NISTIR 7474 

Air-Side Velocity Distribution in Finned-Tube Heat 

Exchangers 

David A. Yashar 

Hong Hyun Cho 

U.S. DEPARTMENT OF COMMERCE 

National Institute of Standards and Technology 

Building Environment Division 

Building and Fire Research Laboratory 

Gaithersburg, Maryland 20899-8631 

National Institute of Standards and Technology 

United States Department of Commerce 

NISTIR 7474 

Air-Side Velocity Distribution in Finned-Tube Heat 

Exchangers 

David A. Yashar 

Hong Hyun Cho 

U.S. DEPARTMENT OF COMMERCE 

National Institute of Standards and Technology 

Building Environment Division 

Building and Fire Research Laboratory 

Gaithersburg, Maryland 20899-8631 

December 2007 

U.S. DEPARTMENT OF COMMERCE 

Carlos M. Gutierrez, Secretary 

National Institute of Standards and Technology 

James Turner, Acting Director 

ii

ABSTRACT 

The performance of finned tube heat exchangers is greatly affected by the distribution of the air 

that passes through it. The air side velocity distribution for finned-tube heat exchangers in 

residential air conditioning installations is not very well documented today because it is difficult 

to measure accurately. In this study, we examined the air velocity distribution approaching 

finned-tube heat exchangers under three different common installation configurations. To this 

end we used a novel, laser based technique called Particle Image Velocimetry (PIV) to measure 

the velocity profile. The heat exchangers examined in this study were a vertically oriented 

single-slab coil, a single slab coil placed at an angle of 65o to the duct wall, and a two slab AShaped coil with a 34o apex angle. 

The measurement results show that the velocity profile for any configuration is strongly 

influenced by the features within the duct and the orientation of the heat exchanger, and therefore 

each installation configuration has its own unique velocity distribution. The information 

presented here documents the magnitude and type of this mal-distribution realized in these 

systems, what features caused it, and which regions were most affected. 

Computational Fluid Dynamics (CFD) simulations were carried out to simulate the air flow 

through the test subjects used for the PIV measurements. We employed momentum resistance 

models to simplify the computational domains and reduce computer time. Our simulation results 

showed good agreement with the measured velocity profiles in each case. This work suggests 

that CFD can be accurately applied as a tool to determine the velocity profile. CFD is preferred 

to laboratory experimentation because of its speed and simplicity. 

Keywords: Air Conditioning, Air Velocity Profile, Computational Fluid Dynamics (CFD), 

finned-tube heat exchanger, Particle Image Velocimetry (PIV) 

iii
Acknowledgements 

Dr. Rodney Bryant of the Fire Research Laboratory provided vital input and equipment for the 

particle image velocimetry measurements taken in this study. Dr. Piotr Domanski and Dr. W.

Vance Payne assisted with formulating the scope of this project and designing the test apparatus. 

Mr. John Wamsley assisted by building the test setup and constructing the ducted coil test 

sections. The authors would also like to thank Mr. Brian Dougherty of NIST and Mr. Dutch 

Uselton of Lennox Industries for reviewing the draft of this report. Finally the authors greatly 

appreciate the guidance and support provided by Michael Raymond of DOE’s Office of Building 

Technology, State and Community Programs.

iv
Table of Contents 

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

Acknowledgements............................................................................................................ iv 

Table of Contents.................................................................................................................v 

List of Tables ..................................................................................................................... vi 

List of Figures................................................................................................................... vii 

Nomenclature..................................................................................................................... ix 

Nomenclature: Greek and other Symbols..........................................................................x 

1: Introduction......................................................................................................................1 

2: Particle Image Velocimetry .............................................................................................3 

3: Experimental Air Flow Apparatus...................................................................................6 

4: PIV Measurement Setup and Operation ..........................................................................8 

5: PIV Measurement Results and Discussion ....................................................................13 

 5.1 Single Slab Vertical Coil ........................................................................................13 

 5.2 Slant Coil ................................................................................................................16 

 5.3 A-Shaped Coil.........................................................................................................19 

6: Computer Based Simulation Results and Discussion....................................................26 

 6.1 Single Slab Vertical Coil ........................................................................................27 

 6.2 Slant Coil ................................................................................................................33 

 6.3 A-Shaped Coil.........................................................................................................39 

7: Summary and Conclusions ............................................................................................50 

References..........................................................................................................................51 

Appendix A: Pressure Drop Data for Flow Resistance Coefficients................................52 

Appendix B: Uncertainty Analysis...................................................................................54 

 B.1 Type A Uncertainty................................................................................................54 

 B.2 Type B Uncertainty ................................................................................................57 

v
List of Tables 

A.1 Data used to Determine Momentum Resistance Coefficients for Vertical Coil.........52 

A.2 Data used to Determine Momentum Resistance Coefficients for Slant Coil..............52 

A.3 Data used to Determine Momentum Resistance Coefficients for A-Shaped Coil......53 

B.1.1 Type A Uncertainty for Vertical Coil ......................................................................55 

B.1.2 Type A Uncertainty for Slant Coil ...........................................................................56 

B.1.3 Type A Uncertainty for A-Shaped Coil ...................................................................56 

B.2.1 Type B Uncertainty for Vertical Coil.......................................................................57 

B.2.2 Type B Uncertainty for Slant Coil ...........................................................................58 

B.2.3 Type B Uncertainty for A-Shaped Coil....................................................................58 

vi
List of Figures 

2.1 Schematic of 2-Dimensional PIV Setup .......................................................................3 

2.2 Cross Correlation Method for Evaluation of PIV Recordings.......................................5 

3.1 Schematic of Test Apparatus.........................................................................................6 

4.1 PIV Setup ......................................................................................................................8 

4.2 Laser Setup ....................................................................................................................9 

4.3 Calibration Photograph ...............................................................................................11 

5.1.1 Measurement Location and Equipment Placement...................................................14 

5.1.2 Piecewise Illustration of Measured Vector Fields for Vertical Coil ........................14 

5.1.3 Two Dimensional Representation of Approach Velocity for Vertical Coil ............15 

5.2.1 Slant Coil Test Section..............................................................................................17 

5.2.2 Velocity Profile at Midpoint for Slant Coil .............................................................18 

5.2.3 Two Dimensional Representation of Approach Velocity for Slant Coil .................19 

5.3.1 A-Shaped Coil Test Section .....................................................................................20 

5.3.2 PIV Data Image File – A-Coil Entrance ..................................................................22 

5.3.3 Velocity Profile at Midpoint for A-Coil ..................................................................23 

5.3.4 A-Coil Recirculation Zone........................................................................................24 

5.3.5 Two Dimensional Representation of Approach Velocity for A-Shaped Coil .........24 

6.1.1 Test Section Sketch with Computational Domain Outline ......................................27 

6.1.2 Computational Domain for Vertical Coil ................................................................28 

6.1.3 Stream-Wise Velocity Component for Simulation with Different 

 Number of Nodes per Line – Vertical Coil..............................................................31 

6.1.4 Approach Velocity Profile for Vertical Coil ............................................................32 

6.1.5 Pressure Profile in a Duct for Vertical Coil .............................................................32 

6.1.6 Comparison of PIV and CFD Data for Vertical Coil................................................33 

6.2.1 Computational Domain for Slant Coil......................................................................33 

6.2.2 Stream-Wise Velocity Component for Simulation with Different 

 Number of Nodes per Line – Slant Coil ..................................................................37 

6.2.3 Pressure Profile for Slant Coil .................................................................................37 

6.2.4 Vector Profile for Slant Coil ....................................................................................38 

6.2.5 Comparison of PIV and CFD Data for Slant Coil ....................................................39 

vii
6.3.1 Computational Domain for A-Shaped Coil ..............................................................39 

6.3.2 Blowup of Computational Domain for A-Shaped Coil ...........................................40 

6.3.3 Stream-Wise Velocity Component for Simulation with Different 

 Number of Nodes per Line – A-Shaped Coil...........................................................43 

6.3.4 Pressure Profile for A-Shaped Coil...........................................................................44 

6.3.5 Vector Profile for A-Shaped Coil ............................................................................45 

6.3.6 CFD Resolution of Recirculation Zone ....................................................................46 

6.3.7 Computational Domain Sections ..............................................................................46 

6.3.8 CFD Velocity Profile at A-Shaped Coil Inlet ..........................................................47 

6.3.9 Comparison of PIV Data with CFD Coil Inlet Data for A-Shaped Coil ..................48 

6.3.10 Comparison of PIV Data with all Data from CFD 

 Computational Sub-Domain IV for A-Shaped Coil ................................................49

viii
Nomenclature

Parameter ......................................................................................................................Units 

A Area...........................................................................................................m

2

Cl Intermediate Linear Momentum Resistance Coefficient ................... kg/m3s 

Cq Intermediate Quadratic Momentum Resistance Coefficient................kg/m4

Dh Hydraulic Diameter.................................................................................... m 

I Turbulence Intensity .................................................................................. % 

k Turbulent Kinetic Energy .....................................................................m

2

/s2 

Kl Linear Momentum Resistance Coefficient ...............................................1/s 

Kq Quadratic Momentum Resistance Coefficient........................................ 1/m

P Pressure.................................................................................................N/m

2

Per Perimeter.................................................................................................... m 

Q Volumetric Flow Rate............................................................................ m3

/s 

Re Reynolds Number ...................................................................dimensionless 

u Component of velocity parallel to main flow direction...........................m/s 

v Component of velocity perpendicular to main flow direction.................m/s 

V

r

 Velocity....................................................................................................m/s 

ix
Nomenclature: Greek Symbols 

Parameter ......................................................................................................................Units 

β Porosity ...................................................................................dimensionless 

ε Turbulent Dissipation Rate .................................................................. m2/s3.

ρ Density .................................................................................................kg/m3

ν Viscosity ................................................................................................ m

2

/s 

x
1: Introduction 

Air-to-refrigerant finned-tube heat exchangers are the predominant type of heat 

exchangers used in comfort cooling and commercial refrigeration applications. An air-torefrigerant finned-tube heat exchanger is made up of a series of parallel, straight tubes 

that are connected to each other. Therefore, the refrigerant passing through the heat 

exchanger will flow back and forth through the tube bank, i.e. in one direction through 

one tube and return through another tube. Air flows through the heat exchanger in a 

direction perpendicular to the tubes in the bank. It passes through the heat exchanger by 

maneuvering through the spaces between adjacent tubes, and thereby exchanges thermal 

energy with the refrigerant in each of the tubes. In order to improve the heat transfer 

between the air and refrigerant, sheets of thermally conductive material, i.e. fins, are used 

to extend the tube surfaces. These fins are stacked along the length of the tubes, parallel 

to each other. 

Designing a highly efficient refrigerant-to-air heat exchanger is a very difficult task. In 

essence, a finned-tube heat exchanger can be described as a number of single tube, air-torefrigerant, cross-flow heat exchangers. Each of these tubes, however, is connected to

other tubes within the heat exchanger; therefore, the parameters associated with the heat 

transfer coefficient of refrigerant flowing in any tube are influenced by the occurrences in 

tubes that are connected upstream and downstream. To complicate the analysis, the tube 

banks are generally layered in multiple rows. Therefore, the air will pass around one tube 

and onto subsequent tubes in consecutive depth rows. The thermophysical properties of 

the air will therefore be different at each location because of the energy exchange with 

the previous tube. To complicate the analysis even further still, the velocity of the air 

approaching a heat exchanger can be vastly different between any two locations within 

the heat exchanger. 

The heat exchange occurring at each tube changes the thermodynamic and transport 

properties of the refrigerant and the air; therefore, the performance of each tube is 

dependent on that of all of the other tubes in some way. Our ability to understand the 

performance of a finned-tube heat exchanger is therefore dependent on our ability to 

understand the performance of each tube. Since the problem is interconnected in this 

manner, it is somewhat difficult; but the thermodynamic and transport properties 

governing the heat exchanger performance can be calculated using computer simulations 

with a software tool such as EVAP-COND [Domanski, 2007]. The approach air velocity 

profile, however, is a very influential parameter which must be known prior to simulating 

the heat exchanger’s performance. The influence of the velocity profile on a heat 

exchanger’s performance can be quite large; one study showed that altering the velocity 

profile can reduce a heat exchanger’s capacity by as much as 30 % [Payne and 

Domanski, 2003]. Another related study [Domanski et. al., 2004] showed that nearly all 

of the capacity reduction due to non-uniformities in the velocity profile can be 

recuperated by simply redesigning the tube-to-tube connection sequence. To date, 

unfortunately, the air side velocity profile is largely left undetermined because it is 

difficult to measure accurately, and because the problem is so complex there is little 

understanding of the most effective way to use this information. The latter is rapidly 

becoming less of an issue through advancements in design software. 

