APPLICATION OF THE THERMAL TRANSIENT ANEMOMETER (TTA) FOR 
VEHICULAR SHROUD ANALYSIS 

By 

Travis Wesley 

A THESIS 

Submitted to 
Michigan State University 
in partial fulfillment of the requirements   
for the degree of 

Mechanical Engineering – Master of Science 

2024 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
ABSTRACT 

Experimental  efforts  were  conducted  with  the  use  of  a  Thermal  Transient  Anemometer 

(TTA)  to  analyze  flow  distributions  exiting  a  vehicular  radiator.  These  experiments  were 

motivated by the interest to explore how modifications to the geometry of the vehicle's shroud 

could potentially improve airflow across the face of the radiator. The TTA instrument is a frame 

composed of twenty-three cells that are capable of measuring the average velocity through the area 

of  the  cell.  The  twenty-three  cells  provide  a  velocity  profile  that  spans  across  the  outlet  cross-

section of the radiator.  

The  experiments  recorded  in  this  paper  consists  of  three  configurations  for  analysis:  (i) 

radiator-only,  (ii)  radiator  with  the  stock  shroud  and  (iii)  radiator  with  a  modified  shroud.  The 

design of the modified shroud was first modeled using ANSYS Fluent to confirm the potential 

improvements to the flow of the system. With the improvements confirmed, the modified shroud 

was  then  constructed  with  the  use  of  additive  manufacturing.  The  radiator  was  first  tested  and 

analyzed without a shroud connected to the outlet to determine the flow distribution of the system 

independent from shroud effects. This analysis consisted of an averaged airflow velocity range of 

2.26  m/s  -  7.00  m/s.  The  airflow  velocity  range  was  accomplished  by  changing  the  pressure 

difference  from  the  ambient  (atmospheric)  conditions  to  the  upper  receiver  of  the  Axial  Fan 

Research  and  Development  (AFRD)  facility.  Following,  the  stock  shroud  and  modified  shroud 

were attached to the radiator and the flow distribution for the two configurations were recorded. 

The stock shroud and modified shroud experiments yielded in an averaged airflow velocity range 

of 0.78 m/s - 3.04 m/s and 0.77 m/s - 2.98 m/s, respectively. The flow rate of the system did not 

have a significant change between the two shroud geometries.  For each shroud's measured flow 

rate, the curves tended to remain within the standard error envelope of each curve. The modified 

shroud  was  determined  to  increase  the  flow  distribution  with  an  improvement  of  the 

homogenization of the radiator's outlet profile.

 
ACKNOWLEDGEMENTS 

I would like to acknowledge and sincerely thank my research advisor, Dr. Ricardo Mejia-

Alvarez for his guidance throughout my graduate school experience. His advice and knowledge 

carried me throughout my research experience. 

I would also like to thank the other faculty members and graduate students that helped me 

along the way. Specifically, Dr. John Foss and Dr. Bei Fan for their participation on my 

committee. Dr. Foss supported my research work throughout the entire process, and without his 

experience and knowledge I could not have been successful. Dr. Fan provided great feedback 

with her participation in my thesis defense. Many other graduate students provided much support 

and ideas to allow me to accomplish the challenges that arose throughout my research. 

Ronald Semel, from the Ford Motor Company, provided much support with consistently 

meeting to provide feedback and advice for the research effort. He also participated in my 

defense committee and provided feedback that allowed to me to accurately correlate my research 

to the industrial applications. 

Lastly, I would like to thank my family and friends for their support and patience 

throughout this project. Their support allowed for me to pursue and finish my graduate school 

research and thesis. 

iii 

 
 
 
TABLE OF CONTENTS 

1 

Introduction ........................................................................................................................... 1 
1.1  Motivation ....................................................................................................................... 1 
1.2  Thermal Transient Anemometer .................................................................................. 1 
1.3 
Previous Work ................................................................................................................ 2 
1.4  Objectives ........................................................................................................................ 3 

2  Facility, Equipment, and Instrumentation .......................................................................... 4 
2.1  AFRD Facility ................................................................................................................. 4 
2.2  Thermal Transient Anemometer .................................................................................. 4 
Pressure Transducer ............................................................................................... 6 
2.2.1 
2.2.2  CTA and Fiber-Film Probe .................................................................................... 9 
LabJack DAQ ........................................................................................................ 10 
2.2.3 
2.3 
Slit-Jet ............................................................................................................................ 11 
2.4  Radiator Housing ......................................................................................................... 12 

3  Calibration ........................................................................................................................... 14 
3.1  TTA Calibration ........................................................................................................... 14 
Pressure Transducer .................................................................................................... 15 
3.2 
Fiber-Film Probe ................................................................................................... 17 
Fiber-Film Probe Calibration ..................................................................................... 20 
Slit-Jet .................................................................................................................... 23 

3.2.1 

3.3 

3.3.1 

4  Numerical Results ................................................................................................................ 26 
4.1  Numerical Method ........................................................................................................ 26 
Set Up and Boundary Conditions ........................................................................ 27 
4.1.1 
4.1.2  Mesh Convergence ................................................................................................ 29 
4.2  Results ........................................................................................................................... 31 
4.2.1 
Stock Shroud Analysis .......................................................................................... 31 
4.2.2  Modified Shroud Analysis .................................................................................... 33 
Shroud Comparison .............................................................................................. 34 
4.2.3 

5.2.1 
5.2.2 

5  Experimental Results .......................................................................................................... 36 
5.1  Experimental Set Up .................................................................................................... 36 
5.2  Radiator Analysis ......................................................................................................... 37 
Flow Distribution .................................................................................................. 38 
Loss Coefficients .................................................................................................... 40 
Shroud Analysis ............................................................................................................ 44 
5.3.1 
Stock Shroud ......................................................................................................... 44 
5.3.2  Modified Shroud ................................................................................................... 46 
Shroud Comparison .............................................................................................. 47 
5.3.3 

5.3 

6  Conclusion ............................................................................................................................ 59 

BIBLIOGRAPHY ....................................................................................................................... 61 

iv 

 
 
 
 
 
 
 
 
 
APPENDIX A: Calibration Results .......................................................................................... 62 

APPENDIX B: Numerical Results ............................................................................................ 76 

APPENDIX C: Radiator Only Results ..................................................................................... 80 

APPENDIX D: Stock Results ..................................................................................................... 94 

APPENDIX E: Modified Shroud Results ............................................................................... 102 

v 

 
 
 
 
 
 
 
 
 
1.1  Motivation 

1  Introduction 

Many  automobiles,  including  both  gasoline-powered  and  electrically  powered,  utilize  a 

radiator  for  thermal  energy  management.  As  an  example,  a  gas-powered  internal  combustion 

engine  produces  excess  thermal  energy  that  is  dissipated  from  the  radiator  as  airflow  passes 

through the fins. The excess thermal energy is carried from the engine to the radiator using a fluid. 

This fluid absorbs the heat from the engine and sheds the heat when passing through the radiator. 

The  radiator's  fins  help  to  distribute  the  thermal  energy  through  conductive  heat  transfer  in 

combination with the airflow that also removes the thermal energy by convective heat transfer. 

Understanding  how  the  airflow  that  passes  through  the  radiator  is  distributed  across  the 

radiator's face can allow for more efficient thermal management designs to be implemented in this 

system. The performance of the radiator can vary as the inlet flow is varied at low to high speeds, 

where at lower speeds an exhaust fan may be utilized to draw flow through the system to increase 

the  cooling  rate.  The  performance  of  the  radiator  can  be  influenced  by  the  shroud  attached 

downstream of the inlet flow which can constrict the flow after it has passed through the radiator, 

causing certain areas of the radiator to experience a difference of the incoming flow velocity. By 

studying  how  changes  to  the  shroud's  geometry  can  be  implemented  to  improve  airflow 

characteristics across the radiator's face, the overall performance of the system can be improved. 

1.2  Thermal Transient Anemometer 

The Thermal Transient Anemometer (TTA) is a device that allows for a planer profile of 

fluid  velocity  to  be  measured.  The  current  TTA  was  built  in  order  to  measure  airflow  velocity 

through a specific radiator, which is used for the studies done in this effort. The frame of TTA is 

split into twenty-three cells that allows for a full profile velocity to be measured as flow exits from 

the radiator. Each cell has tungsten wire that is strung across in a multi-X pattern. These wires 

measure the average flow rate through the individual cell. The frame is connected to an electrical 

control  unit  which  controls  the  operations  of  the  TTA  through  software  located  on  a  local 

computer. This control unit sends heating and sensing electrical currents to the tungsten wires. 

Utilizing the profile of the TTA for the purposes of this research, the effects the shroud has on the 

flow through the radiator can be measured. These measurements allow for the performance of the 

radiator to be analyzed based on the shroud effects. 

1 

 
 
The  measurement  of  the  fluid  flow  velocity  is  determined  by  a  relationship  between 

resistance  decay  of  the  tungsten  wires  and  the  fluid  flow  across  the  wires.  Similar  to  hot  wire 

anemometers,  the  resistance  of  the  heated  wire  changes  in  the  presence  of  a  relatively  cooler 

flowing fluid over the wires as convective heat transfer removes the thermal energy from the wires. 

The rate at which the air is moving is proportional to the change of the wire's electrical resistance. 

However, for the TTA's measurement process, the time duration in which it takes the sensing wire's 

resistance  to  decay  to  a  predetermined  resistance  level  after  being  heated  is  measured.  The 

predetermined resistance level is based on a ratio that allows for the time constant of the rate of 

decay to be measured. The time constant can be related to the velocity, therefore allowing for the 

velocity  of  the  fluid  to  be  determined.  Further  explanation  of  this  process  is  detailed  in  the 

Calibration section. 

The TTA has many advantages for this particular application as it was designed with the 

motivation of being used for measurement of flow exiting a vehicular radiator. These advantages 

include not having to traverse the instrument as one would have to with a hot wire probe, minimal 

obstruction of the flow path through the system while recording data, and the ability to provide an 

averaged velocity distribution across the outlet plane of the radiator. 

1.3  Previous Work 

Previous works have been done in order to construct the TTA and apply the instrument in 

similar measuring environments. In a paper published by Foss et al. (2004) [3], the TTA was first 

introduced. The motivation for developing this instrument was for the use of measuring the flow 

distribution from a vehicular radiator. Dr. Foss et al. (2004) presented the capability of the TTA 

concept and its advantages for the particular use of measuring velocity profiles where the velocity 

may be varied. This paper also contains description behind the development and science of how 

the TTA is able to record averaged velocity readings. The TTA was revisited in a later paper, Dr. 

