paper calentador de agua estratificacion9

www.elsevier.com/locate/apthermeng

Applied Thermal Engineering 27 (2007) 1986–1995

Experimental and numerical study of thermal stratificationin a mantle tank of a solar domestic hot water system

Lana Kenjo a, Christian Inard b,*, Dominique Caccavelli c

a Universite de Tichrine, Faculte de Genie Mecanique et Electrique, Lattaquie, Syrian Arab Republicb LEPTAB, Universite La Rochelle, avenue Michel Crepeau, F17042 La Rochelle Cedex, France

c Centre Scientifique et Technique du Batiment, 290 route des Lucioles, BP 209, F06904 Sophia Antipolis Cedex, France

Received 2 March 2006; accepted 10 December 2006Available online 8 January 2007

Abstract

The simulation and the optimisation of the mantle tank of solar domestic hot water systems needs dynamic simulation over long peri-ods of time (e.g. 1 year). A model for such a mantle tank was developed by using the zonal approach. The dimensions of the zones aredetermined based on physical considerations. A mixing coefficient is identified to model the water flow in the mantle heat exchanger.Comparisons of the results of temperatures distribution of the model and of experiments show a difference <7% for three positionsof the inlet water flow in the mantle heat exchanger.� 2007 Elsevier Ltd. All rights reserved.

Keywords: Experiment; Modelling; Thermal stratification; Mantle tank; Solar domestic hot water system

1. Introduction

The solar-collector, the tank and its heat exchanger arethe essential components which contribute to optimise theperformance of solar domestic hot water (SDHW) systems.Numerous studies have shown that the thermal stratifica-tion inside the tank has a far-reaching effect on the perfor-mance of SDHW systems [1,2]. On one hand, this has theeffect of decreasing the temperature at the collector inletwhich increases its efficiency and, on the other hand, ofdecreasing the periods of operation of the auxiliary energysupply.

Thermal stratification within the tank may be achievedby several methods [3]:

(1) Heating of vertical walls which results in the creationof hot thermal boundary layers drawing hot fluid intothe upper part of the tank.

1359-4311/$ - see front matter � 2007 Elsevier Ltd. All rights reserved.

doi:10.1016/j.applthermaleng.2006.12.008

* Corresponding author. Tel.: +33 5 46 45 72 46; fax: +33 5 46 45 82 41.E-mail address: [email protected] (C. Inard).

(2) Heat exchange between the fluid contained in thetank and that circulating in a heat-exchanger care-fully placed inside or outside the tank.

(3) Direct inlet into the tank of hot fluid at suitableheights.

It has been shown that for a mantle heat exchanger thefirst system is the most efficient and the most economical [4]due to the large exchange surface and the good distributionof fluid from the collector inside the mantle.

Thermal stratification in storage tanks has been thesubject of various experimental and numerical studies[5–7]. It has been shown that the thermal stratificationwithin the tank depends on several factors such as heatlosses to the surrounding environment, heat conductionin the fluid and in the tank wall, mixing during chargingand discharging processes, geometry of inlet and outletports . . . [8–12].

It is well known that a high flow in the solar-collectorimproves its performance by increasing its heat removal fac-tor FR [13]. However, by using a smaller flow, about seventimes smaller than the normal flow, thermal stratification in

Nomenclature

A area (m2)C heat capacity (J/�C)Cp specific heat (J/kg �C)Dt diameter of inner tank (m)Et tank wall thickness (m)g gravitational acceleration (m/s2)Gm mantle gap width (m)Hm inner mantle height (m)Ht inner tank height (m)hc surface convective heat transfer coefficient

(W/m2 �C)hr surface radiative heat transfer coefficient

(W/m2 �C)m mass flow rate (kg/s)mBL mass flow rate of thermal boundary layer

(kg/m s)min mantle inlet mass flow rate (kg/s)mout mantle outlet mass flow rate (kg/s)Nu Nusselt numberPr Prandtl numberR thermal resistance (�C/W)Ra Rayleigh numberRc conductive thermal resistance in fluid (�C/W)

