with specific cooling loads of approximately 100, 50 and 150 W/m2. Capacity measured on the air-side as well as on the brine-side are included. The diagrams also show the integrated mean value of the brine-side capacity, Qbm, according to the principles of section 2.2.1. The problem of achieving accurate air- side measurement is clearly seen from the curves, in particular the drop due to uncertain airflow measurements at low flowrates. Except for test Al, air-side capacities have normally been underestimated.

In addition to the diagrams, table 4.1.2 gives the mean, maximum and minimum values during an integral number of frosting - defrosting cycles, both for the total cycle and for the frosting and defrosting periods respectively.

Table 4.1.2. Mean, maximum and minimum values during frosting and defrosting periods; coil capacity.

<7a = 100 W/m2 Al 50 W/m2 A2 150 W/m2 A3Period Qa (kW) (kW) &(kW) e, (kW) &(kW)Full cyclesMean 3.54 1.85 1.54 1.36 -1.88 2.77Max 4.53 57.37 2.71 28.4 136 27.77Min 0.46 -107 -4.65 -116 -186 -101.26FrostingMean 3.54 2.76 1.73 2.23 4.49 5.39Max 4.53 4.04 2.71 2.40 11.9 6.75Min 0.46 -107 -4.65 0.81 -9.07 2.27DefrostingMean - -8.88 - -5.46 - -9.44Max - 57.3 - 28.4 - 278Min - -123 - -116 - -87

During defrosting, cooling capacity is negative (heating instead of cooling) on the brine-side. Since there is no flow on the air-side during defrosts, measured capacities have no relevance during this period.

Thermally measured defrost capacities, according to the table above, compare favourably with the electrical energy measurements transferred to an equivalent power input during the defrost period. For Al, results are 123 and 112 kW respectively for thermally and electrically measured results and for A3 we have 88 and 86 kW respectively. Bearing in mind the short defrost time and the uncertainty in time resolution agreement is surprisingly good.


Coi

l cap

acity

(kW

) C

oolin

g ca

paci

ty (k

W)

Coi

l cap

acity

(kW

)

69

Test condition Al: Coil capacity

— Qa

Time (h)

Test condition A2: Coil capacity

— Qa

Time (h)


— Qa

Time (h)

Figure 4.1.2. Coil capacity (air-side, brine-side, and integrated mean).


70

4.1.3 Power input

The diagrams of figure 4.1.3 show the time dependent electric power inputs to the heat pump and the defrosting system during operation with specific cooling loads of approximately 100,50 and 150 W/m2.


Table 4.1.3. Mean, maximum and minimum values of electric power input during frosting and defrosting periods; electric input.

<7A- 100 W/m2 A1 50 W/m2 A2 150 W/m2 A3Period Went (kW) ^(kW) Went (kW) Went (kW) ^(kW)

Full cyclesMean 3.02 0.73 2.19 0.75 4.96 0.68Max 4.66 0.86 3.02 0.85 7.26 0.85Min 0.00 0.00 0.00 0.00 0.00 0.00FrostingMean 2.98 0.80 2.16 0.84 5.02 0.80Max 3.49 0.86 2.34 0.85 6.46 0.85Min 0.00 0.00 2.13 0.00 4.39 0.74DefrostingMean 3.36 0.00 2.44 0.00 4.85 0.00Max 4.66 0.00 3.02 0.00 7.26 0:00Min 0.00 0.00 0.00 0.00 0.00 0.00

The diagrams show that the power input to the defrost system has a large peak right after a defrost and then a number of smaller peaks to cover system losses between defrosts. When the defrost system is in full operation, system losses seem to be around 0.6 kW whereas the losses from the storage tank per se were only 0.077 kW. Obviously insulation of the piping was not on a par with that of the tank (polyurethane foamed directly on the tank).

Input to the fan has a maximum at the start of a frosting period, with a clean coil. This situation results in maximum flowrate and thus maximum input whereas during a defrost fan power input is zero by definition in the defrost strategy. During frosting fan power drops continuously.

Input to the compressor motor has a sharp maximum just after a defrost when the heat pump is operating with a high evaporation temperature and thus has a very large capacity.


71

Test condition Al: Electric input (kW)

Wedefr

0 12 24 36 48

Time (h)

Test condition A2: Electric input (kW)

Wedefr

Time (h)


Wedefr

Time (h)

Figure 4.1.3. Electric power inputs (compressor, brine pump, fan, and defrost).


72

4.1.4 Coefficient of Performance

The diagrams of figure 4.1.4 show the time dependent heating and cooling coefficients of performance of the heat pump unit during frosting with specific cooling loads of approximately 100,50 and 150 W/m2. The diagrams also include integrated mean values of the coefficients of performance according to the principles of section 2.2.1. In addition, table 4.1.4.1 gives the mean, maximum and minimum values during an integral number of frosting - defrosting cycles, both for the total cycle and for the frosting and defrosting periods respectively.

Table 4.1.4.L Mean, maximum and minimum values of the coefficient of performance during frosting and defrosting periods.

<7a = 100 W/m2 A1 50 W/m2 A2 150 W/m2 A3Period COP, COP2 COP, COP2 COP, COP2Full cyclesMean 2.77 1.89 2.97 1.95 2.80 1.78Max 3.87 15.8 3.89 5.89 3.94 15.3Min 0.00 -2.68 0.00 0.00 0.00 0.00FrostingMean 2.74 1.80 2.96 1.93 2.87 1.65Max 3.19 1.90 3.16 1.96 3.36 1.75Min 0.00 0.00 2.92 1.82 2.65 1.46Defrosting *Mean 2.97 2.58 3.06 2.04 2.55 2.62Max 3.87 15.8 3.89 5.89 3.94 15.3Min 0.00 -2.68 0.00 0.00 0.00 0.00*During defrosting, COP has no real meaning since the heat pump has only operated for a very short while at the end of the defrost cycle. Most of the energy supply comes from the electrically heated defrost tank.

In the diagrams representing tests A1 and A3, a dashed line indicates the time of the maximum integrated mean value of the heating and cooling coefficients of performance. The indicated optima are based on defrosts with 100 % efficiency (COPim* and COP2m*). As shown by the diagrams, even letting the flowrate drop to 30 % of its original value does not warrant a defrost when the actual defrost energy requirement is used in the optimization (COP,m and COP2m). Generally, the optimum for cooling occurs earlier than does the optimum for heating. In the case of A2, frosting is too slow to warrant a defrost but after 24 h one is carried out anyway.Table 4.1.4.2 below gives the time after a defrost when the maximum integrated mean coefficient of performance occurs.

Table 4.1.4.2. Time for maximum integrated mean coefficient of performance.

<lA = 100 W/m2 A1 50 W/m2 A2 150 W/m2 A3COP, COP2 COP, COP2 COP, COP2

Time (h) 18.2 16.5 - * - 7.0 6.3

The table shows a great diversity in optimum time depending on the operating conditions. In the case of A2, there is no need for defrosting within 24 h and thus the question of optimum time is irrelevant within this time span.


CO

P C

OP

CO

P

73

Test condition Al: COP

COPl

COP2

COPlm

COP2m

-- COPlm*

-• COP2m*

Time (h)

Test condition A2: COP

COP2

COPlm

COP2m

Time (h)


COPl

COP2

COPlm

-- COP2m

- COPlm*f™

Time (h)

Figure 4.1.4. Coefficients of performance (heating, cooling and integrated means).


74

4.1.5 Coil temperatures

The diagrams of figure 4.1.5 show the time dependence of a number of temperatures which are relevant to the performance of the coil. Included are inlet and outlet temperatures of the air and the brine, inlet and outlet dew point temperatures and the mean value of a number of fin surface temperatures. Specific cooling loads are approximately 100,50 and 150 W/m2. In addition, table 4.1.5 gives the mean, maximum and minimum values of the outlet brine and fin temperatures during an integral number of frosting - defrosting cycles, both for the total cycle and for the frosting and defrosting periods respectively.

Table 4.1.5. Mean, maximum and minimum values during frosting and defrosting periods; brine outlet and mean coil surface temperature.

<7a = 100 W/m2 A1 50 W/m2 A2 150 W/m2 A3Period 4,2 (°Q fa, (°Q

OJu3%2 (°Q fa, (°Q

Full cyclesMean -3.17 -0.3 0.17 1.9 -5.98 -1.3Max 34.31 38.1 32.74 28.1 59.52 44.4Min -8.42 -4.3 -1.61 0.6 -14.68 -8.6FrostingMean -4.98 -1.6 -1.15 1.0 -8.65 -2.8Max 9.08 2.1 2.17 2.4 1.32 1.9Min -8.42 -4.3 -1.61 0.6 -14.43 -7.0DefrostingMean 14.04 11.8 10.57 8.7 11.63 9.6Max 34.31 38.1 32.74 28.1 59.52 44.4Min -3.66 -3.9 1.97 2.2 -14.38 -8.6

From the diagrams and the table it is obvious why there is virtually no frosting during test A2. The mean fin surface temperature is above zero so in the inlet section there will be no frosting and in the outlet section, where the surface temperature is below zero, there will only be very little frost. Once the thin frost layer covers this part of the coil the surface temperature of the frost will subsequently reach zero and there will be no further frosting.


Tem

pera

ture

(°C

) Te

mpe

ratu

re (°

C)

Tem

pera

ture

(°C

)

75

Test condition Al: Coil temperatures

y V-\ '■VVy f<*

------ tdp2

— ta2

Time (h)

Test condition A2: Coil temperatures

- - tdplVVX vV^ //XxV V//X W*’7' X-'AV; f/* ■>»*' • ’i*"!j«»»' ‘ v«'«*i **v

------ tdp2

- ta2

Time (h)


5

0

-5

-10

-15

-200 12 24 36 48

Time (h)

Figure 4.1.5. Coil temperatures (DBT, DPT, and brine inlet/outlet, mean fin temp.).


76

4.1.6 Flowrates

The diagrams of figure 4.1.6 show the time dependence of the condenser water flowrate, the brine flowrate and the air flowrate. Specific cooling loads are approximately 100,50 and 150 W/m2. In addition, table 4.1.6 gives the mean, maximum and minimum values of the air and brine flowrates during an integral number of frosting - defrosting cycles, both for the total cycle and for the frosting and defrosting periods respectively.

Table 4.1.6. Mean, maximum and minimum values during frosting and defrosting periods; air and brine flowrates.

9a = 100 W/m2 A1 50 W/m2 A2 150 W/m2 A3Period va (m3/s) vb (nvVh) va (m3/s) v„ (nvVh) va (nvVs) vb (mJ/h)Full cyclesMean 0.47 1.84 0.77 1.88 0.45 1.68Max 0.91 2.05 0.92 2.01 0.91 1.90Min -0.39 1.78 -0.38 1.85 -0.40 1.34FrostingMean 0.55 1.83 0.91 1.88 0.59 1.67Max 0.91 1.89 0.92 1.90 0.91 1.82Min -0.35 1.78 -0.34 1.87 0.05 1.55DefrostingMean -0.34 1.96 -0.35 1.94 -0.34 1.75Max -0.32 2.05 -0.20 2.01 -0.26 1.90Min -0.39 1.76 -0.38 1.85 -0.40 1.37

The air flowrate starts to drop very soon after the onset of frosting. Compared to the drop in coil capacity (figure 4.1.2), the drop in air flow is much greater. This derives from an increase in LHR as flow goes down, which makes total capacity less affected. On the other hand, the dry cooling capacity will drop as flowrate goes down.

The brine flow is fairly constant during a test cycle. Only in situations where viscosity changes markedly will there be a change in flow. This happens during defrosting with warm brine and at the end of a cycle with heavy frosting, in this case during A3.

The condenser water flowrate was very stable at all times. According to Fahlen(8), standard deviation of the mean was < 0.02 %.


Flow

rate

(m3/

h, m

3/s)

Fl

ow ra

te (m

3/h,

m3/

s)

Flow

rate

(m3/

h, m

3/s)

77

Test condition Al: Flow rates

- * Vw(m3/h)

- - Vb(m3/h)

Va (m3/s)

Time (h)

Test condition A2: Flow rates

2.5

2,0

1.5

1,0

0,5

0,00 12 24 36 48

Time (h)

'------------------------------

Va (m3/s)


* * Vw (m3/h)

- - Vb(m3/h)

Va (m3/s)

0 12 24 36 48

Time (h)

Figure 4.1.6. Flowrates (condenser water, brine, and air).


78

4.1.7 Air velocity and coil pressure drop

The diagrams of figure 4.1.7 show the time dependence of the air inlet velocity and pressure drop of the coil. Specific cooling loads are approximately 100, 50 and 150 W/m2. In addition, table 4.1.7 gives the mean, maximum and minimum values of these measurands during an integral number of frosting - defrosting cycles, both for the total cycle and for the frosting and defrosting periods respectively.

Table 4.1.7. Mean, maximum and minimum values during frosting and defrosting periods; air-side velocity and pressure drop.

4a = 100 W/m2 A1 50 W/m2 A2 150 W/m2 A3Period ua (m/s) Apa (Pa) ua (m/s) Apa (Pa) ua (m/s) Apa (Pa)Full cyclesMean 0.98 189 • 1.74 23.5 1.0 165'Max 1.90 386 1.92 28.8 1.9 380Min -0.82 -1.9 -0.78 -2.7 -0.8 -1.6FrostingMean 1.14 207 1.91 26.3 1.2 194Max 1.90 386 1.92 28.8 1.9 380Min -0.74 0.2 1.81 2.2 0.1 27.1DefrostingMean -0.71 1.0 -0.71 0.3 -0.7 1.4Max -0.66 3.5 -0.41 2.2 -0.5 14.8Min -0.82 -1.9 -0.78 -2.7 -0.8 -1.2

Air velocity is based on the measured volume flow and the frontal area of the coil. This velocity is set with a dry coil, hence the set value should be compared with the maximum value during the frosting phase (in tests A1-A3,2 m/s). During defrosting, air velocity may actually be negative, due to natural convection with the fan stopped.

Coil pressure drop has its maximum right at the end of the frosting period. For tests A1 and A2 the final pressure drop is around 380 Pa. For A2, on the other hand, this drop is only 29 Pa due to the very low rate of frosting.


u (m

/s), d

p (P

a/20

0)

u (m

/s), d

p (P

a/20

0)

u (m

/s), d

p (P

a/20

0)

79

Test condition Al: Air velocity and pressure drop

- - dp (Pa/200)

Time (h)

Test condition A2: Air velocity and pressure drop

- - dp (Pa/200)

Time (h)


u (m/s)

dp (Pa/200)

Time (h)

Figure 4.1.7. Air velocity and coil pressure drop (Ap/200).


80

4.1.8 Frost mass

The diagrams of figure 4.1.8 show the time dependence of frost mass in the coil. Specific cooling loads are approximately 100, 50 and 150 W/m2 respectively. In addition, table 4.1.8 gives the mean, maximum and minimum values of these measurands during an integral number of frosting - defrosting cycles, both for the total cycle and for the frosting and defrosting periods respectively.

Table 4.1.8. Mean, maximum and minimum values during frosting and defrosting periods; frost mass and mean growth rate.

<7a = 100 W/m2 Al 50 W/m2 A2 150 W/m2 A3Period %(kg) mJr (kg/h) Mfr (kg) lhfr (kg/h) Mf(kg) mfr (kg/h)Full cyclesMean 8.36 -6.31 0.62 -0.07 7.29 -5.66Max 17.3 30.9 0.72 4.98 15.7 173Min -0.09 -479 -0.17 -19.0 0.00 -235FrostingMean 9.01 0.14 0.65 -0.06 7.94 1.77Max 17.3 30.87 0.72 1.30 15.7 12.6Min 0.34 -112 0.55 -4.38 0.75 -12.0DefrostingMean 1.75 -73 0.40 -0.04 2.79 -36.8Max 15.4 4.38 0.70 4.98 13.9 173Min -0.09 -667 -0.17 -19.0 0.00 -226

The maximum value of frost mass, just before a defrost, is compared with the collected amount of defrost water in section 4.1.9. The diagrams show a fairly even rate of frost growth, which is in agreement with observations from previous researchers. It is also apparent that in test Al, with a slow rate of frosting, the maximum value is larger than in test A3. This derives from a lower density frost being formed with high growth rates than with low growth rates.

During defrosting, the load-cell system returns very nicely to a zero reading prior to the next frosting phase. The defrosting phase is quite violent, with high thermal and mechanical stresses. The violence of the defrosting phase is apparent from the large difference in the frosting mass flux (+) and the defrosting mass flux (-). In this context defrosting mass fluxes of table 4.1.8 in the range 234-667 kg/h may be compared with the estimated evaporation rate of around 700 kg/h (0.2 kg/s) using the Lewis relation in 5.4.


Fros

t mas

s (kg

) Fr

ost m

ass (

kg)

Fros

t mas

s (kg

)

81

Test condition Al: Frost mass

Time (h)

Test condition A2: Frost mass

Time (h)


Time (h)

Figure 4.1.8. Frost mass.


82

4.1.9 Defrost water, defrost time and defrost energy

Table 4.1.9 provides some data from the defrosting phase of tests Al, A2, and A3.

Table 4.1.9. Mean, maximum and minimum values during frosting and defrosting periods; defrost water, defrost time and defrost energy.

Measurand Al (100 W/m2) A2 (50 W/m2) A3 (150 W/m2)Mdw (kg) 14.2 - 11.0Mdw / Mfr (kgft/kgw) 0.81 - 0.69W*dw (kWh/defrost) 32.1 - 14.4T|d(-) 0.05 - 0.11td(s) 125 - 140% (h) 22.5 >24 7.9

Values of defrosting efficiency are based on the latent heat of fusion of ice. If the latent heat of sublimation is used, the efficiencies will be approximately 8.5 times higher.

Due to heavy evaporation during the final phase of a defrost, the quantity of collected defrost water was always smaller than the mass of frost in the coil. The mass of defrost water is generally 20-30 % smaller than the mass of frost.

From the table it also appears that it takes longer to defrost in test A3 than in A1 in spite of a smaller mass of frost in A3. This is because it is generally more difficult to get rid of the porous frost layer that forms during rapid frosting than it is with a more compact frost.

4.1.10 Alternative defrost indicators

The diagrams of figure 4.1.10 show the temporal behaviour of some normalized alternative defrost indicators. The indicator based on brine outlet temperature seems to offer the best compromise in terms of a strong dependence on frosting, ease of realization and insensitivity to spurious effects. It is particularly appealing to see that when frosting starts to be severe and capacity actually drops only then does the brine temperature start to drop. At the same time the diagrams show the wide spread in optimum time to defrost depending on whether you want to optimize capacity, cooling COP or heating COP. This latitude would be wider still if you include defrosting efficiency as a variable.


Nor

mal

ized

cha

nge

Nor

mal

ized

chan

ge

Nor

mal

ized

cha

nge

83

Test condition Al: Defrost indicators

COP2

Time (h)

Test condition A2: Defrost indicators

Time (h)


COPlCOP2

Time (h)

Figure 4.1.10. Alternative defrost indicators.


84


85

4.2 +2 °C: Variation of humidity

Table 4.2 gives an overview of the nominal and actual test conditions during tests with different humidities. Humidity is given nominally as the relative humidity, but was actually measured as dew point temperature. Mean, max and min values refer to the frosting period (i.e. excluding defrosting).


Quantity W°C) f*, (°C) uai (m/s) 4a(W/m=)

Nominal: A1 +2 -0.3 (85 %RH) 2 100Mean 1.8 -0.2 1.2 71Max 2.9 2.4 1.9 87Min 1.1 -1.2 0.1 32

Quantity W°c) W (°Q ual (m/s) &,(W/nf)

Nominal: A4 +2 -2.5 (70 %RH) 2 100Mean 3.1 -2.1 1.9 98Max 10.9 4.1 1.9 127Min -3.5 -13.8 1.7 44

Quantity f., (°C) tw (°C) Ual (m/s) &,(W/m=)

Nominal: A5 +2 +1.2 (95 %RH) 2 100Mean 1.9 1.5 1.3 78Max 2.4 3.3 1.9 93Min 1.4 0.6 -0.7 35

General comments on set values and associated measured values may be found in section 4.1. Fahlen® discusses general problems of humidity measurements and appendix A7 contains a summary of the related uncertainties.

It should be noted that measurement of dew point temperature may have a higher uncertainty around 0 °C than further from this point. On the other hand it has a much higher accuracy than does measurements of relative humidity. For instance, at the nominal condition an uncertainty of ±5 % RH corresponds to ±1.0 K in DPT.


86


Figure 4.2.1 shows the time dependent heating and cooling capacity of the heat pump unit during frosting with a specific cooling load of approximately 100 W/m2. The diagrams also include integrated mean values of the capacities according to the principles of section 2.2.1. In addition, table 4.2.1.1 gives the mean, maximum and minimum values during two frosting - defrosting cycles, both for the total cycle and for the frosting and defrosting periods respectively.


<Pa = 85 % RH A1 70 % RH A4 95 % RH A5Period 6,(kW) &(kW) 6,(kW) &(kW) Qi (kW) &&W)Full cyclesMean 8.54 5.74 10.6 7.17 9.68 6.62Max 18.0 41.4 19.8 30.4 20.3 16.7Min 0.61 -9.63 1.34 5.52 0.85 4.87FrostingMean 8.23 5.41 10.6 7.02 9.21 6.11Max 11.1 6.39 15.3 8.90 11.9 7.23Min 0.91 4.64 8.57 5.52 7.86 5.09DefrostingMean 11.6 8.99 13.7 12.4 10.9 8.51Max 18.0 41.4 19.8 30.4 20.3 16.7Min 0.61 -9.63 1.34 6.48 -11.2 -2.39

The table shows that just after a defrost, when the coil is quite warm, heating capacity is extremely high (defrosting terminates when is +30 °C). During defrosting, cooling capacity is negative (heating instead of cooling).

In the diagrams representing tests A1 and A5, a dashed line indicates the time of the maximum integrated mean value of the heating and cooling capacities, Qlm and Q?m, (the times are virtually the same). In the case of A2, frosting is too slow to warrant a defrost but after 24 h one is carried out anyway. Table 4.2.1.2 below gives the times after a defrost when maximum integrated mean capacity occurs.


85 % RH A1 70 % RH A4 95 % RH A50i 02 0i 02 0i 02

Time (h) 12.8 12.8 - 7.7 7.0



Ther

mal

cap

acity

(kW

) Th

erm

al c

apac

ity (k

W)

Ther

mal

capa

city

(kW

)

87


------Q2m

0 12 24 36 48

Time (h)


0 12 24 36 48

Time (h)

Test condition AS: Thermal capacity

----- Q2m

Time (h)



88

4.2.2 Coil capacity

The diagrams of figure 4.2.2 show the time dependent cooling capacity of the coil during frosting with a specific cooling load of approximately 100 W/m2. Nominal relative humidities of 85,70, and 95 % were used. Capacity measured on the air-side as well as on the brine-side are included. The diagrams also show the integrated mean value, Qbm, of the brine-side capacity according to the principles of section 2.2.1. The problem of achieving accurate air-side measurements is clearly seen from the curves, in particular the drop due to uncertain airflow measurement at low flowrates. Except for test Al, air-side capacities have normally been underestimated.



tPa — 85 % RH Al 70 % RH A4 95 % RH A5Period (kW) Qb (kw) G« (kW) &(kW) g, (kW) &(kW)Full cyclesMean 3.5 1.85 3.4 4.40 0.3 1.91Max 4.5 57.3 5.6 66 462 5.19Min 0.5 -107 -67 -88 -265 -95FrostingMean 3.5 2.76 3.8 4.56 2.9 3.63Max 4.5 4.04 5.6 5.93 5.2 4.31Min 0.4 -107 0.8 2.04 -3.7 1.62DefrostingMean - -8.88 -10.3 -1.00 2.9 -8.45Max 0.0 57.3 3.2 66 462 2.79Min 0.0 -123 -68 -88 -214 -97

During defrosting, cooling capacity is negative (heating instead of cooling).

Thermally measured defrost capacities, according to the table above, are of the same order of magnitude as the electrical energy measurements transferred to an equivalent power input during the defrost period. For Al, results are 123 and 112 kW respectively for thermally and electrically measured results and for A5 we have 265 and 366 kW respectively. Bearing in mind the short defrost time and the uncertainty in time resolution, agreement is acceptable.


Coi

l cap

acity

(kW

) C

oil c

apac

ity (k

W)

Coi

l cap

acity

(kW

)

89


— Qa

Time (h)


Qb

---------- Qa

Qbm

11 A-/•"s'"''V..**'"•-■’V-'Xf

0 12 24 36 48

Time (h)

Test condition AS: Coil capacity

— Qa

Time (h)



90

4.2.3 Power input

The diagrams of figure 4.2.3 show the time dependent electric power inputs to the heat pump and the defrosting system during operation with a specific cooling load of approximately 100 W/m2 and relative humidities of 85, 70 and 95 % respectively.


Table 4.2.3. Mean, maximum and minimum values during frosting and defrosting periods; electric input.

<Pa = 85 % RH A1 70 % RH A4 95 % RH A5Period Wem (kW) w^(kW) Went (kW) Wf (kW) Wem (kW) Wf(kW)

Full cyclesMean 3.02 0.73 3.90 0.82 3.20 0.67Max 4.66 0.86 5.59 0.86 4.85 0.85Min 0.00 0.00 0.00 0.00 0.00 0.00FrostingMean 2.98 0.80 3.90 0.84 3.16 0.80Max 3.49 0.86 4.71 0.86 3.64 0.85Min 0.00 0.00 3.49 0.82 2.89 0.73DefrostingMean 3.36 0.00 4.15 0.00 3.07 0.00Max 4.66 0.00 5.59 0.00 4.85 0.00Min 0.00 0.00 0.00 0.00 -3.68 0.00

The diagrams show that power input to the defrost system has a large peak right after a defrost and then a number of smaller peaks to cover system losses between defrosts (see comments to 4.1.3).