Foss et al. (2006) [2]. This work demonstrated the capability of the TTA to perform in the presence 

of varying turbulence and heat transfer. In a Master's thesis done by James Leung (2018) [4], the 

current  TTA  configuration  was  constructed  and  tested.  Leung  also  described  the  calibration 

process,  as  well  as  documenting  the  performance  of  the  TTA  in  the  presence  of  a  nonuniform 

velocity  distribution.  In  a  Master's  thesis  done  by  Sarah  Plant  (2020)  [5],  the  calibration  and 

performance of the TTA are described. Specifically, the performance of the TTA in nonuniform 

velocity distributions was further explored. These previous works, especially the last two thesis 

2 

 
 
works mentioned by Leung and Plant, provided a guide which allowed the present efforts to be 

accomplished. 

1.4  Objectives 

The aim of this study is to analyze the airflow through the radiator and quantify the effects the 

shroud has on the potential performance of the cooling system. Further, an analysis of the design 

of the shroud is visited to improve the airflow across the radiator. To accomplish this, the stock 

shroud that is currently being utilized (seen in Figure 1.1) is compared against a modified shroud 

constructed through the use of additive manufacturing (seen in Figure 1.2). The knowledge gained 

from this study can be utilized for the improvement of the vehicular cooling systems found in most 

gas-powered and electrical vehicles. 

Figure 1.1: Stock Shroud 

Figure 1.2: Modified Shroud 

3 

 
 
 
 
2  Facility, Equipment, and Instrumentation 

2.1  AFRD Facility 

The  Axial  Fan  Research  and  Development  (AFRD)  facility  is  the  basis  for  which  the 

calibration and experiments with the TTA were conducted. The AFRD facility allows for airflow 

experiments to be conducted in various configurations utilizing the vertical wind tunnel system. 

This  is  accomplished  by  a  blower  inducing  a  pressure  drop  from  the  laboratory  to  the  upper 

receiver  of  the  AFRD,  causing  ambient  air  to  flow  through  the  inlet  exposed  at  the  top  of  the 

facility. The velocity of the air is controlled using a throttle that can adjust the outlet area of the 

blower that removes air from the facility. Increasing or decreasing the area results in a change to 

the mass flow exiting the system, thus allowing for the velocity to be varied. 

The AFRD has a large inlet at the top of the structure. This inlet allows for the staging of 

equipment and behaves as the inlet to the vertical wind tunnel. For the calibration and experiments 

using the TTA in this document, this inlet is where the instrument is placed. The area of the inlet 

can be adjusted by placing frames to only allow airflow through the desired inlet area.  

A  schematic  of  the  AFRD  can  be  seen  in  Figure  2.1.  The  schematic  and  further  detailed 

information regarding how the AFRD facility can be utilized can be found in Plant (2020) [5]. 

Figure 2.1: AFRD Facility Schematic 

2.2  Thermal Transient Anemometer 

The TTA is a device that can be used to measure spatially averaged air velocity; it is built to 

span a large rectangular region such as a vehicular radiator. The present TTA is separated into 

4 

 
 
 
twenty-three rectangular grid cells; see Figure 2.2.  

Figure 2.2: TTA Instrumentation 

The TTA resembles a 4 x 6 grid pattern with a single cell missing. The reference layout of 

the cell numbering system for this research effort can be seen in Figure 2.3.  

Figure 2.3: TTA Cell and Row Orientation 
The cell missing, which would be cell 24, was not fabricated due to design constraints of the testing 

shroud. The TTA frame is made of stainless steel. Each cell is wired with tungsten wire in a multi-

X pattern passing through Garolite rods to insulate the wires from the frame. To prevent contact 

of  the  wires  in  the  multi-X  pattern,  which  could  result  in  conductive  heat  transfer  between  the 

wires, Teflon spacers separate the wires in the crossing patterns. The tungsten wires are electrically 

connected through the use terminal blocks. The instrument is connected to an electronic control 

5 

 
 
 
 
unit, which is ultimately connected to the computer located at the facility. This control unit uses a 

2 A electrical current that heats the tungsten wires, one row at a time, to increase the resistance of 

each wire for a set duration. Following this heating period, the control unit changes the electrical 

current to a 10 mA sensing current and measures the time in which it takes the wires to return to a 

set resistance. The time in which it takes the resistance to decay to this predetermined resistance 

can be related to the average velocity of the airflow through the cell. The rate of decay of the cell's 

sensing wires is shown in equation ( 2.1 ) below as noted by Plant (2020) [5], 

R∗ =

R(t) − R"
R# − R"

$%
& 	, 

= e

( 2.1 ) 

where 𝑅∗ is the dimensionless resistance value, 𝑅 is the resistance of the wire, 𝑡 is the measured 

time,  and τ is  the  time  constant  of  the  decay.  Subscripts 𝑎 and 0 represent  ambient  and  initial 

conditions, respectively. This equation allows for the measurement of the time duration starting 

after the sensing wire is heated to when the dimensionless resistance variable R∗ = e$’ has been 

reached, resulting in the time constant being determined as this is when t	 = 	τ. A full description 

of this process can be found in Leung (2018) [4]. 

The calibration of the TTA allows for each cell to individually measure the average velocity 

through the cell. This calibration is suggested to be done every few months of use to ensure any 

changes  to  the  resistance  of  the  wires  is  captured.  Since  each  cell  measures  the  fluid  velocity 

individually, each cell must also be calibrated individually. This results in a set of three calibration 

constants  found  for  each  cell.  The  process  for  determining  these  constants  is  explained  in  the 

Calibration section. 

2.2.1  Pressure Transducer 

Two different pressure transducers were utilized in this research effort. The first pressure 

transducer, displayed in Figure 2.4, was used to measure the pressure difference from the ambient 

pressure and the pressure in the upper receiver of the AFRD controlled by the blower. This pressure 

transducer had one port open to the ambient pressure and the other connected to a tygon tube, 

connected to the upper receiver of the AFRD facility. This configuration allowed for the difference 

of the two pressures to be recorded with the use of a demodulator and data acquisition device. The 

demodulator used was a Validyne demodulator seen in Figure 2.5, which was able to deliver the 

6 

 
 
 
measurement data to the LabJack data acquisition device. The LabJack data acquisition device is 

discussed  further  in  an  upcoming  section.  This  configuration  allowed  for  the  continuous 

measurements  of  the  pressure  difference  to  be  recorded  for  both  calibration  purposes  and 

experimental purposes. 

Figure 2.4: Pressure Transducer 

7 

 
 
 
Figure 2.5: Validyne Demodulator  

The other pressure transducer that was utilized, the MKS Baratron capacitance manometer 

seen in Figure 2.6, was used for the calibration of the fiber-film probe. This pressure transducer 

was connected to the slit-jet apparatus and was used to determine the pressure difference from the 

ambient pressure and the plenum pressure to determine the fluid flow velocity. The Baratron was 

also  connected  to  the  LabJack  data  acquisition  device  such  that  the  pressure  difference 

measurements  could  be  recorded  throughout  the  fiber-film  probe's  calibration  process.  Further 

explanation about the procedure of this calibration process is detailed in the Calibration section. 

8 

 
 
 
 
Figure 2.6: MKS Baratron Capacitance Manometer 

2.2.2  CTA and Fiber-Film Probe 

A fiber-film probe and constant temperature anemometer (CTA) were used in conjunction 

to measure airflow velocity. The fiber-film probe was used to measure the average flow velocity 

at a single position. This probe was connected to the CTA, which keeps the probe at a constant 

temperature and measures the voltage required to do so. The probe and CTA were then connected 

to the LabJack data acquisition device for recording the velocity measurements. 

Both the CTA and the fiber-film probe were manufactured by Dantec Dynamics. The CTA 

used, referred to as Dantec Dynamic's MiniCTA, can be seen in Figure 2.7.  

9 

 
 
 
Figure 2.7: Dantec Dynamics MiniCTA  

The fiber-film probe can be seen in Figure 2.8. The probe is composed of quartz-fibers with a 

diameter of 70 µm and an active sensing length of 1.2 mm. The fibers are covered by a nickel thin-

film  and  then  coated  by  quartz.  This  probe  is  capable  of  measuring  one-dimensional  gas  flow 

velocities.  

Figure 2.8: Dantec Dynamics Fiber-Film  

2.2.3  LabJack DAQ 

The LabJack data acquisition device used in this paper is the LabJack T-7 Pro board. This 

data acquisition device converts the analog input to a 16 bit digital format output. Software that is 

installed on the computer at the lab is able to store the measurements received from the LabJack. 

The  LabJack  was  used  for  recording  pressure  measurements  with  both  transducers  and 

measurements taken by the fiber-film probe with the CTA. The device can be seen in Figure 2.9. 

10 

 
 
 
 
 
2.3  Slit-Jet 

Figure 2.9: LabJack T-7 Pro  

A  slit-jet  apparatus  was  used  for  the  purpose  of  calibrating  the  fiber-film  probe.  This 

instrument has an established relationship of the fluid flow velocity as a function of the distance 

from the plenum face. The slit-jet configuration can be seen in Figure 2.10. A blower was attached 

to the lower portion of the slit-jet apparatus. The air flow can be controlled by opening and closing 

the inlet gate valve. Adjusting this valve controls the pressure in the plenum, thus allowing the 

flow velocity to be controlled. More details of the velocity relationship used for the calibration 

process are documented in the Calibration section and detailed further in Azar (1997) [1].  

11 

 
 
 
2.4  Radiator Housing 

Figure 2.10: Slit-Jet Instrument 

For the experiments conducted in this paper, a radiator housing structure was constructed 

for  the  mounting  of  the  radiator.  This  configuration  allowed  for  the  flow  to  be  directed  only 

through the radiator and allowed for a shroud to be attached on the opposite side. The radiator 

housing was composed of slotted extruded aluminum bars to build the frame and supports of the 

radiator.  Medium-density  fiberboard  was  used  to  create  an  enclosed  surface  around  the  frame. 

Foam pads were placed around the perimeter of the bottom of the housing structure in order to 

create a seal as the weight of the mount compressed the foam. Any remaining areas of potential 

leakage concern were then covered in tape to ensure an airtight seal. This structure can be seen in 

Figure 2.11. 

12 

 
 
 
Figure 2.11: Radiator Housing 

13 

 
 
 
 
 
3.1  TTA Calibration 

3  Calibration 

This section will give a brief overview of the calibration procedure for the TTA. The Master's 

thesis by Plant (2020) [5] was followed closely to accomplish the calibration for the use of the 

TTA documented in this paper and can be used as a reference for more details about this process. 