T temperature (�C)Ta ambient temperature outside the tank (�C)Tin mantle inlet fluid temperature (�C)Tout mantle outlet fluid temperature (�C)Tw wall temperature (�C)T1 ambient temperature for the thermal boundary

layer inside the tank (�C)t time (s)v velocity (m/s)(z, r) cylindrical co-ordinates (m)

Greek symbols

a thermal diffusivity (m2/s)b thermal volume expansion coefficient (1/K)d thermal boundary layer thickness (m)e long wave emissivityk thermal conductivity (W/m �C)m viscosity (m2/s)q density (kg/m3)r0 Stefan–Boltzmann constants mixing factorUconv convective heat flux (W)

L. Kenjo et al. / Applied Thermal Engineering 27 (2007) 1986–1995 1987

the tank is better and so the performance of the entire sys-tem (i.e. collector, heat exchanger and tank) is improved[14,15]. Moreover, this reduces the investment cost of thesystem (costs of pipes, pump, exchanger, etc.).

The size of SDHW system components may be opti-mised by using experiments. However, this approach isvery expensive. For this reason, the modelling approachmay be helpful. But to have a precise knowledge of thethermal stratification within the tank, which is a key factorin the SDHW systems, simulation tools must be able topredict precisely the inside distribution of the fluid in thetank and the heat exchanger. To do this, some authors[3,16] have used CFD modelling. Although this methodgives detailed and precise results, it needs enormousamounts of calculation time. So it becomes difficult tostudy the performance of systems over a long period oftime such as 1 year.

In this study, a simple method for predicting the thermalstratification within a tank heated by a mantle exchanger isproposed. In order to check the consistency of the numer-ical results, experiments have also been carried out.

2. Experimental study

Tests were carried out on a vertical mantle tank for adomestic hot water system. In order to accurately controlthe inlet conditions (temperature and flow) of the mantle,the primary fluid was provided by a boiler with a powerof 1.6 kW controlled by a PID regulator.

2.1. Experimental apparatus

Fig. 1 shows a view of the test mantle tank and Table 1gives its properties. The test mantle tank has been providedby the Swiss manufacturer Agena energies. The insulationthickness is selected by the manufacturer. It is noticeablethat the tank is well insulated compared to conventionalcommercial DHW tanks since the total heat loss coefficientis equal to 0.8 W/K.

Fig. 2 shows a sketch of the test mantle tank with theposition of the temperature sensors.

The fluid can be injected into the mantle at three levels(high, middle and low). A probe Pt 100 connected in afour-wire circuit was used to measure the ambient temper-ature with an accuracy of ±0.1 �C.

The primary circuit flow was measured using a massflowmeter which uses the principle of Coriolis force allow-ing the mass flow value to be obtained independently of allthe other parameters such as density, viscosity of the fluidor the flow profile. The measurement accuracy is ±0.2%.

The temperatures measured are: the inlet and the outlettemperatures of the primary circuit and the vertical distri-bution of the tank water temperature measured in sevenpoints (see Fig. 2). These measurements were taken usinga type T thermocouple (copper-constantan) with an accu-racy of ±0.5 �C. The same type of sensors were used tomeasure the vertical distribution of the outer surface tem-perature of the mantle wall in four points (see Figs. 1and 2).

Fig. 1. View of the test mantle tank.

