NONUNIFORM FLOW OVER A THERMAL TRANSIENT ANEMOMETER B y James Leung A THESIS Submitted to Michigan State University i n partial fulfillment of the requirements f or the degree of Mechanical Engineering Master of Science 2018 A BSTRACT NONUNIFORM FLOW OVER A THERMAL TRANSIENT ANEMOMETER By James Leung An experiment and a simulation have been created to determine if a Thermal Transient Anemometer (TTA) ha s the capability to measure a nonuniform fluid flow and to output an approp riate average uniform flow . A frame was created with 23 cells that holds a tungsten sensing wire that was heat ed with an electrical current and cooled with a passing flow. The TTA wa s then simulated, using an energy balance equation as a basis, to test wit h more nonuniform flows. The source of axial heat transfer caused the TTA to cool slower with a nonuniform flow than an equivalent uniform flow at an averaged flow speed. The percen t the nonuniform flow differed from this equivalent averaged flow changed based was on two main factors of the flow ; if any region of the flow exist ed at low speeds and if the flow has large gradients. With this in mind the TTA will still have a usable ope rational condition . Namely, if the flow is not at a low speed and if it ha s a modest gradient. iii A CKNOWLEDGEMENTS professors and colleagues at Michigan State University. Special thanks to my advisors, Dr. John Foss and Dr. James Klausner for giving me this chance and guide me through this process. I would also like to thank Paul Sandherr, Kelvin Randh r, Thomas Stuecken and Claus Buchhhoz for their assistance in this project. Their help was greatly needed for this difficult task . Finally, I would like to thank my family and close friends that made any difficulties that may arise bearable . iv TABLE OF CONTENT S L IST OF TABLES ................................ ................................ ................................ ............. v i L IST OF FIGURES ................................ ................................ ................................ .......... vii KEY TO SYM BOLS AND ABBREVIATION S ................................ ................................ x 1.0 Introduction ................................ ................................ ................................ .................. 1 1.1 Motivation ................................ ................................ ................................ .......... 1 1.2 Previous Work ................................ ................................ ................................ ... 2 1.3 Goals ................................ ................................ ................................ ................. 2 2.0 The TTA Sy stem ................................ ................................ ................................ .......... 4 2.1 Design of the TTA ................................ ................................ ............................ 4 2.2 TTA Frame Fabrication ................................ ................................ ..................... 6 2.3 Sensing Wire Characteristics ................................ ................................ ........... 1 3 3.0 Numerical Simulation of TTA Thermal Effects ................................ ...................... 1 5 3.1 Equation Derivation ................................ ................................ ......................... 1 5 3.2 Heat Convection ................................ ................................ ............................... 1 7 3.3 Boundary Condition ................................ ................................ ......................... 18 3.4 Simulation ................................ ................................ ................................ ........ 18 3.5 Verification ................................ ................................ ................................ ...... 19 4.0 Experimental Investigation ................................ ................................ ....................... 2 4 4.1 Test F acility ................................ ................................ ................................ .... 2 4 4.2 Hot - Wire Probe Anemometry ................................ ................................ .......... 3 3 4.3 CTA Calibration ................................ ................................ ............................... 3 3 4.4 TTA Frame Calibration ................................ ................................ .................... 3 5 5.0 Evaluation of the Numerical Simulation ................................ ................................ .. 3 7 6.0 Nonuniform Velocity Profile ................................ ................................ ..................... 4 1 6.1 Experimental Procedure for the Non - uniform Velocity Distribution .............. 4 1 6.2 Experimental Results ................................ ................................ ....................... 4 3 6.3 Simulation Compa rison ................................ ................................ ................... 4 3 7.0 Simulations of Non - Uniform Velocity Profiles ................................ ........................ 4 5 7.1 Simulated Temperature Distributions for Nonuniform Velocity ..................... 4 5 7.2 Simulated Mean Velocity Prediction for Linear Variation in Velocity ........... 5 1 7.3 Convective Heat Trans fer ................................ ................................ ................ 5 3 8.0 Conclusion ................................ ................................ ................................ .................. 5 6 v APPENDICES ................................ ................................ ................................ ................... 5 7 AP P EN D IX A . CTA Calibrations at Low Speed ................................ .................. 58 AP P EN DIX B . Calibration Curves for the Rest of the TTA ................................ . 5 9 AP P EN DIX C . Derivation of Equations 31 and 32 ................................ ............... 6 2 REF ERENCES ................................ ................................ ................................ .................. 6 5 vi L IST OF TABLES Table 7. 1 . Linear Flow Data ................................ ................................ .............................. 52 vii LIST OF FIGURES Figure 1 .1 . Example Engine Cooling System Obtained from ClearMechanic.com [4] ...... 1 Figure 2.1 . Completed Frame Full View ................................ ................................ ............. 5 Figure 2 .2 . Close Up of Completed Frame and Components ................................ .............. 6 Figure 2.3 . Garolite A ................................ ................................ ................................ .......... 8 Figure 2.4 . Garolite B ................................ ................................ ................................ .......... 8 Figure 2.5 . Garolite C ................................ ................................ ................................ .......... 9 Figure 2.6 . Garolite D ................................ ................................ ................................ .......... 9 Figure 2.7 . Garolite E ................................ ................................ ................................ ......... 10 Figure 2. 8 . Garolite Inside an Inside Cell in the Frame ................................ ..................... 1 0 Figure 2.9 . Garolite Inside a Border Cell in the Frame ................................ ..................... 1 1 Figure 2.10 . Partially Wired TTA ................................ ................................ ...................... 1 1 Figure 2.1 1 . Fully Wired TTA ................................ ................................ ........................... 1 2 Figure 2.1 2 . Termina l Block ................................ ................................ .............................. 1 2 Figure 2.1 3 . Diagram of Securing the Wire ................................ ................................ ....... 1 3 Figure 3.1 . Energy Budget for a Wire Segment ................................ ................................ . 1 5 Figure 3.2 . Comparing Exponential Decay to Experimental Nondim ensional Resistance ................................ ................................ ................................ .......................... 2 0 Figure 3.3 . Comparing Numerical Solution to Exact Solution for a Wire with an Initial Linear Temperature P rofile ................................ ................................ ................................ 2 2 Figure 3.4 . Comparing Numerical Solution to Exact Solution for a Wire with an Initial Parabolic Temperature Pro file ................................ ................................ ........................... 2 3 Figure 4.1 . Side View of TTA Testing Facility ................................ ................................ . 2 5 Figure 4.2 . Front View of T TA Testing Facility ................................ ............................... 2 6 viii Figure 4.3 . TTA Testing Facility with TTA Installed ................................ ...................... 2 7 Figure 4. 4 . Frontal View with Honeycomb ................................ ................................ ....... 28 Figure 4. 5 . TTA Testing Facility with No Air Bleed ................................ ........................ 29 Figure 4. 6 . TTA Testing Facility with Large Amount of Bleed ................................ ........ 3 0 Figure 4. 7 . View of Testing Facility with Radiator Installed ................................ ........... 3 1 Figure 4. 8 . View of Testing Facility with Radiator and Shroud Installed ........................ 3 2 Figure 4. 9 . Image of the Hot Wire Probe ................................ ................................ ........... 3 3 Figure 4. 10 . Image of the Hot Wire Probe Close Up ................................ ......................... 3 3 Figure 4. 11 . Hot Wire Probe Calibration Facility ................................ ............................. 3 4 Figure 4. 12 . Hot Wire Probe Calibration ................................ ................................ .......... 3 5 Figure 4. 1 3 . Example of a Row Calibration of the TTA ................................ ................... 3 6 Figure 5.1 . ................................ ............. 3 7 Figure 5. 2 . 2 to Simulation ................................ ............. 38 Figure 5. 3 . 3 to Simulation ................................ ............. 38 Figure 5. 4 . 4 to Simulation ................................ ............. 39 Figure 5. 5 . Between Row 5 to Simulation ................................ ............. 39 Figure 5. 6 . 6 to Simulation ................................ ............. 40 Figure 6.1 . TTA Testing Facility with Cloth Gradient Over the Face ............................... 4 2 Figure 6.2 . Nonuniform Flow Over the Row 3, Cell 3 Measured with Hot Wire Probe ................................ ................................ ................................ ................................ .. 4 3 Figure 7 .1 . Transient Cooling Under Uniform Flow, Speed of 10 m/s ............................. 4 6 Figure 7.2 . Transient Cooling with Linear Variation in Velocity, U avg =10 m /s b=10 m/s ................................ ................................ ................................ ............................ 4 7 Figure 7.3 . Transient Cooling with Parabolic Variation in Velocity, Shown in Equation 3 7 ................................ ................................ ................................ ........................ 48 ix Figure 7. 4 . Transient Cooling with Sinusoidal Variation in Velocity, Shown in Equation 3 8 ................................ ................................ ................................ ........................ 49 Figure 7.5 . Comparison of Simulated Nondimensional Resistance to Exponential Decay with Linear Velocity Profile , Equation 3 6 ................................ ............................. 5 0 Figure 7.6 . Comparison of Simulated No ndimensional Resistance to Exponential Decay with Parabolic Velocity Profile , Equation 3 7 ................................ ........................ 5 0 Figure 7.7 . Comparison of Simulated Nondim ensional Resistance to Exponential Decay with Sinusoidal Velocity Profile , Equation 3 8 ................................ ...................... 51 Figure 7.8 . Suggested O perational Range of the TTA ................................ ....................... 5 2 Figure 7. 9 . Suggested Operational Range of the TTA Zoomed In ................................ .... 5 3 Figure 7. 10 . Initial Convection Coefficient ................................ ................................ ....... 5 4 Figure 7. 11 . Wire Temperature Distribution with Respect to Time ................................ .. 5 5 Figure 7. 12 . Comparison of Temperature Deca y Between a Non - Uniform Velocity Profile to the Average Uniform Velocity Profile ................................ ............................... 5 5 Figure A . 1 . CTA Probe Calibration at Low Air Speeds ................................ .................... 5 8 Figure A.2 . Row 1 Calibration ................................ ................................ .......................... 5 8 Figure A.3 . Row 2 Calibration ................................ ................................ .......................... 59 Figure A.4 . Row 4 Calibration ................................ ................................ .......................... 59 Figure A .5 . Row 5 Calibration ................................ ................................ .......................... 6 0 Figure A.6 . Row 6 Calibration ................................ ................................ ........................... 6 0 x KEY TO SYMBOLS AND AB BREVIATIONS KEY ABBREVIATI ONS CTA Constant Temperature Anemometer TTA Thermal Transient Anemometer ROMAN SYMBOLS Cross sectional area of the wire Specific heat of wire Diameter of wire Voltage Nondimensional term Height of a cell Heat convection coefficient Current through the wire Thermal conductivity of wire Length of wire Nusselt Number Prandlt Number Heat transfer over small wire segment Res istance of wire Reynolds Number Temperature (°C) Time xi Air Speed Position along the wire GREEK SY MBOLS Percent difference between measured and simulated Percent difference between expected and simulated Resistivity of wire Nondimen sional Temperatu re or Nondimensional Resistance Kinematic Viscosity Density of wire Time Constan t Temperature Coefficient of Resistance SUBSCRIPTS/SUPER SCRIP TS Property at ambient air condition Average of vel ocity profile Value a chieved by using the calibration to predict Proper t y at film condit ion Ai r flow with a l inear velocity profile Reference Conditions Ai r flow with a paraboli c velocity profile Value achieved by usin g numeri cal s olution Ai r flow with a paraboli c sinusoidal profile Pro perty of wire 1 1 .0 Introduction 1.1 Motivation Internal c ombustion engines require heat removal for safe operation . The exothermic reaction taking place in the combustion chamber coupled with the mechanical friction generate heat that needs to be evacuated in order to ma intain high performance without compromising reliability. This limits the engine output to the perf ormance of the cooling system. The cooling system is comprised of a radiator, shroud, fan , and cooling fluid. M oving the heat from coolant to air is the prim ary function of the radiator which increases the heat transferred from the engine to the cooling system. A modern cooling system is shown in Figure 1 .1 . Figure 1 .1 . Example Engine Cooling System Obtained from Clear Mechanic.com [ 4 ] There are many approaches to improve the cooling system ; o ptimizing the shroud design to improve the uniformity of the air flow across the radiator is one such strategy . This requires 2 understanding the air flow over the radiator. The Thermal Transient Anemometer or TTA was develope d to address this objective. The total area at the face of the radiator is subdivided in to measurement cells . The TTA respond s to an average velocity at given cells . The TTA was chosen over other designs of anemometer s due to the thin design of the TTA , w hich allows it to fit in between the radiator and the shroud with a relatively low disruption to the air flow. 1.2 Previous Work The initial development of the TTA was reported by Foss, et al. (2004 ) [6] . The basic operating principle, described therein, i s to determine the average v elocity at the face of a cell (U ) by measuring the cooling rate of a previously heated sensor wire. The cooling follows an tempe rature. Namely (1) Hence, can b used as a measure the cooling rate. From Foss, et al. (2004), the average velocity can be related to as ( 2 ) Foss, et al (2006) [5] used an elevated ambient te mperature and turbulent flow to confirm that the TTA is still accurate at higher temperatures and with turbulence, conditions are expected for a TTA mounted in a vehicle radiator for testing. This thesis builds on the previous wo rks by finding a relationsh ip between a non - uniform air flow and the cooling rate of the sensor wire. 1.3 Goals non - uniform velocity at the face of a cell? The present investigation is to answer this question. 3 Specifically, if a non - uniform velocity is present at a cell and if the value is obtained, what is the relationship between the inferred velocity and the spatially averaged velocity at the face of the cell? 4 2.0 The TTA System 2.1 Design of the TTA A n assem bled TTA frame is s hown in Figure 2.1 . The TTA uses tungsten as the sensing wire . It is supported by a metal frame to measure the air speed. The metal frame divides the radiator area into a 4 by 6 grid of cells (ie., s maller areas) . Each cell h o ld s a 1.6 - meter segment of the sensing wire. A cell on the top right (of the Figure 2.1 ) was excluded due to design constraints of the testing shroud, leaving 23 cells. The numb er of cells provide a detailed survey over the radia tor with minimally blocking the face of the radiator and without disturbing the flow of air. The sensor wire was connected by a cable to a control unit made by Sakor Technologies Inc. , which controls llect data , the unit sen ds a n electric current (for a designated time period) to heat the sensor wire it to an elevated temperature . At the end of the designated time period the unit will swi tch the current to a sens ing current (10 mA). The recording A/D c onverter (100 mV full scale) records the sensor wire resistance during the cooling period. Time zero is set after the after the cooling period when the resistance reaches steady state if ther e is a high air speed. If there is a high air speed and the resis tance exceeds 10 ohms then the time zero is set after the resistance reaches 10 ohms after the cooling period. The cooling process will continue for a set period of time, which it will then p roduce a time in which the no n - dimensional resistance will reach . This time becomes the value of which the TTA outputs for the user when calibrating. The significance of was explained in Section 1.2. There is a linear correlation with resistance and temperature, which will be explored further in Sectio n 2.3 . A correlation between the rate of temperature decay and an air speed can be determined after calibration. 