Enhancing and Expanding Conventional Simulation Models Of

Home , Compressor, Economizer, Scroll compressor, Thermal expansion valve

ENHANCING AND EXPANDING CONVENTIONAL SIMULATION MODELS OF

REFRIGERATION SYSTEMS FOR IMPROVED CORRELATIONS

Dissertation

Submitted to

The School of Engineering of the

UNIVERSITY OF DAYTON

In Partial Fulﬁllment of the Requirements for

The Degree of

Doctor of Philosophy in Engineering

Haithem Abualasaad Murgham

Dayton, Ohio

December, 2018 ENHANCING AND EXPANDING CONVENTIONAL SIMULATION MODELS OF

REFRIGERATION SYSTEMS FOR IMPROVED CORRELATIONS

Name: Murgham, Haithem Abualasaad

APPROVED BY:

David H. Myszka, Ph.D. Kevin P. Hallinan, Ph.D. Advisor Committee Chairman Committee Member Associate Professor, Department of Professor, Department of Mechanical Mechanical and Aerospace Engineering and Aerospace Engineering

Andrew Chiasson, Ph.D. Rajan Rajendran, Ph.D. Committee Member Committee Member Associate Professor, Department of Vice President, Emerson Climate Mechanical and Aerospace Engineering Technologies

Robert J. Wilkens, Ph.D., P.E. Eddy M. Rojas, Ph.D., M.A., P.E. Associate Dean for Research and Innovation Dean, School of Engineering Professor School of Engineering

ii © Copyright by

Haithem Abualasaad Murgham

2018 ABSTRACT

ENHANCING AND EXPANDING CONVENTIONAL SIMULATION MODELS OF

REFRIGERATION SYSTEMS FOR IMPROVED CORRELATIONS

Name: Murgham, Haithem Abualasaad University of Dayton

Advisor: Dr. David H. Myszka

This research presents engineering models that simulate steady-state and transient operations of air−cooled condensing units and an automatic commercial ice making machines ACIM, respectively. The models use easily-obtainable inputs and strategies that promote quick computations.

Packaged, air-cooled condensing units include a compressor, condensing coil, tubing, and fans, fastened to a base or installed within an enclosure. A steady-state standard condensing unit system simulation model is assembled from conventional, physics-based component equations. Specifi- cally, a four-section, lumped-parameter approach is used to represent the condenser, while well- established equations model compressor mass flow and power. To increase capacity and efficiency, enhanced condensing units include an economizer loop, configured in either upstream or downstream extraction schemes. The economizer loop uses an injection valve, brazed-plate heat exchanger (BPHE) and scroll compressor adapted for vapor injection. An artificial neural network is used to simulate the performance of the BPHE, as physics-based equations provided insufficient accuracy. The capacity and power results from the condensing unit model are generally within 5% when compared to the experimental data.

iii A transient ice machine model calculates time-varying changes in the system properties and aggregates performance results as a function of machine capacity and environmental conditions. Rapid

”what if” analyses can be readily completed, enabling engineers to quickly evaluate the impact of a variety of system design options, including the size of the air-cooled heat exchanger, finned surfaces, air flow rate, ambient air and inlet water temperatures, compressor capacity and/or efficiency for freeze and harvest modes, refrigerants, suction/liquid line heat exchanger and thermal expansion valve properties. Simulation results from the ACIM model were compared with the experimental data of a fully instrumented, standard 500 lb capacity ice machine, operating under various ambient air and water inlet temperatures. Key aggregate measures of the ice machine’s performance are:

1) cycle time (duration of freeze plus harvest modes), 2) energy input per 100 lb of ice, and 3)

energy usage during 24 hours. For these measures, the model’s accuracy is within 5% for a variety

of operating conditions.

Different strategies for improving the ACIM efﬁciency are explored. The improvement strate-

gies focus on compressor efﬁciency and reducing energy during harvest mode. The primary compo-

nent of ACIM energy use is the compressor, which accounts for approximately 80% of energy input

per 24 hrs. The explored strategies includes compressor efﬁciency, electric heaters to assist harvest,

and a waste heat recovery scheme. In waste heat recovery strategy, the wasted energy during the

freezing mode is stored in a storage media and used during the harvest mode. As a result, harvest

time is reduced up to 48.8%.

iv For whom words are certainly not enough to thank them: my father and mother.

v ACKNOWLEDGMENTS

It is my honor to express my thanks to those who supported and helped me to make this thesis possible.

First, I thank my family for inspiring me. Special thank for my son Laith and my daughter Juri who are my world.

Secondly, I owe my deepest gratitude to my supervisor, Dr. David Myszka, who guided and supported me all along my Ph.D journey. I consider myself lucky to pursue my Ph.D research with him.

Last but not least, I would like to thank Dr. Kevin Hallinan, Dr. Andrew Chiasson and Dr. Rajan

Rajendran for their help and support.

vi TABLE OF CONTENTS

ABSTRACT ...... iii

DEDICATION ...... v

ACKNOWLEDGMENTS ...... vi

LIST OF FIGURES ...... ix

LIST OF TABLES ...... xi

CHAPTER I. INTRODUCTION ...... 1

1.1 Review of Related Work ...... 3 1.1.1 Steady-State ...... 4 1.1.2 Transient ...... 4 1.2 Contribution ...... 5 1.3 Nomenclature ...... 8

CHAPTER II. STEADY-STATE MODEL OF CONDENSING UNIT ...... 10

2.1 Condensing Unit Model Description ...... 10 2.1.1 Standard System ...... 11 2.1.2 Economized Condensing Unit with Upstream Extraction ...... 12 2.1.3 Economized Condensing Unit with Downstream Extraction ...... 13 2.2 System Component Models ...... 14 2.2.1 Compressor ...... 14 2.2.2 Air-Cooled Heat Exchanger ...... 16 2.2.3 Brazed Plate Fluid to Fluid Heat Exchanger ...... 22 2.3 Simulation Model Methodology ...... 26 2.3.1 Inputs ...... 26 2.3.2 Standard Unit Model Simulation Method ...... 28 2.3.3 Upstream Extraction ...... 29 2.3.4 Downstream Extraction ...... 31 2.4 Steady-State Model Results ...... 31

CHAPTER III. TRANSIENT SIMULATION OF AN AUTOMATIC COMMERCIAL ICE MAKER ...... 33

3.1 Ice Maker Description ...... 33 3.2 ACIM Simulation Model Theory ...... 35 3.3 Model Operation Overview ...... 40 3.4 Results ...... 44

vii CHAPTER IV. SIMULATION OF EFFICIENCY IMPROVEMENTS TO AN ACIM . . . 46

4.1 Enhanced ACIM Model Theory ...... 46 4.1.1 Ice Formation Model ...... 46 4.1.2 Water Flow Model ...... 51 4.1.3 Harvest ...... 52 4.1.4 Heat Loss in Connecting Tubes ...... 52 4.2 Results ...... 53 4.3 Strategies for Improving ACIM Energy Efﬁciency ...... 54 4.3.1 Increasing Compressor Efﬁciency ...... 54 4.3.2 Auxiliary Electric Heater ...... 55 4.3.3 Waste Heat Recovery ...... 56

CHAPTER V. CONCLUSION AND FUTURE WORK ...... 59

5.1 Conclusion ...... 59 5.2 Future Work ...... 60

BIBLIOGRAPHY ...... 61

viii LIST OF FIGURES

1.1 Basic refrigeration system...... 2

2.1 Typical condensing unit [1]...... 11

2.2 Standard condensing unit...... 12

2.3 Condensing unit with upstream extracted economizer loop...... 13

2.4 Condensing unit with downstream extracted economizer loop...... 14

2.5 Experimental local heat transfer coefﬁcient for condensation of various refrigerants and test conditions [2]...... 16

2.6 Four-section lumped method for air-cooled ﬁnned-tubes heat exchanger...... 17

2.7 Straight ﬁns of uniform cross section [3]...... 20

2.8 Artiﬁcial neural network...... 23

2.9 Artiﬁcial neural network...... 24

2.10 Brazed plate heat exchanger’s function...... 25

2.11 Brazed plate heat exchanger’s function results...... 25

2.12 Straight ﬁns of uniform cross section [4] ...... 27

2.13 Steady-state condenser model...... 30

2.14 Simulation results vs. experimental data for a standard condenser unit...... 32

2.15 Simulation results vs. experimental data for a downstream economized condenser unit...... 32

3.1 Schematic of an ACIM that produces batches of cubes...... 34

3.2 Ice machine model operating in freeze mode...... 41

ix 3.3 Ice machine model operating in harvest mode...... 43

3.4 Graphical representation of the transient comparisons at 110/100◦F...... 45

3.5 Graphical representation of the transient comparisons at 90/70◦F...... 45

4.1 Schematic of an evaporator tubing coil (in black) and the ice formation grid divided into NCV = 56 control volumes (in grey), having NR = 7 and NC = 8. Grid control volume k and evaporator element j numbering convention is shown. . . . . 47

4.2 Graphical representation of the transient comparisons at 110/100◦F...... 53

4.3 Schematic of an ACIM with a waste heat reclamation circuit...... 57

4.4 ACIM with a waste heat recovery system...... 58

x LIST OF TABLES

3.1 Comparison of summary results between experimental results and simulation model. 44

4.1 Comparison of simulation results between ACIMs using compressors with increased efﬁciency...... 54

4.2 Comparison of simulation results between ACIMs using ice formation grid heating coils of various capacities (in Watts). Scenarios are presented with the compressor turned ON or OFF during harvest...... 55

4.3 Comparison of results between running the model using the waste heat recovery with running the model without the recovery unit...... 57

xi CHAPTER I

INTRODUCTION

The experimental investigation of refrigeration systems can be very complicated due to the large number of variables in the system and the long time required to prepare for the experiment and to collect the data. There are four main components in basic refrigeration system as shown in Figure

1.1. The compressor compress the superheated refrigerant and send it to the condenser (1-2). The condenser is a heat exchanger that condensing the hot gas into a liquid (2-3). The liquid refrigerant goes to the metering valve that forces the refrigerant to go through a small area. The pressure and temperature drop as a result of that (3-4). The cold low pressure refrigerant is directed into the evaporator which is another heat exchanger that boils the refrigerant by taking the heat from the surrounding. Then, the superheated gas is send to the compressor to start a new cycle (4-1). Any other components such as the brazed plate heat exchanger are called accessories.