1
In the late 1980’s, researchers at the National Institute of Standards and Technology used 

smoke injection to qualitatively evaluate air flow fields in the vicinity of installed finnedtube heat exchangers [Chwalowski et. al., 1987]. They also measured air velocity using a 

traversing pitot tube and showed the air distribution to be highly non-uniform. Although 

those efforts laid the groundwork for the current study, the methods available at that time

were rather crude compared to what is available today. The historically available 

measurement tools (pitot tubes, hot-wire anemometers, rotating vane anemometers, etc.) 

are all inadequate for this application because the device must be placed within, and 

properly oriented to, the locality of interest. Such placement is difficult if not impossible. 

Furthermore, the devices themselves interfere with the flow that is being measured. 

Current measurement technology has brought about a number of highly accurate, laserbased, non-intrusive options to characterize the air velocity profile of a heat exchanger’s 

approach flow field. In particular, Planar Laser Induced Fluorescence (PLIF), Laser 

Doppler Velocimetry (LDV) and Particle Image Velocimetry (PIV) all present possible 

options. Each of these methods is in some way based on laser interaction with some type 

of particle that is entrained in the flow, called seed particles. For PLIF, lasers are used to 

excite the seed particles, and flow velocity is inferred from the fluorescence captured by

imaging cameras [Seitzman and Hanson, 1993]. Although this method is very accurate, it 

is relatively complicated and requires a substantial equipment investment. LDV infers

velocity information based on the measured Doppler frequency shift; LDV is typically a 

single point measurement [Durst et. al., 1976]. The study presented in this report focuses 

on PIV, which uses a laser sheet to illuminate a single plane within the flow field, and a 

synchronized camera to track the motion of particles. 

The ultimate goal of this study is to measure and characterize the velocity distribution of 

air approaching 3 typical finned-tube heat exchanger configurations. The information 

obtained in these measurements is used to develop Computational Fluid Dynamics (CFD) 

models of these installations. The goal is to provide design engineers with verified CFD 

models and methodologies that can be used to predict the flow fields associated with 

similar situations. More efficient finned-tube heat exchangers can therefore be designed 

by incorporating features that capitalize on the specific air flow distribution. 

2
2: Particle Image Velocimetry 

PIV is an optically based measurement technique used to obtain flow distributions across 

entire flow fields. A good overview of the technique is presented in [Adrian, 1991]. It is 

very attractive for the application at hand because it is not intrusive and provides very

accurate measurements. The drawbacks of this technique are the cost of equipment and 

the safety hazards resulting from working with lasers. The simplest method of 2-

Dimensional PIV was used in this study, and therefore the discussion is limited to this 

application. Figure 2.1 shows a schematic of the basic 2D PIV setup. 

Double Pulsed Laser

CCD Camera

Seeded Flow

Double Pulsed Laser

CCD Camera

Seeded Flow

Figure 2.1 Schematic of 2-Dimensional PIV Setup 

PIV works on the basis of tracking the motion of particles entrained in the flow field. In 

order for PIV to work particles must be dispersed into the flow. These particles, called 

seed particles or tracer particles, provide 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. These laser 

sheets are generated by spreading laser light beams through a divergence optical lens. 

The laser sheets are oriented in such a manner that the illuminated plane is aligned to the 

main flow direction within the test section. A Charge Coupled Device (CCD) camera is 

used to capture images within the illuminated plane and therefore records the location of 

the seed particles. Velocity information is calculated from the displacement of particles 

between consecutive images. 

3
For this setup, two lasers are required to properly fire the laser sheets with the appropriate 

temporal spacing. These lasers are mounted together, with the beams emitted from each 

passing through the same optical lens. This lens distorts the laser beams and spreads 

them into sheets. In this manner, a set of two identical light sheets can be produced in 

rapid succession with very accurate timing. Also, the camera used to capture images is a 

double framed camera. During the acquisition of a data point, the camera captures two 

image frames coincident with the firing of the lasers. The lasers and camera are all 

triggered by a Programmable Timing Unit (PTU) through a personal computer. 

It is necessary to disperse a well mixed and appropriate quantity of seed particles in the 

flow. A number of trade-offs exist regarding the selection and disbursement of seed 

particles. Ideally, these particles should have the same density as the media in which 

they are entrained. Particles should be selected such that their terminal velocity and 

response time should be very small compared to the velocity magnitudes expected and 

the time scales of the flow. The seed particles must be small enough to respond quickly 

to abrupt changes in the flow, but at the same time they must be large enough to be 

adequately captured and mapped by the imaging camera. Furthermore, determining the 

optimal quantity of particles is a bit of an art form. If too many particles are entrained in 

the flow it becomes difficult to determine the position of individual particles; if not 

enough particles are present, the results computed from the images become heavily 

affected by noise. See [Bryant, 2005] for a comprehensive discussion on particle 

selection. 

As mentioned earlier, each image capture is synchronized with a laser sheet pulse and the 

images are captured in pairs. Therefore, the particle positions that correspond to laser 

pulse #1 are recorded in camera frame #1 and the particle positions that correspond to 

laser pulse #2 are recorded in camera frame #2. These image pairs are transferred to the 

computer for data storage and processing. Data reduction is a very computationally 

intensive process. 

During the data reduction process, each frame is divided into a number of small square 

regions, called interrogation windows. It is assumed that all particles within a given 

interrogation window have moved in the same direction and the same distance between 

image frames. The data reduction software maps the light intensity over each 

interrogation window from the first frame and compares these maps to those from the 

corresponding interrogation windows from the second frame; this method is called crosscorrelation. From this analysis, it probabilistically determines the distance traveled by 

each particle within the interrogation window. A velocity vector for each interrogation 

window is then calculated by dividing the average distance by the time delay between the 

two frames. The velocity vector field is then constructed from the vectors assigned to the 

interrogation windows. This process is depicted in Figure 2.2. 

4
t t+dt

Figure 2.2 Cross Correlation Method for Evaluation of PIV Recordings. 

5
3: Experimental Air Flow Apparatus 

The objective of this study was to measure the approach air velocity profile of finnedtube heat exchangers under adiabatic conditions. A test apparatus that was capable of 

delivering a specified air flow rate through a ducted heat exchanger was constructed for 

this study, Figure 3.1. 

Test Section

Flow Straightener

Nozzle

Blower

Test Section

Flow Straightener

Nozzle

Blower

Figure 3.1 Schematic of Test Apparatus 

In the test apparatus, air is pulled into the straight duct test section as depicted in the 

upper left portion of Figure 3.1, and continues clockwise through the apparatus. The 

view shown is from the top looking downward. There is negligible change in height 

through the apparatus. The air temperature and dew point are measured using a T-type 

thermocouple, calibrated to +/- 0.2 oC (0.36 oF), and chilled mirror hygrometer, calibrated 

to +/- 1.0 oC (1.8 oF), positioned near the inlet of the test section. The air then passes 

through the finned-tube heat exchanger in the test section; the air pressure drop is 

measured across the heat exchanger using a differential pressure sensor calibrated to +/- 

0.5 Pa over the range of (0 to 125) Pa (0.5” H2O). After the air exits the test section, it is 

ducted to a flow straightener and through a venture nozzle where the volumetric flow rate 

is measured using a differential pressure transducer calibrated to +/- 1 Pa over the range 

of (0 to 620) Pa (2.5” H2O). After exiting the nozzle, the air is then drawn through a 

blower module which is controlled by a variable speed drive, and discharged to the 

laboratory environment. 

The inlet air temperature and the dew point measured at the inlet to the apparatus were 

used, along with the atmospheric pressure, to calculate the density of the air entering the 

6
duct. The air density was used along with the pressure difference between the venturi 

inlet and throat to calculate the volumetric flow rate. 

The ducting configuration conformed to ANSI/ASHRAE Standard 37 [1998], with the 

exception that no refrigerant line connections were made to the heat exchanger since we 

are only examining the adiabatic case. The test section was made out of clear plexiglass 

to allow visual communication between the heat exchanger and the PIV measurement 

equipment. 

7
4: PIV Measurement Setup and Operation 

The PIV measurement system was installed around the air flow test apparatus. It consists 

of four components: a particle generator, a pair of lasers, a double framed CCD camera, 

and a computer. The layout of these components is depicted in Figure 4.1. 

Particle Generator

Lasers

CCD Camera

Computer

Figure 4.1 PIV Setup 

To generate seed particles for the flow measurements, we used a theater style fog 

generating machine. The entire laboratory environment was filled with non-hazardous 

particles and the test apparatus drew air from and discharged air to the room. This 

method generated the particles and allowed them to be well dispersed and mixed with the 

air flowing through the test section. It is very important to ensure that the fog particles 

are well mixed with the air so that the dispersion is uniform; poorly dispersed particles 

result in photographs that are difficult to resolve into vector fields. 

The illumination source was the most substantial piece of equipment; we used a pair of

solid state lasers (Nd: YAG) for this setup. Using two laser heads allows the lasers to fire 

a pair of pulses at maximum output energy per pulse within a single flashlamp cycle. 

The lasers were mounted on top of an electronically controlled positioner, which was 

itself mounted onto an industrial strength tripod. The lasers were located in front of the 

test section inlet, oriented such that the lasers were aimed downstream into the test 

section, aligned with the main air flow direction. The laser beams were passed through 

8
beam combining optics, which received light from both laser sources and discharged 

them to a single location and direction. The beams then passed through a divergence lens 

to form them into sheets. These sheets formed planes of light that were oriented 

vertically. A photograph of the assembly consisting of the laser pair, beam combining 

optics, and sheet forming optics is shown in Figure 4.2. 

Laser Heads Sheet Forming Optics

Beam Combining Optics

Laser Heads Sheet Forming Optics

Beam Combining Optics

Figure 4.2 Laser Setup 

Expanding a laser beam into a sheet over a large area reduces the intensity of the light; 

therefore this setup required relatively high pulse energy laser beams. We used lasers 

with pulse energy of 200 mJ, which renders them Class IV lasers under the international 

laser safety standard, IEC 60825 [2007]. Class IV lasers present safety risks for eye and 

skin damage as well as being a fire hazard. For this reason the entire test section was 

covered in heavy black felt to collect all of the laser light, with the exception of a small 

viewing window used by the CCD camera.

Since PIV requires a pair of images taken in very rapid succession, the camera used in 

this system had a specialized feature in that it could operate in a double shuttered mode. 

A CCD camera converts photons to electric charge based on the photoelectric effect. The 

solid state sensor consists of an array of pixels where electrons are accumulated during 

exposure. In double shuttered mode, a part of each pixel is masked off and can not be 

exposed by incident light. When recording a pair of PIV images, the optically sensitive 

area of each pixel is exposed and the accumulated charge is quickly shifted to the masked 

area so that the second image can be exposed onto the optically sensitive area. The 

9
camera that we used for this apparatus can complete this process in 110 ns with pixel 

resolution of 2 megapixels (1600 X 1200), and has the ability to repeat this process at a 

rate of 30 Hz. 

The camera was mounted onto a tripod located alongside the test section, just upstream of 

the heat exchanger. The camera was oriented so that it faced a direction normal to the 

laser sheets generated by the lasers, and perpendicular to the main direction of the air 

flow. It is important to realize that any light reflections that are recorded by the camera 

will severely distort the data; therefore, the camera was positioned such that the fins on

the heat exchanger were not visible by the camera. Also, objects on the opposite side of 

the plexiglass duct from the camera were either masked off with black material or painted 

black to minimize the amount reflected light from these surfaces. 

The camera and the lasers were both controlled and synchronized by a Programmable

Timing Unit (PTU) installed in a dedicated server operating with two 3.8 GHz processors 

and 3 GB of random access memory. Although this level of computing power may seem

rather excessive to control a data acquisition system by modern standards, it is necessary 

to operate the PIV system. The PTU requires higher bandwidth PCI busses than can be 

supported by a standard desktop PC, and the processing power is necessary to handle the 

very intensive computations involved with the data reduction. 

The measurement technique for this setup involved four steps: alignment, calibration, 

measurement, and processing. The goal for the alignment step is to position the plane of 

illumination so that it follows the main flow direction at a predetermined location. This

was done by aligning the laser planes to markings within the test section. Since a plane is 

determined by three points, we used three independent markings to orient our 

illumination plane. During the construction phase of each test section, we placed 

metrically delimitated ruler tapes along the top of the heat exchanger, the bottom of the 

heat exchanger, and along the bottom of the duct inlet. For each measurement, we 

aligned the laser plane to the same tick mark on each ruler so that the light plane was 

aligned with the duct’s sidewalls and was perpendicular to the duct’s upper and lower 

walls. 

The calibration for 2-Dimensional PIV is a relatively simple and straightforward process. 

For this test setup, however, the PIV apparatus must be calibrated prior to acquiring each 

data point, which is time consuming. Furthermore, the entire system must be recalibrated 

if any piece of equipment is moved. The calibration process begins by placing a ruler 

within the test section such that it is aligned to the heat exchanger and lies entirely within 

the plane illuminated by the laser sheets. We used a small tripod to hold the ruler in 

place during the calibration process. Next, the CCD camera is focused on the ruler and a 

photograph is taken. The data acquisition computer examines the photograph in 

‘calibration mode’ where the user is allowed to fix markers to pixels on the photograph, 

see Figure 4.3. The calibration process is completed by marking the crosshairs on the 

ruler and entering the true lineal distance between the markers; the computer scales all 

subsequent work from this calibration data. 

