NIST Technical Note 1806

Improving the Performance of a 

Roof Top Air-Conditioning Unit by 

Refrigerant Circuitry Optimization

David Yashar

Sunil Lee 
NIST Technical Note 1806

Improving the Performance of a 

Roof Top Air-Conditioning Unit by 

Refrigerant Circuitry Optimization

David Yashar 

Sunil Lee 

Energy and Environment Division 

 Engineering Laboratory 

July 2013 

U.S. Department of Commerce 

Penny Pritzker, Secretary

National Institute of Standards and Technology 

Patrick D. Gallagher, Under Secretary of Commerce for Standards and Technology and Director 
Certain commercial entities, equipment, or materials may be identified in this

document in order to describe an experimental procedure or concept adequately.

Such identification is not intended to imply recommendation or endorsement by the

National Institute of Standards and Technology, nor is it intended to imply that the

entities, materials, or equipment are necessarily the best available for the purpose. 

National Institute of Standards and Technology Technical Note 1806 

Natl. Inst. Stand. Technol. Tech. Note 1806, 68 pages (July 2013) 

CODEN: NTNOEF
iii

IMPROVING THE PERFORMANCE OF A ROOF TOP AIR-CONDITIONING 

UNIT BY REFRIGERANT CIRCUITRY OPTIMIZATION

David A. Yashar and Sunil Lee 

National Institute of Standards and Technology 

Gaithersburg, MD 20899 

Abstract

This study demonstrates the performance improvement of an air-to-air roof top unit 

(RTU) achieved by optimizing an evaporator’s refrigerant circuitry using evolutionary 

algorithms. The subject of this study is a unit with a cooling capacity of 7.5 Tons 

(26.4 kW). The RTU employs two separate refrigerant cycles having separate 

compressors, condensers, and thermostatic expansion valves (TXV) but using a single 

evaporator slab in which two separate refrigerant circuits are implemented. 

We modified the RTU by replacing the refrigerant-to-air condensers with water 

cooled brazed plate heat exchangers in order to facilitate testing. Performance tests 

were conducted in a conditioned environmental chamber in line with AHRI standard 

340/360-2007; in order to accomplish this, we maintained the liquid line saturation 

pressure and subcooling from the manufacturer’s test data by adjusting the condenser 

water flow rate and temperature. We also measured the in-situ air velocity profile using 

Particle Image Velocimetry (PIV), a non-intrusive, laser-based technique. The 

measurements showed that the range of air velocities passing through the heat exchanger 

varied from 0.5 ms-1 to 3.0 ms-1, with the area weighted average of the measurements 

being 1.75 ms-1. The PIV data was used to generate a map of the air flow distribution 

through the heat exchanger, which served as the basis for refrigerant circuitry 

optimization. 

We simulated the performance of the original evaporator using the measured air 

velocity distribution and The National Institute of Standards and Technology’s (NIST) 

heat exchanger model, EVAP-COND, and tuned our computational model to exactly 

match the laboratory measurements. We then used the measured air velocity 

distribution with NIST’s evolutionary algorithm optimization module, Intelligent System 

for Heat Exchanger Design (ISHED), to redesign the evaporator circuitry. The 
iv

optimization process resulted in a design with a simulated capacity nearly 8 % higher 

than the original design. 

The RTU manufacturer produced a new evaporator implementing the optimized 

refrigerant circuitry. We replaced the original evaporator with the prototype of the 

optimized evaporator and measured the system’s performance. The system with the 

optimized evaporator showed an improvement of 2.2 % in capacity and 2.9 % in COP

over the performance of the original system, which is consistent with the expected system 

improvement resulting from an evaporator with an 8 % larger capacity. The achieved 

improvement in RTU performance requires no additional material cost since it only 

involves changes to the refrigerant circuitry. 

Keywords: Air Velocity Profile, Roof Top Air Conditioning Unit, Particle Image 

Velocimetry (PIV), Circuitry optimization
v 

Acknowledgement

This study was sponsored by the United States Department of Energy, Building 

Technologies Office under B&R Code BT0302000-05450-1004215-Sp Cond & Ref R&D

with project managers Antonio Bouza and Bahman Habibzadeh. In kind support was 

provided by Jake Rede, Vince Barone, and Dan Arnold of the Nordyne Corporation. Dr. 

W. Vance Payne and Mr. John Wamsley provided assistance with test setup and operating 

the environmental chambers. 
vi 

Table of Contents

Abstract .............................................................................................................................. iii

Acknowledgement ...............................................................................................................v 

Table of Contents ............................................................................................................... vi 

List of Figures .................................................................................................................. viii

List of Tables ........................................................................................................................x 

1. INTRODUCTION ...........................................................................................................1 

2. EXPERIMENTAL SETUP ..............................................................................................3 

 2.1 Roof Top Air Conditioning Unit ............................................................................3 

 2.2 System Modifications ............................................................................................4 

 2.3 Test Apparatus and Instrumentation .......................................................................5 

 2.4 PIV Air Flow Measurement System ....................................................................10 

3. SYSTEM TESTS WITH ORIGINAL EVAPORATOR .................................................14 

4. AIR FLOW DISTRIBUTION TESTS ...........................................................................18 

5. PERFORMANCE OPTIMIZATION .............................................................................24 

 5.1 Modeling and Simulating Performance of the Original Evaporator ....................24 

 5.2 Refrigerant Circuitry Optimization ......................................................................28 

6. SYSTEM TESTS WITH OPTIMIZED EVAPORATOR ..............................................33 

 6.1 System Setup and Test Results.............................................................................33 

 6.2 Discussion of Measured Performance Improvement ...........................................36 

7. SUMMARY ...................................................................................................................41 

8. REFERENCES ..............................................................................................................43 

Appendix A: Data recorded during performance measurement tests with original heat 

exchanger ...............................................................................................................45 
vii 

Appendix B: Data recorded during performance measurement tests with optimized heat 

exchanger ...............................................................................................................49 

Appendix C: Uncertainty analysis .....................................................................................54 
viii

List of Figures 

2.1.1 Schematic of Test Subject ...........................................................................................3 

2.1.2 Middle Compartment of Test Subject .........................................................................4 

2.2.1 Visual Access to RTU’s Evaporator ............................................................................5 

2.3.1 Refrigerant Flow Loop ................................................................................................6 

2.3.2 Water Flow Loop ........................................................................................................7 

2.3.3 Air Flow Loop .............................................................................................................8 

2.3.4 Photo of Test Apparatus ..............................................................................................9 

2.4.1 Schematic of a Basic 2D PIV Setup .........................................................................10 

2.4.2 Layout for PIV Measurements .................................................................................. 11

2.4.3 Projected Laser Light Sheet and Camera ..................................................................12 

2.4.4 PIV Measurement Data: (a) See Particles Exiting Evaporator and (b) Vector Field 

Calculated from Particle Motion ............................................................................13 

4.1 Evaporator with Marked Air Velocity Measurement Planes ........................................18 

4.2 Velocity Vector Field at 330 mm ..................................................................................19 

4.3 Blowup of Velocity Field at Heat Exchanger Outlet ...................................................20 

4.4 Numerical Integration of Data to Remove Periodic Patterns Associated with Tube 

Sites ........................................................................................................................21 

4.5 Air Velocity Flow Map .................................................................................................22 

4.6 1D Flow Distribution ...................................................................................................23 

5.1.1 Sketch of Original Evaporator Design ......................................................................24 

5.1.2 Sketch of Reduced Matrix Representation of Original Evaporator Design ..............25 

5.1.3 Coil Design Data for reduced Evaporator Design ....................................................25 

5.1.4 Simulation Result from Original Evaporator Design................................................27 
ix

5.1.5 Refrigerant Outlet Quality from Simulation .............................................................27 

5.1.6 Refrigerant Outlet Temperature (oC) from Simulation .............................................27 

5.2.1 ISHED Optimized Design Before Post-Processing ..................................................29 

5.2.2 ISHED Optimized Design After Post-Processing .....................................................30 

5.2.3 ISHED Optimized Design After Post-Processing, Full Representation ...................30 

5.2.4 Simulation of Stage 1 Operation of Optimized Evaporator ......................................31 

5.2.5 Simulation of Stage 2 Operation of Optimized Evaporator ......................................32 

6.1 Prototypes of (a) Original Evaporator and (b) Optimized Evaporator ........................33 

6.2.1 Measured Cooling Capacity with Original and Optimized Evaporator ....................36 

6.2.2 Measured COP for Stage 1, Stage 2, and System with Original and Optimized 

Evaporator ..............................................................................................................37 
x 

List of Tables

3.1 Target Refrigerant Conditions During Baseline Performance Tests ............................14 

3.2 Refrigerant Side Capacity and COP Measurements for System with Original 

Evaporator ..............................................................................................................16 

5.1.1 Operating Conditions for Simulation Model ............................................................26 

5.1.2 Coefficient Correction Parameters for Simulation Model ........................................26 

5.2.1 ISHED Control Parameters for Circuitry Optimization Run ....................................28 

6.1.1 Refrigerant Side Capacity and COP Measurements for System with Optimized 

Evaporator ..............................................................................................................35 

6.2.1 Comparison of Stage 1 Operation Between Tests with Original and Optimized 

Evaporators ............................................................................................................40 

6.2.2 Comparison of Stage 2 Operation Between Tests with Original and Optimized 

Evaporators ............................................................................................................40 

A.1 – Test 1 with Original Evaporator ...............................................................................45 

A.2 – Test 2 with Original Evaporator ...............................................................................45 

A.3 – Test 3 with Original Evaporator ...............................................................................46 

A.4 – Test 4 with Original Evaporator ...............................................................................46 

A.5 – Test 5 with Original Evaporator ...............................................................................47 

A.6 – Test 6 with Original Evaporator ...............................................................................47 

A.7 – Test 7 with Original Evaporator ...............................................................................48 

A.8 – Test 8 with Original Evaporator ...............................................................................48 

B.1 – Test 1 with Optimized Evaporator ............................................................................49 

B.2 – Test 2 with Optimized Evaporator ............................................................................49 

B.3 – Test 3 with Optimized Evaporator ............................................................................50 
xi 

B.4 – Test 4 with Optimized Evaporator ............................................................................50 

B.5 – Test 5 with Optimized Evaporator ............................................................................51 

B.6 – Test 6 with Optimized Evaporator ............................................................................51 

B.7 – Test 7 with Optimized Evaporator ............................................................................52 

B.8 – Test 8 with Optimized Evaporator ............................................................................52 

B.9 – Test 9 with Optimized Evaporator ............................................................................53 

C.1 Calculation of Total Uncertainty for Measured Parameters, Test 1 with Optimized 

Evaporator ..............................................................................................................55 
1 

INTRODUCTION

Finned-tube heat exchangers are the predominant type of heat exchangers used in comfort

cooling applications. Finned-tube heat exchangers are generally made up of a bundle of 

several dozen connected tubes. As refrigerant flows through each of the tubes, heat is 

transferred between it and the air flowing along the outside of the tube. The 

performance of the heat exchanger as a whole is the aggregate performance of every tube 

in the bundle. The heat transfer performance of each individual tube is influenced by 

many parameters including the tube and fin geometries; the refrigerant temperature, mass 

flux, and local quality; and the local air velocity, temperature, and humidity. The local 

air velocity is one of the most important parameters because it dictates the amount of air 

that is available for heat exchange and it influences the local air-side heat transfer 

coefficient. To this end, the distribution of the air incident on the heat exchanger has a 

profound impact on its overall performance, since it characterizes the velocity of air at 

each tube location in the bundle. 

There has been long standing interest in air flow distributions through finned tube heat 

exchangers. The first documented study was that of Fagan (1980), which examined the 

effects on small heat exchangers used in room air conditioners. His study showed that 

typical air maldistributions commonly result in quite large velocity variations and that the 

impact on performance is significant. Chwalowski et al. (1989) later showed similar 

results indicating large air velocity maldistributions and went on to demonstrate as much 

as a 30 % variation in capacity for a given evaporator when subject to different air flow 

distributions. Payne et al. (2003) demonstrated that air-side non-uniformity can impose 

a significant reduction in heat exchanger capacity, as much as 30% in the extreme cases, 

which agrees with the earlier work by Chwalowski. 

The current state-of-the-art for measuring air-side velocity distribution is by traversing a 

hot wire anemometer or pitot tube. Although this method is simple and low cost, it is

cumbersome and has high measurement uncertainty both due to precision and the user’s 

ability to maintain the position and orientation of the sensor in the exact location of 

interest. Furthermore, the probes for these tools are obstructive to the flow field. There 

are a few optically based methods available, which eliminate disruptions of the flow by 

the sensor probe. Particle Image Velocimetry (PIV) is used in this study since it 

provides the ability to characterize large sections of the flow field. 
2 

The traditional tendency is to design finned tube heat exchangers with the assumption of 

a uniform air velocity profile or implement a refrigerant circuitry that would offer some 

degree of robustness with non-uniform air distribution (Kaern, 2013). Because new 

tools are available to measure velocity distributions and design components that account 

for these distributions, the problem of air-side velocity distribution is beginning to get 

more attention. An approach described by Yashar et al. (2012), involving recent 

developments in machine learning as incorporated into the Intelligent System for Heat 

Exchanger Design (ISHED), has demonstrated that the capacity degradation due to airside non-uniformity can be mitigated by designing the optimal refrigerant circuitry for the 

actual air flow distribution seen in the system. Furthermore, optimizing the refrigerant 

circuitry designs using machine learning based on knowledge of the air distribution can 

result in significantly improved capacity while simultaneously reducing the size, cost, 

and amount refrigerant charge (Domanski et al., 2010). 