Financially, the experimental investigation cost adds more complexity. Computer simulation model reduces the cost and helps understanding the phenomena related to the problem. Physics- based simulation strategies can be divided into two strategies: the steady-state and transient. The steady-state usually reached after some time in running the system. Steady-state models are suf-

ﬁcient for most refrigeration applications, where the system achieves a stable operating mode and continues to run in that mode for a majority of time. The transient state starts from the beginning of the event until establishing the steady state. The advantage of steady-state models are there short run time and simplicity to use. The transient models are generally used to model more complex

1 dynamic models where the variables change with time. These models continue to serve as the basis for more recent enhancements such as alternative refrigerants [5] and complex system circuits [6].

Figure 1.1: Basic refrigeration system.

Improving the refrigeration systems in order to achieve the optimum design has been the goal for the engineers. Computer simulation models provide the engineers the tool required to achieve that goal. Rapid “what if” analyses can be readily completed, enabling engineers to quickly evaluate the impact of a variety of system design options, including the size of the air-cooled heat exchanger,

finned surfaces, airflow rate, ambient air temperature, compressor capacity and/or efficiency, refrigerants, suction/liquid line heat exchanger and thermal expansion valve properties.

The goal of this research is to develop a steady-state and transient computer simulation models of refrigeration systems based on fundamental principles, generalized and custom correlations.

Once established, the simulation model enables prediction of component conditions, loads under different operating environments, and assessment of system design changes. This research provides

2 unique contribution to modeling refrigeration systems by requiring only basic inputs, creating calibrated functions that reduce simulation time. After this powerful tool is established, it is used to identify the potential improvements in the design to provide more efﬁcient system.

Microsoft Excel visual basic (VBA) is used to develop a steady-state model for an air-cooled condenser with a brazed plate heat exchanger. Lumped-parameter method is used to model the air heat exchange where it is divided into several elements that approximate the system behavior. A physics model and calibrated functions are developed to model the brazed plate heat exchanger.

MATLAB artiﬁcial neural network is used to calculate the weights and the bias that are used to develop the VBA functions. Transient commercial ice machine simulation model is created using

MATLAB Simulink and Simscape library. New blocks have been created and added to the simscape library. The model calculates time-varying changes in the system properties and aggregates performance results as a function of machine capacity and environmental conditions. All ﬂuid properties are obtained using REFPROP [7]. Once established, the models are used to have a better understanding between the inputs and the outputs and used this understanding to develop a better design.

The transient model is used to explore strategies for improving ACIM energy efficiency. The investigation focused on increasing the efficiency during harvest mode. The strategies that have been explored are increasing the compressor efficiency, using auxiliary electric heater, and waste heat recovery.

1.1 Review of Related Work

First practical refrigerating machine was designed by Oliver Evans in 1805 [8] and built in

1834 by Jacob Perkins [9]. After a decade, John Gorrie has built a refrigerator to produce ice [10].

The refrigerating system continued to grow and large plants installed all over the world. Along

3 with the blooming in refrigeration system industry, computer simulation model start getting more attention. Physics-based simulation models for the steady-state operation of a vapor-compression, refrigeration systems have been established several decades ago [11, 12].

1.1.1 Steady-State

Physics-based simulation models for the steady-state operation of vapor-compression refrigeration systems have been established several decades ago and repeatedly modiﬁed over the years.

Hiller and Glicksman 1976 evaluated system performance with a lumped-parameter model that divided the condenser to three and evaporator to two distinct regions, which required user-speciﬁed

fixed evaporator temperature, sup-erheat and subcooling degree [13]. In 1977, Fukushima et al. formulated a heat pump model that required the condensing/evaporating pressures and enthalpies to be specified [14]. In 1984, Domanski and Didion enhanced a heat pump model that required the evaporator saturated temperature, inlet quality, and superheated degree [15]. In 1992, a detailed model created by Stefanuk required evaporator saturated temperature, inlet quality and condensing temperature [16]. In 2002, Hui and Spitler formulated a heat pump model with two zones for both condenser and evaporator, using constant heat transfer coefficients and no subcooling [17]. In 2008,

Winkler, Aute, and Radermacher performed a comprehensive investigation in three algorithms used to simulate a steady-state vapor compression system [18].

1.1.2 Transient

Research on transient simulation can be traced back to 1978 when a ﬁxed time step transient simulation model of a vapor compression system was developed by Dhar [19]. In 1982, Chi and

Didion proposed air-to-air heat pump model using the moving boundary method. First ﬁnite volume discretization approach was used in the simulation in 1984 by MacArthur. In 1995, Vargas and

4 Parise developed a variable speed heat pump model to study the effect of ON-OFF control strategy on the system efﬁciency. In 1998, Williatzen et al. used moving boundary approach to study ON-

OFF control inﬂuence on a system. Real time air-cooled simulation model was established by Rossi and Braun in 1999. In 2008, Thermosys MATLAB/Simulink was used by McKinley and Alleyne to develop a moving boundary transient model for a crossﬂow heat exchanger with a single pass.

In 2011, Zhang created a variable refrigerant ﬂow (VRF) model. He did a regression analysis to an experimental data to model the compressor and expansion valve. In 2016, Tianzhen Hong developed a new VRF model using EnergyPlus for a heat pump operating in heating or cooling

[20]. In 2018, Dongsu Kim presented detailed procedures for model calibration of a (VRF) system with a dedicated outdoor air system (DOAS)[21].

Engineering models for the ice machine presents a particularly challenging application. The ice machine exhibits entirely transient behavior, as the operation continually cycles between the ice formation mode and ice harvest mode. In 2008, Bendapudi et al. discussed various approaches for transient simulation models. Of particular interest for ACIM modeling include refrigeration systems during variable evaporator load [22], startup conditions [23] and hot-gas bypass [24] as used during ice harvest mode. Transient models for the heat exchange between refrigerant ﬂowing through the evaporator tubing to water ﬂowing over an ice forming grid do not exist in the literature and were developed.

1.2 Contribution

The simulation models outlined in this research allow the engineers to have a better understanding of how the system responds to the change in wide range of variables. The contributions can be stated as:

5 1. Generated an accurate steady-state model of condensing unit with brazed plate heat exchanger

is developed based on fundamental, physic-based principles of individual system components.

Artiﬁcial Neural Network is used to model the brazed plate heat exchanger.

2. Modeling super-critical carbon dioxide air-cooled heat exchanger.

3. Created a transient simulation model of refrigeration systems that uses system geometry vari-

ables as inputs to minimizing the need of deﬁning some of the refrigerant properties before

the execution. In the model, the evaporator grid is divided to limited control volumes to

improve the evaporator’s temperature distribution and to model the water ﬂowing over the

evaporator grid. The ACIM simulation model has been patented [25] where I was the primary

contributor.

4. A journal paper ”Simulation of Efﬁciency Improvements to an Automatic Commercial Ice

Maker” [26]. This paper presents a new design for the ice machine maker which increases

the over all system efﬁciency by decreasing the energy consumption and the time required for

the harvest mode.

5. Publishing a paper ”Simulation Model of an Automatic Commercial Ice Machine” [27]. A

physics-based transit simulation model for ACIM to estimate the system behavior is outlined

in this paper.

6. Publishing a paper ”Steady-State Modeling of Condensing Units with an Economizer Loop”

[28]. Physics-based principles, and generalized and custom correlations

7. The enhanced transient ice machine model is used to explore strategies for improving the

efﬁciency. The explored strategies are: increasing compressor efﬁciency, using auxiliary

electric heat during harvest, and wasted heat recovery.

6 8. Invented a new ACIM design to increase the ice machine efﬁciency. In the ACIM and during

harvest, the heat generated by the compressor is used to release the ice from the grid. The

new design stores the wasted heat during freezing mode in a storage medium and uses it to

release the ice during the harvest mode. The process steps are:-

• During freezing cycle, the discharge line exchanges heat with the storage medium.

That will make the refrigerant enters the condenser at lower temperature and increase

the storage medium temperature.

• During harvest cycle, the heat stored in the storage medium is used to release the ice.

The next freezing cycle will start at the same time when harvest cycle starts and will be

used to pre-cool the water in the sump. That means, less freezing and harvest time.

The new invention is in the process of being patented [29]. The absence of the need for the

compressor heat to release the ice during the harvest cycle allows the high efﬁcient compres-

sors to be used in ACIM.

7 1.3 Nomenclature

The following nomenclature is used throughout this dissertation.

A surface area Di inside diameter Do outside diameter f Darcy friction factor h enthalpy k thermal conductivity L tube length m number of elements in one control volume m˙ mass ﬂow rate M mass Nc number of columns in the formation grid NCV number of control grid volumes Ne number of elements along evaporator tube NR number of rows in the formation grid NTU number of transfer units p pressure P r Prandtl Number Q˙ heat transfer rate R thermal resistance Re Reynolds Number s ice thickness t time δt simulation increments through time T temperature U internal energy V˙a condenser fan volume ﬂow V volume W˙ k compressor work ws effective contact width of the tube

xIk ice mass fraction

8 Greek symbols Xtt Lockhart–Martinelli parameter ρ density ω compressor speed ηv volumetric efficiency ηd isentropic efficiency ∆ percent absolute value α heat transfer coefficient χ condenser volume ratio µ dynamic viscosity Subscripts a ambient b bubble point c condenser co condenser outlet d compressor discharge e evaporator e evaporator outlet f final g evaporator grid/plate i injection I ice in inlet j evaporator tube element k control volume l liquid LI BPHE liquid line inlet LO BPHE liquid line outlet o initial out outlet p sump water r refrigerant s suction line sh evaporator super-heated su water supply sup condenser superheating degree sub condenser subcooling degree sc subcooling SI BPHE vapor line inlet t tube tp two-phase VO BPHE vapor line outlet v vapor w water x quality

9 CHAPTER II

STEADY-STATE MODEL OF CONDENSING UNIT

Heating, ventilation, air-conditioning, and refrigeration (HVACR) systems are essential for food preservation, indoor human comfort, and process cooling, such as pharmaceuticals and electronic equipment. Typical HVACR systems utilize a vapor compression system that includes four basic elements: a compressor, condenser, expansion valve and evaporator. For installation, preference is given to split vapor compression systems, where the cooling evaporator unit is packaged separately from a remote condenser unit. Evaporator units are often tailored for the speciﬁc application and integrated within the device, such as a delicatessen display case, a walk-in cooler, or soda machine.