5 Figure 2 .1 . Completed Frame Full View Note: The inside dimension of each cell is 0.166 m by 0.274 m 6 Figure 2 .2 . Close Up of Completed Fram e and Components 2. 2 TTA Frame Fabrication The metal bars used as the structure were machined from stainless steel. Referring to Figure 2 . 2 , t he horizontal bars of the frame have holes for G arolite rod inserts to hold the sensor wire . The G arolite electric ally insulates the sensor wire from the fram e. Garolite is a composite material . It was selected due to its thermal and electrical resistant properties. The G arolite inserts have various designs, dependent on the location on the frame. One version had a ho le drilled down the axial center of the G aro lite rod . The other designs have a hole radially through the center of the G arolite for the G arolite to be secured on to the frame with a small metal pin and another hole radially near the end to hold the wire . T hese designs can be seen in Figure 2. 3 - 2.7 . The placement of each G arolite piece in a cell can be seen in Figure 2.8 and Figure 2.9 . The method of wiring the 7 cell can be seen in Figure 2.11 be tween the wires. Teflon was used due to the high thermal and electrical resistance and ease of machining. It was not used for the tether points (now insulated by the G arolite) because the Teflon was too soft, and the wir e was expected to cut through the Te flon. An initial and an unworkable configuration for the TTA used stainless steel wire. The cell sizes were selected to provide a 4 x 6 array that covered the project radiator. The location for the Garolite members were set to achieve a resistance of ohms resistance. The stainless - steel wire proved unworkable as a result of its insensitivity to increases of temperature: too small of a temperature coefficient of resistance which will be discussed further in Section 2.3. Sa tisfactory performance was obtained with the replacement wire tungsten. The length ( about 1.6 m) and diameter (0.2 mm ) were selected to be compatible with the installed Garolite members and to provide an ambient temperat ure resistance of 2.85 ohms. The ina bility to solder directly to tungsten wire presented a substantial problem for the wiring of the frame. (Note that copper plating was used on tungsten wire in earlier versions of the TTA. That plating process is challenging, and it was not attempted in thi s project.) Plastic coated terminal blocks , shown in Figure 2.1 2 , were used to address this issue. The terminal blocks used metal screw clamps to secure the wire into place. The terminal blocks also providing an ele ctrical connection between a copper wire and the sense wire by soldering the copper wire to a prong, an extension of the clamps, on the terminal block electrical conduction to the rest of the frame. The wire w as secured as show in Figure 2.1 3 , where the te rminal block lays on its side. A copper wire that provides electrical connection was soldered to the extended prongs of the blocks . The copper wire is a part of the Belden Cable used to connect the sense wires to the Sakor Unit. The Belden Cable was chosen because the individual 6 wires, 8 22 - gauge wires, inside the cables were grouped in twisted pairs and the metallic shield over the wires which prevents noise. The Belden Cable was protected from external damage by stainless steel tubes that were welded to v ertical bars of the frame. Figure 2. 3 . Garolite A Figure 2.4 . Garolite B 9 Figure 2. 5 . Garolite C Figure 2.6 . Garolite D 10 Figure 2.7 . Garolite E Figure 2.8 . Garolite Inside an Inside Cell in the Frame 11 Figure 2.9 . Garolite Inside a Borde r Cell in the Frame Figure 2.10 . Partially Wired TTA 12 Figure 2.11 . Fully Wired TTA Figure 2.12 . Terminal Block 13 Figure 2. 13 . Diagram of Securing the Wire 2.3 Sensing Wire Characteristics T ungsten wire was selected to be the sensing wire for the TT A given its high temperature coefficient of resistance . This allows the sensing wire has a linear correlation between temperature and electrical resistance. ( 3 ) The TTA does not have a direct method of measuring the temperature of the sensing wire so with the temperature coefficient of resistance the temperature was calculated from the resistance of the wire. Since the wire was divided into segments, which will be discussed further in Section 3.1, the 14 total wire r esistance can be determined from the resistivity of the wire segments which are changing throughout the wire. (4) The resistivity of the wire has a similar linear correlation to t emperature as resistance which results in ( 5 ) The wire diameter was chosen to be 0.2 mm. If the wire was thicker diameter was chosen, the initial resistance would be lower and the TTA would have difficulty reading. If a thinner wire was selected , it was found that during the fabrication the wire would often break as a result of its small diame ter . The other factor that w as affected by the wire temperature is thermal conductivity of the wire which increases with temperature , shown below . The temperature dependent expression for thermal conductivity is determined by fitting a third order polynomi al to values reported in Fundamentals of Heat and Mass Transfer by Incorpra and DeWitt (2007) [8] . ( 6 ) 15 3.0 Numerical Simulation of TTA Thermal Effects 3.1 Equation Derivation The energy budget of a small segment of wire can be represented as shown in Figure 3.1 . Figure 3.1 . Energy Budget for a Wire Segment The relationship between air speed and the rate of resistance - decay was sim ulated using the energy balance shown in Equation 7 . ( 7 ) Several assumptions were then considered . First, a one - dimensional heat transfer was small diameter and low Biot Number . N amely, the present Biot Number does not exceed 0.0003 , whereas the condition to established 1D heat transfer is a Biot number less than 0.1 . The heat stored in the wire causes the wire to change in temperature over time as expressed in Equation 8 . The main source of heat leaving the system would be through heat convection which can be seen in Equation 9 . ( 8 ) 16 ( 9 ) The heat generated in the wire segment was caused by electrical current as expressed in Equation 10 . Referring to Section 2.3 , the resi stivity of the wire , which increased due to temperature, is use due to the wire separated into segments . ( 10 ) (11 ) ( 12 ) As shown in Figure 3.1 , axial conduction effects are included in the energy budget. (1 3 ) (1 4 ) The equations above were inserted into Equation 7 to produce Equation 1 5 . Equation 1 5 was then simplified to the form shown in Equation 1 6 . (1 5 ) 17 (16) 3.2 Heat Convection The h eat transfer coefficient (h) depends on the Nusselt Number as expressed in Equation 17 . Various Nusselt Number correlations were considered for the simulatio n : i. H ilpert (1933) ii. Fand and Keswani (1961) iii. Zukaukas (1987) iv. Churchill and Burnstein (1977) v. Morgan (1975). These correlations were found in Natural Convection from Circular Cylinders [1] . The selected correlation was established by Bruun (1995) [2] which can be seen in Equation 18 . ( 17 ) ( 18 ) This correlation was created for hot - wire anemometry, which in this correlation and experiment uses a thin wire . It was also determined that using Brunn resulted in the smallest d eviation between the simulation and the experimental results, which will be later discussed in Section 4.3 Various properties of air were reliant on the wire temperature as represented by the film temperature . See Equation 19 . T he Reynolds N umber and the P randlt Number which are dependent upon the film temperature as defined in Equation 20 , 21 , and 2 2 . The information in Equation 2 1 18 and 2 2 was obtained from an extrapolation from the Fundamentals of Heat and Mass Transfer by Incorpra and DeWitt (2007) [8] . (19) (20) (21) (22) 3. 3 Boundary Conditions An adiabatic boundary condition was assumed for the wire : (23) (24) This was due to the material holding the wire having thermally nonconductive material h olding the wire as stated in Section 2.2 . 3. 4 Simulation The simulation used a forward marching scheme in space and time. For the end segments the simulation used first order difference, due to the end segments being adiabatic. Whereas the other segments u sed second order central difference. The dx used for this problem was 1mm and 19 the dt was 0.001 seconds due to the stability criteria. A s maller value for dx would require the dt cremental decrease to keep stability causing the computational time to increase drastically. The simulation was set to end when a non - dimensional resistance reaches 3. 5 V erification The verification process will be carried out in two steps. Step one evaluates the cooling of the wire. A simplified problem was tested to verify cooling of the wire . More lenient assumptions and conditions were introduced for the numerical sol ution. This verification solution applies to the time period after the heating of the wire. Some assumptions include; uniform air flow (removes the axial conduction and the need to separate the wire into segments), the terms in the heat convection are at a mbient air conditions (rather than the changing film temperature) and the removal of the energy generation (t he energy generation was due t o the small sense current that was used to determine R(t) but in this study its contribution was negligible) , see Equation 25 for the simplified equation . This produces an exponential decay which was expected from the previous work (Section 1.2). The exponential decay is shown in Figure 3.2 . ( 25 ) (26) (2 7 ) 20 Figure 3.2 . Comparing Exponential Decay to Experimental Nondimensional Resistance Step two evaluates the axial conduction of the wire. To verify the effects of the axial conduction was implemented correctly Equat ion 16 was solved numerically for the heating of the wire. Several simplifications were made to Equation 16 which were assumin g thermal conductivity and heat convection were constant. To create a need for axial conduction an initial temperature of the wire was imposed. This process of reaching a numerical solution used separation of variables, which can be found in Conduction of Heat in Solids [3] and Heat Conduction [4] . The two initial conditions tested for the wire is expressed in Equations 28 and 29 . Th is produces Equations 30 and 3 1 , which are derived in Appendix C. The two methods were then plotted against each other using a 10 m/s air speed and a current of 2 Amps as inputs. ( 28 ) ( 29 ) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.05 0.1 0.15 0.2 0.25 TIME (s) Exponential Decay of Uniform Velocity Profile (Average Air Speed = 10 m/s) Nondimensional Resistance of Simualtion Exponential Decay 21 (3 0 ) (3 1 ) 22 Figure 3.3 . Comparing Numerical Solution to Exact Solution for a Wire with an Initial Linear Temperature Profile 20 25 30 35 40 45 50 0 200 400 600 800 1000 1200 1400 TEMPERATURE ( C) DISTANCE ALONG THE WIRE (mm) Comparing Numerical Solution to Exact Solution for Initial Linear Temperature Gradients Exact Solution Numerical Solution t=0 s t=0.1 s t=0.3 s Steady State 23 Figure 3.4 . Comparing Numerical Solution to Exact Solution for a Wire with an Initial Parabolic Temperature Profile 20 25 30 35 40 45 0 200 400 600 800 1000 1200 1400 TEMPERATURE ( C) DISTANCE ALONG THE WIRE (mm) Comparing Numerical Solution to Exact Solution for Initial Parabolic Temperature Gradients Exact Solution Numerical Solution t=0 s t=0.1 s t=0.3 s Steady State 24 4.0 Experimental Investigation 4.1 Test Facility The test facility was designed to obtain data from the TTA as shown in Figure 4.1 . T he test facility use d a Buffalo Forge Blower to create an air flow over the frame. Note that a contraction exists in the facility between the TTA and the blower ; see Figure 4.2 . Figure 4 .3 shows the TTA frame mounted at the facility entrance . Shown on the front view of the facility is the TTA held in place during testing. Cardboard cylinders were cut in half and placed around the perimeter of the opening on the plywood , which creates a bell mouth entrance. Another front view can be seen in Figure 4.4 , where a plastic honeycomb (a flow straightener) was placed at the front of the TTA to ensure that the flow was homogenously perpendicular to the TTA . The blower motor was not adju stable ; hence, to change the air speed over the face of the TTA , the facility utili zed a controlled air bleed as shown in Figure 4.1 . This was accomplished with a sliding door on the side of the facility (Figure 4. 