Table 1Data for the test mantle tank and materials

Inner tank volume (l) 450Mantle volume (l) 46Inner tank volume over mantle (l) 90Inner tank volume inside mantle (l) 315Inner tank volume under mantle (l) 45Total height of inner tank (m) 1.72Total height of inner mantle (m) 1.21Diameter of inner tank (m) 0.577Tank wall thickness (m) 0.003Mantle wall thickness (m) 0.003Mantle gap width (m) 0.02Heat transfer area between mantle and tank (m2) 1.5Top insulation thickness (m) 0.15Side insulation thickness (m) 0.12Bottom insulation thickness (m) 0.00

Steel properties

Specific heat (J/kg �C) 500Density (kg/m3) 7800Thermal conductivity (W/m �C) 15

Insulation properties

Specific heat (J/kg �C) 800Density (kg/m3) 15Thermal conductivity (W/m �C) 0.041

T9

T7

T6

T11

T3

T10 T4

T8 T2

T5

T1

0.173 m

0.238 m

0.303 m

0.303 m

0.303 m

0.234 mmout

min

T in

Tout

Fig. 2. Sketch of the test mantle tank with the position of temperaturesensors.

1988 L. Kenjo et al. / Applied Thermal Engineering 27 (2007) 1986–1995

2.2. Experimental protocol

Three tests corresponding to the three inlet levels of thefluid into the mantle were carried out. Test no. 1 corre-sponds to an inlet at the higher level, test no. 2 at the mid-dle level and test no. 3 at the lower level.

The experimental procedure was the following. Thetank is initially at ambient temperature and perfectlymixed. At the initial time t = 0, the fluid inlet valve ofthe mantle is suddenly opened corresponding to a stepinput.

For the three tests, the operating conditions were

Ambient temperature: Ta = 18 �C ± 2 �C.Inlet temperature of the primary fluid: Tin = 43 �C ±2 �C.Inlet mass flow rate of the primary fluid: min = 64 kg/h ± 4 kg/h.

Each test lasted for 20 h and the time step of data acqui-sition was 5 min.

2.3. Experimental results

Figs. 3 and 4 give the time variations of temperaturesmeasured on the outer surface of the mantle wall (T1–T4) and in the tank water (T5–T11).

Although the rate of change of the curves is similar forall the tests, we can see the effect of the fluid inlet level inthe mantle on thermal stratification within it and in thetank.

As an example, the values of the temperature differences(T1–T4) and (T5–T10) measured at t = 5 h are given inTable 2.

It results that the lower the fluid inlet level is in the man-tle, the smaller is the thermal stratification both in the man-tle and in the tank. However, it should be noted that

Mantle wall test no 1

15

20

25

30

35

40

45

0 5 10 15 20Time (h)

Tem

per

atu

re (°

C)

T1exp

T2exp

T3exp

T4exp


20

25

30

35

40

45

0 10 20Time (h)

Tem

per

atu

re (°

C)

T1exp

T2exp

T3exp

T4exp


15

20

25

30

35

40

45

0 5 10 15 20Time (h)

Tem

per

atu

re (°

C)

T1exp

T2exp

T3exp

T4exp

Fig. 3. Measured temperatures on the outer surface of the mantle wall.

Tank test no 115

20

25

30

35

40

45

0 5 10 15 20Time (h)

Tem

per

atu

re (°

C)

Tank test no 3

15

20

25

30

35

40

45

0 5 10 15 20Time (h)

Tem

per

atu

re (

°C)

T5exp

T6exp

T7exp

T8exp

T9exp

T10exp

T11exp

Tank test no 2

15

20

25

30

35

40

45

0 5 10 15 20Time (h)

Tem

per

atu

re (°

C)

Fig. 4. Measured temperatures in the tank.


whatever the inlet level, the upper temperature of the outersurface of the mantle wall is always slightly greater than

others, in other words, that there is no inversion of the tem-perature gradient.

Table 2Temperature differences (T1–T4) and (T5–T10) measured at t = 5 h

T1–T4 (�C) T5–T10 (�C)

Test no. 1 10.5 12.2Test no. 2 8.4 9.3Test no. 3 5.2 5.5


The distribution of the fluid in the mantle is complexand was studied experimentally and numerically [16,17].For a tank initially perfectly mixed (T = 20 �C) and an inlettemperature of the fluid in the mantle above that of thetank (T = 50 �C), it was observed that the flow distributionin the mantle is governed by buoyancy with a reverse flowin the top part of the mantle [3]. That explains the phenom-ena observed considering that our experimental conditionsare very close to that of Shah [3].