10
Figure 4.3 Calibration Photograph 

Data could be taken once the system was calibrated. First, the correct air flow rate was 

established using the variable-speed drive for the blower module. Once the flow rate was 

set, it was kept constant throughout the data acquisition. Next, the particle generator was 

switched on to fill the laboratory with fog and seed the flow with tracer particles. For the 

next step, the lasers and camera were switched on. The PTU controlled and synchronized 

these components. To reiterate, there are two lasers and each fires one pulse per cycle 

coincident with an image capture from the double pulsed camera. The time delay 

between these two snapshots is set within the controls of the PTU. It is recommended for 

optimal computational results that the time delay should result in image pairs where most 

particles travel approximately one fourth of the interrogation window size between image 

captures. Therefore, the time delay is a function of particle velocity, camera resolution, 

detail preferences, and the scaling magnification determined during calibration. It is 

possible to analytically determine what to use as a time delay; however, it is substantially 

faster and simpler to examine an image pair on high magnification and adjust the time

delay accordingly until a good value is located. 

Once these parameters were set, a program was run to record data. Since air flow 

through the duct is inherently turbulent, there were a lot of unsteady components captured 

using this instant snapshot type of data collection method. Therefore, in order to acquire 

data representative of steady state flow pattern, data collection was performed by 

11
capturing many of these snapshots and averaging the results. In this study, we acquired 

100 image pairs for each data point. 

Data reduction was carried out on the server controlling the PIV apparatus. It was not 

performed after each data collection, but rather at the end of each day and after all of the 

data collection was completed because of the excessive amount of computational time

and power required. During the data reduction, each (1648 X 1214) pixel image is 

divided into a number of interrogation windows. The software allows the user to input 

the interrogation window size ranging from (4 X 4) pixels to (1024 X 1024) pixels. We

used interrogation windows ranging from (16 X 16) pixels to (64 X 64) pixels (depending 

on the specifications of each measurement) and used a 50 % overlap of the interrogation 

areas; therefore each image was divided into somewhere between (200 X 150) windows 

to (50 X 38) windows. The image pairs were reduced to vector fields and these vector 

fields were averaged to produce the final data. The entire process typically takes about 3 

hours to reduce each set of 100 image pairs and return the resultant average vector field. 

12
5: PIV Measurement Results and Discussion

In this study, we examined three different finned-tube heat exchanger configurations: a 

vertically oriented single-slab coil, a single-slab coil oriented at an angle, and a two-slab 

A-shaped coil. 

5.1 Single Slab Vertical Coil 

A single slab heat exchanger consisting of 72 tubes (4 depth rows of 18 tubes) with 

louvered fins was examined in the test apparatus. The dimensions of this heat exchanger 

were 455 mm (18”) tall X 455 mm (18”) wide X 63.5 mm (2.5”) thick. The mounting 

brackets for this heat exchanger position it such that its’ air side inlet and exit surfaces are 

perpendicular to the main flow direction within the duct. 

Each data point was taken with a specific laser illumination plane and camera position. 

The laser illumination plane was aimed at the heat exchanger in 5 separate locations, 

creating 5 separate vertical slices of the flow picture. The locations used for this heat 

exchanger were 230 mm from the side wall (midpoint), 300 mm, 360 mm, 405 mm, and 

450 mm (near the wall). 

When determining the best position for the camera relative to the illumination plane in

the test section, we must note that there is a trade off between the resolution and the field 

of view. If the camera is placed close to the illumination plane, the resolution of the 

images is very good, but the field of view is small. To achieve a good balance, we 

positioned the camera as close as possible to the test apparatus and divided the heat

exchanger surface into 4 horizontally stacked overlapping segments; therefore we 

measured the data on each segment separately. The CCD camera was positioned in 

locations that encompassed the following range of distances from the bottom edge of the 

heat exchanger: (0 to 125) mm; (110 to 240) mm; (225 to 355) mm; and 

(330 to 455) mm. We measured the air velocity at a total of 20 different stations on the 

inlet surface of the heat exchanger. A photograph of the heat exchanger and camera 

position is shown in Figure 5.1.1, a representative measurement plane is provided in the 

figure to illustrate the measurement technique. Figure 5.1.2 shows a piecewise 

illustration of the measured vector fields from this coil at the manufacturers’ air flow rate 

of 0.30 m3

/s (635 ft3/min). 

13
Figure 5.1.1 Measurement Location and Equipment Placement 

Position: 230 mm 300 mm 360 mm 405 mm 450 mm

Centerline

5 mm from wall

Position: 230 mm 300 mm 360 mm 405 mm 450 mm

Centerline

5 mm from wall

Centerline

5 mm from wall

Figure 5.1.2 Piecewise Illustration of Measured Vector Fields for Vertical Coil 

14
Figure 5.1.3 shows a 2-dimensional representation of the component of the velocity 

perpendicular to the heat exchanger acquired during the measurements; data for this 

figure was taken from the measured velocity vectors closest to the heat exchanger 

surface. Each data set shown represents the velocity profile along a vertical slice 

upstream of the heat exchanger. The ordinate axis in this figure corresponds to the 

vertical distance from the bottom of the heat exchanger. We can see that the air approach 

velocity is fairly uniform (approximately 1.3 m/s) with the exception of the areas near the 

top and bottom edges. The velocity profile measured 5 mm from the duct wall shows a 

distribution that is similar the other slices, but is about 20 % slower due to interactions 

imposed by the boundary. 

-0.5

0

0.5

1

1.5

2

0 50 100 150 200 250 300 350 400 450 500

Vertical Position Measured from Duct Wall (mm)

Velocity (

m/s)

u-230

u-300

u-360

u-405

u-450

Figure 5.1.3 Two-Dimensional Representation of Approach Velocity for Vertical Coil 

There are a few other items seen in this figure which are worthy of discussion. First of 

all, there are a few data points that show local velocity to be lower than that of the 

neighboring points. This is not actually occurring but rather it is a problem due to image 

distortion. Each data point shown was produced by analyzing a data set consisting of 100 

image pairs. A vector field was calculated for each image pair by tracking the motion of 

the particles between the images. Once the vector fields were calculated for each image 

pair, the vector at each location was averaged with all of the other vectors in the same 

location in the other 99 calculated vector fields. By reducing a large number of image 

pairs into vector fields and then averaging these vector fields, we are able to dampen out 

unsteady components picked up by the instantaneous measurements of turbulent flow; 

therefore we expect the end result to be a fairly smooth curve. The outlying points shown 

here are caused by either light reflection or dirt particles stuck to the plexiglass duct wall. 

These features are captured in each frame of the camera and therefore are picked up by

15
the data processing software as stationary particles. If a dust particle, for example, is 

stuck to the duct wall and is captured by the camera, the data reduction software will map 

its (lack of) movement along with the particles in the flow and therefore determine a 

velocity value that is slower than the true value. This effect is not very large, since the 

duct was cleaned between most tests and great care was taken to minimize any light

reflections; but there are a few outlying points in the data due to this, most notably at the 

lateral midpoint (position 230 mm). 

The data corresponding to the flow at x = 300 mm in Figure 5.1.3 displays another 

interesting feature. A periodic pattern of high and low velocity covers most of the 

measurements at 300 mm. These particular data files were obtained with the optimal 

camera position that allowed images to be captured right against the heat exchanger 

surface without realizing any reflections from the metallic fins. Every attempt was made 

to place the camera in this position for each measurement set. The periodic pattern seen 

here corresponds to the absence or presence of tubes within the first depth row of the heat 

exchanger. Air approaching the heat exchanger at a location corresponding to a tube will 

move towards a location that corresponds to a position between adjacent tubes; therefore 

the high velocity points seen in the figure are located between tubes and the low velocity 

points are located directly upstream of the tubes. 

5.2 Slant Coil 

The slant coil was a single slab coil positioned at an angle of 65o to the duct wall. It has 

72 tubes (4 depth rows of 18 tubes) with louvered fins. The dimensions of this heat 

exchanger are 455 mm (18”) tall X 430 mm (17”) wide X 65 mm (2.5”) deep. There was 

a plastic mounting bracket fastened to the lower portion of this heat exchanger that 

maintains the angle between the heat exchanger and the lower wall of the duct. A short 

metal sheet was attached to the upper edge of the heat exchanger and was used to fasten 

the top of the heat exchanger to the upper wall of the duct. Figure 5.2.1 shows the 

position of the slant coil within the test section. 

16
Figure 5.2.1 Slant Coil Test Section 

The lasers were aimed to capture 5 vertical slices of the flow profile at locations 

corresponding to 215 mm (midpoint), 280 mm, 340 mm, 380 mm, and 420 mm (near the 

outer edge of the heat exchanger). The profile of the heat exchanger was again divided 

into 4 segments. The segments corresponded to positions 60 mm to 180 mm from the 

bottom of the duct (the heat exchanger bottom is elevated off of the duct because of the 

mounting bracket as seen in Figure 5.2.1), 150 mm to 280 mm, 250 mm to 370 mm, and 

350 mm to 480 mm. The measurements were all taken at the manufacturer’s rated air 

flow rate of 0.35 m3

/s (750 ft3/min). 

17
0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 50 100 150 200 250 300 350 400 450 500

Position along HX Surface (mm)

p p

y ( ) V

elo

city (

m/s)

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 50 100 150 200 250 300 350 400 450 500

Position along HX Surface (mm)

p p

y ( ) V

elo

city (

m/s)

Figure 5.2.2 Velocity Profile at Midpoint for Slant Coil 

Figure 5.2.2 shows the component of the air velocity profile perpendicular to the coil 

surface measured at the heat exchanger’s midpoint. Similar to that seen in Figure 5.1.3, 

we see the sinusoidal velocity pattern indicating the location of the tubes within the heat 

exchanger. What is much more interesting, however, is that the flow appears to have 

three distinctly separate regions, which illustrates the magnitude of the non-uniformity 

with which air flows through this heat exchanger. In the lower portion of the coil, 

corresponding approximately to the region between 0 mm and 50 mm from the bottom, 

the air flow is very slow near the bottom edge of the heat exchanger and it rapidly 

increases in locations towards the mid section of the coil. In area between 50 mm and 

250 mm from the bottom of the coil, the flow rate is relatively constant. In the upper 

portion of the heat exchanger, from 250 mm to 455 mm from the bottom, the figure 

shows a long gradual taper of the air flow rate caused by the diminishing duct area. 

It is interesting to examine the location of the maximum air velocity for this coil. As air 

approaches the heat exchanger near the bottom of the duct, it encounters the lower 

mounting bracket, which turns the flow upwards. The air in this region must then 

accelerate around the bracket, which causes the local maximum near the bottom of the

coil. It is also interesting to see the decrease in the flow velocity near the top of the heat 

exchanger. 

This figure illustrates the importance of measuring the air flow distribution by presenting 

the magnitude of the variation of the flow pattern. The amount of air available for heat 

exchange with each tube in strongly related to the tube’s position. There are 18 tubes per 

18
depth row in this heat exchanger; the position of each tube is identifiable by a local 

minimum in the velocity seen in Figure 5.2.2. The first tube near the bottom of the heat 

exchanger (and those occupying the same position within subsequent depth rows) 

receives very little air flow at all. Starting from approximately 25 mm from the bottom 

through the 250 mm from the bottom of the heat exchanger, the air velocity is relatively 

constant. In the region between 250 mm and 455 mm from the bottom of the heat 

exchanger, the amount of air flow approaching each tube is a strong linear function of its 

position; the tube nearest the top of the heat exchanger receives less than one third of air 

flow that a tube positioned in the middle receives. 

Figure 5.2.3 shows the air flow distribution measured along each vertical slice examined 

in this study. Here we see that the variation between the profiles at different slices is 

small. Overall, the general pattern of air flow velocity seems to be relatively insensitive 

to the location of the image plane, indicating that the wall effects are not very important 

here. 

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

0 50 100 150 200 250 300 350 400 450 500

Distance from Coil Bottom Measured along Coil Face (mm)

Velocity (

m/s)

V_perp 215 mm

V_perp 280 mm

V_perp 340 mm

V_perp 380 mm

V_perp 420 mm

Figure 5.2.3 Two Dimensional Representation of Approach Velocity for Slant Coil 

5.3 A-Shaped Coil 

The last heat exchanger tested in this study is described as a two-slab heat exchanger, 

with the slabs assembled in such a way that it resembles the letter ‘A’. A photograph of 

this coil mounted in the test section is shown in Figure 5.3.1. 

19
Figure 5.3.1 A-Shaped Coil Test Section 

This heat exchanger represents a very typical configuration found in residential air 

conditioning systems. Note that there is a condensate pan attached to the left side of the 

coil in the figure. In field use, this heat exchanger would be positioned such that the 

condensate pan would be on the bottom of the assembly and the air flow would be 

upwards. Since this study examined only the adiabatic cases, there was no moisture 

removal from the air. Because there is no moisture removal, it was unnecessary (and

would provide a substantial laboratory burden) to position the heat exchanger vertically; 

therefore measurements were performed on this heat exchanger in the sideways position 

as shown in Figure 5.3.1. 

