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APPENDIX 5A. ENERGY MODELING

TABLE OF CONTENTS

5A.1 INTRODUCTION ........................................................................................................ 5A-1

5A.1.1 FREEZE Model Description .......................................................................... 5A-1

5A.1.2 Supplemental Evaporator Thermal Conductance Spreadsheets for Batch 

Type Machines ............................................................................................... 5A-4

REFERENCES ......................................................................................................................... 5A-8

LIST OF TABLES

Table 5A.1.1 Review of FREEZE Component Modeling ........................................................ 5A-4

LIST OF FIGURES

Figure 5A.1.1 Evaporator Thermal Conductance versus Ice Mass .......................................... 5A-6

Figure 5A.1.2 Calculated Evaporator Overall Thermal Conductance and Refrigerant 

Temperature versus Time into Freeze Cycle .................................................... 5A-7
5A-1

APPENDIX 5A. ENERGY MODELING

5A.1 INTRODUCTION

This appendix describes the FREEZE model that the U.S. Department of Energy (DOE) 

used to conduct energy modeling for the engineering analysis for automatic commercial ice 

makers. FREEZE simulates the performance of both batch ice makers (e.g., cubers) and 

continuous ice makers (e.g., flakers and nugget type machines). FREEZE is a transient model 

that can calculate changes in operating conditions as a function of time. While this feature is not 

needed for continuous ice makers, it is important for batch machines in which refrigerant 

temperatures and pressures change significantly during the freeze cycle due to ice buildup on the 

evaporator. 

5A.1.1 FREEZE Model Description

The original version of FREEZE was developed by Anthony Varone in 19951 to operate 

in an MSDOS environment. It has since been upgraded to operate in a Windows environment. 

The model can simulate systems with a variety of configurations, which include: 

• batch or continuous ice making, 

• air-cooled or water-cooled condensers, 

• batch type or continuous water makeup, 

• internal or external water pump,

• existence of a liquid-line/ suction-line heat exchanger, 

• choice of compressor, and

• choice of common refrigerants. 

FREEZE is a system-level model that calculates the complex interactions among 

individual components. With the exception of air-cooled condensers, component performance 

characteristics are specified by the user. An advantage to this approach is that the model can 

simulate machines of many different configurations as long as component performance data is 

consistent with the input parameters in the FREEZE model.

For batch type machines, output includes: 

• overall ice production rate, energy consumption, and freeze cycle time 

• evaporator, sump water, and refrigeration system temperatures 

• refrigeration system pressures, power input, and ice growth versus time during the freeze 

cycle

The FREEZE process is modeled using energy balances on the evaporator mass, ice 

mass, sump water, and water system. The evaporator plate, ice mass, sump water, and water 

system are each treated as lumped bodies, each at its own uniform temperature to calculate 

transient heat transfer between components. The energy balances account for heat transfer into 

and out of each component, energy storage, latent heat conversion associated with freezing, and 

enthalpy fluxes associated with refrigerant flow and/or makeup water flow in and out of each 

component. External heat transfer into the system includes ambient heat leak and the electrical 

energy associated with the water pump. 
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A major challenge to modeling batch type machines is calculating the overall evaporator 

thermal conductance, which varies throughout the cycle due to ice buildup on the plate and 

decreasing refrigerant mass flow rate with time. This is accomplished using user-defined curves 

for heat transfer versus ice mass on the plate that account for conduction heat transfer from the 

water, through the ice, and through the evaporator plate. Refrigerant heat transfer coefficients are 

calculated within the program and are used along with the evaporator thermal conductance to 

calculate the overall thermal conductance from the water to the refrigerant. Refrigerant 

evaporator heat transfer coefficients and pressure drop are calculated within the program using 

models originally developed by Varone.2

The evaporator thermal conductance curves are generated by a separate conduction heat 

transfer analysis and depend on the specific evaporator design. The curves are described as sixthorder, best-fit polynomials for evaporator thermal conductance as a function of ice mass on the 

plate. The evaporator UA curves were developed using auxiliary spreadsheets for the two most 

common evaporator types, as discussed the following section. 