This process can also be found documented in the Master's thesis by Leung (2018) [4]. The TTA 

was  calibrated  utilizing  the  AFRD  facility  previously  described.  The  TTA  was  placed  on  a 

medium-density fiber board that reduced the inlet of the AFRD to the size of the TTA frame. To 

ensure uniform flow into the inlet, quarter-rounds were placed to straighten the flow as it passes 

over the TTA and into the inlet. The set up of the calibration process can be seen in Figure 3.1. 

Figure 3.1: TTA Calibration Set Up 

In  order  to  perform  the  calibration,  another  technique  must  be  used  to  determine  the 

14 

 
 
 
average  fluid  flow  velocity  of  the  air  entering  through  the  AFRD's  inlet.  This  was  able  to  be 

accomplished  utilizing  two  different  methods  in  this  research.  One  method  utilized  a  pressure 

transducer to determine the pressure difference between the ambient pressure and the pressure in 

the upper receiver of the AFRD. The other method was done by using a calibrated fiber-film probe 

with a CTA. These methods are described in further detail in the following sections. 

At a given flow velocity, determined by using one of the previously described methods that 

is independent of the TTA, software at the lab in combination with the electronic control unit is 

able  to  measure  the  inverse  of  the  time  constant, τ$’,  exhibited  for  each  cell.  This  resulted  in 

fifteen  to  sixteen  measurements  of  the τ$’ value  at  a  single  fluid  flow  velocity  condition.  The 

average of the recorded τ$’ values was determined and related to the separately measured average 

flow velocity condition. This process was repeated again at each of the other desired flow velocity 

conditions to develop the data points necessary for the full velocity range. Once all of the targeted 

velocity steps for the specified range of flow velocity has been fully recorded (recommended at 

least ten velocity steps) the τ$’ values are plotted against the measured average flow velocities. 

The calibration constants for each individual cell can determined through the use of a curve fitting 

tool, utilizing a least squares method for fitting the curve to the relationship of the sensing wires 

and  fluid  velocity.  The  relation  between  the τ$’value  and  fluid  flow  velocity  is  displayed  in 

equation ( 3.1 ).  

τ$’ = 𝐴 ⋅ 𝑈( + 𝐶 

( 3.1 ) 

Post-processing was done after the measurements to ensure the behavior of each cell on the 

TTA were reasonable and no technical malfunctions have occurred. Common issues that can cause 

errors in measurements include loose connection of the sensing wires at the terminal boxes of the 

TTA and/or the sensing wires in contact with the frame of the TTA resulting in electrical short 

circuits. Once the post-processing analysis has been conducted, the TTA could be used to conduct 

measurements with the determined calibration constants. 

3.2  Pressure Transducer 

For one calibration method of the TTA, a pressure transducer was utilized to determine the 

average  flow  velocity  that  entered  through  the  AFRD  inlet.  This  was  done  by  measuring  the 

15 

 
 
 
pressure difference of the ambient pressure and the pressure in the upper receiver of the AFRD. 

The  incoming  flow  velocity  can  be  related  to  that  of  the  measured  pressure  difference  with 

Bernoulli's equation ( 3.2 ), 

Δ𝑃 =

1
2

ρ𝑈), 

( 3.2 ) 

where Δ𝑃 = 𝑃* − 𝑃+, , 𝑃  being  the  pressure  measurements,  subscripts 𝑎  and 𝑈𝑅  denoting  the 

ambient and upper receiver properties, respectively. 

To  determine  the  ambient  air  density  for  the  velocity  calculation,  the  temperature  and 

ambient pressure were measured such that the ideal gas law ( 3.3 ) could be used to calculate the 

density. 

𝑃 = ρ𝑅-𝑇 

( 3.3 ) 

The temperature was measured via a thermometer placed in the laboratory and the ambient 

pressure  was  determined  from  the  Lansing  Airport  measurements,  which  is  nearby  and  at  a 

relatively  same  altitude.  Rearranging  equations  (  3.2  )  and  (  3.3  ),  the  average  velocity  can  be 

determined as displayed in ( 3.4 ). 

𝑈*.- = ;

2 ⋅ Δ𝑃*.-
𝑃*/=𝑅- ⋅ 𝑇*>

( 3.4 ) 

The TTA was calibrated with the pressure transducer at ambient conditions of 1020.6 mb 

and 26 C. The velocity range measured by the pressure transducer resulted in a calibration range 

1.33 - 11.96 m/s. With the flow velocity able to be determined, the previously described calibration 

process of the TTA could be followed. The ten velocity steps used in the calibration process can 

be seen in Table 3.1. Figure 3.2 shows the calibration plot of the first row, containing cells 1 - 4. 

The calibration constants for all cells can be found in Table A.1. Calibration plots for each row 

containing all twenty-three cells can be seen in the Figures A.1 – A.6. 

16 

 
 
 
 
 
 
Table 3.1: Velocity and Pressure Measurements for TTA Calibration with Pressure Transducer 

Velocity Step 

DP (Pa) 

𝑈*.- (m/s) 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

1.05 

1.40 

1.69 

3.03 

4.86 

8.74 

21.07 

38.04 

59.24 

85.04 

1.33 

1.53 

1.69 

2.26 

2.86 

3.83 

5.95 

8.00 

9.98 

11.96 

Figure 3.2: Cells 1-4 Calibration Curves - Pressure Transducer 

3.2.1  Fiber-Film Probe 

The fiber-film probe was also utilized to calibrate the TTA. The fiber-film probe offered 

the ability to calibrate the TTA at a lower velocity range than the pressure transducer due to the 

17 

 
 
 
 
sensitivity of the transducer. This probe needed to be calibrated before being used to calibrate the 

TTA, with details described in the following section. With the probe calibrated, the velocity the 

probe is experiencing can be determined by using the equation below ( 3.5 ).  

’
/

𝐸) − 𝐴
𝐵

B

𝑈 = ?

( 3.5 ) 

This equation relates the voltage measurements, 𝐸, to the flow velocity, 𝑈, using the calibration 

constants. The calibration constants of probe are displayed in the following section. 

The fiber-film was placed slightly below the sensing wires of the TTA, approximately 4 

cm below, in order to determine the average velocity of flow entering the inlet of the AFRD during 

the TTA calibration process. This configuration can be in Figure 3.3. 

Figure 3.3: Fiber-film probe position for TTA calibration 

18 

 
 
 
 
 
 
Similar to the pressure transducer, the probe was also used to determine the average 

velocity throughout the entire calibration process of the TTA. The average velocity range 

measured by the fiber-film probe was 0.34 - 9.32 m/s. The twelve velocity steps used in the 

calibration process can be seen in 

Table 3.2. Figure 3.4 shows the calibration plots of row 1, containing cells 1 - 4. The 

change from ten velocity steps to twelve when going from the pressure transducer to the fiber-

film probe was done to ensure more lower velocity points were recorded for a better curve fitting 

in the lower velocity range. The calibration constants for the TTA with this method can be seen 

in Table A.2. All calibration plots can be seen in the Figures A.7 – A.12. 

Table 3.2: Velocity and Pressure Measurements for TTA Calibration with Fiber-film Probe Data 

Velocity Step 

E (V) 

𝑈*.- (m/s) 

1 

2 

3 

4 

5 

6 

7 

8 

9 

10 

11 

12 

1.33 

1.42 

1.48 

1.53 

1.61 

1.67 

1.72 

1.85 

1.94 

2.09 

2.22 

2.26 

0.34 

0.53 

0.71 

0.90 

1.27 

1.59 

1.87 

2.93 

3.92 

6.03 

8.30 

9.32 

19 

 
 
 
 
Figure 3.4: Cells 1-4 Calibration Curves - Fiber-film Probe 

3.3  Fiber-Film Probe Calibration 

The calibration of the fiber-film probe was done using a slit-jet instrument located in the 

facility.  The  probe  was  calibrated  by  traversing  the  probe  at  a  series  of  determined  positions 

relative to the plenum of the slit-jet. These positions spanned from inside to outside of the slit-jet's 

plenum plane. The traversing was done with the probe attached to a linear translation stage that 

used a micrometer, allowing for precise traversing of the probe. The advantage of using the slit-

jet was the relationship that existed from the variation of air velocity with the distance relative to 

the plenum of the slit-jet. This relationship is described more in the following section and can also 

be found documented in Azar (1997) [1]. 

The calibration was split into two continuously measured processes: (i) adjustment of the 

probe  location  relative  to  the  plenum  using  the  linear  stage  while  keeping  the  flow  velocity 

constant and (ii) adjustment of the gated valve that controlled the flow velocity while keeping the 

probe in a fixed location. The velocity adjustment was accomplished by increasing the area of the 

inlet to the blower, resulting in an increased velocity at the outlet of the slit-jet. 

First, the probe began inside the plenum of the slit-jet at a particular slit-width value. This is 

determined by measuring the width of the outlet of the slit-jet, 𝑊, and determining the distance 

20 

 
 
 
the fiber-film is from the plenum, 𝑥, resulting in the slit-width ratio 𝑥/𝑊 which can be seen in 

Figure  3.5.  Using  the  relationship  between  the  slit-width  and  the  velocity  distribution  (seen  in 

Figure 3.7 in the slit-jet subsection), the target stations were determined in order to record velocity 

steps for the lower region for the calibration velocity range. The probe was traversed to the eleven 

different stations, beginning at a slit-width position of 𝑥/𝑊	 = 	 −1.0 and ending at 𝑥/𝑊	 = 	0.0. 

Figure 3.5: Diagram of Slit-Jet Dimensions for Slit-width Measurement 

Continuing the measurements with the probe fixed at the 𝑥/𝑊	 = 	0.0 position, the 

throttle of the slit-jet was increased in six steps in order to reach velocity points at the higher 

region of the calibration range. 

This calibration process yielded seventeen total measurement locations in which the 

calibration range of the probe resulted in 0.48 - 9.46 m/s. The velocity measurements can be seen 

in Table 3.3 and the calibration curve displayed in Figure 3.6. 