Each coil in the assembly had 60 tubes (3 depth rows of 20 tubes) with louvered fins; 

giving a total of 120 tubes in the dual slab A-Shaped coil. The dimensions of each coil 

were 520 mm in height, 400 mm in width, and 65 mm in thickness. The condensate pan 

fully occluded the plexiglass duct and had outer dimensions of 511 mm X 495 mm. The 

coils were attached together with an apex with an angle of 34o between them, and the 

opposite side of each coil was attached to the condensate pan. 

20
PIV measurements were taken along 4 vertical slices corresponding to positions of 

270 mm (the midpoint), 340 mm, 400 mm, and 420 mm (35 mm from the edge of the 

heat exchanger) from the duct wall. Each data set was measured in three segments. 

Since these heat exchangers were positioned at such a small angle (17o to the duct wall) 

the camera field of view was limited by the horizontal distance and therefore the 

measurement segments were divided along the horizontal. The segments corresponded to 

horizontal positions of 0 mm to 75 mm, 165 mm to 340 mm, and 330 mm to 480 mm. 

The measurements were all taken at the manufacturers rated air flow rate of 

0.65 m3

/s (1380 ft3/min). 

Figure 5.3.2 shows a picture of tracer particles in the illumination plane near the entrance 

of this heat exchanger. The main flow direction in this picture is left to right, and the air 

entering the heat exchanger in this portion would turn downwards to flow through the 

lower coil (the lower coils’ return bends can be seen along the bottom of this picture). 

When the illumination source lit up the imaging plane, it was obstructed by the metal 

condensate pan and illuminated the coil surface beginning from approximately the 6th

tube in the coil. A secondary illumination plane caused by the diffracting light is also 

seen in this figure, which illuminated the coil surface from approximately the 4th tube in 

the coil. Unfortunately, since we could not bend the light around or transmit it through 

the condensate pan, we could not illuminate the bottom most 3 tubes in the coil and 

therefore could not measure the flow in this region at the coil surface. We may also note 

that this image shows some distortion near the edge of the heat exchanger between the 8th

and 9th tubes, this is caused by light scattering within the silicone based sealant used to 

join the plexiglass duct to the heat exchanger; the data from these distorted pixels were 

removed from the data set. 

What is most interesting about this configuration is that the condensate pan causes a 

recirculation zone, which effectively blocks the air flow to a substantial portion of the 

coil. As air flows over the pan’s edge, it turns downward towards the coil and continues 

to circulate between the coil and the pan. Figure 5.3.3 shows the profile of the 

perpendicular component of velocity measured along the midline of the heat exchanger, 

close examination of the data points near the entrance of the heat exchanger shows that 

there is a very steep velocity gradient in this region. Here, each data point represents a 

single interrogation window used in the PIV data reduction algorithm. The locus of data 

points corresponding to the edge of the diffracted illumination plane closest to the coil 

surface is the set that shows negative velocity in Figure 5.3.3; the first set above this 

corresponds to the set of interrogation windows just above the illumination plane’s edge, 

etc. These large velocity gradients are the two dimensional representation of the 

recirculation zone. Upon examining the velocity in this area, the steepest gradients occur 

in the vicinity of the 3rd tube from the bottom of the coil, with flow away from the coil at 

the nearest measured point. 

21
Figure 5.3.2 PIV Data Image File – A-Coil Entrance 

-1

0

1

2

3

4

5

6

-100 0 100 200 300 400 500 600

Distance along coil (mm)

-0

0

0

0

0

1

1

1

Velocity (m/s)

-1

0

1

2

3

4

5

6

-100 0 100 200 300 400 500 600

Distance along coil (mm)

-0

0

0

0

0

1

1

1

Velocity (m/s) -0

0

0

0

0

1

1

1

Velocity (m/s)

Figure 5.3.3 Velocity Profile at Midpoint for A-Coil 

22
Figure 5.3.4 is a better illustration of the recirculation zone. This figure shows the 

computed vector field from the diffracted laser light portion of the PIV measurements; 

the triangular region between the edge of the condensate pan and the 4th and 6th heat 

exchanger tubes. The most interesting thing about these pictures is that they illustrate 

that the first 3 or 4 tubes in each coil do not receive a significant amount of air flow. 

These tubes, therefore, can not provide much (if any) heat transfer because the 

condensate pan prevents air from flowing to these tubes. 

Figure 5.3.4 A-Coil Recirculation Zone 

This large inefficient portion of the heat exchanger illustrates the importance of knowing 

the air flow distribution prior to manufacturing heat exchangers. In this case, 

approximately 20 % of the entire heat exchanger provides little or no functionality to this 

product. Had this air flow distribution pattern been known during the design phase of 

this heat exchanger, the manufacturer could have designed around this flow distribution 

pattern by either saving costs through elimination of tubes that receive no air flow, by 

reducing the penalty by providing a spacer for the recirculation zone between the 

condensate pan and the heat exchanger so that the heat exchanger is separated from this 

region, or by other means. 

Figure 5.3.5 shows the measurement results from each slice of data from this heat 

exchanger. Here, again we see that the distance from the wall does not significantly 

impact the velocity distribution. 

23
-1

0

1

2

3

4

5

6

0 100 200 300 400 500

Position along Coil (mm)

U_270 mm

U_340 mm

U_400 mm

U_420 mm

V

elo

city (

m/s) -1

0

1

2

3

4

5

6

0 100 200 300 400 500

Position along Coil (mm)

U_270 mm

U_340 mm

U_400 mm

U_420 mm

V

elo

city (

m/s) Figure 5.3.5 Two Dimensional Representation of Approach Velocity for A-Shaped Coil 

We have seen a few consistencies throughout the PIV measurements of all three tested 

heat exchangers. The most important point is that the air flow, in general, is not uniform. 

The fins and tubes of the heat exchanger provide resistance to the air flow, which in 

general has the affect of evening out the distribution; however, it seems that other factors 

are more influential on the air flow distribution. The presence of any irregularities in the 

duct boundaries or heat exchanger mounting has a much more profound impact. These 

discontinuities locally alter the air flow and change its direction. 

With the first single slab heat exchanger, the test section was relatively free from any 

boundary discontinuities. The heat exchanger had mounting brackets which effectively 

reduced the ducts’ cross sectional area right at the heat exchanger interface; but this 

reduction was very small and occurred right at the point of transition to the introduction 

of the flow resistance and therefore this did not largely impact the air flow. Since the 

heat exchanger itself was uniformly distributed throughout the ducts’ cross section, the 

measurements showed that the air flow distribution through this heat exchanger was 

fairly constant at any location. 

The slanted single slab heat exchanger showed a very different air flow distribution 

pattern because the heat exchanger was positioned at an angle and abrupt area changes 

were introduced by the mounting brackets. The measurements for this test subject 

showed that there was a high flow region caused by the acceleration of the air flow 

around the lower mounting bracket. Also, the measurements showed that positioning the 

24
coil at an angle caused about half of the coil to be subject to a somewhat linearly 

declining air velocity profile. 

For the A-shaped coil, the velocity profile had a lot of similarities to that of the slanted 

coil. The A-shaped coil showed a relatively linearly declining air velocity profile as we

moved closer towards the apex, although not as pronounced as seen on the slanted coil. 

More importantly, though, the condensate pan attached to this coil was an obstructive 

feature, much more so than the ones attached to the slanted coil, and therefore its effects 

were more pronounced. The metal plated used to catch the condensate running off the 

coil acted as an airfoil and caused the presence of a recirculation zone between it and the 

coil. This severely reduced the air supply to approximately 1/5 of the entire heat 

exchanger. 

Another observation that was common to each test specimen is that the velocity profile 

did not change significantly as the image plane is traversed within the duct. All of these 

heat exchangers effectively had 2-dimensional geometry; the geometry of the duct and 

heat exchanger changed dramatically in the downstream and vertical directions, but not in 

the lateral direction. Also, since air has a low viscosity, the effects of the boundaries did 

not seem to be very influential. Together, these aspects resulted in flow maps that were 

2-dimensional and image planes captured at different lateral locations showed the same 

flow pattern. This is a very important point because ultimately we would like to have the 

ability to predict the air flow distribution using computer generated algorithms, and 2-

dimensional solutions offer much faster, less complicated calculations than 3-dimensional 

simulations. This point, however, may not hold for all possible heat exchanger 

installation configurations. In many typical household installations, the blower module is 

attached directly to the coil assembly, which would likely cause three dimensional 

velocity variation. These effects were removed from this study because the blower 

module was located very far downstream from the test section, with two 90o bends and a 

venturi flow meter between them. The present study provides a very good starting point 

but future work is necessary to examine this issue in more detail. 

25
6: Computer Based Simulation Results and Discussion 

In this section our goal was to use computer simulations to numerically replicate the 

velocity distribution of the heat exchangers that we examined with the PIV system. For 

this task, we employed a commercially available Computational Fluid Dynamics (CFD) 

software package to model the flow field. Successful replication of the measured data 

with computer simulations demonstrates that we can use CFD to predict the air flow 

distribution of similar heat exchanger/duct configurations. Once verified, we can use 

computer simulations as the preferred method to predict the air velocity distribution, 

since it is far less expensive, time consuming, and cumbersome than laboratory PIV 

measurements. 

In order to achieve a reasonable computational model of the flow, we first graphically 

replicated the flow domain. This is generally accomplished by modeling each and every 

boundary that interacts with the flow, and using these boundaries and the space between 

them to create a network of nodes at which the conservation equations can be numerically 

solved. However, this approach is not possible with the current state of the art computing 

power, nor is it a very efficient way of modeling the flow field at hand. Since every tube 

and fin on the heat exchanger is an individual boundary, any given flow passage would 

consist of the small gap between adjacent fins bounded by adjacent tubes. Therefore, 

using a conventional approach, the number of nodes required would be astronomical. We 

sought a much simpler approach through momentum resistance modeling [ESI Group, 

2005]. 

Momentum resistance models are used to model flow domains that include obstructions 

or elements which are smaller than the desired grid resolution. This approach is based on 

the idea that we can model the momentum resistance imparted to the flow by these 

elements by characterizing the pressure drop using lumped parameters called momentum

resistance coefficients and assigning them to nodes that reside within the resistive 

domain. To employ this method, we first characterized the resistive domain by relating 

the pressure gradient to the velocity through the following relationship: 

[ ] [ ] V

K

V K P l q r r

⋅ ⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛ ∇ = + 2 2β 2β ρ

Where P is the pressure, ρ is the air density, Kl and Kq are linear and quadratic 

momentum resistance coefficient matricies, β is the porosity factor (flow volume/total 

volume), and V

r

 is the velocity. We determined the values of the momentum resistance 

coefficients specific to our test subjects through laboratory measurement, since the test 

burden was minimal due to the already constructed test apparatus. Alternatively, we 

could have determined these coefficients through numerical simulation. Prior to each set 

of PIV measurements we measured the volumetric flow rate and the differential pressure 

through each heat exchanger test section. This data was used to determine the 

coefficients for the momentum resistance models used in each of the simulations. 

26
6.1 Single Slab Vertical Coil 

We began the CFD simulation of the single slab vertical coil by constructing a 

geometrical representation of the heat exchanger and the attached ducting. Since all of 

the measurement data showed that the flow through each heat exchanger was 2-

dimensional, it is unnecessary to perform a much more involved 3-dimensional CFD 

simulation. Three dimensional simulations were explored at the onset of this work; 

however, their results did not provide any additional information and the simulations

proved to be far more computationally demanding. 

The first step was to characterize the domain over which we solved the flow field. For 

this coil we used a 2-dimensional slice, in the same orientation as the laser light pulses. 

We took advantage of the symmetrical line that divides the plane in half vertically. 

Figure 6.1.1 shows a sketch of the geometrical domain that was used to compute the flow 

domain for the single slab vertical coil; here the domain is represented by the area within 

the red lines. 

Figure 6.1.1 Test Section Sketch with Computational Domain Outline 

Figure 6.1.2 shows the domain as constructed with the CFD software package. The 

domain was comprised of six separate sub-domains; two that represented the flow field 

upstream of the heat exchanger, two that represented the flow through the heat 

exchanger, and two that represented the flow field downstream of the heat exchanger. 

The boundary at the lower edge of the domain represented the wall of the duct, the upper 

line represented the symmetry line, the duct inlet was on the left side, and the duct outlet 

was on the right side (air flow is left to right). Each portion of the domain (e.g. upstream)

was represented by two sub-domains because the heat exchanger’s mounting bracket 

27
obstructs the air flow to the lowest 25.4 mm (1 inch) of the duct, and modeling this 

required a break in the associated entities. 