The objective of this study is to experimentally demonstrate the system performance 

improvement achieved by optimizing the evaporator’s refrigerant circuitry. In the first 

part of this study, the in-situ air velocity distribution was measured using PIV. This 

detailed mapping was then used as input to the optimization tool ISHED to determine a 

better performing refrigerant circuitry. Next, a prototype of an evaporator with the 

optimized circuitry was built, installed in the system, and the predicted performance 

improvement was verified by laboratory measurements. 
3 

EXPERIMENTAL SETUP

This section discusses the roof top test unit, the modifications that were made to the unit 

in order to perform the air flow distribution measurements, and the measurement 

instrumentation and methods used to obtain all of the data. 

2.1 Roof Top Air-Conditioning Unit

The system examined in this study is a small commercial roof top unit (RTU). The unit 

is an air-to-air R410A air conditioning system and has a nominal capacity of 7.5 Tons 

(26.4 kW). It consists of two separate vapor compression systems so that it can operate 

in stages under part load conditions or with both stages operating to meet full load 

conditions. Each stage has its own compressor, condenser and expansion valve; the unit 

has a single evaporator slab that is shared by the two stages with each stage utilizing half 

of the available heat transfer area. The two stages are designated by the names Stage 1 

and Stage 2 throughout this document. 

A cutaway schematic of the unit is shown in Figure 2.1.1. The unit is sectioned into 

three compartments. The condenser compartment (left side) consists of two condensers 

and a single fan that draws air from the outside through the condensers. The right side 

of the unit is the air discharge compartment, which delivers conditioned air to the 

building. The middle evaporator compartment is the focus of this study; it is where the 

building air is conditioned and blown into the discharge compartment. 

Figure 2.1.1 Schematic of Test Subject
4 

Figure 2.1.2 shows a side view of the middle compartment. The building air enters this 

compartment through an intake port (not shown) located at the bottom right in 

Figure 2.1.2. Included in this compartment are a set of air filters, an evaporator fed by 

two separate refrigerant loops, a condensation collecting tray, and a blower that circulates 

air through the compartment and out to the discharge compartment. 

Figure 2.1.2 Middle Compartment of Test Subject

The evaporator is slanted at an angle of 15 degrees from the vertical and is made up of 

144 tubes located in four depth rows with louvered fins. The tubes have an outside 

diameter of 9.52 mm (3/8”) and are spaced 25.4 mm (1”) apart along the height of the 

heat exchanger. The depth rows were layered in a staggered configuration and are spaced 

22 mm (7/8”) apart. The overall dimensions of the evaporator are 914 mm (36”) high, 

864 mm (34”) wide, and 101.6 mm (4”) thick. The total heat transfer area provided by the 

evaporator is divided amongst the two stages of the system. In total the evaporator is 

divided into 16 circuits with 8 circuits used by each stage; each circuit consists of either 8 

or 10 tubes. 

2.2 System Modifications

Two aspects of the test unit were modified for the purpose of experimentation. The first 

modification was to the condensing section of the unit. The RTU was designed to operate 

as an air-to-air unit, but was modified to be an air-to-water unit to facilitate testing. 

Each finned-tube condenser was replaced with a brazed-plate heat exchanger, which was 

connected to a cold water loop with variable water temperature and flow rate in order to 
5 

control the refrigerant condensation. Replacing the air-cooled condensers with water

cooled heat exchangers allowed measurement of the system performance while only 

operating a single environmental chamber. 

The second modification to the system involved the RTU’s enclosure. Several of the 

insulated metal panels that made up the walls of the enclosure were removed and 

replaced with 6.35 mm (1/4”) thick transparent acrylic panels. These panels provided 

the visual access necessary to measure the air flow distribution inside the enclosure with 

optical techniques. Figure 2.2.1 shows a picture of the RTU from the top looking 

downward through one of the acrylic panels. The evaporator and blower are visible 

through this panel. 

Figure 2.2.1 Visual Access to RTU’s Evaporator 

2.3 Test Apparatus and Instrumentation

The test apparatus is described in three parts. The first portion of the apparatus is the 

refrigerant loop shown in Figure 2.3.1. The unit is comprised of two separate 

refrigerant flow loops, one for each stage of cooling. Each stage has its own compressor, 
6 

condenser, thermostatic expansion valve (TXV), and uses half of the heat transfer 

refrigerant tubes in the interlaced evaporator which are distributed across the total heat 

transfer area of the evaporator. Figure 2.3.1 shows the position of the points along the 

refrigerant loops where the refrigerant properties were measured. The stage 1 loop is 

described by the refrigerant exiting the stage 1 compressor at point 1A, and then

condensed in a water cooled heat exchanger. The liquid refrigerant exiting the stage 1 

condenser flows through a coriolis mass flow meter and then onto point 1B, just before 

entering the enclosure for the RTU. Once inside, it is flashed by passing through the 

stage 1 TXV. After expansion, the refrigerant is distributed amongst 8 different circuits 

of the evaporator, which exit the evaporator through a header tube at point 1C, and then 

continue out of the enclosure and back to the stage 1 compressor. The stage 2 loop is 

identical, and the measurement positions are likewise labeled 2A-2C. 

Figure 2.3.1 Refrigerant Flow Loop 

The refrigerant pressure at each of these points was measured using pressure transducers 

with a 0 to 3447 kPa (0 to 500 psig) range and uncertainty of ±0.13 full scale at 95 % 

confidence. The refrigerant temperature was measured using T-type thermocouples 

probes immersed in the flow, calibrated to 0.15 K (0.3 oF) at 95 % confidence. We also 

measured the refrigerant temperature at several of the heat exchanger return bends using 

thermocouples adhered to the outside of the select tubes. The refrigerant mass flow rate 

for each refrigerant loop was measured using a coriolis mass flow meter calibrated to ±1 % 
7 

at 95 % confidence. The capacity of the RTU could be readily calculated using the 

refrigerant enthalpy method based on the mass flow rate and the difference between the 

liquid line and suction line enthalpy for each stage. The electrical power input to the 

blower and each compressor was measured using three separate power analyzers 

calibrated to ±0.25 % at 95 % confidence. 

The second portion of the apparatus is the water flow loop shown in Figure 2.3.2. The 

purpose of this loop is to control the flow rate and temperature of the water that is 

supplied to each condenser of the refrigerant loop. Water circulates between the 

condensers and a water-to-water vapor compression chiller which rejects heat to the 

laboratory chilled water supply. The temperature of the water supplied to the 

condensers is set by the controls on the chiller. After water exits the chiller it is divided 

into two paths, each one being routed to one of the condensers. The volumetric flow 

rate of water is measured downstream of the split point for each path. A needle valve is 

located just upstream of each condenser to control the flow rate through each path. The 

water temperature is monitored at the inlet and exit of each condenser. The chiller is 

capable of delivering up to 1.4 l/s (22 GPM) of water at a constant temperature by 

removing up to 24 kW (82 kBTU/h) of heat. 

Figure 2.3.2 Water Flow Loop 
8 

The third portion of the apparatus is the air flow loop shown in Figure 2.3.3. 

Conditioned air is supplied to the apparatus by controlling the conditions in the 

laboratory environmental chamber. The air temperature and humidity are measured at 

the inlet portion of the RTU using a grid of 25 thermocouples and a capacitive relative 

humidity sensor. The conditioned air enters the RTU and passes through the evaporator 

where it is cooled and dehumidified. Then it enters the blower and flows through an 

insulated duct to an air flow measurement section. Upon entering this straight section of 

duct, the air is mixed, straightened, and then temperature and humidity are measured. 

The temperature and humidity are measured using a thermocouple grid and sampling tree 

connected to a chilled mirror hygrometer. In addition, the junctions of a 9 junction 

thermopile are connected to the thermocouple grids located at the air intake to the RTU 

and the air flow measurement section to measure the sensible temperature difference. 

The air then passes through a nozzle to measure the flow rate and then onto a booster fan 

(not shown) connected at the measurement section exit before being discharged back into 

the environmental chamber. 

Figure 2.3.3 Air Flow Loop

The T-type thermocouples used to measure the air temperature at each point were

calibrated to 0.15 K (0.3 oF) at 95 % confidence and the thermopile had an uncertainty of 

0.8 % at 95 % confidence. The air flow rate was measured using a nozzle with a
9 

diameter of 254 mm (10”) in accordance with ANSI/AMCA 210 (1985). The pressure 

difference across the nozzle was measured with an electronic differential pressure 

transducer with an uncertainty of ±0.25 % at 95 % confidence. The evaporator capacity 

was calculated using the air enthalpy method according to ASHRAE Standard 37-2009. 

The entire apparatus, shown in Figure 2.3.4, is located in a conditioned environmental 

chamber which is capable of maintaining the air conditions between 10 oC (50 oF) and 

60 oC (140 oF) dry bulb and relative humidity within 2 % of the target setpoint. 

Figure 2.3.4 Photo of Test Apparatus 
10 

2.4 PIV Air Flow Measurement System

Particle Image Velocimetry (PIV) works on the basis of tracking the motion of particles 

entrained in the flow field. These “seed” particles act as markers within the flow field 

whose displacement can be mapped between two points in time. As the seed particles 

move through the test section they are illuminated by a series of laser light sheets. The 

laser sheets are oriented in such a way that the illuminated plane is aligned to the main 

flow direction within the test section; therefore particles moving downstream will remain 

within the illuminated plane between successive light sheet pulses. A camera is used to 

capture images within this plane and therefore records the distance traveled by the seed 

particles during the time between the light flashes, velocity is extracted from this 

information. Figure 2.4.1 shows a schematic of a basic 2D PIV setup. 

Figure 2.4.1 Schematic of a Basic 2D PIV Setup

The PIV measurement system includes of a pair of Class IV pulsed lasers outfitted with a 

sheet forming optical lens, a double framed Charged Coupled Device camera, a theater 

style fog generator, and a Programmable Timing Unit (PTU) controlled by personal 

computer. A detailed description of the measurement equipment can be found in Yashar et 

al. (2007). 
11

Figure 2.4.2 shows the layout for the PIV equipment as set up to measure the air flow 

leaving the evaporator. In this configuration, the lasers are positioned on a tripod high 

above the top of the test unit. The laser light sheets pass through the acrylic window at 

the top of the test unit and illuminate planes perpendicular to the exit surface of the 

evaporator. The camera is set up on the side of the test subject and its view faces the 

light sheet through a second acrylic window. The operation of the camera and the lasers 

are synchronized by the PTU, and data is reduced by mapping the motion of particles 

entrained in the flow within the illuminated plane between successive laser pulses.

Figure 2.4.3 shows the projected laser and image-capturing camera.

Figure 2.4.2 Layout for PIV Measurements 
12 

Figure 2.4.3 Projected Laser Light Sheet and Camera

The PIV system was aligned and calibrated prior to every measured data set at each

specific measurement location. The detailed process for alignment and calibration was

the same as that in previous study by Yashar et al. (2007). After completing the 

alignment and calibration process, the entire environmental chamber was filled with 

glycerin-based theater fog, which served as seed particles for the PIV measurements. The 

camera then captured a series of 100 image pairs of the seeded air flow in the 

measurement area. Each image pair consists of two pictures separated in time by (160 

to 750) μs, depending on the data set. Successive image pairs were taken every 67 ms. 

The velocity field was calculated by tracking the motion of particles from each image to 

its paired image, which resulted in a series of 100 time elapsed vector fields. These vector 

fields were then averaged in time to dilute the unsteady components of the turbulent flow 

structures and produce a more steady-state representation of the flow field. Figure 2.4.4 

shows one snapshot of PIV measurements of the air particles flowing from left to right. 

Figure 2.4.4 (a) shows a camera image of an illuminated plane of seed particles; Figure 

2.4.4 (b) shows the velocity vector field computed from a pair of images. 
13 

(a) (b)

Figure 2.4.4 PIV Measurement Data: (a) Seed Particles Exiting Evaporator and (b) Vector 

Field Calculated from Particle Motion
14 

3. SYSTEM TESTS WITH ORIGINAL EVAPORATOR

A series of tests were performed to characterize the performance of the unit operating 

with the original evaporator. To facilitate the performance measurement, the RTU’s airto-refrigerant finned-tube condensers were replaced with water-cooled brazed-plate heat 

exchangers. The tests of the modified system were performed in such a way that the 

evaporator operated exactly as it would in the original configuration. Since the unit is a 

production model of a commercially available air conditioner, its performance was tested 

by its manufacturer in accordance with AHRI Standard 340/360 (2007) as part of the 

certification process. The manufacturer assisted with this project by providing their test 

data for this unit, which served as a basis for the evaporator operation during the 

laboratory measurements in this study.

This rating standard requires operating two environmental chambers simultaneously; one 

to supply indoor conditions and one to supply outdoor conditions. The indoor chamber 

must supply 1.42 m3s

-1 (3000 CFM) of conditioned air at 26.7 oC (80.0 oF) dry bulb and 

19.4 oC (67.0 oF) wet bulb to the evaporator and the outdoor chamber must provide an 

environment for the condenser at a temperature of 35.0 oC (95.0 oF). While the 

manufacturer performed these tests, they recorded enough data to calculate the refrigerant 

state properties at the inlet of each TXV and the outlet of the evaporator. The refrigerant 

charge and the condenser water temperature and flow rate were adjusted in order to 

match each of the parameters shown in Table 3.1 during the performance tests of the 

baseline system. 