The other half of the split system is the condensing unit (often air-cooled) which includes a compressor, condenser coil, liquid receiver, connecting tubing, and fans, assembled into a modularized package. A Condensing unit is an important component in refrigeration and air conditioning systems. The overall system efﬁciency will be affected by the condenser performance. A commercial condensing unit is shown in Figure 2.1. Economized condensing units also include a brazed plate heat exchanger, injection valve and a scroll compressor adapted for vapor injection. While condensing units do not have an evaporator, their capacity is rated by the amount of heat that could be absorbed if an evaporator was present.

2.1 Condensing Unit Model Description

The simulation model is constructed in a manner that is compatible with the standard test methods for rating condensing units [30]. The ambient air used to cool the condenser is designated by

10 Figure 2.1: Typical condensing unit [1].

˙ its temperature Tain and the volumetric flow rate Va produced by the cooling fan. To designate a cooling condition, an evaporator refrigerant dew point temperature Te, and subcooling temperature of the refrigerant exiting the condenser coil Tsc are specified. Vapor return to the compressor is specified with a suction temperature Ts. The compressor suction pressure pe is the dew point pressure associated with Te. Condensing units are configured as either standard or economizer, with upstream and downstream extraction options. The various condensing unit configurations are discussed in the following sections.

2.1.1 Standard System

A typical condensing unit schematic is shown in Figure 2.2. Refrigerant vapor is presented to the compressor suction inlet at temperature Ts and pressure pe. The compressor produces a refrigerant mass ﬂow m˙ d, and discharges a high temperature Td refrigerant that is directed to the condenser. The condenser is a heat exchanger that removes heat from the refrigerant, changing the hot gas into a warm liquid. The condenser has de-superheat, saturation, and subcool zones.

˙ Based on the design of the coil and ﬁns, along with Tain and Va, a steady-state temperature Tc and corresponding saturation dew point pressure pc is attained within the saturation zone of the

11 condenser. The temperature of the refrigerant exiting the condenser Tco is related to the speciﬁed

sub-cooling and condenser bubble point temperature Tcb , Tco = Tcb − Tsc. The liquid receiver is a storage vessel that contains excess refrigerant not in circulation. The refrigerant stored in the liquid receiver accommodates varying operational conditions. The liquid receiver does not signiﬁcantly alter performance of the condensing unit and is not included in the model.

Figure 2.2: Standard condensing unit.

2.1.2 Economized Condensing Unit with Upstream Extraction

An economized vapor compression cycle is able to provide more cooling than a standard cycle by increasing the amount of subcooling. Figure 2.3 shows an economizer loop added to the standard system, with upstream extraction. Notice that a portion of the subcooled liquid exiting the condenser is expanded through a valve, reducing its pressure pSI with a correspondingly lower saturation temperature TSI . After expansion, the extracted portion is routed into one side of a counter-flow, brazed plate heat exchanger (BPHE). The extracted portion is ultimately injected into an intermediate pressure port within a scroll compressor, and aptly termed the injection mass flow m˙ i. The remaining portion of refrigerant exiting the condenser, at Tco,pc, and flow rate m˙ d, is routed into the other side of the counter-flow BPHE. Since TSI < TLI , heat is exchanged from the high pressure, warm

12 liquid to the cool saturated refrigerant. Thus, the BPHE acts as a subcooler, reducing the liquid

temperature from Tco to TLo and provides additional system cooling capacity.

Figure 2.3: Condensing unit with upstream extracted economizer loop.

2.1.3 Economized Condensing Unit with Downstream Extraction

Figure 2.4 illustrates a schematic of the downstream extraction conﬁguration of an economized condensing unit. With downstream extraction, a portion of refrigerant is removed after passing through the BPHE. The performance of the two conﬁgurations are very similar. Downstream extraction ensures that only liquid enters the injection control valve which improves its operation.

However, the injection mass passes through the heat exchanger twice and the higher liquid-side mass ﬂow increases the pressure loss. In addition, more connections and tubing are required on the subcooled liquid side, all of which need to be insulated to ensure minimal heat gain. While the operational aspects are similar, the simulation model must account for the different conﬁgurations.

13 Figure 2.4: Condensing unit with downstream extracted economizer loop.

2.2 System Component Models

The steady-state simulation model developed in this research incorporates algebraic equations for the system components as identified below. These individual component models are assembled into a comprehensive simulation for the condenser unit configurations described above. That comprehensive simulation methodology is presented in Section 2.3. In formulating component models, the state postulate of thermodynamic properties is repeatedly used to determine the condition of the refrigerant. The state postulate asserts that the state of a compressible substance is completely defined by two independent properties [3]. That is, two given properties of a superheated refrigerant are sufficient to determine any other thermodynamic property. For instance, with values of Ts and pe at the compressor inlet, the compressor suction density ρs and enthalpy hs can be determined by using refrigerant databases such as RefProp 9.1 [7].

2.2.1 Compressor

The amount of mass ﬂow rate m˙ d delivered by the compressor to the system components is a function of compressor speed ω, compressor suction density ρs, displacement Vd and volumetric

14 efﬁciency ηv [31] is

m˙ d = ηv ω ρs Vd (2.1)

A polytropic approach can be used to determine power consumed by the compressor, which is inﬂuenced by the evaporator pressure pe, condenser pressure pc, compressor efﬁciency ηd, and polytropic exponent k,

(k−1)/k ˙ k − 1 pc W k = ηd ω Vd pe 1 − (2.2) k pe

Alternatively, compressor manufacturers conventionally provide rating information across an

operating map in accordance with AHRI Standard 540 [30]. The compressor performance values

are tabulated over a range of evaporator saturation temperatures Te and condenser saturation tem-

peratures Tc. The tabular data is ﬁt to a ten-coefﬁcient, third-order polynomial equation of the form

2 2 3 2 2 3 X = C1 + C2Te + C3Tc + C4Te + C5TeTc + C6Tc + C7Te + C8Te Tc + C9TeTc + C10Tc (2.3)

˙ where X can represent power consumption W k or mass ﬂow rate m˙ d. The appropriate rating

coefﬁcients Ci are commonly provided by compressor manufacturers for engineers designing a

system or components. Dabiri and Rice, (1981) developed adjustments to the capacity version of

Equation (2.3) for the level of suction gas superheat (Ts − Te) [32]. Fischer and Rice, (1981)

established a compressor shell loss factor fq to compensate for heat transfer through the compressor

wall to the ambient air [12]. An energy balance is applied on the compressor to determine the

discharge enthalpy hd as shown in Equation (2.4).

W˙ k(1 − fq) +m ˙ i(hvo) +m ˙ d(hs) hd = (2.4) m˙ c

Knowing hd and pc, a refrigerant database is used to determine the compressor discharge temperature Td.

15 2.2.2 Air-Cooled Heat Exchanger

The heat exchanger is analyzed using a lumped method [2], where the total heat exchanger volume Vc is divided into a few limited control volumes. An average heat transfer coefﬁcient (HTC) and pressure drop (∆P ) are determined for each control volume. HTC and (∆P ) calculations are

related to the heat exchanger geometry and air/refrigerant input properties. The single-phase regions

(desuperheat and subcool) have a little variation of HTC with the temperature when the mass ﬂow

rate is constant. Therefore, each single-phase region is modeled as a single control volume, Vsup

and Vsub, respectively. In the two-phase region, the HTC is affected by the refrigerant quality and

varies along the tube. Refrigerant quality below 0.4 is observed to have a major change in HTC

as shown in Figure 2.5; Therefore, the two-phase region is divided into two control volumes, from

saturated vapor to 0.4, represented as Vsat1, and from 0.4 to saturated liquid, represented as Vsat2.

Figure 2.5: Experimental local heat transfer coefﬁcient for condensation of various refrigerants and test conditions [2].

16 Air-cooled condensers usually have several circuits where the tubes are arranged in different ways according to the design. The detailed tube arrangement is not required in lumped approach.

However, the condenser geometry and other inputs such as fin type, fin pitch, fins density, tube inner diameter, and airflow rate are required. The air / refrigerant flow is considered a cross-flow. The refrigerant flow rate leaves the superheated control volume (Vsuper) to the saturated control volumes

(Vsat1 ) and (Vsat2 ) to the subcooling control volume (Vsub) as shown in Figure 2.6. The ratio of each control volume to the total volume Vc is χ1,...,4.

Some assumptions have been considered before applying conservation equations for each control volume. These assumptions are: system is in steady-state, air mass ﬂow rate is uniformly distributed over the condenser and no conduction heat transfer in the direction of the tube axis.

Figure 2.6: Four-section lumped method for air-cooled ﬁnned-tubes heat exchanger.

• The refrigerant side: The refrigerant side satisﬁes the mass conservation by the steady state

assumption. The pressure drop calculations is used to represent the momentum equation in

each control volume. The energy balance for the kth control volume is

˙ Qk =m ˙ d(hink − houtk ) (2.5)

17 th where hink and houtk are the inlet and outlet refrigerant enthalpy at the k control volume

respectively. At a speciﬁc condenser pressure, hink and houtk are known since the quality at each interface in known.

– Single phase: For the single phase control volumes, V1 = Vsup and V4 = Vsub, Gnielin-

ski correlation is used to calculate the heat transfer coefﬁcient α1,4 as shown in Equation

2.6. The correlation is valid for Prandtl number 0.5 ≤ P r ≤ 2000 and Reynolds num-

6 ber 3000 ≤ ReD ≤ 5 × 10 [3, 2]. The pressure drop ∆Pk is calculated using Darcy

Weisbach equation.

! k (f /8)(Re − 1000)P r α = k k Dk k , k = 1, 4 k 2/3 (2.6) Di 1/2 1 + 12.7(fk/8) (P rk − 1)

2 χk L ρk vk ∆Pk = fk (2.7) 2 Di

where k is the thermal conductivity, Di is the tube diameter, and v is the refrigerant ﬂow

velocity, ρ is the refrigerant density, L is the tube length, and f is Darcy friction factor.

– Two phase: In two phase regions, Dobson and Chato correlation provided the best

prediction for the heat transfer coefﬁcient [3] as shown in Equation (2.9). The two-

phase pressure drop ∆Pk can be expressed as a function of the mass ﬂow rate m˙ d, the

tube length, and two-phase friction factor ftp as shown in Equation 2.8.