The refrigerant cycle model is a descendent of the NIST CYCLE73 model, modified to 

incorporate the transient effects associated with ice buildup on the evaporator plate. There is a 

choice of six refrigerants, including R-404A, the most common refrigerant used in ice making 

applications. Refrigerant thermodynamic and thermophysical properties are calculated using

Refprop 8.0.4 Refrigerant thermal conductivity and viscosity are calculated using curve fits 

developed from refrigerant manufacturer literature. 

Continuous ice makers operate at steady-state; thus, conditions do not change with time. 

Program output includes ice production rate, energy consumption, and refrigerant cycle 

conditions. As with the modeling of batch type machines, evaporator thermal performance is a 

user-defined parameter and is not calculated within the program. Additional inputs include ice 

quality, auger motor power and efficiency, and heat leak from the ambient air into the 

evaporator.

Compressor performance is determined from user-created data files based on compressor 

maps provided by compressor manufacturers. Compressor capacity and power are adjusted at 

each point in the calculation to reflect suction conditions different from rating conditions. 

Machines with either air-cooled or water-cooled condensers can be modeled. For aircooled condensers, refrigerant and air-side heat transfer coefficients and pressure drop are 

calculated within the program using models originally developed by Varone2 and enhanced to 

incorporate more recent correlations. Required heat exchanger input data include tube diameter 

and wall thickness, number of tubes, tube spacing, fin type, spacing, and material, airflow rate 

and inlet temperature, fan power, and refrigerant subcooling. 

Water-cooled condenser operation is based on maintaining a constant condensing 

pressure and therefore temperature, and is thus modeled based on maintaining a constant 

condensing bubble-point temperature as defined by the user. User inputs include condensing 

temperature, refrigerant subcooling, and pressure drop. 
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The expansion device (e.g., thermal expansion valve) is not modeled explicitly. Instead, it 

is simulated in the model as maintaining a constant evaporator superheat throughout the freeze 

cycle as specified by the user. 

The program can model systems with a liquid-line/suction-line heat exchanger and 

accounts for suction line heat gain from the ambient air and refrigerant pressure drop. User 

inputs include heat exchanger effectiveness, suction line heat transfer, and pressure drop. 

Each freeze cycle requires a flow of water necessary to flush impurities from the system 

and to provide water to make up for the water harvested as ice. Generally, one of two strategies 

for providing makeup water is used. The first, referred to as a batch fill strategy, involves filling 

the sump with the water needed to produce a batch of ice. The second strategy, referred to as a 

continuous fill strategy, involves supplying a flow of makeup water corresponding to the rate at 

which ice is frozen on the evaporator plate. Both strategies can be modeled.

Evaporator cold compartment configurations vary widely and thus are not amenable to 

general analytical treatment. Some designs enclose the evaporator in a fully insulated cabinet 

with a plastic liner, while others form the evaporator cold compartment using cabinet sheet metal 

with Styrofoam insulation. Some designs have parts of walls or even entire walls that are 

uninsulated. Some place the sump entirely inside the cold compartment, while others have the 

sump straddling the cold compartment and the compressor compartment. Because of the wide 

variety of designs, the model does not calculate the heat leak into the cold compartment from 

basic cabinet design parameters. Instead, it is modeled using a user-defined evaporator cold 

compartment thermal conductance parameter.

The harvest process involves bypassing the condenser to allow hot refrigerant to flow 

directly from the compressor to the evaporator to provide the heat input to free the ice from the 

plate. A number of manufacturers also assist the harvest process by mechanical means or by 

using the heat contained in the makeup water. Thus, the harvest process has complexities similar 

to those involved with the freeze process. In FREEZE, the effects of harvest on performance are 

determined based on input data for the harvest time, ice meltage, and harvest energy 

consumption. 

Parasitic power consumption of components such as control circuit boards, solenoid 

valves, and harvest assist devices are modeled by entering the power consumption of each 

component. 

A summary of the FREEZE modeling approach by component is summarized in Table 

5A.1.1 and in the following section. 
5A-4

Table 5A.1.1 Review of FREEZE Component Modeling

Component Model Approach

Compressor Performance determined using manufacturer’s performance data adjusted for conditions 

different from rating conditions.