5 and 4. 6 ) and by removing the plates on the top and the bottom to increase the bleed and reduce the airflow over the TTA. This reduce d the volume air flow from the front of the facility. When the airspeed was required to increase, ridged plastic sheets were used to block the upper or lower two rows of the frame . When the top three rows were tested , the fifth and sixth row were blocked . When t he bottom three rows were tested , the first and second rows were blocked. Later when testing the radiator, the radiator was supported behind the plywood ( with several brackets ) . The TTA was attached behind the radiator and the shroud was placed behin d the radiator as shown in Figure 4. 8 . 25 Figure 4.1 . Side View of TTA Testing Facility 26 Figure 4.2 . Front View of TTA Testing Facility 27 Figure 4.3 . TTA Testing Facility with TTA Installed 28 Figure 4.4 . Frontal View with Honeycomb 29 Figure 4.5 . TTA Test ing Facility with No Air Bleed 30 Figure 4.6 . TTA Testing Facility with Large Amount of Bleed 31 Figure 4.7 . View of Testing Facility with Radiator Installed 32 Figure 4.8 . View of Testing Facility with Radiator and Shroud Installed 33 4.2 Hot - Wire Probe Anemo metry A Disa 55M Constant Temperature Anemometer (CTA) was used to define the velocity magnitudes in this study. The associated hot wire probe is shown in Figure 4.9 . The two pr ongs hold a plates 5 - micron tungsten wire that is maintained at an elevated cons tant tempera ture. The CTA measures air speed by interpreting the magnitude of the input power that is required to maintain a constant resistance of the 5 - micron wire . Figure 4.9 . Image of the Hot Wire Probe Figure 4.10 . Image of the Hot Wire Probe Clos e Up 4.3 CTA C alibration The hot - wire probe was placed in a calibration facility as shown in Figure 4.11 . The blower provided a known air flow at the hot wire probe. The plenum pressure can be utilized directly for the upper range ( m/s) velocity values ( U ) at the vena contracta of the slit jet (x/w . Appendix A describes the unique procedure to resolve the measurement uses associated in the lower range velocity values. Blockage was placed over the blower to get various 34 speeds of air over the probe. Data was taken over a one - minute interval . The hot wire probe was connected to the Sakor Unit which collected the voltage used to keep a constant temperature. The data was averaged over the one - minute interval and was compared to the a i r speed of the air. This created a relationship between the voltage (E) to maintain a constant temperature of the hot - wire probe see Figure 4.1 2 . ( 32 ) Figure 4.11 . Hot Wire Probe Calibration Facility 35 Figure 4.12 . Hot Wire Probe Calibration 4.4 TTA Frame Calibration The TTA frame was placed in the TTA test facility. The hot - wire probe was clamped to a rod that moved verticall y . The CTA sensor was placed 5 cm behind the TTA frame at the third cell. This cell was selected because it was displaced from the walls of the facility and would experience the least effect from the side wall boundary layer. The probe w as able to move fro m row to row with respect to the frame . E ach cell was tested with a four - secon d test interval for four minutes. The Sakor unit creates a text file for each four - minute trial . Hence, with data handing overhead, each datum point in Figure 4.13 represents nomin ally 1 0 TTA samples. The calibration for the other rows can be viewed in Appendix B. y = 5.3838x + 8.7944 R² = 0.9996 15 17 19 21 23 25 27 1.5 2 2.5 3 3.5 VOLTAGE 2 [E] 2 VELOCITY 0.43 (m/s) 0.43 Probe Calibration 36 Figure 4.13 . Example of a Row Calibration of the TTA Note, y i (i=1, 2, 3, 4) represent the cell number for a given row. 0 1 2 3 4 5 6 7 0 0.5 1 1.5 2 2.5 3 3.5 4 1/ (1/s) U 0.43 (m/s) 0.43 TTA Row 3 Calibration 37 5.0 Numerical Simulation Results Compared wi th Experiments S hown below is the comparison between the values of tau between the simulation to the TTA at the given air speed from the calibration. The values of from the TTA system was typically greater than the values from the simulation. This demonstr ates the effect of the Garolite and the Teflon spacers acting as heat sinks that was not taken to account in the simulation , which caused the simulation to becom e unstable. ( 33 ) Figure 5 . 1 . Comparison of Between Row 1 to Simulation -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 0 1 2 3 4 5 6 7 8 AIR SPEED(m/s) Comparison of Row 1 to Simulation 38 Figure 5.2 . Comparison of Between Row 2 to Simulation Figure 5.3 . Comparison of Between Row 3 to Simulation 0 0.5 1 1.5 2 2.5 3 3.5 4 0 2 4 6 8 10 AIR SPEED(m/s) Comparison of Row 2 to Simulation 0 1 2 3 4 5 6 0 1 2 3 4 5 6 7 8 9 AIR SPEED (m/s) Comparison of Row 3 to Simulation 39 Figure 5.4 . Comparison of Between Row 4 to Simulation Figure 5.5 . Comparison of Between Row 5 to Simulation -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 0 1 2 3 4 5 6 7 8 AIR SPEED(m/s) Comparison of Row 4 to Simulation -12 -10 -8 -6 -4 -2 0 2 4 6 0 2 4 6 8 10 AIR SPEED(m/s) Comparison of Row 5 to Simulation 40 Figure 5.6 . Comparison of Between Row 6 to Simulation 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 1 2 3 4 5 6 7 8 AIR SPEED(m/s) Comparison of Row 6 to Simulation 41 6.0 Non - uniform Velocity Profile 6.1 Experimenta l Procedure for the Non - uniform Velocity Distribution The TTA was removed from the test facility and the probe was moved forward two inches at the equivalent third cell of the third row . Hence, the probe measure d the air velocity at the plane of the sensin g wires of the TTA. A cloth was wrapped around a wooden frame at with an incre asing layer every 1/8 of an inch, beginning 3/16 of an inch from the bottom of the cell ; see Figure 6.1 . The result was to create a gradient in the air flow velocity field . M easur ements were made for 1 - minute intervals at each 1/8 - inch interval of the cloth thickness . The probe was removed and the TTA frame was returned to the test facility. TTA data were then obtained in a 4 - minute interval with samples collected every 4 seconds . Th ese data w ere averaged over the four - minute interval. 