Upstream HX Coil Downstream

Symmetry Line Lower Duct Wall

Upstream HX Coil Downstream

Symmetry Line Lower Duct Wall

Figure 6.1.2 Computational Domain for Vertical Coil 

Each line was divided into a number of sections by overlaying them with a specified 

number of nodes. We determined the number of nodes required to accurately solve this 

flowfield by iteratively performing the simulation, adding nodes and re-simulating, and 

comparing the results. Through this process, we consistently used a geometric spacing 

pattern for the nodes with a geometric transition factor of 1.25; the finer nodal spacing 

was located closest to the heat exchanger for the upstream and downstream portions, 

closest to the wall for the vertical boundaries, and we used a double sided geometric 

pattern for the entities within the heat exchanger section (as shows in Figure 6.1.2). 

This computational domain was imported into the CFD solver software environment. We

performed our simulations using the flow, turbulence, and momentum resistance models. 

Boundary conditions were set for each lined edge of each sub-domain. The boundaries at 

the top edge of the domain represented a symmetry line; therefore all gradients were set 

to zero along these boundaries. The boundaries on the far left side represented the 

domain’s inlet; here we used a constant inlet velocity and pressure boundary conditions. 

At the far right side of the domain was the outlet; here we used a constant farfield 

velocity and pressure. The boundaries along the bottom of the domain represented the 

duct wall; here we enforced a no-slip boundary condition (u = v = 0). The vertical lines 

at the interfaces between the open duct and the heat exchanger nearest to the duct wall 

represented the heat exchanger’s mounting bracket. This element was modeled as a thin 

wall, we set u = v = 0 along its surface. Finally, all other boundaries were interfaces 

between adjacent sub-domains, and they were unbounded. 

Our next step was to calculate the Reynolds number to determine the parameters 

necessary for the k-ε turbulence model. During our PIV measurements, we used a 

constant flow rate of 0.30 m3

/s, which divided by the upstream duct cross sectional area 

of 0.470 m x 0.508 m = 0.239 m2

, gives an average upstream velocity of 1.255 m/s. 

The hydraulic diameter based on the duct dimensions is: 

28
( )

( ) 0.488m

2 0.470m 0.508m

4 4 0.239m2

= + = =

er

h P

A D

We used the constant values for thermophysical properties for air at 25 oC and 

101.325 kPa [Lemmon et. al. 2007]: 

s

m 1.562 10

m

kg 1.184

2

5

3

− = ⋅

=

ν

ρ

Therefore, the Reynolds number for this case is: 

( )

39,200

s

m 1.562 10

0.488m

s

m 1.255

Re 2

5

=

⋅

⎟

⎠

⎞ ⎜

⎝

⎛

= = ν −

UDh

The turbulence intensity, I, was calculated from this Reynolds number: 

0.16Re 0.0427 8

1

= = −I

The turbulent kinetic energy, k, is therefore: 

( ) 2

2

2

2

2 2 1.5 1.5 1.255 0.0427 0.00431

s

m

s

m k U I ⎟ = ⎠

⎞ ⎜

⎝

⎛ = =

And the dissipation rate, ε, is: 

( ) 3

2

2

3

2

2

2

3

s

m 0.000136

0.07 0.488m

s

m 0.01643 0.00431

0.07

0.01643 =

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

= ⋅ = Dh

k

ε

These values of k and ε were used as input to the CFD k-ε turbulence model [ESI Group, 

2007]. 

Lastly, we needed to characterize the pressure drop through the heat exchanger to 

implement the momentum resistance model. For the single slab flat coil, we measured 

10 points with the laboratory apparatus, varying the flow rate between 0.165 m3

/s 

(350 ft3

/min) and 0.467 m3/s (990 ft3/min). Pressure taps were located 150 mm upstream

and downstream of the heat exchanger, and the flow rate was measured using the venturi 

tube located between the test section and the blower module as shown in Figure 3.1. 

29
Assuming that the entire pressure drop was realized linearly through the coil, we declared 

that the pressure gradient is equal to the pressure difference divided by the coil thickness. 

x

P

x

P

∆

∆ = ∂

∂

Next, we approximated the average air flow velocity through the heat exchanger as the 

volumetric flow rate divided by the cross sectional area. Then we fit a curve to the 

measured data with the functional form: 

C [ ] u C [u]

x

P = q + l ∂∂ 2

And determined the values of Cq and Cl using the least squares method. The 

measurement data and reduction is shown in Appendix A. 

0.9975

s m

kg 226.19

m

kg 123.23

2

3

4

=

⋅ =

=

R

C

C

l

q

Cq and Cl were then used with the heat exchangers’ porosity, β, and the air density, ρ, to 

calculate the momentum resistance coefficients Kq and Kl through the following 

relationships: 

s

1 389.41

m

kg 1.184

s m

kg 2 226.19

2

m

1 212.15

m

kg 1.184

m

kg 2 123.23 2

3

3

3

4 2

=

⎟

⎠

⎞ ⎜

⎝

⎛

⋅ ⋅

= =

=

⎟

⎠

⎞ ⎜

⎝

⎛

⋅

= =

ρ

β

ρ

β

l

l

q

q

C K

C

K

Note that here we used a value of β = 1 rather than the actual value of the porosity of this 

heat exchanger. In effect, by doing this we are simplifying the problem by incorporating 

the porosity directly into the momentum resistance coefficients; therefore, these values 

for Kq and Kl are valid for simulation purposes as long as the porosity used in the 

simulation is also set to unity. 

All of the above values were used as input to the CFD solver and the flow simulation 

converged to a solution. As mentioned earlier, we examined the solutions that were 

calculated when each entity was divided into (10, 15, and 20) nodes. Visual inspection of 

the charted results showed that the solution found with 15 nodes per entity was similar to 

the solution found with 20 nodes per entity indicating that 15 nodes were sufficient for 

30
this simulation. We compared these results by using the results of the 20 point solution 

to calculate the vectors at nodal locations for the 15 point solution. These solutions 

differed by 0.15 %. Figure 6.1.3 shows the results of these three simulations, the stream

wise velocity component is shown for each picture. 

10 nodes per line

15 nodes per line

20 nodes per line

Figure 6.1.3 Stream-Wise Velocity Component for Simulation with Different Number of 

Nodes per Line – Vertical Coil 

Figure 6.1.4 shows the velocity distribution upon approach to the heat exchanger. This 

figure shows that the velocity profile is altered by the presence of the mounting bracket in 

the lower portion of the domain. The profile changes with the distance to the coil 

surface. At 50 mm upstream, the velocity profile resembles that of free stream turbulent 

flow; at 25 mm upstream, the simulation shows that the air must begin to accelerate to 

navigate around the bracket, which causes a small region near the bottom of the coil to 

receive a slightly higher flow rate of air than the rest of the coil. At 1 mm upstream, the 

peak velocity is realized in the vicinity of the mounting bracket. 

31
50 mm upstream 25 mm upstream 1 mm up 1 mm upstream

Figure 6.1.4 Approach Velocity Profile for Vertical Coil 

Figure 6.1.5 shows the pressure distribution throughout the flow domain. Here we can 

see that the entire pressure drop occurs as a result of the flow resistance encountered as 

the air passes through the coil. 

Figure 6.1.5 Pressure Profile in a Duct for the Vertical Coil 

 

The CFD simulations show that the velocity profile changes with distance to the coil 

surface for the 20 mm upstream of the mounting bracket, as the air redistributes to 

navigate around the bracket. All of the simulation data shows a fairly constant velocity 

of 1.35 m/s for locations further than 20 mm upstream of the mounting bracket, which 

agrees very well with the measured data. Since the camera was positioned manually for 

the PIV data acquisition, the data taken from these images were all measured with 

slightly different locations upstream of the coil surface, but were between 10 mm and 

16 mm. The only set of PIV data to capture this accelerated zone near the bottom of the 

coil was the set taken at the center of the coil, which was measured at 10 mm from the 

surface. Figure 6.1.6 shows this set of PIV data compared to the simulation data at 

locations 2 mm, 5 mm, 7 mm, 9 mm, and 12 mm upstream of the coil surface. This 

figure shows that the measured PIV data is bounded by the simulated data in the 2 mm to 

12 mm range. 

32
0

0.25

0.5

0.75

1

1.25

1.5

1.75

2

0 0.05 0.1 0.15 0.2 0.25

Position along Coil Surface (m)

V

elocity (m/s)

U_PIV

U(2)

U(5)

U(7)

U(9)

U(12)

Figure 6.1.6 Comparison of PIV and CFD Data for Vertical Coil

6.2 Slant Coil 

The CFD simulations for the slant coil were much more involved than those for the 

vertical coil because of the more complicated coil and duct geometry. In order to prepare 

a two-dimensional computational domain representative of the slant coil’s flow field, the 

domain was divided into three regions with a total of seven sub-domains, and there were 

no available symmetry planes to simplify the domain. Figure 6.2.1 shows the wire mesh 

representation of the flow domain, with each region outlined in red and each sub-domain 

labeled with roman numerals I through VII. The flow through the domain is left to right. 

I

IV

V VI

VII

III II

I

IV

V VI

VII

III II

Figure 6.2.1 Computational Domain for Slant Coil 

The first region, comprised of sub-domains I, II, and III, represent the duct inlet and the 

flow area upstream of the heat exchanger. Here, the flow inlet is located at the left-most 

boundary, the upper and lower boundaries represent the duct walls, and the right-most 

33
boundary represents the inlet surface of the heat exchanger. As the flow approaches the 

heat exchanger, it encounters some changes in the top and bottom boundaries. At the 

lower boundary, the flow approaches a step, which is representative of the heat 

exchanger’s lower mounting bracket. At the top boundary, the flow encounters the upper 

mounting bracket, which angles downward. 

The second region is entirely comprised of sub-domain IV. This region represents the 

heat exchanger, positioned at an angle to the duct. This region is where the flow will 

encounter all of the momentum resistance assigned by the momentum resistance CFD 

model. 

The third region represents the computational domain downstream of the heat exchanger 

and is comprised of sub-domains V, VI, and VII. The air flow enters this region through 

sub-domain V on the left side, and exits through sub-domain VII on the right side. Note 

that sub-domain V is a very thin portion of the region. The reason for this sub-domain is 

that there exists a short plate attached to the lower portion heat exchanger, which acts to 

collect and direct water that condenses during operation. This plate is located at the back 

side of the heat exchanger, at a distance of 19 mm downstream, and follows the heat 

exchanger to a height of 51 mm above the lower duct wall. 

Once the domain was constructed with the CFD software package, we used this domain 

for all of the CFD simulations for the slant coil. Again, we applied the same technique to 

determine the grid resolution; that of iteratively solving the flowfield within the 

computation domain, reducing the grid spacing, solving the flowfield again, and 

repeating until the solution matches that of the previous simulation. We consistently used 

a geometric spacing pattern throughout the simulations. We used a double sided spacing 

pattern for the inlet plane and all boundaries in sub-domains III, IV, and V; nodes were 

spaced along all other boundaries with a single sided geometric spacing pattern, with 

finer nodal spacing located in the areas with the largest expected velocity gradients. All 

of the nodes were dispersed along the boundaries with a geometric transition factor of 

1.1, with the exception of the exit plane, which required a larger transition factor (varying 

between 1.2 and 1.25) to ensure a proper grid. 

Constant velocity and pressure boundary conditions were set along the domain inlet, and 

constant farfield velocity and pressure boundary conditions were set along the domain 

outlet. The top and bottom of the flow domain represented the duct walls and therefore 

were set with no-slip boundary conditions. The short plate downstream of the heat 

exchanger, near the bottom of the duct, was modeled as a thin wall obstruction therefore 

no-slip boundary conditions were also set here. Lastly, all of the remaining boundaries 

were modeled as unbounded interfaces, which served to connect adjacent sub-domains. 

The next step was to determine the kinetic energy and dissipation rate for the turbulence 

model. We started by calculating the Reynolds number from the measured data. During 

our PIV measurements, we used a constant flow rate of 0.355 m3

/s, which divided by the 

upstream duct cross sectional area of 0.470 m x 0.533 m = 0.251 m2

, gives an average 

velocity of 1.416 m/s. 

34
The hydraulic diameter based on the duct dimensions is then: 

( )

( ) 0.500m

2 0.470m 0.533m

4 4 0.251m2

= + = =

er

h P

A D

We again used the same constant values for the density and viscosity of air as were used 

with the previous simulation; therefore, the Reynolds number is: 

( )

45,300

s

m 1.562 10

0.500m

s

m 1.416

Re 2

5

=

⋅

⎟

⎠

⎞ ⎜

⎝

⎛

= = ν −

UDh

The turbulence intensity, I, was calculated from this Reynolds number: 

0.16Re 0.0419 8

1

= = −I

The turbulent kinetic energy, k, is therefore: 

( ) 2

2

2

2

2 2

s

m 0.0419 0.00528

s

m 1.5 1.5 1.416 ⎟ = ⎠

⎞ ⎜

⎝

⎛ k = U I =

And the dissipation rate, ε, is: 

( ) 3

2

2

3

2

2

2

3

s

m 0.001801

0.07 0.500m

s

m 0.1643 0.00528

0.07

0.1643 =

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

⋅

= ⋅ = Dh

k

ε

These values of k and ε were imposed along the inlet and exit planes of the simulation 

domain and were also used as an initial guess for the simulations. The next step was to 

calculate the momentum resistance coefficients based on the measured data from the 

laboratory measurements of the pressure drop through the slant coil. The momentum 

resistance coefficients were again based on 10 measured data points of the air volumetric 

flow rate and pressure drop through the coil; a table containing the data is included in 

Appendix A. We again curve fit this data with a least squares quadratic best fit to obtain 

the coefficients that relate the pressure gradient with the average velocity. 