91


Wedefr

LlLLi- V ::0 12 24 36 48

Time (h)


Wedefr

Time (h)

Test condition AS: Electric input (kW)

Wedefr

Time (h)



92


The diagrams of figure 4.2.4 show the time dependent heating and cooling coefficients of performance of the heat pump unit during frosting with a specific cooling load of approximately 100 W/m2. The diagrams also include integrated mean values of the coefficients of performance according to the principles of section 2.2.1. In addition, table 4.2.4.1 gives the mean, maximum and minimum values during an integral number of frosting - defrosting cycles, both for the total cycle and for the frosting and defrosting periods respectively.

Table 4.2.4. Mean, maximum and minimum values during frosting and defrosting periods; coefficients of performance.

<pfl = 85 % RH A1 70 % RH A4 95 % RH A5Period COP, COP2 COP, COP2 COP, COP2Full cyclesMean 2.77 1.89 2.70 1.79 2.93 2.05Max 3.87 15.8 3.55 2.12 4.19 13.6Min 0.00 -2.68 0.00 0.00 0.00 0.00FrostingMean 2.74 1.80 2.71 1.80 2.91 1.93Max 3.19 1.90 3.25 1.95 3.28 2.00Min 0.00 0.00 2.46 1.58 2.71 1.76DefrostingMean 2.97 2.58 2.55 1.47 2.70 2.47Max 3.87 15.8 3.55 2.12 4.19 13.6Min 0.00 -2.68 0.00 0.00 -3.33 -2.03*During defrosting, COP has no real meaning since the heat pump has only operated for a very short while at the end of the defrost cycle. Most of the energy supply comes from the electrically heated defrost tank.

In the diagrams representing tests A1 and A5, a dashed line indicates the time of the maximum integrated mean value of the heating and cooling coefficients of performance. The indicated optima are based on defrosts with 100 % efficiency (COPIm* and COP2m*) whereas curves based on real defrosting efficiency (COP]m and COP2m) never intersect the instantaneous curves. For further comments, see 4.1.4. Table 4.2.4.2 below gives the time after a defrost when the maximum integrated mean coefficient of performance occurs.


<P* = 85 % RH A1 70 % RH A4 95 % RH A5COP, COP2 COP, COP2 COP, COP2

Time (h) 18.2 16.5 - - 11.0 9.7



CO

P C

OP

93


COPl

COP2

COPlm

COP2m

COPlm*

-• COP2m*

Time (h)


-------------COPl

— — COP2

-------------COPlm

------COP2m

, .... :—

: COPl

(

Ki.

COP21:

!:

i:i:

0 12 24 36 48

Time (h)

Test condition AS: COP

COP2

COPlm

------COP2m

COPlm*

-' COP2m*

Time (h)



94


The diagrams of figure 4.2.5 show the time dependence of a number of temperatures which are relevant to the performance of the coil. Included are inlet and outlet temperatures of the air and the brine, inlet and outlet dew point temperatures and the mean value of a number of fin surface temperatures. Specific cooling load was approximately 100 W/m2 and humidities were around 85, 70 and 95 % respectively. In addition, table 4.2.5 gives the mean, maximum and minimum values of the outlet brine and fin temperatures during an integral number of frosting - defrosting cycles, both for the total cycle and for the frosting and defrosting periods respectively.


<Pa = 85 % RH A1 70 % RH A4 95 % RH ASPeriod fw (°C) 4. (°Q 42 (°Q fa, (°C) 42 (°C) 4, (°C)Full cyclesMean -3.17 -0.32 -4.91 0.7 -0.97 1.3Max 34.31 38.14 42.10 32.9 59.57 42.8Min -8.42 -4.29 -10.78 -5.8 -8.20 -3.6FrostingMean -4.98 -1.60 -5.47 0.4 -4.00 -0.6Max 9.08 2.06 2.06 6.2 1.42 1.9Min -8.42 -4.29 -10.78 -5.8 -8.20 -3.4DefrostingMean 14.04 11.81 14.04 11.6 13.63 10.3Max 34.31 38.14 42.10 32.9 59.57 42.8Min -3.66 -3.94 -2.68 0.2 -8.20 -4.4

From the diagrams and the table it is obvious why there is virtually no frosting during test A4. The mean fin surface temperature is around zero so in the inlet section there will be no frosting and in the outlet section, where the surface temperature is below zero, there will only be very little frost. Once the thin frost layer covers this part of the coil, the surface temperature of the frost will reach zero and there will be no further frosting.


Tem

pera

ture

(°C

) Te

mpe

ratu

re (°

C)

Tem

pera

ture

(°C

)

95


V *“ '“Y -s ■**/• -v-- tdp2

Time (h)


- tdpl

--------tdp2

— ta2

Time (h)

Test condition AS: Coil temperatures

• “ tdp2

-----ta2

Time (h)



96

4.2.6 Flowrates

The diagrams of figure 4.2.6 show the time dependence of the condenser water flowrate, the brine flowrate and the air flowrate. Specific cooling load was approximately 100 W/m2 and humidity was 85, 70 and 95 % approximately. In addition, table 4.2.6 gives the mean, maximum and minimum values of the air and brine flowrates during an integral number of frosting - defrosting cycles, both for the total cycle and for the frosting and defrosting periods respectively.


(Pa — 85 % RH A1 70 % RH A4 95 % RH A5Period va (m3/s) vb (mj/h) va (m7s) vb (m7h) va (m7s) v„ (mTh)

Full cyclesMean 0.47 1.84 0.85 1.30 0.47 1.63Max 0.91 2.05 0.93 1.47 0.91 1.80Min -0.39 1.78 -0.44 1.21 -0.37 1.50FrostingMean 0.55 1.83 0.89 1.29 0.64 1.62Max 0.91 1.89 0.93 1.39 0.91 1.67Min -0.35 1.78 -0.33 1.21 -0.33 1.56DefrostingMean -0.34 1.96 -0.37 1.41 -0.31 1.60Max -0.32 2.05 -0.33 1.47 -0.03 1.80Min -0.39 1.76 -0.44 1.24 -0.37 -0.10


The brine flow is fairly constant during a test cycle. Only in situations where viscosity changes markedly will there be a; change in flow ..This happens during defrosting with warm brine and at the endi of a cycle with heavy frosting.. The condenser water flowrate was very stable at all'times.


Flow

rate

(m3/

h, m

3/s)

Fl

ow ra

te (m

3/h,

m3/

s)

Flow

rate

(m3/

h, m

3/s)

97


* " Vw(m3/h)

• - Vb(m3/h)

Va (m3/s)

Time (h)


— " ~ Vb(m3/h)

— ----- ............. Va (ni3/s)

0 12 24 36 48

Time (h)

Test condition AS: Flow rates

" " Vw(m3/h)

Time (h)



98


The diagrams of figure 4.2.7 show the time dependence of the air inlet velocity and pressure drop of the coil. Specific cooling load was approximately 100 W/m2. In addition, table 4.2.7 gives the mean, maximum and minimum values of these measurands during an integral number of frosting - defrosting cycles, both for the total cycle and for the frosting and defrosting periods respectively.


tPa — 85 % RH A1 70 % RH A4 95 % RH ASPeriod Mfl (m/s) Apa (Pa) ua (m/s) Apa (Pa) ua (m/s) Apa (Pa)Full cyclesMean 0.98 189 1.82 50 1.06 142Max 1.90 386 1.93 95 1.90 374Min -0.82 -1.9 -0.92 -1.8 -0.78 -2FrostingMean 1.14 207 1.86 52 1.32 170Max 1.90 386 1.93 95 1.90 374Min -0.74 0.2 1.74 2.3 -0.69 -2DefrostingMean -0.71 1.0 -0.77 0.3 -0.60 4Max -0.66 3.5 -0.69 3.3 -0.07 59Min -0.82 -1.9 -0.92 -1.8 -0.78 -2

Air velocity is based on the measured volume flow and the frontal area of the coil. This velocity is set with a dry coil, hence the maximum value during the frosting phase should be compared with the set value (in tests A1-A5, 2 m/s). During defrosting, air velocity may actually be negative, due to natural convection with the fan stopped.

Coil pressure drop has its maximum right at the end of the frosting period. For tests A1 and A2 the final pressure drop is around 380 Pa. For A4, on the other hand, this drop is only 95 Pa due to the very low rate of frosting.


u (m

/s), d

p (P

a/20

0)

u (m

/s), d

p (P

a/20

0)

u (m

/s), d

p (P

a/20

0)

99


u (m/s)

- - dp (Pa/200)

Time (h)


u (m/s)

- - dp (Pa/200)

Time (h)

Test condition AS: Air velocity and pressure drop

u(m/s)

- - dp (Pa/200)

Time (h)



100

4.2.8 Frost mass

The diagrams of figure 4.2.8 show the time dependence of frost mass in the coil. Specific cooling load was approximately 100 W/m2 and humidity was 85,70, and 95 % respectively. In addition, table 4.2.8 gives the mean, maximum and minimum values of these measurands during an integral number of frosting - defrosting cycles, both for the total cycle and for the frosting and defrosting periods respectively.


% — 85 % RH A1 70 % RH A4 95 % RH ASPeriod Mfr (kg) mfr (kg/h) Mp (kg) mfr (kg/h) Mfr (kg) ,hfr (kg/h)Full cyclesMean 8.36 -6.31 2.86 -0.24 7.03 -1.70Max 17.3 30.9 8.68 4.09 17.3 587Min -0.09 -479 -0.33 -85.7 0.00 -337FrostingMean 9.01 0.14 2.93 0.16 7.97 1.37Max 17.3 30.9 8.68 4.09 17.3 5.97Min 0.34 -112 0.01 -1.33 0.75 -5.00DefrostingMean 1.75 -72.6 0.40 -20.2 2.83 3.15Max 15.4 4.38 3.88 2.94 16.1 587Min -0.09 -667 -0.33 -85.7 0.00 -272

The maximum value of frost mass, just before a defrost, is compared with the collected amount of defrost water in section 4.2.9. The diagrams show a fairly even rate of frost growth, which is in agreement with observations from previous researchers.

During defrosting, the load-cell system returns very nicely to a zero reading prior to the next frosting phase. The defrosting phase is quite violent, with high thermal and mechanical stresses. The violence of the defrosting phase is apparent from the large difference in the frosting mass flux (+) and the defrosting mass flux (-). In this context defrosting mass fluxes of table 4.2.8 in the range 337-677 kg/h may be compared with the estimated evaporation rate of around 700 kg/h (0.2 kg/s) using the Lewis relation in 5.4.


Fros

t mas

s (kg

) Fr

ost m

ass (

kg)

Fros

t mas

s (kg

)

101


Time (h)


Time (h)

Test condition AS: Frost mass

Time (h)



102




Measurand Al (100 W/m2) A4 (50 W/m2) A5 (150 W/m2)Mdw (kg) 14.2 - 13.0Maw / Mfr (kgft/kgw) 0.81 - 0.74W*dw (kWh/defrost) 32.1 - 18.2Tlrf(-) 0.05 - 0.09'td(s) 125 - 151tc(h) 22.5 >48 14.0

Values of defrosting efficiency are based on the latent heat of fusion of ice. If the latent heat of sublimation is used, the efficiencies will be approximately 8.5 times higher. Due to heavy evaporation during the final phase of a defrost, the quantity of collected defrost water was always smaller than the mass of frost in the coil.


The diagrams of figure 4.2.10 show the temporal behaviour of some normalized alternative defrost indicators. The indicator based on brine outlet temperature seems to offer the best information on frosting. The pressure difference, air flowrate, and fan power provide a very gradual change whereas the outlet air temperature gives no information at all. At the same time the diagrams show the wide spread in optimum time to defrost depending on whether you want to optimize capacity, cooling COP or heating COP. This latitude would be wider still if you include defrosting efficiency as a variable.


Nor

mal

ized

chan

ge

Nor

mal

ized

chan

ge

Nor

mal

ized

cha

nge

103


COP2

Time (h)


1,0

0,8

0,6

0,4

0,2

0,0

----------- ta2

— -----tb2

----------- dp

— ■ " Wcf

12

Time (h)

18 24

Test condition AS: Defrost indicators

COPlCOP2Q1.Q2I

Time (h)



105

4.3 +2 °C: Variation of air velocity

Table 4.2 gives an overview of the nominal and actual test conditions during tests with different coil face velocities. The face velocity is based on the volume flow and frontal area of the coil. Mean, max and min values refer to the frosting period (i.e. excluding defrosting).


Quantity (°Q uai (m/s) qa(W/m2)

Nominal: A1 +2 -0.3 (85 %RH) 2 100Mean 1.8 -0.2 1.2 71Max 2.9 2.4 1.9 87Min 1.1 -1.2 0.1 32

Quantity W°C) tW (°Q uai (m/s) 4* (W/m2)Nominal: A6 +2 -0.3 (85 %RH) 1 100Mean 2.1 0.1 0.68 81Max 3.1 2.9 0.81 95Min 1.4 -0.9 0.38 43

Quantity ual (m/s) 4a (W/m2)

Nominal: A7 +2 -0.3 (85 %RH) 4 100Mean 1.6 0.1 2.72 116Max 2.8 2.8 3.51 145Min 1.0 -0.9 0.09 49

General comments on set values and associated measured values may be found in section 4.1. Fahlen® discusses the specific problems regarding air flow and air velocity measurements experienced in this work. Appendix A3 and B8 provide examples of uncertainty budgets for air flowrate and face velocity respectively.

Initial values of the coil face velocity in retrospect turned out to be lower than the set values due to a calibration problem wiht the air flowmeter. Values in the table are the corrected values after a subsequent recalibration.


106


Figure 4.3.1 shows the time dependent heating and cooling capacity of the heat pump unit during frosting with a specific cooling load of approximately 100 W/m2 and inlet air velocities of 2,1, and 4 m/s respectively. The diagrams also include integrated mean values of the capacities according to the principles of section 2.2.1. In addition, table 4.3.1.1 gives the mean, maximum and minimum values during two frosting - defrosting cycles, both for the total cycle and for the frosting and defrosting periods respectively.


ua = 2 m/s A1 1 m/s A6 4 m/s A7Period 2, (kW) 0.2 (kW) &(kW) &(kW) &(kW) 0.2 (kW)Full cyclesMean 8.54 5.74 10.5 7.01 9.52 6.42Max 18.0 41.4 21.5 15.8 18.7 19.9Min 0.61 -9.63 0.85 4.75 1.03 5.47FrostingMean 8.23 5.41 10.2 6.59 9.34 6.22Max 11.1 6.39 15.5 8.99 12.4 7.33Min 0.91 4.64 8.95 5.69 8.32 5.43DefrostingMean 11.6 8.99 12.6 9.90 12.3 9.83Max 18.0 41.4 21.5 15.8 21.8 21.2Min 0.61 -9.63 0.85 4.75 1.03 4.75

In the diagrams dashed lines indicate the time of the maximum integrated mean value of the heating and cooling capacities, Q]m and Q2m, (the times are very close). In the case of A7, frosting is rather slow. Table 4.3.1.2 below gives the times after a defrost when maximum integrated mean capacity occurs.


\ia — 2 m/s A1 1 m/s A6 4 m/s A7Q\ <h Qi Qi Qi e2

Time (h) 12.8 12.8 6.3 5.9 14.7 14.7



Ther

mal

capa

city

(kW

) Th

erm

al ca

paci

ty (k

W)

Ther

mal

capa

city

(kW

)

107


------Q2m

Time (h)



Time (h)



108

4.3.2 Coil capacity

The diagrams of figure 4.3.2 show the time dependent cooling capacity of the coil during frosting with a specific cooling load of approximately 100 W/m2. Nominal air velocities of 2,1, and 4 m/s were used. Capacity measured on the air-side as well as on the brine-side are included. The diagrams also show the integrated mean value, Qbm, of the brine-side capacity according to the principles of section 2.2.1. The problem of achieving accurate air-side measurements is clearly seen from the curves, in particular the drop due to uncertain airflow measurement at low flowrates. Except for test Al, air-side capacities have normally been underestimated.



Ua = 2 m/s Al 1 m/s A6 4 m/s A7Period g, (kW) &(kW) (kW) G„(kW) e, (kW) &(kW)Full cyclesMean 3.54 1.85 4.1 2.15 1.5 3.20Max 4.53 57.3 1169 14.8 23.1 4.53Min 0.46 -107 -151 -89 -247 -113FrostingMean 3.54 2.76 2.8 3.76 4.0 4.12Max 4.53 4.04 4.3 4.44 23.1 4.53Min 0.46 -107 0.00 2.01 -2.1 1.68DefrostingMean - -8.88 15.2 -4.56 -44.8 -10.8Max 0.00 57.3 1169 14.8 4.1 16.3Min 0.00 -123 -151 -36.8 -247 -115


Thermally measured defrost capacities, according to the table above, are of the same order of magnitude as the electrical energy measurements transferred to an equivalent power input during the defrost period. For Al, results are 123 and 112 kW respectively for thermally and electrically measured results, for A6 corresponding values are 151 and 117 kW arid for A7 we have 247 and 136 kW respectively. Bearing in mind the short defrost time and the uncertainty in time resolution, agreement is acceptable.


Coi

l cap

acity

(kW

) C

oil c

apac

ity (k

W)

Coi

l cap

acity

(kW

)

109


— Qa

Time (h)


— Qa

Time (h)


— Qa

Time (h)



110

4.3.3 Power input

The diagrams of figure 4.3.3 show the time dependent electric power inputs to the heat pump and the defrosting system during operation with a specific cooling load of approximately 100 W/m2. Air inlet velocities are 2, 1, and 4 m/s respectively.



Ua = 2 m/s A1 1 m/s A6 4 m/s A7Period Wem (kW) ^ (kW) Wem (kW) (kW) Wem (kW) Wf (kW)

Full cyclesMean 3.02 0.73 3.79 0.66 3.21 0.88Max 4.66 0.86 5.74 0.78 4.69 0.99Min 0.00 0.00 0.00 0.00 0.00 0.00FrostingMean 2.98 0.80 3.82 0.76 3.19 0.91Max 3.49 0.86 4.79 0.78 3.69 0.99Min 0.00 0.00 3.56 0.74 3.00 0.00DefrostingMean 3.36 0.00 3.75 0.00 3.49 0.00Max 4.66 0.00 5.74 0.00 5.06 0.00Min 0.00 0.00 0.00 0.00 0.00 0.00

The diagrams show that the power input to the defrost system has a large peak right after a defrost and then a number of smaller peaks to cover system losses between defrosts (see comments to 4.1.3).




Ill


•• Wedefr

‘-i-v-:-:

0 12 24 36 48

Time (h)


Wedefr

Time (h)




112


The diagrams of figure 4.3.4 show the time dependent heating and cooling coefficients o performance of the heat pump unit during frosting with a specific cooling load of approximately 100 W/m2. The diagrams also include integrated mean values, COPjm and COP22m, of the coefficients of performance according to the principles of section 2.2.1. In addition, table 4.3.4.1 gives the mean, maximum and minimum values during an integral number of frosting - defrosting cycles, both for the total cycle and for the frosting and defrosting periods respectively.

Table 4.3.4.1. Mean, maximum and minimum values during frosting and defrosting periods; coefficient of performance.

ua = 2 m/s A1 1 m/s A6 4 m/s A7Period COP, COP2 COP, COP2 COP, COP2Full cyclesMean 2.77 1.89 2.63 1.80 2.93 1.97Max 3.87 15.79 3.74 10.91 3.99 5.59Min 0.00 -2.68 0.00 0.00 0.00 0.00FrostingMean 2.74 1.80 2.66 1.72 2.92 1.95Max 3.19 1.90 3.34 1.93 3.37 2.01Min 0.00 0.00 2.51 1.60 2.77 1.81DefrostingMean 2.97 2.58 2.54 2.41 2.99 2.32Max 3.87 15.79 3.74 10.91 4.32 5.92Min 0.00 -2.68 0.00 0.00 0.00 0.00*During defrosting, COP has no real meaning since the heat pump has only operated for a very short while at the end of the defrost cycle. Most of the energy supply comes from the electrically heated defrost tank.

In the diagrams, dashed lines indicate the times of maximum integrated mean values of the heating and cooling coefficients of performance. The indicated optima are based on defrosts with 100 % efficiency (COPIm* and COP2m*) whereas curves based on real defrosting efficiency {COP,m and COP2m) never intersect the instantaneous curves. For further comments, see 4.1.4. Table 4.3.4.2 below gives the time after a defrost when the maximum integrated mean coefficient of performance occurs.

Table 4.3A.2. Time for maximum integrated mean coefficient of performance.

Ua = 2 m/s A1 1 m/s A6 4 m/s A7COP, COP2 COP, COP2 COP, COP2

Time (h) 18.2 16.5 9.6 8.6 23.0 23.0

The table shows a great diversity in optimum time depending on the operating conditions.


CO

P C

OP

113


COP2

COPlm

COP2m

COPlm*

•• COP2m*

Time (h)


COP2

COPlm

-----COP2m

— COPlm*

-• COP2m*

Time (h)


COP2

COPlm

-----COP2m

COPlm*

-• COP2m*

Time (h)



114


The diagrams of figure 4.3.5 show the time dependence of a number of temperatures which are relevant to the performance of the coil. Included are inlet and outlet temperatures of the air and the brine, inlet and outlet dew point temperatures and the mean value of a number of fin surface temperatures. Specific cooling load was approximately 100 W/m2 and air velocities were around 2,1, and 4 m/s. In addition, table 4.3.5 gives the mean, maximum and minimum values of the outlet brine and fin temperatures during an integral number of frosting - defrosting cycles, both for the total cycle and for the frosting and defrosting periods respectively.


Ua = 2 m/s A1 1 m/s A6 4 m/s A7Period (°C) fa, CQ (°C) fm, (°C) f« (°C) fa, (°C)Full cyclesMean -3.17 -0.3 -5.07 -0.7 -2.54 0.4Max 34.31 38.1 49.58 23.1 36.71 21.8Min -8.42 -4.3 -10.89 -4.8 -6.53 -1.4FrostingMean -4.98 -1.6 -7.50 -1.9 -3.54 0.0Max 9.08 2.1 2.15 2.3 2.23 2.2Min -8.42 -4.3 -10.72 -4.2 -6.72 -1.5DefrostingMean 14.04 11.8 11.35 7.7 14.99 9.0Max 34.31 38.1 49.58 23.1 66.83 38.4Min -3.66 -3.9 -10.82 -4.7 -6.83 -1.7

From the diagrams and the table it is obvious why frosting is slow during test A7. The mean fin surface temperature is around zero for a long time so in the inlet section there will be no frosting and in the outlet section, where the surface temperature is below zero, there will only be very little frost.

t.


Tem

pera

ture

(°C

) Te

mpe

ratu

re (°

C)

Tem

pera

ture

(°C

)

115


*- v v *- -s ■'*/• -s, 1 - - tdpl

------ tdp2

— ta2

Time (h)


v -vA-* -Zz- *s s-v* - tdpl0 •

------- tdp2

— ta2

Time (h)


------ tdp2

---- ta2

Time(h)



116

4.3.6 Flowrates

The diagrams of figure 4.3.6 show the time dependence of the condenser water flowrate, the brine flowrate and the air flowrate. Specific cooling load was approximately 100 W/m2 and air velocity 2,1, and 4 m/s approximately. In addition, table 4.3.6 gives the mean, maximum and minimum values of the air and brine flowrates during an integral number of frosting - defrosting cycles, both for the total cycle and for the frosting and defrosting periods respectively.


ua = 2 m/s A1 1 m/s A6 4 m/s A7Period va (nrVs) vb (nrVh) va (m7s) vb (m7h) va (m7s) vb (mTh)Full cyclesMean 0.47 1.84 0.27 1.28 1.31 1.89Max 0.91 2.05 0.39 1.47 1.68 2.08Min -0.39 1.78 -0.06 1.16 0.03 1.85FrostingMean 0.55 1.83 0.32 1.27 1.31 1.89Max 0.91 1.89 0.39 1.40 1.68 1.93Min -0.35 1.78 -0.02 1.21 0.04 1.85DefrostingMean -0.34 1.96 -0.05 1.39 0.04 1.99Max -0.32 2.05 0.01 1.47 0.16 2.09Min -0.39 1.76 -0.06 1.16 0.03 1.81


The brine flow is fairly constant during a test cycle. Only in situations where viscosity changes markedly will there be a change in flow. This happens during defrosting with warm brine and at the end of a cycle with heavy frosting. The condenser water flowrate was very stable at all times.


Flow

rate

(m3/

h, m

3/s)

Fl

ow ra

te (m

3/h,

m3/

s)

Flow

rate

(m3/

h, m

3/s)

117


- - Vb(m3/h)

Va (m3/s)

Time (h)


“ ” " Vw (m3/h) -

— — Vb(m3/h)

; *

—i—ii

Jrii ■............ Va (m3/s)

_________^

0 12 24 36 48

Time (h)


- - Vw (m3/h)

- - Vb (m3/h)

Va (m3/s)

Time (h)



118


The diagrams of figure 4.3.7 show the time dependence of the air inlet velocity and pressure drop of the coil. Specific cooling load was approximately 100 W/m2. In addition, table 4.3.7 gives the mean, maximum and minimum values of these measurands during an integral number of frosting - defrosting cycles, both for the total cycle and for the frosting and defrosting periods respectively.