21 

 
 
 
 
 
Table 3.3: Fiber-film Probe Calibration Data 

𝑥/𝑊 

𝑢(𝑥)/𝑈# 

ΔP (Pa) 

𝑈# (m/s) 

𝑈0*10 (m/s) 

-1.0 

-0.9 

-0.8 

-0.7 

-0.6 

-0.5 

-0.4 

-0.3 

-0.2 

-0.1 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.0 

0.184 

0.201 

0.221 

0.246 

0.276 

0.313 

0.358 

0.414 

0.482 

0.562 

0.648 

0.648 

0.648 

0.648 

0.648 

0.648 

0.648 

4.36 

4.36 

4.36 

4.36 

4.36 

4.36 

4.36 

4.36 

4.36 

4.36 

4.36 

5.62 

12.65 

22.49 

50.60 

89.96 

123.00 

2.72 

2.72 

2.72 

2.72 

2.72 

2.72 

2.72 

2.72 

2.72 

2.72 

2.72 

3.09 

4.63 

6.17 

9.26 

12.35 

14.44 

0.48 

0.52 

0.57 

0.64 

0.71 

0.81 

0.92 

1.07 

1.24 

1.45 

1.66 

1.94 

2.97 

3.96 

6.00 

7.95 

9.46 

22 

 
 
 
Figure 3.6: Fiber-film Calibration Curve 
Table 3.4: Fiber-film Probe Calibration Constants 

A 

0.656 

B 

1.765 

C 

0.416 

3.3.1  Slit-Jet 

The  slit-jet  was  utilized  for  the  calibration  of  the  fiber-film  probe.  This  instrument  was 

used due to the known velocity variation, 𝑢(𝑥)/𝑈#, related to the slit-width, 𝑥/𝑊, position from 

the  plenum,  for  both  into  and  out  from  the  plane  of  the  plenum.  The  variable 𝑢(𝑥) is  the  flow 

velocity as a function of 𝑥 and 𝑈# is the maximum flow velocity measured at the vena contracta. 

This relationship can be seen in Figure 3.7 and described in Azar (1997) [1].  

23 

 
 
 
 
Figure 3.7: Slit-Jet Centerline Velocity Distribution 

Due to this relationship, lower velocities are able to be achieved by traversing the probe 

into  the  slit-jet.  This  was  important  due  to  the  sensitivity  of  the  pressure  transducer  used  to 

determine the flow velocity of the slit-jet, which would not be able to accurately measure the lower 

velocities needed for the analysis done in the experiments. Therefore, a higher flow velocity could 

be  set,  knowing  that  the  velocity  inside  of  the  plenum  would  be  lower  as  the  probe  is  moved 

inward. The fiber-film probe can be seen in relation to the slit-jet plenum in Figure 3.8. 

24 

 
 
 
Figure 3.8: Slit-Jet Configuration for Fiber-film probe Calibration 

25 

 
 
 
 
 
4  Numerical Results 

A  numerical  analysis  was  conducted  for  both  the  stock  shroud  and  modified  shroud 

geometries.  First,  the  stock  shroud  was  analyzed  to  determine  the  current  performance  of  the 

shroud configuration to serve as a baseline for the modified shroud. Following, the shroud was 

redesigned  to  create  the  modified  shroud's  geometry  with  the  goal  of  improving  the  flow  by 

relieving the restriction through the radiator caused downstream by the shroud. Once the modified 

shroud  was  modeled,  the  geometry  was  analyzed  in  the  same  way  as  the  stock  shroud  to 

demonstrate an increased performance of the flow through the system. Following the numerical 

analysis, the redesign of the shroud was 3D printed for experimental testing and is described further 

in the experimental results section.  

For the purposes of this research, the numerical analysis was conducted to substantiate that 

flow improvements have been made with the redesigned geometry of the stock shroud in order to 

create  the  modified  shroud.  This  numerical  analysis  was  not  done  in  order  to  draw  reliable 

conclusions about the performance of either shroud geometries. Therefore, many simplifications 

and default software options were utilized for the set up and solution of the analysis in order to get 

a proof of concept for the modifications that were made. 

4.1  Numerical Method 

ANSYS  Fluent  was  used  as  the  Computational  Fluid  Dynamics  (CFD)  software  for  the 

numerical  computations.  This  software  utilizes  a  Finite  Volume  Method  (FVM)  to  solve  the 

governing  equations  of  the  system.  The  shroud  simulations  were  done  using  the  modeled 

geometries of the stock shroud and the modified shroud. The CFD geometries were prepared in 

SolidWorks by creating a volume in which the fluid would be modeled. This process consisted of 

taking the original shroud geometry, which was provided for the stock shroud, and surrounding it 

with the potential fluid field. The volume of the shroud geometry was then subtracted from the 

fluid field and the region that would remain inside of the shroud was kept. This region served as a 

negative image of the shroud, allowing for the volume to represent the area that would come into 

contact with the shroud surfaces. This area began at the rectangular inlet of the shroud and moved 

to  the  circular  outlet.  An  example  of  the  fluid  volume  with  the  surfaces  of  the  stock  shroud 

subtracted can be seen in Figure 4.1. 

26 

 
 
4.1.1  Set Up and Boundary Conditions 

Figure 4.1: Stock Shroud CFD Volume 

The shroud simulations were set up with identical boundary conditions to keep consistency 

when comparing the geometries. A distributed velocity inlet condition was used to simulate the 

distributed outlet velocity from the radiator as it enters the inlet of the shroud. This velocity was 

measured  from  a  previously  recorded  experiment  consisting  of  the  radiator  without  a  shroud 

attached. A uniform pressure outlet condition was used to simulate the pressure difference from 

the inlet of the radiator to the upper receiver in the AFRD facility, which was also determined from 

previous  measurements.  For  the  remaining  area  between  the  simulated  TTA  cells,  the  average 

measured velocity was implemented as a velocity inlet condition. All other boundaries, composed 

of the sides of the simulated TTA cell pattern and the surfaces of the shrouds, were set to solid 

wall no-slip boundary condition. This was done to remove the effects of the material surfaces and 

measure the effects due to the geometry only.  

For  the  inlet  velocity  condition,  a  grid  of  twenty-four  TTA  cell  sized  rectangles  were 

positioned to form a distributed inlet flow that would be imposed based on TTA measurements 

from the radiator, this geometry can be seen in Figure 4.2. These rectangular surfaces were raised 

2 cm from the surface of the shrouds inlet such that the flows had time to develop. The cell walls 

parallel with the inlet plane of the shroud were assigned a velocity value corresponding to previous 

measurements,  displayed  in  Figure  4.3.  These  measurements  were  recorded  from  a  previous 

27 

 
 
 
radiator only velocity recording at a pressure difference of ΔP = 	57.04 Pa. 

Figure 4.2: Inlet View of Shroud CFD Geometry 

Figure 4.3: Inlet Velocity Boundary Condition Distribution 

More information regarding specifics of the mesh sizing parameters, solution procedure, 

and convergence criteria can be found in the Numerical Results section of the Appendix. 

28 

 
 
 
 
4.1.2  Mesh Convergence 

To determine if the mesh size was sufficient, a mesh convergence check was done for the 

stock shroud geometry. This consisted of running the simulation with a relatively coarse and a 

relatively  fine  mesh,  then  comparing  the  results  following  the  simulations  to  ensure  that  the 

changes to the mesh size did not significantly impact the solutions. 

Figure 4.4: Pressure Contour Mesh Comparison 
(Above: Default Mesh, Below: Fine Mesh) 

29 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 4.5: Outlet Velocity Contour Mesh Comparison  
(Above: Default Mesh, Below: Fine Mesh) 

30 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
The contours for both the shroud wall pressure and the outlet velocity appeared to be nearly 

identical. The shape of the contours appeared to remain unchanged when increasing the mesh. The 

maximum  and  minimum  pressures  modeled  on  the  shroud  surface  remained  within  5%  of  the 

default  mesh,  with  the  majority  of  the  values  that  are  on  the  surface  inferred  to  be  even  more 

similar than the extremes. Similarly, the maximum outlet velocity increased by approximately 2% 

and the minimum remained at 0 m/s. This step confirmed that the mesh process used was adequate 

in sizing for this analysis. 

4.2  Results 

4.2.1  Stock Shroud Analysis 

The geometry of the stock shroud was provided for the use of numerical simulation and 

can be seen in Figure 4.6. This geometry needed to be altered slightly by removing miscellaneous 

holes and geometries that caused issues when preparing for the CFD simulation.  

Figure 4.6: Stock Shroud CAD Model  
(Left: Angled View, Middle: Inlet View, Right: Outlet View) 

A mesh was applied to the volume of the fluid domain, with more details in the Appendix, and 

was used to solve the modeled fluid volume for the simulation. The statistics of the mesh used can 

be seen in Table 4.1. 

31 

 
 
 
Table 4.1: Stock Shroud CFD Mesh Statistics 

Nodes 

Faces 

Boundary 

1,228,487 

330,104 

Cells 

- 

Interior 

6,971,362 

10,489,797 

1,971,575 

Utilizing the imposed boundary conditions described previously, the CFD simulation was 

solved. The modeled pressure contours on the shroud and the velocity contour of the outlet can be 

seen in Figure 4.7. 

Figure 4.7: Stock Shroud CFD Results  
(Above: Shroud Wall Pressure Contour, Below: Outlet Velocity Contour) 

32 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
4.2.2  Modified Shroud Analysis 

The geometry of the modified shroud was modeled based on the inlet and outlet dimensions 

of the current stock geometry. To attempt to create a more uniform flow and to reduce the effect 

of  the  shroud  on  the  radiator,  some  other  design  considerations  were  imposed.  This  included 

smoothing  the  walls  such  that  there  were  no  areas  with  protruding  geometries.  Another 

consideration involved adding additional space from where the contours begin to change restrict 

the flow backwards towards the outlet. This was accomplished by adding an additional 20 mm of 

depth before the shroud begins to converge towards the outlet. The resulted geometry is shown in 

Figure 4.8. 

Figure 4.8: Modified Shroud CAD Model 
(Left: Angled View, Middle: Inlet View, Right: Outlet View) 

Following the same mesh process used previously the volume of the fluid domain could be 

modeled. The statistics of the mesh that was used for the modified shroud analysis can be seen in 

Table 4.2. 

Table 4.2: Modified Shroud CFD Mesh Statistics 

Nodes 

Faces 

Boundary 

218,504 

70,184 

Cells 

- 

Interior 

1,031,570 

1,514,640 

274,339 

33 

 
 
 
 
 
Utilizing the imposed boundary conditions described previously, the CFD simulation was 

solved. The modeled pressure contours on the shroud and the velocity contour of the outlet can be 

seen in Figure 4.9.  

Figure 4.9: Modified Shroud CFD Results 
(Above: Shroud Wall Pressure Contour, Below: Outlet Velocity Contour) 

4.2.3  Shroud Comparison 

The results of the two shroud geometries were compared to determine if the changes made 

to the modified shroud resulted in an improved performance. When comparing Figure 4.7 (above) 

and Figure 4.9 (above), the stock shroud can be seen to have an overall higher maximum pressure 

on the surface of the shroud. The modified shroud also appears to have a more gradual change of 

pressure when moving from the inlet towards the outlet of the shroud. The lower pressure on the 

surface of the modified shroud indicates that there is less restriction of the flow, suggesting the 

flow would pass through more easily relative to the stock shroud. 