We made some assumptions to account for the momentum resistance model’s 

applicability within this test section geometry. The measured data shows the pressure 

difference between points upstream and downstream of the heat exchanger, which 

includes portions of the flow domain that may impart some pressure drop to the flow, 

specifically the obstructive mounting bracket. Also, we know that the flow must turn to 

35
pass through the heat exchanger, which may induce further pressure losses. However, the 

momentum resistance model that we used for this simulation is based on the assumptions 

that the entire measured pressure drop through the test section occurs within the heat 

exchanger, and that any other losses will be negligible. 

Our momentum resistance model is based on the average velocity through the heat 

exchanger; therefore the velocity used in the calculations is based on the measured 

volumetric flow rate divided by the face area of the heat exchanger. Through this 

analysis, we assigned a quadratic curve fit to the data and obtained the following 

coefficients for pressure gradient vs. velocity relationship: 

0.9963

s m

kg 212.33

m

kg 134.8

2

3

4

=

⋅ =

=

R

C

C

l

q

Cq and Cl were then used to calculate the momentum resistance coefficients Kq and Kl

through the following relationships, again using the simplifying value of unity for the 

heat exchanger’s porosity: 

s

1 358.67

m

kg 1.184

s m

kg 2 212.33

2

m

1 227.71

m

kg 1.184

m

kg 2 134.8 2

3

3

3

4 2

=

⎟

⎠

⎞ ⎜

⎝

⎛

⋅ ⋅

= =

=

⎟

⎠

⎞ ⎜

⎝

⎛

⋅

= =

ρ

β

ρ

β

l

l

q

q

C K

C

K

We performed simulations using these values to solve the flow field within the 

computational domain with four different mesh resolutions. We began with 15 nodes 

dispersed across each entity, as described in the previous section, and increased the 

number of nodes to 20, 25, and 30. Visual inspection of the charted results showed that 

the solution found with 25 nodes per entity was similar to the solution found with 30 

nodes per entity indicating that 25 nodes were sufficient for this simulation. We

compared these results by using the results of the 30 point solution to calculate the 

vectors at nodal locations for the 25 point solution. These solutions differed by 0.7 %. 

Figure 6.2.2 shows the maps depicting the downstream component of velocity for each of 

the simulations. 

36
15 nodes per line

25 nodes per line 30 nodes per line

15 nodes per line 20 nodes per line

25 nodes per line 30 nodes per line

20 nodes per line

Figure 6.2.2 Stream-Wise Velocity Component for Simulation with Different Number of 

Nodes per Line – Slant Coil 

Figure 6.2.3 shows the pressure distribution over the computational domain. Here we can 

see that the majority of the drop in pressure occurs within the sub-domain representative 

of the heat exchanger slab; however, there exists some pressure drop occurring outside of 

the momentum resistance domain. 

Figure 6.2.3 Pressure Profile for Slant Coil 

Figure 6.2.4 shows the velocity vector field upon approach to the vector field at various 

locations measured from the duct inlet. The first two pictures in this sequence show 

image planes that are entirely upstream of the heat exchanger, the third picture (location 

1118 mm) shows the point where the bottom of the image plane first touches the inlet 

37
surface of the heat exchanger, and the last two pictures show the plane passing through a 

portion of the heat exchanger. In this sequence, we can see that the flow reacts to the 

mounting bracket by accelerating around it causing an increase in the local flow rate near 

the lower portion of the heat exchanger. 

Location:1042mm 1080mm 1118mm 1156mm 1195mm

Figure 6.2.4 Vector Profile for Slant Coil 

Figure 6.2.5 shows the comparison of the CFD simulations with the measured PIV data. 

Here, the perpendicular component of velocity is plotted against the position along the 

coil. We can see that there is very good agreement between the predicted data and the 

measured data. 

38
Comparison of CFD Simulation with PIV Measurements

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 50 100 150 200 250 300 350 400 450 500

Position along HX Surface (mm)

Perpindicular Component of Velocity (

m/s)

V_perp_PIV

V_perp_CFD

Figure 6.2.5 Comparison of PIV and CFD Data for Slant Coil 

6.3 A-Shaped Coil 

The CFD simulations for the A-shaped coil were the most complicated of those examined 

in this study due to the complexity of the geometry. We began by preparing the 

geometrical domain for the solver in the same manner as the other two heat exchangers, 

two dimensional and in alignment with the PIV measurement slices. The A-shaped coil 

did provide an opportunity for a simplification in the domain due to symmetry; therefore, 

only one slab of the heat exchanger is modeled in this domain. The computational 

domain used for these simulations is shown below in Figure 6.3.1. 

VII

VI

V

III IV

II

I

VII

VI

V

III IV

II

I

Figure 6.3.1 Computational Domain for A-Shaped Coil 

We divided the computational domain into three regions with a total of seven subdomains as shown. Sub-domains I through IV are upstream of the heat exchanger slab, 

sub-domain V represents the heat exchanger itself, and sub-domains VI and VII represent 

the flow domain downstream of the heat exchanger. The inlet is the left-most entity 

39
located in sub-domain II, and the exit is the right-most entity located in sub-domain VI. 

The entities that span the top portion of this figure represent the symmetry line that we

used to simplify the computational domain. The lines along the lower portion of the 

figure represent the duct walls and the rigid obstructions connected to the heat exchanger 

slab. The lines partitioning sub-domains I from II; II from III; III from IV; and VI from

VII merely serve to divide the sub-domains and are not physical boundaries. Figure 6.3.2 

shows an enlarged portion taken from Figure 6.3.1, as this section requires a more 

detailed explanation. 

VII

VI

V

IV

III

II

I

VII

VI

V

IV

III

II

I

Figure 6.3.2 Blowup of Computational Domain for A-Shaped Coil 

In this figure, rigid boundaries (specifically the duct wall and the condensate drain pan) 

are represented by the blue lines. These are fixed boundaries; therefore air cannot pass 

though them. Here we can see that the flow coming from sub-domains I and II must 

accelerate around the edge of the condensate pan and approach the heat exchanger 

through sub-domain III. All flow into the heat exchanger must, therefore, pass through

sub-domain III then through sub-domain IV before entering sub-domain V. 

Once we completed the wire grid domain, we again applied the iterative simulate/tighten 

mesh/re-simulate technique until the solution matched the previous simulation. We

consistently used geometric nodal spacing with a transition factor of 1.2 throughout the 

simulations. Single sided geometric spacing was applied for entities that approached the 

symmetry plane, the domain inlet, and the domain exit, with the finer nodal spacing 

nearest the wall or the center of the domain. Double sided geometric nodal spacing was 

applied to all other entities. We again imposed the inlet boundary conditions of constant 

velocity and pressure, and the exit boundary conditions of constant farfield velocity and 

pressure. 

40
Next we determined the parameters for use in the CFD solver’s k-ε turbulence model in 

the same manner as with the other simulated cases. First the duct’s cross sectional area 

and the hydraulic diameter: 

( )( ) 2 A = 0.511m 0.495m = 0.253m

( )

( ) 0.503m

2 0.511m 0.495m

4 4 0.253m2

= + = =

er

h P

A D

And therefore the average velocity based on the tested flow rate is: 

s

m 2.574

0.253m

s

m 0.651

2

3

= = = A

Q V

We again used the same constant values for the density and viscosity of air as were used 

with the previous simulation; therefore, the Reynolds number is: 

( )

82,900

s

m 1.562 10

0.503m

s

m 2.574

Re 2

5

=

⋅

⎟

⎠

⎞ ⎜

⎝

⎛

= = ν −

UDh

The turbulence intensity, I, is calculated from this Reynolds number: 

0.16Re 0.03884 8

1

= = −I

The turbulent kinetic energy, k, is therefore: 

( ) 2

2

2

2

2 2

s

m 0.03884 0.01499

s

m 1.5 1.5 2.574 ⎟ = ⎠

⎞ ⎜

⎝

⎛ k = U I =

And the dissipation rate, ε, is: 

( ) 3

2

2

3

2

2

2

3

s

m 0.00856

0.07 0.503m

s

m 0.1643 0.01499

0.07

0.1643 =

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

= ⋅ = Dh

k

ε

Lastly, we again determined the momentum resistance coefficients for this configuration. 

Using the laboratory apparatus, we measured 10 points relating the flow rate to the 

pressure drop through the heat exchanger. Data was taken over a range of flow rates 

41
between 0.151 m3

/s (319 ft3/min) and 0.661 m3/s (1400 ft3/min); the measurement data 

are shown in Appendix A. As we did with the slant coil, we assumed that the entire 

measured pressure drop occurs within the heat exchanger slab, thereby allowing us to 

assign momentum resistance coefficients solely to the heat exchanger. We determined 

the average velocity through the heat exchanger by dividing the flow rate by the sum of 

the surface areas of both slabs of the A-Shaped coil. We then used the least squares 

method to determine the coefficients of the curve fit of the model’s functional form: 

0.999

s m

kg 56.49

m

kg 258.11

2

3

4

=

⋅ =

=

R

C

C

l

q

And then used these intermediate coefficients to determine the momentum resistance

model coefficients as was done in the previous cases with the porosity equal to unity: 

s

1 95.416

m

kg 1.184

s m

kg 2 56.49

2

m

1 435.99

m

kg 1.184

m

kg 2 258.11 2

3

3

3

4 2

=

⎟

⎠

⎞ ⎜

⎝

⎛

⋅ ⋅

= =

=

⎟

⎠

⎞ ⎜

⎝

⎛

⋅

= =

ρ

β

ρ

β

l

l

q

q

C K

C

K

Once we had determined all of the relevant parameters, we began the computational 

simulations to determine the required mesh resolution for this flow domain. We began 

our simulations with a resolution of 15 nodes spaced over each entity and added 5 nodes 

per entity until we reached a solution that coincided with the previous simulation. In this 

case, we repeated this iterative process with 20, 25, 30, 35 and 40 nodes per entity. 

Visual inspection of the charted results showed that the solution found with 40 nodes per 

entity was similar to the solution found with 35 nodes per entity indicating that 35 nodes 

were sufficient for this simulation. We compared these results by using the results of the 

40 point solution to calculate the vectors at nodal locations for the 35 point solution. 

These solutions differed by 3 %. The results of these simulations is shown in 

Figure 6.3.3, both the plots depicting the u and v components of velocity are shown, since 

these results involve substantial contributions from each. 

42
15 nodes per line

30 nodes per line

25 nodes per line

35 nodes per line

40 nodes per line

20 nodes per line

x-component y-component

15 nodes per line

30 nodes per line

25 nodes per line

35 nodes per line

40 nodes per line

20 nodes per line

x-component y-component

Figure 6.3.3 Stream-Wise Velocity Component for Simulation with Different Number of 

Nodes per Line – A-Shaped Coil 

At the onset of this simulation, we made an assumption for our momentum resistance 

model that the entire measured pressure drop occurred within the heat exchanger slab. 

Our simulation results do not agree very well with this assumption, as shown in 

Figure 6.3.4. 

43
Figure 6.3.4 Pressure Profile for A-Shaped Coil 

Our simulation results show that although most of the pressure drop occurs within the 

slab, there are significant contributions from two other the locations within the domain. 

The first location is where the condensate pan impacts the approaching flow; here the 

condensate pan blocks off almost half of the entire flow path forcing the flow to 

accelerate considerably, and then turn abruptly to approach the heat exchanger. The 

other location is at the heat exchanger exit. Here, since the angle between the heat 

exchanger and the duct is very small, the flow leaving the heat exchanger impacts the 

duct and turns towards the exit plane. Although these points reiterate the fact that our 

initial assumptions are not completely accurate, the solutions offered here are quite 

realistic. Although not perfect, this simulation provides us with a wealth of information 

about this flow field, and shows that the simulated velocity profile agrees well with the 

measured profile. 

In order to provide a much more accurate simulation in the future, a better method would 

be to calculate the momentum resistance coefficients from laboratory data taken using the 

heat exchanger slab positioned at 90o to the flow (as was done with the first coil in this 

study). Again, however, for the purposes of this study, the solution provided by 

coefficients that were calculated from overall pressure drop matched the measured data. 

