saif abdulameer thesis prepared for the degree of master .../67531/metadc...field validation of zero...

FIELD VALIDATION OF ZERO ENERGY LAB WATER-TO-WATER GROUND

COUPLED HEAT PUMP MODEL

Saif Abdulameer

Thesis Prepared for the Degree of

MASTER OF SCIENCE

UNIVERSITY OF NORTH TEXAS

May 2016

APPROVED:

Young Tao, Major Professor and Chair of the Department of Mechanical & Energy Engineering.

Kyle Horne, Committee Member Weihuan Zhao, Committee Member Costas Tsatsoulis, Dean of the College of

Engineering Mark Wardell, Dean of the Toulouse

Graduate School Assistant Professor, MEEN Department

Abdulameer, Saif. Field Validation of Zero Energy Lab Water-to-Water Ground

Coupled Heat Pump Model. Master of Science (Mechanical and Energy), May 2016, 59

pp., 8 tables, 29 figures, references, 34 titles.

Heat pumps are a vital part of each building for their role in keeping the space

conditioned for the occupant. This study focuses on developing a model for the ground-

source heat pump at the Zero Energy lab at the University of North Texas, and finding

the minimum data required for generating the model. The literature includes many

models with different approaches to determine the performance of the heat pump. Each

method has its pros and cons. In this research the equation-fit method was used to

generate a model based on the data collected from the field. Two experiments were

conducted for the cooling mode: the first one at the beginning of the season and the

second one at the peak of the season to cover all the operation conditions. The same

procedure was followed for the heating mode. The models generated based on the

collected data were validated against the experiment data. The error of the models was

within ±10%. The study showed that the error could be reduced by 20% to 42% when

using the field data to generate the model instead of the manufacturer’s catalog data.

Also it was found that the minimum period to generate the cooling mode model was two

days and two hours from each experiment, while for the heating mode it was four days

and two hours from each experiment.

ii

Copyright 2016

by

Saif Abdulameer

iii

ACKNOWLEDGEMENT

I want to thank God for guidance through my life and study, and for providing me

this opportunity and granting me the capability to proceed successfully.

I would like to express my deepest appreciation and thanks to my advisor Dr. Yong

Tao, for his generous and continues support through this work. Thanks for your patient

and motivation during my dark hours. This project would not be possible without his

immense knowledge, wisdom and leadership.

I would like to extend my gratitude to Dr. Jungyon Mun for helping me

understanding the modeling and programing of EnergyPlus, and for keeping his door

open whenever I needed help.

Finally I wish to thank my fellow lab mates and friends Suraj, Pooya, Caleb and

Rodolfo for the stimulating discussions, for their support and for all the good time we had

together

iv

TABLE OF CONTENTS

ACKNOWLEDGEMENT .................................................................................................. iii

LIST OF TABLES ............................................................................................................vi

LIST OF FIGURS ........................................................................................................... vii

NOMENCLATURE ..........................................................................................................ix

CHAPTER 1 INTRODUCTION ........................................................................................ 1

1.1 Background ............................................................................................................ 1

1.2 Objective ................................................................................................................ 2

1.3 Impact of Research ................................................................................................ 3

CHAPTER 2 LITERATURE REVIEW .............................................................................. 4

2.1 Allen and Hamilton Model ...................................................................................... 4

2.2 Scarpa et al. Model ................................................................................................ 6

2.3 Stefanuk et al. Model ........................................................................................... 10

2.4 Jin and Spitler Model............................................................................................ 11

2.5 Lash Model .......................................................................................................... 14

2.6 Shenoy Model ...................................................................................................... 16

2.7 Tang Model .......................................................................................................... 17

CHAPTER 3 METHODOLOGY ..................................................................................... 20

3.1 Parameters Selection ........................................................................................... 20

3.2 Water-to-Water Heat Pump EnergyPlus Model Modification ................................ 23

3.3 Zero Energy Lab Testing Facility ......................................................................... 25

3.4 Experiment Setup ................................................................................................ 26

3.5 Experiments ......................................................................................................... 29

3.6 Data Collection ..................................................................................................... 30

3.7 Linear Regression Analysis .................................................................................. 32

3.8 Coefficients Generation........................................................................................ 33

3.9 EnergyPlus ........................................................................................................... 33

v

3.10 Water-to-Water Curve Fit Model Simulation in EnergyPlus ................................ 35

CHAPTER 4 MODEL VERIFICATION .......................................................................... 37

4.1 Cooling Mode Verification .................................................................................... 37

4.2 Heating Mode Verification .................................................................................... 40

4.3 EnergyPlus Simulation ......................................................................................... 43

4.3.1 EnergyPlus Simulation Using Field Data Model ............................................. 44

4.3.2 EnergyPlus Simulation Using Catalog Data Model ........................................ 47

4.5 Results ................................................................................................................. 49

4.6 Error Analysis ....................................................................................................... 50

CHAPTER 5 CONCLUSION AND RECOMMENDATION ............................................. 53

5.1 Conclusions ......................................................................................................... 53

5.2 Future Work ......................................................................................................... 54

REFERENCES .............................................................................................................. 56

vi

LIST OF TABLES

Table 3.1: Heat pump models in EnergyPlus ................................................................ 23

Table 4.1: Cooling capacity Error for different models................................................... 40

Table 4.2: Cooling power Error for different models ...................................................... 40

Table 4.3: Heating capacity Error for different models .................................................. 43

Table 4.4: Heating power Error for different models ...................................................... 43

Table 4.5: EnergyPlus field coefficients ......................................................................... 43

Table 4.6: EnergyPlus field coefficients ......................................................................... 44

Table 4.7: Model error analysis ..................................................................................... 52

vii

LIST OF FIGURES

Figure 2.1: Water chiller system schematic ..................................................................... 6

Figure 2.2: scheme of model input/output. ...................................................................... 9

Figure 2.3: Water to air heat pump schematics ............................................................. 15

Figure 3.1: Water Furnance heat pump catalog data .................................................... 21

Figure 3.3: Heat pump capacity VS load side temp....................................................... 22

Figure 3.2: Heat pump capacity VS load side temp....................................................... 22

Figure 3.5: Heat pump power VS source side temp ...................................................... 22

Figure 3.4: Heat pump power VS load side temp .......................................................... 22

Figure 3.6: Zero Energy lab HVAC system drawing ...................................................... 25

Figure 3.8: Fluxis F601 flow meter installation .............................................................. 28

Figure 3.9: WATTNODE PULSE energy meter installation ........................................... 29

Figure 3.10: Loop reaction time for cooling mode ......................................................... 31

Figure 3.12: Multiple linear regression. ......................................................................... 32

Figure 3.13: EnergyPlus structure ................................................................................. 34

Figure 3.14: Water-to water heat pumps simulation lay out .......................................... 35

Figure 4.3: Validating 4 days 2 hours cooling capacity model ....................................... 39

Figure 4.5: Validating 10 days 10 hours heating capacity model .................................. 41

Figure 4.6: Validating 10 days 10 hours heating power model ...................................... 41

Figure 4.7: Validating 8 days 2 hours heating capacity model ...................................... 42

Figure 4.8: Validating 8 days 2 hours heating power model .......................................... 42

Figure 4.9: Field data model validation for cooling capacity simulation ......................... 45

Figure 4.11: Field data model validation for heating capacity simulation....................... 46

Figure 4.12: Field data model validation for heating power simulation .......................... 46

viii

Figure 4.13: Catalog data model validation for cooling capacity simulation .................. 47

Figure 4.14: Catalog data model validation for cooling power simulation ...................... 48

Figure 4.15: Catalog data model validation for heating capacity simulation .................. 48

Figure 4.16: Catalog data model validation for heating power simulation ..................... 49

Figure 4.17: Single day cooling capacity error analysis............................................... 511

Figure 4.18: Single day heating capacity error analysis .............................................. 511

ix

NOMENCLATURE

Cp Water specific heat

m Mass flow rate

Powerc Cooling power

Powerc,ref Cooling reference letter

Qc Cooling capacity

Qc,ref Reference cooling capacity

Qh heating capacity

Qh,ref Reference heating capacity

QL Load heat transfer

Qsource,c Cooling source heat transfer

Qsource,c,ref Cooling reference source heat transfer

Qsource,h Heating source heat transfer

Qsource,h,ref Heating reference source heat transfer

TL in Inlet load temperature

Tref 283 K

TS in Inlet Source temperature

VL Load side flowrate

VS Source side flowrate

CHAPTER 1

INTRODUCTION

The rapid increase in energy costs in the last decades draws more attention to find

alternative solutions for the conventional space condition units. Both building simulation

and actual utility bills show a great impact of the space heating and cooling on energy

usage. The ground source heat pumps use the ground as a source or sink for heat

because its temperature is more stable than the air temperature, leading to more energy

saving. While integrating the heat pump into simulation programs such as Energyplus is

based on the catalog data that is collected from laboratories to determine the unit

performance in partial and full load. This work offers a protocol to extract the data from

the field and generate a model for the heat pump based on the data.

1.1 Background

Heat pumps are a vital part of each building for their role in keeping the space

conditioned for the occupant. Heat pumps have a great impact on the utility bill, so

modeling them is the point of interest for many researchers. These models fall in a wide

spectrum ranging between curve fit models and deterministic models. Curve fit models

deal with the heat pump as a black box, and a model could be generated depending on

the catalog data. These models are simple and do not need a long time for the simulation.