34 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Looking at the velocity outlet contours of Figure 4.7 (below) and Figure 4.9 (below), the 

stock shroud is displayed to have an overall faster maximum measured velocity. However, when 

comparing the contours, the area of the modified shroud appeared to have more relatively high-

velocity contours displayed in the outlet than that of the stock shroud. The stock shroud also shows 

relatively low-velocity contours around the edges of the circular outlet, where the opposite effect 

is seen in the modified shroud.  

With a more, well-distributed wall pressure and outlet velocity, as well as a relatively lower 

wall pressure and relatively increased outlet velocity contours, the modified shroud appeared to 

perform  as  anticipated.  The  geometry  of  the  redesigned  modified  shroud  accomplished  the 

objective of allowing for a less restricted airflow caused by the geometry of the shroud and was 

used to manufacture the shroud to be tested in the AFRD facility. This shroud was 3D printed with 

the material PA 2200, a white powder based polyamide. 

35 

 
 
 
 
5  Experimental Results 

The  TTA  was  utilized  to  record  data  in  several  experimental  analyses.  These  experiments 

consisted of analyzing the flow through the radiator in three separate configurations: (i) radiator 

only,  (ii)  radiator  with  the  stock  shroud,  and  (iii)  radiator  with  the  modified  shroud.  All 

experiments were able to be accomplished utilizing the AFRD facility. This section examines the 

effects on the flow in all three configurations. Further, the analysis of how the modified shroud 

compared to the stock shroud is examined. 

5.1  Experimental Set Up 

The  experiments  were  carried  out  with  the  use  of  the  AFRD  facility.  Following  the 

calibration of the TTA, the instrument was attached directly to the outlet face of the radiator with 

four bolts. This position, displayed in Figure 5.1 (Upper Right), allows for the TTA to measure the 

flow as it is exiting from the radiator. The radiator was mounted in the housing configuration and 

any remaining gaps or areas of concern were sealed using tape or foam to prevent air from entering 

the AFRD around the radiator or radiator housing. To ensure uniform inlet flow into the radiator, 

quarter-rounds were placed around the boundary of the inlet of the housing device to straighten 

the flow as it entered the radiator. This can be seen in the top view of the setup in Figure 5.1 (Upper 

Left). 

The  configuration  described  above  details  the  experimental  setup  for  measurements 

consisting of the radiator without a shroud attached. For the measurements consisting of either the 

stock shroud or modified shroud, the same experimental set up is utilized and the shroud would be 

fixed onto the outlet face of the radiator. The TTA remained between the radiator and shroud for 

measurements with minimal interference to the placement of the shroud. For both shrouds, any 

areas of potential air leakage are sealed with tape. The stock shroud is attached using bolts around 

the perimeter of the radiator and can be seen in Figure 5.1 (Lower Left). For the modified shroud, 

the shroud is supported on the exterior side of the shroud instead of the bolt holes to keep good 

contact with the radiator as seen in Figure 5.1 (Lower Right).  

36 

 
 
Figure 5.1: Experimental Set Up Configurations 
(Upper Left: Top View for All Configurations, Upper Right: Radiator Only Configuration, 
Lower Left: Stock Shroud Configuration, Lower Right: Modified Shroud Configuration) 

5.2  Radiator Analysis 

The radiator was analyzed independently to evaluate the effect of the radiator on the flow 

through the system. The average recorded outlet velocity of the radiator ranged from 0.37 m/s - 

7.00 m/s in fifteen velocity steps. However, due to the calibration range of the TTA at the time of 

the  measurements,  the  velocities  below  1.33  m/s  could  not  be  kept  as  these  values  are  being 

extrapolated past the calibration range. This resulted in a total of thirteen velocity steps with an 

average recorded outlet velocity of 2.26 m/s - 7.00 m/s. These velocities were measured using the 

calibration constants located in Table A.1.  

The areas of interest for the radiator analysis consisted of the flow distribution through the 

radiator  and  the  loss  coefficients  of  the  radiator.  The  flow  distribution  of  the  radiator  sets  a 

37 

 
 
benchmark of how the radiator independently distributes the flow across the face of the radiator 

without  the  influence  of  a  shroud.  The  causes  of  flow  distribution  can  be  caused  by  internal 

configurations  in  the  radiator.  Another  source  of  flow  distribution  can  come  from  possible 

damaged  fins  blocking  passages  through  the  radiator.  Determining  this  benchmark  allowed  for 

analysis  of  how  the  shroud  effects  the  radiator's  independent  flow  distribution.  Knowing  the 

radiator's flow distribution and relationship between the pressure drop across the radiator versus 

the velocity exiting the radiator allows for the loss coefficients to be determined for each cell. The 

loss coefficients of the radiator are important to understanding the pressure drops across the face 

of the radiator. These pressure drops correlate to lower flow rates in the regions of the radiator.  

5.2.1  Flow Distribution 

The flow distribution was measured using the TTA placed at the outlet face of the radiator. 

The measurements resulted in thirteen velocity steps, with the average outlet velocity ranging from 

2.26 m/s - 7.00 m/s as mentioned previously. Each velocity step recorded approximately sixteen 

measurements per cell. The equation used to determine percent difference of the velocity ( 5.1 ) is 

displayed below, 

%𝑈!"## =

𝑈!"## − 𝑈$%&
𝑈$%&

⋅ 100% 

( 5.1 ) 

where  𝑈  is  the  measure  of  the  fluid  velocity  and  subscripts  𝑐𝑒𝑙𝑙  and  𝑎𝑣𝑔  correspond  to  an 

individual cell measurement and the average velocity of all cells of the TTA in that velocity step, 

respectively. This calculation allows for the areas of the radiator that have relatively slower or 

faster flow to be visualized and compared to the overall average flow velocity. 

For the measured velocity range, the velocity flow distribution and the velocity percent 

difference for the minimum, median, and maximum velocity steps can be seen in Figure 5.2, Figure 

5.3, and Figure 5.4, respectively. The average velocity percent difference distribution across all 

velocity ranges can be seen in Figure 5.5. The complete set of measurements and full sized figures 

can be referred to in Appendix C, Figures C.1 – C.13. 

38 

 
 
 
Figure 5.2: Radiator Flow Distribution at DP = 33.99 Pa 

Figure 5.3: Radiator Flow Distribution at DP = 124.13 Pa 

39 

 
 
 
 
 
Figure 5.4: Radiator Flow Distribution at DP = 217.98 Pa 

Figure 5.5: Average Velocity Percent Difference Distribution of Radiator 

The flow distribution of the radiator began to become more homogeneous as the pressure 

difference and flow velocity increased. However, the areas of relatively higher and lower flow 

concentrations appeared to have remained consistent for all velocity steps. This indicates that the 

velocity profile exiting the radiator is likely unique to the performance of the radiator distributing 

the flow itself, not attributed to the changes of the flow velocity entering the radiator. 

5.2.2  Loss Coefficients 

The loss coefficients were calculated for each region of the radiator relating to the TTA 

40 

 
 
 
cells. The passages in which the air flows through the radiator are defined by the spaces between 

the fins, which can be seen in Figure 5.6. A closer view of the triangular cross-sectional geometry 

of the passages, as well as how the dimensions of the passages were measured, can be seen in 

Figure 5.6 (Below). 

Figure 5.6: Radiator Fin Geometry 
(Above: Radiator Face, Below: Fin Geometry) 

A sample of ten fins were measured to determine the average passage dimensions, resulting 

an  average  height  (α)  of  6.06  mm  and  base  (β)  of  2.55  mm.  These  dimensions  resulted  in  an 

average area of 7.72 mm2 and perimeter of 14.93 mm.  

To determine the loss coefficients through the radiator and shroud system, the measured 

flow velocity (TTA) and pressure differential (atmosphere to the upper receiver) are related. It is 

clear  that  pressure  losses  are  present  in  the  system  due  to  the  relatively  lower  flow  velocity 

41 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
measured by the TTA in the presence of the measured pressure differential. Additionally, it can be 

predicted that in the cross section of the radiator fins the flow would increase in Reynolds number 

when moving from the top of the triangle towards the wider portion of the triangle. It is known 

that the lower Reynolds number area is dominated by viscous shearing effects and scales by the 

flow velocity (𝑈) and the relatively higher Reynolds number region is dominated by inertial effects 

(turbulent) and scales by the flow velocity squared (𝑈)). Therefore, the experimental data for the 

loss coefficients of each cell are represented as: 

𝑃*23 − 𝑃+, = 𝐾’ + 𝐾)𝑈 + 𝐾4𝑈). 

( 5.2 ) 

The  dimensional  homogeneity  is  ensured  by  the  dimensions  of  the  coefficients 𝐾’, 𝐾),  and 𝐾4. 

The coefficient 𝐾’ is non-physical and is used to smooth the fit of the experimental data. 

The loss coefficients (𝐾) and 𝐾4) and zero-offset coefficient (𝐾’) are determined by fitting 

a curve to the recorded pressure differential and flow velocity data. This curve fitting technique 

used the least squares method. The coefficients that resulted from the fitted curve can be seen in 

Figure 5.7. These coefficients can be used to estimate the pressure drop across each cell of the 

TTA for a known velocity. 

42 

 
 
 
 
 
 
 
 
Figure 5.7: Coefficients for the Radiator Pressure Losses 
(Top: K1 zero-offset coefficient, Middle: K2 loss coefficient, Bottom: K3 loss coefficient) 

43 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
5.3  Shroud Analysis 

The TTA was utilized to determine the effect the shroud had on the flow through the radiator. 

The configuration of the shroud causes airflow to be restricted downstream and slows the through 

flow in certain regions of the the radiator. The analysis done on the shroud effects consisted of: (i) 

the effects both shrouds had relative to a radiator-only configuration and (ii) how the change in the 

geometry of the modified shroud can improve the flow through the radiator relative to the stock 

shroud.  

To determine the effect the shroud has compared to a radiator-only configuration, the results 

of each shroud were compared independently to the radiator-only baseline results. The distribution 

of  the  velocity  percent  difference  was  determined  for  each  configuration.  This  allowed  for  a 

comparison to the baseline of the radiator-only configuration. The stock shroud and the modified 

shroud were also statistically compared to each other to determine the effect of the geometry has 

on the flow. 

The experimental measurements were recorded in a similar manner as the radiator analysis 

was  done,  with  an  attempt  at  remaining  close  to  the  pressure  differences  to  mimic  similar 

conditions as recorded with the radiator-only configuration for a more representative comparison.  