Figure 6.3.5 shows a series of velocity distribution patterns as determined by the CFD 

simulation. This figure well illustrates the complexity of this problem. The first velocity 

distribution pattern shown upstream of the heat exchanger is a typical pattern found in 

unobstructed turbulent flow. As the flow approaches the second position in the sequence, 

the air begins to negotiate around the condensate pan, i.e. flow near the bottom

decelerates and the flow near the top accelerates to compensate for the increased mass 

flow. At the third position, the velocity distribution gets quite interesting. Along this 

line, most of the locations realize forward moving flow; however, the region between the 

condensate pan and the heat exchanger slab realizes backwards flow. The 4th and 5th

44
position show how the flow passes through the heat exchanger and then change course to 

flow towards the exit plane. 

Figure 6.3.5 Vector Profile for A-Shaped Coil 

Figure 6.3.6 shows the computed vector field located within the lower portion of subdomain IV. The results of this simulation predicted the recirculation zone seen during the 

PIV measurements. The presence, location, and magnitude of this recirculation zone 

agree with the information that we have from Figure 5.3.4 from the PIV measurements. 

The amount of information in Figure 5.3.4 is somewhat limited, though, since the laser 

sheet was obstructed by the condensate pan; but the simulation results agree very well 

with the measured data that we do have. 

45
Condensate Pan

Heat Exchanger

Condensate Pan

Heat Exchanger

Figure 6.3.6 CFD Resolution of Recirculation Zone 

The important information from this simulation is the air velocity profile as it enters the 

heat exchanger. Since we have computationally solved the entire flow domain, we can 

readily extract the velocity at any point within the domain, unlike with the PIV

measurements where we are limited by line-of-sight. Figure 6.3.7 shows an enlarged 

picture of the computational domain used for the simulation. In this figure, the heat

exchanger slab is shown in grey, with its inlet surface shown by the red line AD. The 

edge of the condensate pan is shown by the black lines connecting points A and B. The 

blue line connected by points B and C represent the bottom edge of the line-of-sight 

plane used during the PIV measurements; therefore the PIV measurements used for 

comparison from this point onward are taken along B-C-D. 

A

D

C

B

Figure 6.3.7 Computational Domain Sections 

46
Figure 6.3.8 shows the perpendicular component of the velocity field entering the lower 

slab of the heat exchanger, as computed by the CFD simulation. The data set shows the 

inlet velocity profile as realized by the heat exchanger along the line connecting points A 

and D from Figure 6.3.7. 

This simulation shows that there exists a very large inefficient portion of this heat

exchanger. There is a very small amount of air entering the coil along the very bottommost portion of the heat exchanger (between 0 mm and 21 mm from the edge). Then, 

between 21 mm and 80 mm, the air flow is actually moving away from the coil. After

about 80 mm, a somewhat normal positive air flow pattern is established. This positivenegative-positive pattern indicates a recirculation zone. As a direct result of this 

recirculation zone a large portion of the heat exchanger receives very little or no air flow

at all. 

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

3.5

0 50 100 150 200 250 300 350 400 450 500

Position along HX Surface (mm)

Vel

ocit

y (

m/s)

U (line AD)

Figure 6.3.8 CFD Velocity Profile at A-Shaped Coil Inlet 

We can compare the simulation results to the PIV measurements. Figure 6.3.9 shows the 

two data sets overlaid onto the same plot. In a few areas the computed velocity field 

differs from the measured velocity field; however, these differences can be explained. 

47
-2

-1

0

1

2

3

4

5

6

0 50 100 150 200 250 300 350 400 450 500

Position along Coil Surface (mm)

Perpendicular Compo

n

e

nt of Velocity (m/s)

V_perp_CFD

V_perp_PIV

Figure 6.3.9 Comparison of PIV Data with CFD Coil Inlet Data for A-Shaped Coil 

The CFD data plotted in Figure 6.3.9 shows the perpendicular component of velocity 

right at the heat exchanger interface; whereas the PIV data was measured at points that 

are slightly upstream from the heat exchanger interface. As was seen in the previous

example, the simulation shows that the air flow decelerates at the interface, therefore, 

points slightly upstream show velocities that are a little higher than those at the interface. 

Figure 6.3.10 shows the measured PIV data overlaid with the perpendicular component of 

velocity for entire computational sub-domain IV. This figure shows that the simulated 

data does, in fact, agree very well with the measured data. This indicates that it is 

important to measure the velocity with PIV as close to the heat exchanger surface as 

allowed by line-of-sight because of the very large velocity gradients in this region. 

48
-2

-1

0

1

2

3

4

5

6

0 50 100 150 200 250 300 350 400 450 500

Position (mm)

Velocit

y (m/s)

CFD

PIV

Figure 6.3.10 Comparison of PIV Data with all Data from CFD Computational SubDomain IV for A-Shaped Coil 

Throughout the simulations of the more complicated installation configurations, some of 

the governing assumptions for the momentum resistance models were not strictly 

followed, but the consequences were minimal. The momentum resistance models are 

lumped parameter models that were used to impede the flow within a specific domain, 

and as such we assigned quadratic and linear impedance terms to a given domain. In our 

analysis, we used pressure differential information that was measured from the approach 

and discharge of the heat exchangers, and these regions included features outside of the 

heat exchanger that also reduce the static pressure and alter the local velocity. By taking 

this approach, the effects of the condensate pans, mounting brackets, etc. were doubly 

accounted for in the simulations because they were included in the momentum resistance 

coefficients and then simulated outside of the resistive domain. By taking this approach, 

we avoided the substantial burden of determining the momentum resistance coefficients 

through detailed simulation or additional laboratory experimentation; however, the 

velocity profiles found in simulation (the main intent of this study) were nearly identical 

to the measured ones. 

49
7: Summary and Conclusions 

We studied the air side inlet velocity profiles of three common finned-tube heat 

exchanger installations. We measured the air velocity profile for each using Particle 

Image Velocimetry. We performed CFD simulations for the tested setups and replicated 

the measured air flow velocity distribution patterns. 

Our measurements showed that the velocity distribution is strongly influenced by features 

within the duct and the orientation of the heat exchanger; therefore it is generally not 

uniform. Features, such as mounting brackets and condensate collection pans, greatly 

alter the local flow direction. 

We also saw for the tested configurations that the air velocity profiles had very little 

variation in the lateral direction. This enabled us to accurately describe the air side 

velocity distribution with a simple two dimensional model. The test apparatus used in 

this study, however, maintained the flow by using a blower module that was located far 

downstream from the test section. It is therefore possible that this observation may not 

hold true for cases with the blower attached directly to the heat exchanger, where their 

three dimensional effects may be present in the duct upstream of the heat exchanger. 

This point requires further investigation. 

The information documented in this report is very important for the design of finned-tube 

heat exchangers because the air distribution has a profound impact on the performance of 

such heat exchangers. Finned-tube heat exchangers can, in essence, be thought of as a 

network of single-tube cross flow heat exchangers, where the performance of the heat 

exchanger as a whole is dependent on the performance of each tube. If every tube in the 

heat exchanger is subject to a different amount of air flow, with different tube side and air 

side thermodynamic properties, each tube will perform differently. Ideally, the amount 

and thermodynamic state of refrigerant flowing through each tube should be well 

matched to the air side properties and velocity distribution so that the performance of the 

heat exchanger as a whole is maximized. Tubes which are included in the heat exchanger 

and receive very little or no air flow (which were located through the course of this study) 

reduce the overall performance of the coil. A design engineer armed with information 

about the air flow distribution can use it to incorporate features that minimize the losses 

associated with its pattern. 

50
References:

Adrian, R. J. Particle-Imaging Techniques for Experimental Fluid-Mechanics, Annual

Review of Fluid Mechanics, no. 23, pp 261-304, 1991. 

ASHRAE 1998. ANSI/ASHRAE Standard 37. Methods of testing for rating unitary air 

conditioning and heat pump equipment. American Society of Heating, Refrigerating and 

Air-Conditioning Engineers. Atlanta, GA. 

Bryant, R. A., Particle Image Velocimetry Measurements of Buoyancy Induced Flow 

Through a Doorway, NISTIR 7252, National Institute of Standards and Technology, 

Gaithersburg, MD (2005). 

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

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

Transactions, Vol. 95, no. 1, 1987. 

Domanski, P. A., Yashar, D. A., Kaufman, K. A. and Michalski, RK. An Optimized 

Design of Finned-Tube Evaporators Using the Learnable Evolution Model HVAC&R

Research April 01, 2004. 

Domanski, P.A., 2007, EVAP-COND - Simulation models for finned-tube heat 

exchangers, Version 2.2, National Institute of Standards and Technology, Gaithersburg, 

MD, USA. http://www2.bfrl.nist.gov/software/evap-cond/

Durst, F., Melling, A. and Whitelaw, J.H., Principles and Practice of Laser Doppler 

Anemometry, Academic Press Inc., New York, NY, 1976. 

ESI Group, Guidelines for Specification of Turbulence at Inflow Boundaries, ESI Group 

CFD Customer Portal, http://support.esi-cfd.com/esi-users/turb_parameters/, March 2007. 

ESI Group, Momentum Resistance or Source, CFD-ACE+ V2006 User Manual, pp 133-

138, 2005. 

IEC 60825-1, Safety of Laser Products – Part I: Equipment Classification and 

Requirements. International Electrotechnical Commission, Geneva, Switzerland (2007). 

Lemmon, E.W., Huber, M.L., McLinden, M.O. NIST Standard Reference Database 23: 

Reference Fluid Thermodynamic and Transport Properties-REFPROP, Version 8.0, 

National Institute of Standards and Technology, Standard Reference Data Program, 

Gaithersburg, 2007. 

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

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

Seitzman, J. M.; Hanson, R. K. (1993). Planar Fluorescence Imaging in Gases, in 

Taylor, A. M. K. P.: Instrumentation for Flows with Combustion. Academic Press, pp. 

405-466. 

Taylor, B. N. and Kuyatt, C. E. Guidelines for Evaluating and Expressing the 

Uncertainty of NIST Measurement Results, NIST Technical Note 1297, NIST, 

Gaithersburg, MD, (1994).

51
Appendix A: Pressure Drop Data for Flow Resistance Coefficients 

Table A.1. Data used to Determine Momentum Resistance Coefficients for Vertical Coil 

Flow Rate 

[m3

/s]

Pressure Drop 

[Pa] 

Average Velocity 

[m/s] 

Pressure Gradient 

[Pa/m]

0.3658 49.569 1.767 780.609

0.2799 32.382 1.352 509.946

0.1652 15.942 0.798 251.050

0.4200 63.019 2.029 992.433

0.3011 37.363 1.454 588.399

0.3384 44.836 1.635 706.079

0.1935 21.422 0.935 337.349

0.2270 25.158 1.097 396.189

0.4672 71.239 2.257 1121.881

0.2454 27.898 1.185 439.338

Table A.2. Data used to Determine Momentum Resistance Coefficients for Slant Coil 

Flow Rate 

[m3

/s]

Pressure Drop 

[Pa] 

Average Velocity 

[m/s] 

Pressure Gradient 

[Pa/m]

0.6183 123.466 3.1032 1899.475

0.2549 31.883 1.279182 490.5135

0.2973 40.426 1.492379 626.5544

0.3681 54.725 1.847707 841.9205

0.5239 101.529 2.629429 1561.979

0.1652 16.684 0.829099 256.6765

0.4366 70.273 2.191191 1081.123

0.5663 112.090 2.842626 1724.462

0.3351 47.833 1.681887 735.8853

0.2737 35.084 1.373936 539.7565

52
Table A.3. Data used to Determine Momentum Resistance Coefficients for A-Shaped Coil 

Flow Rate 

[m3

/s]

Pressure Drop 

[Pa] 

Average Velocity 

[m/s] 

Pressure Gradient 

[Pa/m]

0.4776 28.583 1.1572 409.22

0.6612 51.853 1.6017 742.34

0.3511 16.300 0.8504 233.37

0.1506 3.579 0.3646 51.26

0.4012 20.806 0.9715 297.89

0.4460 24.971 1.0805 357.50

0.2855 11.807 0.6921 169.04

0.2313 7.687 0.5598 110.04

0.5394 36.198 1.3060 518.23

0.6088 45.850 1.4739 656.39

53
Appendix B. Uncertainty Analysis

The uncertainty analysis of the PIV based measurements is presented in this appendix. 

This analysis is based on the guidelines adopted by NIST [Taylor and Kuyatt, 1994]; 

whereas two components of uncertainty are presented, statistically based Type A 

uncertainty and judgment based Type B uncertainty. 

B.1 Type A Uncertainty

Type A uncertainty is based on the variation of repeated measurement results. In this 

study, we obtained the steady-state components of the flow velocity by capturing many 

instantaneous measurements within a turbulent flow field and averaging the resultant 

vector fields. 

We acquired 100 image pairs for each data point so that the transient effects of turbulent 

flow would be dampened out and would not influence the data. We used each pair of 

images to compute a vector field representative of the instantaneous flow velocity 

distribution. We then computed the average of the 100 vectors at each location within the 

vector field. Therefore, each computed steady-state vector within each data file was 

computed by averaging 100 vectors that were captured through independent 

measurements. Therefore, the measurement uncertainty of each vector obtained through 

this method is equal to the standard deviation of the measured values of that vector, σ, 

divided by the square root of the number of samples, 10. 