On the other hand, there are the complicated deterministic models that are based on the

thermodynamic law and need data for each component of the heat pump, which may not

be available. Applying these models provides more accurate results but consumes more

time for the simulation. In addition, there are models that fall in between and get the

1

advantage of both methods. Furthermore, there are numerical models that employ

iterative solvers and catalog data to determine the heat pump performance.

1.2 Objective

The focus of this research is to generate an equation fit model (which will be

referred as field data model) for a ground source water-to-water heat pump based on data

collected from the field and find the minimum time required for data collection. The model

will predict the performance of the heat pump capacity and power in both heating and

cooling modes. This study would provide a good tool for simulating aged heat pumps

when no catalog data is available or performance is degraded. Also it will determine the

actual performance of the equipment to help engineers to make the decision of

replacement or maintenance.

There are many approaches to simulate unitary heat pumps. Therefore, existing

models in EnergyPlus along with other models developed by other researchers are

discussed in Chapter 2. The data collection from the field and model development are

discussed in Chapter 3. The model was modified based on previous researchers’ models

so the coefficients could be generated based on constant flow rate. Two experiments

were conducted for each mode, one at the beginning of the season and the second one

at the peak of the season. The results of the models were described in Chapter 4 in

addition to the simulation results in EnergyPlus using the coefficients that were generated

based on field data and compared to the EnergyPlus simulation results of coefficients

generated from manufacturer catalog data. Finally, the results of the models were

discussed in Chapter 5 with recommendation for future work.

2

1.3 Impact of Research

The field model presented in this study will help in improving the results of energy

simulation process especially for the installed heat pumps in existing buildings. For

example this method could be used in performing the base line energy simulation for an

existing building to acquire a LEED Green Building certification that proves the

sustainability of the structure. By utilizing this model the base line energy simulation

results would be closer to the actual performance. Most of the current methods perform

the heat pumps simulation based on the catalog data which is recorded in a laboratory

environment and often over estimating the performance leading to inaccurate results.

Also the field model could help the mechanical, electrical and plumping engineers (MEP)

to evaluate the efficiency of their designs based on the actual operational conditions.

Furthermore the heat pump manufacturers could use this study to evaluate the long-term

performance of heat pumps beyond the laboratory conditions.

3

CHAPTER 2

LITERATURE REVIEW

The heat pump performance accuracy is a challenge for the HVAC designers and

energy auditors because it depends on the boundary conditions. This problem led to the

development of many models, each one with a different approach and requirements. The

energy simulation programs always prefer the simple models that do not demand many

inputs for the ease of use and less simulation time, but that is in the favor of results

accuracy. Implementing complex models to perform the simulation faces the obstacle of

data availability as the heat pump manufacturers do not provide comprehensive data in

the catalog. These models provide more accurate results but require longer time to

simulate. A literature review reveals the pros and cons of the existing models.

2.1 Allen and Hamilton Model

This model was developed by Allen and Hamilton (1983) to model a steady state

reciprocation water chiller in full and part load performance. They generated this model

by using catalog data only, treated the unit as one component, and did not use any

internal pressures or temperatures. Figure 2.1 shows the components of the water chiller

system and the parameters used to generate the model. Basic heat transfer laws could

have been used to find the heat transfer through the evaporator and the condenser.

However, the author used a six-term polynomial to find these values as follow.

Evaporator heat transfer

𝑄𝐸 = 𝑏1𝑇𝐸2 + 𝑏2𝑇𝐶2 + 𝑏3𝑇𝐸2𝑇𝐶2 + 𝑏4𝑇𝐸22 + 𝑏5𝑇𝐶2

2 + 𝑏6 (2.1)

Compressor polynomial

𝑄𝐸 = 𝑏1𝑇𝐸2 + 𝑏2𝑇𝐶2 + 𝑏3𝑇𝐸2𝑇𝐶2 + 𝑏4𝑇𝐸22 + 𝑏5𝑇𝐶2

2 + 𝑏6 (2.2)

4

The energy balance for the system is described by the following equations.

𝑄𝐸 = 𝑀𝐸 ∙ 𝐶𝑝 ∙ (𝑇𝐸1 − 𝑇𝐸2) (2.3)

𝑄𝐶 = 𝑀𝐶 ∙ 𝐶𝑝 ∙ (𝑇𝐶1 − 𝑇𝐶2) (2.4)

𝑄𝐶 = 𝑄𝐸 + 𝑃 (2.5)

Where

b1-b12 Coefficients fitted by polynomial regression

TE1,TE2 Evaporator water entering and leaving temperature

TC1,TC2 Condenser water entering and leaving temperature

Cp Specific heat at constant pressure

P Compressor Power

QE Evaporator heat transfer rate

QC Condenser heat transfer rate

mE Evaporator mass flow rate

mC Condenser mass flow rate

The polynomial constant coefficients B1-B12 are determined by regression

approach. The performance of the water chiller represented by energy rates QC and QC

and leaving water temperature TC2 and TE2 is determined by solving the above five

equations and providing the inlet evaporator temperature TE1 with the mass flow rate ME

and condenser inlet temperature TC1 with the mass flow rate MC.

5

Figure 2.1: Water chiller system schematic

2.2 Scarpa et al. Model

Scarpa et al. (2012) proposed a numerical model to simulate a chiller driven by

volumetric compressor or a vapor compression-based heat pump. Employing an iterative

solver and boundary conditions, the model could predict the thermodynamic inverse

cycle. However, the model is derived from the catalog data, and it is able to determine

the behavior of the heat pump under boundary conditions far from the ones it is derived

from by utilizing the user side and ambient side heat flow rates and electrical power

consumption, under boundary conditions. The model runs in two calculation steps: the

first one is determination of the basic parameters of the specific heat pump from catalog

data as shown in Figure 2.2, and the output would be the parameter that is used in the

second step as shown in Figure 2.2. The equations used in this phase are as follow:

Compressor power

Condenser

Expansion valve

TE2

Compressor

TC1

TE1

Evaporator

TC2 MC

ME

P

6

��𝐶𝑜𝑚𝑝𝑟𝑁𝑜𝑚 (

��𝐼𝑛𝑡𝑁𝑜𝑚

𝐶𝑂𝑃𝑁𝑜𝑚 − ��𝐴𝑢𝑥𝑁𝑜𝑚) . 𝜂𝑀𝑜𝑡𝑜𝑟 (2.6)

Computing the fluids flow rate at the source side and the sink side from the catalog

data.

��𝑆𝐹:𝐼𝑛𝑡𝑁𝑜𝑚 =

𝑄𝐼𝑛𝑡𝑁𝑜𝑚

𝐶𝑝,𝑆𝐹:𝐼𝑛𝑡.|Ɵ𝑆𝐹:𝐼𝑛𝑡,𝑂𝑢𝑡𝑁𝑜𝑚 −Ɵ𝑆𝐹:𝐼𝑛𝑡,𝐼𝑛

𝑁𝑜𝑚 |(2.7)

��𝑆𝐹:𝐸𝑥𝑡𝑁𝑜𝑚 =

𝑄𝐸𝑥𝑡𝑁𝑜𝑚

𝐶𝑝,𝑆𝐹:𝐸𝑥𝑡 .|Ɵ𝑆𝐹:𝐼𝑛𝑡,𝑂𝑢𝑡𝑁𝑜𝑚 −Ɵ𝑆𝐹:𝐸𝑥𝑡,𝐼𝑛

𝑁𝑜𝑚 |(2.8)

The effectiveness index of the heat exchanger is the only user assumption, and it is

selected from a scale of 0 to 10. Then the thermal effectiveness is calculated for the

evaporator and condenser

ԑ𝐼𝑛𝑡 =|Ɵ𝑆𝐹:𝐼𝑛𝑡,𝐼𝑛

𝑁𝑜𝑚 −Ɵ𝑆𝐹:𝐼𝑛𝑡,𝑂𝑢𝑡𝑁𝑜𝑚 |

|Ɵ𝑆𝐹:𝐼𝑛𝑡,𝐼𝑛𝑁𝑜𝑚 −Ɵ𝑅𝐹:𝐼𝑛𝑡

𝑁𝑜𝑚 |(2.9)

ԑ𝐼𝑛𝑡 =|Ɵ𝑆𝐹:𝐸𝑥𝑡,𝐼𝑛

𝑁𝑜𝑚 −Ɵ𝑆𝐹:𝐸𝑥𝑡,𝑂𝑢𝑡𝑁𝑜𝑚 |

|Ɵ𝑆𝐹:𝐸𝑥𝑡,𝐼𝑛𝑁𝑜𝑚 −Ɵ𝑅𝐹:𝐸𝑥𝑡

𝑁𝑜𝑚 |(2.10)

Calculate flow rate for the refrigerant

�� = ��𝑅𝐹𝑁𝑜𝑚 . 𝑉2

𝑁𝑜𝑚 =��𝑆𝐹:𝐸𝑣𝑎𝑝

𝑁𝑜𝑚

ℎ2𝑁𝑜𝑚 . 𝑉2

𝑁𝑜𝑚 (2.11)

Calculate enthalpy at the compressor outlet

ℎ3𝑁𝑜𝑚 = ℎ2

𝑁𝑜𝑚 +��𝐶𝑜𝑚𝑝𝑟

𝑁𝑜𝑚

��𝑅𝐹𝑁𝑜𝑚 (2.12)

Calculation of compressor efficiency using catalog data

𝜂𝐼𝑠𝑁𝑜𝑚 =

𝑚𝑅𝐹𝑁𝑜𝑚 .(ℎ3𝑖

𝑁𝑜𝑚−ℎ2𝑁𝑜𝑚)

��𝐶𝑜𝑚𝑝𝑟𝑁𝑜𝑚 (2.13)

Step two of the simulation starts using the above parameters to determine the full load

performance of the heat pump at the desired actual boundary conditions. To start the

process the following inputs are required.