2 2 2ftpk χk L (4m ˙ d)/(πDi ) ∆Pk = , k = 2, 3 (2.8) Di

" # 2.22 α = 0.023 Re0.8 P r0.4 1 + (2.9) k Lk Lk X0.98 ttk

18 0.9 0.5 0.1 1 − xk ρLk µLk Xttk = (2.10) xk ρvk µvk

The average refrigerant heat transfer coefﬁcient in the tube is:

Z xout 1 k 0.8 0.8 hmk = F1k (1 − x) + F2k xk dx (2.11) xout − xin k k xink where 0.8 Gdi 0.4 kLk F1k = 0.023 P rL (2.12) µLk Di 2.22 x0.8 F = k (2.13) 2k 0.445 0.089 ρLk µLk

ρvk µvk 2 where kL is the thermal conductivity (W/m K), G is the mass ﬂux (kg/m s), µ is the

dynamic viscosity, and x is the quality.

• The air side: For the air side, the mass conservation is satisﬁed with a constant air mass

ﬂow rate m˙ a = ρaV˙a, where ρa is the density of the ambient air. The momentum equation is

represented by the pressure drop calculations. The heat transfer is described as a function of

air mass ﬂow rate m˙ a, isobaric heat capacity Cpa, air inlet temperature Tain , and air outlet

temperature Taout .

˙ Q =m ˙ aCpa(Tain − Taout ) (2.14)

Wang correlations are used to calculate Colburn j-factor, which is used to calculate the airside

heat transfer coefﬁcient αair as shown in Equation 2.7. Wang 1999 is used for louvered ﬁn

[33] and wavy fin [34], Wang 2000 for Plain fin [35], and Wang 2001 for Enhanced(Slid) fin

[36].

19 Figure 2.7: Straight ﬁns of uniform cross section [3].

j CpG α = max (2.15) air P r2/3

where Gmax is the mass ﬂux of the air through the minimum area between the tubes and ﬁns,

As is the secondary (ﬁnned) surface area.

Wang correlations have tube spacing restrictions 0.5 in < longitudinal tube spacing <1.1 in

and 0.7 in < transverse tube spacing <1.2 in, ﬁn pitch is limited to 4 ﬁns/in < FP < 18

ﬁns/in, the air velocity range is limited to 3 ft/s < Velocity < 17.4 ft/s, and for the louver

ﬁn, the louver height is restricted to 0.031 in < Lh < 0.055 in, and the louver pitch 0.067 in

< LP < 0.147 in.

• The overall heat transfer coefﬁcient: The overall heat transfer coefﬁcient in each control

volume is determined by accounting for conduction and convection resistances between the

ﬂuid, tube wall, and the air as shown in the Equation (2.16).

1 1 ln(D /D ) 1 = + o i + , k = 1...4 (2.16) (UA)k αref k χk Aref 2π k χk L αair ηo χk Aair

Heat transfer rate per unit mass can be calculated using Equation (2.17) where ∆Tm is the

mean temperature difference[3].

20 q = UA∆Tm (2.17)

A η = 1 − f (1 − η ) (2.18) 0 A f where the Af is the entire fin surface area and ηf is a single fin efficiency.

tanh(mL) η = (2.19) f mL where L is the ﬁn length.

hP m2 = (2.20) kAc

Hong and Webb proposed a modify equation to improve the accuracy in 1996.

tanh(m Re Φ) ηf = cos(0.1 m Re Φ) (2.21) ReΦ

In 2003, Perrotin and Clodic proposed a modiﬁed Φ parameter as shown in Equation (2.24).

m (R − r ) H = e t (2.22) 1 2.5 0.3 Re H2 = 0.26 − 0.3 (2.23) rt

  1Re   1.5 − Re   12 rt  Re  Φ = − 1 1 + 0.3 + H2 H1  ln  (2.24) rt    rt 

where rt is the outside tube radius.

21 2.2.3 Brazed Plate Fluid to Fluid Heat Exchanger

Brazed plate heat exchangers (BPHE) were developed in the 1970s for the refrigeration industry [37]. They are designed to transfer heat from one ﬂuid to another ﬂuid across a solid surface.

It is constructed from a series of thin plates that are brazed together [38]. The two fluids are al- lowed to flow through alternating passages created between the thin plates. Geometric features on the plates are optimized to promote efficient heat transfer at a minimal pressure loss. A BPHE is more efficiently implemented in a counter-flow arrangement, as is shown in Figures 2.3, and 2.4.

When configured in the economized condensing unit, a flow of refrigerant m˙ LI exiting the condenser enters the warm side of the BPHE with liquid-in temperature TLI and pressure pc, and exits at a liquid-out temperature TLO. The cool refrigerant flow m˙ i enters the other side of the BPHE at

saturated-in temperature TSI and pressure pSI , and exits at a vapor-out temperature TVO. Physics-

based models of the BPHE were created calculating the evaporation and condensation heat transfer

coefﬁcient [39]. Heat transfer coefﬁcients and pressure drops in single phase, boiling and conden-

sation regions are calculated using different approaches [40]. The physics-based model provided

unacceptable accuracy as shown in Figure 2.8a.

Wilson (1915) developed a method, which has been modiﬁed over the years, for calibrating

overall HTC of the theoretical model with experimental data. The Wilson Plot method is widely

used in HVACR research, which utilizes prescribed heat transfer relationships and establishes a

curve ﬁt for the HTC. Alternatively, an Artiﬁcial Neural Network (ANN) was used to calibrate the

BPHE [41]. ANNs are a class of techniques that provide advantages to other data-driven modeling

techniques such as the Wilson plot. They have the ability to detect non-predeﬁned relations, such as

nonlinear effects and/or interactions. Over 2.4 million, manufacturer-supplied data points were used

to train the ANN. Three functions were created to model the BPHE behavior for different models

using a wide range of refrigerant properties for upstream and downstream extractions.

22 (a) Physics based model. (b) ANN model.

Figure 2.8: Artiﬁcial neural network.

Artiﬁcial Neural Network

The beginnings of Neural Network was in 1943 when McCulloch and Pitts published a research article that showed a simple neural network can solve a logical functions. The golden age of

Neural Networks was in 1950s when the ﬁrst successful neuro-computer was developed. In 1980s researchers became more interested in exploring Neural Networks [42]. ANNs consist multiple nodes connected by links, which allow them to interact with each other. Each link is associated with weight, where it’s value changes during ANNs learning. The results are then passed to other neurons.

The purpose of Neural Network training is to minimize the output errors on a particular set of training data by adjusting the weights. In principle, any raw input-output data can be used to train our networks. However, in practice, it often helps the network to learn appropriately if some pre-processing of the training data is carried out before feeding it to the network. The best number

23 of hidden units depends on a complex number of factors, including: number of training patterns, number of input and output units, amount of noise in the training data, the complexity of the function or classification to be learned, and training algorithm. Too few hidden units will generally leave high training and generalization errors due to under-fitting. Too many hidden units will result in low training errors, but will make the training unnecessarily slow, and will result in poor generalization unless some other technique is used to prevent over-fitting.

Figure 2.9: Artiﬁcial neural network.

Brazed Plate Heat Exchanger’s Function

The results from the training process, ”weights (W) and Bias (B)”, are used to build three functions that predict how the BPHE behaves. The outputs from each process or layer U(k) are the inputs for the next process or layer. Where L is number of Layers and k is number of neurons.

Short simulation time and the results accuracy as appears in ﬁgure (2.11) were the main reason for choosing this method.

24 Figure 2.10: Brazed plate heat exchanger’s function.

Figure 2.11: Brazed plate heat exchanger’s function results.

25 The ANN function for the injection mass ﬂow that generates heat transfer necessary to achieve the speciﬁed injection superheat TVO − TSI is

m˙ i = f(BP HEgeometry, P N, TLI , m˙ LI ,TVO − TSI ,Pc,Tc, ρLI , CpLI ,VLI ,KLI ) (2.25)

The injection pressure that, with m˙ i, achieves the necessary TVO is

pi = (BP HEgeometry, P N, TLI , m˙ LI , m˙ i,TVO − TSI ,Pc,Tc, ρLI , CpLI ,VLI ,KLI ) (2.26)

The warm, liquid-side outlet temperature,

TLO = (BP HEgeometry, P N, TLI , m˙ LI , m˙ i,TVO − TSI ,Pc,Tc, ρLI , CpLI ,VLI ,KLI ) (2.27)

In the three functions of Equations 2.25, 2.26, and 2.27, the BPHE geometry includes the dimensions of the plates, PN is number of plates, Pc and Tc are the critical pressure and temperature, respectively, ρLI , CpLI , VLI , and KLI are the density, isobaric heat capacity, kinematic viscosity, and thermal conductivity at the liquid line, respectively. The ANN ﬁts the training data points with

R-squared 0.99985. The data used in the training includes SWEP models from B8TH to B14TH, plate number from 6 to 30, liquid line inlet temperature from 65 to 175 oF , mass injection ﬂow rate from 2.5 to 3442 lb/hr, injection superheat degree from 1 to 21 oF , and refrigerants properties for

R409A, R408A, R411A, R414B, R404A, R507A, R407A, R407C, R407F, R32, R134A, R410A,

R448A, R449A, R452A, R513A, R450A and R22. The results of the ANN applied to the liquid-out temperature are shown in Figure 2.8b.

2.3 Simulation Model Methodology

2.3.1 Inputs

Condenser simulation model starts with specifying the inputs which are divided into four sections as follows:

26 ˙ 1. Operating condition: Te, Tain , Tco, Ts, Va and refrigerant name.

2. Condenser geometry inputs: Number of tubes, Do, Di, finned length L, fin type, and fin

density as shown in Figure 2.12.

3. Economizer loop information, including extraction type and BPHE geometry.

4. Compressor physical parameters: ω, Vd, ηv, ηd, or empirical constants: Ci.

Figure 2.12: Straight ﬁns of uniform cross section [4]

27 2.3.2 Standard Unit Model Simulation Method

After all the required input values are speciﬁed, the simulation model starts as follows:

1. The air heat transfer coefﬁcient αair and overall heat exchanger surface efﬁciency ηo are

determined from Equations (2.15) and (2.18), respectively. The air-side heat transfer does not

change with the state of the refrigerant, therefore, does not need to be included within the

convergence iterations.

2. Use the saturation pressure of the evaporator pe, suction temperature Ts and refrigerant

database to obtain the suction enthalpy hs and density ρs.

o 3. Assume an initial condenser temperature of Tc = Tair + 10 F , and determine the associated

saturation dew pressure pc.