Condenser

Air-cooled: Air-side and refrigerant-side heat transfer coefficients and pressure drop are 

calculated based on condenser design and airflow rate.

Water-cooled: Modeled to maintain a constant specified condensing temperature.

Expansion device Modeled as constant specified evaporator superheat.

Evaporator

Batch type: Thermal conductance calculated using user-defined data for thermal 

conductance as a function of ice mass on the evaporator combined with refrigerant heat 

transfer coefficients calculated based on instantaneous refrigerant mass flow rate and 

properties. The cycle is defined by the preharvest batch weight as defined by the user.

Continuous: Performance calculated based on user-defined thermal conductance, auger 

motor power, ice quality, and ambient heat leak.

Suction line heat 

exchanger Performance calculated based on user-defined thermal effectiveness.

Suction line Heat leak from ambient and refrigerant pressure drop specified by user.

Cold compartment Heat transfer calculated based on user-defined thermal conductance parameter.

Harvest Requires user to input data for harvest time, duration, and power consumption.

Auxiliary electrical 

loads Power consumption specified by user.

Refrigerant 

properties References 2 and 4, and curve fits of manufacturer data.

Heat transfer 

coefficients and 

pressure drop

References 5, 6, 7, 8, 9, and 10. 

5A.1.2 Supplemental Evaporator Thermal Conductance Spreadsheets for Batch Type 

Machines

For batch type machines, the FREEZE model requires the user to input the evaporator 

thermal characteristics in the form of a sixth-order polynomial curve fit for evaporator thermal 

conductance as a function of ice mass on the plate. In addition to the six coefficients, the curve is 

defined in terms of the evaporator thermal conductance at the start and end of the freeze process. 

This approach allows FREEZE to simulate the performance of any evaporator design since 

evaporator design specifics are not considered in the FREEZE model. 

The majority of batch type machines incorporate one of two evaporator designs: (1) the 

copper plate-grid; or (2) the stainless steel sheet-copper tube. Each of these is described in the 

following. 

• The copper plate-grid, also called a “waffle” evaporator, consists of copper gridwork 

bonded to a copper plate. Copper refrigerant tubing is bonded to the back of the copper 

plate. The components are bonded by brazing. 
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The evaporators are mounted vertically. Water is introduced at the top of the evaporator 

and cascades over the copper grid. Ice builds up inside each cell formed by the grid until 

each cell is filled with ice. Ice also forms on the edges of the copper grid, forming a 

“bridge” between cubes. The bridge serves two purposes. First, in many ice makers 

harvest is initiated when the bridge thickness reaches a predetermined thickness. Second, 

the bridge creates a monolithic slab of ice on the plate that ensures all cubes fall off the 

plate simultaneously. Ideally, the bridge should break when the ice falls into the bin to 

create individual cubes. Most machines of this type also assist the harvest process by 

using a mechanical means to push the ice slab off the plate.

The copper gridwork determines cube size. The most common cube sizes are (a) 3/8 inch 

wide by 7/8 inch high by 7/8 inch deep; and (b) 7/8 inch wide by 7/8 inch high by 7/8 

inch deep. The cube face is not usually flat, but often has concavities or “divots” due to 

relatively poor heat transfer through the cube compared to the copper grid. 

• The stainless steel sheet-copper tube evaporator consists of pleated stainless steel sheets 

soldered to both sides of a flattened copper serpentine tube. The pleats are vertical, 

forming channels that direct water down the sheet. Ice forms as water freezes where the 

sheet is bonded to the copper tube. The stainless steel sheet is relatively thin, resulting in 

relatively poor heat transfer along the sheet and pleats. Most of the heat transfer is 

directed through the ice directly toward the contact patch between the sheet and tube.

The ice is harvested using a combination of hot-gas bypass and incoming makeup water 

introduced between the two stainless steel sheets. The resulting cube has an 

approximately semicircular cross section and is 1-1/2 inches long by 1-1/8 inches wide 

by 1/2 inch thick. 

Spreadsheets have been created to help the user develop the thermal conductance curves 

of each evaporator design described above. Normally, the thermal analysis involves calculating 

the ice growth as a result of the heat removed from the ice and water. The analysis used in the 

spreadsheets is actually the reverse of that process, in that the thermal conductance is calculated 

based on an assumed pattern of ice growth. Note that this analysis does not include the effects of 

the refrigerant heat transfer coefficient, which is calculated in the FREEZE model during the 

simulation.