Finally, we note that the temperature measured at thebottom of the tank (T11) increases very slowly. It seemsthat for this part of the tank, the heat transfer is mainlyconductive, as we will show in the theoretical modelling.

3. Numerical model of the mantle and the tank

To predict the thermal stratification in the tank, a sim-plified model which allows us to make simulations overlong periods with reasonable calculation times has beendeveloped. The modelling comprises three main parts:

(1) The mantle and the tank walls as well as their insula-tion (solid part).

(2) The fluid in the mantle and in the tank (fluid part).

z

axis of rotation

I

Ht

Rt

tank wall

tank water

T(I,J)

Fig. 5. Computational mesh of the soli

(3) The heat transfer between the solid part and the fluidpart.

The model was developed in the TRNSYS computingenvironment.

3.1. Modelling the solid part

In the solid part of the system, heat transfers are conduc-tive and the boundary conditions are the fluid temperatureand the outside ambient air temperature. The solid partconsists of the metal (mantle and tank walls) and the insu-lation (see Table 1). The method of finite differences usingcylindrical co-ordinates was used to solve numerically theheat conduction equation. An axis of symmetry allows thenumber of calculation nodes to be reduced. For numericalstability problems, an implicit scheme was used. Fig. 5 givesthe computational mesh adopted. The number of nodes isequal to 64.

Generally, the thermal balance of node i is written:

CidT i

dtþXl

j¼1

T i � T j

Rij¼ 0 ð1Þ

with l number of nodes in contact with node i.The resistances Rij may be relative to a conductive heat

transfer in the solid or to a convective heat transferbetween the solid and the inner fluid or outside ambient air.

3.2. Modelling the fluid part

To model the fluid, we have to distinguish between thefluid in the mantle and that in the tank.

r

J

insulation

mantle wall

mantle water

d domain for the numerical model.

min

min

min

τ minτ min

Fig. 6. Flow scenario of the fluid in the mantle (a: inlet at the higher level; b: inlet at the middle level; c: inlet at the lower level).


3.2.1. Modelling the fluid in the mantle

As previously mentioned (see Section 2.3), the flow fieldin the mantle is complex and depends on the inlet level. Totake into account the reverse flow which appears in the toppart of the mantle, a mixing factor s such as shown inFig. 6 is introduced.

Factor s is taken into account in the thermal balance ofthe zones considered.

Once the entire model was implemented, we identifiedthe optimum values of factor s by using the measuredand calculated temperatures of the outer surface of themantle wall (T1–T4).

To do that, the following root mean square errors(RMSE) have been calculated:

ETi ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiPni¼1ðT measured;i � T calculated;iÞ2

n

sð2Þ

with n = 240, total number of values for temperature Ti.Table 3 gives the values of the RMSE E ¼

P41ETi for the

four temperatures considered (T1–T4) as a function of thefactor s and for the middle and the lower inlet levels (testnos. 2 and 3).

The optimum values of s obtained are equal to 0.5 fortest no. 2 and 0.9 for test no. 3, respectively. These valueshave been adopted in the remainder of the study. However,the relatively high values of E show the limits of the modelused. Hence, additional studies are needed and the imple-mentation of a two-dimensional fluid model will certainlyimprove the results. The problem will be when identifyingthe exchanges of mass flow between the various zones ofthe fluid.

Table 3Values of RMSE E (�C) as a function of s for test nos. 2 and 3

s 0 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Test no. 2 7.6 6.3 5.7 5.3 5.1 5.2 5.5 6.0 6.6Test no. 3 11.6 10.3 9.8 9.4 9.1 8.9 8.6 8.4 8.2

3.2.2. Modelling the fluid in the tank

When the tank wall is heated by the fluid into the mantle,hot thermal boundary layers develop along the inner sur-face of the vertical tank wall. This will have the effect ofcausing an upward flow along the inner tank wall and adownward flow in its core. This phenomenon was recentlyconfirmed experimentally and numerically by Knudsenet al. [18].