4. Use Equation (2.4) to determine the compressor discharge enthalpy hd. Using refrigerant

database, the discharge temperature Td is obtained.

5. Knowing the inlet and outlet refrigerant conditions for all control volumes in the condenser,

the heat transfer from the superheated and the two two-phase regions Q˙ 1,2,3 are determined

using Equation (2.5).

6. Calculate the heat transfer coefﬁcient in the condenser superheated and subcooling regions

α1,4 from Equation (2.6), and the two two-phase regions α2,3 using Equation (2.9).

7. Using Q˙ 1,2,3 from Step 5, along with Equations (2.16) and (2.17), the condenser volume ratios

for the superheated region χ1 and the two two-phase regions χ2,3 are calculated.

8. Determine the subcooling region volume ratio χ4 = 1 − (χ1 + χ2 + χ3).

28 9. The pressure drop in each condenser region ∆P1,..,4 is calculated using Equation (2.7) for

the superheated and subcooling regions and Equation (2.8) for the two two-phase regions.

Chisholm, (1983) approximates the single-phase and two-phase pressure drop in a bend by

simply substituting the equivalent length of the bend for the straight pipe length [43].

10. Calculate temperature Tco that leaves the subcooling region by solving Equations (2.16),

(2.17) and Q˙ 4 =m ˙ cCp(Tc − Tco).

11. Calculated condenser subcooling Tsub = Tcb − Tco.

12. Compare the calculated condenser subcooling Tsub with the value user-speciﬁed Tsc. If

|Tsub − Tsc| is below a convergence tolerance ε, the simulation will continue to Step 13.

If |Tsub − Tsc| > ε, the condenser temperature Tc will be adjusted Tc = Tc ± ∆ and the

simulation ﬂow will go back to Step 4. The value of ∆ is based on the error value.

13. Determine condenser unit capacity, Q˙ =m ˙ d(hs − hLO), where hLO = hco for standard

condensing units.

2.3.3 Upstream Extraction

As shown in the system schematic in Figure 2.3, the refrigerant mass ﬂow rate that exits the

condenser m˙ c is divided into evaporator m˙ d and injection mass ﬂow rate m˙ i; m˙ c =m ˙ d +m ˙ i. The

ﬂow rate entering the liquid side of the BPHE continues to the evaporator. Thus, m˙ LI =m ˙ d in

Equations (2.25), (2.26), and (2.27). In operation, the injection valve is either a thermal expansion

valve (TXV) or electronic expansion valve (EXV) and is set to provide a certain level of injection

superheat. That is, TVO − TSI is speciﬁed in the simulation. Assuming a constant enthalpy process across the injection expansion valve, hSI = hco.

29 Figure 2.13: Steady-state condenser model.

30 2.3.4 Downstream Extraction

As shown in the system schematic in Figure 2.4, the refrigerant mass flow rate that exits the condenser flows directly into the BPHE. Thus, m˙ LI =m ˙ c in Equations (2.25), (2.26), and (2.27). The refrigerant mass flow rate that exits the BPHE is divided to injection mass flow rate and evaporator mass flow rate. Again, TVO − TSI is specified in the simulation. Since hSI = hLO which are both

unknown, downstream extraction typically requires convergence, since the liquid-out conditions

require convergence of both condenser and BPHE models.

2.4 Steady-State Model Results

Results from the steady-state simulation model are compared with experimental results from

different refrigeration systems. The model results are in general within 5%. Figure 2.14 shows a

comparison between the model results and the experiment data for a refrigeration system with no

brazed plate heat exchanger. Figure 2.15 shows the comparison between the model results and the

experimental data for a refrigeration system with brazed plate heat exchanger.

31 (a) (b)

Figure 2.14: Simulation results vs. experimental data for a standard condenser unit.

(a) (b)

Figure 2.15: Simulation results vs. experimental data for a downstream economized condenser unit.

32 CHAPTER III

TRANSIENT SIMULATION OF AN AUTOMATIC COMMERCIAL ICE MAKER

A self-contained automatic commercial ice makers(ACIM) that produce a batch of cube ice at regular interval is a major segment of the ACIM market. These machines, known as cubers, are primarily used in restaurants, hotels, convenience stores, and hospitals. Cube ice weight typically range from approximately 1/6 to 1/2 oz. and each manufacturer usually produces a unique shape

(cubic, rectangular, crescent, and pillow) to distinguish themselves from other manufacturers [44].

To assist in the design of ACIM systems, Varone developed an empirically based simulation model

[45]. Since the design changes necessary to improve the ACIM will likely exceed the bounds of an empirical model, a physics-based ACIM simulation model is desired to assess the performance implications.

3.1 Ice Maker Description

A schematic of an ”cuber” is given in Figure 3.1. This ACIM consists of two major subsystems: the vapor compression refrigeration system and water supply/circulation/purge system. The typical refrigeration system components include a compressor, air-cooled condenser, thermostatic expansion device, liquid line/suction line interchanger, and an evaporator that consists of copper tubing attached to copper or stainless-steel grid forming the ice making surface. During harvest, a hot- gas solenoid valve switches and channels refrigerant directly from compressor to evaporator, which melts a boundary layer and releases the ice. The water system consists of a water sump, circulation pump, plastic tubing and an evaporator water distributor. A potable water supply connection supply

Condenser

Condenser Fan

Hot Gas Valve

Evaporator Grid

Expansion Valve Compressor Heat Exchanger

Drain Circulation Water Fill Pump

Figure 3.1: Schematic of an ACIM that produces batches of cubes.

control valve and purge drain controls water inﬂow and from the ice maker. The basic ice making

process is a batch process and is described as follows [44]

1. Water ﬁlls the sump. The sump usually contains 10 - 40 percent more water than required to

make a given batch of ice.

2. The freeze mode is activated. The hot gas valve is closed, causing the compressor to pull

refrigerant from the evaporator and push the ﬂow into the condenser. About 80% of ACIMs

have air-cooled condensers, as is considered in this research. The condenser fan and water

circulating pump are commanded to operate during the freeze mode. The pump circulates the

water, passing it through a manifold which distributes the ﬂow over the ice formation grid.

3. The water temperature ﬂowing over the formation grid reduces and begins to freeze. Ice

gradually builds up in the grid until a full cube is formed as detected by a sensor measuring

either the thickness of ice in the grid, sump water level, or compressor suction pressure.

34 4. Upon reaching the prescribed ice weight, the machine switches to the harvest mode.

5. Most machines use hot gas harvest, in which hot refrigerant vapor is sent directly from the

compressor to the evaporator to warm the evaporator and melt enough ice to free the cube

from the plate. Typically, about 5 - 10 percent of the ice is melted during the harvest process.

Once free, the ice falls by gravity into the storage bin below. During the harvest process, the

condenser fan for air-cooled machine is off and the water circulating pump may be operat-

ing, depending on the design. Some machines use a limited amount of hot gas for melting

combined with mechanical means for removing the ice.

6. Water ﬁlls the sump and the system returns to the freeze mode as detected by evaporator

temperature and/or time.

3.2 ACIM Simulation Model Theory

The transient ice machine model incorporates a combination of algebraic and time-based differential equations for the main components [46]. The speciﬁc operating conditions include the ambient air temperature Ta and the supply water temperature Tsu. Throughout the analysis, refrigerant properties must be determined. One approach is to use a database such as RefProp [7]. To reduce computation time, Laughman (2012) demonstrated the use of lookup tables that store thermodynamic properties for selected refrigerants that are generated from a database [47]. The lookup table approach is used in the ACIM simulation model.

• Compressor: The compressor has the fast transient behavior in start-up and shutdown oper-

ations. During these two events, the simulation time step is very small (1 × 10−3sec) until

it reaches the semi steady-state. The compressor mass ﬂow rate is calculated from equation

(2.1) or (2.3). Compressor work can be calculated using equation (2.2) or (2.3). The conser-

35 vation of energy principle is applied to the compressor to ﬁnd the outlet enthalpy as shown

below [48].

h V 2 i ∂ m u + 2 V 2 V 2 =m ˙ h + in − m˙ h + out − Q˙ + W˙ (3.1) ∂t in in 2 out out 2 comp comp

Where u is the internal energy, V is the velocity, h is the enthalpy, Q˙ is the heat transfer rate

from the compressor, and W˙ is the compressor work.

• Expansion Valve: The expansion valve operates during the freeze portion of the cycle and

involves only algebraic equations. The valve restricts ﬂow and creates a pressure differential

between the low-side evaporator and the high-side condenser. Since refrigerant liquid at

temperature Tl and density ρl is expected through the expansion valve, a one-dimensional,

incompressible ﬂow equation is used to model the device [49],

p m˙ l = Al 2 ρl (pc − pe) (3.2)

An effective valve flow area of Al is fixed for an orifice or capillary tube expansion valves.

Thermal expansion valve (TXV) or electronic expansion valve (EXV) provides a feedback

system (mechanical or electronic) that alters Al to maintain a certain level of evaporator su-

perheat ∆Tsh = Teout −Te, where Teout is the temperature of the vapor exiting the evaporator.

The feedback gain Gl and time constant τv serve as input into the expansion valve model,

Al = Ass + Gl [(Tb − Teout ) − ∆Tsh] (3.3)

where the Tb is the sensing element (thermobulb) temperature and Ass is a steady state ﬂow

area. Since the feedback for a TXV is purely mechanical, a time delay is associated with the

temperature response of the sensing bulb. The response lag is modeled by

dTb/dt = (Tb − Teout )/τv (3.4)

36 • Air-Cooled Heat Exchanger: Developing a transient air-cooled heat exchanger can be done

by integrating the equations of conservation of mass, conservation of energy and conservation

of momentum, represented in equations (3.5, 3.6 and 3.7) respectively [48].

dm =m ˙ − m˙ (3.5) dt in out

h V 2 i ∂ m u + 2 + gz V 2 V 2 =m ˙ h + in + gz − m˙ h + out + gz − Q˙ ∂t in in 2 in out out 2 out (3.6)

(dmV ) =m ˙ V − m˙ V + mg cos θ + (P − P ) A + F V ol (3.7) dt in in out out in out cs fric

1 1 F = f ρV 2 (3.8) fric D 2

where f is the Darcy friction factor, ρ is the density, g is the acceleration of gravity, P is the

pressure, V ol is the volume, z is the distance (parallel with the gravity vector) and θ is the

angle between refrigerant line and vertical.