Ua — 2 m/s A1 1 m/s A6 4 m/s A7Period ua (m/s) Apa (Pa) ua (m/s) Apa (Pa) ua (m/s) Apa (Pa)Full cyclesMean 0.98 189 0.59 90 2.73 163Max 1.90 386 0.81 269 3.49 386Min -0.82 -1.9 -0.13 -1 0.06 -1FrostingMean 1.14 207 0.68 105 2.72 187Max 1.90 386 0.81 269 3.51 386Min -0.74 0.2 0.38 1 0.09 0DefrostingMean -0.71 1.0 -0.10 2 0.09 1Max -0.66 3.5 0.03 20 0.33 19Min -0.82 -1.9 -0.13 -1 0.05 -2

Air velocity is based on the measured volume flow and the frontal area of the coil. This velocity is set with a dry coil, hence the maximum value during the frosting phase should be compared with the set value. During defrosting, air velocity may actually be negative, due to natural convection with the fan stopped.

Coil pressure drop has its maximum right at the end of the frosting period. For tests A1 and A7 the final pressure drop is around 386 Pa. For A6, on the other hand, this drop is only 279 Pa due to the low initial setting of the flowrate (adjusted by means of an outlet damper).


u (m

/s), d

p (P

a/20

0)

u (m

/s), d

p (P

a/20

0)

u (m

/s), d

p (P

a/20

0)

119


u(m/s)

- - dp (Pa/200)

Time (h)


u(m/s)

- - dp (Pa/200)

Time (h)


u (m/s)

- - dp (Pa/200)

Time (h)



120

4.3.8 Frost mass

The diagrams of figure 4.3.8 show the time dependence of frost mass in the coil. Specific cooling load was approximately 100 W/m2 and air velocity was 2,1, and 4 m/s respectively. In addition, table 4.3.8 gives the mean, maximum and minimum values of these measurands during an integral number of frosting - defrosting cycles, both for the total cycle and for the frosting and defrosting periods respectively.


Ua = 2 m/s A1 1 m/s A6 4 m/s A7Period Mfr (kg) mfr (kg/h) Mfr (kg) ,hfr (kg/h) Mfr (kg) mfr (kg/h)Full cyclesMean 8.36 -6.31 5.93 3.24 4.62 -2.36Max 17.3 31 13.4 1485 14.1 25Min -0.09 -479 0.00 -191 0.23 -314FrostingMean 9.01 0.14 6.34 1.23 5.49 0.72Max 17.3 31 13.4 3.96 14.8 24.9Min 0.34 -112 0.47 -1.41 0.51 -5.56DefrostingMean 1.75 -73 2.92 19 1.96 -56.9Max 15.4 4.38 12.5 1485 13.2 5.16Min -0.09 -667 0.00 -191 -0.34 -314


During defrosting the load-cell system returns very nicely to a zero reading prior to the next frosting phase. The defrosting phase is quite violent, with high thermal and mechanical stresses. The violence of the defrosting phase is apparent from the large difference in the frosting mass flux (+) and the defrosting mass flux (-). In this context defrosting mass fluxes of table 4.3.8 in the range 191-667 kg/h may be compared with the estimated evaporation rate of around 700 kg/h (0.2 kg/s) using the Lewis relation in 5.4.


Fros

t mas

s (kg

) Fr

ost m

ass (

kg)

Fros

t mas

s (kg

)

121






122



Table, 4.3.9. Mean, maximum and minimum values during frosting and defrosting periods; defrost water, defrost time and defrost energy.

Measurand Al (100 W/m2) A6 (50 W/m2) A7 (150 W/m2)Mdw (kg) 14.2 8.9 -

Mdw / Mfr (kgfi/kgw) 0.81 0.67 -

W*dw (kWh/defrost) 32.1 16.4 39.0rid(-) 0.05 0.08 0.04'td(s) 125 142 114tc(h) 22.5 9.6 27.5



The diagrams of figure 4.3.10 show the temporal behaviour of some normalized alternative defrost indicators. At the same time the diagrams show the wide spread in optimum time to defrost depending on whether you want to optimize capacity, cooling COP or heating COP. In test A7 there is a difference of around 9 h between optima for capacity and coefficient of performance. This latitude would be wider still if you include defrosting efficiency as a variable. In the case of 100 % defrosting efficiciency the maximum of the mean COP is very flat so time is not really critical as long as you leave the defrost until after the maximum. The more energy required by a defrost the more important the actual time of defrosting becomes.


Nor

mal

ized

cha

nge

Nor

mal

ized

cha

nge

Nor

mal

ized

cha

nge

123


COP iCOP2

Time (h)


: ccpi

Time (h)


COP1COP21; J.

Q1.Q2

Time (h)



124

4 Resultsmith a frosting coil

125

4.4 -7 °C: Variation of air velocity

Table 4.4 gives an overview of the nominal and actual test conditions during tests with different velocities at -7 °C. Air inlet and outlet temperatures were measured both with PRTs and grids of thermocouples. Mean, max and min values of temperature refer to temporal variations of the spatial means of thermocouple grids during the frosting period (i.e. excluding defrosting). Air velocities are based on volume flowrate and frontal area of the coil.


Quantity WQ uai (m/s) &,(W/m=)Nominal: A8 -7 -8.9 (85 %RH) 2 100Mean -7.0 -8.9 1.31 87Max -5.8 -5.8 1.93 104Min -7.5 -10.1 -0.64 50

Quantity (°C) Ual (m/s) qa(W/m2)Nominal: A9 -7 -8.9 (85 %RH) 1 100Mean -7.0 -8.9 0.70 75Max -6.1 -6.3 0.80 86Min -7.8 -9.8 0.14 50

Quantity WO WQ Ual (m/s) 4a (W/m2)Nominal: A10 -7 -8.9 (85 %RH) 4 100Mean -6.5 -8.9 2.8 83Max -5.7 -7.4 3.1 89Min -7.2 -9.7 2.2 30

General comments on set values and associated measured values may be found in section 4.1. Fahlen(8) discusses general problems of air temperature measurements and appendix A5 contains a summary of the related uncertainties.


126

4.4.1 Heat pump capacity .

Figure 4.4.1 shows the time dependent heating and cooling capacity of the heat pump unit during frosting with specific cooling loads of approximately 100 W/m2 and velocities of 2, 1, and 4 m/s at an inlet temperature of -7 °C. The diagrams also include integrated mean values of the capacities according to the principles of section 2.2.1. In addition, table 4.4.1 gives the mean, maximum and minimum values during two frosting - defrosting cycles, both for the total cycle and for the frosting and defrosting periods respectively.

Table 4.4.1. Mean, maximum and minimum values during frosting and defrosting periods; thermal capacities.

Ua = 2 m/s A8 1 m/s A9 4 m/s A10Period Q, (kW) &(kW) &(kW) &(kW) A(kW) &(kW)Full cyclesMean 10.3 6.45 10.6 6.55 9.75 6.21Max 20.0 29.6 25.2 40.8 16.9 36.8Min 1.14 4.69 1.16 4.81 1.00 5.31FrostingMean 10.2 6.18 10.0 5.89 9.43 5.77Max 16.0 8.20 16.3 8.46 12.0 6.10Min 8.21 4.78 8.37 4.81 9.04 5.58DefrostingMean 13.6 11.3 15.8 12.8 . 12.6 10.1Max 20.0 29.6 25.2 40.8 16.9 36.8Min 1.14 4.69 1.16 4.83 1.00 5.31

In the diagrams a dashed line indicates the time of the maximum integrated mean value of the heating and cooling capacities, QIm and Q2m, (the times are virtually the same). In the case of A10, frosting is too slow to warrant a defrost but after 30 h one is carried out anyway. Table 4.4.1.2 below gives the times after a defrost when maximum integrated mean capacity occurs.


ua = 2 m/s A8 1 m/s A9 4 m/s A10Qi Qi Qi Qi Qi Qi

Time (h) 11.6 11.6 9.6 9.6 20.9 20.9

The table shows a great diversity in optimum time depending on the operating conditions of the coil. In the case of A10 the optimized curve is extremely flat and consequently the optimum time is quite uncertain.


Ther

mal

cap

acity

(kW

) Th

erm

al c

apac

ity (k

W)

Ther

mal

cap

acity

(kW

)

127


Time (h)


------Q2m

Time (h)


------Q2m

Time (h)



128

4.4.2 Coil capacity

The diagrams of figure 4.4.2 show the time dependent cooling capacity of the coil during frosting with a specific cooling load of approximately 100 W/m2, a relative humidity of 85 % and an air temperature of -7 °C. Nominal inlet velocities of 2,1, and 4 m/s were used. Capacity measured on the air-side as well as on the brine-side are included. The diagrams also show the integrated mean value, Qbm, of the brine-side capacity according to the principles of section 2.2.1. The problem of achieving accurate air-side measurements is clearly seen from the curves, in particular the drop due to uncertain airflow measurement at low flowrates. In the case of A10, however, flow is up and hence accuracy of the air-side coil capacity is much improved. Except for test Al, air-side capacities have normally been underestimated.



Ua - 2 m/s A8 1 m/s A9 4 m/s A10Period 6* (kW) &(kW) e* (kW) G„ (kW) &(kW)Full cyclesMean 0.4 3.20 2.2 2.16 2.3 2.73Max 4.9 7.76 3.5 8.09 4.4 4.13Min -189 -100 -1.1 -126 -6.5 -103FrostingMean 3.1 4.13 2.5 3.50 2.8 3.85Max 4.7 4.84 3.5 4.02 4.4 4.13Min -7.4 2.31 -1.1 2.35 -6.5 1.38DefrostingMean -49 -13.41 0.0 -10.40 -2.2 -7.07Max 4.9 7.76 1.3 8.09 0.2 3.64Min -189 -100 -0.4 -126 -3.7 -103


Thermally measured defrost capacities, according to the table above, are of the same order of magnitude as the electrical energy measurements transferred to an equivalent power input during the defrost period. For A8, results are 100 and 151 kW respectively for thermally and electrically measured results, for A9 we have 126 and 129 kW, and for A10 we have 103 and 105 kW respectively. Bearing in mind the short defrost time and the uncertainty in time resolution, agreement is acceptable.


Coi

l cap

acity

(kW

) C

oil c

apac

ity (k

W)

Coi

l cap

acity

(kW

)

129


Time (h)


— Qa

Time (h)


— Qa

Time (h)



130

4.4.3 Power input

The diagrams of figure 4.4.3 show the time dependent electric power inputs to the heat pump and the defrosting system during operation with a specific cooling load of approximately 100 W/m2, inlet temperature -7 °C, inlet humidity 85 %, and inlet velocities of 2, 1, and 4 m/s.



Ua- 2 m/s A8 1 m/s A9 4 m/s A10Period Wem (kW) we/ (kW) Wem (kW) ^(kW) Wem (kW) ^(kW)

Full cyclesMean 3.99 0.78 4.02 0.71 3.51 0.84Max 5.89 0.87 6.64 0.80 4.77 0.96Min 0.00 0.00 0.00 0.00 0.00 0.00FrostingMean 3.99 0.83 3.96 0.78 3.45 0.93Max 5.04 0.87 5.11 0.80 3.99 0.96Min 3.51 0.75 3.55 0.75 3.38 0.89DefrostingMean 4.13 0.00 4.61 0.00 3.99 0.00Max 5.89 0.00 6.64 0.00 4.77 0.00Min 0.00 0.00 0.00 0.00 0.00 0.00





131



:: •. :• r. ;.••• xH*-r.'—i1' ”■ *

Time (h)


Wedefr

Time (h)



132


The diagrams of figure 4.4.4 show the time dependent heating and cooling coefficients o performance of the heat pump unit during frosting with a specific cooling load of approximately 100 W/m2. The diagrams also include integrated mean values of the coefficients of performance, COP,m and COP22m, according to the principles of section 2.2.1. In addition, table 4.4.4.1 gives the mean, maximum and minimum values during an integral number of frosting - defrosting cycles, both for the total cycle and for the frosting and defrosting periods respectively.


ua = 2 m/s A8 1 m/s A9 4 m/s A10Period COP, COP2 COP, COP2 COP, COP2Full cyclesMean 2.54 1.59 2.54 1.54 2.76 1.75Max 3.49 11.3 3.79 6.11 3.54 9.86Min 0.00 0.00 0.00 0.00 2.21 1.49FrostingMean 2.53 1.54 2.53 1.49 2.73 1.67Max 3.18 1.70 3.19 1.69 3.08 1.70Min 0.00 0.00 2.35 1.35 2.67 1.49DefrostingMean 2.62 • 2.55 2.70 2.11 3.11 2.52Max 3.49 11.3 3.79 6.11 3.54 9.86Min 0.00 0.00 0.00 0.00 2.21 1.51♦During defrosting, COP has no real meaning since the heat pump has only operated for a very short while at the end of the defrost cycle. Most of the energy supply comes from the electrically heated defrost tank.

In the diagram, a dashed line indicates the time of the maximum integrated mean value of the heating and cooling coefficients of performance. The indicated optima are based on defrosts with 100 % efficiency (COP,m* and COP2m*) whereas curves based on real defrosting efficiency (COP,m and COP2m) never intersect the instantaneous curves. For further comments, see 4.1.4. Table 4.4.4.2 below gives the time after a defrost when the maximunvintegrated mean coefficient of performance occurs.


Ua~ 2 m/s A8 1 m/s A9 4 m/s A10COP, COP2 COP, COP2 COP, COP2

Time (h) 16.0 14.6 12.6 11.6 24.2 22.6



CO

P C

OP

CO

P

133


COP2

COPlm

-----COP2m

COPlm*

Time (h)


COPlm

------COP2m

COPlm*

-• COP2m*

Time (h)


COPl

COP2

COPlm

-----COP2m

- COPlm*

Time (h)



134


The diagrams of figure 4.4.5 show the time dependence of a number of temperatures which are relevant to the performance of the coil. Included are inlet and outlet temperatures of the air and the brine, inlet and outlet dew point temperatures and the mean value of a number of fin surface temperatures. Specific cooling load was approximately 100 W/m2, humidity around 85 %, and air inlet temperature -7 °C. Air velocity was adjusted to 2,1, and 4 m/s respectively. In addition, table 4.4.5 gives the mean, maximum and minimum values of the outlet brine and fin temperatures during an integral number of frosting - defrosting cycles, both for the total cycle and for the frosting and defrosting periods respectively.


ua = 2 m/s A8 1 m/s A9 4 m/s A10Period 42 (°Q tf!n (°C) 42 (°Q 4. (°Q 42 (°Q 4. (°QFull cyclesMean -14.60 -10.7 -14.54 -10.3 -10.18 -7.6Max 21.04 11.2 27.58 12.9 20.31 17.4Min -19.51 -14.6 -19.19 -16.6 -12.43 -9.0FrostingMean -15.55 -11.3 -16.40 -11.3 -11.51 -8.6Max -7.22 -6.4 -7.42 -4.7 -6.55 -6.1Min -19.34 -14.6 -19.19 -16.6 -12.43 -9.0DefrostingMean 2.35 -0.9 2.98 -0.9 1.48 1.1Max 21.04 11.2 27.58 12.9 20.31 17.4Min -19.51 -14.5 -18.94 -13.1 -5.60 -6.3

From the diagrams and the table it is obvious why there is virtually no frosting during test A10. The mean fin surface temperature is very close to the dew point temperature so in the inlet section there will be no frosting and in the outlet section, where the surface temperature is lower, there will only be very little frost. Once a thin frost layer covers this part of the coil the surface temperature will start dropping in the rest of the coil and further frosting will take place.


Tem

pera

ture

(°C

) Te

mpe

ratu

re (°

C)

Tem

pera

ture

(°C

)

135


V—* A —• \ ^ 1

- - tdpl

------tdp2

— ta2

Time (h)


Time (h)

%

Test condition AID: Coil temperatures

\ v- V<v< aV ■'“a •'**'* vX**1

- - tdpl

Time (h)



136

4.4.6 Flowrates

The diagrams of figure 4.4.6 show the time dependence of the condenser water flowrate, the brine flowrate and the air flowrate. Specific cooling load was approximately 100 W/m2, humidity was 85 % and air inlet temperature was -7 °C approximately. In addition, table 4.4.6 gives the mean, maximum and minimum values of the air and brine flowrates during an integral number of frosting - defrosting cycles, both for the total cycle and for the frosting and defrosting periods respectively.


Ua = 2 m/s A8 1 m/s A9 4 m/s A10Period va (m3/s) vb (m3/h) va (m3/s) vb (m3/h) va (m3/s) vb (m3/h)Full cyclesMean 0.58 1.72 0.30 1.68 1.24 1.85Max 0.93 2.13 0.38 2.14 1.47 2.07Min -0.34 1.58 -0.06 1.56 0.36 1.82FrostingMean 0.63 1.71 0.34 1.65 1.34 1.84Max 0.93 1.93 0.38 1.90 1.47 1.92Min -0.31 1.58 0.07 1.56 1.06 1.82DefrostingMean -0.32 1.97 -0.04 1.96 0.37 1.96Max -0.30 2.13 0.18 2.14 0.38 2.07Min -0.34 1.59 -0.06 1.57 0.36 1.85

At test condition A9 the initial air flowrate should have been around 0.48 m3/s and this was indeed the set-value. However, subsequent recalibration indicated that the original calibration constant was quite severely overestimated at low flowrates so the actual flow was only around 0.38 m3/s (Fahlen(8)).




Flow

rate

(m3/

h, m

3/s)

Fl

ow ra

te (m

3/h,

m3/

s)

Flow

rate

(m3/

h, m

3/s)

137


Va (m3/s)

Time (h)


1 — ” - Vw (m3/h) ■

— - - Vb (m3/h) .

..Va (m3/s)

i 4~ \

.y

0 12 24 36 48

Time (h)


• - Vw(m3/h)

• - Vb (m3/h)

Va (m3/s)

Time(h)



138


The diagrams of figure 4.4.7 show the time dependence of the air inlet velocity and pressure drop of the coil. Specific cooling load was approximately 100 W/m2. Air velocity was set to 2,1, and 4 m/s respectively.

In addition, table 4.4.7 gives the mean, maximum and minimum values of these measurands during an integral number of frosting - defrosting cycles, both for the total cycle and for the frosting and defrosting periods respectively.


Ua = 2 m/s A8 1 m/s A9 4 m/s A10Period ua (m/s) Apa (Pa) ua (m/s) Apa (Pa) ua (m/s) Apa (Pa)Full cyclesMean 1.20 191 0.62 82 2.58 107Max 1.93 400 0.80 271 3.07 214Min -0.71 -2 -0.13 -1 0.75 -1FrostingMean 1.31 202 0.70 89 2.79 119Max 1.93 400 0.80 271 3.07 214Min -0.64 ' 2 0.14 7 2.22 72DefrostingMean -0.66 0 -0.09 12 0.78 1Max -0.62 7 0.38 269 0.79 3Min -0.71 -2 -0.13 -1 0.75 -1

Air velocity is based on the measured volume flow and the frontal area of the coil. This velocity is set with a dry coil, hence the maximum value during the frosting phase should be compared with the set value (2,1, and 4 m/s respectively). During defrosting, air velocity may actually be negative, due to natural convection with the fan stopped.

Coil pressure drop has its maximum right at the end of the frosting period. For test A8 the final pressure drop is around 400 Pa whereas it will only be 271 Pa for test A9 with the low flowrate. For A10 the drop is also low, 214 Pa, due to the very low rate of frosting.


u (m

/s),

dp (P

a/20

0)

u (m

/s), d

p (P

a/20

0)

u (m

/s), d

p (P

a/20

0)

139


- - dp (Pa/200)

Time (h)


u (m/s)

- - dp (Pa/200)

Time (h)


u(m/s)

- - dp (Pa/200)

Time (h)



140

The diagrams of figure 4.4.8 show the time dependence of frost mass in the coil. Specific cooling load was approximately 100 W/m2, humidity was 85 % and air inlet temperature -7 °C respectively. Alternative air velocities of 2,1, and 4 m/s were tested. In addition, table 4.4.8 gives the mean, maximum and minimum values of these measurands during an integral number of frosting - defrosting cycles, both for the total cycle and for the frosting and defrosting periods respectively.

4.4.8 Frost mass


Ua = 2 m/s A8 1 m/s A9 4 m/s A10Period Mfr (kg) mfr (kg/h) Mfr (kg) mfr (kg/h) Mfr (kg) rilfr (kg/h)Full cyclesMean 5.41 -2.87 . 4.96 -2.06 1.72 -1.13Max 13.8 5.77 10.8 261 5.52 3.84Min -0.21 -239 -0.20 -218 -0.26 -124FrostingMean 5.54 0.42 5.27 0.42 1.85 0.06Max 13.8 4.14 10.8 5.51 5.52 3.84Min -0.21 -10 0.00 -14 -0.26 -5.8DefrostingMean 3.04 -62 2.04 -25.3 0.57 -12.4Max 12.9 5.77 10.7 261 5.20 3.74Min 0.00 -239 -0.20 -218 0.00 -124


During defrosting the load-cell system returns very nicely to a zero reading prior to the next frosting phase. The defrosting phase is quite violent, with high thermal and mechanical stresses. The violence of the defrosting phase is apparent from the large difference in the frosting mass flux (+) and the defrosting mass flux (-). In this context defrosting mass fluxes of table 4.4.8 in the range 124-239 kg/h may be compared with the estimated evaporation rate of around 700 kg/h (0.2 kg/s) using the Lewis relation in 5.4. In this case, however, the ambient temperature is -7 °C instead of +2 °C and therefore losses will be higher and the surface temperature lower at the point of interrupting the defrost (tb2 = 30 °C). Hence the driving potential for evaporation will be lower.


Fros

t mas

s (kg

) Fr

ost m

ass (

kg)

Fros

t mas

s (kg

)

141


Time (h)


Time (h)


Time (h)



142

Table 4.4.9 provides some data from the defrosting phase of tests A8, A9, and A10.



Measurand A8 (2 m/s) A9 (1 m/s) A10 (4 m/s)Mdw (kg) 9.6 *Mdw / Mfr (kgft/kgw) 0.65 * *W*dw (kWh/defrost) 28.1 24.5 30.6T|rf(-) 0.05 0.04 0.02Ti( s) 132 94 77Tc(h) 24.1 14.9 30.7*Not measured.

Values of defrosting efficiency are based on the latent heat of fusion of ice. If the latent heat of sublimation is used, the efficiencies will be approximately 8.5 times higher. Due to heavy evaporation during the final phase of a defrost, the quantity of collected defrost water was always smaller than the mass of frost in the coil. Defrost efficiency goes down when there is little frost in the coil since then the portion of energy used just to heat the coil will be relatively more significant (see test A10).


The diagrams of figure 4.4.10 show the temporal behaviour of some normalized alternative defrost indicators. In test A10, with very little frosting, it would be difficult to find the optimum time with any of the indicators if defrost efficiency were high. However, with normal efficiency, frosting must be fairly advanced before reaching the optimum and so the pictured indicators would probably work to some extent. At the same time the diagrams show the wide spread in optimum time to defrost depending on whether you want to optimize capacity, cooling COP or heating COP. This latitude would be wider still if you include defrosting efficiency as a variable.


Nor

mal

ized

cha

nge

Nor

mal

ized

cha

nge

Nor

mal

ized

chan

ge

143


COP2

Q1.Q2

Time#


! COP2

Q1-Q2

Time (h)


COPl

31. Q2

Time (h)



144

4.5 -7 °C: Variation of specific cooling load

Table 4.5 gives an overview of the nominal and actual test conditions during tests with different specific cooling loads at -7 °C. In the end, it turned out not possible to reach more than 100 W/m2 at -7 °C. Therefore, this section will only serve as a measure of reproducibility of two tests at similar specific loads. Mean, max and min values refer to the frosting period (i.e. excluding defrosting).


Quantity 4,7 (°Q WQ Ual (m/s) 4* (W/m2)Nominal: A8 -7 -8.9 (85 %RH) 2 100Mean -7.0 -8.9 1.31 87Max -5.8 -5.8 1.93 104Min -7.5 -10.1 -0.64 50Nominal: All -7 -8.9 (85 %RH) 2 50Mean * * * *Max * * * *Min * * *Nominal: All -7 -8.9 (85 %RH) 2 150Mean -6.9 -9.5 1.32 74Max -5.7 -7.2 1.94 87**Min -7.7 -11.8 0.10 31

*Due to problems during the test, it was not possible to use the data. **This was maximum available capacity.


Figure 4.5.1 shows the time dependent heating and cooling capacity of the heat pump unit during frosting with specific cooling loads of approximately 100 W/m2. The diagrams also include integrated mean values of the capacities according to the principles of section 2.2.1. In addition, table 4.5.1.1 gives the mean, maximum and minimum values during integral frosting. 1

Table 4.5.1.1. Mean, maximum and minimum values during frosting; thermal capacity.

<?A = 100 W/m2 A8 50 W/m2 All 150 W/m2 A12Period Qi (kW) &(kW) 6,(kW) &(kW) A(kW) &&W)FrostingMean 10.2 6.18 * * 8.88 5.35Max 16.0 8.20 * * 12.4 6.13Min 8.21 4.78 * * 7.54 ' 4.33*Due to problems during the test, it was not possible to use the data.


145

In the diagrams, a dashed line indicates the time of the maximum integrated mean value of the heating and cooling capacities, Qlm and Q2m, (the times are virtually the same). Table 4.5.1.2 below gives the times after a defrost when maximum integrated mean capacity occurs.


u- 100 W/m2 A8 50 W/m2 All 150 W/m2 A122i & Qi & e, Qi

Time (h) 11.6 11.6 * * 14.7 14.7*Due to problems during the test, it was not possible to use the data.