Table 3.1 Target Refrigerant Conditions During Baseline Performance Tests

TXV Inlet Evaporator Outlet

Temperature 

(oC) 

Pressure 

(kPa)

Subcooling 

(oC) 

Temperature 

(oC) 

Pressure 

(kPa)

Superheat 

(oC)

Stage 1 38.1 2690 6.2 12.5 1120 1.4 

Stage 2 37.4 2760 8.1 11.1 1120 3.2 

Throughout this study, the expectation is that the overall improvement in system capacity 

would be fairly small because of the nature of the system’s operation. Domanski (1988) 

provides a method of predicting the performance of a system with a replacement 

evaporator in a residential split system while keeping all other components the same. 
15 

This model generally predicts a change in system capacity that is on the order of 1/3 of 

the difference in capacity between the new and original evaporator measured at the same 

saturation temperature because the system must rebalance itself at a different set of 

saturation temperatures in the evaporator and condenser. For this reason, best efforts were 

taken to minimize all of the measurement uncertainty.

During the tests conducted as part of this study, the capacity measured by the air enthalpy 

method was 2 % - 3 % lower than the capacity measured by the refrigerant enthalpy. 

The main contribution for this difference is conduction of heat through the enclosure 

walls, which is enhanced due to the fact that insulation was removed from the RTU’s 

enclosure in order to outfit it with the acrylic panels and provide visual access inside 

during operation. Other factors, including air infiltration into the negative pressure 

compartment of the enclosure, make significant contributions to this difference. For this 

reason it was determined that the refrigerant side capacity measurements would provide a 

better basis for this work than the air-side capacity measurements, which are required by 

the standard test method, since it is a direct measurement of the evaporator’s performance. 

A total of eight individual measurements of the system’s capacity were recorded over a 

two week period; relevant portions of the recorded data are provided in Appendix A. 

The results of these tests measurements are shown below in Table 3.2. The average 

capacity from these tests is (26.42 ±0.29) kW ((90±1) kBTU/h), which is within 1.8 % of 

the value from the manufacturer’s certification data of 26.85 kW (91.6 kBTU/h). 

It is interesting to examine the values obtained for the ratio of cooling capacity to 

compressor power, which is a measure of the Coefficient of Performance (COP). There 

are four different values for COP listed in the Table. COP Stage 1 is the ratio of cooling 

capacity from Stage 1 to the compressor power for Stage 1; it is a measure of the 

efficiency of the Stage 1 system. Likewise, COP Stage 2 is a measure of the Stage 2 

system efficiency. These values are useful to compare the efficiency of each stage in the 

system, because they exclude the electrical power consumption of the shared components. 

The system COP w/o blower is the ratio of the total cooling capacity from both stages to 

the total compressor power input to the system. The last column in the table lists the 

System COP, which includes the electrical power input from both compressors and the 

blower. Since this system was modified to operate as an air-to-water unit, the system 

COP does not include the influence attributed to the electric energy input to the 

condensing section that was originally built with the system.
16 

Table 3.2 Refrigerant Side Capacity and COP Measurements for System with Original Evaporator

Test 

Number

Capacity 

stage 1

(kW)

Capacity 

stage 2

(kW)

Capacity 

total

(kW)

Stage 1 

Comp 

power 

(W)

COP 

Stage 1

Stage 2 

Comp 

power 

(W)

COP 

Stage 2

System 

COP w/o 

blower 

Blower 

Power 

(W)

System 

COP

1 13.21±0.21 13.13±0.24 26.34±0.32 2927±7 4.51±0.07 3069±5 4.30±0.08 4.39±0.05 1036±27 3.75±0.05 

2 13.18±0.20 13.20±0.23 26.38±0.30 2921±3 4.51±0.07 3067±5 4.30±0.08 4.41±0.05 1014±27 3.77±0.05 

3 13.23±0.20 13.24±0.24 26.47±0.31 2923±8 4.53±0.07 3069±8 4.31±0.08 4.42±0.05 1010±20 3.78±0.05

4 13.24±0.17 13.15±0.19 26.39±0.25 2935±3 4.51±0.06 3072±6 4.28±0.06 4.39±0.04 1019±28 3.76±0.04 

5 13.23±0.18 13.21±0.20 26.44±0.26 2926±5 4.52±0.06 3067±3 4.31±0.07 4.41±0.04 1030±25 3.76±0.04 

6 13.27±0.26 13.16±0.20 26.43±0.33 2932±6 4.53±0.09 3071±3 4.29±0.07 4.40±0.05 1023±30 3.76±0.05 

7 13.31±0.18 13.17±0.21 26.48±0.28 2931±2 4.54±0.06 3054±13 4.31±0.07 4.42±0.05 1018±27 3.78±0.04 

8 13.25±0.15 13.19±0.21 26.44±0.26 2925±4 4.53±0.05 3050±4 4.33±0.07 4.43±0.04 997±19 3.79±0.04 

Average 13.24±0.19 13.18±0.22 26.42±0.29 2927±7 4.52±0.06 3065±10 4.30±0.07 4.41±0.05 1018±26 3.77±0.04

The expressed values are shown as the average of all measurements ± the total combined uncertainty at 95% confidence as described 

in Appendix C.
17 

It is important to note that the values for uncertainty are strictly based on the variance and 

measurement uncertainty of the measured refrigerant mass flow rates, pressures, and 

temperature data and do not consider the uncertainty of the calculated values of 

refrigerant enthalpy inherent to the subroutines in REFPROP (Lemmon et al., 2010), 

which are typically on the order of 1 % (Lemmon and Jacobsen, 2004). This was left 

out of the uncertainty calculations because these performance measurements will be 

compared to performance measurements of the system with the optimized evaporator, 

which will include the same uncertainty components and these components will not 

influence the comparison of the two systems. By accepting this approach, the 

measurement uncertainty for comparative purposes is close to 1 %, which is significantly 

better than that which could be obtained had the air-side capacity measurements been 

used. Example calculations for the measurement uncertainty are provided in 

Appendix C. 
18 

4. AIR FLOW DISTRIBUTION TESTS 

The air flow distribution at the evaporator was measured while operating the unit under 

performance test conditions. In order to ensure that the heat exchanger was operating in 

a steady manner with an adequate level of condensate on the outside surface, the unit was 

operated for a minimum of 30 min between calibrating the PIV measurement system and 

collecting the air flow distribution data. Air velocity data was collected at six different 

lateral positions along the surface of the heat exchanger and the air flow distribution 

exiting the evaporator along each of these planes was determined from the measurements. 

The positions that were queried were 70 mm, 210 mm, 330 mm, 450 mm, 560 mm, and 

740 mm from the edge of the heat exchanger, as indicated in Figure 4.1. 

Figure 4.1 Evaporator with Marked Air Velocity Measurement Planes
19 

Figure 4.2 shows a representative set of PIV data collected during these tests. These

data were taken at the position of 330 mm from the edge. The data was collected in 

seven separate scans and is assembled piecewise with the first picture, labeled V(a), at the 

top of the heat exchanger and V(g) at the bottom, and aligned to form a complete velocity 

profile data set.

Figure 4.2 Velocity Vector Field at 330 mm

Notice that these figures include patterns with several bands of high and low velocities 

exiting the evaporator. There are two aspects that contribute to these patterns. First, the 

pattern stamped into the heat exchanger’s fins cause a distinct pattern of small jets. 

Secondly, the tubes in the last depth row of the heat exchanger cause larger obstructions 

which locally impede the flow. The patterns induced by these two factors are 

highlighted in Figure 4.3. 
20 

Figure 4.3 Blowup of Velocity Field at Heat Exchanger Outlet

The tube locations and jet patterns are quite useful for ensuring proper alignment of the 

data sets when assembling the piecewise segments. It is, however, not information that 

can be used for the simulation phase of this study, and for that reason the flow jet patterns 

were removed from the data set by numerically integrating the measured velocity 

between each pair of adjacent tube locations and assigning a value of the average velocity 

to each midpoint between them. Figure 4.4 illustrates the integration process. The 

dashed black lines represent the measured velocity as a function of position extracted 

from the PIV data, the light blue vertical lines represent the locations of tubes in the last 

depth row of the heat exchanger, and the red markers indicate the average velocity 

between adjacent tube locations as determined by numerical integration of the data.
21 

Figure 4.4 Numerical Integration of Data to Remove Periodic Patterns Associated with 

Tube Sites

Once velocity distribution data set was compiled for each of the 6 lateral positions, it was

assembled into the flow map shown in Figure 4.5. This figure was constructed by 

linearly interpolating between the data collected at each of the adjacent data sets; i.e. data 

collected along the 210 mm and 330 mm lateral positions were used to fill in the area 

between them. Data for lateral positions between the heat exchanger’s edge and the 

location of 70 mm was assumed constant for the purposes of generating the flow map; 

likewise for the data at lateral positions greater than 740 mm. The coordinates listed on 

the flow map reference the upper left-most position on the exit side of the heat exchanger 

shown in Figure 2.1.1 as the origin. This flow map does show several patterns that are a 

result of the features within the RTU enclosure; for example, the air flow near the bottom 

of the heat exchanger (vertical distance > 800 mm) is significantly impeded by the 

condensate collection pan located there and it is also impeded near the lateral midline of 

the map by a mounting bracket for the unit’s air filter located upstream of the heat 

exchanger.
22 

Figure 4.5 Air Velocity Flow Map

Once the flow map was complete, data was extracted from it for the simulation phase of 

this study. The form of the data required as input to the simulation model,

EVAP-COND, is that of a 1D distribution used as the basis for a tube-by-tube analysis. 

Therefore, the velocity map was numerically integrated to determine the appropriate flow 

distribution. The tubes in the heat exchanger are laid out in such a way that each tube is 

located at a constant vertical position and span the horizontal distance shown on the map;

therefore we integrated the flow map in the horizontal direction at every vertical position 

to generate the 1D distribution shown in Figure 4.6. The return bends for the heat 

exchanger are also shown on this figure for illustrative purposes; each air velocity data 

point represents the average air velocity that a tube in that location would realize. 

0 100 200 300 400 500 600 700 800

900

800

700

600

500

400

300

200

100

0

Horizontal distance (mm)

Vertical distance (mm)

0

0.375

0.750

1.125

1.500

1.875

2.250

2.625

3.000
23 

Figure 4.6 1D Flow Distribution

0 100 200 300 400 500 600 700 800 900

0.0

0.5

1.0

1.5

2.0

2.5

3.0

Velocity (m/s)

Position from the top (mm)
24 

5. PERFORMANCE OPTIMIZATION

The next phase of the study involves the computational effort of modeling, simulating, 

and optimizing the performance of the evaporator based on the measurement results. 

5.1 Modeling and Simulating Performance of the Original Evaporator

The first step of this phase was to prepare a model of the evaporator using NIST’s heat 

exchanger simulation software EVAP-COND (Domanski and Yashar, 2010), which uses a 

first principles based, tube-by-tube approach to simulate the performance of finned-tube 

air-to-refrigerant heat exchangers. 

EVAP-COND requires all of the general dimension information of the heat exchanger at 

the onset. One challenge associated with using the current version of EVAP-COND is 

that the program’s structure is currently limited to heat exchangers whose total number of 

tubes is 130 or less. Since the evaporator used in this study has a total of 144 tubes 

(4 rows of 36 tubes) the model had to be modified so that the design would fit within this 

constraint. The original design of the evaporator is laid out as shown below in 

Figure 5.1.1. In this figure, the inlet tubes are shown as thick-walled red circles and the 

exit tubes are shown as thick-walled blue circles. The return bends are shown as lines 

connecting the tubes, the solid lines represent return bends on the near side of the heat 

exchanger, and the dashed lines represent return bends on the far side of the heat 

exchanger.

 Figure 5.1.1 Sketch of Original Evaporator Design 

One simplifying aspect of this design is that the return bends on the far side of the heat 

exchanger are patterned in such a way that they all connect adjacent tubes within the 

same depth row. This pattern is called a “hairpin” pattern because each of the tube pairs 

resembles a large hairpin. This pattern simplifies the manufacturing process because 

each hairpin is one long tube that is bent 180o at its midpoint. Given the fact that this 

design connects each tube to its neighbor in the same depth row and that the air flow 

distribution is continuous, the layout of the evaporator simulation model was reduced by 
25 

redefining each tube pair as a single tube with twice the length of the original tubes. 

This resulted in a reduced matrix model with the total number of tubes cut in half. The

72 tube reduced matrix representation of the evaporator is shown in Figure 5.1.2. 

Figure 5.1.2 Sketch of Reduced Matrix Representation of Original Evaporator Design 

The information required by EVAP-COND includes the number of tubes and how they 

are distributed in the slab; the length, inner, and outer diameter of the tubes; the tube 

spacing, material, and inner surface patterning; as well as information about the fins. 

The coil design data used for this model is shown in Figure 5.1.3.