• Evaporator: Heat transfer from the water and into the refrigerant within the evaporator in-

cludes the interfaces through the water, ice, evaporator grid, plate, tubing and refrigerant.

As with the condenser, the refrigerant within the evaporator tube is divided into N discrete

elements. A lumped resistance model is used to determine the evaporator heat ﬂow,

N X 1 Q˙ = (T − T ) (3.9) e R ei w i=1 Ti

th Where Tei is the refrigerant temperature in the i element of the evaporator, Tw is the time

varying circulation water temperature, and RT is the effective resistance. The thermal re-

sistance involves: 1) convection from the ﬂowing water, 2) conduction through the ice being

37 formed, 3) conduction through the evaporator tubes, 4) the convection to the refrigerant within

the evaporator tubes. These individual interface components are

R1 = 1/ (hw Aw) R2 = s/ (kI AI ) (3.10)

R3 = tg/ (kg Ag) R4i = 1/ (hei Ae)

with the cumulative resistance being

RTi = R1 + R2 + R3 + R4i (3.11)

1) The convection coefﬁcient for a ﬂowing liquid over a plate is denoted hw and Aw is the

surface area of ice in contact with the ﬂowing water. 2) The thermal conductivity of ice is kI ,

AI is the surface area of the grid, and s is the ice thickness. 3) The thermal conductivity of

the evaporator grid and plate is kg, Ag is the surface area of the plate, and tg is the effective

thickness of the evaporator plate. 4) The convection coefﬁcient for the two-phase refrigerant

th in the i element of the evaporator is hei and Ae is the surface area of the evaporator tube.

The ice thickness s is zero at the start of the freeze cycle and increases in relation to the

P cumulative evaporator heat transfer Q˙ e∆t. The conduction through the ice is observed to

be the dominant resistance.

• Circulating Water: At the start of the freeze cycle, the circulating water has a total mass

Mw at a temperature Tw0 . At the end of the freeze cycle, an amount of water has been

transformed into ice, having mass MI . The remaining water in the sump has a mass Mw −MI

and temperature Twf . Prior to the start of the subsequent cycle a mass Msu of water at a

temperature Tsu is supplied to the sump. Since the amount of water circulating is constant

for each freeze cycle, Msu = MI . As the supply water mixes with the remaining water in the

sump, the resulting temperature of the circulating water at the start of the freeze cycle is

MsuTsu + (Mw − MI ) Twf Tw0 = (3.12) Mw

38 • Liquid/Suction Line Heat Exchanger: Suction line heat exchanger heat ﬂow Q˙ s between

the compressor suction line at Ts and the condenser liquid line at temperature Tco. The value

Q˙ s is based on an effective contact width ws of the tubing, the length of contact Ls and an

appropriate heat transfer coefﬁcient hs [3],

Q˙ s = hs Ls ws (Ts − Tco) (3.13)

• Connection Tubing: Customary relationships are used to account for heat transfer from the

connection tubing to the ambient air [50].

• Hot Gas Valve: As the ice machine simulation switches to harvest mode, an alternate ﬂow

path permits refrigerant discharged from the compressor to ﬂow through a bypass restric-

tion deﬁned by Av and directly into the evaporator. The condenser and expansion valve are

bypassed. The governing equations for each the components remain unchanged in harvest

mode. p m˙ v = Av 2 ρd (pd − pe). (3.14)

The state postulate is an important principle of thermodynamics that is required to assemble

the equations describing each component. The state postulate asserts that the state of a com-

pressible substance is completely deﬁned by two independent properties [51]. That is, two

given properties of a superheated refrigerant are sufﬁcient to determine any other thermody-

namic property. For instance, with values of Ts and pe at the compressor inlet, the suction

density ρs, enthalpy hs and entropy ss can be determined by using refrigerant databases such

as RefProp. To enhance computation time, look-up tables that store thermodynamic prop-

erties for selected refrigerants are generated from a database [47] and used to determine the

state variables of the refrigerant as it ﬂows through the components.

39 The theories and equations presented above are general and equally apply to the freeze cycle

and harvest, when heat removed from the ice and into the evaporator.

The simulation will increment through time t until a speciﬁed number of freeze and harvest

cycles are encountered. Implicit routines within the SimScapeTM modeling environment [52]

are used to solve set of overall algebraic and differential equations as needed such, that Kirch-

hoff’s ﬁrst and second laws are satisﬁed at the nodes where components are connected. That

is, all through variables (mass ﬂow rate and heat ﬂow rate) need to sum to zero and all the

across variables (pressure and enthalpy) should be equal.

3.3 Model Operation Overview

The model of the ACIM contains:

1. Simulation begins with a speciﬁed the parameters:

• Operating conditions include the temperature of the ambient air Ta and supply water

Tsu. Empirical equations are used to determine the density of supply water ρsu at Tsu

[3].

• Compressor parameters include displacement Vd, speed ω, volumetric efﬁciency ηv and

isentropic efﬁciency ηd, or 10 performance-based coefﬁcients [30].

• Sizing parameters include dimensions necessary to determine the volume of the con-

denser Vc, evaporator Ve, connecting tubes Vt, ice formation grid Vg, and water sump

Vp. The total system refrigerant volume Vr is calculated from Vc, Ve, Vt, and Vd. The

mass capacity of ice MIf that can be formed within the evaporator grid during the freeze

mode is calculated using Vg and the density of ice. The mass of water in the sump Mpo

is determined from ρp and sump capacity.

40 • System design settings include the refrigerant charge Mr and condenser fan volume ﬂow

rate V˙a. Settings for the condenser consist of ﬁn style and geometry. Settings for the

expansion valve are a desired evaporator superheat Tsh , steady state ﬂow area, feedback

gain, and time constant. Design parameters for liquidline/suction-line heat exchanger

include the length of contact Ls, and diameters of liquid and suction tubes.

2. Simulation is initialized by ﬁlling the sump with a volume Vsu of water supply at Tsu. It

is assumed that the startup temperatures of the evaporator Teo , and condenser Tco , are in

equilibrium with the ambient, Tco = Teo = Ta. A startup system pressure (evaporator and

condenser) peo = pco is determined by using refrigerant properties with Vr,Mr and Ta.

3. The transient simulation begins with the freeze stage at time to. A schematic of the ACIM

model operating in freeze mode is shown in Figure(3.2).

Environment ܶ௔, ܸ௔ሶ

Condenser heat rejection: ܳሶ௖ subcool saturated desuperheat ݉ሶ ௗ

Condenser ܯ௖, ܸ௖ Harvest Valve: ܣ௛=0

Suction line heat exchanger:ܳሶ௦ Compressor: ܸ௣, ܰ௣, ߟ௣, Expansion Valve:, ݉ሶ ௩ or 10-coeffs ݉ሶ ௘ ܣ௩, ܩ௩, ߬௩ saturated superheat

Evaporator ܯ௘, ܸ௘ Evaporator heat gain: ܳሶ௘

Ice MI, TI

Figure 3.2: Ice machine model operating in freeze mode.

41 4. The compressor mass ﬂow m˙ d and power W˙ k is calculated from physics-based equations

[31] using Vd, ω, ηv and ηd, or from performance-based coefﬁcients [30]. When using the

coefﬁcients, m˙ d is adjusted for the compressor inlet temperature Ts [32]. An energy balance

on the vapor in the compressor chamber is used to determine the temperature exiting the

compressor Td, which includes shell losses to ambient air [12].

5. The air-cooled condenser heat rejection Q˙ c is determined by dividing the total volume of the

heat exchanger into Ncc discrete elements along its length and using a ﬁnite-volume method.

Wang and his collaborators developed appropriate models for the heat transfer correlations of

ﬁn and tube heat exchangers that depend on V˙a, ﬁn material and geometry, including smooth

[35], corrugated [34], wavy [36] and louvered [33]. As outlined in Ge and Cropper (2005),

the effectiveness-NTU method is used with refrigerant properties to determine the refriger-

ant temperature Tcj for each discrete element, j = 1,...,Nc. The refrigerant properties

within the condenser is governed by a conservation of refrigerant mass and energy along with

pressure drop due to friction [2]. These equations are integrated to remove the spatial de-

pendence, resulting in a lumped-parameter, time-based, ordinary differential equation [53].

Transient system properties determined include the condenser inlet temperature Tcv, pressure

pc, saturation temperature Tc, and exit temperature Tco .

6. The expansion valve operates during the freeze portion of the cycle. The valve restricts liquid

ﬂow m˙ l and creates a pressure differential between the low-side evaporator and the high-

side condenser. A one dimensional, incompressible ﬂow equation is used to model m˙ l as a

function of pe, pc, the effective valve ﬂow area Al, and the state of the refrigerant. For an

oriﬁce or capillary tube expansion valve, Al is ﬁxed. A thermal expansion valve (TXV) or

electronic expansion valve (EXV) provides a feedback system (mechanical or electronic) that

alters the valve area to maintain a certain level of evaporator superheat Tsh = Tev −Te, where

42 Tev is the temperature of the vapor exiting the evaporator. A steady state ﬂow area, feedback

gain, and time constant, characterize the dynamic response of the expansion valve [49].

7. Evaporator heat ﬂow Q˙ e is based on standard refrigerant-side heat exchanger models. Water-

side equations involve custom developed equations for heat transfer from evaporator tube wall

to ﬂowing water through an increasing ice resistance.

8. The freeze cycle simulation will increment through time ti + 1 = ti + ∆t, tracking transient

system properties such as Te, pe,Tev,Td,Tc, pc,Tco, W˙ k, and MI .

9. Once the ice mass MI reaches the capacity of the formation grid MIf , the harvest mode is

initiated. A schematic of the ACIM model operating in harvest mode is shown in Figure (3.3).

Environment , 0 0

Condenser , Harvest Valve:

Compressor: , , , Expansion Valve or 10-coeffs , , superheat

Evaporator , Evaporator heat loss:

Ice MI, TI

Figure 3.3: Ice machine model operating in harvest mode.

10. Hot-gas bypass valve is opened during the harvest cycle, routing the compressor discharge

line mass ﬂow m˙ d directly into the evaporator. During harvest, a restriction Ah is inserted

within the bypass valve.