42 Figure 6.1 . TTA Testing Facility with Cloth Gradient Over the Face 43 6.2 Experimental Results The non - uniform flow that was present at the face with Row 3, Cell 3 ( measured by the hot wire probe ) is sh own in Figure 6.2 . The non - uniform flow produced a tau value of 0. 254 seconds. This caused the TTA to consider the flow to be 4.55 m/s based on the calibration. This differs from the spatially averaged velocity: 5. 35 m/s that has a percent difference of 1 5. 0 % to what the TTA system to consider . Figure 6.2 . Non - uniform Flow Over Row 3 , Cell 3 Measured with Hot - Wire Probe 6.3 Simulation Comparison The temperature decay in the TTA subjected to the velocity profile shown in Figure 6. 2 was simulated. The temper ature decay with the non - uniform flow form Equation 3 4 ( which fit a fi fth order polynomial over the data points of the points on Figure 6.2 ) as an input . When this equation was simulated , the resulting tau of 0.254 seconds matche d the experimental data. Uni form flows were simulated over a large range to create a relationship between a uniform velocity and tau. Various non - uniform fluid flows were then tested and compared to what the TTA would 0 1 2 3 4 5 6 7 8 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 AIR SPEED (m/s) POSITITON IN CELL (m) Non - uniform Air Velocity Profile Nonuniform Velocity Averaged Velocity 44 considers to be the uniform flows based on the tau to air velocity correlation done with uniform flow . As seen in this table various parameter s caused the difference between a non - uniform flow and the perceived uniform flow , which will be discussed in Section 7. 3 . ( 3 4 ) 45 7 .0 Simulations of Non - Uniform Velocity Pro file s 7.1 Simulated Temperature Distribution for Non - U niform Velocity Various velocity profiles were inserted as input for the simulat ion of the temperature decay. Velocity profiles such as linear (Equation 3 5 and 3 6 ) , parabolic (Equation 3 7 ) , and sinusoidal (Equation 38 ) for example were tested with a straight wire (diameter of 0.2 mm, length of 1.556 meters). (3 5 ) (3 6 ) (3 7 ) (3 8 ) T he resulting temperature transi ent distributions are associated with these velocity fields are shown in Figures 7 . 2 - 7. 4 ( with Figure 7.1 , a uniform velocity profile , as a comparison) . Then the nondimensional resistance (or nondimensional average temperature) was compared to the exponential decay from Section 1.2. This is shown in Figures 7 .5 - 7.7 . The tempera ture decay follows the exponential decay, regardless of the different velocity dis tribution . 46 Figure 7.1 . Transient Cooling Under Uniform Flow, Speed of 10 m/s 47 Figure 7.2 . Transient Cooling with Linear Variation in Velocity, U avg =10 m /s b=10 m/s 48 Figure 7.3 . Transient Cooling with Parabolic Variation in Velocity, Shown in Equation 3 7 49 Figure 7.4 . Transient Cooling with Sinusoidal Variation in Velocity, Shown in Equation 3 8 50 Figure 7.5 . Comparison of Simulated Nondimensional Resistance to Exponential Decay with Linear Velocity Profile , Equation 3 6 Figure 7.6 . Comparison of Simulated Nondimensional Resistance to Exponential Decay with Parabolic Velocity Profile , Equation 3 7 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.05 0.1 0.15 0.2 0.25 TIME (s) Exponential Decay of Linear Velocity Profile (Average Air Speed = 10 m/s) Nondimensional Resistance of Simualtion Exponential Decay 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.05 0.1 0.15 0.2 TIME (s) Exponential Decay of Parabolic Velocity Profile (Average Air Speed = 10 m/s) Nondimensional Resistance of Simualtion Exponential Decay 51 Figure 7.7 . Comparison of Simulated Nondimensional Resistance to Exponential Decay with Sinusoidal Velocity Profile , Equation 3 8 7. 2 S imulated Mean Velocity Prediction for Linear Variation in Velocity Various linear velocity profiles were used as inputs in the simulation of the temperature decay. The data for the simulation were tabulated in Table 1. Note the inferred velocity is derive d from and the calibration from the uniform data. As seen from these data, there were various uniform flow calibrations). A non - dimensional term G was introduced t o relate the parameters of the velocity profile to the percent difference that was seen in the data. This non - dimensional term was then compared to the percent difference, shown in Equation 39. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.05 0.1 0.15 0.2 0.25 TIME (s) Exponential Decay of Sinusoidal Velocity Profile (Average Air Speed = 10 m/s) Exponential Decay Nondimensional Resistance of Simualtion (3 9 ) ( 40 ) 52 Table 7.1 . Linear Flow Data Flow Speed Range (m/s) G Simulated Tau (sec) Mean Velocity (m/s) Inferred Velocity (m/s) Percent Difference % 0 - 10 2.00 0.294 5.0 3.17 57.8 0 - 20 2.00 0.236 10 .0 6.13 63.1 1 - 11 1.67 0.267 6.0 4.21 42.5 1 - 21 1.82 0.229 11.0 6.72 63.7 5 - 10 0.67 0.223 7.5 7.22 3.9 5 - 15 1.00 0.207 10.0 9.12 9.7 5 - 20 1.20 0.195 12.5 10.85 15.2 10 - 15 0.40 0.187 12.5 12.32 1.4 10 - 20 0.67 0.177 15.0 14.41 4.1 10 - 30 1.00 0.164 20 .0 18.25 9.6 15 - 20 0.29 0.167 17.5 17.34 0.9 Figure 7.8 . Suggested Operational Range of the TTA 0 10 20 30 40 50 60 70 0 0.5 1 1.5 2 2.5 V G Operational Range with a Linear Velocity Profile 53 Figure 7.9 . Suggested Operational Range of the TTA Zoomed In 7. 