5.3.1  Stock Shroud 

Fifteen velocity steps were recorded for the stock shroud analysis. However, due to the 

calibration range of the TTA, fourteen velocity steps were able to be used for the analysis. These 

velocities ranged from 0.78 m/s - 3.04 m/s. The velocity steps and pressure differences recorded 

at  each  step  are  displayed  in  Table  D.1.  These  velocities  were  measured  using  TTA  with  the 

calibration constants displayed in Table A.1. 

The velocity percent difference distribution (as introduced for Figure 5.2Figure 5.4) for the 

minimum and maximum velocity steps recorded can be seen in Figure 5.8. The average velocity 

percent difference distribution can be seen in Figure 5.9. The entire results (and full sized figures) 

of the velocity percent difference for the stock shroud configuration can be seen in Figures D.1 – 

D.13. 

44 

 
 
 
Figure 5.8: Stock Shroud Velocity Percent Difference 
(Left: Minimum DP, Right: Maximum DP) 

Figure 5.9: Average Velocity Percent Difference for Stock Shroud 

The distribution of the flow with the stock shroud attached to the radiator displayed a relatively 

slower and more restricted region along the perimeter, specifically cells 1 through 4. This would 

be expected as that region of the shroud's geometry is closer to the outlet plane of the radiator, 

therefore restricting the flow and forcing the air to turn towards the center. The center portion of 

the flow, cells 6, 7, 10, 11, 14, 15, 18 and 19, flows relatively faster. This was also expected as the 

opening of the shroud's outlet overlaps this region, allowing air flow to pass more freely through 

the  configuration.  Although  the  severity  of  the  percent  differences  fluctuate  as  the  pressure 

45 

 
 
 
difference increases, the pattern of which cells are relatively slower and faster than the average 

flow velocity remains consistent. 

5.3.2  Modified Shroud 

Fifteen velocity steps were also recorded for the modified shroud analysis. Similarly to the 

stock  shroud,  only  fourteen  velocities  were  within  the  range  of  the  TTA  calibration.  These 

velocities ranged from 0.77 - 2.98 m/s and are displayed in Table E.1 along with the recorded 

pressure  differences.  These  velocities  were  measured  using  TTA  with  the  calibration  constants 

displayed in Table A.2. An issue with the TTA caused cells 9 through 12 to be unable to record 

data. This did not affect the other cells which could still be used for the analysis. 

The velocity percent difference distribution for the minimum and maximum velocity steps 

recorded can be seen in Figure 5.10. The average velocity percent difference distribution can be 

seen in Figure 5.11. The entire results (and full sized figures) of the velocity percent difference for 

the stock shroud configuration can be seen in Figures E.1 – E.13. 

Figure 5.10: Modified Shroud Velocity Percent Difference 
(Left: Minimum DP, Right: Maximum DP) 

46 

 
 
 
 
Figure 5.11: Average Velocity Percent Difference for Modified Shroud 

Similarly to the stock shroud, the modified shroud experienced relatively slower flow in 

the first row of cells. However, the severity of the velocity percent differences appeared to lessen 

when moving to the modified shroud from the stock shroud. Specifically cells 3 and 4 appeared to 

improve significantly when compared to that of the stock shroud. 

5.3.3  Shroud Comparison 

The stock shroud and modified shroud had a significant impact on the flow through the 

radiator. The measurements from the three configurations allow for the impact of the shrouds on 

flow can be determined and compared. The average velocity percent difference across all pressure 

steps  for  the  radiator  only  configuration,  the  radiator  and  stock  shroud  configuration,  and  the 

radiator and the modified shroud configuration can be seen in Figure 5.12. 

47 

 
 
 
 
 
 
Figure 5.12: Average Velocity Percent Difference for All Configurations 
(Top: Radiator Only, Middle: Stock Shroud, Bottom: Modified Shroud) 

48 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
The average velocity percent difference for the radiator only configuration can be seen to 

have  a  relatively  homogeneous  flow  distribution,  with  some  perimeter  cells  above  the  average 

velocity and some middle cells below the average velocity. Both the stock shroud and modified 

shroud displayed a similar pattern in which the perimeter cells, specifically cells 1, 2, 3, and 4, 

experience  below  average  velocity.  Also,  the  middle  cells,  without  being  able  to  definitively 

confirm for the modified shroud, experienced a relatively higher velocity than the average.  

The  change  in  the  velocity  percent  difference  from  the  radiator  to  either  to  stock  or 

modified  shroud  can  be  seen  in  Figure  5.13  and  Figure  5.14,  which  are  at  the  minimum  and 

maximum pressure differences. This was calculated as shown in equation ( 5.3 ).  

Δ%𝑈 = %𝑈’()*+, − %𝑈-$, 

( 5.3 ) 

The average change in velocity percent difference for all velocity steps can be seen in Figure 

5.15. 

49 

 
 
 
Figure 5.13: Shroud Velocity Percent Difference from Radiator at minimum DP 
(Above: Stock Shroud Difference from Radiator, Below: Modified Shroud Difference from 
Radiator) 

50 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5.14: Shroud Velocity Percent Difference from Radiator at Maximum DP 
(Above: Stock Shroud Difference from Radiator, Below: Modified Shroud Difference from 
Radiator) 

51 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure 5.15: Shroud Average Velocity Percent Difference from Radiator 
(Above: Stock Shroud Difference from Radiator, Below: Modified Shroud Difference from 
Radiator) 

The stock shroud and modified shroud behaved in a similar manner as far as most of the 

perimeter  cells  decreasing  the  flow  and  the  inner  core  cells  increasing  the  flow.  However,  the 

severity of the changes decrease in the modified shroud compared to the stock shroud. This results 

in a more homogeneous flow distribution in the modified shroud than the stock shroud. To compare 

the difference of homogeneity of the flow distribution between the stock and modified shroud, the 

52 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
standard deviation of the absolute values of the velocity percent difference for all cells at each 

velocity step was calculated. The absolute value was chosen such that the deviation from the mean 

did not benefit for the deviation being both negative and positive. This standard deviation for each 

shroud is displayed in Figure 5.16. 

Figure 5.16: Absolute Value of the Standard Deviation of Velocity Percent Difference 

The stock shroud has a higher amount of deviation from the mean flow velocity throughout 

the range of pressure differences which results in a high velocity flow regions through the radiator. 

This  indicated  that  the  modified  shroud  performs  better  at  allowing  the  flow  to  become  more 

homogeneous than the stock shroud. 

Another flow characteristic that was explored was the flow rate difference between the two 

shroud geometries. The flow rate is determined by ( 5.4 ),  

𝑄	 = 	𝑈	 ⋅ 𝐴	, 

( 5.4 ) 

where 𝑈 is the velocity of the fluid flow and 𝐴 is the area in which the flow is passing through. 

For these experimental analyses, the area remains constant for all three configurations. Due to the 

fixed area, the flow rate can be directly represented by the velocity and equation ( 5.4 ) is modified 

and becomes equation ( 5.5 ).  

53 

 
 
 
 
𝑄" =

𝑄
𝐴

=

𝑈 ⋅ 𝐴
𝐴

= 𝑈 

( 5.5 ) 

The  flow  rate  of  the  stock  shroud  and  modified  shroud  relative  to  the  radiator  only 

configuration can be seen in Figure 5.17, where the flow rate of the radiator only configuration is 

plotted as reference. 

Figure 5.17: Flow Rate of Radiator, Stock Shroud, and Modified Shroud 

This plot shows that both shrouds significantly impact the flow rate through the radiator. 

Both shrouds have a similar overall impact relative to the radiator only configuration. A closer 

look at only the shrouds can be seen in Figure 5.18.  

54 

 
 
 
Figure 5.18: Flow Rate of Stock and Modified Shroud 

The plot in Figure 5.18 shows the calculated standard error as well, showing that the flow 

rate for both shrouds tend to overlap each other with the error bars present. The standard error was 

determined using the following equation ( 5.6 ),  

𝑆𝐸 =

σ

√𝑛

	, 

( 5.6 ) 

where 𝑆𝐸 is  the  standard  error, σ is  the  standard  deviation,  and 𝑛 is  the  sample  size.  With  this 

being  determined,  the  more  efficient  shroud  design  in  terms  of  flow  rate  between  the  shrouds 

cannot be definitively determined as they perform in such a similar behavior.  

Lastly, a statistical approach was taken in order to further look into the flow distribution 

between the stock shroud and modified shroud. The skewness and kurtosis of the velocity percent 

difference data was analyzed. The skewness represents if the data tends to be on the higher or 

lower side of the distribution, where a value of zero is symmetrically distributed, above zero is 

more  data  on  the  higher  side,  and  below  zero  is  more  data  on  the  lower  side.  For  the  use  of 

skewness in this analysis, a positive value of skewness shows the velocity percent difference tends 

to be higher values or a negative value shows the data tends to be lower. The kurtosis represents if 

the  data  is  grouped  together  around  the  mean  or  is  more  distributed,  where  the  value  of  three 

55 

 
 
 
 
matches that of a normal distribution kurtosis value. For the use of kurtosis in this analysis, a higher 

value could suggest a more homogeneous flow and a lower value could suggest the opposite.  

The skewness and kurtosis of the velocity percent differences for both the stock shroud and 

modified shroud can be seen in Figure 5.19 and Figure 5.20, respectively. 

Figure 5.19: Skewness of Stock and Modified Shroud 

Figure 5.20: Kurtosis of Stock and Modified Shroud 

The skewness of both shrouds can be seen relative to a value of zero, the dashed line in 

56 

 
 
 
 
Figure  5.19.  For  reference,  Figure  5.21  displays  the  difference  of  negative  (right),  zero,  and 

positive  (left)  skewness.  As  can  be  inferred,  the  amount  of  skew  in  the  stock  shroud  remains 

consistently right skewed. The modified shroud begins relatively close to no skew, then trends to 

a  right  skew  behavior  similar  to  the  stock  shroud.  However,  the  modified  shroud  remains 

significantly less, roughly 50%, than that of the stock shroud as the pressure difference and flow 

velocity steps increased. These skewness values indicate that mean of the data is lower than that 

of the median for both shrouds. 