Figure 5.1.3 Coil Design Data for reduced Evaporator Design 

Once the layout of the evaporator model was constructed, the refrigerant circuitry and the 

1D air flow distribution were input to the model. The operating conditions measured 

during the laboratory tests were used for the simulations. 
26 

Table 5.1.1 Operating Conditions for Simulation Model

Refrigerant saturation temperature at evaporator outlet 11.7 oC 

Refrigerant superheat at evaporator outlet 4 oC 

Refrigerant mass flow rate (estimate for beginning iterative calculations) 595 kgh-1

Inlet refrigerant quality 22.4 %

Air inlet temperature 26.7 oC 

Air inlet pressure 101.325 kPa 

Air inlet relative humidity 51.1 % 

The correlations in EVAP-COND that are used to calculate heat transfer coefficients and 

pressure drop are typically based on measured data with significant uncertainty and are 

also affected by the specific patterning on the tubes and fins. For this reason, EVAPCOND allows the user to input correction factor multipliers for the refrigerant heat 

transfer coefficient, refrigerant pressure drop, and air-side heat transfer coefficient. 

These correction parameters were adjusted until the computational result matched the 

laboratory data for the total heat transfer rate and the temperature of refrigerant exiting 8 

of the 16 individual circuits of the heat exchanger. The correction parameters found 

through these iterations were: 

Table 5.1.2 Coefficient Correction Parameters for Simulation Model 

Refrigerant heat transfer coefficient: 1.02 

Refrigerant pressure drop: 1.20

Air-side heat transfer coefficient: 0.83 

The simulation result using this model is shown in Figure 5.1.4. One aspect of this 

design that is particularly interesting is the significant variation of refrigerant exit 

temperature between the various circuits. While this variation provided a good metric to

use to determine the proper correction parameters, it also highlights the opportunity for 

improving the performance through circuitry optimization. The refrigerant exiting from 

the tubes numbered 9, 10, 11, 12, and 15 in Figure 5.1.4 contain high quality two-phase

refrigerant, and the refrigerant exiting from each of the other exit tubes is significantly 

superheated in order to compensate for the fact that some of the streams contain liquid 

droplets. The refrigerant quality and temperature exiting each of the heat exchanger 

tubes is shown in Figure 5.1.5 and Figure 5.1.6, respectively. 
27 

Figure 5.1.4 Simulation Result from Original Evaporator Design 

Figure 5.1.5 Refrigerant Outlet Quality from Simulation

Figure 5.1.6 Refrigerant Outlet Temperature (oC) from Simulation 
28 

The original heat exchanger design consists of 16 circuits and each circuit is comprised of 

either 8 or 10 tubes because an even number of tubes per circuit is required to preserve 

the hairpin pattern. The 10-tube circuits would impart more pressure drop on the 

refrigerant flowing through them than the 8-tube circuits, if all other factors were equal. 

However, since the pressure drop through each circuit must be equal, the 8-tube circuits 

will generally receive a higher mass flow rate of refrigerant than the 10-tube circuits. It 

is important to know that the variation of the air flow also plays a significant role in the 

refrigerant distribution. This is because it influences the heat transfer rate on the local 

level, and as the refrigerant absorbs heat it changes phase from liquid to vapor. This 

phase change results in a significant acceleration due to the change in density, and the 

resulting higher velocity increases the frictional pressure drop per length of tube. 

It is not surprising that all of the 10-tube circuits resulted in superheated refrigerant at 

their exit because the length of these circuits would cause refrigerant to be preferentially 

routed through the 8-tube circuits and because they have 25 % more heat transfer area

than the 8-tube circuits. Three of the 8-tube circuits also resulted in a refrigerant exit 

condition of superheated vapor while the other five did not. The 8-tube circuits that

resulted in a superheated exit condition were concentrated in locations that received more 

air flow than the other 8-tube circuits.

5.2 Refrigerant Circuitry Optimization

Once a model of the heat exchanger was developed, it was used as the basis for 

optimizing the refrigerant circuitry using the Intelligent System for Heat Exchanger 

(ISHED) module. Since ISHED is based on evolutionary algorithms, rather than 

employing calculus based techniques, independent optimization runs result in different 

designs. For this reason, seven independent optimization runs were performed and the 

best design from each one was selected for further analysis. The following parameters 

were used as input to control each optimization run: 

Table 5.2.1 ISHED Control Parameters for Circuitry Optimization Run

Number of designs per generation 40 

Number of generations 250 

Minimum number of inlet tubes 12 

Maximum number of inlet tubes 18
29 

In addition, the search space was limited to include designs that had evaporator exit tubes 

located in the first depth row of the heat exchanger, since this is a desirable design feature

to connect the exit tubes to a header. 

The best out of the seven designs, with a capacity that is 7.9 % higher than the original 

design, is shown in Figure 5.2.1. This design contains many long, complicated 

crossover return bends and therefore would be extremely difficult or impossible to 

manufacture; however, it can be altered into a buildable design. 

Figure 5.2.1 ISHED Optimized Design Before Post-Processing 

The main reason that this design shows a significant improvement in capacity over the 

baseline design is that it does a better job of balancing the heat transfer, refrigerant 

pressure drop, and mass flow rate between the individual circuits. Furthermore, this 

design consists of 18 circuits, each with 8 tubes and each circuit providing a similar 

amount of heat transfer. The refrigerant pressure drop through this heat exchanger will 

be smaller than that through the original design because the refrigerant has more paths 

through it and the paths are shorter; this design will therefore accommodate a larger total 

mass flow rate.
30 

This design was manually altered by swapping tube connections to untangle the crossover bends. The resulting “cleaned” design is shown below in Figure 5.2.2, which 

preserves the balance between the circuits and maintains the capacity. Figure 5.2.3 

shows the same design without the reduced matrix representation.

Figure 5.2.2 ISHED Optimized Design After Post-Processing

Figure 5.2.3 ISHED Optimized Design After Post-Processing, Full Representation 

The next step was to group the circuits in this design into two stages. This was done 

with two objectives. The first objective was that of keeping an even balance between 

the capacity and mass flow rate between the two stages. This was accomplished by 

tabulating the refrigerant mass flow rate and capacity for each circuit and determining all 

of the possible combinations that would result in an even split between the stages. The 
31 

second objective was to arrange the circuits of each stage so that they were spread across 

the entire height of the evaporator, which will improve the performance of the system in

single stage operation. Through this step, the circuits with exit tubes 3, 4, 7, 8, 10, 13, 

14, 16, and 18 were grouped into stage 1 and the remaining circuits into stage 2. 

The performance of the heat exchanger in single stage operation was also simulated in 

order to ensure that the circuits are balanced during part load operation. The simulation 

results for single stage operation of each stage are shown in Figures 5.2.4 and 5.2.5. 

Figure 5.2.4 Simulation of Stage 1 Operation of Optimized Evaporator 
32 

Figure 5.2.5 Simulation of Stage 2 Operation of Optimized Evaporator 

The simulations for the original design show capacities of 17.42 kW and 17.11 kW for 

Stage 1 and Stage 2, respectively. Therefore, these results show that there is a 

significant improvement for each individual stage of operation. 
33 

6. SYSTEM TESTS WITH OPTIMIZED EVAPORATOR

6.1 System Setup and Test Results

After completing the simulation and optimization phase of this study, the equipment 

manufacturer built a prototype of the evaporator with the optimized circuitry. Figure 6.1 

shows both the original and optimized evaporators side by side. While the optimized 

evaporator has a much more complicated circuitry design than the original evaporator, it 

is manufacturable. 

 

(a) (b)

Figure 6.1 Prototypes of (a) Original Evaporator and (b) Optimized Evaporator 
34 

Operating the RTU with the new evaporator required the replacement of one other 

component. The new evaporator required different thermostatic expansion valves 

(TXVs). The first reason for this is that the optimized design includes stages that each 

have nine circuits whereas the original stages had eight. Each TXV needed to have nine 

circuit distributors in order to accommodate the new design. The second reason for the 

new TXVs is that the optimized design requires a larger refrigerant mass flow rate than 

the original design at the same level of superheat. The optimized design was generated 

with the same refrigerant exit state as the original design and, according to the simulation 

results, the TXVs must deliver 7.9 % more refrigerant flow at that condition in order to 

maintain this state with the optimized evaporator. For these reasons, TXVs with 

9 circuit distributors and adjustable spring settings were installed on each stage of the 

RTU.

The optimized evaporator and new TXVs were installed in the RTU, and the unit was 

charged with refrigerant R410A. In order to match the operating conditions of the tests 

with those of the original unit, the flow rate and temperature of the water used to cool the 

condensers were adjusted along with the amount of refrigerant in the system and the 

spring settings on the TXVs. Best efforts attempted to match the liquid line pressure 

and temperature for each stage and the superheat at the exit from each evaporator header.

As stated in Chapter 3, the results of these performance measurements are needed to 

compare against the performance measurements with the original evaporator. 

Considering the magnitude of the expected improvement, it was necessary to measure the 

RTU performance with a low level of measurement uncertainty. For this reason, nine 

independent measurements of the system performance were acquired with the optimized 

evaporator over a two week period in the same manner as described in Chapter 3. The 

average value from these nine tests shows a total capacity of (27.01±0.25) kW with the 

optimized evaporator and a system COP of 3.88±0.04. Relevant portions of the 

recorded data are provided in Appendix B. The tabulated results are shown in 

Table 6.1.1. 
35 

Table 6.1.1 Refrigerant Side Capacity and COP Measurements for System with Optimized Evaporator

Test 

Number 

Capacity 

stage 1

(kW)

Capacity 

stage 2

(kW)

Capacity 

total

(kW)

Stage 1 

Comp 

power 

(W)

COP 

Stage 1

Stage 2 

Comp 

power 

(W)

COP 

Stage 2

System 

COP w/o 

blower 

Blower 

Power 

(W)

System 

COP

1 13.28±0.14 13.70±0.15 26.98±0.21 2913±8 4.56±0.05 3048±8 4.50±0.05 4.53±0.03 991±9 3.88±0.03 

2 13.23±0.16 13.61±0.23 26.84±0.28 2918±8 4.54±0.06 3040±8 4.48±0.08 4.50±0.05 986±11 3.87±0.04 

3 13.29±0.15 13.75±0.17 27.04±0.23 2912±8 4.56±0.05 3048±8 4.51±0.06 4.54±0.04 999±16 3.89±0.03

4 13.26±0.15 13.71±0.15 26.97±0.21 2911±8 4.56±0.05 3041±8 4.51±0.05 4.53±0.04 983±9 3.89±0.03 

5 13.26±0.15 13.62±0.16 26.88±0.22 2902±8 4.57±0.05 3045±8 4.47±0.05 4.52±0.04 1012±10 3.86±0.03 

6 13.34±0.15 13.86±0.18 27.20±0.23 2906±8 4.59±0.05 3059±8 4.53±0.06 4.56±0.04 998±13 3.91±0.04 

7 13.32±0.14 13.80±0.18 27.11±0.23 2902±8 4.59±0.05 3061±9 4.51±0.06 4.55±0.04 1003±15 3.89±0.03 

8 13.27±0.15 13.73±0.19 26.99±0.24 2910±9 4.56±0.05 3042±9 4.51±0.06 4.54±0.04 1010±17 3.88±0.04 

9 13.25±0.16 13.67±0.19 26.92±0.24 2919±9 4.54±0.06 3040±8 4.50±0.06 4.52±0.04 987±12 3.88±0.04

Average 13.28±0.15 13.72±0.18 27.01±0.25 2910±8 4.56±0.05 3047±8 4.50±0.06 4.53±0.04 997±13 3.88±0.04 

The expressed values are shown as the average of all measurements ± the total combined uncertainty at 95% confidence as described 

in Appendix C.
36 

6.2 Discussion of Measured Performance Improvement

The system capacity with the optimized evaporator was 2.2 % larger than the capacity 

with the original evaporator. The measured increase may not be large, but it is 

significant. As shown in Figure 6.2.1, the upper limit of the 95 % confidence interval 

for the system capacity with the original evaporator is marginally lower than the lower 

limit of the 95 % confidence interval for the system capacity with the optimized 

evaporator. However, it should be noted that the 2.2 % capacity increase is in line with 

the improvement prediction by the analytical method in Domanski (1988) which 

estimates a 2.9 % system capacity increase if the evaporator capacity were increased by 

7.9 %. 

It is interesting to examine the capacity for the individual stages. The Stage 1 capacity 

did not change significantly in response to the new evaporator but the Stage 2 capacity 

changed by more than 4 %. Figure 6.2.1 shows the capacity measured during both sets 

of tests; the individual stages are shown on the left and the total system capacity to the 

right. 

Figure 6.2.1 Measured Cooling Capacity with Original and Optimized Evaporator 
37 

The COP of the system with the optimized evaporator is 3.88±0.04, which represents 3.1 % 

increase in efficiency over the system with the original evaporator. Examining the 

change in COP of the individual stages is helpful in order to determine where the 

performance enhancement was realized. Figure 6.2.2 compares the COP of each stage 

and the system as measured during both sets of tests. The data shows that the COP for 

Stage 2 realized a significant increase of 4.7 %, while Stage 1 did not. The efficiency of 

the system as a whole did increase beyond the measurement uncertainty, and is shown 

both with and without consideration of the blower power in Figure 6.2.2. 

Figure 6.2.2 Measured COP for Stage 1, Stage 2, and System with Original and 

Optimized Evaporator 

Closer examination of the data revealed that the Stage 1 condenser subcooling was too 

low during the tests with the optimized evaporator. Tables 6.2.1 and 6.2.2 show data 

extracted from Appendices A and B related to the RTU operation during both sets of tests. 