The table just displays the effect on optimum times of a small variation in specific cooling load.


Time (h)


------Q2m

Time (h)



146

4.5.2 Coil capacity

The diagrams of figure 4.5.2 show the cooling capacity of the coil with a specific cooling load of approximately 100 W/m2. Capacity measured on the air-side as well as on the brine-side are included. The diagrams also show the integrated mean value,Qbm, of the brine-side capacity according to the principles of section 2.2.1. Table 4.2.2 gives the mean, maximum and minimum values during an integral number of frosting.

Table 4.5.2. Mean, maximum and minimum values during frosting periods; coil capacity.9a = 100 W/m2 A8 50 W/m2 All 150 W/m2 A12Capacity G* (kW) &(kW) Go (kW) Q„ (kw) G« (kW) &(kW)Mean 3.1 4.13 * $ 2.5 3.43Max 4.7 4.84 * * 3.9 4.06Min -7.4 2.31 * * -6.6 1.42*Due to problems during the test, it was not possible to use the data.


U 2,0 - — Qa

Time (h)


-- Qa

-Zz-^vV VV '-.A./

U 2

Time(h)



147

4.5.3 Power input

The diagrams of figure 4.5.3 show the electric inputs to the heat pump and the defrosting system with a specific cooling load of approximately 100 W/m2. Table 4.5.3 gives the mean, maximum and minimum values during an integral number of frosting cycles.

Table 4.5.3. Mean, maximum and minimum values during frosting periods; electric input._______________________________________________________________9a = 100 W/m2 A8 50 W/m2 All 150 W/m2 A12Power Went (kW) ^(kW) Went (kW) wef (kW) Wem (kW) (kW)

Mean 3.99 0.83 * * 3.29 0.82Max 5.04 0.87 * * 3.96 0.88

Min 3.51 0.75 * * 2.99 0.75*Due to problems during the test, it was not possible to use the data.


— Wep

- Wef

" Wedefr

Time (h)


Wedefr

0 12 24 36 48

Time (h)



148


The diagrams of figure 4.5.4 show the heating and cooling coefficients of performance of the heat pump with a specific cooling load of approximately 100 W/m2. The diagrams also include integrated mean values of the coefficients of performance according to the principles of section 2.2.1. In addition, table 4.5.4.1 gives the mean, maximum and minimum values during an integral number of frosting.

Table 4.5.4. Mean, maximum and minimum values during frosting periods; COP.

9a = 100 W/m2 A8 50 W/m2 All 150 W/m2 A12COP COP, COP2 COP, COP2 COP, COP2Mean 2.53 1.54 * * 2.69 1.62Max 3.18 1.70 * * 3.21 1.71Min 0.00 0.00 * * 2.51 1.45*Due to problems during the test, it was not possible to use the data.


— — COP2

COPlm

-----COP2m

------ COPlm*

Time (h)


COP2

COPlm

-----COP2m

COPlm*

Time (h)



149


The diagrams of figure 4.5.5 show inlet and outlet temperatures of the air and the brine, inlet and outlet dew point temperatures and the mean value of a number of fin surface temperatures. Specific cooling load was approximately 100 W/m2. In addition, table 4.5.5 gives the mean, maximum and minimum values of the outlet brine and fin temperatures during an integral number of frosting.

Table 4.5.5. Mean, maximum and minimum values during frosting and defrosting periods; brine outlet and mean coil surface temperature.____________________-?A = 100 W/m2 A8 50 W/m2 All 150 W/m2 A12Temp. (°C) fa, (°Q f« (°Q 4. (°C) 42 (°Q fa, (°C)Mean -15.55 -11.3 * * -13.94 -11.1Max -7.22 -6.4 * * -7.86 -7.2Min -19.34 -14.6 * -17.67 -14.8*Due to problems during the test, it was not possible to use the data.



Time (h)



150

4.5.6 Flowrates

The diagrams of figure 4.5.6 show the condenser water flowrate, the brine flowrate and the air flowrate. Specific cooling load was approximately 100 W/m2 and humidity was 85 % approximately. In addition, table 4.5.6 gives the mean, maximum and minimum values of the air and brine flowrates during an integral number of frosting cycles.

Table 4.5.6. Mean, maximum and minimum values during frosting and defrosting periods; air and brine flowrates._______________________________________<lA = 100 W/m2 A8 50 W/m2 All 150 W/m2 A12Flow va (m3/s) vb (nrVh) va (md/s) vb (mJ/h) va (mVs) vb (m3/h)Mean 0.63 1.71 * * 0.63 1.76Max 0.93 1.93 * * 0.93 1.90Min -0.31 1.58 * * 0.05 1.63*Due to problems during the test, it was not possible to use the data.

Test condition AS: Flow rates

Vw (m3/h)

Vb (m3/h)

Va (m3/s)

Time(h)


- - Vb (m3/h)

Va (m3/s)

Time (h)



151


The diagrams of figure 4.5.7 show the air inlet velocity and pressure drop of the coil. Specific cooling load was approximately 100 W/m2. In addition, table 4.5.7 gives the mean, maximum and minimum values of these measurands during an integral number of frosting cycles.

Table 4.5.7. Mean, maximum and minimum, values during frosting and defrosting periods; air-side velocity and pressure drop._____________________________9a = 100 W/m2 A8 50 W/m2 All 150 W/m2 A12

ua (m/s) Apa (Pa) ua (m/s) Apa (Pa) ua (m/s) APa (Pa)Mean 1.31 202 * * 1.32 200Max 1.93 400 * 1.94 391Min -0.64 2 * * 0.10 30*Due to problems during the test, it was not possible to use the data.


u (m/s)

,---- '- - dp (Pa/200)

Time (h)


u(m/s)

- - dp (Pa/200)

Time (h)



4.5.8 Frost mass

The diagrams of figure 4.5.8 show the time dependence of frost mass in the coil. Specific cooling load was approximately 100 W/m2 and humidity was 85 %. In addition, table 4.5.8 gives the mean, maximum and minimum values of these measurands during an integral number of frosting cycles.

Table 4.5.8. Mean, maximum and minimum values during frosting and defrosting periods; frost mass and mean growth rate.9a = 100 W/m2 AS 50 W/m2 All 150 W/m2 A12Mass Mfr{kg) mfr (kg/h) Mfr (kg) mfr (kg/h) %(kg) mfr (kg/h)

Mean 5.54 0.42 * * 6.86 0.36Max 13.8 4.14 * * 15.2 4.60Min -0.21 -9.96 * * 0.00 -8.67*Due to problems during the test, it was not possible to use the data.


Time (h)


Time (h)



153


Table 4.5.9 provides some data from the defrosting phase of tests A8 and A12. Even though the tests were nominally fairly equal there is a large difference in the frosting cycle times. On the other hand, the total frost mass at the time of defrost was almost identical at 14.8 and 14.7 kg respectively. The only real difference between the two tests is that for A8 the dew point temperature was 0.6 higher than in A12 and that the specific cooling load is 17 W/m2 higher in test A8 (corresponds to the brine temperature being 1.5 K lower in A8). This illustrates how even fairly small differences in the test conditions have great effects on the frosting of a coil.


Measurand A8 (100 W/m2) All (50 W/m2) A12 (150 W/m2)Mdw (kg) 9.6 * 10.4Mdw / Mfr (kgfr/kgw) 0.65 * 0.71W*dw (kWh/defrost) 28.1 * 34.8T|d(-) 0.05 * 0.04%i (s) 132 * 142Tc(h) 24.1 * 30.8



The diagrams of figure 4.5.10 show the temporal behaviour of some normalized alternative defrost indicators. The indicator based on brine outlet temperature works well in test A12 but for some reason it is not as distinct in test A8 as in A12. This can also be seen in the diagrams of coil temperature in 4.5.5 where the decline in brine temperature is more gradual for A8 than for A12.

Pressure difference, air flowrate, and fan power show much the same behaviour. Air temperature difference is virtually constant and cannot be used at all.


Nor

mal

ized

cha

nge

Nor

mal

ized

cha

nge

154

Test condition AS: Defrost indicators

COP1COP2

Q1.Q2

Time (h)


COPl

----- ti>2Q1IQ2

Time (h)



155

4.6 Simulated rain - coil A

Table 4.6 gives an overview of the nominal and actual test conditions during tests with different air velocities and conditions of simulated rain for coil A with a fin spacing of approximately 3.5 mm. Mean, max and min values refer to the frosting period (i.e. excluding defrosting).


Quantity (°C) Ual (m/s) &,(W/nf)

Nominal: A13 +2 +2 (100 %RH) 2 100Mean 1.8 0.6 1.23 105Max 2.4 1.5 1.95 128Min 1.4 -0.1 -0.51 40

Quantity 4,; (°C) 4W (°C) Ual (m/s) &,(W/m:)

Nominal: A14 +2 +2 (100 %RH) 1* 100Mean 2.0 1.0 0.59 97Max 2.6 1.7 0.80 116Min 1.6 0.5 0.36 44

Quantity f.,(°C) 4W (°Q uai (m/s) 4a(W/m:)

Nominal: A15 +2 +2 (100 %RH) 4 100Mean 1.8 1.4 2.07 135Max 3.2 3.2 3.55 170Min 0.6 -0.4 0.56 31

*There were problems with the airflow measurement, probably due to water droplets affecting the dp-sensor.


The dew point was measured in the ambient air of the coil whereas the water curtain, simulating the rain, was mounted directly in front of the coil. Hence the deviation from a saturated condition in the measured humidity.

Air velocities are lower than projected. This is due to a problem with the calibration factor of the air flowmeter. After the measurements it was discovered that the actual flow was around 10 % lower than indicated.


156


Figure 4.6.1 shows the time dependent heating and cooling capacity of the heat pump unit during frosting with a specific cooling load of approximately 100 W/m2 and simulated rain. The diagrams also include integrated mean values of the capacities according to the principles of section 2.2.1. In addition, table 4.6.1.1 gives the mean, maximum and minimum values during two frosting - defrosting cycles, both for the total cycle and for the frosting and defrosting periods respectively.


ua — 2 m/s A13 1 m/s A14 4 m/s A15Period fi, (kW) Qi (kW) A(kW) &(kW) &(kW) &(kW)Full cyclesMean 11.5 7.57 11.2 7.77 13.6 9.19Max 18.6 19.8 17.0 51 23 22Min 0.74 5.20 0.80 4.43 1.36 6.01FrostingMean 11.2 7.02 11.0 6.79 13.4 8.57Max 15.2 7.80 15.1 7.67 19.0 10.1Min 9.32 5.74 9.44 5.79 10.7 6.77DefrostingMean 13.1 9.83 12.5 12.4 14.7 12.2Max 18.6 19.8 17.0 51 23 22Min 0.74 5.61 0.95 4.43 1.36 6.01

The table shows that just after a defrost, when the coil is quite warm, heating capacity is extremely high (defrosting terminates when is +30 °C). During defrosting, cooling capacity is negative (heating instead of cooling).

In the diagrams a dashed line indicates the time of the maximum integrated mean value of the heating and cooling capacities, QJm and Q2m, (the times are virtually the same). Table 4.6.1.2 below gives the times after a defrost when maximum integrated mean capacity occurs.


ua = 2 m/s A13 1 m/s A14 4 m/s A150i 02 0i 02 0i 02

Time (h) 3.9 3.9 2.9 2.9 2.9 2.9

The table shows rather a small variation in the optimum time in relation to the air velocity.


Ther

mal

cap

acity

(kW

) Th

erm

al ca

paci

ty (k

W)

Ther

mal

cap

acity

(kW

)

157


------Q2m

Time (h)


-----Q2m

Time (h)


------Q2m

Time (h)



158

4.6.2 Coil capacity

The diagrams of figure 4.6.2 show the time dependent cooling capacity of the coil during frosting with a specific cooling load of approximately 100 W/m2 and conditions of simulated rain. Nominal air velocities of 2,1 and 4 m/s were used. Capacity measured on the air-side as well as on the brine-side are included. The diagrams also show the integrated mean value of the brine-side capacity, Qbm,

according to the principles of section 2.2.1. The problem of achieving accurate air- side measurements is clearly seen from the curves, in particular the deviations due to uncertain airflow measurement at low flowrates.



ua = 2 m/s A13 1 m/s A14 4 m/s A15Period Qa (kW) &(kW) (kW) &(kW) Qa (kW) &(kW)Full cyclesMean 1.0 1.56 -5.1 0.86 -1.2 3.90Max 646 5.95 10.2 21.3 163 8.43Min -240 -100 -161 -98 -222 -106FrostingMean 4.5 4.90 3.53 4.51 6.8 6.27Max 30.4 5.95 10.2 5.38 35 7.90Min -6.0 1.87 -2.4 2.05 -2.9 1.42DefrostingMean 23 -7.70 -38 -9.39 -41 -7.73Max 646 5.09 3.8 21.3 163 8.43Min -240 -86 -161 -98 -222 -106

In test A14, with a low air flowrate, there is a reproducible, strong deviation regarding the air-side capacity. This could possibly be caused by uneven distribution of frost causing a disturbed velocity profile or something else affecting the flowmeter. During defrosting, cooling capacity is negative (heating instead of cooling).

Thermally measured defrost capacities, according to the table above, are of the same order of magnitude as the electrical energy measurements transferred to an equivalent power input during the defrost period. For A13, results are 100 and 77 kW respectively for thermally and electrically measured results, for A14 correspondingly 98 kW and 68 kW, and for A15 we have 106 and 66 kW respectively. Bearing in mind the short defrost time and the uncertainty in time resolution, agreement is acceptable.


Coi

l cap

acity

(kW

) C

oil c

apac

ity (k

W)

Coi

l cap

acity

(kW

)

159


— Qa

Time (h)


1

11

——

Qb

---------- Qa

A Z/'

it,/—Yli x" \

Qbm

Wy'W

!U' \ 1 |

r 1

1

0-6 12 18 24

Time (h)


— Qa

Time (h)



160

4.6.3 Power input

The diagrams of figure 4.6.3 show the time dependent electric power inputs to the heat pump and the defrosting system during operation with a specific cooling load of approximately 100 W/m2 and simulated rain.



Ua - 2 m/s A13 1 m/s A14 4 m/s A15Period Went (kW) w„(kW) Went (kW) Wf (kW) Went (kW) wtS (kW)Full cyclesMean 3.80 0.66 3.73 0.63 4.69 0.73Max 4.98 0.87 4.81 0.80 6.24 1.01Min 0.00 0.00 0.00 0.00 0.00 0.00FrostingMean 3.83 0.82 3.81 0.78 4.74 0.88Max 4.52 0.87 4.51 0.80 5.76 1.01Min 3.47 0.76 3.50 0.76 4.22 0.76DefrostingMean 4.08 0.00 3.67 0.00 4.44 0.00Max 4.98 0.00 4.81 0.00 6.24 0.00Min 0.00 0.00 0.00 0.00 0.00 0.00





Elec

tric

inpu

t (kW

) El

ectr

ic in

put (

kW)

Elec

tric

inpu

t (kW

)

161


Wedefr

0 6 12 18 24

Time (h)


Wedefr

Time (h)


Wedefr

Time (h)



162


The diagrams of figure 4.6.4 show the time dependent heating and cooling coefficients of performance of the heat pump unit during frosting with a specific cooling load of approximately 100 W/m2 and simulated rain. The diagrams also include integrated mean values of the coefficients of performance, COP]m and COP22m, according to the principles of section 2.2.1. In addition, table 4.6.4.1 gives the mean, maximum and minimum values during an integral number of frosting - defrosting cycles, both for the total cycle and for the frosting and defrosting periods respectively.


ua — 2 m/s A13 1 m/s A14 4 m/s A15Period COP, COP2 COP, COP2 COP, COP2Full cyclesMean 2.97 1.96 2.92 1.88 2.83 1.94Max 3.73 7.95 3.53 6.85 3.64 7.36Min 0.00 0.00 0.00 0.00 0.00 0.00FrostingMean 2.92 1.83 2.89 1.78 2.81 1.80Max 3.36 1.94 3.34 1.86 3.31 1.96Min 2.68 1.65 2.69 1.65 2.54 1.60DefrostingMean 3.09 2.24 3.07 2.40 2.95 2.78Max 3.73 4.89 3.53 6.85 3.64 7.36Min 0.00 0.00 0.00 0.00 0.00 0.00*During defrosting, COP has no real meaning since the heat pump has only operated for a very *.short while at the end of the defrost cycle. Most of the energy supply comes from the electrically heated defrost tank.

In the diagrams, a dashed line indicates the time of the maximum integrated mean value of the heating and cooling coefficients of performance. The indicated optima are based on defrosts with 100 % efficiency (COPim* and COP2m*) whereas curves based on real defrosting efficiency (COPIm and COP2m) never intersect the instantaneous curves. For further comments, see 4.1.4. Table 4.6.4.2 below gives the time after a defrost when the maximum integrated mean coefficient of performance occurs.


ua = 2 m/s A13 1 m/s A14 4 m/s A15COP, COP2 COP, COP2 COP, COP2

Time (h) 5.1 4.9 3.9 3.9 4.1 3.9

The table shows a great diversity in optimum time depending on the operating conditions.


CO

P C

OP

CO

P

163


COPlm

COP2m

COPlm*

Time (h)


COP2

COPlm

COP2m

COPlm*

Time (h)


COP2

COPlm

- COP2m

COPlm*

COP2m*

Time (h)



164


The diagrams of figure 4.6.5 show the time dependence of a number of temperatures which are relevant to the performance of the coil. Included are inlet and outlet temperatures of the air and the brine, inlet and outlet dew point temperatures and the mean value of a number of fin surface temperatures. Specific cooling load was approximately 100 W/m2 with simulated rain. Air velocities were around 2,1, and 4 m/s respectively. In addition, table 4.6.5 gives the mean, maximum and minimum values of the outlet brine and fin temperatures during an integral number of frosting - defrosting cycles, both for the total cycle and for the frosting and defrosting periods respectively.


Ua = 2 m/s A13 1 m/s A14 4 m/s A15Period 4,2 (°Q fa, (°Q 4,2 (°Q 4%, (°C) 4,2 (°Q (°C)Full cyclesMean -2.36 -0.8 -3.60 -1.7 -3.76 -1.3Max 48.31 40.3 25.78 20.8 50.89 43.4Min -10.53 -7.6 -10.69 -7.9 -12.38 -8.6FrostingMean -5.58 -3.2 -6.44 -3.8 -6.52 -3.4Max 1.88 2.1 1.83 2.2 2.35 2.7Min -10.53 -7.6 -10.62 -7.7 -12.38 -8.5DefrostingMean 12.66 10.7 8.09 7.8 9.72 8.8Max 48.31 40.3 25.78 20.8 50.89 43.4Min 3.09 0.8 -10.69 -7.9 -12.27 -8.6

The diagrams illustrate that fin temperature comes closer to the brine temperature as frosting continues. Due to frosting, fin efficiency will increase and in the final stages be close to 100 %. Furthermore, as the surface sensors become covered with frost, the installation error due to heat exchange between air and sensor will decrease and the bulk part of the temperature drop be in the frost layer and air-side heat resistance. When this happens, the temperature difference between fin surface and brine mainly corresponds to the difference across the thermal boundary layer on the inside of tubes.


Tem

pera

ture

(°C

) Te

mpe

ratu

re (°

C)

Tem

pera

ture

(°C

)

165


------ tdp2

— ta2

Time (h)


Time (h)


------ tdp2

---- ta2

Time (h)



166

4.6.6 Flowrates

The diagrams of figure 4.6.6 show the time dependence of the condenser water flowrate, the brine flowrate and the air flowrate. Specific cooling load was approximately 100 W/m2 with simulated rain. Air velocity was 2,1, and 4 m/s approximately. In addition, table 4.6.6 gives the mean, maximum and minimum values of the air and brine flowrates during an integral number of frosting - defrosting cycles, both for the total cycle and for the frosting and defrosting periods respectively.


Ua = 2 m/s A13 1 m/s A14 4 m/s A15Period (nrVs) v„ (mJ/h) va (mVs) vb (m3/h) va (nrVs) vb (nrVh)

Full cyclesMean 0.44 1.96 0.22 1.95 0.83 1.93Max 0.94 2.11 0.39 2.11 1.70 2.16Min -0.36 1.80 -0.06 1.82 0.03 1.74FrostingMean 0.59 1.94 0.29 1.93 0.99 1.91Max 0.93 2.01 0.39 2.02 1.70 2.00Min -0.24 1.87 0.17 1.87 0.05 1.82DefrostingMean -0.33 2.05 -0.05 2.03 0.06 2.01Max -0.31 2.10 0.00 2.11 0.24 2.16Min -0.35 1.97 -0.06 1.82 0.03 1.74

The air flowrate starts to drop very soon after the onset of frosting. Compared to the drop in coil capacity (figure 4.6.2), the drop in air flow is much greater. This derives from an increase in LHR as flow goes down, which makes total capacity less affected. On the other hand, the dry cooling capacity will drop as flowrate goes down. Regarding test A14, see comments on coil capacity in 4.6.2.



Flow

rate

(m3/

h, m

3/s)

Fl

ow ra

te (m

3/h,

m3/

s)

Flow

rat

e (m

3/h,

m3/

s)

167


- * Vw (m3/h)

- - Vb(m3/h)

Va (m3/s)

Time (h)


A <

— - “ Vb(m3/h)

..............Va (ui3/s)

0 6 12 18 24

Time (h)


- - Vb(m3/h)

Va (m3/s)

Time (h)



168


The diagrams of figure 4.6.7 show the time dependence of the air inlet velocity and pressure drop of the coil. Specific cooling load was approximately 100 W/m2 and humidity controlled by simulated rain. Air velocities were 2, 1, and 4 m/s respectively. In addition, table 4.6.7 gives the mean, maximum and minimum values of these measurands during an integral number of frosting - defrosting cycles, both for the total cycle and for the frosting and defrosting periods respectively.


Ua = 2 m/s A13 1 m/s A14 4 m/s A15Period ua (m/s) Apa (Pa) ua (m/s) Apa (Pa) ua (m/s) APa (Pa)Full cyclesMean 1.02 149 0.48 89 1.80 210Max 1.95 379 0.80 304 3.55 396Min -0.73 -2 -0.13 -1 0.09 -1FrostingMean 1.23 190 0.59 110 2.07 249Max 1.95 376 0.80 304 3.55 396Min -0.51 10 0.36 24 0.56 2DefrostingMean -0.68 0 -0.11 2 0.14 23Max -0.64 4 0.00 15 0.50 356Min -0.70 -2 -0.13 -1 0.09 -1

Air velocity is based on the measured volume flow and the frontal area of the coil. This velocity is set with a dry coil, hence the maximum value during the frosting phase should be compared with the set value. During defrosting, air velocity may actually be negative, due to natural convection with the fan stopped. In test A14, the calculated face velocity will obviously suffer from the same measuring problem as the volume flowrate.

Coil pressure drop has its maximum right at the end of the frosting period. For tests A13 and A15 the final pressure drop is around 380-400 Pa. For A14, on the other hand, this drop is only 304 Pa due to the low flowrate setting.


u (m

/s),

dp (P

a/20

0)

u (m

/s),

dp (P

a/20

0)

u (m

/s),

dp (P

a/20

0)

169


u (m/s)

- - dp (Pa/200)

Time (h)


u (m/s)

■ - dp (Pa/200)

Time (h)


u (m/s)

■ - dp (Pa/200)

Time (h)



170

4.6.8 Frost mass

The diagrams of figure 4.6.8 show the time dependence of frost mass in the coil. Specific cooling load was approximately 100 W/m2 with simulated rain and air velocity was 2,1, and 4 m/s respectively. In addition, table 4.6.8 gives the mean, maximum and minimum values of these measurands during an integral number of frosting - defrosting cycles, both for the total cycle and for the frosting and defrosting periods respectively.


ua — 2 m/s A13 1 m/s A14 4 m/s A15Period Mfr (kg) m/r (kg/h) Mfr (kg) mfr (kg/h) %(kg) ihfr (kg/h)

Full cyclesMean 5.59 -1.08 4.23 -7.97 7.25 -5.29Max 13.2 821 10.6 11.6 15.0 207Min -0.63 -304 -0.20 -205 -0.25 -282FrostingMean 6.68 2.91 4.73 2.62 8.07 4.10Max 13.2 38.6 10.6 11.6 15.0 40Min -0.10 -9.55 0.06 -4.55 0.31 -6.25DefrostingMean 0.98 29.30 1.66 -48.6 3.22 -51Max 12.0 821 9.44 4.90 14.7 207Min -0.63 . -304 -0.20 -205 -0.25 -282


During defrosting the load-cell system returns very nicely to a zero reading prior to the next frosting phase. The defrosting phase is quite violent, with high thermal and mechanical stresses. The violence of the defrosting phase is apparent from the large difference in the frosting mass flux (+) and the defrosting mass flux (-). In this context defrosting mass fluxes of table 4.6.8 in the range 200-800 kg/h may be compared with the estimated evaporation rate of around 700 kg/h (0.2 kg/s) using the Lewis relation in 5.4. In this case, with a very high ambient humidity, it would be natural to have a lower evaporation rate than the estimate from 5.4.


Fros

t mas

s (kg

) Fr

ost m

ass (

kg)

Fros

t mas

s (kg

)

171


Time (h)


Time (h)


Time (h)



172

Table 4.6.9 provides some data from the defrosting phase of tests A13, A14, and A15.