7

Where:

COP coefficient of performance

Cp specific heat of fluid (J/(kg

K))

f factor

h specific enthalpy (J/kg)

I index

m mass flow rate (kg/s)

Q power or heat flow (W)

T temperature (K)

v specific volume (m3/kg)

˙V volumetric flow rate (m3/s)

ε effectiveness

𝜂 efficiency

Ɵ temperature (◦C)

Aux auxiliary devices

Compr compressor

Cond condenser

Cool cooling

El electric

Evap evaporator

Ex exergetic

Ext external side

In inlet

Int internal side

Is isentropic

Motor motor

Out outlet

RF refrigerant fluid

SF secondary fluid

Tot total

X part load

Nom nominal

8

Figure 2.2: scheme of model input/output.

Secondary fluids

Efficiency of electric motor

Refrigerant fluid

Effectiveness index

COP

Thermal capacity

Auxiliary power

Condenser fluid temp

Evaporator Fluid temp

Secondary fluids

Thermal effectiveness of condenser

Thermal effectiveness of evaporator

Refrigerant flow rate

Isentropic compressor efficiency

Mass flow rates of secondary fluids

Phase one

Condenser flow rate Evaporator flow rate

Condenser inlet Temp Evaporator inlet Temp

Running Mode

Hourly output:

Maximum thermalCapacity

COP

Outlet temperature ofsecondary fluids

Phase Two

9

Mass flow rate and inlet temperature of the external side (ambient side) secondary

fluid

Mass flow rate and inlet temperature of the internal side (user side) secondary fluid

Running model (cooling or heating);

Electrical power consumed by the auxiliary components

The nominal capacities for the evaporator and condenser assumed to be the start

values for the heat flow, considering constant effectiveness of the heat exchanger, the

software calculates the evaporating and condensing temperature of the refrigerant from

the previous calculation and step one outputs the reverse cycle could be determined.

After that the program compares the calculated heat capacity against the assumed. If the

error is within the acceptable tolerance limits, the process stops. If not, the new iteration

starts and assumes the calculated heat flow rates as starting points. This model is easy

to integrate into a simulation program, and according to the author the error would be

within ±10%, but it is not possible to determine the heat pump performance in partial load

conditions and this is a critical value for the energy simulation.

2.3 Stefanuk et al. Model

The Stefanuk et al. (1992) model presents a steady state model for a water-to-

water heat pump. The model is based on the equations of states, basic conservation laws

of mass, energy, and momentum in addition to the correlation of heat transfer. According

to the author the model could predict the performance of the heat pump over the full

operation range because it is derived from the basic laws. The heat pump was divided

into four main components: compressor, evaporator, condenser, and expansion device.

Each part has its own model and algorithm. The evaporator model accounts for both heat

10

transfer modes: the forced convective boiling of the two-phase refrigerant and forced

convection through a superheated refrigerant vapor. A simulation algorithm is used to

calculate the unknown heat transfer variables (the mass flow rate of refrigerant in the

evaporator and the required surface area for heat transfer) using the inlet source fluid

temperature and mass flowrate, the refrigerant mass flow rate, the refrigerant evaporation

temperature, and pressure. The condenser model and algorithm are similar to the

evaporator, but they account for the three different phases of the refrigerant: forced

convection in the inlet superheated refrigerant vapor, forced-convection condensation of

the two-phase refrigerant, and forced convection in the outlet subcooled at the outlet of

the condenser. The compressor model accounts for the pressure drop in the inlet and

outlet valves, and it predicts the mass flow rate, electrical power, and thermodynamics of

refrigerant compression fit data. The expansion device model assumed the device is

adiabatic and did not account for any thermal or electrical control for it. The model

assumed no pressure or temperature drop in the connecting pipes. Though the model

shows a good error percentage of ±10%, it is considered a deterministic model, which

demands many inputs and at some point it uses correlation to variables.

2.4 Jin and Spitler Model

Jin and Spitler (2002) developed a parameter estimation model for both water-to-

water heat pump and water-to-air heat pump. The author used deterministic model to

describe each part of the heat pump. Although this selection requires many parameters

that may not be available by the manufacturer catalogs, the model utilizes a multivariable

unconstrained optimization algorithm to estimate these parameters. The heat pump is

modeled as four main components: compressor, evaporator, condenser, and expansion

11

device. Other parts were neglected due to minor effect on the thermodynamic properties

of the system. The compressor model assumes an isentropic pressure for the

compression, no effects on the refrigerant by the oil, and that the pressure drops in suction

and discharge valves are isentropic. The estimation of compressor parameters leads to

estimating the refrigerant mass flow rate. Evaporator and condenser models assume a

negligible pressure drop in the heat exchangers. The model was derived from the

fundamental analysis of the counter-flow heat exchangers. The expansion device does

not model directly. Instead of that the amount of super heat is held constant, and the

refrigerant mass flow rate is determined by the compressor model. This approach works

for heat pumps with thermostatic expansion valve but may not work if the devise is a

capillary tube. The estimation procedure starts by inputting catalog data and applying

routines to adjust the parameter values to minimize the error between the model results

and the actual values. The flow diagram of the parameter estimation model shown in

Figure 2.3.

12

Figure 2.3: Flow diagram for model implementation computer program

Inputs

The values of the parameters for both cooling & heating mode Load & Source

water mass flow rates & entering temps Thermostat signal

Initial guess for condenser and evaporator heat flow rate

Evaporator and condenser effectiveness

Refrigerant condensing and evaporating temp

Determine evaporator and condesor Exit points

Apply pressure drop for suction and discharge

Calculate mass flow rate for refrigerant

From compressor model find: Power consumption W

Cooling Capacity ��𝐿 = ��𝑟 · (ℎ𝐴 − ℎ𝐵)

Heat rejection ��𝑠 = 𝑊 + ��𝐿

Output: Cooling capacity Power Consumption

if

Suction pressure < low pressure cut off

Discharge pressure > High pressure cut off

If

𝐴𝐵𝑆(��𝐿𝑔𝑢𝑒𝑠𝑠 − ��𝐿)/��𝐿𝑔𝑢𝑠𝑠 < 𝑒𝑟𝑟

𝐴𝐵𝑆(��𝑆𝑔𝑢𝑒𝑠𝑠 − ��𝑆)/��𝑆𝑔𝑢𝑠𝑠 < 𝑒𝑟𝑟

END

if

Evaporating pressure < low pressure cut off

Condenser pressure > High pressure cut off

END

END

13

2.5 Lash Model

This model has been developed to simulate the heat pump performance in a water-

loop heat pump that consists of other three components including a heat rejection unit, a

supplementary heating unit, and water circulation pump. A model has been developed for

each one of these parts and then combined and implemented into BLAST energy analysis

program. The model intended to simulate a water-to-air packaged unit with a reversible

cycle as shown in Figure 2.3. Lash proposed that the heat pump performance is a function

of the loop temperature, ambient air temperature, and mass flow rate because the heat

pump always works at a specific inlet source temperature. The proposed parameters are

always available as a requirement of the ARI certification program for the water source

heat pump. The equations that govern the heat pump performance are as follow:

Cooling mode:

𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑦

𝐵𝑎𝑠𝑒𝑐𝑎𝑝= 𝐴1 + 𝐵1 [

𝑇𝐿𝑜𝑜𝑝

𝑇𝑅𝑒𝑓] + 𝐶1 [

𝑇𝑅𝑒𝑓

��𝐵𝑎𝑠𝑑] [

��

𝑇𝑤𝑏] (2.14)

𝐸𝐸𝑅

𝐵𝑎𝑠𝑒𝐸𝐸𝑅= 𝐷1 + 𝐸1 [


𝑇𝑅𝑒𝑓] + 𝐹1 [

𝑇𝑅𝑒𝑓


��

𝑇𝑤𝑏] (2.15)

Heating mode:

𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑦

𝐵𝑎𝑠𝑒𝑐𝑎𝑝= 𝐴2 + 𝐵2 [


𝑇𝑅𝑒𝑓] + 𝐶2 [

𝑇𝑅𝑒𝑓


��

𝑇𝑤𝑏] (2.16)

𝐶𝑂𝑃

𝐵𝑎𝑠𝑒𝐶𝑂𝑃= 𝐷2 + 𝐸2 [


𝑇𝑅𝑒𝑓] + 𝐹2 [

𝑇𝑅𝑒𝑓


��

𝑇𝑤𝑏] (2.17)

Tref 283 K or 511 °R

TLoop The loop temperature (°R or K)

mBase The rated mass flow per unit of capacity multiplied by the base capacity

14

mBase 𝑄𝐵𝑎𝑠𝑒 [��

𝑄]

𝑅𝑒𝑓

m The mass flow rate of water through the pump.