The target conditions were intended to match the amount of superheat at the exit of each 

evaporator stage and simultaneously match the liquid line saturation temperature and 
38 

subcooling. The data in Table 6.2.2 shows very good agreement in these parameters for 

Stage 2; however, Table 6.2.1 shows a (2.7±0.3) K ((5.0±0.5) oF) difference in the level 

of subcooling for Stage 1. This difference in subcooling effectively reduced the 

enthalpy difference between the evaporator inlet and exit by 3.5 %, which would result in 

a comparable reduction in cooling capacity. The fact that the optimized Stage 1 portion 

of the evaporator shows lower subcooling for the same liquid pressure and evaporator 

exit superheat indicates that there was not enough refrigerant in the Stage 1 loop during 

these tests. Had the Stage 1 loop been charged with the proper amount of refrigerant, it 

is likely that Stage 1 would have realized a performance enhancement comparable to that 

realized by Stage 2. It was difficult to accurately charge the unit with the exact amount 

of refrigerant needed to mimic the manufacturer’s test data because the modifications that 

were made to the unit (replacing the air-cooled condensers with water-cooled 

brazed-plate heat exchangers) reduced the total required charge by nearly 70 %.

Nevertheless, the argument is still valid that the optimized evaporator did improve the 

performance of the system. One key aspect of the data shown in Tables 6.2.1 and 6.2.2 is 

that the exit evaporation temperature was significantly higher in each stage during the 

tests with the optimized evaporator than with the original evaporator. The evaporator 

saturation temperature for Stage 1 was (11.5±0.1) oC ((52.7±0.2) oF) under the test 

conditions with the original evaporator and the optimized evaporator circuitry raised it to 

(12.4±0.1) oC ((54.3±0.2) oF); an increase of (0.9±0.1) K ((1.7±0.2) oF). Similarly, the 

saturation temperature for Stage 2 was raised from (11.4±0.1) oC ((52.5±0.2) oF) to 

(12.1±0.1) oC ((53.8±0.2) oF) with the optimized evaporator, an increase of (0.7±0.1) K 

((1.3±0.2) oF). This increase in evaporating temperature realized in each stage is quite 

significant compared to the limits of the 95 % confidence intervals and it does indicate 

that there is a real benefit resulting from the optimized circuitry. 

This increase in evaporating temperature comes from two aspects of the design. First, 

this design provides a better match between the air and refrigerant temperature profiles;

therefore, the temperature difference between the air and refrigerant is reduced. Second, 

since the optimized evaporator consists of the same amount of heat transfer area as the 

original evaporator, but provides 18 circuits instead of 16, the overall refrigerant pressure 

drop through the optimized evaporator is lower. Both of these differences contribute to 

an improvement in the overall RTU performance.
39 

Overall, the data collected demonstrated that the optimized circuitry design does improve 

the efficiency of the system. Due to the magnitude of the capacity improvement and the 

slightly off-design charge amount, the data at first sight did not conclusively demonstrate 

the improvement beyond the uncertainty of the measured parameters. However, 

examination of the parameters pertaining to the individual stages does conclusively 

demonstrate that a real improvement exists. The benefit resulting from the optimized 

refrigerant circuitry in one of the two stages was offset by the influence of improper 

refrigerant charge. Had both stages been charged with the exact amount of refrigerant 

for the tests with the optimized evaporator, these tests would have enabled an exact 

apples-to-apples comparison which would have shown a more significant improvement 

as evidenced by the increased evaporating temperature in both stages.
40 

Table 6.2.1 Comparison of Stage 1 Operation Between Tests with Original and Optimized Evaporators

Liquid Line Parameters Suction Line Parameters

Pressure 

(kPa)

Saturation 

Temperature 

(oC)

Temperature 

(oC)

Subcooling 

(K)

Pressure 

(kPa)

Saturation 

Temperature 

(oC)

Temperature 

(oC)

Superheat

(K)

Original 

Evaporator 

2695.0±6.3 44.4±0.1 37.8±0.2 6.6±0.2 1137.4±2.1 11.5±0.1 16.1±0.2 4.6±0.2 

Optimized 

Evaporator 

2696.9±6.4 44.4±0.1 40.6±0.2 3.9±0.2 1169.0±4.0 12.4±0.1 17.36±0.3 4.9±0.3 

The expressed values are shown as the average of all measurements ± the total combined uncertainty at 95% confidence as described 

in Appendix C.

Table 6.2.2 Comparison of Stage 2 Operation Between Tests with Original and Optimized Evaporators

Liquid Line Parameters Suction Line Parameters

Pressure 

(kPa)

Saturation 

Temperature 

(oC)

Temperature 

(oC)

Subcooling 

(K)

Pressure 

(kPa)

Saturation 

Temperature 

(oC)

Temperature 

(oC)

Superheat

(K)

Original 

Evaporator 

2767.9±4.7 45.5±0.1 36.9±0.4 8.6±0.4 1133.2±2.1 11.4±0.1 15.6±0.2 4.2±0.2 

Optimized 

Evaporator 

2775.4±7.4 45.6±0.1 36.9±0.4 8.8±0.4 1157.6±5.7 12.1±0.1 16.3±0.2 4.1±0.3 

The expressed values are shown as the average of all measurements ± the total combined uncertainty at 95% confidence as described 

in Appendix C.
41 

7. SUMMARY

This study demonstrates the improvement in the 7.5 Ton RTU performance that was

achieved by applying the evolutionary algorithms for optimizing the refrigerant circuitry

of the evaporator. 

First, the performance of the RTU was benchmarked by conducting performance tests in 

a conditioned indoor chamber. The unit was modified by replacing the air-cooled 

condensers with water-cooled heat exchangers in order to facilitate testing. The unit 

was operated in such a manner as to match the operational parameters for the evaporator 

section to those from the manufacturer’s rating data. The results of the performance 

benchmark for the unit operating with original evaporator showed a capacity of 

(26.42±0.29) kW and a COP of 3.77±0.04. 

Next, the in-situ air velocity profile through the evaporator was measured using Particle 

Image Velocimetry (PIV). The PIV measurements were recorded over several segments 

of the heat exchanger and were used to generate a map of the distribution of the air 

velocity passing through the heat exchanger. 

A model of the evaporator was generated using the NIST simulation tool for finned-tube 

heat exchangers, EVAP-COND, which included the air velocity distribution characterized 

using the PIV data. The EVAP-COND model of the heat exchanger was tuned to the 

laboratory measurements, and the simulated performance resulted in a capacity of 

26.38 kW. The Intelligent System for Heat Exchanger Design (ISHED), embedded in 

EVAP-COND, was implemented to improve the performance of the heat exchanger by 

redesigning the tube connection sequence. ISHED produced a design with 18 circuits 

and a simulated capacity of 28.46 kW, which is an increase of 7.9 %. Since ISHED only 

modifies the tube connection sequence and does not alter the heat exchanger layout, the 

size, shape, and material weight of the ISHED design are identical to the original design. 

A prototype of the optimized evaporator was produced by the original RTU manufacturer. 

The original evaporator was replaced by the optimized prototype, and a new set of 

performance tests were carried out. The results of the tests showed that the RTU 

capacity changed from (26.42±0.29) kW to (27.01±0.25) kW, a 2.2 % increase. The data 

also showed that the COP increased from 3.77±0.04 to 3.88±0.04 with the new 

evaporator, an increase of 3.1 %. 
42 

The overall increase in cooling capacity did not provide a strong indicator of the 

performance enhancement because the lower limit on the 95 % confidence interval 

surrounding the capacity measurement with the optimized evaporator is very close to the 

upper confidence limit around the capacity measured with the original evaporator. 

The measured improvement in the RTU performance was corroborated by a change in the 

evaporator saturation temperature. The optimized refrigerant circuitry caused an 

increase in the evaporating temperature in both stages, (0.9±0.1) K ((1.7±0.2) oF) for 

Stage 1 and (0.7±0.1) K ((1.3±0.2) oF) for Stage 2, which indicates that the performance

improvement is real. However, closer examination of the data showed that the all of the 

improvement was realized in only one of the two stages, and it became apparent that the 

stage which did not realize any significant improvement was slightly undercharged with 

refrigerant during the tests with the optimized evaporator. This undercharge offset the 

optimized circuitry benefit that would have been realized by that stage. 
43 

8. REFERENCES

AMCA 2007. ANSI/AMCA 210-07, Laboratory Methods of Testing Fans for Certified 

Aerodynamic Performance Rating. Air Movement and Control Association, Arlington 

Heights, IL

ASHRAE 2009. ANSI/ASHRAE Standard 37-2009, Methods of Testing for Rating 

Electrically Driven Unitary Air-Conditioning and Heat Pump Equipment. American 

Society of Heating, Refrigerating and Air-Conditioning Engineers, Atlanta, GA. 

ARI 2007. Standard 340/360-2007, Performance Rating of Commercial and Industrial 

Unitary Air-Conditioning and Heat Pump Equipment. Air-Conditioning ,Heating, and 

Refrigeration Institute, Arlington, VA. 

Chwalowski, M., Didion, D. A., Domanski, P. A. 1989. Verification of Evaporator 

Computer Models and Analysis of Performance of an Evaporator Coil. ASHRAE 

Transactions 95(1): 793-802. 

Domanski, P.A. Rating of Mixed Split Residential Air Conditioners. Proceedings of the 

Fifth Symposium on Improving Building Systems in Hot and Humid Climates, Houston, 

TX. September 12-14, 1988.

Domanski, P.A., and Yashar, D.A., 2010. EVAP-COND Version 3-Simulation Models 

for Finned Tube Heat Exchangers with Circuitry Optimization. National Institute of 

Standards and Technology, Gaithersburg, MD. 

http://www.nist.gov/el/building_environment/evapcond_software.cfm 

Domanski, P.A., Yashar, D. A., and Lee, S., Evaporator Optimization for Non-Uniform 

Air Distribution. Sustainable Refrigeration and Heat Pump Technology. June 13-16, 

2010, Stockholm, Sweden. 

Fagan, T. J. 1980. The effects of air flow maldistributions on air-to-refrigerant heat 

exchanger performance. ASHRAE Transactions 86(2): 699-715. 

Kaern, M.R., Elmegaard, B., and Larsen, L.F.S., 2013.Comparison of fin-and-tube 

interlaced and face split evaporators with flow maldistribution and compensation, Int. J. 

of Ref. 36: 203-214. 
44 

Lemmon, E.W., Huber, M.L., McLinden, M.O., 2010. NIST Standard Reference 

Database 23: Reference Fluid Thermodynamic and Transport Properties-REFPROP, 

Version 9.0, National Institute of Standards and Technology, Standard Reference Data 

Program, Gaithersburg. 

Lemmon, E.W. and Jacobsen, R.T. Equations of State for Mixtures of R-32, R-125, 

R-134a, and R152a. J. Phys. Chem. Ref. Data, 33(2), 2004. 

Payne, W. V. and Domanski, P. A. Potential Benefits of Smart Refrigerant Distributors 

(ARTI-21CR/605-200-50-01; 196 p.) January 01, 2003. 

Taylor, B.N., and Kuyatt, C.E., 1994. Guidelines for evaluating and expressing the 

uncertainty of NIST measurement results, NIST Technical Note 1297, 1994 edition, U.S. 

Department of Commerce.

Yashar, D.A., Wojtusiak, J., Kaufman, K., and Domanski, P.A., 2012. A Dual Mode 

Evolutionary Algorithm for Designing Optimized Refrigerant Circuitries for Finned-Tube 

Heat Exchangers HVAC&R Research 18(5), SPECIAL ISSUE: Optimization in 

HVAC&R, 834-844. 

Yashar, D.A., and Cho, H.H., 2007. Air-Side Velocity Distribution in Finned-Tube Heat 

Exchangers. NIST Internal Report 7474, U.S. Department of Commerce, National 

Institute of Standards and Technology, Gaithersburg, MD.
45 

Appendix A – Data recorded during performance measurement tests with original heat exchanger

Table A.1 - Test 1 with Original Evaporator 

Stage 1 Stage 2

Scan Evaporator 

Outlet 

Temp (oC)

Evaporator 

Outlet 

Pressure 

(kPa)

Liquid 

Line 

Temp 

(oC)

Liquid 

Line 

Pressure 

(kPa)

Mass 

Flow 

Rate 

(gs-1)

Compressor 

Power (W)

Evaporator 

Outlet 

Temp (oC)

Evaporator 

Outlet 

Pressure 

(kPa)

Liquid 

Line 

Temp 

(oC)

Liquid 

Line 

Pressure 

(kPa)

Mass 

Flow 

Rate 

(gs-1)

Compressor 

Power (W)

Blower 

Power 

(W)

1 15.823 1139.35 37.689 2692.28 0.0805 2927 15.398 1130.83 37.345 2763.66 0.0775 3072 1058

2 15.960 1139.68 37.795 2695.24 0.0786 2939 15.392 1130.01 37.505 2764.65 0.0771 3072 1046

3 15.989 1138.76 37.421 2700.74 0.0783 2932 15.383 1130.44 37.196 2769.76 0.0791 3075 995

4 15.939 1137.04 37.676 2690.49 0.0799 2920 15.378 1130.77 37.270 2762.03 0.0788 3067 1010

5 15.953 1138.34 37.456 2688.37 0.0796 2925 15.372 1129.61 37.318 2761.28 0.0798 3070 1049

6 15.976 1137.83 37.514 2689.77 0.0710 2920 15.419 1131.41 37.259 2767.28 0.0798 3060 1061

Avg 15.940 1138.50 37.592 2692.81 0.0795 2927.2 15.390 1130.51 37.316 2764.78 0.0787 3069.3 1036.5