Measurand A13 (2 m/s) A14 (1 m/s) A15 (4 m/s)Mdw (kg) 7.9 7.1 8.8

Mjw / Mfr (kgft/kgw) 0.69 0.49 0.59W*dw (kWh/defrost) 7.1 8.8 8.1T|d(-) 0.15 0.15 0.17*d(s) 157 120 121Tc(h) 4.0 5.1 4.1



The diagrams of figure 4.6.10 show the temporal behaviour of some normalized alternative defrost indicators. All indicators, except the air outlet temperature, show a significant change as frosting continues. The indicator based on brine outlet temperature has the best characteristic behaviour and only changes significantly in the range between the defrosting optima for capacity and coefficient of performance. At the same time the diagrams show the wide spread in optimum time to defrost depending on whether you want to optimize capacity, cooling COP or heating COP. This latitude would be wider still if you include defrosting efficiency as a variable. The indicator based on air flow will not be useable in test A14 due to the aforementioned measuring problem.


Nor

mal

ized

cha

nge

Nor

mal

ized

cha

nge

Nor

mal

ized

cha

nge

173


Q1.Q2

Time (h)


COP2

QI.Q2

Time (h)


- tb2

COP2 COP1

Time (h)



174


175

4.7 Simulated rain - Coil B

Table 4.6 gives an overview of the nominal and actual test conditions during tests with different air velocities and conditions of simulated rain for coil B with a fin spacing of approximately 6.1 mm. Mean, max and min values refer to the frosting period (i.e. excluding defrosting).


Quantity WQ uai (m/s) 4a(W/m')

Nominal: B13 +2 +2 (100 %RH) 2 100Mean 1.5 1.5 1.25 155Max 3.6 4.5 1.85 183Min 0.6 -0.4 0.34 48

Quantity W°C) WQ ua] (m/s) 4a(W/m=)

Nominal: B14 +2 +2 (100 %RH) 1 100Mean 1.5 1.8 0.69 131Max 3.2 4.0 0.98 165Min 0.7 0.0 -0.45 0

Quantity f.;(°C) (°Q uaI (m/s) &,(W/m=)Nominal: B15 +2 +2 (100 %RH) 4 100Mean 1.3 1.3 2.0 162Max 2.7 3.5 3.7 190Min 0.4 -0.5 0.33 53


The dew point was measured in the ambient air of the coil whereas the water curtain, simulating the rain, was mounted directly in front of the coil. Hence the deviation from a saturated condition in the measured humidity.


176


Figure 4.7.1 shows the time dependent heating and cooling capacity of the heat pump unit during frosting with a specific cooling load of approximately 100 W/m2 and simulated rain. The diagrams also include integrated mean values of the capacities according to the principles of section 2.2.1. In addition, table 4.7.1.1 gives the mean, maximum and minimum values during two frosting - defrosting cycles, both for the total cycle and for the frosting and defrosting periods respectively.


Ua - 2 m/s B13 1 m/s B14 4 m/s B15Period e, (kW) &(kW) &(kW) &(kW) &(kW) &(kW)Full cyclesMean 15.3 10.1 14.2 9.12 15.6 10.2Max 24.9 30.8 23.8 24.8 24.3 31.3Min 1.26 4.22 3.07 5.94 1.41 4.21FrostingMean 15.3 9.51 14.7 8.82 15.6 9.74Max 22.0 11.4 22.7 22.4 22.0 11.4Min 12.3 7.54 12.1 -22.5 12.4 7.63DefrostingMean 15.6 13.8 11.4 15.6 15.6 13.2Max 24.9 30.8 23.9 72.9 24.3 . 31.3Min 1.26 4.22 1.21 5.94 1.41 4.21

The table shows that just after a defrost, when the coil is quite warm, heating capacity is extremely high (defrosting terminates when %2 is +30 °C). During defrosting, cooling capacity maybe negative (heating instead of cooling).

In the diagrams a dashed line indicates the time of the maximum integrated mean value of the heating and cooling capacities, QJm and Q2m, (the times are virtually the same). Table 4.7.1.2 below gives the times after a defrost when maximum integrated mean capacity occurs.


ua — 2 m/s B13 1 m/s B14 4 m/s B156, Qi Qi Qi Qi Qi

Time (h) 4.5 4.5 4.5 4.5 4.5 4.5

In cotrast to the tests with coil A and no rain, there was little difference in the times for initiating a defrost to achieve optimum capacity in the case of coil B.


Ther

mal

cap

acity

(kW

) Th

erm

al c

apac

ity (k

W)

Ther

mal

cap

acity

(kW

)

177

Test condition B13: Thermal capacity

10 - 1—

------Q2m

Time (h)


-----Q2m

Time (h)


-----Q2m

Time (h)



178

4.7.2 Coil capacity

The diagrams of figure 4.7.2 show the time dependent cooling capacity of the coil during frosting with a specific cooling load of approximately 100 W/m2 and conditions of simulated rain. Nominal air velocities of 2,1 and 4 m/s were used. Capacity measured on the air-side as well as on the brine-side are included. The diagrams also show the integrated mean value of the brine-side capacity, Qbm, according to the principles of section 2.2.1. The problem of achieving accurate air- side measurements is clearly seen from the curves, in particular the deviations due to uncertain airflow measurement at low flowrates.



ua = 2 m/s B13 1 m/s B14 4 m/s B15Period G« (kW) G* (kW) &(kW) G. (kW) &(kW)Full cyclesMean 33 3.67 -4.6 -1.34 -0.45 4.63Max 5246 36 24 7.66 216 9.84Min -260 -115 -163 -107 -253 -105FrostingMean 6.46 7.29 -0.38 6.14 7.76 7.61Max 14.2 8.58 8.3 7.73 41 8.89Min -3.07 2.23 -216 -26 -5.83 2.48DefrostingMean 196 -19 117.29 -22.3 -56 -15.5Max 5246 36 - 85 216 10Min -260 -115 -377 -106 -253 -105*There were problems with the airflow and temperature measurement, probably due to water droplets affecting the sensors.

In test A14, with a low air flowrate, there is a reproducible, strong deviation regarding the air-side capacity. This could possibly be caused by uneven distribution of frost causing a disturbed velocity profile or something else affecting the flowmeter. During defrosting, cooling capacity may be negative (heating instead of cooling).

Thermally measured defrost capacities, according to the table above, are of the same order of magnitude as the electrical energy measurements transferred to an equivalent power input during the defrost period. For B13, results are 115 and 127 kW respectively for thermally and electrically measured results, for B14 correspondingly 107 kW and 118 kW, and for A15 we have 105 and 273 kW respectively. Bearing in mind the short defrost time and the uncertainty in time resolution, agreement is acceptable.


Coi

l cap

acity

(kW

) C

oil c

apac

ity (k

W)

Coi

l cap

acity

(kW

)

179

Test condition B13: Coil capacity

— Qa

0 6 12 18 24

Time (h)

Test condition B14: Coil capacity

— Qa

Time (h)

Test condition BIS: Coil capacity

-- Qa

Time (h)



180

4.7.3 Power input

The diagrams of figure 4.7.3 show the time dependent electric power inputs to the heat pump and the defrosting system during operation with a specific cooling load of approximately 100 W/m2 and simulated rain. ■



Ua - 2 m/s B13 1 m/s B14 4 m/s B15Period Went (kW) ^(kW) Went (kW) ^(kW) Went (kW) % (kW)

Full cyclesMean 5.49 0.73 5.20 0.68 5.60 0.81Max 7.50 0.93 7.29 0.83 7.44 1.06Min 0.00 0.00 0.00 0.00 0.00 0.00FrostingMean 5.64 0.86 5.52 0.80 5.71 • 0.93Max 7.04 0.93 7.06 0.83 6.93 1.06Min 4.95 0.77 4.91 0.76 5.03 0.77DefrostingMean 4.83 0.00 3.94 0.00 4.90 0.00Max 7.50 0.00 7.34 0.00 7.44 0.00Min 0.00 0.00 0.00 0.00 0.00 0.00


Input to the fan has a maximum at the start of a frosting period, with a clean coil. This situation results in maximum flowrate and thus maximum input whereas during a defrost fan power input is zero by definition in the defrost strategy. In the tests with coil B fan power will be higher than for coil A since the required flowrates are higher. During frosting fan power drops continuously.



Elec

tric

inpu

t (kW

) El

ectr

ic in

put (

kW)

Elec

tric

inpu

t (kW

)

181

Test condition B13: Electric input (kW)

Wedefr

Time (h)

Test condition B14: Electric input (kW)

Wedefr

Time (h)

Test condition BIS: Electric input (kW)

Wedefr

Time (h)



182


The diagrams of figure 4.7.4 show the time dependent heating and cooling coefficients of performance of the heat pump unit during frosting with a specific cooling load of approximately 100 W/m2 and simulated rain. The diagrams also include integrated mean values of the coefficients of performance, COP,m and COP22m, according to the principles of section 2.2.1. In addition, table 4.7.4.1 gives the mean, maximum and minimum values during an integral number of frosting - defrosting cycles, both for the total cycle and for the frosting and defrosting periods respectively.


ua = 2 m/s B13 1 mIs B14 4 m/s B15Period COP] COP2 COP, COP2 COP, COP2Full cyclesMean 2.73 1.97 2.66 1.92 2.73 1.92Max 3.45 18.18 3.27 14.49 3.33 18.53Min 0.00 0.00 2.46 0.86 0.00 0.00FrostingMean 2.70 1.68 2.65 1.60 2.72 1.70Max 3.16 1.79 3.24 3.82 3.17 1.82Min 2.47 1.36 2.40 -3.34 2.47 1.38DefrostingMean 2.89 4.11 2.42 4.12 2.74 3.60Max 3.45 18.18 3.31 14.49 3.33 18.53Min 0.00 0.00 0.00 0.00 0.00 0.00*During defrosting, COP has no real meaning since the heat pump has only operated for a very short while at the end of the defrost cycle. Most of the energy supply comes from the electrically heated defrost tank.

In the diagrams, a dashed line indicates the time of the maximum integrated mean value of the heating and cooling coefficients of performance. The indicated optima are based on defrosts with 100 % efficiency (COP,m* and COP2m*) whereas curves based on real defrosting efficiency (COP,m and COP2m) never intersect the instantaneous curves. For further comments, see 4.1.4. Table 4.7.4.2 below gives the time after a defrost when the maximum integrated mean coefficient of performance occurs.


ua — 2 m/s B13 1 m/s B14 4 m/s B15COP, COP2 COP, COP2 COP, COP2

Time (h) 6.5 6.2 6.7 6.2 6.9 6.2

The table shows very little difference between optimum times in relation to air velocity.


CO

P C

OP

CO

P

183

Test condition B13: COP

COPlm

COP2m

COPlm*

Time (h)

Test condition B14: COP

COP2

COPlm

COP2m

COPlm*

COP2m*

Time (h)

Test condition BIS: COP

COP2

COPlm

COP2m

COPlm*

COP2m*

Time (h)



184


The diagrams of figure 4.7.5 show the time dependence of a number of temperatures which are relevant to the performance of the coil. Included are inlet and outlet temperatures of the air and the brine, inlet and outlet dew point temperatures and the mean value of a number of fin surface temperatures. Specific cooling load was approximately 100 W/m2 with simulated rain. Air velocities were around 2,1, and 4 m/s respectively. In addition, table 4.7.5 gives the mean, maximum and minimum values of the outlet brine and fin temperatures during an integral number of frosting - defrosting cycles, both for the total cycle and for the frosting and defrosting periods respectively.


Ua — 2 m/s B13 1 m/s B14 4 m/s BISPeriod fw(°C) fa,(°Q 4w(°Q fa, (°Q f„2 (°Q fa, (°C)Full cyclesMean -4.67 -2.6 -7.09 -5.0 -4.33 -2.2Max 26.18 20.9 25.00 17.3 24.88 21.1Min -12.91 -10.3 -13.70 -11.6 -12.15 -10.0FrostingMean -6.80 -4.3 -7.94 -5.4 -6.14 -3.6Max 2.10 2.7 9.86 10.2 1.70 2.1Min -12.62 -10.3 -13.34 -11.4 -12.12 -9.8DefrostingMean 9.03 8.3 10.70 9.8 7.81 7.3Max 26.18 20.9 38.27 33.9 24.88 21.1Min -12.91 -9.7 -13.06 -11.2 -12.15 -10.0

The diagrams illustrate that fin temperature comes closer to the brine temperature as frosting continues. Due to frosting, fin efficiency will increase and in the final stages be close to 100 %. Furthermore, as the surface sensors become covered with frost, the installation error due to heat exchange between air and sensor will decrease and the bulk part of the temperature drop be in the frost layer and air-side heat resistance. When this happens, the temperature difference between fin surface and brine mainly corresponds to the difference across the thermal boundary layer on the inside of tubes.


Tem

pera

ture

(°C

) Te

mpe

ratu

re (°

C)

Tem

pera

ture

(°C

)

185

Test condition B13: Coil temperatures

— tdp2

- ta2

Time (h)


----- tdp2

— ta2

Time (h)


<4in —-crr7-#Tv/

1

— — tal

— " “ tdpl

--------- tdp2

--------- ta2

— “ ■ tfin

,b2

5

X

s

>*v - * - -s.-;v.'S

L:;v,'L

V- _\ X

\ X <—.

--------- tbl

N

0 6 12 18 24

Time (h)



186

4.7.6 Flowrates

The diagrams of figure 4.7.6 show the time dependence of the condenser water flowrate, the brine flowrate and the air flowrate. Specific cooling load was approximately 100 W/m2 with simulated rain. Air velocity was 2, 1, and 4 m/s approximately. In addition, table 4.7.6 gives the mean, maximum and minimum values of the air and brine flowrates during an integral number of frosting - defrosting cycles, both for the total cycle and for the frosting and defrosting periods respectively.


ua = 2 m/s B13 1 m/s B14 4 m/s B15Period Va (m7s) vb (m7h) va (m7s) vb (mTh) va (m7s) vb (mTh)Full cyclesMean 0.85 1.83 0.39 1.78 1.35 1.83Max 1.46 2.12 0.77 2.06 2.54 2.08Min 0.03 1.63 -0.37 1.65 0.02 1.67FrostingMean 0.99 1.81 0.54 1.79 1.54 1.81Max 1.46 1.90 0.77 1.97 2.54 1.89Min 0.27 1.68 -0.36 1.66 0.26 1.69DefrostingMean 0.04 1.95 -0.32 1.94 0.04 1.93Max 0.05 2.12 0.06 2.17 0.06 2.08Min 0.03 1.73 -0.39 1.65 0.02 1.67


The brine flow is fairly constant during a test cycle. Only in situations where viscosity changes markedly will there be a change in flow. This happens during defrosting with warm brine and at the end of cycle with heavy frosting. The condenser water flowrate was very stable at all times.


Flow

rate

(m3/

h, m

3/s)

Fl

ow ra

te (m

3/h,

m3/

s)

Flow

rate

(m3/

h, m

3/s)

187

Test condition B13: Flow rates

■ - Vb(m3/h)

Va (m3/s)

0 6 12 18 24

Time (h)

Test condition B14: Flow rates

Vw (m3/h)

Va (m3/s)

Time (h)

Test condition BIS: Flow rates

- ■ Vw(m3/h)

Va (m3/s)

Time (h)



188


The diagrams of figure 4.7.7 show the time dependence of the air inlet velocity and pressure drop of the coil. Specific cooling load was approximately 100 W/m2 and humidity controlled by simulated rain. Air velocities were 2, 1, and 4 m/s respectively. In addition, table 4.7.7 gives the mean, maximum and minimum values of these measurands during an integral number of frosting - defrosting cycles, both for the total cycle and for the frosting and defrosting periods respectively.


Ua~ 2 m/s B13 1 m/s B14 4 m/s B15Period ua (m/s) Apa (Pa) ua (m/s) Apa (Pa) ua (m/s) Apa (Pa)Full cycles *Mean 1.08 147 0.51 129 1.71 172Max 1.85 375 0.97 353 3.21 374Min 0.04 -1 -0.47 -1 0.03 -1FrostingMean 1.25 171 0.69 132 1.96 197Max 1.85 375 0.98 355 3.21 374Min 0.34 16 -0.45 2 0.33 44DefrostingMean 0.05 1 -0.41 21 0.05 2Max 0.07 4 0.07 353 0.08 24Min 0.04 -1 -0.50 -1 0.03 -1

Air velocity is based on the measured volume flow and the frontal area of the coil. This velocity is set with a dry coil, hence the maximum value during the frosting phase should be compared with the set value. During defrosting, air velocity may actually be negative, due to natural convection with the fan stopped. In test A14, the calculated face velocity will obviously suffer from the same measuring problem as the volume flowrate.

Coil pressure drop has its maximum right at the end of the frosting period. All tests B13-B15 end up with similar final pressure drops of 355-375 Pa. B14 has the lowest value due to the lowest flowrate setting.


u (m

/s), d

p (P

a/20

0)

u (m

/s), d

p (P

a/20

0)

u (m

/s), d

p (P

a/20

0)

189

Test condition B13: Air velocity and pressure drop

u(nVs)

- - dp (Pa/200)

Time (h)

Test condition B14: Air velocity and pressure drop

u (m/s)

dp (Pa/200)

Time (h)

Test condition BIS: Air velocity and pressure drop

u(m/s)

- dp (Pa/200)

Time (h)



190

The diagrams of figure 4.7.8 show the time dependence of frost mass in the coil. Specific cooling load was approximately 100 W/m2 with simulated rain and air velocity was 2, 1, and 4 m/s respectively. In addition, table 4.7.8 gives the mean, maximum and minimum values of these measurands during an integral number of frosting - defrosting cycles, both, for the total cycle and for the frosting and defrosting periods respectively.

4.7.8 Frost mass


Ua = 2 m/s B13 1 m/s B14 4 m/s B15Period Mfr (kg) mfr (kg/s) Mf(kg) m{r (kg/s) Mf(kg) thfr (kg/s)Full cyclesMean 9.00 36.5 8.77 -6.99 10.3 -6.17Max 18.2 * 16.6 34.4 22.1 274Min 0.00 -330 0.52 -205 0.00 -321FrostingMean 9.57 2.31 8.54 -2.28 11.0 3.41Max 18.0 15.7 16.6 9.94 21.9 50Min 0.11 -8.28 0.00 -273 0.30 -12.3DefrostingMean 4.98 250 7.86 151 6.11 -71Max 18.0 * 17.0 * 22.1 274Min 0.00 -330 0.43 -477 0.00 -321*Outliers


During defrosting the load-cell system returns very nicely to a zero reading prior to the next frosting phase. The defrosting phase is quite violent, with high thermal and mechanical stresses. The violence of the defrosting phase is apparent from the large difference in the frosting mass flux (+) and the defrosting mass flux (-). In this context defrosting mass fluxes of table 4.7.8 in the range 321-477 kg/h may be compared with the estimated evaporation rate of around 700 kg/h (0.2 kg/s) using the Lewis relation in 5.4. In this case, with a very high ambient humidity, it is natural to have a lower evaporation rate than the estimate from 5.4.


Fros

t mas

s (kg

) Fr

ost m

ass (

kg)

Fros

t mas

s (kg

)

191

Test condition B13: Frost mass

Time (h)

Test condition B14: Frost mass

Time (h)

Test condition BIS: Frost mass

Time (h)



192

Table 4.7.9 provides some data from the defrosting phase of tests B13, B14, and B15.



Measurand B13 (2 m/s) B14 (1 m/s) B15 (4 m/s)Mdw (kg) 22.4 * 22.7Mdw / Mfr (kgft/kgw) >1 * 1

W*dw (kWh/defrost) 12.0 12.4 13.0fid(-) 0.16 0.17 0.16Trf(s) 157 176 181% (h) 3.9 5.2 4.2

Values of defrosting efficiency are based on the latent heat of fusion of ice. If the latent heat of sublimation is used, the efficiencies will be approximately 8.5 times higher. For some reason, there was no real difference between defrost water and frost mass for tests B13 and B15. Either this derives from measuring errors, e.g. checking the zero level prior to a test, or water may have been added to the drip tray from the water curtain that simulated rainy conditions.


The diagrams of figure 4.7.10 show the temporal behaviour of some normalized alternative defrost indicators. All indicators, except the air outlet temperature, show a significan change as frosting continues. The indicator based on brine outlet temperature has the best characteristic behaviour and only changes significantly in the range between the defrosting optima for capacity and coefficient of performance. At the same time the diagrams show the wide spread in optimum time to defrost depending on whether you want to optimize capacity, cooling COP or heating COP. This latitude would be wider still if you include defrosting efficiency as a variable.


Nor

mal

ized

cha

nge

Nor

mal

ized

cha

nge

Nor

mal

ized

cha

nge

193

Test condition B13: Defrost indicators

- - tb2

COPlCOP1

Time (h)

Test condition B14: Defrost indicators

COPlCO >2

- — tb2

- - Wcf

Time (h)

Test condition BIS: Defrost indicators

- - ti>2

COPl

Time (h)



194

4.8 Commercial defrost controller

Tests were carried out with two commercially available defrost controllers made by Lidstrdm AB (see 2.1.11). Both use the temperature difference between the coil inlet air and a representative temperature inside the coil or refrigerant/brine piping. This corresponds to the f# criterion in figure 4.9.1 below.

One of the controllers is based on analogue electronics and is adapted manually to a specific system. The adaptation is made by setting three potentiometers. This controller has been used with good results in a number of large air-source heat pumps (Bergstrom05 et al). The other unit has a self-adaptive feature and is built on digital electronics. Although not much time was spent on making this unit work, it was felt that it was more difficult to understand the digital controller than the analogue one.

Figure 4.8.1 shows one example of test results with the analogue controller at test condition A5. The output relay of the controller is read by the DAS via a 10 V DC supply (the output signal has been normalized to 0 - 1 in the diagram). In the example it was adjusted not to effect a defrost until the coil was heavily frosted. This corresponds to optimum defrost intervals with the defrost efficiency of the actual system. The diagram includes optimum defrost times with a defrost efficiency of 100 % based on the latent heat of fusion of ice. The less energy that is needed to defrost, the more frequently it pays to actuate such a defrost.

Test condition A5LiA3: Defrost indicators

Figure 4.8.1. Comparison of normalized defrost indicators and the output from the Lidstrdm analogue controller.

The diagram shows that with the chosen setting a defrost will only be effected when other common indicators have changed significantly. On the other hand, results presented in 4.1-4.7 show that optimum defrost times will correspond to different levels of the normalized indicators depending on the operating conditions and hence it appears not to be possible to achieve fully optimized control with any of the systems based on one indicator. However, for practical purposes it could still be quite sufficient.


195

5 Discussion and presentation of finalresults

There are many possible ways of investigating frosting and defrost control. This report demonstrates a new way by means of continuous weighing of the frosting coil. It also takes a close look at alternative defrost indicators. To make possible direct comparisons of measurands of different kinds, the indicators have been normalized to values between 0 and 1.

5.1 Defrost indicators

A number of practical aspects must be considered regarding indicators for defrost control. Firstly, the indicator must bear a strong relationship with the degradation of performance caused by frost. Secondly, the indicator must be measurable in a simple and inexpensive manner. Thirdly, the indicator should not be sensitive either to its exact position in the heat pump system (often the coil itself) or to other external influences.

Looking at the test results, which largely support experience from regular testing and field investigations, the outlet temperature from the coil emerges as the best candidate and it fulfils all three of the aforementioned requirements. Firstly, there is very little change until coil capacity actually starts to drop. The reason is that although air flow and pressure difference start to change almost directly at the onset of frosting, the air- side coefficient of heat transfer will rise from increased surface roughness and decreasing hydraulic diameter of the flow channel between fins. Hence capacity will not drop in relation to air flow during the initial frosting period and as long as the overall coefficient of heat transfer does not change appreciably, neither will the outlet brine temperature (this reasoning, of course, applies equally well to coils cooled by evaporating refrigerant). Therefore we have the desired close link between capacity and indicator.

Regarding the second point, measurement of temperature is commonplace and reasonably inexpensive. Although the outlet temperature of the coil is the most obvious temperature indicator, a change in capacity can also be indicated as a temperature change on the condenser side and such systems are becoming increasingly popular since there is no need for sensors in the exposed outdoor unit.

Finally, as to the third requirement, outlet brine temperature has an integrating quality that alleviates the problem of non-representative positions inside the coil. This is also the case for fan power (or current), another feasible indicator. Fan power, however, will greatly depend on the type of fan and fan motor and its use is not easily applicable on systems with variable fan-speed. Regarding variable fan-speed, most traditional defrost systems will have some problems in accommodating this feature.

Even though the outlet brine temperature is a reasonably good indicator of frosting, practical experience according to Bergstrom(1) and Fahlen(S) still indicates that there is a need for individual adjustment on-site of each system. This is rarely done in practice unless there is a devoted and competent person involved in the commissioning of an installation. Hence there seems to be a need for systems that somehow automatically

5 Discussion and presentation of final results

196

carry out or totally removes the need for the adjustment phase. The digital Lidstrom system mentioned in this report has some features in that respect and there are other systems which try to optimize frosting cycle times in relation to the time required for the previous defrost, but the final answer would be a system that actually optimizes capacity or COP as the case may be.

5.2 Optimized defrost control

The question of optimized control is largely a matter of finding a suitable way of feedback control. Invariably present control systems are open-loop, mapped systems (possibly with the exception of systems observing defrost time). This will only work with products that show little scatter in their actual performance and in the operating conditions they are exposed to. Obviously this is generally not the case in real life. Indeed, Fahlen(5) reports of a situation where tests of two nominally identical heat pumps, under controlled laboratory operation, showed one to have twice the defrosting cycle time of the other.