43 11. The harvest cycle simulation will continue to increment through time, tracking Te, pe,Tev,Td, W˙ k,

and MI . Harvestis complete when a speciﬁed percentage of the ice is melted.

12. Water inlet at a designated temperature Tsu is used to replenish the mass of ice harvested ice,

and mixed with existing water in the sump.

13. The simulation returns to the freeze stage (Step 3).

3.4 Results

A 500lb ACIM was equipped with instrumentation to measure the operational characteristics of

the machine. Physical parameters that deﬁne the machine are given in Table 3.1. The instrumented

machine was run at various operating points deﬁned by the ambient temperature and the water inlet

temperature. A summary of the experimental values (E) and the predictions made by the simulation

model (S) are given in Table 3.1. Also provided is the percent absolute value of error (∆) between

the experiment and simulation.

Table 3.1: Comparison of summary results between experimental results and simulation model.

Operating Condition: Ta/T su 100/110 F 90/70 F 70/50 F ES ∆ ES ∆ ES ∆ Cycle time (min) 26.1 25.4 2.6% 18.3 17.4 4.7% 14.5 15.2 4.9% Ice per 24 hrs. (lbs.) 268 279 4.3% 393 393 0.1% 497 473 4.7% Energy input (kWh/100lb) 8.8 8.6 2.8% 5.6 5.6 0.0% 4.1 4.2 3.7% Energy input (kWh/24hr) 23.7 24.0 1.2% 21.9 21.7 1.0% 20.3 20.1 0.8%

The key aggregate measures reported in Table 3.1 are the ice machines performance include the freeze and harvest cycle time, energy input per 100 lb of ice, and energy usage during 24 hours.

For these measures, the model accuracy is within 5% for variety of operating conditions. Figures

44 3.4 and 3.5 provide a comparison of transient response of pressures, temperatures and compressor power at various locations on the ice machine.

Figure 3.4: Graphical representation of the transient comparisons at 110/100◦F.

Figure 3.5: Graphical representation of the transient comparisons at 90/70◦F.

45 CHAPTER IV

SIMULATION OF EFFICIENCY IMPROVEMENTS TO AN ACIM

This chapter presents an enhanced model that extends the transient simulation model of an automatic commercial ice maker from Chapter III, compares the simulation results to an instrumented

ACIM, and utilizes the model for exploration of strategies to improving efﬁciency.

4.1 Enhanced ACIM Model Theory

Enhancements are made to the model described above to increase the ﬁdelity and assess the effect of minor design changes. The primary advances include ice formation, water ﬂow, harvest, and heat losses through connection tubes, as described in the following sections.

4.1.1 Ice Formation Model

In Chapter III, the entire ice formation grid was treated as a lumped system. The actual ice formation process and interaction between the grid and evaporator is complex. The lumped model lacks ﬁdelity to investigate design parameters related to evaporator. The enhanced model discretizes the grid, which allows more representative simulation of water ﬂow and heat exchange with the evaporator tubing. The evaporator tubing is typically arranged as a single layer of coils attached to the back side of the ice formation grid. In modeling the ice formation, the grid is divided into a rectangular array of NCV control volumes, having NR rows and NC = NCV /NR columns. As illustrated in Figure 4.1, the evaporator tubing coils are shown in black and the formation grid control volumes are in grey. Note that in order to maintain symmetry between the control volumes

46 and the evaporator tube, NR is set to the number of rows in the evaporator coil. Also notice that control volumes are numbered along the evaporator tube. A lumped parameter approach is used for

th each control volume. Thus, the k control volume has water mass Mwk , water temperature Twk ,

ice mass MIk and ice temperature TIk . A grid control volume may include several ice cube pockets.

Figure 4.1: Schematic of an evaporator tubing coil (in black) and the ice formation grid divided into NCV = 56 control volumes (in grey), having NR = 7 and NC = 8. Grid control volume k and evaporator element j numbering convention is shown.

As with the condenser, the refrigerant within evaporator tube is divided into Ne discrete elements along the length of the tube and a ﬁnite-volume method is used to calculate heat transfer Q˙ e.

The refrigerant model requires ﬁner resolution than the ice, Ne NCV . Thus, each grid control volume transfers heat with m = Ne/NCV evaporator refrigerant elements, where bxe represents the

th integer nearest to x. Correspondingly, the k grid control volume has a volume of Vk = Vg/NCV

and will contain evaporator tube elements jk = b(k − 1)m + 1e through jk+1 = b(k)me. Mass

conservation, energy balance, and the momentum equations are satisﬁed in each control volume.

At the start of the freeze mode, all grid control volumes have the same water properties Twk =

Tw ∀ k, Mwk = Mwk = ρwVk∀ k, and no ice mass, MIk = 0 ∀ k. Heat transfer from the water

in the ice formation grid to the refrigerant in the evaporator tube includes the interfaces through the

water, ice, evaporator grid, tubing and refrigerant. The heat transfer in the kth grid control volume

47 is, jk+1 X 1 Q˙ = T − T (4.1) ek wk ekj RTk n=jk j where R is the effective thermal resistance for the jth element in the kth grid control volume, Tkj

R = m(R + R + R + R ) + R (4.2) Tkj wk Ik g t rj

The number of evaporator elements within a grid control volume is accounted by including m.

The total heat transfer to the ice formation grid is

NCV ˙ X ˙ Qe = Qek (4.3) k=1

The individual thermal resistance components are:

1. Thermal resistance for convection heat transfer from the ﬂowing water,

RWk = 1/(αw Awk ) (4.4)

The convection coefﬁcient for the water ﬂowing over the evaporator grid in each control

volume is denoted αw and Awk is the water surface area in contact with the ice for the same

control volume. An average water heat transfer coefﬁcient is used in Equation (4.4) as the

water thermal resistance is small comparing to the ice resistance.

2. Thermal resistance for conduction heat transfer through the ice being formed,

RIk = sIk /(klAl) (4.5)

The thermal conductivity of ice is kl, Al is the surface area of the grid for one control volume,

th and SIk is the ice thickness in the k control volume.

48 3. Thermal resistance for conduction heat transfer through the grid,

Rg = sg/(kgAg) (4.6)

The thermal conductivity of the evaporator grid and plate is kg, Ag is the surface area of the

plate in each grid control volume, and sg is the effective thickness of the evaporator plate.

4. Thermal resistance for conduction heat transfer through the evaporator tubes,

Rt = st/(ktAt) (4.7)

where kt is the thermal conductivity of the evaporator tube, At is the tube surface area in each

grid control volume, and st is the effective tube thickness.

5. Thermal resistance for convection heat transfer to the refrigerant within the evaporator tubes

m Rrj = (4.8) αrj Ar

th where the surface area of the refrigerant within the k grid control volume is Ar, and the

th convection coefﬁcient for the j refrigerant evaporator element is αrj . Single-phase heat

transfer coefﬁcient for the refrigerant is calculated using Gnielinski correlation for Prandtl

6 number 0.5 6 P r 6 2000 and Reynolds number 3000 6 ReDi 6 5 × 10 [3].

! k (f /8)(Re − 1000)P r α = r i Di j rj 2/3 (4.9) Di 1/2 1 + 12.7(fj/8) (P rj − 1)

where k is the thermal conductivity, Di is the tube inside diameter, and f is Darcy friction

factor.

For the two-phase refrigerant heat transfer coefﬁcient, Dobson and Chato correlation [3] is

used as shown below. Where Xtt is Lockhart–Martinelli parameter.

49 " #! k 2.22 α = r 0.023Re0.8P r0.4 1 + (4.10) rj D Lj Lj X0.98 i ttj

Appropriate correlations were selected for the thermal conductivities kt,kg,kI , and heat transfer coefﬁcients αw [3].

Since heat is being exchanged with the water in the kth control volume, water internal energy

Uwk will change during each time increment

˙ Qek ∆t Uwk (ti + ∆t) = Uwk − (4.11) Mwk

The corresponding water temperature Twk is determined from water property lookup tables with

Uwk and atmospheric pressure. Once Twk reaches the freezing temperature, a mass fraction xIk of

Mwk will be converted to MIk . The latent energy of water is used with Uwk to determine xIk . The mass distribution in the grid control volume is

M = x M Ik Ik wko (4.12)

M = (1 − x )M wk Ik wko (4.13)

M where wko is the mass of water at the start of the freeze mode. The corresponding ice thicknesses

SIk increases as the heat transfer from the water. The conduction through the ice is observed to be

the dominant resistance and it increases as the ice thickness increases. In the physical ACIM, ice at

the top of the grid is the last to freeze. A sensor is placed towards the top to measure ice thickness

and signal when the ice is fully formed. In the simulation model, the freeze mode is considered

complete when all water is converted to ice, Mwk = 0 ∀ k.

50 4.1.2 Water Flow Model

To simulate water ﬂowing over the ice formation grid, the water properties in each control volume is passed to the next control volume in the same column. With the grid numbering scheme

th outlined above, the set of control volumes in the c column include {c = [c, 2Nc − c + 1, c +

2Nc, 4Nc − c + 1, c + 4Nc, .., Ncv − Nc − c], for 1 6 c 6 Nc. The control volumes in the

ﬁrst row have the same water temperature as the sump from the previous time iteration, Twk = Tp, k = 1,...,NC . During the heat transfer analysis described in the prior section, water thermal properties are passed from a control volume to the next control volume in the same column. That is, at the end of each time increment,

Twr+1 = Twr (4.14)

where r and r + 1 are adjacent members of the set {c.

The water mass in the sump after each time increment is determined by subtracting the ice mass

MIk and water mass Mwk in each control volume from the initial water mass in the sump Mpo .

N XCV Mp(ti+1) = Mpo − [Mwk + MIk ] (4.15) k=1

The water in the last control volume in each column is mixed with the water in the sump where the overall sump water temperature is

 N  1 Xe Tp(ti+1) = TpMp + Twk Mwk  (4.16) Mp(t + ∆t) k=Ne−Nc+1

51 Prior to the start of the subsequent cycle, a mass Msu of water at a temperature Tsu is supplied

to the sump. Since the amount of circulating water is constant for each freeze cycle, the supplied

water mass is equal to the mass of ice produced MI in the freezing cycle. As the supply water

mixes with the remaining water in the sump, which will equal for ﬁnal temperature computed from

Equation (4.14), designated as Tpf . The resulting temperature of the circulating water at the start of

the freeze cycle is

MsuTsu + MI Tpf Tp = (4.17) Mpo

4.1.3 Harvest

As the ice machine simulation switches to harvest mode, an alternate ﬂow path permits refrigerant discharged from the compressor to ﬂow through a bypass valve restriction and directly into the evaporator, bypassing the condenser and expansion valve. Accordingly, the refrigerant mass that is trapped in the condenser is removed from the total simulation during harvest. Within the condenser

th model, Tci , pci , and the state of the refrigerant are determined within each i ﬁnite volume at each time increment. At the onset of harvest, the refrigerant mass trapped within the condenser is readily determined and subtracted from Mr when simulating the harvest mode.