Each data set consists of 100 data files and each data file consists of several hundred or in 

some cases several thousand vectors, therefore it is not feasible to include the uncertainty 

for each individual vector. Therefore, tables B.1.1 through B.1.3 show the average Type 

A uncertainty calculated for each data file from the results within each data set. The xand y- component values and standard deviations are shown, but the uncertainty is 

calculated for the vector lengths. Since the y- component of velocity is generally much 

smaller than the x-component due to the layout of the test apparatus, the y-component 

uncertainty is much greater compared to the measured values, but this is not very 

significant to the overall result. Overall, the type A uncertainty was small, typically in

the range of 0.1 %. 

54
Table B.1.1 Type A Uncertainty for Vertical Coil 

x-component y-component Vector length

File 

name

Average

[m/s]

Standard

Deviation 

[m/s]

Average

[m/s]

Standard

Deviation 

[m/s]

Average

[m/s]

Standard

Deviation 

[m/s]

Vector 

Length 

Uncertainty 

[m/s]

Vector 

Length 

Uncertainty 

[%]

230-I 1.3929 0.1151 0.0818 0.1758 1.4070 0.1128 0.0011 0.0802

230-II 1.1561 0.1776 0.1438 0.1908 1.2289 0.1700 0.0017 0.1384

230-III 1.1016 0.1272 0.1053 0.1755 1.1502 0.1132 0.0011 0.0984

230-IV 1.1560 0.1649 0.0515 0.1872 1.2010 0.1365 0.0014 0.1137

300-I 1.3968 0.1790 0.1577 0.1673 1.4164 0.1773 0.0018 0.1252

300-II 1.3111 0.1675 0.1469 0.1865 1.3111 0.1675 0.0017 0.1278

300-III 1.2838 0.1405 0.1080 0.2202 1.3131 0.1342 0.0013 0.1022

300-IV 0.8757 0.2021 0.0356 0.1469 0.9494 0.1859 0.0019 0.1958

360-I 1.3897 0.1967 0.1813 0.1922 1.4150 0.2006 0.0020 0.1418

360-II 1.3177 0.1796 0.2538 0.2412 1.3656 0.1768 0.0018 0.1294

360-III 1.3211 0.1117 0.2181 0.2510 1.3631 0.1151 0.0012 0.0844

360-IV 1.2723 0.1245 0.1742 0.1628 1.2962 0.1262 0.0013 0.0974

405-I 1.3223 0.1589 0.1345 0.1791 1.3420 0.1578 0.0016 0.1176

405-II 1.2634 0.1313 0.2850 0.2163 1.3122 0.1458 0.0015 0.1111

405-III 1.2861 0.1318 0.3020 0.2927 1.3519 0.1505 0.0015 0.1113

405-IV 1.2464 0.1440 0.1972 0.2192 1.2821 0.1434 0.0014 0.1119

450-I 1.0156 0.2313 0.0169 0.1788 1.0488 0.1862 0.0019 0.1776

450-II 1.0613 0.1469 0.3730 0.2103 1.1424 0.1699 0.0017 0.1487

450-III 1.1136 0.1577 0.4667 0.2652 1.2349 0.1754 0.0018 0.1420

450-IV 1.0247 0.1652 0.3018 0.2263 1.0927 0.1784 0.0018 0.1633

55
Table B.2 Type A Uncertainty for Slant Coil 

x-component y-component Vector length

File 

name

Average

[m/s]

Standard

Deviation 

[m/s]

Average

[m/s]

Standard

Deviation 

[m/s]

Average

[m/s]

Standard

Deviation 

[m/s]

Vector 

Length 

Uncertainty 

[m/s]

Vector 

Length 

Uncertainty 

[%]

215-I 1.9411 0.1407 0.0497 0.1582 1.9518 0.1435 0.0014 0.0735

215-II 1.9369 0.1275 -0.0225 0.1806 1.9479 0.1252 0.0013 0.0643

215-III 1.8006 0.1358 -0.0713 0.2212 1.8187 0.1314 0.0013 0.0722

215-IV 1.6783 0.1395 -0.2678 0.1984 1.7151 0.1227 0.0012 0.0715

280-I 2.0045 0.1658 0.2800 0.1587 2.0322 0.1760 0.0018 0.0866

280-II 1.9052 0.1397 0.1375 0.2215 1.9254 0.1457 0.0015 0.0757

280-III 1.7559 0.1809 0.0032 0.2117 1.7711 0.1792 0.0018 0.1012

280-IV 1.1442 0.0994 -0.1671 0.1486 1.1683 0.0855 0.0009 0.0731

340-I 1.8991 0.1614 0.1642 0.1871 1.9168 0.1716 0.0017 0.0895

340-II 1.9604 0.1561 0.1999 0.2874 1.9917 0.1706 0.0017 0.0857

340-III 1.7211 0.1995 0.0289 0.3129 1.7545 0.1966 0.0020 0.1121

340-IV 1.6491 0.1284 -0.1095 0.1830 1.6654 0.1225 0.0012 0.0735

380-I 1.8613 0.1399 0.1906 0.1801 1.8817 0.1468 0.0015 0.0780

380-II 1.9874 0.1725 0.2419 0.2423 2.0181 0.1849 0.0018 0.0916

380-III 1.8932 0.1251 0.2017 0.2417 1.9197 0.1401 0.0014 0.0730

380-IV 1.6154 0.2155 0.0738 0.1956 1.6388 0.2053 0.0021 0.1253

420-I 1.6699 0.1639 0.1768 0.2109 1.6955 0.1676 0.0017 0.0989

420-II 1.7761 0.2024 0.1900 0.3671 1.8289 0.2134 0.0021 0.1167

420-III 1.7634 0.1717 0.3102 0.3024 1.8192 0.1994 0.0020 0.1096

420-IV 1.0610 0.1415 0.0690 0.1685 1.1219 0.1459 0.0015 0.1301

Table B.3 Type A Uncertainty for A-Shaped Coil 

x-component y-component Vector length

File 

name

Average

[m/s]

Standard

Deviation 

[m/s]

Average

[m/s]

Standard

Deviation 

[m/s]

Average

[m/s]

Standard

Deviation 

[m/s]

Vector 

Length 

Uncertainty 

[m/s]

Vector 

Length 

Uncertainty 

[%]

270-I 5.2304 0.1400 -0.0681 0.1910 5.2615 0.1381 0.0014 0.0262

270-II 4.8501 0.2144 -0.0500 0.2765 4.8586 0.2136 0.0021 0.0440

270-III 4.2874 0.1656 -0.1538 0.1373 4.2963 0.1634 0.0016 0.0380

340-I 4.9038 0.2278 -0.2294 0.1968 4.9213 0.2227 0.0022 0.0452

340-II 4.7701 0.2739 -0.0870 0.2831 4.7819 0.2711 0.0027 0.0567

340-III 3.8374 0.1737 -0.1007 0.1201 3.8488 0.1705 0.0017 0.0443

400-I 5.6473 0.2687 -0.2317 0.2364 5.6865 0.2631 0.0026 0.0463

400-II 4.1773 0.3210 -0.2296 0.2720 4.2112 0.3213 0.0032 0.0763

400-III 4.2832 0.2603 -0.0292 0.2017 4.2925 0.2582 0.0026 0.0602

420-I 5.6321 0.2969 -0.2062 0.2944 5.6752 0.2899 0.0029 0.0511

420-II 3.9877 0.3056 -0.0643 0.2193 4.0187 0.3037 0.0030 0.0756

420-III 2.3433 0.3143 0.0776 0.1443 2.3622 0.3175 0.0032 0.1344

56
B.2 Type B Uncertainty

Type B uncertainty is based on scientific judgment of factors such as knowledge of the 

materials and instruments used for the measurements. There are a number of factors in 

these measurements that introduce some uncertainty under this category. The 

measurement uncertainty due to the pixel resolution is the only significant contributor. 

For this reason, we tabulated the type B uncertainty in tables B.2.1 through B.2.3 below 

based on the pixel resolution induced measurement uncertainty. The quoted accuracy of 

the pixel displacement measurement was 1/10 of a pixel; therefore our uncertainty is

based on the pixel size and the time difference between image pulses for each data set. 

The type B uncertainty is much larger than the type A. The type B uncertainty was 

generally better than 2 %, except for the A-shaped coil which is better than 3.5 %; due to 

the very short time between measurement pulses. The combined uncertainty is calculated 

from the type A and type B uncertainty by taking the square root of the sum of the 

squares of both elements. Since the type B uncertainty is typically on the order of 20 

times larger than the type A, it may be regarded as the combined uncertainty for the PIV 

measurements. 

Table B.2.1 Type B Uncertainty for Vertical Coil 

File name Pixel size [μm] ∆t [μs] Uncertainty [m/s] Average Velocity [m/s] Uncertainty [%] 

230-I 144.0070 600.0000 0.0240 1.4070 1.7059

230-II 142.5820 600.0000 0.0238 1.2289 1.9337

230-III 143.5070 600.0000 0.0239 1.1502 2.0794

230-IV 144.4690 600.0000 0.0241 1.2010 2.0049

300-I 133.5240 600.0000 0.0223 1.4164 1.5712

300-II 133.8830 600.0000 0.0223 1.3111 1.7020

300-III 134.8860 600.0000 0.0225 1.3131 1.7120

300-IV 133.7570 600.0000 0.0223 0.9494 2.3482

360-I 124.8390 600.0000 0.0208 1.4150 1.4704

360-II 125.0060 600.0000 0.0208 1.3656 1.5256

360-III 125.9380 600.0000 0.0210 1.3631 1.5398

360-IV 126.1230 600.0000 0.0210 1.2962 1.6218

405-I 118.4470 600.0000 0.0197 1.3420 1.4710

405-II 118.1370 600.0000 0.0197 1.3122 1.5005

405-III 119.7800 600.0000 0.0200 1.3519 1.4767

405-IV 119.4940 600.0000 0.0199 1.2821 1.5534

450-I 111.4030 600.0000 0.0186 1.0488 1.7703

450-II 111.9020 600.0000 0.0187 1.1424 1.6326

450-III 112.1290 600.0000 0.0187 1.2349 1.5133

450-IV 112.9860 600.0000 0.0188 1.0927 1.7233

57
Table B.2.2 Type B Uncertainty for Slant Coil 

File name Pixel size [μm] ∆t [μs] Uncertainty [m/s] Average Velocity [m/s] Uncertainty [%] 

215-I 140.7780 380.0000 0.0370 1.9518 1.8981

215-II 141.2010 380.0000 0.0372 1.9479 1.9076

215-III 140.8150 380.0000 0.0371 1.8187 2.0376

215-IV 141.5020 380.0000 0.0372 1.7151 2.1711

280-I 130.6460 380.0000 0.0344 2.0322 1.6918

280-II 131.0110 380.0000 0.0345 1.9254 1.7907

280-III 130.9060 380.0000 0.0344 1.7711 1.9451

280-IV 131.4700 380.0000 0.0346 1.1683 2.9612

340-I 123.3160 380.0000 0.0325 1.9168 1.6930

340-II 124.1210 380.0000 0.0327 1.9917 1.6399

340-III 123.8820 380.0000 0.0326 1.7545 1.8581

340-IV 122.9480 380.0000 0.0324 1.6654 1.9428

380-I 117.6620 380.0000 0.0310 1.8817 1.6455

380-II 116.7120 380.0000 0.0307 2.0181 1.5219

380-III 117.0930 380.0000 0.0308 1.9197 1.6051

380-IV 117.2730 380.0000 0.0309 1.6388 1.8832

420-I 111.0150 380.0000 0.0292 1.6955 1.7230

420-II 112.1460 380.0000 0.0295 1.8289 1.6137

420-III 112.2220 380.0000 0.0295 1.8192 1.6234

420-IV 111.8570 380.0000 0.0294 1.1219 2.6239

Table B.2.3 Type B Uncertainty for A-Shaped Coil 

File name Pixel size [μm] ∆t [μs] Uncertainty [m/s] Average Velocity [m/s] Uncertainty [%] 

270-I 150.2650 100.0000 0.1503 5.2615 2.8559

270-II 152.4970 100.0000 0.1525 4.8586 3.1387

270-III 150.2250 100.0000 0.1502 4.2963 3.4966

340-I 141.0440 100.0000 0.1410 4.9213 2.8660

340-II 139.4970 100.0000 0.1395 4.7819 2.9172

340-III 140.7580 100.0000 0.1408 3.8488 3.6572

400-I 133.4910 100.0000 0.1335 5.6865 2.3475

400-II 131.6150 100.0000 0.1316 4.2112 3.1254

400-III 132.1700 100.0000 0.1322 4.2925 3.0791

420-I 130.0240 100.0000 0.1300 5.6752 2.2911

420-II 130.3810 100.0000 0.1304 4.0187 3.2444

420-III 129.6110 100.0000 0.1296 2.3622 5.4870

58