Tdb, Twb The dry bulb and wet bulb air temperatures. (°R or K)

Qbase The base capacity of the heat pump unit. (kW)

[��

𝑄]

𝑅𝑒𝑓The ratio of design mass flow rate to design capacity. (kg/kJ)

Figure 2.3: Water to air heat pump schematics

The model did not account for the transient start up behavior because the transient

effect diminishes after 3 minutes of running time as proposed by equation (2.18), which

correlates the transient performance of simple on-off control scheme heat pumps.

��

𝑄𝑠𝑠= 1 − 𝐴𝑒(−𝑡/𝑟) (2.18)

Compressor

Fan

Air

ref

rige

ran

t

hea

t ex

chan

ger

Reversing valve

Expansion valve Water refrigerant

heat exchanger

15

A, r are constants. (Experimental values are .5 and 1 respectively)

Q is the transient heat transfer of the coil.

Qss is the steady state heat transfer rate of the coil.

t is the time that the heat pump operates.

This model is considered to be insensitive to the change of air flow rates from the

base value because it did not account for the change of capacities with different air flow

rates.

2.6 Shenoy Model

Shenoy (2004) presented an equation fit model by developing Lash (1990) model

to be used in the Energyplus model. The model also accounted for the sensible and latent

heat capacities for heat pump while working in the cooling mode. Based on the

psychometric chart and the manufacturer data the model variables relationships were

presented as below:

∆ ℎ ∝ ∆ 𝑊𝐵 (2.19)

𝑇𝑤𝑖𝑛 ∝ 1

𝑇𝑤𝑏(2.20)

𝑇𝐶 ∝ ��𝑤 (2.21)

𝑆𝐶 ∝ ��𝑤

The final equations for the developed model are listed below:

Cooling Mode:

𝑄𝑐

𝑄𝑏𝑎𝑠𝑒= 𝐴1 + 𝐵1 [

𝑇𝑊𝑖𝑛

𝑇𝑟𝑒𝑓

��𝑎−𝑏𝑎𝑠𝑒

��𝑎] + 𝐶1 [

𝑇𝑟𝑒𝑓

𝑇𝑤𝑏] [

��𝑤

��𝑤−𝑏𝑎𝑠𝑒] (2.22)

16

𝐸𝐸𝑅

𝐸𝐸𝑅𝑏𝑎𝑠𝑒= 𝐷1 + 𝐸1 [

𝑇𝑊𝑖𝑛

𝑇𝑟𝑒𝑓


��𝑎] + 𝐹1 [

𝑇𝑟𝑒𝑓

𝑇𝑤𝑏] [

��𝑤

��𝑤−𝑏𝑎𝑠𝑒] (2.23)

𝑄𝑆𝑒𝑛𝑠

𝑄𝑠𝑒𝑛𝑠−𝑏𝑎𝑠𝑒= 𝐺1 + 𝐻1 [

𝑇𝑊𝑖𝑛

𝑇𝑟𝑒𝑓


��𝑎] + 𝐼1 [

𝑇𝑟𝑒𝑓

𝑇𝑤𝑏] [

��𝑤

��𝑤−𝑏𝑎𝑠𝑒] + 𝐽1 [

𝑇𝑟𝑒𝑓

𝑇𝑑𝑏] [

��𝑤

��𝑤−𝑏𝑎𝑠𝑒] (2.24)

Heating Mode:

𝑄ℎ

𝑄𝑏𝑎𝑠𝑒= 𝐴1 + 𝐵1 [

𝑇𝑊𝑖𝑛

𝑇𝑟𝑒𝑓


��𝑎] + 𝐶1 [

𝑇𝑟𝑒𝑓

𝑇𝑤𝑏] [

��𝑤

��𝑤−𝑏𝑎𝑠𝑒] (2.25)

𝐶𝑂𝑃

𝐶𝑂𝑃𝑏𝑎𝑠𝑒= 𝐷1 + 𝐸1 [

𝑇𝑊𝑖𝑛

𝑇𝑟𝑒𝑓


��𝑎] + 𝐹1 [

𝑇𝑟𝑒𝑓

𝑇𝑤𝑏] [

��𝑤

��𝑤−𝑏𝑎𝑠𝑒] (2.26)

The model was applied on two different manufacturer heat pumps with the same

capacities. Shenoy (2004) also investigated the data out of the catalog range by

expanding the data points using the correction factors. The error reached 13% for the

sensible cooling capacity.

2.7 Tang Model

Tang (2005) proposed two models: one for the water-to-air heat pump and the

other for the water-to-water heat pump to be implemented in Energyplus. The water-to-

air heat pump model is a modification for Lash (1992) and Shenoy (2004) in order to

reduce the error from the last two models. The model was derived from the catalog data

after expanding the data points by using the catalog correction factors. The modification

to Shenoy (2004) is to add other terms to the equation to separate the inlet temperature,

air flow rate, and water flow rate because the heating capacity and heat absorption are a

strong function of the water inlet temperature and a weak function of the air flow rate. The

final forms of the equations are:

Cooling Mode:

17

𝑄𝑡𝑜𝑡𝑎𝑙

𝑄𝑡𝑜𝑡𝑎𝑙,𝑟𝑒𝑓= 𝐴1 + 𝐴2 [

𝑇𝑤𝑏

𝑇𝑟𝑒𝑓] + 𝐴3 [

𝑇𝑤,𝑖𝑛


��𝑎𝑖𝑟

��𝑎𝑖𝑟,𝑟𝑒𝑓] + 𝐴5 [

��𝑤

��𝑤,𝑟𝑒𝑓] (2.27)

𝑄𝑠𝑒𝑛𝑠

𝑄𝑠𝑒𝑛𝑠,𝑟𝑒𝑓= 𝐵1 + 𝐵2 [

𝑇𝑑𝑏

𝑇𝑟𝑒𝑓] + 𝐵3 [

𝑇𝑤𝑏


𝑇𝑤,𝑖𝑛


��𝑎𝑖𝑟

��𝑎𝑖𝑟,𝑟𝑒𝑓] + 𝐵6 [

��𝑤

��𝑤,𝑟𝑒𝑓] (2.28)

𝑃𝑜𝑤𝑒𝑟𝑐

𝑃𝑜𝑤𝑒𝑟𝑐,𝑟𝑒𝑓= 𝐶1 + 𝐶2 [

𝑇𝑤𝑏

𝑇𝑟𝑒𝑓] + 𝐶3 [

𝑇𝑤,𝑖𝑛


��𝑎𝑖𝑟

��𝑎𝑖𝑟,𝑟𝑒𝑓] + 𝐶5 [

��𝑤

��𝑤,𝑟𝑒𝑓] (2.29)

𝑄𝑠𝑜𝑢𝑟𝑐𝑒,𝑐

𝑄𝑠𝑜𝑢𝑟𝑐𝑒,𝑐,𝑟𝑒𝑓= 𝐷1 + 𝐷2 [

𝑇𝑤𝑏

𝑇𝑟𝑒𝑓] + 𝐷3 [

𝑇𝑤,𝑖𝑛


��𝑎𝑖𝑟

��𝑎𝑖𝑟,𝑟𝑒𝑓] + 𝐷5 [

��𝑤

��𝑤,𝑟𝑒𝑓] (2.30)

Heating mode:

𝑄ℎ

𝑄ℎ,𝑟𝑒𝑓= 𝐸1 + 𝐸2 [

𝑇𝑑𝑏

𝑇𝑟𝑒𝑓] + 𝐸3 [

𝑇𝑤,𝑖𝑛


��𝑎𝑖𝑟

��𝑎𝑖𝑟,𝑟𝑒𝑓] + 𝐸5 [

��𝑤

��𝑤,𝑟𝑒𝑓] (2.31)

𝑃𝑜𝑤𝑒𝑟ℎ

𝑃𝑜𝑤𝑒𝑟ℎ,𝑟𝑒𝑓= 𝐹1 + 𝐹2 [

𝑇𝑑𝑏

𝑇𝑟𝑒𝑓] + 𝐹3 [

𝑇𝑤,𝑖𝑛


��𝑎𝑖𝑟

��𝑎𝑖𝑟,𝑟𝑒𝑓] + 𝐹5 [

��𝑤

��𝑤,𝑟𝑒𝑓] (2.32)

𝑄𝑠𝑜𝑢𝑟𝑐𝑒,ℎ

𝑄𝑠𝑜𝑢𝑟𝑐𝑒,ℎ,𝑟𝑒𝑓= 𝐺1 + 𝐺2 [

𝑇𝑑𝑏

𝑇𝑟𝑒𝑓] + 𝐺3 [

𝑇𝑤,𝑖𝑛

𝑇𝑟𝑒𝑓] + 𝐺4 [

��𝑎𝑖𝑟

��𝑎𝑖𝑟,𝑟𝑒𝑓] + 𝐺5 [

��𝑤

��𝑤,𝑟𝑒𝑓] (2.33)

After applying these modifications the error was around 6%. The results were verified by

using Jin’s (1999) parameter estimation model. The water-to-water heat pump model

developed using the water-to-air heat pump methodology. To find the coefficient the

generalized least square method is implemented on the catalog data at indicated

reference conditions. The heating and cooling models equations are as below:

Cooling Mode:

𝑄𝑡𝑜𝑡𝑎𝑙

𝑄𝑡𝑜𝑡𝑎𝑙,𝑟𝑒𝑓= 𝐴1 + 𝐴2 [

𝑇𝐿,𝑖𝑛


𝑇𝑆,𝑖𝑛


��𝐿

��𝐿,𝑟𝑒𝑓] + 𝐴5 [

��𝑆

��𝑆,𝑟𝑒𝑓] (2.34)


𝑃𝑜𝑤𝑒𝑟𝑐,𝑟𝑒𝑓= 𝐵1 + 𝐵2 [

𝑇𝐿,𝑖𝑛


𝑇𝑆,𝑖𝑛


��𝐿

��𝐿,𝑟𝑒𝑓] + 𝐵5 [

��𝑆

��𝑆,𝑟𝑒𝑓] (2.35)


𝑄𝑠𝑜𝑢𝑟𝑐𝑒,𝑐,𝑟𝑒𝑓= 𝐶1 + 𝐶2 [

𝑇𝐿,𝑖𝑛


𝑇𝑆,𝑖𝑛


��𝐿

��𝐿,𝑟𝑒𝑓] + 𝐶5 [

��𝑆

��𝑆,𝑟𝑒𝑓] (2.36)

Heating mode:

18

𝑄ℎ

𝑄ℎ,𝑟𝑒𝑓= 𝐷1 + 𝐷2 [

𝑇𝐿,𝑖𝑛


𝑇𝑆,𝑖𝑛


��𝐿

��𝐿,𝑟𝑒𝑓] + 𝐷5 [

��𝑆

��𝑆,𝑟𝑒𝑓] (2.37)


𝑃𝑜𝑤𝑒𝑟ℎ,𝑟𝑒𝑓= 𝐸1 + 𝐸2 [

𝑇𝐿,𝑖𝑛


𝑇𝑆,𝑖𝑛


��𝐿

��𝐿,𝑟𝑒𝑓] + 𝐸5 [

��𝑆

��𝑆,𝑟𝑒𝑓] (2.38)


𝑄𝑠𝑜𝑢𝑟𝑐𝑒,ℎ,𝑟𝑒𝑓= 𝐹1 + 𝐹2 [

𝑇𝐿,𝑖𝑛


𝑇𝑆,𝑖𝑛


��𝐿

��𝐿,𝑟𝑒𝑓] + 𝐹5 [

��𝑆

��𝑆,𝑟𝑒𝑓] (2.39)

Where:

TL in Inlet load temperature

TS in Inlet Source temperature

Tref 283 K

VS Source side flowrate

VL Load side flowrate

Q total Cooling capacity

Q total,ref Reference cooling capacity

Powerc Cooling power

Powerc,ref Cooling reference letter

The reference conditions are critical for this model. The same references used to

generate the model should be used when applying the model. Tang’s (2005) model could

not be used to generate model from fixed inlet conditions.

19

CHAPTER 3

METHODOLOGY

This chapter will discuss the development of one of Energyplus models in addition

to its bases in order to meet the purpose of this research to simulate the actual

performance of ground-coupled heat pump by using field data instead of the catalog data.

Basically there are two models for the water-to-water heat pump available in Energyplus:

the curve fit water-to-water model, which was developed by Tang (2005) and the

parameter estimation, which was implemented by Jin (2002).

3.1 Parameters Selection

In order for a heat pump manufacturer to sell its product, the equipment should

comply with ARI or ISO 13256-1. The rating program provides a good picture of the

factors that impact the rated performance of ground source heat pump. These standards

require the manufacturer to provide the performance of the heat pump under different

interring water temperatures to demonstrate the efficiency of the heat pump. Most of

ground-source heat pump manufacturer provide that in addition to the performance under

different load temperature and mass flow rates. An example for a manufacturer’s catalog

data for water furnace heat pump in cooling mode is shown in Figure 3.1.

20

Figure 3.1: Water Furnance heat pump catalog data

21

The advantage of implementing these parameters to generate a model from the

field data to compare its results to the results generated form catalog data model. Also

these physical properties do not need invasive measurement tools. In addition field

measurements also showed a correlation between these parameters and the heat pump

performance as shown in Figures 3.2 -3.5.

30

35

40

45

50

55

60

65

70

17000 19000 21000 23000

Load

Tem

pra

ture

F

Cooling Capacity (Btu/h)

TL in

65

67

69

71

73

75

77

15000 17000 19000 21000 23000Su

rce

Tem

pra

ture

F

Capacity (Btu/h)

TS in

40

45

50

55

60

1 1.2 1.4 1.6Load

Sid

e Te

mp

erat

ure

F

Cooling Power kW

TL in

72

74

76

78

80

82

84

86

88

1 1.2 1.4 1.6

Sou

rce

Tem

pra

ture

F

Cooling Power KW

TS in

Figure 3.2: Heat pump capacity VS

load side temp

Figure 3.3: Heat pump capacity VS

load side temp

Figure 3.5: Heat pump power VS

source side temp

Figure 3.4: Heat pump Power VS

load side temp

22

3.2 Water-to-Water Heat Pump EnergyPlus Model Modification

There are several models for the heat pumps in EnergyPlus depending on the

equipment type, and the method used to make the model whether it is a curve-fit of

parameter estimation. Table 3.1 shows a summary of heat pump models in EnergyPlus.

Heat pump type Implemented to E+ by Developer

Cu

rve

-fit mod

el

Air-to-Air Buhl & Shirey DOE 2

Water-to-Air Shenoy (2004) & Tang

(2005) Lash (1992)

Water-to-Water Tang (2005) Tang (2005)

Pa

ram

ete

r

Estim

atio

n

mo

de

l

Water-to-Air Fisher and Tang Jin (2002)

Water-to-Water Murugappan (2002) Jin (2002)

Table 3.1: Heat pump models in EnergyPlus

The current equation-fit model in EnergyPlus was implemented by Tang (2005). It

is based on the manufacturer catalog data to generate a set of performance coefficients

by using the generalized least square method according to the following equations:

Cooling mode:

𝑄𝑐

𝑄𝑐,𝑟𝑒𝑓= 𝐴1 + 𝐴2 [

𝑇𝐿,𝑖𝑛


𝑇𝑆,𝑖𝑛


��𝐿

��𝐿,𝑟𝑒𝑓] + 𝐴5 [

��𝑆

��𝑆,𝑟𝑒𝑓] (3.1)



𝑇𝐿,𝑖𝑛


𝑇𝑆,𝑖𝑛


��𝐿

��𝐿,𝑟𝑒𝑓] + 𝐵5 [

��𝑆

��𝑆,𝑟𝑒𝑓] (3.2)



𝑇𝐿,𝑖𝑛


𝑇𝑆,𝑖𝑛


��𝐿

��𝐿,𝑟𝑒𝑓] + 𝐶5 [

��𝑆

��𝑆,𝑟𝑒𝑓] (3.3)

Heating mode:

𝑄ℎ


𝑇𝐿,𝑖𝑛


𝑇𝑆,𝑖𝑛


��𝐿

��𝐿,𝑟𝑒𝑓] + 𝐷5 [

��𝑆

��𝑆,𝑟𝑒𝑓] (3.4)

23



𝑇𝐿,𝑖𝑛


𝑇𝑆,𝑖𝑛


��𝐿

��𝐿,𝑟𝑒𝑓] + 𝐸5 [

��𝑆

��𝑆,𝑟𝑒𝑓] (3.5)



𝑇𝐿,𝑖𝑛


𝑇𝑆,𝑖𝑛


��𝐿

��𝐿,𝑟𝑒𝑓] + 𝐹5 [

��𝑆

��𝑆,𝑟𝑒𝑓] (3.6)

This model is not capable of generating the coefficients for constant flow rate conditions,

but the water-to-water heat pump in the Zero Energy Lab has a constant flow for the load

side and source side. In order to overcome this obstacle, a modification is proposed to

the original equations by removing the flow coefficients because they will not affect the

results as long as the flow is constant during the heat pump operation. The simple linear

regression is used to find the performance coefficients. The equations after modification

to generate a field data model become as follow:

Cooling mode:

𝑄𝑐

𝑄𝑐,𝑟𝑒𝑓= 𝐴1 + 𝐴2 [

𝑇𝐿,𝑖𝑛


𝑇𝑆,𝑖𝑛

𝑇𝑟𝑒𝑓] (3.7)



𝑇𝐿,𝑖𝑛


𝑇𝑆,𝑖𝑛

𝑇𝑟𝑒𝑓] (3.8)



𝑇𝐿,𝑖𝑛


𝑇𝑆,𝑖𝑛

𝑇𝑟𝑒𝑓] (3.9)

Heating mode:

𝑄ℎ


𝑇𝐿,𝑖𝑛


𝑇𝑆,𝑖𝑛

𝑇𝑟𝑒𝑓] (3.10)



𝑇𝐿,𝑖𝑛


𝑇𝑆,𝑖𝑛

𝑇𝑟𝑒𝑓] (3.11)



𝑇𝐿,𝑖𝑛


𝑇𝑆,𝑖𝑛

𝑇𝑟𝑒𝑓] (3.12)

24

3.3 Zero Energy Lab Testing Facility

The experiment has been conducted at the University of North Texas in the Zero

Energy Lab, which is a 1,200 square foot facility that is designed to imitate a small

residence. The occupants of the building are students practicing normal activities. The

building is conditioned by two ground-source heat pumps: the first is a water-to-water

heat pump that supplies hot or cold water to a radiant slab and the second unit is a water-

to-air heat pump. The heat pumps are programmed so the WAHP works when the WWHP

can not meet the load. Figure 3.6 shows a schematic of the system. Both heat pumps are

connected to a six parallel vertical ground heat exchanger and each bore is 67 meter in

depth.