Many authors, e.g. Granryd(15) and Young(23), have proposed methods on the determination of optimum times to initiate a defrost. This is important to analyze the prerequisites for improved control and the analysis indicates that the optimizing function increases fairly rapidly after a defrost but then has a very shallow maximum. Thus it is important not to defrost too soon but leaving initiation past the optimum point has little significance on the overall result. This is contrary to how many air- source heat pumps operate, defrosting long before the optimum point has been reached (c.f. the discussion in 5.3 regarding defrost efficiency).

Fahlen(4) describes a method whereby the optimizing function could be implemented in an operating system. The idea is to use two pressure sensors (condensing and evaporating pressure) and three temperature sensors (for the compressor discharge and suction pipes and the sub-cooled refrigerant) to calculate the instantaneous value of COP. Via a current sensor, electric input can also be measured and multiplied by COP and this could provide heating or cooling capacity as well. The sensors can also act as safety devices to prevent excessive motor current, condensing or discharge temperature or too low evaporating pressure and can also provide on-line status reports of heat pump performance (a form of Integrated Refrigeration Management, IRM). By comparing the instantaneous value and the integrated mean value of e.g. COP, we can find the correct time to defrost. This comparison is beneficial in that it provides a much more distinct decision point than does the very shallow maximum of the optimizing function.

The experimental results in this report illustrate the concept of optimized defrost control. In this case, however, optimizing functions rely on directly measured capacity data. In the actual experimental situation it was not practical to carry out a continuous measurement and integration process. Instead measurements were taken at 60 s intervals except during the defrosting period when the interval was reduced to 3 s. During normal test periods of 24 h this would generate around 1500 measurements for each of the 76 measured or calculated quantities, i.e. in total approximately 114 000 values for each test condition (in some cases up to 5200 measurements per channel and 395000 measured values in total). This was possible to handle on the original


197

main-frame computer but transferring the data to a PC-environment required a reduction in data volume to make evaluations practical. Therefore 20 minute mean values were formed except during the period 30 minutes before until 30 minutes after the defrost period when 1 minute intervals were used. This, of course will smooth the curves from random variations but has no bearing on the general, fairly slow, changes due to frosting.

5.3 Defrost time and energy

Two defrost principles were tried, direct electric defrosting and defrosting by means of warm brine. During actual testing only warm brine was used, mainly due to time considerations. Direct electric defrosting took over 30 minutes whereas defrosting by warm brine would only take around 2 minutes.

The energy required will naturally depend on the quantity of frost, the type of frost (e.g. crystal habitus), the thermal mass of the coil itself and its fin arrangement as well as on the termination criterion. In this case an outlet brine temperature of +30 °C signalled that defrosting was complete. Tests showed that +15 °C was not sufficient and some previous reports recommend a minimum of +25 °C. In the present work we were less concerned with efficiency than with ascertaining a frost-free coil, hence the safety margin on the temperature criterion.

Measured defrost energy was typically around 1-2 kWh per kg frost resulting in a rather dismal defrosting efficiency of 5-10 %. The basis of this efficiency is the latent heat of fusion of water/ice, i.e. the energy required to melt the frost. If, however, the latent heat of sublimation is used, as in many previous investigations, then defrosting efficiency will be in the range 40-80 %. This report uses the first definition since in the ideal situation there is no need to evaporate the water, only to melt the ice. Even this would not be necessary if frost were removed by mechanical means or by some other method. The energy used in a defrost is of course important since the larger this quantity is the longer the heat pump must run to compensate for this loss.

However, in the tests with simulated rain the energy requirement was only 0.5-0.6 kWh per kg frost and defrost efficiency was up to 15 %. The plausible explanation for this deviant behaviour is that either water droplets were sucked into the coil and then absorbed in the porous frost layer as liquid water and/or part of the water vapour condensed without actually freezing. Since the air temperature was +2 °C, frost growth would probably enter the final growth domain with successive freezing and melting of the surface layer. In the latter stages there would not be sufficient cooling capacity to freeze directly water absorbed in the surface layer and therefore this would obviously not have to be melted during the defrost.

Defrost times varied between 2-2.5 minutes. A large quantity of frost takes longer to remove than does a small provided it was formed under the same circumstances. However, the same mass of dense frost takes less time than does a porous layer. For instance, 11.5 kg of low density frost, formed during rapid frosting in test A13, took 157 seconds to clear whereas 14.4 kg of high density frost from test A7 only took 114 seconds. The high density of test A7 derives from high air velocity, which tends to promote formation of compact frost.


198

5.4 Frost mass, defrost water and some characteristics of the frost

There was generally a deviation between the quantity of collected defrost water and the measured frost mass of the coil. The mean value of this deviation was 4.3 kg and this was fairly independent of the total quantity of frost. Since the criterion for terminating a defrost was set at an outlet brine temperature of +30 °C, to ensure that no frost remained when the next cycle started, water would evaporate from the coil surface (the effect was visually quite dramatic). This water would not be collected and hence there was a deficit in the collection vessel. Figure 5.4.1 illustrates this deficit by comparing the collected mass of defrost water with the frost mass in the coil.

8,0-A

g) e A5> Mean value 4.3 kg a ■a-u 4,0-S ■ A ■

6 ■ +2-cS 2,0- ♦ -7'C

& Rain

0,0- ---------1----------------- ------- 1-------------------------1--------0,0 5,0 10,0 15,0 20,0

Mfr (kg)

Figure 5.4.1. Deviation between mass of collected defrost water and the weighed frost mass versus frost mass in the coil.

Using the Lewis equation(see 5.5) it is possible to estimate the rate of evaporating during the final phase of a defrost. As an example, if the water temperature were +10 °C, then the driving potential between the coil surface and the ambience at +2 °C would be Ax = 7.64 - 4.36 g/kga. The heat transfer coefficient from natural convection between fins can be estimated from the relation

Nu = 0.065 -Grm -| —H-1/9

with Gr =g.y-H3 - At

and this gives a ~ 3.5 W/m2/K and mw = 11.5 g/m2/s. With a total area of 46.5 m2,

total rate of evaporation would be Mw ~ 0.53 kg/s. However, according to Sanders™only that part of the surface nearest to the ambient room is active with a penetration depth into the coil of approximately 0.1 m. This will also depend on the fin spacing (penetration is larger with larger fin spacing) but even with only half the coil active, evaporation may be substantial and hence account for the deficit in collected water.

5 Discussion and presentation offinal results

199

For instance, an evaporating rate of 0.2 kg/s would yield 4 kg in 20 seconds.Therefore it is critical for the defrosting efficiency not to have some part of the coil requiring much longer defrosting than other parts because this means the rest of the coil will use a lot of energy to evaporate liquid water. This also indicates that determinations of frost mass from collection of defrost water will tend to underestimate the true quantity unless defrosting is made very slowly with a high ambient humidity. Finally, time of termination becomes more critical the higher the available defrosting input. In this project we used a defrosting temperature of +70 °C to achieve a rapid defrost but for reasons of efficiency a lower temperature might have been more appropriate.

5.5 Use of the Lewis equation

The Lewis equation relates the heat and mass transfer coefficients and this is used to estimate precipitation of water in the coils,

mfr= -^5- • (xw - xw.. fin ) (eq. 5.5.1)cpa'

where cpa- is the specific heat capacity of humid air referred to the mass of dry air, i.e.

Cpa' = Cpa "b CpW • xw (eq. 5.5.2)

To compare measured and calculated mass fluxes of water, we need the air side heat transfer coefficient. Section 3.3 give the relations used in this report regarding film coefficients of heat transfer and annex E provides results for the different test conditions. Figure 5.5.1 summarizes results of growth rates in the form of a plot of calculated versus measured results.

20 40 60 80

Calculated frost growth (g/m2/h)100

Figure 5.5.1. Calculated versus measured results of the mass flux of water in the form of frost in coil A (mean values over one frosting cycle).


200

5.6 Quality of results

SP-report 1994:01® provides an in-depth discussion of the quality of measured and calculated results from this project. Appendix A summarizes the quality of measured values in terms of uncertainty budgets and appendix B gives similar budgets for derived results. The electric measurements and the measurements in the liquid flows, all have the desired accuracy. As an example, even with a temperature difference as low as 3.21 K, the cooling capacity could be determined with an uncertainty of less than ±5 %. The dominating contribution to this uncertainty was the uncertainty of the physical properties of the brine, in particular regarding the specific heat capacity. The heating capacity, on the other hand, was accurate within ±2 %.

The air-side measurements, however, were not up to the expected quality. The major culprit in this respect was the air flowmeter, which had been incorrectly installed. Therefore there was poor agreement both regarding cooling capacities, measured on the brine and air sides respectively, and mass fluxes measured by the weighing system and calculated from the air flow/humidity difference. The heat and mass balances of the coil indicate that the air flow was underestimated by 10 to 20 % in the low flow range. This is also consistent with comparisons of measured and calculated coil pressure drops.


201

6 References1. Bergstrom, U, Larsson, R, 1987. Defrosting of evaporators in air source

heat pumps - Evaluation of defrosting methods. (Swedish Council for Building Research, report R52:1987; in Swedish.) Stockholm, Sweden.

2. CEN, 1994. prEN 255: Air conditioners and heat pumps with electrically driven compressors - Heating mode - Part 2: Testing and requirements for marking for space heating.

3. CEN, 1994. prEN 255: Air conditioners and heat pumps with electrically driven compressors - Heating mode - Part 3: Testing and requirements for marking for sanitary hot water.

4. Fahlen, P 0,1988. Defrosting - An approach to optimal control. (Scanref, vol. 17, no. 4.) Tullinge, Sweden.

5. Fahlen, P O, 1991. Laboratory testing of heat pumps - Experience 1984 - 1986. (The Swedish National Testing and Research Institute, SP Report 1990:19.) Boras, Sweden.

6. Fahlen, P O, Johansson, C, 1991. Air conditioning heat pumps. (The Swedish National Testing and Research Institute, Report SP-AR 1991:43; in Swedish.) Boras, Sweden.

7. Fahlen, P O, Axell, M, 1991. Frosting - An experimental evaluation of frost growth and defrost control strategies. (XVHIth International Congress of Refrigeration, August 1991, Montreal.) Canada.

8. Fahlen, P 0,1994. Performance tests of air source heat pumps under frosting conditions - Quality of Results. (The Swedish National Testing and Research Institute, SP Report 1994:01, Boras.) Sweden.

9. Fahlen, P 0,1995. Frosting of air-coils - A new experimental approach. (XIVth International Congress of Refrigeration, August 1995, Haag.) The Netherlands.

10. Fahlen, P 0,1996. Frosting and defrosting of air-coils - A literature survey. (The Swedish National Testing and Research Institute, SP Report 1996:02, Boras.) Sweden.

11. Fahlen, P 0,1996. A test facility for air-source heat pumps. (The Swedish National Testing and Research Institute, SP-AR 1996:18, Boras.) Sweden.

12. Fehrm, M, 1986. Air source heat pumps - Defrosting methods. (Swedish Council for Building Research, report R39:1986; in Swedish.) Stockholm, Sweden.

6 References

202

13. Glas, L-O, Karlsson G, Kenne H, 1982. Development of residential heat pump systems. (Swedish Council for Building Research, R73:1982; in Swedish) Stockholm, Sweden.

14. Granryd, E, 1965. Forced convection heat transfer and pressure drop at finned tube heat exchangers. (Royal Technical University of Stockholm, UDK 536.2, August 1965; in Swedish.) Stockholm, Sweden.

15. Granryd, E, 1969. Comments on the choice of defrost intervals. (Royal Technical University of Stockholm, UDK 621.565, November 1969; in Swedish.) Stockholm, Sweden.

16. Lidstrom, 1987. Defrost Control. (K Lidstrdm AB, instruction manual; in Swedish.) Skelleftea, Sweden.

17. Lidstrom, 1987. Adaptive Defrost Control. (K Lidstrdm AB, instruction manual; in Swedish.) Skelleftea, Sweden.

18. Malhammar, A, 1986. Frost formation on finned surfaces. (Royal Technical University of Stockholm, PhD Thesis, 1986, Stockholm; in Swedish.)Sweden.

19. NEN 1876, 1979. Air coolers - Determination of the performance of frosted air coolers with forced circulation. (NNI, Delft, 1979: Dutch standard.) The Netherlands.

20. O'Neal, D L, Tree, D R, 1985. A review of frost formation in simple geometries. (ASHRAE Transactions, 91, part 2A, 1985, M 754.) USA.

21. Sanders, C T, 1974. The influence of frost formation and defrosting on the performance of air coolers. (PhD Dissertation, Technische Hogeschool, Delft University, 1974.) The Netherlands.

22. SMS, 1986. SS 2095: Heating equipment - Heat pumps - Laboratory testing of performance. (Sveriges Mekanstandardisering, 25 December, 1986; in Swedish.) Stockholm, Sweden.

23. Young, D J, Lange, H F, 1980. Optimization and evaluation of a northern climate residential air-source heat pump. (Canadian Electrical Association, Research contract No. 76-12, October 1980.) Canada.

6 References

203

Appendix A:

Uncertainty budgets of measured quantities

Contents

A1 Brine flowrate

A2 Water flowrate

A3 Air flowrate

A4 Liquid temperature

A5 Air temperature

A6 Surface temperature

A7 Humidity

A8 Liquid pressure difference

A9 Air pressure difference

A10 Frost mass

A11 Electric power input

App. A: Uncertainty budgets of measured quantities

204

Table Al. Uncertainty budget for the determination of brine flowrate according to Fahlen(4).

A1 Uncertainty budget: Brine flowrate

Cause of the uncertainty Propagation constant, Pj

Uncertainty type A(%)

Uncertainty type B(%)

Calibration ?l = 1 sKb,cal < o 05

KbWKb'cal. < o.29

Kb

Meter reading* *4= 1 [ S^ead < 0 014,

S*b-nad <0.007

Vb1*

Operating point ?1 = 1 SKb,opt < o IQKb

<0 04

Kb(excluding the temperature influence)

P3 = 0.001

(Meal < 10 K)

■ S‘b—r<3.00,\tb~tcal\

■ Wtb ,<2.00

fa-tcall

Operating conditions II

<c SKh,opc<019*

Installation |P2I = 0,|p31=0.001

WVb,inst nvb

Total contribution of types A and B respectively

5^- < 0.22 %Vbs~-p- < 0.02 %Vb

2% < 0.29 %vb

Combined uncertainty of brine flowrate UVh U7r,u1* <0.37 %, <0.29 %Vb Vb

Total uncertainty of brine flowrate (k = 2.0)< 0.8 % —r^- < 0.6 %

Vb vb♦Random uncertainties due to the meter reading are included in the variations due to fluctuations in the operating conditions and are therefore not included in the summation of variances.

sv=^sv,j2’ Wv=^wv,j2

*Uy = .Sy2 + Wy2 , Uy=k-Uy (k = 2)


205

A2 Uncertainty budget: Water flowrate

Table A 2. Uncertainty budget for the determination of water flowrate according to Fahled4).

Cause of the uncertainty Propagation constant, Py.



Calibration ?1 = 1 ^'<0.05,Kw

WfCw'cal <0.12

Kw

Meter reading*

1—4

II [ SVb,read < 0.034,

%,read <0.007]*Vb

Operating point ii

qT ^'^<0.08,Kw

< Q QiKw

(excluding the temperature influence)

P3 = 0.001

(Meal < 10 K)

Stw <0.50rw ~^cal\

i Wtw ,<2.00yw ^cal\

Operating conditions P; = l ^'^<0.15,K

Installation |P2l«0,\p31-0.001

WVw,instV. ’°

Total contribution of types A and B respectively <0.18%

< 0.02 %

w •-rp- < 0.12 %

Combined uncertainty of water flowrate

A o to ►—1 “tT-p- <0.13%

Total uncertainty of water flowrate (k = 2.0)< 0.5 %

*>V

U-r< 0.3 %

*Random uncertainties due to the meter reading are included in the variations due to fluctuations in the operating conditions and are therefore not included in the summation of variances.

sv =^sv,j2 ’ wv =^wv,j2

Uy — yj Sy + Wy , Uy = k ’ Uy (k = 2)


206

Table A3. Uncertainty budget for the determination of air flowrate according to Fahled4).

A3 Uncertainty budget: Air flowrate

Cause of the uncertainty Propagation constant, P}



Calibration *(call and cal2; "’“<0.9, W*"‘,Z2<1.2)

Pl = 1 SKa'cal < 0.3Ka

WKa’cal < 1.5*Ka

P4=1.5 Sn'cal<Q.\n

Wn’cal <0.3 n

P7 = 0.5 (see 4.9.5) APaf

TW'&wf.od < I Q APaf

Meter reading P8 = 0-5 WVa,read < 0.06

Operating point

(assuming pa has actually been measured)

P5 = 0.0061 St,opt < ? Wt,opt , < 7<1./ta~tcal

<1./ta-tcal

P6 = 0.052 i. wApaf,opt „ „ ^APaf

Pjq = 0.05 w<0.2

PaOperating conditions P2 = l

<0.5

Installation |P3I = 1 - WV'inst ~ 0.6V

P9 = 0.5 (see 4.9.5)

WApaf,inst — 06 *Paf


**Based on the standard deviation during test Al.

fvs. < 0.65VaSVa < 0.2**

5k <1.8Va

Combined uncertainty of air flowrate % < 1.9 %, %L < 1.8 %

Total uncertainty of air flowrate (k = 2.0) 5k < 3.8 %, 5k < 3.6 %

After the project we discovered substantial deviations, up to 8 %, between the initial and the final calibrations in the lowest flowrate range. Subsequent investigations of this problem lead to the conclusion that the flowmeter was affected both by swirl (generated by the fan) and by changes in the downstream flow profile (caused by the outlet throttling cone). The flowmeter had been incorrectly installed from the onset; it should have been located upstream of the fan, which would have avoided both the swirl effect and most of the back-pressure changes.


207

A4 Uncertainty budget: Liquid temperature

Table A4.1. Uncertainty budget for the determination of brine temperatures ' according to Fabled4).


Uncertainty type A (K)

Uncertainty type B(K)

Calibration 1 S,b.cal < 0 01,Stb,cal < 0.005

wtb,can < 0.012,

1 Wtb,cal2 < 0-03Meter reading 1 - ^,^<0.006Operating point 1 < 0-0004,

1w< 0.00004w,b.opt < 0.006

Operating conditions 1 Sfb.opc ^ 0.30,%.„c<0.03

Installation 1 - w'b,inst < 0.02


stb < 0.30 K,Sjb < 0.03 K

wtb < 0.039 K

Combined uncertainty of brine temperature utb < 0.30 K, uIb < 0.05 K

Total uncertainty of brine temperature (k=2.0) Utb < 0.60 K,Ujb < 0.10 K

Table A4.1 shows that the dominating influences on measuring uncertainty derived from variations in the operating conditions (type A) and the long-term stability of the sensors (type B). If recalibrations had been carried out more frequently, then the effect of drift would have been reduced substantially and become surpassed by the installation effects.

In tables A4.1 and A4.2 the total uncertainties have been calculated as

«- Jiy.

ut = 4st2+wt2 ,

j=nWt =

1

Ut=k-ut

5>,/j=1

In the case of the temperature difference, we have:

lb <V^12 + Uib2 = V2-[/% “ 0.11 K


208

For the temperature difference, however, the correct evaluation would be to first calculate the standard deviation of the difference, The temperature differencemeasurement can be checked by just circulating the brine through the coil at the ambient temperature and with no heat loading of the coil. Systematic uncertainties in the measurement of a temperature difference tend to cancel. Indeed, for these two sensors the drift over a 3-year period was 0.04 K and 0.05 K respectively. Hence the change in the difference due to long-term drift would only be 0.01 K.

The only possibility to really improve on the results above would be to keep a closer control on the temporal variations. This is readily recognized from the results in table A4.2 regarding the water temperature sensors. The water side was not directly exposed to the random variations caused by the frosting process and the return temperature to the heat pump was closely controlled by the test installation.

Table A4.2. Uncertainty budget for the determination of water temperatures according to Fahleff4).


Uncertainty type A(K)

Uncertainty typeB (K)

Calibration 1 stw,cal < 0.01, stw,cai < 0 005

Wtw,call < 0-012,

1 Wtw,cal2 < 0 03Meter reading 1 - Wtw,read<°-006

Operating point 1 Stw,op, < 0.0004, stw,opt < 0.00004

ww< 0.006

Operating conditions 1 ^tw,opc < 0.05, 0005

"

Installation 1 - Wtw,inst < 0.02


sM < 0.051 K, sJw < 0.007 K

wM < 0.039 K

Combined uncertainty of water temperature uM < 0.06 K, uiw < 0 04 K

Total uncertainty of water temperature (k=2.0) Um< 0.13 K,< 0.08 K


209

Table A5.1. Uncertainly budget for the determination of air temperatures using PRTs according to Fahlen(4K

A5 Uncertainty budget: Uncertainty budget:Air temperature

Cause of the uncertainty Propagation constant, P.}

Uncertainty typeA(K)


Calibration 1 $ta,cal\ ^ 0-01, Sta,call <0'005

wta,call < 0 012

1 - Wta,cal2 < 0 04Meter reading 1 - W,a,read < 0 006Operating point 1 s,a,opt < 0.0004,

^,<0.00004wta,opt<0.000008

Operating conditions 1 Sta,opc < 0.33,

Installation 1 - W,a,inst < 010


J,„<0.33KsTa< 0.035 K

Wto<0.11 (inlet) wto<0.21 (outlet)

Combined uncertainty of air temperature (PRTs)

uta < 0.35 K uTa< 0.11 K

Total uncertainty of air temperature (k=2.0) (PRTs)

Uta < 0.69 KU-ta< 0.22 K


s, =' 1

j=nzv.j=1

u, = ^js2 + w2 ,

U-nW,r = JIX/

j=1

Ut=k-ut

Results from tables A5.1 and A5.2 indicate that the objective regarding uncertainty of measurement was readily met regarding mean values. The objective uncertainty of 0.3 K for the absolute air temperature level was no problem to achieve. Regarding individual readings, however, this was not possible.

As far as the uncertainty of the temperature difference is concerned, it should definitely be less than

Um < fhF+Vm -V2.C7fc-0.31K

The measurement of temperature difference can be checked by just flowing air through the coil at ambient temperature with no heat load. Systematic uncertainties in the measurement of a temperature difference tend to cancel.


210

Table A5.2. Uncertainty budget for the determination of air temperatures using thermocouples according to Fahlen(4K


Uncertainty type A (K)


Calibration 1 Sta,cal\ < 0-02,Sta,call < °-01

Wta,call < 0-03

1 W,a,call < 0 06

Meter reading 1 - W,a,read < °-006

Operating point 1 sta,opt < 0-01,o-ooi

wta,opt< 0-0002

Operating conditions 1 Sta,opc < 0.33, %,.„<0.03

Installation: Inlet

: Outlet

1 [•s/a,&wr<0'13,%.,w<0-052]*

W'ajnst < 010

1 [‘sfo,m?Z<'0-24,%.m,<0.099]*

Wta,inst < 0-20


sta< 0.33 s7a< 0.032

wto<0.12 K (inlet) wta< 0.22 K (outlet)

Combined uncertainty of air temperature (T-type thermocouples, inlet)

uta < 0.35 K uTa < 0.13 K

Total uncertainty of air temperature (k=2.0)(T-type thermocouples, inlet)

Uta< 0.69 K U-ta< 0.26 K

*The installation uncertainty is considered either as type A or as type B (B in this case).

It is interesting to note that even though the PRTs as sensors have a much higher accuracy than the thermocouples, the net results regarding uncertainty are not much different. By far the most important uncertainty factor was the random variations of temperature, caused by control variations of the installation and operational fluctuations of the heat pump. When mean values are considered, the random variations loose their importance and instead the uncertainties in the sampled value of the bulk temperature dominate.


211

A6 Uncertainty budget: Surface temperature

The uncertainty budget for the measurement of surface temperatures is displayed in table A6. By far the most important uncertainty factor was the random variations of temperature, caused by control variations of the installation and operational fluctuations of the heat pump. When mean values are considered the random variations loose their importance and instead the uncertainties in the sampled value of the bulk temperature dominate.

In table A6 the total uncertainties have been calculated as

Stfsj-n

17=1

j=n

1 2>«s./7=1

Utfs^Stfs Wtfs ’ Utfs=k-utfs

Table A6. Uncertainty budget for the determination of surface temperatures in the coil by means of thermocouples according to FahlenU).


Uncertainty typeA(K)

Uncertainty typeB (K)

Calibration 1 Stfs,cal < 0.02, Stfs,cal<0-01

wtfs,call < 0 03

1 - wtfs,cal2 < 0-06Meter reading 1 - w#,read< 0.006Operating point 1 fys,opt < 0.01,

Stfs,opt < 0-001

wtfs,opt< 0.0002

Operating conditions 1 stfs,opc < 0.33, stfs,opc < 0 03

Installation 1 - Wtfs,inst < 0.2


,#<0.33,#<0.032

Wtfs < 0.21

Combined uncertainty of surface temperature a# < 0.39 K m# < 0.21 K

Total uncertainty of surface temperature (k = 2.0)

OO

o oV V


212

A7 Uncertainty budget: Humidity

Three budgets are shown:

• One for the uncertainty of measurement regarding dew point temperature

• One for the determination of the operating condition, which was specified in terms of relative humidity

• One for the determination of the moisture content, which is needed for the calculation of frost growth

In table A7.1 the total uncertainty of the DPT has been calculated as

J]=n2\Stdp,j »

j=nW,tdp J^E/Wtdp,J

utdp -yjstdp wtdp ’ Utdp=k-Utdp

Table A7.1. Uncertainty budget for the determination of dew point temperatures according to Fahlen(4K


Uncertainty type A(K)


Calibration 1 Stdp,cal < °-°05 ^tdp,call ^ 0.04,

1 (long-term drift)-* ™tb,call < 012

Meter reading 1 - W,dp,read < 0 006Operating point 1 Stdp,opt ~ 0 ^’tdp,opt ~ 0Operating conditions 1 $tdp,opc < 0.50,

^c<005Installation 1 wtdp\,inst < 0.03,

wtdp2,inst ^ 0.3Total contribution of types A and B respectively

stdp < 0.53 K, sidP < 0 05 K

wtdpl < 013 K, wtdp2 < 0.33 K

Combined uncertainty of dew point temperatures

utdp < 0.55 K, utdP < 0.14 K

Total uncertainty of dew point temperatures (k=2.0)

< 11 %< 0.28 K


213

Results from table A7.1 indicate that the objective regarding uncertainty of measurement was readily met in most situations. The objective uncertainty of 0.5 K for the absolute DPT-level was no problem concerning mean values. Individual measurements, however, would fall outside the aspired limits of uncertainty due to insufficient quality of the humidity control.