StDev 0.060 0.98 0.1493 4.55 0.00092 7.36 0.0172 0.64 0.1063 3.23 0.00114 5.28 27.33

Table A.2 - Test 2 with Original Evaporator 

Stage 1 Stage 2

Scan Evaporator 

Outlet 

Temp (oC)

Evaporator 

Outlet 

Pressure 

(kPa)

Liquid 

Line 

Temp 

(oC)

Liquid 

Line 

Pressure 

(kPa)

Mass 

Flow 

Rate 

(gs-1)

Compressor 

Power (W)

Evaporator 

Outlet 

Temp (oC)

Evaporator 

Outlet 

Pressure 

(kPa)

Liquid 

Line 

Temp 

(oC)

Liquid 

Line 

Pressure 

(kPa)

Mass 

Flow 

Rate 

(gs-1)

Compressor 

Power (W)

Blower 

Power 

(W)

1 15.846 1137.07 37.800 2693.12 0.07824 2925 15.433 1132.07 37.432 2763.00 0.07994 3069 984

2 15.924 1126.32 37.766 2685.17 0.07930 2919 15.389 1130.50 37.507 2764.11 0.07924 3070 1047

3 16.160 1136.09 37.319 2686.56 0.07864 2924 15.404 1130.33 37.261 2762.65 0.07707 3069 948

4 15.845 1135.76 37.491 2687.79 0.07881 2920 15.415 1131.06 37.295 2768.99 0.07876 3062 1000

5 15.957 1136.56 37.797 2689.35 0.07837 2921 15.422 1132.54 37.541 2763.41 0.07982 3073 1000

6 15.852 1135.87 37.790 2687.55 0.08051 2917 15.426 1133.58 37.239 2768.40 0.07981 3061 1007

Avg 15.931 1134.61 37.660 2688.26 0.07898 2921 15.415 1131.68 37.379 2765.09 0.07911 3067.3 997.7

StDev 0.122 4.09 0.205 2.76 0.00084 3.03 0.016 1.27 0.131 2.84 0.00109 4.76 32.20
46 

Table A.3 - Test 3 with Original Evaporator 

Stage 1 Stage 2

Scan Evaporator 

Outlet 

Temp (oC)

Evaporator 

Outlet 

Pressure 

(kPa)

Liquid 

Line 

Temp 

(oC)

Liquid 

Line 

Pressure 

(kPa)

Mass 

Flow 

Rate 

(gs-1)

Compressor 

Power (W)

Evaporator 

Outlet 

Temp (oC)

Evaporator 

Outlet 

Pressure 

(kPa)

Liquid 

Line 

Temp 

(oC)

Liquid 

Line 

Pressure 

(kPa)

Mass 

Flow 

Rate 

(gs-1)

Compressor 

Power (W)

Blower 

Power 

(W)

1 15.963 1137.93 37.678 2692.76 0.07823 2927 15.454 1132.89 37.124 2762.12 0.07994 3067 1000

2 15.987 1136.92 37.575 2689.24 0.08054 2916 15.470 1132.34 37.100 2777.31 0.07924 3060 996

3 15.962 1137.62 37.748 2692.12 0.07921 2921 15.476 1129.73 37.212 2760.30 0.07894 3065 984

4 15.934 1138.91 37.712 2695.21 0.07897 2939 15.446 1130.36 37.104 2772.66 0.07924 3077 1030

5 15.877 1139.83 37.650 2686.84 0.08037 2920 15.325 1130.08 36.850 2764.44 0.07728 3062 1012

6 15.752 1138.19 37.562 2696.19 0.07972 2920 15.361 1131.47 37.031 2767.72 0.07721 3081 1035

Avg 15.912 1138.23 37.654 2692.06 0.07951 2923.8 15.422 1131.14 37.070 2767.43 0.07864 3068.7 1009.5

StDev 0.092 1.02 0.074 3.54 0.00088 8.23 0.064 1.29 0.122 6.53 0.00113 8.45 20.00

Table A.4 - Test 4 with Original Evaporator 

Stage 1 Stage 2

Scan Evaporator 

Outlet 

Temp (oC)

Evaporator 

Outlet 

Pressure 

(kPa)

Liquid 

Line 

Temp 

(oC)

Liquid 

Line 

Pressure 

(kPa)

Mass 

Flow 

Rate 

(gs-1)

Compressor 

Power (W)

Evaporator 

Outlet 

Temp (oC)

Evaporator 

Outlet 

Pressure 

(kPa)

Liquid 

Line 

Temp 

(oC)

Liquid 

Line 

Pressure 

(kPa)

Mass 

Flow 

Rate 

(gs-1)

Compressor 

Power (W)

Blower 

Power 

(W)

1 15.805 1139.07 37.828 2699.31 0.07958 2935 15.390 1132.35 37.144 2765.44 0.07773 3070 1046

2 15.825 1136.36 37.679 2700.03 0.07947 2937 15.376 1131.73 37.002 2771.02 0.07876 3068 987

3 15.872 1135.61 37.745 2699.72 0.07908 2939 15.481 1133.13 37.016 2770.29 0.07982 3068 1010

4 15.837 1136.23 37.495 2700.17 0.08047 2933 15.482 1133.31 37.155 2767.37 0.07894 3072 1042

5 15.886 1132.47 38.016 2698.25 0.07886 2930 15.517 1133.41 37.048 2772.58 0.07923 3073 988

6 15.811 1138.25 37.959 2700.30 0.07946 2935 15.528 1134.86 37.280 2770.03 0.07798 3083 1043

Avg 15.839 1136.33 37.787 2699.63 0.07949 2934.8 15.462 1133.13 37.108 2769.45 0.07874 3072.3 1019.3

StDev 0.034 2.31 0.191 0.76 0.00055 3.13 0.065 1.06 0.106 2.59 0.00078 5.61 27.93
47 

Table A.5 - Test 5 with Original Evaporator 

Stage 1 Stage 2

Scan Evaporator 

Outlet

Temp (oC)

Evaporator 

Outlet 

Pressure 

(kPa)

Liquid 

Line 

Temp 

(oC)

Liquid 

Line 

Pressure 

(kPa)

Mass 

Flow 

Rate 

(gs-1)

Compressor 

Power (W)

Evaporator 

Outlet 

Temp (oC)

Evaporator 

Outlet 

Pressure 

(kPa)

Liquid 

Line 

Temp 

(oC)

Liquid 

Line 

Pressure 

(kPa)

Mass 

Flow 

Rate 

(gs-1)

Compressor 

Power (W)

Blower 

Power 

(W)

1 15.927 1138.91 37.644 2687.30 0.07833 2922 15.616 1133.55 37.111 2772.00 0.07821 3065 1002

2 15.779 1139.83 37.916 2694.77 0.07818 2926 15.643 1135.30 37.156 2775.25 0.07923 3061 1038

3 16.204 1137.21 37.872 2696.47 0.07962 2927 15.690 1135.77 37.184 2767.39 0.07728 3068 1050

4 16.264 1137.08 37.714 2699.39 0.07929 2935 15.683 1135.50 36.985 2768.54 0.07769 3068 998

5 16.194 1135.63 37.992 2700.16 0.07835 2924 15.734 1136.46 37.118 2769.14 0.07713 3070 1058

6 16.220 1136.08 37.852 2694.09 0.07804 2923 15.726 1136.29 36.867 2775.54 0.07876 3067 1035

Avg 16.098 1137.46 37.832 2695.36 0.07864 2926.2 15.682 1135.48 37.070 2771.31 0.07805 3066.5 1030.2

StDev 0.197 1.63 0.129 4.64 0.00065 4.71 0.046 1.05 0.121 3.51 0.00084 3.15 24.82

Table A.6 - Test 6 with Original Evaporator 

Stage 1 Stage 2

Scan Evaporator 

Outlet 

Temp (oC)

Evaporator 

Outlet 

Pressure 

(kPa)

Liquid 

Line 

Temp 

(oC)

Liquid 

Line 

Pressure 

(kPa)

Mass 

Flow 

Rate 

(gs-1)

Compressor 

Power (W)

Evaporator 

Outlet 

Temp (oC)

Evaporator 

Outlet 

Pressure 

(kPa)

Liquid 

Line 

Temp 

(oC)

Liquid 

Line 

Pressure 

(kPa)

Mass 

Flow 

Rate 

(gs-1)

Compressor 

Power (W)

Blower 

Power 

(W)

1 16.272 1137.36 37.897 2707.35 0.07961 2934 15.745 1136.26 36.808 2776.85 0.07765 3065 997

2 16.215 1139.33 38.254 2716.48 0.07996 2943 15.805 1135.61 37.146 2768.88 0.07906 3073 1015

3 16.309 1137.76 38.132 2699.41 0.07828 2931 15.790 1134.19 36.987 2761.89 0.07976 3073 1036

4 16.218 1137.79 37.933 2695.89 0.08054 2931 15.786 1135.54 36.750 2768.45 0.07982 3072 1060

5 16.267 1138.56 37.466 2697.49 0.07829 2927 15.801 1135.38 36.698 2770.60 0.07982 3073 1047

6 16.290 1138.16 37.638 2692.89 0.08164 2925 15.788 1135.30 36.547 2778.40 0.07894 3069 981

Avg 16.262 1138.16 37.887 2701.59 0.07972 2931.8 15.786 1135.38 36.823 2770.84 0.07917 3070.8 1022.7

StDev 0.039 0.703 0.295 8.77 0.00131 6.34 0.022 0.675 0.214 6.05 0.00084 3.25 30.39
48 

Table A.7 - Test 7 with Original Evaporator 

Stage 1 Stage 2

Scan Evaporator 

Outlet 

Temp (oC) 

Evaporator 

Outlet 

Pressure 

(kPa)

Liquid 

Line 

Temp 

(oC)

Liquid 

Line 

Pressure 

(kPa)

Mass 

Flow 

Rate 

(gs-1)

Compressor 

Power (W)

Evaporator 

Outlet 

Temp (oC)

Evaporator 

Outlet 

Pressure 

(kPa)

Liquid 

Line 

Temp 

(oC)

Liquid 

Line 

Pressure 

(kPa)

Mass 

Flow 

Rate 

(gs-1)

Compressor 

Power (W)

Blower 

Power 

(W)

1 16.295 1138.08 37.812 2696.77 0.08068 2929 15.827 1134.80 36.589 2771.45 0.07924 3069 986

2 16.336 1139.42 37.815 2705.49 0.08039 2932 15.814 1134.03 36.592 2775.03 0.07780 3071 1011

3 16.421 1136.74 37.943 2700.24 0.07942 2933 15.813 1133.68 36.556 2762.66 0.07721 3053 1023

4 16.336 1137.12 37.748 2699.68 0.08041 2933 15.878 1133.13 36.234 2761.41 0.07773 3047 1042

5 16.335 1138.26 37.724 2697.88 0.08058 2932 15.896 1134.03 36.100 2769.20 0.07876 3040 1054

6 16.359 1138.41 38.072 2699.21 0.07916 2929 15.873 1133.70 36.247 2767.96 0.07957 3042 991

Avg 16.347 1138.00 37.852 2699.88 0.08011 2931.3 15.850 1133.90 36.386 2767.95 0.07838 3053.7 1017.8

StDev 0.043 0.963 0.132 3.02 0.00065 1.86 0.037 0.550 0.218 5.19 0.00094 13.44 27.20

Table A.8 - Test 8 with Original Evaporator 

Stage 1 Stage 2

Scan Evaporator 

Outlet 

Temp (oC)

Evaporator 

Outlet 

Pressure 

(kPa)

Liquid 

Line 

Temp 

(oC)

Liquid 

Line 

Pressure 

(kPa)

Mass 

Flow 

Rate 

(gs-1)

Compressor 

Power (W)

Evaporator 

Outlet 

Temp (oC)

Evaporator 

Outlet 

Pressure 

(kPa)

Liquid 

Line 

Temp 

(oC)

Liquid 

Line 

Pressure 

(kPa)

Mass 

Flow 

Rate 

(gs-1)

Compressor 

Power (W)

Blower 

Power 

(W)

1 16.253 1137.72 37.920 2693.36 0.07989 2923 15.860 1135.40 36.091 2769.01 0.07899 3053 984

2 16.315 1137.45 37.778 2681.93 0.07907 2925 15.832 1135.99 36.284 2768.78 0.07715 3051 991

3 16.366 1137.89 37.882 2689.61 0.07908 2924 15.868 1133.53 36.448 2762.52 0.07731 3048 1011

4 16.229 1137.18 37.964 2689.08 0.07979 2921 15.838 1134.56 36.374 2761.12 0.07899 3044 1028

5 16.170 1136.83 37.685 2694.76 0.07941 2932 15.839 1132.84 36.403 2767.86 0.07907 3056 978

6 15.922 1137.76 37.868 2694.57 0.07888 2925 15.829 1133.74 36.842 2767.52 0.07806 3048 987

Avg 16.209 1137.47 37.849 2690.55 0.07935 2925 15.844 1134.34 36.407 2766.13 0.07826 3050 996.5

StDev 0.158 0.407 0.102 4.88 0.00042 3.74 0.017 1.198 0.248 3.42 0.00088 4.24 19.09
49 

Appendix B – Data recorded during performance measurement tests with optimized heat exchanger

Table B.1 - Test 1 with Optimized Evaporator 

Stage 1 Stage 2

Scan Evaporator 

Outlet 

Temp (oC)

Evaporator 

Outlet 

Pressure 

(kPa)