The space is monitored and controlled by using a building management software TAC

Vista and 160 sensors that measures different values.

Figure 3.6: Zero Energy lab HVAC system drawing

25

3.4 Experiment Setup

The subject of the experiment is a Florida water-to-water heat pump that is shown

in Figure 3.7. The capacity of the unit is 7 kW in cooling and 9 kW in heating. The load

side is connected to a radiant concrete floor with embedded 573 m Polyethylene pipes of

0.0127 m inside diameter while the source (or skink) side is connected to a ground source

heat exchanger of 0.0635m radiuses. U-bend pipes manufactured from Polyethylene

material are inserted into the boreholes. The boreholes are then grouted with thermal

conductivity of 0.6926 W/m-k. In order to collect the data for generating the model for the

ground-source heat pump, different types of sensors were used to measure each physical

variable of the experiment parameters. Also measuring tools were used to find the

necessary values to do the simulation in EnergyPlus.

Figure 3.7: Water-to-water Florida heat pump

26

Measuring the temperatures was done using four ET series sensors shown in

Figure 3.8. The ET sensor is an immersion temperature transmitter that is installed in the

inlet and the outlet of both the condenser and the evaporator. The transmitter converts

the measured temperature into an electronic current signal. The sensor was installed in

a pocket that was immersed in the fluid. The sensor accuracy is ±0.1 % C of range. For

measuring the flow rates Fluxis F601 flow meter, which is shown in Figure 3.9, was used,

and it is an ultra-sonic flow meter that has clamp-on transducers for non-intrusive

measured installation and measurement. This device requires a laminar flow to give

accurate results, but because of the limitation of free pipe from fittings, the sensors were

installed on a point close to the fitting. The error of this installation, according to the

manufacturing company’s technical department, is ±5%.

Figure 3.8: ET temperature sensors

Temperature sensors

27

The energy and power are a critical part of the experiment for measuring these

parameters. The WATTNODE PULSE is used, which is an accurate AC watt-hour

transducer with pulse output (solid state relay closure) proportional to kWh consumed or

produced. The WATTNODE meter provides real energy measurement for sub-metering,

energy management and performance applications. The heat pump is a single phase two

wire without neutral connection with 208 to 240 Vac. The two conductors have AC

waveforms 120° or 180° out of phase. For this configuration, the meter is powered from

the ØA and ØB (phase A and phase B) terminals as shown in Figure 3.9.

Figure 3.8: Fluxis F601 flow meter installation

Transducers

Flow meter

28

Figure 3.9: WATTNODE PULSE energy meter installation

3.5 Experiments

The experiments were conducted to collect the necessary data for generating the

model. Two experiments were conducted to generate the cooling model: the first one at

the beginning of the cooling season to provide the performance of the heat pump under

mild conditions. The experiment continued for ten days. The set point for the space was

72 F while the water-to-air heat pump was off during the experiment time so it had no

effect on the experiment. The radiant floor loop had a mixing valve to control the slab

temperature. Since the slab temperature was not the subject of the experiment, the valve

was bypassed to eliminate water temperature changing by mixing. The second

experiment was conducted on the peak of the season to collect data when the heat pump

29

worked in its highest performance. The experiment continued for 30 days to collect more

data. The set point was 66 F for the Zero Energy Building to ensure that the heat pump

would work for longer hours to collect more data. The temperature sensors were installed

on the outlet and inlet of the heat pump’s load side and source side. The power meter

was connected to the unit electric input. Since the heat pump had no fan, the recorded

values represent the compressor power only. Temperatures and power values were

stored and recorded every 15 minutes in TAC Vista. The same methodology was followed

for conducting the heating mode experiment but with set points that were more compatible

with the heating mode. The set point for the first experiment was 74 F and for the second

one was 85 F.

3.6 Data Collection

After finishing the experiments the data was collected and divided into groups of

10 hours of continuous operation periods. In order to get accurate data points, two types

of the recorded points were excluded from each group: First the data related to the power

measured at the moment when the heat pump turned off because the value was not

accurate due to current dissipation. The second type of data that was excluded was the

first hour of heat pump operation to eliminate the effect of the loop reaction time. This was

determined by calculating the mass of the water in the radiant floor loop based on the

length and cross section of the embedded pipe and water density. The total mass of the

water was 72 kg. According to Lash (1990) the loop reaction time for this loop should

have been 25 minutes as its total mass was 72 and it had a 3 GPM/Ton flow rate as

shown in Figures 3.10 and 3.11. For more conservative approach 60 minutes were

selected to be the loop reaction time.

30

Figure 3.10: Loop reaction time for cooling mode

Figure 3.11: Loop reaction time for heating mode

The measured heat transfer for the load side was calculated based on heat transfer law

by using the interning and leaving water temperatures for the coil and the mass flow rate

as follows:

𝑄𝐿 = �� ∙ 𝑐𝑃 ∙ (𝑇𝐿𝑖𝑛 − 𝑇𝐿𝑜𝑢𝑡) (3.13)

0

5

10

15

20

25

30

-10 10 30 50 70 90

Loo

p c

oo

ld d

ow

n t

ime

(min

)

Loop mass per ton installed capacity (kg)

Coolign mode

2 GPM/ Ton

3 GPM/Ton

5 GPM/Ton

0

10

20

30

40

50

60

0 20 40 60 80 100 120 140

Loo

p H

eat

up

tim

e (m

in)

Loop mass per ton installed capacity (kg)

Heating mode

2 GPM/ Ton

3 GPM/Ton

5 GPM/Ton

31

3.7 Linear Regression Analysis

Several methods were used to model and investigate the relationship between

variables. Regression analysis is one of the best statistical techniques for representing

these relations. In this paper the linear regression method will be used to develop the

heat pump model. This method assumes a linear relationship to predict the response from

regressors or predictor variables as shown in Equation 3.14. Nonlinear regression models

are also available, but they were not selected to keep the model simple as much as

possible, so generating the model and applying it in the simulation software will not

consume a lot of time.

𝑦 = 𝛽0 + 𝛽1𝑥1 + 𝛽2𝑥2 + 𝜀 (3.14)

The number of predictor variables investigated in this research is two, so the model would

be a multiple linear regression and described as a plain in the three-dimensional space

as shown in Figure 3.12.

Figure 3.12: Multiple linear regression.

32

The regression coefficients β0, β1, and β2 were estimated by the method of least squares

so that the sum of the squares of the differences between the observations and the plain

is a minimum.

3.8 Coefficients Generation

One of the goals of this study is to find the minimum hours and days for generating

the heat pump performance model. Several attempts were made on the data to find the

minimum days and hours required to generate the model without losing the accuracy of

predicting the values. The first model started with ten days (5 days from each experiment)

and ten hours for each day and taking the average of the hours of each day, then applying

the linear regression to generate the model coefficients for the heat pump capacity and

power consumption. The model results were compared to the measured data of the unit

cooling capacity and power consumption. The same procedure was followed to generate

the coefficients when reducing the number of days and hours to reach the minimum time

for determining the models’ coefficients. Microsoft Office Excel was used to generate the

coefficients for each approach.

3.9 EnergyPlus

The simulation software that is used in this research is EnergyPlus, which is an

energy analysis and thermal load simulation program. The program was developed by

the Department of Energy based on both Building Loads Analysis and System

Thermodynamics (BLAST) and DOE-2 programs in such a way to combine the best

features of the two programs and offer a tool for design engineers or architects to size

appropriate HVAC equipment, optimize energy performance, develop retrofit studies for

life cycling cost analyses, etc. Energyplus was designed to be a part of a group of

33

programs that provide CAD interface to enable the user to draw the building, though it

can run standalone without such programs. After providing the necessary inputs, such as

HVAC systems, building dimensions, etc, the program will determine the heating and

cooling loads for maintaining the set points in addition to other simulations to ensure that

the building is running as the actual conditions. To increase the number of developers

with less investment resources, EnergyPlus was designed to easily connect to other

programs. Figure 3.13 shows how other programs have already linked to the program

and how the simulation flows.

Figure 3.13: EnergyPlus Structure

34

3.10 Water-to-Water Curve Fit Model Simulation in EnergyPlus

Simulating an HVAC system in EnergyPlus is done systematically by dividing the

system hierarchically to a set of objects starting with loops (air loop, condenser loop, etc.),

supply and demand sides, branches, components (water-to-water heat pump) and finally

nodes that store components inlet and outlet conditions. Figure 3.14 shows the water-to-

water heat pump lay out in EnergyPlus and its connection to the ground heat exchanger

and the radiant floor.

Figure 3.14: Water-to water heat pumps simulation lay out

In order to meet the demand and temperatures on each loop, a successive substitution

solver was used for the simulation. The condenser loop is divided into two parts: the supply

side solves for the ground heat exchanger, while the demand side models the energy

35

conversion from the water-to-water heat pump. The same procedure is followed for the

plant loop: the demand side simulates the radiant floor; however, the heat transfer from

the equipment is solved on the supply side.