To model this phenomenon, the zonal method, used fora long time for the prediction of the thermo-convectivefield inside buildings, was adopted [19,20]. The methodconsists of splitting the domain studied into zones anddescribing the driving flows, here the thermal boundarylayers, by integral method. Fig. 7 gives the flow scenarioof the fluid adopted for the tank. To be able to apply theintegral method, the velocity and temperature profiles ofthe thermal boundary layer proposed by Bejan [21] wereused:

Velocity: vðr; zÞ ¼ 1:86vmaxðzÞ 1� rdðzÞ

� �4 rdðzÞ

� �17

ð3Þ

Temperature:

T ðr; zÞ � T1 ¼ ðT w � T1Þ 1� rdðzÞ

� �17

!ð4Þ

Solving the continuity equation, conservation of momen-tum and energy equations by the integral method enables usto express the thickness d(z), the maximum velocity vmax(z)and the mass flow rate mBL(z) of the boundary layer:

dðzÞ ¼ 0:566Ra

1þ 0:494Pr23

� �� 110

Pr�35z ð5Þ

vmaxðzÞ ¼ 2:21Ra

1þ 0:494Pr23

� �12

Pr�12mz�1 ð6Þ

mBLðzÞ ¼ 0:098aqPr

115

1þ 0:494Pr23

� �25

gbma

� �25

T w � T1ð Þ25z

65 ð7Þ

upward flow (hot thermal boundary layer)

downward flow in the core of the tank

Fig. 7. Flow scenario of the fluid in the tank.


Eq. (5) enables us to set an order of magnitude to the thick-ness of the boundary layer. The mass flows of the boundarylayer and in the core of the mantle (downward flow) maybe calculated by solving the system of mass balance equa-tions. Finally, the thermal balance enables the tempera-tures of each zone to be calculated. Generally, thethermal balance of a fluid zone in the tank is written as

CidT i

dtþPn

j¼1T i � T j

Rc;ijþ Uconv;i þ

Xk

j¼1

mijCpðT i � T jÞ ¼ 0

ð8Þwith mij mass flow rate between zones i and j.

The convective heat flux exchanged between the fluidand the tank wall is given by

Uconv;i ¼ hc;iAiðT i � T w;iÞ ð9Þ

The expression for hc are given in Section 3.3.Moreover, it should be noted that temperature node T11

only exchanges by conduction with the surrounding fluidnode i.e. T10 given the flow scenario adopted (see Fig. 7).

3.3. Modelling the surface heat transfers

The fluid/solid surface heat transfers are done within themantle, the tank and between the outer surface of the insu-lation and the ambient air. Heat transfers are determinedby knowing the surface heat transfer coefficients.

For the vertical walls of the tank and the mantle, verycomplete studies were made by Shah [22].

3.3.1. Surface convective heat transfer coefficient of the

vertical tank wall

The relation proposed by Shah [22] is

NuðzÞ ¼ 4:501� 3:103Dt

H t

� �gbðT w � T1Þz3

maz

H t

� �0:19

ð10Þ

After integration over height Ht, the expression for theaverage convective heat transfer coefficient is obtained:

hc;i ¼ 1:315kH�0:24t 4:501� 3:103

Dt

H t

� �gbðT wi � T iÞ

H tma

� �0:19

ð11Þ

3.3.2. Surface convective heat transfer coefficientof the vertical mantle wall

The relation proposed by Shah [22] is the following:

NuðzÞ ¼ 0:28Gm

Dt

2þ Et

!�0:63gbðT w � T1Þz3

maz

H m

� �0:28

ð12Þ

In the same way, after integration over height Hm, theexpression for the average convective heat transfer coeffi-cient is obtained:

hc;i ¼kH 0:12

m

3

Gm

Dt

2þ Et

!�0:63gbðT wi � T i

maHm

� �0:28

ð13Þ

3.3.3. Surface convective heat transfer coefficient

at the top and the bottom tank walls

For these walls, the correlations in relation to a horizon-tal plate with the face heated above for the bottom wall andthe face heated below for the top wall are used [21]:

Top wall: hc;i ¼ 0:15kgbðT w;i � T iÞ

ma

� �13

ð14Þ

Bottom wall: hc;i ¼ 0:38kD�1

4t

gbðT w;i � T iÞma

� �14

ð15Þ

3.3.4. Convective and radiative heat transfer coefficients

of the outer insulation surfacesThe outer surface of the insulation exchanges by convec-

tion with ambient air and by long wave radiation with the


surrounding walls. For the radiative heat transfer, weassume that the walls are in thermal equilibrium with theambient air. The surface radiative heat transfer coefficientis expressed by

hr;i ¼ 4er0

T w;i þ T a

2þ 273:15

� �3

ð16Þ

For the convective heat transfer coefficient of the outer ver-tical surface, we use the relation proposed by Mc Adams[23] for a plane vertical plate because the thickness of thethermal boundary layer is negligible compared with thediameter of the tank:

hc;i ¼ 0:13kgbðT w;i � T aÞ

ma

� �13

ð17Þ

T5

1520

2530

3540

45

0 5 10 15 20Time (h)

Tem

per

atu

re (°

C)

T7

15

20

25

30

35

40

45

0 5 10 15 20Time (h)

Tem

per

atu

re (°

C)

T9

15

20

25

30

35

40

45

0 5 10 15 20Time (h)

Tem

per

atu

re (°

C)

T11

15

20

25

30

35

0 10 20

Time (h)

Tem

per

atu

re (°

C)

Fig. 8. Measured and calculated temp

As for the upper and the lower outer faces of the insula-tion, the thermal configuration is similar to that encoun-tered in the tank. So Eqs. (14) and (15) are used.

Writing the thermal balance at each temperaturenode results in an differential equations system of theform:

½C� d~T

dtþ ½M �~T ¼ 0 ð18Þ

Solving the system in TRNSYS for a time step of 5 min(equal to the acquisition time step for the experimentaldata) enables the temperature field to be calculated.Because of the non-linearity of some exchanges, an itera-tive procedure is used with a convergence criterion on tem-peratures equal to 0.01 �C.

T6

1520

2530

3540

45

0 5 10 15 20Time (h)

Tem

per

atu

re (°

C)

T8

15

20

25

30

35

40

45

0 5 10 15 20Time (h)

Tem

per

atu

re (°

C)

T10

15

20

25

30

35

40

45

0 5 10 15 20Time (h)

Tem

per

atu

re (°

C)

T measured

T calculated without boundary layer model

T calculated with boundary layer model

eratures in the tank for test no. 1.


4. Comparison between numerical and experimental results

Test nos. 1, 2 and 3 were simulated considering asboundary conditions the ambient temperature, the temper-ature and the mass flow rate of the fluid entering into themantle measured for these tests. Moreover, in order toprove the suitability of the model of the thermal boundarylayer in the tank, two simulations with and without thethermal boundary layer model for test no. 1 have been car-ried out. For the first case, the mass flows mij of Eq. (8)were neglected and only seven temperature nodes in thetank were considered; for the second case, all 19 tempera-ture nodes were considered (see Fig. 7).

Fig. 8 gives the measured and the calculated tempera-tures in the tank for test no. 1. Fig. 9 gives the differencesbetween the measured and the calculated values.