Liquid 

Line 

Temp 

(oC)

Liquid 

Line 

Pressure 

(kPa)

Mass 

Flow 

Rate 

(gs-1)

Compressor 

Power (W)

Evaporator 

Outlet 

Temp (oC)

Evaporator 

Outlet

Pressure 

(kPa)

Liquid 

Line 

Temp 

(oC)

Liquid 

Line 

Pressure 

(kPa)

Mass 

Flow 

Rate 

(gs-1)

Compressor 

Power (W)

Blower 

Power 

(W)

1 17.602 1170.08 40.709 2703.74 0.0812 2915 16.514 1159.06 36.917 2769.36 0.0812 3046 933

2 17.570 1170.17 40.735 2701.39 0.0820 2912 16.423 1158.84 36.783 2768.67 0.0817 3050 1010

3 17.752 1171.55 40.615 2694.47 0.0823 2908 16.541 1159.56 37.012 2771.99 0.0841 3048 1022

4 17.602 1171.66 40.542 2691.21 0.0816 2906 16.411 1160.20 36.932 2772.67 0.0805 3046 987

5 17.614 1172.30 40.634 2704.72 0.0806 2917 16.448 1160.14 37.043 2770.70 0.0816 3048 979

6 17.556 1171.24 40.709 2705.02 0.0812 2920 16.479 1161.58 36.829 2771.88 0.0806 3049 1017

Avg 17.616 1171.17 40.657 2700.09 0.0815 2913.0 16.469 1159.90 36.920 2770.88 0.0816 3047.8 991.3

StDev 0.071 0.88 0.073 5.85 0.00063 5.37 0.052 0.99 0.101 1.59 0.00131 1.60 33.23

Table B.2 -Test 2 with Optimized Evaporator 

Stage 1 Stage 2

Scan Evaporator 

Outlet 

Temp (oC)

Evaporator 

Outlet 

Pressure 

(kPa)

Liquid 

Line 

Temp 

(oC)

Liquid 

Line 

Pressure 

(kPa)

Mass 

Flow 

Rate 

(gs-1)

Compressor 

Power (W)

Evaporator 

Outlet 

Temp (oC)

Evaporator 

Outlet 

Pressure 

(kPa)

Liquid 

Line 

Temp 

(oC)

Liquid 

Line 

Pressure 

(kPa)

Mass 

Flow 

Rate 

(gs-1)

Compressor 

Power (W)

Blower 

Power 

(W)

1 17.103 1173.51 40.784 2707.10 0.0816 2926 16.112 1165.84 37.487 2768.58 0.0821 3040 1029

2 17.240 1173.62 40.758 2693.73 0.0823 2912 16.022 1164.89 37.190 2770.97 0.0800 3040 1007

3 17.155 1174.07 40.639 2698.92 0.0811 2916 16.003 1164.54 37.392 2767.76 0.0813 3036 974

4 16.961 1171.51 40.718 2705.49 0.0806 2922 15.947 1163.20 37.249 2768.33 0.0853 3041 965

5 16.979 1171.37 40.676 2705.31 0.0804 2923 15.839 1163.23 37.343 2772.60 0.0810 3044 973

6 17.114 1169.36 40.742 2696.25 0.0819 2909 15.876 1163.24 37.485 2771.89 0.0799 3039 965

Avg 17.092 1172.24 40.720 2701.13 0.0813 2918.0 15.966 1164.16 37.358 2770.02 0.0816 3040.0 985.5

StDev 0.107 1.81 0.054 5.58 0.00072 6.72 0.101 1.11 0.122 2.06 0.00199 2.61 26.40
50 

Table B.3 -Test 3 with Optimized Evaporator 

Stage 1 Stage 2

Scan Evaporator 

Outlet 

Temp (oC)

Evaporator 

Outlet 

Pressure 

(kPa)

Liquid 

Line 

Temp 

(oC)

Liquid 

Line 

Pressure 

(kPa)

Mass 

Flow 

Rate 

(gs-1)

Compressor 

Power (W)

Evaporator 

Outlet 

Temp (oC)

Evaporator 

Outlet 

Pressure 

(kPa)

Liquid 

Line 

Temp 

(oC)

Liquid 

Line 

Pressure 

(kPa)

Mass 

Flow 

Rate 

(gs-1)

Compressor 

Power (W)

Blower 

Power 

(W)

1 17.570 1170.17 40.735 2701.39 0.0820 2912 16.423 1158.84 36.783 2779.34 0.0817 3050 1010

2 17.752 1171.55 40.615 2694.47 0.0823 2908 16.541 1159.56 37.012 2779.27 0.0841 3048 1022

3 17.602 1171.66 40.542 2691.21 0.0816 2906 16.411 1160.20 36.932 2781.08 0.0805 3046 987

4 17.614 1172.30 40.634 2704.72 0.0806 2917 16.448 1160.14 37.043 2780.06 0.0816 3048 979

5 17.556 1171.24 40.709 2705.02 0.0812 2920 16.479 1161.58 36.829 2779.20 0.0806 3049 1017

6 17.587 1172.85 40.588 2689.97 0.0816 2907 16.422 1159.80 36.920 2777.64 0.0816 3049 979

Avg 17.613 1171.63 40.637 2697.80 0.0816 2911.7 16.454 1160.02 36.920 2779.43 0.0817 3048.3 999.0

StDev 0.072 0.92 0.073 6.76 0.00062 5.75 0.050 0.91 0.101 1.13 0.00130 1.37 19.59

Table B.4 -Test 4 with Optimized Evaporator 

Stage 1 Stage 2

Scan Evaporator 

Outlet 

Temp (oC)

Evaporator 

Outlet 

Pressure 

(kPa)

Liquid 

Line 

Temp 

(oC)

Liquid 

Line 

Pressure 

(kPa)

Mass 

Flow 

Rate 

(gs-1)

Compressor 

Power (W)

Evaporator 

Outlet 

Temp (oC)

Evaporator 

Outlet 

Pressure 

(kPa)

Liquid 

Line 

Temp 

(oC)

Liquid 

Line 

Pressure 

(kPa)

Mass 

Flow 

Rate 

(gs-1)

Compressor 

Power (W)

Blower 

Power 

(W)

1 17.311 1167.29 40.759 2700.59 0.0818 2917 16.268 1157.60 37.123 2771.51 0.0811 3042 1013

2 17.192 1170.39 40.464 2696.44 0.0803 2910 16.171 1157.96 37.108 2772.45 0.0814 3043 984

3 17.162 1168.56 40.622 2704.08 0.0806 2916 16.126 1157.52 36.845 2773.36 0.0824 3041 972

4 17.158 1167.68 40.651 2697.27 0.0822 2911 16.109 1157.70 36.877 2769.79 0.0807 3041 976

5 17.184 1167.15 40.511 2682.87 0.0818 2900 16.063 1156.72 36.938 2770.14 0.0818 3041 976

6 17.129 1165.14 40.649 2700.86 0.0815 2911 16.094 1155.90 36.953 2773.09 0.0811 3040 975

Avg 17.189 1167.70 40.609 2697.02 0.0813 2910.8 16.138 1157.23 36.974 2771.72 0.0814 3041.3 982.7

StDev 0.064 1.73 0.106 7.46 0.00074 6.05 0.073 0.77 0.117 1.51 0.00062 1.03 15.38
51 

Table B.5 -Test 5 with Optimized Evaporator 

Stage 1 Stage 2

Scan Evaporator 

Outlet 

Temp (oC)

Evaporator 

Outlet 

Pressure 

(kPa)

Liquid 

Line 

Temp 

(oC)

Liquid 

Line 

Pressure 

(kPa)

Mass 

Flow 

Rate 

(gs-1)

Compressor 

Power (W)

Evaporator 

Outlet 

Temp (oC)

Evaporator 

Outlet 

Pressure 

(kPa)

Liquid 

Line 

Temp 

(oC)

Liquid 

Line 

Pressure 

(kPa)

Mass 

Flow 

Rate 

(gs-1)

Compressor 

Power (W)

Blower 

Power 

(W)

1 17.219 1161.73 40.279 2679.76 0.0817 2888 16.689 1145.00 35.839 2776.61 0.0798 3043 965

2 17.111 1162.86 40.348 2695.68 0.0799 2905 16.677 1144.54 35.775 2774.32 0.0818 3045 1011

3 17.299 1161.60 40.510 2699.42 0.0800 2909 16.638 1146.15 36.205 2776.14 0.0794 3044 1031

4 17.239 1161.80 40.611 2699.40 0.0814 2908 16.557 1148.74 36.471 2774.00 0.0801 3044 1023

5 17.326 1162.85 40.608 2692.05 0.0819 2905 16.499 1149.37 36.524 2774.54 0.0802 3046 1018

6 17.412 1165.09 40.430 2686.19 0.0826 2897 16.534 1151.81 36.332 2776.72 0.0812 3047 1021

Avg 17.268 1162.66 40.464 2692.08 0.0812 2902.0 16.599 1147.60 36.191 2775.39 0.0805 3044.8 1011.5

StDev 0.103 1.32 0.137 7.83 0.00108 8.05 0.080 2.84 0.318 1.23 0.00091 1.47 23.70

Table B.6 -Test 6 with Optimized Evaporator 

Stage 1 Stage 2

Scan Evaporator 

Outlet 

Temp (oC)

Evaporator 

Outlet 

Pressure 

(kPa)

Liquid 

Line 

Temp 

(oC)

Liquid 

Line 

Pressure 

(kPa)

Mass 

Flow 

Rate 

(gs-1)

Compressor 

Power (W)

Evaporator 

Outlet 

Temp (oC)

Evaporator 

Outlet 

Pressure 

(kPa)

Liquid 

Line 

Temp 

(oC)

Liquid 

Line 

Pressure 

(kPa)

Mass 

Flow 

Rate 

(gs-1)

Compressor 

Power (W)

Blower 

Power 

(W)

1 17.380 1170.18 40.269 2690.99 0.0819 2904 16.218 1159.41 36.974 2787.19 0.0838 3061 977

2 17.434 1171.65 40.283 2692.39 0.0814 2904 16.207 1159.20 37.148 2788.39 0.0817 3062 1012

3 17.451 1171.19 40.306 2700.26 0.0806 2909 16.230 1159.43 37.062 2783.40 0.0833 3062 1030

4 17.119 1168.91 40.409 2698.25 0.0811 2914 16.001 1160.83 37.082 2761.56 0.0830 3041 995

5 16.895 1169.79 40.592 2694.62 0.0823 2908 15.981 1158.30 37.109 2795.62 0.0831 3069 976

6 17.070 1170.98 40.446 2683.71 0.0825 2897 16.302 1159.87 36.914 2781.53 0.0849 3059 995

Avg 17.225 1170.45 40.384 2693.37 0.0816 2906.0 16.156 1159.51 37.048 2782.95 0.0833 3059.0 997.5

StDev 0.229 1.02 0.124 5.88 0.00073 5.76 0.134 0.83 0.088 11.56 0.00104 9.44 20.79
52 

Table B.7 -Test 7 with Optimized Evaporator 

Stage 1 Stage 2

Scan Evaporator 

Outlet 

Temp (oC)

Evaporator 

Outlet 

Pressure 

(kPa)

Liquid 

Line 

Temp

(oC)

Liquid 

Line 

Pressure 

(kPa)

Mass 

Flow 

Rate 

(gs-1)

Compressor 

Power (W)

Evaporator 

Outlet 

Temp (oC)

Evaporator 

Outlet 

Pressure 

(kPa)

Liquid 

Line 

Temp 

(oC)

Liquid 

Line 

Pressure 

(kPa)

Mass 

Flow 

Rate 

(gs-1)

Compressor 

Power (W)

Blower 

Power 

(W)

1 17.381 1165.40 40.351 2695.04 0.0811 2903 16.066 1152.69 36.901 2793.06 0.0832 3066 1016

2 17.420 1166.42 40.297 2697.25 0.0811 2903 16.116 1153.82 36.779 2791.45 0.0811 3064 1003

3 17.347 1165.82 40.285 2690.43 0.0815 2902 16.162 1153.72 36.778 2783.90 0.0816 3058 978

4 17.412 1165.89 40.314 2692.36 0.0815 2901 16.038 1153.95 36.631 2786.22 0.0812 3059 1032

5 17.293 1166.60 40.379 2691.25 0.0807 2904 16.016 1153.73 36.719 2785.28 0.0818 3064 977

6 17.317 1165.74 40.355 2691.91 0.0815 2900 16.001 1155.48 36.691 2783.83 0.0819 3055 1009

Avg 17.362 1165.98 40.330 2693.04 0.0813 2902.2 16.067 1153.90 36.750 2787.29 0.0818 3061.0 1002.5

StDev 0.052 0.45 0.037 2.59 0.00034 1.47 0.062 0.90 0.093 3.98 0.00074 4.29 21.66

Table B.8 -Test 8 with Optimized Evaporator 

Stage 1 Stage 2

Scan Evaporator 

Outlet 

Temp (oC)

Evaporator 

Outlet 

Pressure 

(kPa)

Liquid 

Line 

Temp 

(oC)

Liquid 

Line 

Pressure 

(kPa)

Mass 

Flow 

Rate 

(gs-1)

Compressor 

Power (W)

Evaporator 

Outlet 

Temp (oC)

Evaporator 

Outlet 

Pressure 

(kPa)

Liquid 

Line 

Temp 

(oC)

Liquid 

Line 

Pressure 

(kPa)