For the waffle design, input parameters include the cell dimensions, number of cubes, 

copper grid thickness, copper tube dimensions, bond thickness, and material thermal properties. 

Cube input parameters include ice thermal properties, bridge thickness, and divot dimensions. 

The water heat transfer coefficient is also an input parameter.

For the pleated stainless steel sheet-copper serpentine design, input parameters include 

dimensions of the cube, contact patch, and copper tube; the water heat transfer coefficient; and 

material thermal properties.

The output of the spreadsheets consists of the evaporator thermal conductance at the start 

and end of the freeze process along with the six polynomial coefficients of best-fit polynomial 

curve of thermal conductance versus ice mass on the plate. An example of the results of a 
5A-6

thermal conductance analysis for a waffle evaporator from a 250 lb/24 hr capacity machine is 

shown in Figure 5A.1.1. 

The results shown in Figure 5A.1.1 demonstrate the effect that the ice has on the 

evaporator thermal conductance. At the start of the freeze process, the conductance is roughly 

620 Btu/hr -F. The conductance decreases rapidly as ice builds up on the plate until it is reaches 

a value of about 100 Btu/hr -F. 

Figure 5A.1.1 Evaporator Thermal Conductance versus Ice Mass

The effect of the refrigerant heat transfer coefficient on the calculated overall thermal 

conductance as a function of time into freeze cycle is shown in Figure 5A.1.2. Also shown is the 

resulting effect on refrigerant evaporator temperature. At the start of the freeze cycle, the overall 

conductance is about 350 Btu/hr-F. The conductance declines throughout the cycle as a result of 

ice buildup on the plate, reaching a minimum of about 70 Btu/hr-F at the end of the freeze 

process.

The effect on the refrigerant evaporator temperature is dramatic. The refrigerant 

temperature is about 65 °F at the start of the freeze cycle then decreases continuously throughout 

the cycle until reaching a minimum value of about -2 °F at the end of the freeze process.

0

100

200

300

400

500

600

700

0 0.5 1 1.5 2 2.5 3

Evaporator Thermal Conductance, Btu/hr-F

Ice Mass (lb)
5A-7

Figure 5A.1.2 Calculated Evaporator Overall Thermal Conductance and Refrigerant 

Temperature versus Time into Freeze Cycle
5A-8

REFERENCES

 

1. Varone, A. F. Program FREEZE for Ice Machine Product Development. August 1995. 

2. Varone, A. F. Condenser, evaporator, and fin-tube heat transfer coefficient and pressure 

drop analysis programs, COND, EVAP, and UAIR. Unpublished. 

3. McLinden, M. Theoretical Vapor Compression Cycle, CYCLE7. Unpublished. 

4. Lemmon, E. W., M. L. Huber, and M. O. McLinden. Reference Fluid Thermodynamic and 

Transport Properties. NIST Standard Reference Database 23, Version 8.0.

5. Dittus, F. W. and Boelter, L. M. K. Heat Transfer in Automobile Radiators of the Tubular 

Type. University of California Publications in Engineering. 2(1930):443–461. 

6. Pierre, B. Kytleknisk Tidskript. May 1957. 3:129. 

7. Lockhart, R. W. and R. C. Martinelli. Proposed Correlation of Data for Isothermal TwoPhase, Two-Component Flow in Pipes. Chemical Engineering Progress. 45(1):39–48. 

8. Wang, C. Recent Progress on the Air-side Performance of Fin-and-Tube Heat Exchangers.

International Journal of Heat Exchanges. 1524-5608, 1(2000):49-76. 

9. Vera-Garcia, F., et al. Assessment of Condensation Heat Transfer Correlations in the 

Modeling of Fin and Tube Heat Exchangers. International Journal of Refrigeration. 

30(2007):1018–1028. 

10. Shah, M. M. A General Correlation for Heat Transfer during Film Condensation in Pipes. 

International Journal of Heat and Mass Transfer. 22(1979): 547–556.