4.1.4 Heat Loss in Connecting Tubes

The major heat loos in connecting tubes occurs in the uninsulated compressor discharge line.

The fan airﬂow crosses the discharge line and cools it before it cools the condenser. Churchill and

Bernstein comprehensive equation is used to calculate heat transfer coefﬁcient for the air crossing discharge line with outside tube diameter do [3].

 1/2 !4/5 k 0.62Re P r1/3 Re 5/8 α = a 0.3 + Do 1 + Do a  2/3  (4.18) Do [1 + (0.4/P r) ] 282000

52 4.2 Results

A 500 lb, instrumented ACIM was equipped with sensors to measure the operational characteristics of the machine. The instrumented machine was run at various operating points deﬁned by the ambient temperature and the water inlet temperature. Figure 4.2 provides a comparison of the transient response of pressures, temperatures and compressor power at various locations on the ice machine.

Figure 4.2: Graphical representation of the transient comparisons at 110/100◦F.

53 4.3 Strategies for Improving ACIM Energy Efﬁciency

The enhanced simulation model is used to explore strategies for improving the energy efﬁciency.

The improvement strategies focus on compressor efﬁciency and reducing energy during harvest.

The primary component of ACIM energy use is the compressor, which accounts for approximately

80% of energy input per 24 hrs. The batch-type ACIMs discussed in this paper use superheated refrigerant vapor discharged from the compressor to release the ice from the evaporator grid during the harvest cycle. This strategy is effective, but requires energy to reverse a portion of the freeze mode. Thus, exploring strategies for improving harvest is warranted.

4.3.1 Increasing Compressor Efﬁciency

Typically, reciprocating compressors are used in ACIMs, as is the case for the 500 lb ice maker described in the previous section. Using current technology, compressor efﬁciency can be improved

5 to 10% by replacing the reciprocating compressor with a scroll, and/or adopting motor enhancements. A comparison in simulation results from 500 lb ACIM model with compressor efﬁciencies that are 5% and 10% higher than the production model are shown in Table 4.1.

Table 4.1: Comparison of simulation results between ACIMs using compressors with increased efﬁciency.

Operating Condition: Ta/T su 100 / 110 oF 90 / 70 oF 70 / 50 oF Compressor Eff. increase 0% 5% 10% 0% 5% 10% 0% 5% 10% Freezing (min) 24.6 24.3 24.1 16.4 16.4 16.3 13.8 13.7 13.7 Harvest (min) 0.81 0.85 0.93 1.07 1.10 1.2 1.41 1.61 1.63 Ice per 24 hrs. (lbs.) 279 280 281 393 391 390 473 469 469 Energy input (kWh/100lb) 8.61 8.23 7.82 5.57 5.30 5.10 4.24 4.06 3.88 Energy input (kWh/24hr) 24.0 23.1 22.0 21.9 20.7 19.9 20.1 19.0 18.2

54 With a hot-gas harvest method, the refrigerant vapor temperature depends on the compressor efficiency. Higher compressor efficiency will increase the system efficiency during the freezing cycle, but it decreases the vapor temperature during the harvest cycle, increasing the time to release the ice. The overall energy input decreases by 9.2% per ice mass, which is lower percentage than compressor efficiency increase 10%. It must be noted that a cost premium is required to realize these compressor efficiency increases.

4.3.2 Auxiliary Electric Heater

A second efﬁciency improvement strategy focuses on harvest and involves use of an electric heater to assist, or replace, the compressor discharge. Table 4.2 shows the simulation performance results for the 500 lb ACIM model with various levels of electric heat (in Watts) and the compressor being turned ON or OFF during harvest. Table 4.2 Comparison of simulation results between

ACIMs using ice formation grid heating coils of various capacities (in Watts). Scenarios are presented with the compressor turned ON or OFF during harvest.

Table 4.2: Comparison of simulation results between ACIMs using ice formation grid heating coils of various capacities (in Watts). Scenarios are presented with the compressor turned ON or OFF during harvest.

Operating Condition: Ta/T su 100 / 110 oF 90 / 70 oF 70 / 50 oF Elec. heater (Watt) 0 500 500 1000 0 500 500 1000 0 500 500 1000 Comp. harvest ON ON OFF OFF ON ON OFF OFF ON ON OFF OFF Harvest (min) 0.81 0.58 1.10 0.71 1.07 0.75 1.44 0.87 1.61 0.89 1.54 0.70 Ice per 24 hrs. (lbs.) 279 281 276 280 393 400 385 398 473 479 458 485 Energy input (kWh/100lb) 8.61 8.66 8.35 8.38 5.57 5.58 5.28 5.30 4.24 4.20 3.95 4.21

The simulation results show that by turning the compressor off and using an electrical heating coil to release the ice during harvest will decrease the harvest time by up to 19% and decrease the

55 energy input per 24 hr by 2.4% to 7.3%. Moreover, using the heating coil will cause the harvest cycle to be independent from the compressor, which allows higher efﬁcient compressors to be used in this type of commercial ice machines to increase the overall system efﬁciency.

4.3.3 Waste Heat Recovery

A third efficiency improvement strategy introduces a warm-liquid to capture and reclaim a portion of the condenser waste heat. A schematic of this strategy is shown in Figure 4.3, where a warm-liquid circuit is added to the existing refrigerant and water circuits shown in Figure 4.3. A heating tank is inserted within the refrigerant circuit between the compressor and condenser. The compressor discharge tube containing the hot refrigerant enters the heating tank and exchanges heat with a liquid, prior to entering the condenser to reject any remaining waste heat. During the freeze mode, the remainder of the system operates as the conventional ACIM. As the ice cubes are fully formed, the ice maker enters a harvest mode. A pair of harvest bypass valves redirect the flow of the refrigerant from the ice formation grid to the water sump. Simultaneously, a pair of warm-liquid valves open and a circulation pump begins flow of the warm-liquid from the heating tank to a second set of tubes that are formed within the ice formation grid. Thus, the warm-liquid is used to release the ice while the refrigeration system is used to pre-cool the water that fills the sump.

The results from the simulation model using 1 L of warm liquid and 1m of refrigerant coil within the heating tank are shown in Table 4.3.

The results shows that using the heat recovery unit saves up to 48.8% of the harvest time and

8.6% of the energy required per ice weight. As a result of decreasing cycle time, the amount of ice produced per 24 hr is increased by 2.6% to 7.9%.

56 Figure 4.3: Schematic of an ACIM with a waste heat reclamation circuit.

Table 4.3: Comparison of results between running the model using the waste heat recovery with running the model without the recovery unit.

Operating Condition: Ta/T su 100 / 110 oF 90 / 70 oF 70 / 50 oF Recovery system NO YES ∆ NO YES ∆ NO YES ∆ Freezing (min) 24.5 24.2 -1.2% 16.4 16.3 -0.7% 13.8 13.7 -0.2% Harvest (min) 0.8 0.4 -48.8% 1.1 0.6 -43.9% 1.6 1.4 -14.6% Ice per 24 hrs. (lbs.) 279 287 2.6% 393 424 7.9% 473 505 6.8% Energy input (kWh/100lb) 8.61 8.24 -4.3% 5.57 4.78 -14.1% 4.24 3.88 -8.6% Energy input (kWh/24hr) 24.0 23.6 -1.8% 21.7 20.3 -6.5% 20.1 19.7 -2.1%

57 Figure 4.4: ACIM with a waste heat recovery system.

58 CHAPTER V

CONCLUSION AND FUTURE WORK

5.1 Conclusion

This research outlined a steady-state and transient simulation models of the operation of an air cooled condenser with brazed plate heat exchanger and an automatic commercial ice maker respectively. The models are based on fundamental, physics-based principles of individual system components. An Artificial Neural Network is used to model the brazed plate heat exchanger. Governing equations for the compressor, condenser, expansion valve, and connecting tubing were adapted from prior research available in the literature. A custom evaporator model was developed to describe the heat transfer between the refrigerant and water over an ice formation grid. Simulation results from the ACIM model were compared with the experimental data of a fully instrumented, standard 500 lb capacity ice machine, operating under various ambient air and water inlet temperatures. Key aggregate measures of the ice machine’s performance include the freeze and harvest cycle time, energy input per 100 lb of ice, and energy usage for 24 hours. For these measures, the model’s accuracy is within 5% for a variety of operating conditions. The simulation model was used to assess strategies for improving the energy efficiency of the ice maker. Increasing the compressor efficiency by 10%, decreases the energy input per ice weight by up to 9.2%. Harvest mode become longer and freezing mode become shorter. Over all, there is almost no change in ice produced per day ±1%. Waste heat recovery strategy saves up to 8.6% of the energy input per ice weight. The harvest time has reduced by up to 48.8% and freezing time by up to 1.2%.

59 5.2 Future Work

The models presented in this research provide a powerful tool that can be used to understand how the overall system responds to the change in any of its components or to the change in the operating conditions. More saving energy opportunities can be discovered and new system designs can be assessed by using these models. Future work can improve the model accuracy and add more features to it.

The work have been accomplished in this research can be extended to include modeling micro- channel air heat exchangers witch have better performance enhancement than cross ﬁn and tube heat exchangers [54]. Most vehicles use micro-channel air heat exchangers in their heating systems.

However, they are not commonly used in residential air-conditioner. The extended model can be used to investigate the potential energy saving in using the micro-channel and to predict the overall system behavior.

The transient model presented in this research can be extend to include wider range of refrigerants. Different generation of refrigerants have been explored since the cooling systems was invented.

The overall cooling system efﬁciency is depend on the refrigerant characteristic. Part of improving the cooling system is improving the working medium.

The current ice machine model releases the ice from the evaporator grid after melting a speciﬁc percentage of the ice. Advanced modeling for melting the ice during the harvest mode will allow the model to be used to investigate how the gird surface roughness, material and shape affect the energy and time required for the harvest.

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