Mass 

Flow 

Rate 

(gs-1)

Compressor 

Power (W)

Blower 

Power 

(W)

1 17.492 1160.55 40.485 2694.69 0.0803 2906 16.042 1147.45 36.428 2765.08 0.0793 3037 1003

2 17.605 1161.89 40.599 2700.52 0.0806 2909 16.203 1149.28 36.615 2766.58 0.0808 3039 1021

3 17.617 1163.49 40.644 2698.72 0.0812 2914 16.264 1151.51 36.503 2770.74 0.0804 3040 1019

4 17.798 1166.05 40.585 2697.16 0.0812 2910 16.372 1152.92 36.484 2772.35 0.0803 3044 976

5 18.057 1168.67 40.605 2700.80 0.0812 2912 16.602 1152.61 36.752 2776.72 0.0816 3045 1031

6 18.071 1169.53 40.573 2698.88 0.0812 2912 16.685 1155.17 36.256 2772.89 0.0794 3044 1011

Avg 17.773 1165.03 40.582 2698.46 0.0809 2910.5 16.361 1151.49 36.506 2770.72 0.0803 3041.5 1010.2

StDev 0.245 3.66 0.053 2.28 0.00040 2.81 0.245 2.76 0.168 4.30 0.00085 3.27 19.23
53 

Table B.9 -Test 9 with Optimized Evaporator 

Stage 1 Stage 2

Scan Evaporator 

Outlet 

Temp (oC)

Evaporator 

Outlet 

Pressure 

(kPa)

Liquid 

Line 

Temp 

(oC)

Liquid 

Line 

Pressure 

(kPa)

Mass 

Flow 

Rate 

(gs-1)

Compressor 

Power (W)

Evaporator 

Outlet 

Temp (oC)

Evaporator 

Outlet 

Pressure 

(kPa)

Liquid 

Line 

Temp 

(oC)

Liquid 

Line 

Pressure 

(kPa)

Mass 

Flow 

Rate 

(gs-1)

Compressor 

Power (W)

Blower 

Power 

(W)

1 17.291 1175.57 40.724 2690.38 0.0826 2915 16.177 1166.01 37.445 2769.46 0.0820 3045 963

2 17.213 1176.72 40.634 2705.62 0.0806 2925 16.092 1165.37 37.398 2770.40 0.0803 3036 985

3 17.103 1173.51 40.784 2707.10 0.0816 2926 16.112 1165.84 37.487 2768.58 0.0821 3040 1029

4 17.240 1173.62 40.758 2693.73 0.0823 2912 16.022 1164.89 37.190 2770.97 0.0800 3040 1007

5 17.155 1174.07 40.639 2698.92 0.0811 2916 16.003 1164.54 37.392 2767.76 0.0813 3036 974

6 16.961 1171.51 40.718 2705.49 0.0806 2922 15.947 1163.20 37.249 2768.33 0.0853 3041 965

Avg 17.161 1174.17 40.710 2700.21 0.0814 2919.3 16.059 1164.98 37.360 2769.25 0.0818 3039.7 987.2

StDev 0.118 1.81 0.061 7.00 0.00084 5.79 0.084 1.03 0.116 1.25 0.00190 3.39 26.06
54 

Appendix C – Uncertainty analysis 

The methods of calculating the reported values listed in this report are presented in this 

appendix. Each of the presented uncertainty values is derived from the methods 

outlined in Taylor and Kuyatt (1994) and is derived from two components. The first 

component, called type A uncertainty, is based on the variation of repeated measurement 

results and the second component, type B, is based on scientific judgment. The overall 

uncertainty is derived from a Pythagorean relationship between the two types of 

uncertainty.

The calculations presented in this Appendix use the data set from the first test of the RTU 

with the optimized heat exchanger. The same methods were applied to all data sets. 

Values for the type A uncertainty were calculated for each of the measured values as 

follows, based on a sampling size of six independent measurements; the data used to 

calculate the performance included in this report were based on many more scans, but the 

six scans reported for this data set in Appendix B are used in this analysis for illustrative 

purposes. 

Parameter: Evaporator Outlet Temperature, stage 1

Average of 6 measurements: 17.616 oC 

Standard deviation of the 6 measurements: 0.071 oC 

First, the Standard Error surrounding this value is calculated by dividing the standard 

deviation by the square root of the number of samples 

SE = 0.071 °C

√6

= 0.0290 °C

The Student t-value for two sided confidence limits at 95 % confidence based on 6 

degrees of freedom is

t(0.975, 6) = 2.447 

Therefore the bounds for the upper and lower confidence limits around the reported value 

are calculated by multiplying the t-value by the Standard Error 

Confidence interval = 2.447 ∗ (0.0290 °C) = 0.071 °C

The type B uncertainty for this measurement is based on the calibration data for the 

instrument used to measure the parameter. In this case, the data was collected with a Ttype thermocouple calibrated to with 0.15 oC of true value at 95 % confidence.

Therefore the total uncertainty for the stage 1 evaporator outlet temperature is calculated 

by the square root of the sum of the squares of the type A and type B uncertainties 

U = �(0.071 °C)2 + (0.150 °C)2 = 0.166 °C
55 

These calculations were repeated for each of the measured parameters listed in the data 

set in Appendix B and the values are shown in the table below. 

Table C.1 – Calculation of Total Uncertainty for Measured Parameters, Test 1 with Optimized 

Evaporator

ParameterAverage of MeasurementsStandard DeviationStandard Error Confidence IntervalMeasurement bias Total Uncertainty

Stage 1

Mass Flow Rate (g/s) 0.08149 0.00063 0.00026 0.00063 0.00081 0.00103 

Evaporator Outlet 

Pressure (kPa) 1171.17 0.88 0.36 0.88 3.50 3.61 

Evaporator Outlet 

Temperature (oC) 17.616 0.071 0.029 0.071 0.150 0.166 

Compressor Power 

(W) 2913.00 5.37 2.19 5.36 7.28 9.04 

Liquid Line 

Temperature (oC) 37.764 0.013 0.005 0.013 0.150 0.151 

Liquid Line Pressure 

(kPa) 2700.09 5.85 2.39 5.85 3.50 6.81 

Stage 2

Mass Flow Rate (g/s) 0.08161 0.00131 0.00054 0.00131 0.00082 0.00155 

Evaporator Outlet 

Pressure (kPa) 1159.90 0.99 0.41 0.99 3.50 3.64 

Evaporator Outlet 

Temperature (oC) 16.469 0.052 0.021 0.052 0.150 0.159 

Compressor Power 

(W) 3047.83 1.60 0.65 1.60 7.62 7.79 

Liquid Line 

Temperature (oC) 41.380 0.039 0.016 0.039 0.150 0.155 

Liquid Line Pressure 

(kPa) 2770.88 1.59 0.65 1.59 3.50 3.84 

RTU

Fan Power (W) 991.33 33.23 13.57 33.20 2.48 33.29 

The next step is to calculate the cooling capacity and COP from the measured values. 

Although the reported values listed in Table 6.1 were calculated using REFPROP 9, the 

difference between the upper and lower confidence limits were calculated using 

Engineering Equation Solver. A short code, shown below, was written to calculate the 

propagation of uncertainty for the cooling capacity and COP, example shown uses the 

values listed in Table B.1 
56 

m_stage1=0.0815

T_liq1=40.657

P_liq1=2700.09

T_vap1=17.616 

P_vap1=1171.17

W_comp1=2.913

h_liq1=ENTHALPY(R410A,T=T_liq1,P=P_liq1)

h_vap1=ENTHALPY(R410A,T=T_vap1,P=P_vap1)

Q1=m_stage1*(h_vap1-h_liq1)

COP1=Q1/W_comp1

m_stage2=0.0816

T_liq2=36.92

P_liq2=2770.88

T_vap2=16.469

P_vap2=1159.9

W_comp2=3.0478

h_liq2=ENTHALPY(R410A,T=T_liq2,P=P_liq2)

h_vap2=ENTHALPY(R410A,T=T_vap2,P=P_vap2)

Q2=m_stage2*(h_vap2-h_liq2)

COP2=Q2/W_comp2

W_fan=0.9913

Q_total=Q1+Q2

W_total=W_comp1+W_comp2+W_fan

COP_total=Q_total/W_total
57 

Results:

Variable±Uncertainty Partial derivative % of uncertainty

Q1 = 13.32±0.171

mstage1 = 0.0815±0.00103 ∂Q1/∂mstage1 = 163.5 96.97 %

Pliq1 = 2700±6.81 ∂Q1/∂Pliq1 = 0.0001076 0.00 %

Pvap1 = 1171±3.61 ∂Q1/∂Pvap1 = -0.002226 0.22 %

Tliq1 = 40.66±0.151 ∂Q1/∂Tliq1 = -0.1573 1.93 %

Tvap1 = 17.62±0.166 ∂Q1/∂Tvap1 = 0.09659 0.88 %

COP1 = 4.574±0.0604 

mstage1 = 0.0815±0.00103 ∂COP1 /∂mstage1 = 56.13 91.61 %

Pliq1 = 2700±6.81 ∂COP1 /∂Pliq1 = 0.00003692 0.00 % 

Pvap1 = 1171±3.61 ∂COP1 /∂Pvap1 = -0.000764 0.21 %

Tliq1 = 40.66±0.151 ∂COP1 /∂Tliq1 = -0.05401 1.82 %

Tvap1 = 17.62±0.166 ∂COP1 /∂Tvap1 = 0.03316 0.83 %

Wcomp1 = 2.913±0.00904 ∂COP1 /∂Wcomp1 = -1.57 5.52 %

Q2 = 13.84±0.2644

mstage2 = 0.0816±0.00155 ∂Q2/∂mstage2 = 169.6 98.79 %

Pliq2 = 2771±3.84 ∂Q2/∂Pliq2 = 0.00007928 0.00 %

Pvap2 = 1160±3.64 ∂Q2/∂Pvap2 = -0.002275 0.10 %

Tliq2 = 36.92±0.155 ∂Q2/∂Tliq2 = -0.1499 0.77 %

Tvap2 = 16.47±0.159 ∂Q2/∂Tvap2 = 0.09728 0.34 %

COP2 = 4.539±0.08753

mstage2 = 0.0816±0.00155 ∂COP2 /∂mstage2 = 55.63 97.05 %

Pliq2 = 2771±3.84 ∂COP2 /∂Pliq2 = 0.00002601 0.00 %

Pvap2 = 1160±3.64 ∂COP2 /∂Pvap2 = -0.0007464 0.10 %

Tliq2 = 36.92±0.155 ∂COP2 /∂Tliq2 = -0.04919 0.76 %

Tvap2 = 16.47±0.159 ∂COP2 /∂Tvap2 = 0.03192 0.34 %

Wcomp2 = 3.048±0.00779 ∂COP2 /∂Wcomp2 = -1.489 1.76 %

Qtotal = 27.16±0.3149

mstage1 = 0.0815±0.00103 ∂Qtotal /∂mstage1 = 163.5 28.60 %

mstage2 = 0.0816±0.00155 ∂Qtotal /∂mstage2 = 169.6 69.65 %

Pliq1 = 2700±6.81 ∂Qtotal /∂Pliq1 = 0.0001076 0.00 %

Pliq2 = 2771±3.84 ∂Qtotal /∂Pliq2 = 0.00007928 0.00 %

Pvap1 = 1171±3.61 ∂Qtotal /∂Pvap1 = -0.002226 0.07 %

Pvap2 = 1160±3.64 ∂Qtotal /∂Pvap2 = -0.002275 0.07 %

Tliq1 = 40.66±0.151 ∂Qtotal /∂Tliq1 = -0.1573 0.57 %

Tliq2 = 36.92±0.155 ∂Qtotal /∂Tliq2 = -0.1499 0.54 %

Tvap1 = 17.62±0.166 ∂Qtotal /∂Tvap1 = 0.09659 0.26 %

Tvap2 = 16.47±0.159 ∂Qtotal /∂Tvap2 = 0.09728 0.24 %

COPtotal = 3.907±0.04946

mstage1 = 0.0815±0.00103 ∂COPtotal /∂mstage1 = 23.52 23.98 %

mstage2 = 0.0816±0.00155 ∂COPtotal /∂mstage2 = 24.39 58.41 %

Pliq1 = 2700±6.81 ∂COPtotal /∂Pliq1 = 0.00001547 0.00 %

Pliq2 = 2771±3.84 ∂COPtotal /∂Pliq2 = 0.0000114 0.00 %

Pvap1 = 1171±3.61 ∂COPtotal /∂Pvap1 = -0.0003201 0.05 %

Pvap2 = 1160±3.64 ∂COPtotal /∂Pvap2 = -0.0003272 0.06 %

Tliq1 = 40.66±0.151 ∂COPtotal /∂Tliq1 = -0.02263 0.48 %

Tliq2 = 36.92±0.155 ∂COPtotal /∂Tliq2 = -0.02157 0.46 %

Tvap1 = 17.62±0.166 ∂COPtotal /∂Tvap1 = 0.01389 0.22 %

Tvap2 = 16.47±0.159 ∂COPtotal /∂Tvap2 = 0.01399 0.20 %

Wcomp1 = 2.913±0.00904 ∂COPtotal /∂Wcomp1 = -0.562 1.05 %

Wcomp2 = 3.048±0.00779 ∂COPtotal /∂Wcomp2 = -0.562 0.78 %

Wfan = 0.9913±0.03329 ∂COPtotal /∂Wfan = -0.562 14.30 %