The suitability of the thermal boundary layer modelappears clearly on these figures. Thus, without the bound-ary layer model, the heat transfers in the tank are made by

-10

-5

0

5

10

15

20

25

0 5 10 15 20

Time (h)

Tm

easu

red

- T

calc

ula

ted

(°C

)

T5 T6 T7 T8

T9 T10 T11

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

0 5 10 15 20

Time (h)

Tm

easu

red

- T

calc

ula

ted

(°C

)

T5 T6 T7 T8

T9 T10 T11

Fig. 9. Difference between the measured and the calculated temperatures (a: tmodel, c: test no. 2 with boundary layer model, d: test no. 3 with boundary la

convection with the tank wall and only by conductionwithin the fluid. Hence, the fluid temperatures are underes-timated in the upper part of the tank (T5 and T6) whilethey are overestimated in the lower part of the tank (T 7–T11). The maximum difference observed is of the order of23 �C (see Fig. 9). The thermal boundary layer modelenables more realistic description of the thermal stratifica-tion which is confirmed by the experimental results [18].Thus, the maximum difference observed is reduced to2.5 �C (see Fig. 9). Finally, it should be noted that the max-imum difference observed for temperature T11 is of theorder of 0.8 �C which confirms the hypothesis made forheat exchanges between this temperature node and theothers, being uniquely conductive heat transfer within thefluid.

Table 4 gives the values of ETi for the two models i.e.without and with the boundary layer (BL) model. The totalRMSE is virtually divided by 10 between the two mod-els. Moreover, the RMSE values obtained without the

-3

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

0 5 10 15 20

Time (h)

Tm

easu

red

- T

calc

ula

ted

(°C

)

T5 T6 T7 T8

T9 T10 T11

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

0 5 10 15 20

Time (h)

Tm

easu

red

- T

calc

ula

ted

(°C

)

T5 T6 T7 T8

T9 T10 T11

est no. 1 without boundary layer model, b: test no. 1 with boundary layeryer model).

Table 4Values of ETi (�C) for test nos. 1, 2 and 3

T5 T6 T 7 T8 T9 T10 T11 Total

Test no. 1 without boundary layer model 19.7 13.5 3.3 1.9 1.6 1.1 2.1 43.2Test no. 1 with boundary layer model 0.4 0.5 0.5 0.6 1.0 1.2 0.4 4.6Test no. 2 with boundary layer model 1.1 1.2 1.4 1.0 0.4 1.8 0.5 7.4Test no. 3 with boundary layer model 0.5 0.6 0.8 0.8 0.7 1.7 0.7 5.8


boundary layer model clearly increase with the height ofthe tank showing that the flow distribution within the tankis not well described. Conversely, the RMSE values calcu-lated using the boundary layer model are nearly constantover the height of the tank. In this case, the upward flownear the tank wall induced by the heat transfer from thehot fluid in the mantle is accurately performed by themodel. Given these results, the model with boundary layerhas been adopted.

Fig. 9 also gives the differences between the measuredand calculated temperatures for test nos. 2 and 3 and Table4 the corresponding values of ETi. The time variations ofthe differences are similar to that obtained for test no. 1and the RMSE values are nearly constant over the heightof the tank but the values are slightly higher. As previouslymentioned, the improvement of the flow model in the man-tle should reduce the differences between the experimentaland the numerical values. However, the discrepanciesobserved remain reasonable.

5. Conclusion

The thermal stratification in the mantle tank of a solardomestic hot water system can be modelled with reason-able precision (<7%) by using a zonal model. The modelof the flow in the thermal boundary layer increases consid-erably the precision of the model. The flow in the mantle ismodelled by a mixing coefficient s; its value is identifiedfrom experiments and is specific for a mantle and a flowrate.

The advantages of the zonal model is that it is muchmore faster than CFD modelling and describes the flowin the boundary layer as opposed to lumped models thatconsider only the conduction within the fluid and the con-vection along the walls. This model may be used fordynamic simulations over a long period such as 1 year.

One of the perspectives of this work is to improve themodel of the flow distribution in the mantle which is verysimplified at the current time. Finally, we plan toconnect the mantle tank model to a solar-collector modelin order to study the annual performance of the entiresystem.

References

[1] C.W.J. Van Koppen, J.P.S. Thomas, W.B. Veltkamp, The actualbenefits of thermally stratified storage in a small and medium sizesolar systems, in: Proceedings of ISES Solar World Congress,Atlanta, USA, 1979, pp. 579–580.