36

CHAPTER 4

MODEL VERIFICATION

The equation-fit model for the water-to-water heat pump is verified by using actual

measured data from the experiment. The model for unit capacity and power were verified

for both heating and cooling modes. The EnergyPlus simulation results of the field data

model and catalog data model were also verified.

4.1 Cooling Mode Verification

Twenty-four models were generated based on both experiments by using different

number of days and hours to determine the minimum number of days and hours, and

each one of the models were verified against the measured data. First model was based

on 10 days and 10 hours. Figure 4.1 shows the cooling capacity model. The generated

model was applied to the 1225 data points of the two experiments.

Figure 4.1: Validating 10 days 10 hours cooling capacity model

The error percentage of the model was within ±10%, and the maximum error was 5.12

%, while the minimum error was -4.54%. The root mean square error percentage (RMS)

4.39 4.89 5.39 5.89 6.39 6.89

4.39

4.89

5.39

5.89

6.39

6.89

15000

16000

17000

18000

19000

20000

21000

22000

23000

24000

25000

15000 17000 19000 21000 23000 25000

Cooling capacity measured (kW)

Co

olin

g ca

pac

ity

mo

del

(kW

)

Co

olin

g ca

pac

ity

mo

del

(Btu

/h)

Cooling capacity measured(Btu/h)

+10%

-10%

37

for the model was 1.56 %. Figure 4.2 shows the power model for cooling mode that was

generated based on 10 days and 10 hours. The model predicted the power consumption

of the heat pump within ±10 % error. The points seem to be grouped and clustered at

different distances. That is because the heat pump has a constant power for a range of

inlet load and source temperatures. The minimum days and hours to generate the cooling

performance model were 4 days 2 hours. Figures 5.3 and 5.4 show the validation of the

water-to-water heat pump capacity and power consumption. The error is still within the

range of ±10 %. Tables 4.1 and 4.2 list the error percentage of each model. The error

increment of the 4 days 2 hours model compared to the 10 days 10 hours model in the

cooling capacity is negligible, also the same observation can be noticed for the power

model.

.

Figure 4.2: Validating 10 days 10 hours power model

1

1.1

1.2

1.3

1.4

1.5

1.6

1 1.1 1.2 1.3 1.4 1.5 1.6

Po

wer

mo

del

(kW

)

Power measured (kW)

+10 %

-10 %

38

Figure 4.3: Validating 4 days 2 hours cooling capacity model

Figure 4.4: Validating 4 days 2 hours cooling power model

4.98 5.18 5.38 5.58 5.78 5.98 6.18 6.38 6.58

2.928

3.928

4.928

5.928

6.928

7.928

8.928

9.928

17000

18000

19000

20000

21000

22000

23000

17000 18000 19000 20000 21000 22000 23000


Co

olin

g ca

pac

ity

mo

del

(kW

)

Co

olin

g ca

pac

ity

mo

del

(BTU

H)

Cooling capacity measured(BTUH)

+10%

-10%

1.1

1.15

1.2

1.25

1.3

1.35

1.4

1.45

1.5

1.55

1.6

1.1 1.2 1.3 1.4 1.5 1.6

Po

wer

mo

del

(kW

)

Power measured (kW)

39

No. Model Max Capacity Error Min Capacity Error RMS error Capacity

1 10 days 10 hours 5.12 % - 4.5 % 1.56 %

2 4 days 2 hours 5.38 % - 4.48 1.63 %

Table 4.1: Cooling capacity Error for different models


1 10 days 10 hours 6.85 % - 4.09 % 1.95 %

2 4 days 2 hours 7.39 % - 3.45 % 2.08 %

Table 4.2: Cooling power Error for different models

4.2 Heating Mode Verification

The same procedure was followed to generate the models for the heating mode,

starting from 10 days 10 hours model reaching to 4 days 2 hours, keeping in mind the

first hour is neglected. Figure 4.5 shows the 10 days 10 hours heating capacity model.

The prediction of the model showed a good agreement with the measured data, and the

error was within ± 10 %. The power model for the same number of days and hours is

shown in Figure 4.6, just like in the cooling mode points clustering noticed for the power

model. The minimum period to generate the model with accurate results was 8 days and

2 hours. Using less data caused scattering for the model results. Figures 4.7 and 4.8

show the verification of the heating capacity and power models for the minimum period

of time. Tables 4.3 and 4.4 summarize the error for both models

40

Figure 4.5: Validating 10 days 10 hours heating capacity model

Figure 4.6: Validating 10 days 10 hours heating power model

2.928 3.928 4.928 5.928 6.928 7.928 8.928 9.928

2.928

3.928

4.928

5.928

6.928

7.928

8.928

9.928

20000

21000

22000

23000

24000

25000

26000

27000

28000

29000

30000

24000 25000 26000 27000 28000 29000 30000

Cooling capacity measured (Kw)

Co

olin

g ca

pac

ity

mo

del

(Kw

)

Co

olin

g ca

pac

ity

mo

del

(BTU

H)


+10%

-10%

1.3

1.4

1.5

1.6

1.7

1.8

1.9

1.3 1.4 1.5 1.6 1.7 1.8 1.9

Po

wer

mo

del

(kW

)

Power measured (kW)

41

Figure 4.7: Validating 8 days 2 hours heating capacity model

Figure 4.8: Validating 8 days 2 hours heating power model

2.928 3.928 4.928 5.928 6.928 7.928 8.928 9.928

2.928

3.928

4.928

5.928

6.928

7.928

8.928

9.928

20000

21000

22000

23000

24000

25000

26000

27000

28000

29000

30000

24000 25000 26000 27000 28000 29000 30000


Co

olin

g ca

pac

ity

mo

del

(kW

)

Co

olin

g ca

pac

ity

mo

del

(BTU

H)


+10%

-10%

1.4

1.45

1.5

1.55

1.6

1.65

1.7

1.75

1.8

1.85

1.9

1.4 1.5 1.6 1.7 1.8 1.9

Po

wer

mo

del

(kW

)

Power measured (kW)

42


1 10 days 10 hours 4.1 % - 2.86 % 1.42 %

2 8 days 2 hours 3.63 % - 3.1 1.27 %

Table 4.3: Heating capacity Error for different models


1 10 days 10 hours 4.6 % - 4.76 % 1.27 %

2 8 days 2 hours 4.53 % - 5.49 1.79 %

Table 4.4: Heating power Error for different models

4.3 EnergyPlus Simulation

The coefficients generated based on the data collected from the field were

implemented in EnergyPlus to perform the simulation for Zero Energy Lab. Table 4.5 lists

the cooling and heating mode coefficient, which were generated based on the measured

data. The simulation was also performed for the building using the coefficients generated

from the catalog data using the existing method in EnergyPlus. Since the heat pump

manufacturer catalog provides operating conditions based on constant flow rate, another

manufacturer catalog with similar capacity was used to generate the model. The

coefficients are listed in Table 4.6

Mode Model Coefficient

1

Coefficient

2

Coefficient

3

Cooling Capacity -1.73911 5.721991 -2.94572

Power -5.73419 -1.09828 7.427062

Heating

Capacity -2.91077 -1.74665 5.534539

Power -3.87588 4.944718 -0.49151

Table 4.5: EnergyPlus field coefficients

43

Table 4.6: EnergyPlus Catalog coefficients

4.3.1 EnergyPlus Simulation Using Field Data Model

To cover the two experiment periods of the cooling mode, two simulation runs were

performed. The results then were validated against the measured data. Figure 4.9 shows

the cooling capacity validation of simulation results. The results show the error still within

±10%, but the scattering increased. That is because each model of the simulation

components has an error percentage that may affect the water-to-water heat pump

model. The validation of the simulation results for the cooling power model is shown in

Figure 4.10. The results show the power of the unit was within ± 10 % of the measured

data. The simulation was also performed for the heating mode. Two runs were executed

to include both experiments. The results’ validation for both heating capacity and power

are shown in Figures 4.11 and 4.12, and the results show good agreement between the

measured data and simulation results the error was within ±10 %.