Figure 5.21: Skewness Reference (www.scribber.com) 

The kurtosis of both shrouds can be seen relative to a value of three, the dashed line in 

Figure 5.20 which indicates no excess kurtosis, similarly to a normally distributed data set. For 

reference, Figure 5.22 displays the difference between high (leptokurtic), moderate (mesokurtic), 

and low (platykurtic) kurtosis data sets. The stock shroud's kurtosis measurements decrease as the 

pressure difference and flow velocity increases. This indicates that the data moves more towards 

a lower trend meaning the data set is more grouped around the mean value with less outliers. The 

modified shroud acts in the opposite manner, starting a relatively low kurtosis value and increases 

with the increased pressure difference and flow velocity steps. 

57 

 
 
 
Figure 5.22: Kurtosis Reference (www.scribbr.com) 

58 

 
 
 
 
 
6  Conclusion 

The TTA was utilized in determining and testing the effects of a shroud's geometry on the 

flow  through  the  vehicular  radiator  system.  This  effort  was  built  off  of  previous  works  that 

introduced  the  concept  of  the  TTA,  fabricated  the  present  day  TTA  configuration,  and 

demonstrated the use of the TTA in similar experimental environments.  

A  redesigned  shroud  for  objective  of  pursuing  an  improved  thermal  energy  management 

system in automotive applications was explored with the use of the TTA. The design of the shroud 

was  able  to  be  achieved  through  the  use  of  numerical  modelling  of  the  system  to  confirm  a 

preliminary  design.  The  numerical  model  applied  a  measured  velocity  distribution  previously 

measured in order to simulate the incoming flow to the shroud design. The currently used stock 

shroud design was compared to the modified shroud design. The results inferred that the modified 

shroud allows for a better flow distribution to occur through the shroud and relieve pressure on the 

shroud's  surface,  indicating  an  ease  of  flow.  This  effort  allowed  for  the  modified  shroud  to  be 

manufactured utilizing a 3D printer. 

To perform the analysis of newly designed shroud, the TTA was first applied to determine the 

velocity  distribution  of  the  radiator  independent  of  an  attached  shroud.  This  distribution  was 

measured for an average flow velocity range of 2.26 - 7.00 m/s. These distribution measurements 

provided a baseline to compare how the shroud effects the flow independently of how the radiator 

may  affect  the  flow.  Further,  the  analysis  of  the  radiator-only  configuration  allowed  for  loss 

coefficients to be determined for the radiator which can be useful when looking at specific areas 

of cooling to improve on for the radiator. 

Following the experiments consisting of the radiator-only configuration, the stock shroud and 

modified shrouds were able to be analyzed for their effects to the flow through the system. The 

stock shroud was measured at an average flow velocity range of 0.78 - 3.04 m/s. The stock shroud 

displayed a consistent pattern of restricting flow of cells 1 - 4 and an increased velocity in the cells 

in the core of the grid. The modified shroud was tested similarly, with an average flow velocity 

range of 0.77 - 2.98 m/s. It is important to note that the third row, cells 9 - 12, were unable to 

record measurements for the modified shroud testing. The modified shroud displayed a similar 

pattern to that of the stock shroud, however the severity in which the distribution deviated from 

the mean velocity of each step decreased significantly. A further look determined that no definitive 

conclusions  could  be  drawn  from  the  flow  rate  of  the  two  shroud  geometries.  However,  the 

59 

 
 
deviation of the flow can be determined to become more homogeneous with the modified shroud 

when compared to the stock shroud. 

This research has shown that the geometry of the shroud has a significant effect on the flow 

through  the  radiator.  The  effort  to  improve  the  shroud's  geometry  (keeping  the  inlet  and  outlet 

dimensions the same) involves: i) adding more space for flow to enter the shroud and ii) smoothing 

of the contours of the shroud from inlet to outlet to improve the distribution of the airflow through 

the radiator. Future improvements could potentially lead to an improvement of flow rate and other 

important  characteristics  of  the  thermal  energy  management  design.  These  improvements  may 

consist  of  a  further  increase  in  allowing  the  flow  to  enter  the  shroud  unobstructed.  Another 

improvement may look to improve the geometry of the shroud's contours further.  

60 

 
 
 
 
[1] Azar, Kaveh. Thermal measurements in electronics cooling. CRC press, 1997. 

BIBLIOGRAPHY 

[2] JF Foss, JA Peabody, MJ Norconk, and AR Lawrenz. Ambient temperature and free stream 
turbulence  effects  on  the  thermal  transient  anemometer.  Measurements  Science  and 
Technology, 13(9):2519, 2006. 

[3] JF Foss, JK Schwannecke, AR Lawrenz, MW Mets, SC Treat, and MD Dusel. The thermal 

transient anemometer. Measurements Science and Technology, 15(11):2248, 2004. 

[4] James  Leung,  Nonuniform  Flow  over  a  Thermal  Transient  Anemometer.  Michigan  State 

University, 2018. 

[5] Sarah  Plant.  The  Performance  of  a  Thermal  Transient  Anemometer  (TTA)  for  Nonuniform 

Velocity Measurements. Michigan State University, 2020. 

61 

 
 
 
 
 
 
 
 
A.1 Calibration with Pressure Transducer 

APPENDIX A: Calibration Results 

Table A.1: Calibration Constants of TTA with Pressure Transducer 

Cell No. 

4 

8 

12 

16 

20 

NaN 

A 

B 

C 

R2 

0.5717 

0.7183 

1.3298 

0.9989 

1.1074 

0.5137 

0.7212 

0.9996 

1.1494 

0.5162 

0.6741 

0.9977 

2.8585 

0.2458 

1.9813 

0.3508 

-1.0503 

-0.1822 

0.998 

0.9998 

Cell No. 

3 

7 

11 

15 

19 

X 

X 

X 

X 

23 

A 

B 

C 

R2 

0.8697 

0.5868 

1.0257 

0.9996 

0.7154 

0.6328 

1.1606 

0.9986 

0.8964 

0.5728 

1.0044 

0.9997 

0.7504 

0.6213 

1.1585 

0.9999 

0.8549 

0.5789 

1.0253 

0.9997 

0.9881 

0.5436 

0.8413 

0.9996 

Cell No. 

2 

6 

10 

14 

18 

22 

A 

B 

C 

R2 

0.813 

0.6065 

1.1127 

0.9997 

Cell No. 

1 

A 

B 

C 

R2 

0.562 

0.7193 

1.3544 

0.9984 

0.4777 

0.7582 

1.4826 

0.9966 

5 

1.0038 

0.5032 

0.8221 

0.9975 

0.931 

0.5647 

0.9517 

0.9995 

9 

1.2179 

0.4794 

0.519 

0.9975 

1.0714 

0.5214 

0.7745 

0.9997 

13 

0.9542 

0.5431 

0.7927 

0.9979 

1.1648 

0.4982 

0.6726 

0.9986 

17 

0.8715 

0.5801 

0.9856 

0.999 

0.816 

0.5662 

0.9892 

0.9995 

21 

1.0158 

0.5247 

0.9892 

0.9996 

62 

 
 
Figure A.1: Cell 1 - 4 Calibration Curves - Pressure Transducer 

63 

 
 
 
 
Figure A.2: Cell 5 - 9 Calibration Curves - Pressure Transducer 

64 

 
 
 
 
 
Figure A.3: Cell 9 - 12 Calibration Curves - Pressure Transducer 

65 

 
 
 
 
 
Figure A.4: Cell 13 - 16 Calibration Curves - Pressure Transducer 

66 

 
 
 
 
 
Figure A.5: Cell 17 - 20 Calibration Curves - Pressure Transducer 

67 

 
 
 
 
 
Figure A.6: Cell 21 - 23 Calibration Curves - Pressure Transducer 

68 

 
 
 
 
 
A.2 Calibration with Pressure Transducer 

Table A.2 Calibration Constants of TTA with Fiber-film Probe 

Cell No. 

4 

8 

12 

16 

20 

NaN 

A 

B 

C 

R2 

1.0633 

0.6099 

1.1096 

0.9995 

1.5051 

0.5254 

0.7679 

0.9992 

1.6586 

0.5046 

0.639 

1.4697 

0.5384 

0.856 

0.9998 

0.9996 

1.3623 

0.5533 

0.9523 

0.9981 

Cell 

3 

7 

11 

15 

19 

X 

X 

X 

X 

23 

A 

B 

C 

R2 

1.1542 

0.5861 

1.0109 

0.9999 

1.6682 

0.4625 

0.5138 

0.9968 

1.5991 

0.499 

0.678 

1.1546 

0.5972 

1.0991 

0.9997 

0.999 

1.0702 

0.6106 

1.1612 

0.9993 

1.464 

0.5347 

0.7549 

0.9999 

Cell 

2 

6 

10 

14 

18 

22 

A 

B 

C 

R2 

1.6091 

0.4909 

0.6235 

0.9998 

Cell 

1 

A 

B 

C 

R2 

1.7967 

0.4706 

0.4827 

0.9997 

1.6377 

0.4815 

0.5684 

0.9997 

5 

1.6183 

0.481 

0.5405 

0.9997 

1.6303 

0.4958 

0.5949 

0.9997 

9 

1.6252 

0.4954 

0.5418 

0.9995 

1.7177 

0.4822 

0.4707 

0.9993 

13 

1.3985 

0.5589 

0.6836 

0.9984 

1.6548 

0.4935 

0.512 

0.9997 

17 

1.314 

0.5536 

0.745 

0.9994 

1.6009 

0.4844 

0.4926 

0.9998 

21 

1.7385 

0.4631 

0.3601 

0.9998 

69 

 
 
 
Figure A.7: Cell 1 - 4 Calibration Curves - Fiber-film Probe 

70 

 
 
 
Figure A.8: Cell 5 - 8 Calibration Curves - Fiber-film Probe 

71 

 
 
 
 
Figure A.9: Cell 9 - 12 Calibration Curves - Fiber-film Probe 

72 

 
 
 
Figure A.10: Cell 13 - 16 Calibration Curves - Fiber-film Probe 

73 

 
 
 
Figure A.11: Cell 17 - 20 Calibration Curves - Fiber-film Probe 

74 

 
 
 
 
Figure A.12: Cell 21 - 23 Calibration Curves - Fiber-film Probe 

75 

 
 
 
 
 
APPENDIX B: Numerical Results 

B.1 Stock Shroud 

B.1.1 Coarse Mesh 

The mesh used for the coarse stock shroud simulation has the mesh model parameters that were 

used in the mesh considerations below (Table B.1). 