3 Convective Heat Transfer The non - uniform airflow was shown to differ in cooling from a u niform airflow. Specifically, the measured value of the former corresponded to a smaller velocity magnitude The difference between the inferred average flow and the actual average flow is the large distribution of heat convection that exist due to the non - uniform flow of air . The overall heat los s due to convections has nonlinearity, shown in Equation 41. (41) The non - uniform velocity distribution causes uneven heat loss along the wire, which causes an uneven wire temperature for the first - time step of heating. This causes a change i n the 0 1 2 3 4 5 6 7 8 9 10 0 0.2 0.4 0.6 0.8 1 1.2 1.4 V G Operational Range with a Linear Velocity Profile 54 convection coefficient which begins the cycle again. This will propagate the effects of the initial non - un iform velocity profile compared to the uniform velocity profile. This affects the resistance which in turn affects the . A linear velocity profile from 1 - 21 m/s over a straight piece of wire was used as an example. Figure 7.10 shows the initial heat co nvection coefficient. Figure 7.11 shows the wire temperature as it increases over time during this heating period . Figure 7.12 shows the effect of a linear velo city pr ofile compared that of a uniform velocity distribution with the same average value (11 m/s) . Figure 7. 10 . Initial Convection Coefficient 0 100 200 300 400 500 600 700 800 900 1000 0 200 400 600 800 1000 1200 1400 h(x,t) (W/mK) POSITION IN THE WIRE (mm) Initial Convection Coefficient 55 Figure 7.11 . Wire Temperatu r e Distribution with Respect to Time Figure 7.12 . Comparison of Temperature Decay Between a Non - Uniform Velocity Pro file to the Average Uniform Velocity Profile 0 50 100 150 200 250 300 350 400 0 200 400 600 800 1000 1200 1400 TEMPERATURE ( C) POSITION ALONG THE WIRE (mm) Wire Temperature Distribution with Respect to Time t=0 s t=0.1 s t=0.6 s t=0.9 s t=1.3 s 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.05 0.1 0.15 0.2 0.25 TIME (s) Comparison of Temperature Decay Between a Non - Uniform Velocity Profile to the Average Uniform Velocity Profile Nonuniform Averaged Uniform 56 8 .0 Conclusion A TTA was built and tested to measure velocity over a cell. During calibrations the TTA and the simulation had small amounts of differences. Using the simulation, it can be determined that the TTA could operate under certain non - uniform flows. Due to the large effect of axial heat conduction, the TTA could not oper ate under flows with large velocity gradients or with low air speed. During testing with a vehicle, the expected speed of air over the radiator would be approximately 7 .5 m/s (with a vehicle moving at 30 mph) or more . Additionally, the goal of the shroud w ould be to create a velocity gradient closely resembling a uniform flow, reducing the velocity gradient. This would help the flow fall into a reasonable operational ran ge. During a practical test inside a vehicle the TTA user could make measurements despite the error by using the tau value from the TTA and the adjacent cells. Similar to finding finite difference approximations for differential equations, the user could estim ate a profile of a cell based on the adjacent cells. In the future the goal would be to find a correlation between the average air speed and the average gradient of air speed for all flow types. 57 A PPENDICES 58 Appendix A . CT A Calibrations at Low Speed Figure A . 1 . CTA Probe Calibration at Low Air Speeds 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 -1 -0.5 0 0.5 1 AIR SPEED U/U max PROBE DISTANCE TO SLIT JET x/W jet CTA Probe Calibration at Low Air Speeds Series1 Series2 59 Appendix B . Calibration Curves for the Rest of the TTA Figure A . 2 . Row 1 Calibration Figure A . 3 . Row 2 Calibration y 1 = 1.6749x + 0.7117 R² = 0.9996 y 2 = 1.583x + 0.8354 R² = 0.9992 y 3 = 1.5484x + 0.8833 R² = 0.9991 y 4 = 1.7701x + 0.6702 R² = 0.9994 0 1 2 3 4 5 6 0 0.5 1 1.5 2 2.5 3 1/ (1/s) U 0.43 (m/s) 0.43 Row 1 y 1 = 1.2664x + 1.1026 R² = 0.9999 y 2 = 1.3273x + 1.0839 R² = 0.9989 y 3 = 1.3175x + 1.1005 R² = 0.9997 y 4 = 1.3612x + 1.1201 R² = 0.9997 0 1 2 3 4 5 6 0 0.5 1 1.5 2 2.5 3 1/ (1/s) U 0.43 (m/s) 0.43 Row 2 60 Figure A . 4 . Row 4 Calibration Figure A . 5 . Row 5 Calibration y 1 = 1.2078x + 1.1657 R² = 0.9997 y 2 = 1.2817x + 1.1071 R² = 0.9999 y 3 = 1.2078x + 1.1916 R² = 0.9993 y 4 = 1.2056x + 1.2085 R² = 0.9987 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 0 0.5 1 1.5 2 2.5 3 1/ (1/s) U 0.43 (m/s) 0.43 Row 4 y 1 = 1.2516x + 1.1289 R² = 0.9998 y 2 = 1.315x + 1.0902 R² = 0.9997 y 3 = 1.2747x + 1.1192 R² = 0.9991 y 4 = 1.3255x + 1.1052 R² = 0.9985 0 1 2 3 4 5 6 0 0.5 1 1.5 2 2.5 3 1/ (1/s) U 0.43 (m/s) 0.43 Row 5 61 Figure A . 6 . Row 6 Calibr ation y 1 = 1.662x + 0.7151 R² = 0.9998 y 2 = 1.7372x + 0.6259 R² = 0.9996 y 3 = 1.7503x + 0.5778 R² = 1 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 0 0.5 1 1.5 2 2.5 3 1/ (1/s) U 0.43 (m/s) 0.43 Row 6 62 Appendix C. Derivation of Equations 31 and 32 The resistivity linear coefficient to temperature (Equation 5) was inserted into Equation 16. (4 2 ) (4 3 ) Equation 41 was manipulated to Equation 43 or Equation 44 . This is to allow the equation to be separated easier, (4 4 ) (4 5 ) BC1: BC2: IC: The equation is separated into a steady state part and a transient part. (4 6 ) (4 7 ) BC1: BC2: (4 8 ) 63 After integrating and applying boundary conditions it shows that the steady state is constant which is expected wit h uniform flow (the point where the energy from heat generation balances the energy from the heat loss due to convection). (49) The transient part of the Equation 45 is evaluated below ( 50 ) BC1: BC2: IC: The transient part is broken down even further to special variable and time variable. ( 51 ) ( 5 2 ) ( 5 3 ) ( 5 4 ) (5 5 ) BC1: BC2: The boundary condition was applied to get the eigen condition . (5 6 ) The special component (50) and the time (49) component combine , their constants were merged to get . 64 (5 7 ) (5 8 ) (5 9 ) The initial condition is substituted for F(x) ( 60 ) ( 61 ) ( 6 2 ) ( 6 3 ) ( 6 4 ) ( 6 5 ) ( 6 6 ) ( 6 7 ) 65 REFERENCES 66 RE F ERENCES Boetcher, S. K. 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