Mode Model Coefficient

1

Coefficient

2

Coefficient

3

Coefficient

4

Coefficient

5

Cooling

Capacity -1.34975 2.20872 -0.28712 0.07445 -0.03697

Power -5.02849 -0.01616 6.04059 0.00250 -0.17484

Heating

Capacity -2.4666 -0.7030 3.7706 -0.000863 0.077808

Power -7.21472 7.71538 0.38778 -0.09405 0.00683

44

Figure 4.9: Field data model validation for cooling capacity simulation

Figure 4.10: Field data model validation for cooling power simulation

4.98 5.18 5.38 5.58 5.78 5.98 6.18 6.38 6.58

4.98

5.18

5.38

5.58

5.78

5.98

6.18

6.38

6.58

5000

5200

5400

5600

5800

6000

6200

6400

6600

6800

7000

5000 5500 6000 6500 7000


Co

olin

g ca

pac

ity

mo

del

(kW

)

Co

olin

g ca

pac

ity

mo

del

(BTU

H)


+10%

-10%

1100

1150

1200

1250

1300

1350

1400

1450

1500

1550

1600

1100 1200 1300 1400 1500 1600

Po

wer

mo

del

(W)

Power measured (W)

-10%

+10%

45

Figure 4.11: Field data model validation for heating capacity simulation

Figure 4.12: Field data model validation for heating power simulation

4.98 5.18 5.38 5.58 5.78 5.98 6.18 6.38 6.58

4.98

5.18

5.38

5.58

5.78

5.98

6.18

6.38

6.58

23000

24000

25000

26000

27000

28000

29000

30000

23000 24000 25000 26000 27000 28000 29000 30000


Co

olin

g ca

pac

ity

mo

del

(kW

)

Co

olin

g ca

pac

ity

mo

del

(BTU

H)


+10%

-10%

1400

1450

1500

1550

1600

1650

1700

1750

1800

1400 1450 1500 1550 1600 1650 1700 1750 1800

Po

wer

mo

del

(W)

Power measured (W)

-10%

+10%

46

4.3.2 EnergyPlus Simulation Using Catalog Data Model

The validation of the cooling capacity of the water-to-water heat pump is shown in

Figure 4.13. The simulation included two runs to cover the experiment on the beginning

of the cooling season and the experiment at the peak of the season. The error of the

model reached 30 % of the actual value. The simulation results of the two runs of cooling

power model are shown in Figure 4.14. The error of the model exceeded 10% and

reached 40%. The overprediction of the cooling capacity and cooling power resulting from

using a different manufacturer catalog, and the actual flow rate is not available in the

catalog. The validation of the heating catalog models also showed overprediction for both

the heating capacity and the power for heating as shown in Figures 4.15 and 4.16. The

error of the heating capacity reached 38%, while the compressor power reached 52%.

Figure 4.13: Catalog data model validation for cooling capacity simulation

4.98 5.18 5.38 5.58 5.78 5.98 6.18 6.38 6.58

4.98

5.18

5.38

5.58

5.78

5.98

6.18

6.38

6.58

17000

18000

19000

20000

21000

22000

23000

24000

25000

17000 18000 19000 20000 21000 22000 23000 24000 25000


Co

olin

g ca

pac

ity

mo

del

(kW

)

Co

olin

g ca

pac

ity

mo

del

(BTU

H)


-10%

+30%

47

Figure 4.14: Catalog data model validation for cooling power simulation

Figure 4.15: Catalog data model validation for heating capacity simulation

900

1100

1300

1500

1700

1900

900 1100 1300 1500 1700 1900

Po

wer

mo

del

(W)

Power measured (W)

Cooling power

-10%

+40%

4.98 5.18 5.38 5.58 5.78 5.98 6.18 6.38 6.58

4.98

5.18

5.38

5.58

5.78

5.98

6.18

6.38

6.58

24000

26000

28000

30000

32000

34000

36000

38000

24000 26000 28000 30000 32000 34000 36000 38000

Cooling capacity measured (Kw)

Co

olin

g ca

pac

ity

mo

del

(Kw

)

Co

olin

g ca

pac

ity

mo

del

(BTU

H)


+38%

-10%

48

Figure 4.16: Catalog data model validation for heating power simulation

4.5 Results

The field data model assumed a linear relationship between the heat pump

capacity and the temperatures of the load and source sides. The validation of the direct

results of the model and the simulation results in EnergyPlus showed an error within ±

10%. The cooling mode model was generated based on two days from each experiment

and two continues operation hours. The data was recorded every fifteen minute. The

generalized square method was used to generate the coefficients from the collected data

(Excel or Matlab could be used). The following equations were applied in EnergyPlus to

find the performance of the heat pump.

𝑄𝑐

𝑄𝑐,𝑟𝑒𝑓= −1.73911 + 5.721991 [

𝑇𝐿,𝑖𝑛

𝑇𝑟𝑒𝑓] − 2.94572 [

𝑇𝑆,𝑖𝑛

𝑇𝑟𝑒𝑓] (4.1)


𝑃𝑜𝑤𝑒𝑟𝑐,𝑟𝑒𝑓= −5.73419 − 1.09828 [

𝑇𝐿,𝑖𝑛

𝑇𝑟𝑒𝑓] + 7.427062 [

𝑇𝑆,𝑖𝑛

𝑇𝑟𝑒𝑓] (4.2)

900

1100

1300

1500

1700

1900

2100

2300

2500

900 1100 1300 1500 1700 1900 2100 2300

Po

wer

mo

del

(W)

Power measured (W)

-10%

+52%

49

The same procedure was followed to predict the performance of the heat pump in heating

mode except the period of time was four days of each experiment and two hours of

continues operation. The EnergyPlus equations are:

𝑄ℎ

𝑄ℎ,𝑟𝑒𝑓= −2.91077 − 1.74665 [

𝑇𝐿,𝑖𝑛

𝑇𝑟𝑒𝑓] + 5.534539 [

𝑇𝑆,𝑖𝑛

𝑇𝑟𝑒𝑓] (4.3)


𝑃𝑜𝑤𝑒𝑟ℎ,𝑟𝑒𝑓= −3.87588 + 4.944718 [

𝑇𝐿,𝑖𝑛

𝑇𝑟𝑒𝑓] − 0.49151 [

𝑇𝑆,𝑖𝑛

𝑇𝑟𝑒𝑓] (4.4)

4.6 Error Analysis

It is important to determine the quality of the measurement of physical quantity

because it would enable those who use it to assess its reliability, and giving a quantitative

value of the quality of the result would allow comparing the measurements among

themselves and with reference values. The transform of error equation 4.1 was used to

determine the uncertainty of the measured quantities and the results of the models.

∆𝑦 = |𝑑𝑓

𝑑𝑥1∆𝑥1| + |

𝑑𝑓

𝑑𝑥2∆𝑥2| … … … . + |

𝑑𝑓

𝑑𝑥𝑛 ∆𝑥𝑛| (4.5)

The error analysis of measured cooling capacity was investigated. The results of

single day is shown in Figure 4.17. The maximum error of the measurements is 0.86 %.

The same procedure was followed for the heating capacity measurement. The results of

single day is shown in Figure 4.18. The maximum error of the measurements is 0.85 %.

The error of the models was also investigated, and the results are listed in Table 4.7

50

Figure 4.17: Single day cooling capacity error analysis

Figure 4.18: Single day heating capacity error analysis

17000

17500

18000

18500

19000

19500

20000

20500

4/25 4/25 4/25 4/25 4/25 4/25 4/25 4/25

Cap

acit

y (B

tu/h

)

Date

25000

25500

26000

26500

27000

27500

28000

28500

12/5 12/5 12/5 12/5 12/5 12/5 12/5 12/5 12/5 12/5

Cap

acit

y (B

tu/h

)

Date

51

Mode Model Max error %

Cooling

Capacity .0451

Power .6590

Heating

Capacity .02892

Power .3618

Table 4.7: Model error analysis

52

CHAPTER 5

CONCLUSION AND RECOMMENDATION

5.1 Conclusions

This study included the development and modeling of a water-to-water ground-

source heat pump based on data collected from the field. The model was developed

based on the existing model in EnergyPlus, which was implemented by Tang (2005)

based on catalog data. The original model is not able to generate coefficients based on

constant flow rate. The coefficients dependent on flow rate were removed since the heat

pump in the Zero Energy Lab operates on fixed flow.

The cooling model was generated from data collected from two experiments: the

first one conducted at the beginning of the season and the second one conducted at the

peak of the season because one experiment was not sufficient to cover the heat pump

range of operation, which results in error in determining the performance of the heat pump

capacity and power consumption. The minimum period to generate the model was two

days and two hours from each experiment, the prediction of the heat pump cooling

capacity and power was validated against the measured data, and the error of the models

was within ± 10% of the measured data. The same procedure was followed to generate

the heating mode capacity and power. The error also was within ± 10%, but the required

time to generate the model was four days and two hours of each experiment. The reason

for that was the load of the heat pump is radiant floor and because of the bouncy effect

more time was required to cover the operation range of the heat pump.

The coefficients were applied in EnergyPlus to perform the simulation for Zero Energy

Lab in both modes, the heating and cooling. The results were more scattered when

53

compared to the measured data but still within ± 10%. The increase in error is related to

the inaccuracy of each model in the simulation process. When using the coefficients

generated based on the catalog data to perform the simulation, the error of cooling

capacity reached +30% and +40 % for the cooling power, while the simulation error for

the heating mode capacity is +38% and +52 % for the heating power. This high

percentage of error was because the operation conditions were not available in the

catalog and the manufacturer performance data based on constant conditions so another

catalog data with the same capacity were used to generate the coefficients.

It can be concluded that using the actual data from the field to generate the model

would reduce the simulation error reduced by 20% to 42%, which would increase the

confidence in the simulation results.

5.2 Future Work

This model was generated from experiments on Florida heat pump. Other brands

with the same and different capacities could also be used to generate the model to

generalize its application. The data was collected in laboratory environment to further

validate the model. The data could be collected from residential and commercial buildings

that have old or new installed heat pumps.

The load side of the heat pump was a radiant floor that was controlled by a three-

way valve. In this study the valve control effects on the heat pump performance have not

been investigated by keeping the valve open for all experiment periods. Further study

could include different valve positon and its effects on the model. Furthermore, additional

experiments could be conducted for a fan coil as a load instead of the radiant floor.

54

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