Table A7.2 presents the total uncertainty regarding the determination of relative humidity, calculated in analogy with the total uncertainty of the dew point temperature.

Table A7.2. Uncertainty budget for the determination of relative humidity according to FahlenU).


Uncertainty type A(%RH)

Uncertainty type B(%RH)

Calibration 1 Srh,cal < 0-24 Wrh,call < °-57

1 ^rh,cal2 <12

Meter reading 1 $rh,read ~ ® Wrh,read ~ ®Operating point 1 Srh,optl ~ 0 Wrft,oprl ~ 0

*Srh,opt2 ~0-5 *^rh,opt2 ~ 1.0

Operating conditions 1 $rh,opc < 2 0, srh,opc < 0'2

Installation 1 - ^rh,inst < l-®Total contribution of types A and B respectively

srh < 2.0,Sfh < 0.3;

<2 .1,*srh < 0-3

<2.1;*"r*, <2.3

Combined uncertainty of relative humidity urh < 2.9 % RH, *urh<3.1 % RH, uTh < 2.1 % RH *u7h < 2.3 % RH

Total uncertainty of relative humidity (k=2.0)

Urh < 5.8 % RH, * Urh<6.1 % RH, UTh < 4.2 % RH *UTh<4.6 % RH

*At temperatures below 0 °C there is an increased uncertainty due to the large temperature derivative of the calibration curve, see appendix F.


214

Table A7.3. Uncertainty budget for the determination of the vapour ratio according to FahlenU). This budget applies to the state of the inlet air. The uncertainty of the outlet air will be substantially larger.




Calibration 1 S™'cal < 0.04 xw

Wxw,call <Q 29

Xw

1 <Q gg

Meter reading 1 Sxw,read = qxw

Wxw,read <Q.Q4

xwOperating point 1 Sxw,opt .q

XwWxw,opt q

Operating conditions 1<3.65,

xwS™'cal <0.36

xw1 w

<0.2*.

vvxw,opc ^ j Q**

Installation 1 WxwUnst <0.22, xwl

wxw2,inst -0^2

xw2Total contribution of types A and B respectively

^<3.65,xw^ < 0.36 xw

—251 < 0.97*; xw^ < 1.38**

Combined uncertainty for the vapour ratio Uxw <3.78%*, U™ <3.90%**, xw xw

< 1.04 %* < 1.43 %**xw xw

Total uncertainty for the vapour ratio (k=2.0)

Uxw < 7 6*? UXW < 7 8 %**xw xw

<2.1* U*w < 2.9 %**xw xw

These values apply when the atmospheric pressure was actually measured. **Increased uncertainty when the nominal atmospheric pressure 101.34 kPa was used.


215

A8 Uncertainty budget: Liquid pressure difference

Table A8 summarizes the uncertainty discussion on differential pressures in liquid flows.

Table A8. Uncertainty budget for the determination of differential pressures in liquid flows according to Fahled4\

Cause of the uncertainty Propagationconstant,



Calibration 1 SApbc,cal „ q 0Me Me

Meter reading 1 [s6pbc.read <0 05]*APbc

WApbc,read ^ q 1

MeOperating point 1 ~ -

Operating conditions 1 S&pbc,opc _ q „Me

Installation 1 '

<0.6Me


00("4

Ji "4"* < 0.61Me

Combined uncertainty of liquid pressure difference <0.7%

Me

Total uncertainty of liquid pressure difference (uncertainty of a single measurement, k = 2.0) <1.4%

Me

*Only applicable when a number of readings have actually been used to calculate s.

In table A8 the total uncertainties have been calculated as

Âpbc ^j^hÂpbcJ ’ Âpbc ^^y'jÂnhr. i

/ 2 2M'Apbc yÂpbc ~^Âpbc ’ UApbc — ^ ' UApbc (k = 2)


216

A9 Uncertainty budget: Air pressure difference

Tables A9.1 and A9.2 sum up the results of the component uncertainties from 4.9.3. Table A9.1 accounts for the results of the coil pressure drop sensor and table A9.3 for the airflow pressure difference sensor.

Table A9.1. Uncertainty budget for the determination of the pressure drop on the air- side of the cooling coil according to Fahlen(4K

Cause of the uncertainty Propagation constant, P.

Uncertainty type A (Pa)

Uncertainty typeB (Pa)

Calibration 1 [sApac,cal < 2]*,

sApac,cal < ^Âpac,call ^ 0.06

1 - Âpac,cal2 ^ 0-21 - WApac,cal3 ^ 0-6

Meter reading 1 pac,read <0.03**

Operating point 1 - -

Operating conditions 1 $Apac,opc < Âpac.opc < 0 5

Installation 1 - Âpac,inst ^ 0 2Total contribution of types A and B respectively

SApac < ^"0>Âpac

wApac < 0 67

Combined uncertainty of the air-coil pressure difference

UApac < 5 Pa> uApac < 13 Pa

Total uncertainty of the air-coil pressure difference (uncertainty of a single measurement, k = 2.0)

uApac<iov&,UApac < 2-6 Pa

Calibration constants are normally based on several measurements so only the standard deviation of the mean is applicable.**Either the A-component (several measured values) or the B-component (a single measured value) but not both should be used.

In tables A9.1 and A9.2 the total uncertainties have been

sApa pa,j > pa

I 2 2uApa ~ yjÂpa 4rÂpa » UApa

calculated as

= a/XwApa,j2

= k-u&pa (k = 2)


217

Table A9.2. Uncertainty budget for the determination of the air-flowmeter pressure difference according to FahlenW.


Uncertainty type A (Pa)

Uncertainty typeB (Pa)

Calibration 1

sApaf,cal < 01

WApaf,call < 0.06

1 - Âpaf,cal2 < 0.2

1 [WApaf,caB < 0-4] ***

Meter reading 1 Âpaf.read <'0.03**


Operating conditions 1 SApaf,opc < 0.21,SApaf,opc < 0-021

Installation 1 ^-Âpafjnst <0-13] ***


SApaf < 0.24,SApaf <0-11

™Apaf < 0-47 [< 0.21]***

Combined uncertainty of liquid pressure difference

uApaf < 0-9 Pa, [< 0.32]***^ < 0.9 Pa [<0.24]***

Total uncertainty of liquid pressure difference (uncertainty of a single measurement, k = 2.0)

Uiiwf < 1.8 Pa, [< 0.7]*" ^<1.8 Pa ]< 0.5]***

^Calibration constants are normally based on several measurements so only the standard deviation of the mean is applicable.**Either the A-component (several measured values) or the B-component (a single measured value) but not both should be used.^Ûncertainties regarding 'cal3' and 'inst' are included in the flowrate calibration and will therefore be disregarded for the pressure difference part in chapter 4.3 concerning air flowrate.

There is a remarkable difference between the results of the uncertainty budgets of the two sensors. The uncertainty of the coil pressure drop derives almost entirely from the the random fluctuations experienced during the frosting process. These fluctuations were partly caused by the actual frosting process and partly by the repeatability of the sensor. The repeatability of the Autotran sensor was not nearly as good as that of the Furness sensor. Hence the A-type uncertainty was completely dominant.

The uncertainty in the air-flowmeter pressure difference, on the other hand, was entirely related to the installation uncertainty and the long-term stability of the calibration factor. In this case the B-type uncertainty component dominated the overall uncertainty.


218

A10 Uncertainty budget: Frost mass

Uncertainty budgets along the lines of tables A10.1 (coil A) and A10.2 (coil B) may be laid out. The uncertainties were referred to the maximum frost load of test condition Al, i.e. Mjr tnax = 17.72 kg. Condition B1 will result in a slightly higher frost mass but this will not affect the relative uncertainty in any significant way. In the uncertainty budgets, the reading errors were treated as a type B uncertainties since the tables refer to the maximum frost loads, i.e. to single measured values.


f7V 2

SMfr ~ JZ,SMfrj » WMfr = ^j=n^hWMfr,j

7=1

uMfr ~ ^sMfr2 +wMfr2 > II

IuMfr

Table A10.1. Uncertainty budget for the determination of frost load with coil A according to Fahlen(4K

Cause of the uncertainty Propagation constant, P.



Calibration 1

^fr,maxWMfr,can <on

max

1 ' WMfr,cal2 , ^ p Mfr,max

Meter reading 1' "Mr.,,*,

Mfr,m axOperating point 1

Mfr,maxWMfr,opt < o 0003

^fr,maxOperating conditions 1

<0.68Mfrjnax

Installation 1 - ^MfrJnst S55 0

^/r.maxCorrection constant C 1 ~ ^ < 0.09

CTotal contribution of types A and B respectively

SWl—<0 88 %^fr.max

^ <=1.15 %Mfr, max

Combined uncertainty of frost load UWr < 1.5 %Mfr,max

Total uncertainty of frost load (k=2.0) UWr <3.0%Mjr.max


219

Results from table A10.1 indicate that the objective uncertainty of 5 %, as presented in table 3.1 from the planning procedure, was met in the case of coil A but not quite in the case of coil B. The major causes of uncertainty were non-reproducibilities during calibration and long-term drift. Both these causes can be markedly reduced by taking more care during installation of the coil in the supporting frame. An uncertainty of less than 2 % should be well within reach with the current equipment.

Table A10.2. Uncertainty budget for the determination of frost load with coil B according to Fahled4h

Cause of the uncertainty Propagation constant, P.}



Calibration 1

Mfr, max

WMfr,cal\ <Q17

Mfir, max

1 '

<2.82Mfr, max

Meter reading 1< 0.03

Mjr, max

Operating point 1

Mfr,.max

WMfr,°pt < 0 0003

Mfr, max

Operating conditions 1<Q.68

Mfr, max

Installation 1 ^Mfrjnst nM/r,m "°

Correction constant C . 1 “ —^ < 0.09c

Total contribution of types A and B respectively <1.82 %

Mfrjaax.Wm <2.83 %

^fr,m ax

Combined uncertainty of frost load UMfr ■ < 3.8 %Mfir,max.

Total uncertainty of frost load (k=2.0)— < 7.6 %

•^/r.max


220

All Uncertainty budget: Electric power input

Table All provides an overview of the uncertainties experienced in the electric power measurements. The uncertainty budget shows that by far the most important contribution to the overall uncertainty was the random variations of the power input to the heat pump during the measuring period. If, however, a mean value over the measuring period was calculated, the overall uncertainty of this would be 0.7 % instead of the 1.6 % estimated for a single measured value.

Table All. Uncertainly budget for the determination of electric power according to Fahlen(4h




Calibration 1 WKe’cal1 <0.03Ke

1<0.06

K1

< 0.006R

Meter reading 1 - -


Operating conditions 1

We

SWe,opc < o 07

WeInstallation 1 "V- <0.3

WeTotal contribution of types A and B respectively

YreSWe fipc < o o?

We

7: <mi

Combined uncertainty of electric power

< 0.32We

Total uncertainty of electric power (uncertainty of a single measurement, k = 2.0) 7; ^

*:<oj


221

Appendix B:

Uncertainty budgets of derived quantities

Contents

B1 Heating capacity

B2 Cooling capacity - Liquid side of heat pump

B3 Cooling capacity - Liquid side of coil

B4 Cooling capacity - Air side of coil

B5 Balances of energy and mass

B6 Coefficient of performance

B7 Specific cooling load

B8 Air inlet velocity

B9 Specific frost load

B10 Indirectly measured frost load

App. B: Uncertainty budgets of derived quantities

222

B1 Uncertainty budget: Heating capacity

Table Bl. Uncertainty budget regarding the determination of heating capacity on the condenser side of the heat pump, Qy, according to Fahlen(4K

Cause of the uncertainty

Propagation constant, Pj

Uncertainty type A,(%)

Uncertainty type B,(%)

Measurands:AVw(N,T,K0w) Py = 1.0012 <0.18,

<0.02<0.12

Azw P3=0 ~ 0 = 0P4 ~ -0.59 <1.6,

<0.22<0.75

P5 = l < 1.6,<0.22

<0.75

Constants:Apw P7 -1 = 0 <0.02

4 = 1 — 0 <0.02

Total contribution of types A andB respectively;

< 1.87, !ll< 0.13a a .

%.<1.18*, !ll<0.12*a &

-0- < 0.88 a

Combined uncertainty of the heating capacity (calculated and measured for individual values and mean values respectively)

uo\ u7>\r < 2.07 96, 8' < 0.89 %,a a

UQl U—“ <i.47*%, ei <089„%

' a

Total uncertainty of the heating capacity (k=2.0)

Ud\J: <4.1%, -# < i.8 %,a a

Vf<^° "?'<i,*%

a*These uncertainties are based on the measured instantaneous capacities. There is obviously a high degree of correlation between two and twp Hence large variations intw do not reflect in large variations in Qy and the derived uncertainty of Qy will be considerably overestimated, c.f. equations 5.1.10 and 5.1.11.


223

Table B2. Uncertainty budget regarding the determination of cooling capacity on the evaporator side of the heat pump, Q2, according to Fahlen(4K

B2 Uncertainty budget: Cooling capacity -Liquid side of heat pump


Propagation constant, P}



Measurands:P, = 1.0019 < 0.22,

<0.02<0.29

Az& P3 =-0.271 = 0 = 2.3

AL P4 = -1.0025 <9.3,<0.93

<0.75

Af*, P5 = l <9.3,<0.93

<0.75

Constants:Ap6 P7 = l = 0 <0.12

A^ 4 = i = 0 <1.9


fcfa-'j? ■ £(Wfgi<13.17, fli<1.32 & &

f&L<1.13*e2!h<o.u*

Qi

<2.20Gz

Combined uncertainty of the cooling capacity (calculated and measured for individual values and mean values respectively)

U02 U7ir)j: < 13.35 %, < 2.81 %,62 &UQ2 U—

. <2.47 % J£i <220* %^ Gz

Total uncertainty of the cooling capacity (k=2.0) ^ <26.7%, -J&. < 5 6 %

& 02

^ GzThese uncertainties are based on t ie measured instantaneous capacities. There isobviously a high degree of correlation between and typ Hence large variations in tfr do not reflect in large variations in Q2 and the derived uncertainty of Q2 will be considerably overestimated, c.f. equations 5.2.10 and 5.2.11.


224

The liquid (brine) side cooling capacity measured at the coil, Qb, was calculated from the relation

B3 Uncertainty budget: Cooling capacity -Liquid side of coil

Qb~Vb'Pb • (cpb2'4,2 " Cpbl • tb\ ) (eq. B3.1)

This is the same way that was used in the case of Q2, the only difference being the exchange of {tbo~tbi) for (tb2 -tbl).

Calculation of the uncertainties in this determination was carried out in the same manner as for the cooling capacity measured on the brine side of the heat pump. SinceQ2 and Qb were measured in the same liquid circuit, the same flowmeter and identical types of temperature sensors were used. Furthermore, the same stability criteria and physical property data apply. Thus, the estimated and expected uncertainties will be the same as those presented in B2.

Figure B3. Sensor locations for the determination of cooling capacity on the liquid side of the coil.


225

Both the dry bulb and dew point temperature differences are so small that random variations severely affect the accuracy both of individual measurements. The only reasonable method is to calculate capacities from simultaneously measured values and then determine the mean capacity based on the instantaneous capacities.

B4 Uncertainty budget: Cooling capacity -Air side of coil

Table B4.1. Uncertainty budget regarding the determination of cooling capacity on the air side of the coil, Qa, according to FahlenU).Cause of the uncertainty




Measurands:A(Apaf) Pi = 0.5 < 1.1; <0.5** <1.0$

P2® 0.74 < 11.3; < 1.1** <3.8£

P3 ~ 0.75 <11.3; <1.1** <3.8^dpi P4 ~ -0.27 <37.1; <3.7** <2.2

P5« 0.24 <37.1; <3.7** <22.8

% = 1.52 - <1.2

Constants:Pj ~ 1 < 0.65; < 0.07** <1.2

APa ^8 ~ 1 <0.02 <1.2

Acpa P9 ~ 0.74 ~ 0 <0.06= 0.0026 ~ 0 <0.3

A r0 Pu =0.26 ~ 0 <0.1


f$L < 17.9, 3k < 1.8 Qa Qa

3l<2.7*, ^.<0.27* Qa Qa

<7.3QaH'r'j)1-

Combined uncertainty of the air side cooling capacity (calculated and measured for individual values and mean values respectively)

< 20.6 %, < 7.5 %,Qa Qa3l<7.8*%, %<73*%

a aTotal uncertainty of the air side cooling capacity (k=2.0)

UQ° < 41.3 % . UQa < 15 0 %,

a,< 15'5* % "5. < 14.6* %

a aThese uncertainties are based on the measured instantaneous capacities. There is obviously a high degree of correlation between ta],ta 2 and ]Jc{p2- Hence large variations in thesemeasurands do not necessarily reflect in large variations in Qa and the derived uncertainty of

Qa will be considerably overestimated.**Standard deviation of the mean value based on 100 measured values.


226

B5 Balances of energy and mass

B5.1 Balance of the brine circuit

QlosS2 *s a loss of cooling capacity, i.e. it represents a heat gain, since the brine isalways colder than the ambient air. Equation 5.5.3 gives us the magnitude of this loss as

Qlossl = Qi-Qb~ WeP3 (eq. B5.1)

Since the length of tubing was substantial between the heat pump unit outside the testroom and the cooling-coil inside, the heat exchange also proved to be substantial. Table B5.1 reflects this by showing large imbalances between the capacities measured at the heat pump evaporator and at the cooling-coil respectively, even though the tubing was fairly well insulated outside the test chamber.

Table B5.1. Examples of the power balance of the brine circuit according to FahlenW.

Test no.Qi(kW)

Qb(kW)

7^3

(kW).100 (%)

A1 5.887 3.836 1.463 +15.3A2 4.178 2.311 1.447 +10.0

A3 8.921 6.499 1.694 +8.2

A4 7.011 4.632 1.724 +9.3A5 6.181 3.978 1.583 +10.0

A6 6.434 3.937 1.734 +11.9A7 6.376 4.419 1.360 +9.4A8 6.476 4.565 1.232 +10.5A9 5.984 3.876 1.234 +14.6

A10 5.859 4.046 1.229 +10.0

All - - - -

A12 5.715 3.909 1.236 +10.0

A13 7.405 5.773 1.223 +5.5


227

B5.2 Balance of the air-coil

The cooling-capacity of the coil was measured both on the brine-side and on the air- side. In table B5.2 the 'wet' capacities are based on the measured mass of the coil.

Table B5.2. Examples of the power balance of the air-coil according to Fahlen(4l

Test no.Qa,wet

fkW)Qa,dry

fkW>Qa

(kW)Qb

(kW)^W-100 (%)

&A1 0.497 3.741 4.238 3.836 -10.5A2 0.000 1.901 1.901 2.311 +17.7A3 1.053 4.873 5.926 6.499 +8.8

A4 0.044 3.760 3.805 4.632 +17.9A5 1.270 2.091 3.361 3.978 +15.5A6 1.076 2.001 3.077 3.937 +21.8

A7 0.286 4.011 4.298 4.419 +2.7A8 0.450 3.304 3.754 4.565 +17.8A9 0.613 2.435 3.049 3.876 +21.4

A10 0.086 3.647 3.732 4.046 +7.8All - - - - -A12 0.409 2.929 3.338 3.909 +14.6A13 2.114 3.162 5.275 5.773 +8.6

The rate of frost growth was measured in two different ways simultaneously.

Table B5.2. Examples of the mass balance of frost in the air-coil. ma jrA is the frost mass flux determined by airflow and humidity measurements, thjrA is the corresponding flux determined by weighing, and aihfrA is the difference between these.

Test no. ihfrA (kg/h/m2) ™a,frA

(kg/h/m2)AmfrA(kg/h/m2)

A1 0.01237 0.00735 -0.00502A2 0.00000 0.00335 +0.00335A3 0.02622 0.00288 -0.02333A4 0.00144 0.00982 +0.00872A5 0.03163 0.03387 +0.00224A6 0.02681 0.03130 +0.00450A7 0.00713 0.02731 +0.02017A8 0.01122 0.01836 +0.00715A9 0.01528 0.01983 +0.00455

A10 0.00213 0.00603 +0.00816All - - -A12 0.01019 0.00477 -0.00541A13 0.05265 0.02856 -0.02408

~QTable B5.2 shows that there is a considerable difference between the mass flux derived by means of weighing and by means of the change in humidity. This tends to support the theory that frost is formed by sublimation directly in the air stream and then carried out of the coil.


228

B6 Uncertainty budget: Coefficient of performance

Table B6 presents the results regarding the uncertainty budget of calculated values of COP. The table applies to test number A1 (the nominal test condition with coil A).

Table B6. Uncertainty budget regarding the determination of coefficients of performance, COP1 and COP2 according to Fahleni*).


Propagation constant, P:



Afii.kW P = 1 <1.18; <0.12* <0.88

A<22,kW ■Jo ii <1.13; <0.11* <2.20

AW^.kW P3=-l < 0.70; < 0.07* <0.31

Total contribution of types A andB respectively; co£<L37;

scZ;

<0.93COP,

C0P2<^ coV2-22

Combined uncertainty of COPj and COP2 COP,' <US6%; cop' <0-94%*

“copl <223%*

Total uncertainty of COPj and COP2 (k=2.0)

coP: <“* cop: <4j%*

^Standard deviation of the mean value based on 100 measured values.


229

B7 Uncertainty budget: Specific cooling load

Table B7 presents the uncertainty budget concerning the specific cooling load for coil A.

Table B7. Uncertainty budget regarding the determination of specific cooling load according to Fahled4).





A&, Pj = 1 < 1.13; < 0.11* <2.20

AL P2 ~ -0.96 - <0.29AH P3 ~ -0.96 - <0.10

ANf P4«- 0.96 0 <0.57AD P5=-0.040 < 0.73; < 0.09* <0.70AW P5=-0.040 - <0.14^Ntube P6=-0.040 0 0

Total contribution of types A andB respectively; <1.13;

4b,A

% <0,11.

4b,A

W<M <2.29

4b,A

Combined uncertainty of the specific cooling load (calculated and measured for individual values and mean values respectively)

< 2.55 %; f ’ < 2.29 %*

4b,A 4b,A

Total uncertainty of the specific cooling load (k=2.0)

U*A <5.1%; ^ <4.6%.

4b,A 4 b, A^Standard deviation of the mean value.


230

B8 Uncertainty budget: Air inlet velocity

The propagation coefficients will be Pj = -P2 = -Pj = 1. Hence the uncertainty budget of table B8 can be produced.

Table B8. Uncertainty budget regarding the air inlet velocity to the coil according to Fahlen(4K





pi = 1 <0.65; <0.07* <1.5

AW P2 = -l - < 0.25AH P3=-l - <0.10


^2. <0.65; <0.07* VV< 1.52

VX(Prs/) ’ A Ek-;)2

Combined uncertainty of the velocity of approach

-^2. <1.66%; ^2-<1.53%*va va

Total uncertainty of the velocity of approach (k=2.0)

Uva < 3.3 %; Svs < 3.1 %*va vfl

*Standard deviation of the mean value.


231

B9 Uncertainty budget: Specific frost load

Using results for the total frost mass for coil A, together with results for the total coil area, table B9 can be produced. This table summarizes the uncertainty of specific frost load determinations for coil A.

■kTable B9. Uncertainty budget regarding the determination of specific frost load according to Fahlen(4K





P1 = l <0.88 <1.15AL P2 ~ -0.96 - <0.29AH P3 ~ -0.96 - <0.10

ANf P4 ~ -0.96 0 <0.57AD P5=-0.040 < 0.09* <0.70AW P5 ~ -0.040 < 0.09* <0.14

tube P6 =-0.040 0 0

Total contribution of types A andB respectively; < 0.88

mfrmfF < 1.31

MfrU(pr4^

2(WCombined uncertainty of the specific frost load (calculated and measured for individual values and mean values respectively)

< 1.58 %;mfr

Total uncertainty of the specific frost load (k=2.0)

U-r< 3.2 %;

mfr

*Specific frost load was only calcu ated as a mean value; hence only the mean valuesof individual measurands were of interest.


232

BIO Uncertainty budget: Indirectly measured frost load

Table BIO clearly indicates the dominant influence of the uncertainty involved in the measurement of humidity. If the hygrometers were to be connected differentially and the output zeroed with no cooling of the coil, then of course the accuracy could be much improved as demonstrated in table B 10.2.