Table B.1: Stock Shroud - Coarse Mesh Considerations 

Surface Mesh Parameters 

Minimum Size 
Maximum Size 
Growth Rate 
Size Functions 

Transition 
Number of Layers 
Transition Ration 
Growth Rate 
Grown On 

9.5924e-4 
2.45565e-2 
1.2 
Curvature and Proximity 

Boundary Layers 

Smooth Transition 
3 
0.272 
1.2 
Only Walls 

Volume Mesh 

Growth Rate 
Maximum Cell Length 

Boundary Mesh Size 

Interior Mesh Size 

Nodes 
Faces 

Nodes 
Faces 
Cells 

1.2 
3.207809e-2 

568,347 
160,570 

3,163,889 
4,703,394 
868,883 

76 

 
 
 
 
 
B.1.2 Fine Mesh 

The mesh used for the fine stock shroud simulation has the mesh model parameters that were 

used in the mesh considerations below (Table B.2). 

Table B.2: Stock Shroud - Fine Mesh Considerations 

Surface Mesh Parameters 

Minimum Size 
Maximum Size 
Growth Rate 
Size Functions 

Transition 
Number of Layers 
Transition Ration 
Growth Rate 
Grown On 

6e-5 
1.2e-2 
1.2 
Curvature and Proximity 

Boundary Layers 

Smooth Transition 
3 
0.272 
1.2 
Only Walls 

Volume Mesh 

Growth Rate 
Maximum Cell Length 

Boundary Mesh Size 

Interior Mesh Size 

Nodes 
Faces 

Nodes 
Faces 
Cells 

1.2 
1.596611e-2 

1,228,487 
330,104 

6,971,362 
10,489,797 
1,971,575 

77 

 
 
 
 
 
B.2 Modified Shroud 

B.2.1 Fine Mesh 

The mesh used for the modified shroud simulation, which was a relatively fine mesh, has the 

mesh model parameters that were used in the mesh considerations below (Table B.3). 

Table B.3: Modified Shroud - Fine Mesh Considerations 

Surface Mesh Parameters 

Minimum Size 
Maximum Size 
Growth Rate 
Size Functions 

Transition 
Number of Layers 
Transition Ration 
Growth Rate 
Grown On 

9.5924e-4 
2.45565e-2 
1.2 
Curvature and Proximity 

Boundary Layers 

Smooth Transition 
3 
0.272 
1.2 
Only Walls 

Volume Mesh 

Growth Rate 
Maximum Cell Length 

Boundary Mesh Size 

Interior Mesh Size 

Nodes 
Faces 

Nodes 
Faces 
Cells 

1.2 
3.207809e-2 

218,504 
70,184 

1,031,570 
1,514,640 
274,339 

78 

 
 
 
 
 
B.3 Model Set Up 

The parameters considerations for the model set up of the stock shroud and modified shroud can 

be summarized in the following table, Table B.4. 

Table B.4: CFD Model Considerations 

Set Up Settings 
Solver Settings 

Solver 

Density 
Viscosity 

Pressure-Based and Steady 

Fluid Properties 

1.225 kg/m3 
1.7894e-5 kg/(m s) 

Boundary Conditions 
TTA Cell Inlets 

Velocity Condition 
Turbulence Intensity 
Viscosity Ratio 

Applied Velocity (see Figure 4.3) 
5% 
10 

Velocity Condition 

Flow cell slip interface 

TTA Cell Sides 

Inlet (Other) 

Velocity Condition 
Turbulence Intensity 
Viscosity Ratio 

Average Velocity (see Figure 4.3) 
5% 
10 

Velocity Condition 

Solid walls, no-slip condition 

Sides of Inlet Flow 

Shroud Walls 

Velocity Condition 

Solid walls, no-slip condition 

Pressure Condition 

Shroud Outlet 

Convergence Criteria 

Maximum Iterations 

-57.04 Pa 

1500 

79 

 
 
 
 
 
APPENDIX C: Radiator Only Results 

Table C.1: Radiator Velocity Measurement Steps 

Velocity Step 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
13 

U"56 (m/s) 
2.26 
2.83 
3.30 
3.74 
4.19 
4.61 
4.93 
5.34 
5.68 
6.04 
6.36 
6.72 
7.05 

DP (Pa) 
33.99 
49.89 
64.60 
78.90 
95.52 
111.62 
124.13 
140.29 
155.23 
171.20 
185.81 
202.38 
217.98 

80 

 
 
 
 
 
Figure C.1 Radiator Flow Distribution at DP = 33.99  Pa 

(Above: Velocity Distribution, Below: Velocity Percent Difference Distribution) 

81 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure C.2 Radiator Flow Distribution at DP = 48.89 Pa 

(Above: Velocity Distribution, Below: Velocity Percent Difference Distribution) 

82 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure C.3 Radiator Flow Distribution at DP = 64.60 Pa 

(Above: Velocity Distribution, Below: Velocity Percent Difference Distribution) 

83 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure C.4 Radiator Flow Distribution at DP = 78.90 Pa 

(Above: Velocity Distribution, Below: Velocity Percent Difference Distribution) 

84 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure C.5 Radiator Flow Distribution at DP = 95.52 Pa 

(Above: Velocity Distribution, Below: Velocity Percent Difference Distribution) 

85 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure C.6 Radiator Flow Distribution at DP = 116.20 Pa 

(Above: Velocity Distribution, Below: Velocity Percent Difference Distribution) 

86 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure C.7 Radiator Flow Distribution at DP = 124.13 Pa 

(Above: Velocity Distribution, Below: Velocity Percent Difference Distribution) 

87 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure C.8 Radiator Flow Distribution at DP = 140.29 Pa 

(Above: Velocity Distribution, Below: Velocity Percent Difference Distribution) 

88 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure C.9 Radiator Flow Distribution at DP = 155.23 Pa 

(Above: Velocity Distribution, Below: Velocity Percent Difference Distribution) 

89 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure C.10 Radiator Flow Distribution at DP = 171.20 Pa 

(Above: Velocity Distribution, Below: Velocity Percent Difference Distribution) 

90 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure C.11 Radiator Flow Distribution at DP = 185.81 Pa 

(Above: Velocity Distribution, Below: Velocity Percent Difference Distribution) 

91 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure C.12 Radiator Flow Distribution at DP = 202.38 Pa 

(Above: Velocity Distribution, Below: Velocity Percent Difference Distribution) 

92 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Figure C.13 Radiator Flow Distribution at DP = 217.98 Pa 

(Above: Velocity Distribution, Below: Velocity Percent Difference Distribution) 

93 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
APPENDIX D: Stock Results 

Table D.1: Stock Shroud Velocity Measurement Steps  

Velocity Step 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
13 
14 

U"56 (m/s) 
0.78 
1.07 
1.32 
1.52 
1.68 
1.87 
2.04 
2.21 
2.36 
2.50 
2.63 
2.78 
2.90 
3.04 

DP (Pa) 
18.22 
32.77 
48.32 
63.77 
76.59 
92.91 
109.46 
125.72 
140.89 
155.84 
170.16 
187.64 
202.13 
218.72 

94 

 
 
 
 
 
Figure D.1: Velocity Percent Difference at DP = 48.32 Pa (Uavg = 1.32 m/s) 

Figure D.2: Velocity Percent Difference at DP = 48.31 Pa (Uavg = 1.32 m/s) 

95 

 
 
 
 
 
Figure D.3: Velocity Percent Difference at DP = 63.77 Pa (Uavg = 1.52 m/s) 

Figure D.4: Velocity Percent Difference at DP = 76.59 Pa (Uavg = 1.68 m/s) 

96 

 
 
 
 
Figure D.5: Velocity Percent Difference at DP = 92.91 Pa (Uavg = 1.87 m/s) 

Figure D.6: Velocity Percent Difference at DP = 109.46 Pa (Uavg = 2.04 m/s) 

97 

 
 
 
 
Figure D.7: Velocity Percent Difference at DP = 125.72 Pa (Uavg = 2.21 m/s) 

Figure D.8: Velocity Percent Difference at DP = 140.89 Pa (Uavg = 2.36 m/s) 

98 

 
 
 
 
Figure D.9: Velocity Percent Difference at DP = 155.84 Pa (Uavg = 2.50 m/s) 

Figure D.10: Velocity Percent Difference at DP = 170.16 Pa (Uavg = 2.63 m/s) 

99 

 
 
 
 
Figure D.11: Velocity Percent Difference at DP = 187.64 Pa (Uavg = 2.78 m/s) 

Figure D.12: Velocity Percent Difference at DP = 202.13 Pa (Uavg = 2.90 m/s) 

100 

 
 
 
 
Figure D.13: Velocity Percent Difference at DP = 218.72 Pa (Uavg = 3.04 m/s) 

101 

 
 
 
 
APPENDIX E: Modified Shroud Results 

Table E.1: Modified Shroud Velocity Measurement Steps 

Velocity Step 
1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
13 
14 

U"56 (m/s) 
0.77 
1.07 
1.30 
1.49 
1.68 
1.83 
2.00 
2.17 
2.30 
2.42 
2.57 
2.70 
2.81 
2.98 

DP (Pa) 
18.79 
33.14 
48.94 
63.35 
78.82 
93.30 
108.75 
126.64 
140.89 
153.86 
171.13 
186.45 
199.51 
219.76 

102 

 
 
 
 
 
Figure E.1: Velocity Percent Difference at DP = 33.14 Pa (Uavg = 1.07 m/s) 

Figure E.2: Velocity Percent Difference at DP = 48.94 Pa (Uavg = 1.30 m/s) 

103 

 
 
 
 
Figure E.3: Velocity Percent Difference at DP = 63.35 Pa (Uavg = 1.49 m/s) 

Figure E.4: Velocity Percent Difference at DP = 78.82 Pa (Uavg = 1.68 m/s) 

104 

 
 
 
 
Figure E.5: Velocity Percent Difference at DP = 93.30 Pa (Uavg = 1.83 m/s) 

Figure E.6: Velocity Percent Difference at DP = 108.75 Pa (Uavg = 2.00 m/s) 

105 

 
 
 
 
Figure E.7: Velocity Percent Difference at DP = 126.64 Pa (Uavg = 2.17 m/s) 

Figure E.8: Velocity Percent Difference at DP = 140.89 Pa (Uavg = 2.30 m/s) 

106 

 
 
 
 
Figure E.9: Velocity Percent Difference at DP = 153.86 Pa (Uavg = 2.42 m/s) 

Figure E.10: Velocity Percent Difference at DP = 171.13 Pa (Uavg = 2.42 m/s) 

107 

 
 
 
 
Figure E.11: Velocity Percent Difference at DP = 186.45 Pa (Uavg = 2.70 m/s) 

Figure E.12: Velocity Percent Difference at DP = 199.51 Pa (Uavg = 2.81 m/s) 

108 

 
 
 
 
Figure E.13: Velocity Percent Difference at DP = 219.76 Pa (Uavg = 2.98 m/s) 

109