[2] S. Furbo, S.E. Mikkelsen, Is low-flow operation an advantage forsolar heating systems? in: Proceedings of ISES Solar World Congress,Hamburg, vol. 1, 1987, pp. 962–966.

[3] L.J. Shah, Investigation and modeling of thermal conditions in low-flow SDHW systems, Ph.D. thesis, Department of Buildings andEnergy, Technical University of Denmark, Report R-034, 1999.

[4] S. Furbo, Optimum design of small DHW low flow solar heatingsystems, in: Proceedings of ISES Solar World Congress, Budapest,Hungary, 1993.

[5] M.K. Kandari, Thermal stratification in hot storage-tanks, Appl.Energy 35 (1990) 299–315.

[6] N.M. Al-Najem, A.M. Al-Marafie, K.Y. Ezuddin, Analytical andexperimental investigation of thermal stratification in storage tank,Int. J. Energy Res. 17 (1993) 77–88.

[7] M.S. Shin, H.S. Kim, D.S. Jang, S.N. Lee, H.G. Yoon, Numericaland experimental study on the design of a stratified thermal storagesystem, Appl. Therm. Eng. 24 (2004) 17–27.

[8] Y.H. Zurigat, A.J. Ghajar, P.M. Moretti, Stratified thermal storage-tank inlet mixing characterization, Appl. Energy 30 (1998) 99–111.

[9] Y.H. Zurigat, P.R. Liche, A.J. Ghajar, Influence of inlet geometry onmixing in thermocline thermal-energy storage, Int. J. Heat MassTrans. 34 (1) (1991) 115–125.

[10] J.V. Berkel, Mixing in thermally stratified energy stores, Solar Energy58 (4–6) (1996) 203–211.

[11] N.M. Al-Najem, M.M. El-Refae, A numerical study for the predic-tion of turbulent mixing factor in thermal storage tanks, Appl.Therm. Eng. 17 (12) (1997) 1173–1181.

[12] A.A. Hezagy, M.R. Diab, Performance of improved design forstorage-type domestic electric water heaters, Appl. Energy 71 (4)(2002) 287–306.

[13] J.A. Duffie, W.A. Beckman, Solar Engineering of Thermal Processes,Wiley Intersciences, New York, 1980.

[14] K.G.T. Hollands, M.F. Lighstone, A review of low-flow, stratifiedtank solar water heating systems, Solar Energy 43 (1989) 97–105.

[15] C. Cristofari, G. Notton, P. Poggi, A. Louche, Influence of the flowrate and the tank stratification degree on the performance of a solarflat-plate collector, Int. J. Therm. Sci. 42 (2003) 455–469.

[16] L.J. Shah, G.L. Morrison, M. Behnia, Characteristics of verticalmantle heat exchangers for solar heaters, Solar Energy 67 (1999)79–91.

[17] S. Knudsen, S. Furbo, Thermal stratification in vertical mantle heat-exchangers with application to solar domestic hot-water systems,Appl. Energy 78 (2004) 257–272.

[18] S. Knudsen, G.L. Morrison, M. Behnia, S. Furbo, Analysis of theflow structure and heat transfer in a vertical mantle heat exchanger,Solar Energy 78 (2005) 281–289.

[19] C. Inard, A. Meslem, P. Depecker, Energy consumption and thermalcomfort in dwelling-cells: a zonal model approach, Build. Environ. 33(1998) 279–291.

[20] Z. Ren, J. Stewart, Simulation air flow and temperature distributioninside buildings using a modified version of COMIS with sub-zonaldivisions, Energy Build. 35 (2003) 271–275.

[21] A. Bejan, Convection Heat Transfer, second ed, John Wiley & Sons,New York, 1995.

[22] L.J. Shah, Heat transfer correlations for vertical mantle heatexchangers, Solar Energy 69 (2000) 157–171.

[23] W.H. Mc Adams, Heat Transmission, third ed, McGraw Hill, NewYork, USA, 1954.

paper calentador de agua estratificacion9

Documents