Table B10.1. Uncertainty budget regarding the indirectly measured frost load according to Fahlen(4K____________________________________________Cause of the uncertainty


Uncertainty type A, (%)


AV* P1 = l <0.07 <1.5

APa P2 = l <0.02 <1.2

Ax,,2 P3 ~ -9.05 <0.36 <1.4Axlvl P4 = 10.05 <0.36 <2.8

Total contribution of types A andB respectively; —< 4.87 %

Mfr< 30.92 %

Mfr

Combined uncertainty of the indirectly measured frost load

iV < 31.3 %;Mfr

Total uncertainty of the indirectly measured frost load (k=2.0)

um < 62.6 %;Mfr

In table B 10.2 the propagation coefficient P3 is approximated as the mean of P3 and P4 in table B 10.1.

Table BIO.2. Possible uncertainty budget regarding the indirectly measured frost load using differentially connected humidity sensors according to FahlenUlCause of the uncertainty

Propagation constant, P:

Uncertainty type A, (%)


Af, P1 = l <0.07 <1.5

APa P2 = l <0.02 <1.2

A(x,v2-^,) P3 ~ 9.6 < 0.073 <0.22

Total contribution of types A andB respectively; < 0.70 %

Mfr< 2.85 %

Mfri^(pj-sjf ’ ijEh 'wif

Combined uncertainty of the indirectly measured frost load

um < 2.94 %;Mfr

Total uncertainty of the indirectly measured frost load (k=2.0)

UMff < 5.9 %;Mfr


233

Appendix C: List of measurands and measuring channels

Evaluation of measured results from frosting of cooling-coilsThe original measurements were made with a main-frame computer, In the subsequent evaluation, the data files were converted to Excel format on PC:

1. Convert DTA-files to excel

2. Rename files

Xm(Yn).xls where

X = type of coil (A = small coil, B = large coil) m = number of the test-case (operating conditions)Y = type of file (M = measured results, E = evaluated results including corrections and calculations)n = serial number if several tests were made with the same test conditions and the same coil

Example: Al(Ml).xls => nominal test conditions of the small coil, test no. 1.

3. Create evaluation files

From Al(Ml).xls a new file Al(El).xls is made. First a time-channel is entered and then mean values are formed of sets of 10 values excluding the defrosting period and the first 10 minutes after and last 20 minutes before this period. On top of each column of values the following comments are entered: Designation of parameter (e.g. tbl), date of measurement, date of correction, reference to excel and measurement channel(s), type of correction or modification of the measured values.

Appendix C: List of measurands and measuring channels

234

Measuring channels and corrections

Channel

Measurand Correction or meter constant in the DAS

New correction or calculation

Analogue channels: AA1 LidstromA2 LidstromA3 Vb (analogue)

A4 tn (Vaisala)A5 Reg.lA6 Reg. 2A7 Reg. 3A9 Supply, load-cell,

(&(V)A42 COS(p

A46 cp (Vaisala)A50 MfX mV)A58 Ap„f(mV)A59 ±

A60 hp„r (mV)Thermocouple channels: DD81 tnl - -0.04 KD82 tf* - -0.04 KD83 L - -0.04 KD84 tf* - -0.04 KD85 L - -0.04 KD86 tf* - -0.04 KD87 tnl - -0.04 KD88 tf* - -0.04 KD89 l, - -0.04 KD90 tf* - -0.04 KD91 L - -0.04 KD92 tf* - -0.04 KD93 i* - -0.04 - Wef / (Va • pa • cpa )

D94 ta 2 - -0.04 - Wef / (Va ■ pa ■ cpa )

D95 ta 2 - -0.04 - Wef / (Va • pa ■ cpa )

D96 ta 2 - -0.04-Wef /(Va-pa-cpa)

D97 ta 2 - -0.04- Wef /(Va-pa-Cpa)

D98 ta 2 - -0.04 - Wef / (Va ■ pa ■ cpa )

D99 tf* - -0.04 KD100 i - -0.04 K

Appendix C: List ofmeasurands and measuring channels

235

Channel

Measurand Correction or meter constant in the DAS


PRT channels: EE23 twi +0.01 (+0.01) -0.06E21 turn -0.01 (-0.01) -0.08E27 thi +0.09 (+0.09) -0.04E33 thn +0.06 (+0.06) -0.05E71 thi -0.22 (-0.22) +0.00

E67 tM -0.16 (-0.16) +0.00

E65 u -0.12 (-0.12) +0.00

E69 tn7 -0.07 (-0.07) -0.03E29 Lip / 0.00 (0.00) +0.00 (varies ±0.2 K)E63 t/lp7 0.00 (0.00) +0.00 (varies ±0.2 K)E39 trpf 0.00 (0.00) -0.04Electric power: FF47 21505.92 (21505.92). 1.000F51 4316.76 (4316.76). 1.000F55

. i1321.80 (1321.80).1.006

F57 4319.37 (4319.37)-1.000F53 jLa 6596.04 (6596.04)-1.000Pulses: H and IHO K 0.1 (0.1)0.9975

HI K 0.1 (0.1)0.985

10 v„ 0.1 (0.1)0.997511 V, 0.1 (0.1)0.985Integrated mean values: JJ1

J2J3 So,Thermal capacities: KK1 Qi (Q i )• 1.00-1.00-1.000 (V w, Atw,

KJK2 Ql (G2)'0-99-1.00 1(^,6%,%,)K3 Ob (Gb)0.991.00.1(Vf,,Af6,^)


236

Channel

Measurand Correction or. meter constant in the DAS


Other calculated values: IVMl COP,M2 costpM3 Mfr A:

0.185559+53.2187UB:-0.39197+63.0030U

A: (0.185559+53.2187U) 1 -0B: (-0.39197+63.0030U)1.0

M4 &Pnr 62.5-rU - 2] (62.5-rU-21)0.986M5 *Paf -0.045545 +

0.03992-u(t0.045545 + 0.03992u)0.993

M6 va A:l, A:2, A:4 B:l, B:2, B:4

Instead of 6 different equations, use

M7 tAn (Vaisala)M8 jcoplm

M9 COP,M10 WmMil + WpAM12 Ap(3%)M13 \coplmM14 COPoM15 !&M16 Mfr (running

mean values)M17M18

TO T(S)


237

Appendix D: List of data files of measured values

Test condition Coil A (small coil) Coil B (large coil)

No. (t JtyJuJ C[a ) OriginalPDF name

Current PCname

OriginalPDF name

Current PCname

1 2/85/2/100 M1L04K1L04(interrupted)

A1(E1)*A1(E2)

Bl*

2 2/85/2/50 KYL2L0404 A2(E1)* — B2*

3 2/85/2/150 K3L04 A3 (El)* — B3*

4 2/70/2/100 K46L03 A4(E1)* " B4*

5 2/95/2/100 K5L01 A5(E1)* — B5*

6 2/ 85/ 1/ 100 K61L04 A6(E1)* — B6*

7 2/85/4/100 K71L04 A7(E1)* — B7*

8 -7/85/2/100 K12L02 A8(E1)* — B8*

9 -7/ 85/ 1/ 100 K92L02K A9(E1)* — B9*10 -7/85/4/100 K10L02 A10(E1)* — B10*

11 -7/85/2/50 KL1102** All(El)* — Bll*

12 -7/85/2/150 (actual ^ =100)

E12L02(C12L02**)

A12(E1)* — B12*

13 2/rain/ 2/max E3L06 A13(E1)* REG206 B13*

14 2/rain/ 1/max E1L06 A14(E1)* E1S06 B14*

15 2/rain/ 4/max E5L06, (E4L06**, too low flow!)

A15(E1)*A15(E2)*

REG406 B15*

16 20/50/1/50 ALFA1 A16* — B16*

17 20/50/1/ 150 ALFA2 A17* " B17*

*A data file converted to xls format has the addendum ...(M).XLS while the processed file has the addendum (E1).XLS (mean values of groups of 20 measured values, i.e. 20 minute means). **Problem with the measurements.

Appendix D: List of datafiles

238

Test condition Coil A (small coil) Coil B (large coil)

No. (f tJtyJuJ Qa ) OriginalPDF name

Current PCname

OriginalPDF name

Current PCname

Dig. Lidstrom 2/98/2/max

LIDD05 A5E1LDD* B*

Lidstrom2/98/2/100

LIDL06 (Tpl =-135 mV)

A5E2LIA* B*

Lidstrom2/98/2/100

LIL06 (Tpl =-102 mV)

A5E3LIA** B*

LEDD02 A11E1LID*

LIDD03 A11E2LID*

Surfacetemperature,2/98/2/max

YT6106 A5E1YT* B*

Surfacetemperature,2/98/2/100

YTL06 A5E2YT* B*

Photos,2/ 98/ 2/ max

FOT62L06 A5E1FO* B*

Photos,2/98/2/100

FOIL06 A5E2FO* B*

Photos,2/98/2/100

FOTLL06 A5E3FO*

*A data file converted to xls format has the addendum ...(M).XLS while the processed file has the addendum (El).XLS (mean values of groups of 20 measured values, i.e. 20 minute means). **ProbIem with the measurements.

Appendix D: List of data files

239

Appendix E: Mass flux of water vapour

The Lewis relation, which relates the heat and mass transfer coefficients, can be used to estimate the mass flux of water vapour from the air to the coil surface. As a check, this appendix provides measured and calculated results of the precipitation in the coil. In all cases, the mass flux is referred to the total air-side heat transfer area of the coil, hence the area efficiency must be considered. With this in mind and calculating the driving potential as the logarithmic mean difference in specific humidity between the air and the coil surface temperature, we have:

with

and

aamw=mfr=-—

cpa'(eq. El)

(AxJln =(Axw)j-(Axw)0

In ^(Axw)0 JA(Xyf,)j — (xw %w" fin)\ ^d ^w"fin^2

presuming that all water vapour precipitates as frost. To use this relation we need the air-side coefficient of heat transfer, the area efficiency, the specific humidities of the inlet and outlet air of the coil, and the saturated specific humidities at the inlet and outlet surface temperatures.

The air-side coefficient of heat transfer (see appendix G), aa, is based on the effective air-side heat transfer area Aa. The effective area relates to the total area by means of the area efficiency:

At = 7lA-A0 (eq. E2)with

rtA = 1------- ■(l~rlfin)~1lfin since Afin = A0 (eq. E3)A)

The fin efficiency, of course, will depend on the value of aa. For each test condition aa is both calculated and inferred from measured data. This cannot be done correctly without consideration of the heat resistance of the accumulated frost but this complicates matters and will be dealt with in a separate report. Furthermore, previous researchers report an increase in aa of up to 60 % due to the surface roughness of the frost layer. On the other hand, heat resistance of the frost layer is quite small in comparison to the air-side film resistance for a reasonable frost thickness and the current range of Reynolds number. Hence the frost surface temperature can be approximated with the wall temperature. For instance, in the density range 100 to 300 kg/m3, which is relevant for the measurements presented here, the thermal conductivity of frost varies between 0.1 to 0.3 W/m/K. Hence, for a typical thickness of 1 mm, we have:

= ———-r = 200 » cca ~ 20 8fr 1-10-3


240

Since the calculated air-side heat transfer coefficient using dry conditions will not be representative for the main part of the frosting process, and measured surface temperatures will be uncertain, both aa and are inferred from the measured brine- side heating capacity Qb and heat transfer coefficient ab (see appendix G),

and

since

FA,__ L_^ Qb ab’Ab

1 _FAn

Uq'Aq Qb

(eq. E4)

(eq. E5)

(eq. E6)

where F is the correction factor in consideration of not having true counter-flow conditions. a'a is a heat transfer coefficient which also contains the latent heat transfer and thus

. Qs (eq. E7)\£a

whereQa ~ % ' Va " A) ’ (^a—A )ln

and

«c = «Z)~+Ca-as- Tlfin^A) A)

Using the above procedure is indeed a very rough approach but if for instance ab is overestimated, and consequently aa is underestimated, then ta - tw will be overestimated. Hence the error in cta(ta - tw), which is the driving potential, will not be overly large.

A set of linked spread-sheets was used to calculate general coil performance and in particular the mass transfer under frosting conditions. Two spread-sheets, AIR.xls and BRINE.xls provided the thermo-physical properties by importing the reference temperatures from one sheet, TEST.xls, which described the operating conditions. AIR.xls also converts dew-point temperatures to relative humidity and specific humidity. Finally, TEST.xls imported the relevant coil-data from COIL.xls. One example of results is shown below.

The quantity of defrost water was measured after a test as the depth in a vessel outside the test-room according to Mdw = pw ■ • Hw = 998.2 • 0.281 • Hw. The waterwas pumped from the drain-pan of the coil by a pump, which was triggered by a level switch. In the spread-sheet, values calculated using the Dittus-Boelter and Hausen relations have been indexed turb and lam respectively.


241

Test condition Al: tai=+2°C ^ — 85 %rh Mal =2 m/s % = 100 W/m2

Ual (m/s)2.0

w CQ1.7

tdpl (°C) -0.1

97 (%rh)88

JW (gv/kga) 3.8

tfinlm (°C)-1

%2(°C) Vb (m3/h)-4.04 AIR INLET 1.87

BRINEOUTLET

40(W/m2)76

(kW)

BRINEINLET

3.5

\ G& (kW)-5.97 AIR OUTLET 3.53

(m3/s) W(°Q '4,2 (°C) <P2 (%RH) *w>2 (kgVkga) tfin2m (°C)0.93 -1.5 -2.0 97 3.3 -4

AIR: W = >al + —■&?.; Dry heat transfer

• An fitQa =aa'rlA -A)-(Ata-A) In with aa =aD-~^+ Ca • (Xs ■ Vfin

ta,ref{° C) p (kg/m3) (i(mPas) v (mm2/s) X (W/m/K) Pr(-)-1.2 1.30 17.1 13.1 0.0245 0.70(m/s) <7/, ,=2.sy (mm) Res Nils, lam NUs.turb

2.06 6.96 1090 5.0 7.2Umax.D (m/s) dh = D (mm) ReD Vfin VA Nud

3.08 16.6 3891 0.91 0.91 39Cta, lam eta.turb OCs,lam (Xs.turb ad

Air-side dry (W/m2/K) (W/m2/K) (W/m2/K) (W/m2/K) (W/m2/K)heat transfer: 18.9 26.2 17.5 25.2 51.2

SMV£:

tb.refC C) p (kg/m3) jj. (mPas) v (mm2/s) X (W/m/K) Pr(-)-5.01 1069 7.74 7.25 0.392 65.2

M6 (m/s) = d (mm) Red Nud,lam Nud.turb -

1.49 14.9 3069 8.4 75.3Brine-side heat transfer: (Xfr.ton (W/m2/K) a&fw* (W/m2/K)

222 1980


242

TOTAL COEFFICIENT OF HEAT TRANSFER: —-— = —-—+—-—,Uq ' A) ' Az % ■ A>

Uo(W/m2/K)

Uo-Ao(W/K)

Oa-Ac (W/K) a&-A& (W/K)Laminar Turbulent Laminar Turbulent

5.8 268 798 — 403 ——

14.1 653 798 — — 35946.4 295 — 1110 403 —

18.2 848 — 1110 — 3594

INFERRED AIR-SIDE COEFFICIENT OF HEAT TRANSFER:

1Uq'Aq

F-ein

Qa\

1A, < <2f,

1 x-1

ab' A ,and aa = a'a Qs_

Q

Cta(b=lam)(W/m2/K)

C6'a(b=lam)(W/m2/K)

Ctb'Ab(b=lam) Qln(b=lam) tflnl(b=lam)rQ

tfin2(b=lam)(°C)(W/K) (K)

- - 403 - 0.8 -1.10la(b=turb) OC'a(b=turb) (Xb’Ab(b=turb) Qln(b=turb) tfinl(b=turb) tfin2(b=turb)(W/m2/K) (W/m2/K) (W/K) (K) (°Q (°C)

20.8 24.3 3594 4.5 -3.5 -5.4Q (kW) = 3.53 (kW) = 3.03 F= 0.98

MASS FLUX OF WATER VAPOUR: (Axw )ln = 0.27 g/kga

(Axw)z(g/kga)

(Axw)o(g/kga)

Xwl

(g/kga)Xw",finl

(g/kga)*w2

(g/kga)Xw",fln2

(g/kga)0.25 0.28 3.75 3.49 3.25 2.97

Lewis: nip = • % • (Axw)ln = 5.01-10"6 kg/s/m2 = 18.0 kg/h/m2'/7fl

Mfr = —s- -TIa-Aq- (Axw)ln = 0.233-10-6 kg/s = 0.84 kg/hcpa'

- Mfi. ,Measured: thp = —-----— = 4.75-10 ^ kg/s/m2 = 17.1 kg/h/m2

‘ A)

M/r =■M/rT>

Mp = 17.7 kg,

m/> = 0.38 kg/m2

= 220-10-6 kg/s = 0.79 kg/h

Mdw = 14.2 kg,

Tc = 22.3 h

W^, =32.1 kWh,

= 125 s


243

Appendix F: Equations for pressure drop

This appendix provides the relations that have been used to calculate pressure drop. Fahlen(10) gives a number of alternative possibilities, including those referenced below.

FI Air-side pressure drop

Fl.l GranrydGranryd gives the following relations for finned-tube coils,

APac = 4Pl;2 + APtube + APfin (eT F1-L1)

where A/7^2 = the sum of inlet and outlet acceleration pressure drops, &Pfin = the pressure drop caused by friction along the fins, Aptube = the pressure drop caused by the presence of tubes.

Apac = Z-kz P‘“s Cl,2 + nl -Gtube + Cfi'fs"uflndu

(eq. FI. 1.2)

where Cjt = coefficient for the interaction between fins and tubes, z = number of continuous fins in the direction of air flow, kz = correction related to the number of successive fins,= number of tube rows in the longitudinal direction of air flow, dft = the hydraulic diameter of the air channel between fins ~2s, s = fin spacing, us = air velocity between fins,^ = friction factor for the flow channel between fins without tubes, Lfin = length of one fin in the direction of flow,

z Re?<1000 -2000 -3000 - 5000 - 8000

k, for in-line tube arrangement1 1 1 1 1 1 11 2 0.78 0.81 0.85 0.91 0.911 3 0.72 0.76 0.81 0.89 0.891 5 0.67 0.71 0.77 0.86 0.86

2 and 3 1 1 1 1 1 12 and 3 2 0.85 0.86 0.89 0.91 0.912 and 3 3 0.81 0.83 0.85 0.89 0.89

k, for staggered tube arrangement1 and 2 1 1 1 1 1 11 and 2 2 0.88 0.89 0.91 0.92 0.931 and 2 3 0.85 0.86 0.88 0.90 0.911 and 2 5 0.82 0.83 0.85 0.87 0.89


244

Cl ;2^-= —fl" as long as -^-<0.2

w s + 8fin w(eq. FI.1.3)

where 5^n = the fin thickness, w = the specific width of the coil (i.e. the fin pitch, Pfin), s = fin spacing.

Gtube C10 ' xt _1,(eq. FI. 1.4)

where £tube = coefficient of pressure loss caused by a tube bundle, gio = the coefficient of pressure loss caused by a tube bundle with 10 tube rows in the flow direction, and

The friction factor for fins without tubes is given by

fs ~ K ~fin \dh,s J

■Re* n'T (eq. FI. 1.5)

500 < Res < 2000: 2000 < Res < 7000: 7000 < Res < 20000:

ks = 22.5 msks = 3.35 msks = 0.577 ms

= 0.3 ns = 0.65 = 0.3 ns = 0.4 = 0.3 ns = 0.2

where d^s = 2s = the hydraulic diameter of the fin spacing, L^n = the length of one continuous fin in the flow direction, Res = the Reynolds number with respect to the hydraulic diameter d^,

Rej =us'dh us-2s

(eq. FI. 1.6)

The interaction between fins and tubes in the range 700 < Res < 10,000; 2.5 < xt <4.5:

Re,10000

I* 8.4 | ,I------ h 0.05 • |xz — 3|

xt(eq. FI. 1.7)

where kCjt = 1 for tubes in line and kCj-t = 1.05 in the case of staggered tubes. The exponent k varies with the number of tubes in a row according to the table below.

nj 1 2 3k 0.05 0.17 0.25

Valid range'. Finned-tube coils with 500 < Res < 20,000 and 3 < Lj-ir/dh s < 20.


245

F1.2 GlasGlas offers a simplified version of Granryd’s relations,

Apac = • pti •V (eq. Fl.2.1)Pfin

where Nrow is the number of tube rows in the direction of air flow and pfm is the fin pitch, i.e. the fin spacing plus the fin thickness.

F2 Brine-side pressure drop

F2.1 VDI-Warmeatlas: Laminar flowVDI-Warmeatlas recommends this relation,

APbc ~ fbc ^tube Pb 'ub

with

fbc —64

Rew

(eq.F2.Ll)

(eq. F2.1.2)

Valid range:Single phase laminar flow with Red < 2320 (in smooth tubes up to 8000).

F2.2 VDI-Warmeatlas: Turbulent flowVDI-Warmeatlas recommends equation F2.1.1 with the following friction factor for smooth tubes and turbulent flow

x 0.3164

Valid range: Single phase flow with 3000 < Red < 100

For the fully developed rough regime, with the relative

trough

dh

(eq. F2.2.1)

000 (turbulent)

roughness given by

(eq. F2.2.2)

/is given by-ji= = 21g[e]

VJbc(eq. F2.2.3)

and for the transitional regime between rough and smooth flow

(eq. F2.2.4)


246

Appendix G: Equations for heat transfer

This appendix provides the relations that have been used to calculate heat transfer.Fahlen(10) gives a number of alternative possibilities, including those referenced below.

G1 Air-side heat transfer

Gl.l GranrydGranryd gives the following relation for finned-tube air coils:

( AD)+ • as • 1 - (eq. Gl.1.1)

A) y

Often Ad«A0 and the equation can be approximated by

(eq. Gl.l.2)

where kza = factor accounting for the number of consecutive fins (kz=ia = 1), aD = coefficient of heat transfer on the outside of the tubes (diameter = D), as = coefficient of heat transfer on fins without the tubes (fin spacing = f), AD = total tube heat transfer area, A0 = total heat transfer area including fins, and Ca = factor accounting for the interaction between tubes and fins.

The interaction between fins and tubes is expressed by:

Ca —1.05 + fcRe • (kA ■ kn —1.05) (eq. Gl.l.3)

where kRe = factor depending on the Reynolds number (see table below), kA = factor depending on the area ratio (see table below), kn = factor depending on the number of tube rows per fin in the flow direction (see table below), a, = coefficient of heat transfer of fins with no tubes (see equation below), and a# = coefficient of heat transfer of tubes with no fins according to Schmidt.

In-line arrangement: kA = 1.92 • {Atube / Ay)0'13 (eq. Gl.l.4)

Staggered arrangement: kA = 2.39 • (Atube / Ay)019 (eq. Gl.1.5)

Equations Gl.1.4 and Gl.1.5 are valid for Ay/Ay < 0.15.

The heat transfer of fins without tubes is obtained from

(eq. Gl.l.6)


247

Valid range: Finned-tube coils with 500 < Res < 20,000 and 3 < L^/d^ < 20. Please note that Granryd's relations assume identical fin and tube temperatures. In the case of actual coils, the fin efficiency must be accounted for.

G1.2 GlasGlas proposes a much simplified relation, depending only on the face velocity of the coil:

aa = 20- Ma0,3 ua< 1.5 m/s (eq. 1.2.1)

aa =18-Ma0-6 ua> 1.5 m/s

G1.3 FahlenFahlen uses a weighted mean of the heat transfer coefficient calculated for the flow channel between fins and that of unfinned tubes in cross-flow

Vfin " Afin ‘ Mfin "**

^Ifiin ' A-fin *** A-D(eq.Gl.3.1)

where Op„ is calculated according to the Hausen (eq. G2.1.1) or Dittus-Boelter (eq. G2.2.1) equations for tube flow. The Reynolds number is based on the fin spacing, i.e. Res ~ 2s and aD is based on Grimison’s relations for bare tubes in cross-flow, i.e.

aD ~ clD

X»,/ua, max ' ^

Va,f .•Pr1/3 (eq. Gl.3.2)

Gl.3.2 overestimates heat transfer in the case of Nrow < 10 and cj is a corresponding correction factor (in this case Nrow = 4 and c/ = 0.90). Constants C and n will depend on the tube arrangement (in this case we have tubes in-line with p,/D = pi/D = 3.0 and hence C = 0.317 and n = 0.608).

Valid range: Finned-tube coils with 500 < Res < 2500


248

G2 Brine-side heat transfer

G2.1 Hausen: laminar flowQuoted by Sunden.

___ 0.0668 Re^-Pr—Nud =3.656+------------------------x

1+0.04 Re. Pr -2/3 (eq. G2.1.1)

with x being the distance from the inlet of the tube. For long tubes, the value approaches 3.656 asymptotically. In case of viscous liquids, exposed to large temperature differences, the relation can be improved by multiplying the right hand side with the following empirical correction based on viscosity at the bulk and wall temperatures respectively:

f(eq. G2.1.2)

Valid, range-. Single phase laminar flow, Red < 2300, constant wall temperature. According to VDI-Warmeatlas, it is possible to have laminar flow for Red up to 8000 in smooth tubes.

G2.2 Dittus-Boelter: turbulent flow

Quoted by Sunden, Kayansayan, Gates et al among others; evaluated at the bulk temperature.

~Nu^ = 0.023(Rerf )0-8 • Pr" (eq. G2.2.1)with

n = 0.4 if tw > tB and n = 0.3 if tw < tB

Gates, however, relates the following expression:

= 0.0243(Red )°'8 • Pr04 (eq. G2.2.2)

Valid range: Single phase turbulent flow with a constant wall temperature with 0.7 <Pr< 100, Red >10 000, L/d > 60. In this case we have Prb ~ 60-70, Red ~ 2000- 3000, Ud = 1300-2100.

The Dittus-Boelter relation is reportedly prone to over-estimating heat transfer.


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