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`WL-TAR-96-2091
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`TURBULENT HEAT TRANSFER
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`INVESTIGATION: TURBULENCE LENGTH
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`SCALES AND TURBINE HEAT TRANSFER
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`Jason Sharp
`Pete Harris
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`3 MAY 1996
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`FINAL REPORT 1 NOVEMBER 1995--9 JULY 1996
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`Approved for public release; distribution unlimited
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`AERO PROPULSION 8: POWER DIRECTORATE
`WRIGHT LABORATORY
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`<1»;
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`4;;/fifl//£4///A
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`ICHARD B. RIVIR
`CHARLES D. MACARTHUR
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`Manager, Aerothermal Research
`Chief
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`Turbine Branch
`Turbine Branch
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`Turbine Engine Division
`Turbine Engine Division
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`Aero Propulsion & Power Directorate
`Aero Propulsion & Power Directorate
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`. HILL
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`Chief of Technology
`Turbine Engine Division
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`1 V 9 - 9 Jul 96
`Fnal
`5. FUNDING NUMBERS
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`4. TITLE AND SUBTITLE
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`3 Ma 1996
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`Turbulent Heat Transfer Investigation: Turbulence Length Scales and
`Turbine Heat Transfer
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`Jason Sharp, Pete Harris
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`7. PERFRMING ORGANIZATION NAME(S) AND ADDRESS(ES)
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`Aero Propulsion & Power Directorate
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`Wright Laboratory
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`Wright-Patterson Air Force Base, OH 45433-7650
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`9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)
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`Aero Propulsion & Power Directorate
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`This experiment was designed to study the effects of turbulent length scales on turbine blade heat transfer in
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`a steady state cascade wind tunnel. Turbine blade heat transfer is of interest due to the beneficial effects
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`engine perfonnance that can arise from improvements in turbine blade cooling and design. Turbulence in
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`this experiment was generated by means of passive grids in the upstream flow. This experiment uses a
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`steady state liquid crystal in combination with resistance heating to measure heat transfer. The liquid
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`crystals provide surface temperature data and the resistance heating in the blade can be computed from
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`allows for conclusions on the effects of length scales on heat transfer to be made. This experiment showed
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`that the turbine blade heat transfer exhibited the trends already investigated for turbulence intensity,
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`namely an increase in heat transfer with increased turbulence, the forward movement of boundary layer
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`transition and the elimination of pressure side spanwise variations. Comparison of the two different length
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`scales at the same turbulence intensity showed that the length scale evidenced no affect on transition
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`location or post-transition heat transfer. However, pre—transition heat transfer was significantly increased as
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`the integral length scale decreased from 2.78 to 0.51. This demonstrates that smaller more compact eddies in
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`the turbulent flow have a more significant impact on increasing heat transfer than do larger eddies of the
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`14. SUBJECT TERMS
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`Table of Contents
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`Abstract ............................................................................................................. .. i
`Table of Contents ........................................................................................... .. iii
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`List of Tables and Figures ............................................................................. .. iv
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`Nomenclature List........................................................................................... .. V
`Introduction ..................................................................................................... .. 1
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`Theoretical Background ........................................................................ .. 1
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`Experimental Background .................................................................... .. 1
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`Experimental Methods ................................ ..I ................................................ .. 5
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`Experiment Setup .................................................................................. .. 5
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`Experiment Procedure ......................................................................... .. 11
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`Uncertainty Analysis ........................................................................... .. 12
`Results and Discussion ................................................................................. .. 13
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`”Clean” Tunnel Configuration (No Turbulence Grid) ..................... .. 14
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`2 3/8 in Grid Configuration ................................................................ .. 16
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`1 / 2 in Grid Configuration................................................................... .. 18
`Overall Discussion ............................................................................... .. 19
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`Conclusions ................................................................................................... .. 20
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`Recommendations ......................................................................................... .. 20
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`Acknowledgments ........................................................................................ .. 21
`References ...................................................................................................... .. 22
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`Appendix A: Heat Transfer Graphs ............................................................ .. 23
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`Appendix B: Heat Transfer Data Sheets ..................................................... .. 32
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`Appendix C: Length Scale Data Sheets ....................................................... .. 34
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`Appendix D: Uncertainty Analysis ............................................................. .. 43
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`List of Tables and Figures
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`Figure 1: Taylor-Gortler Vortices .................................................................. .. 2
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`Figure 2: Cascade Wind Tunnel Schematic ................................................. .. 7
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`Figure 3: Test Section Diagram ..................................................................... .. 7
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`Figure 4: Traversable Test Probe .................................................................. .. 8
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`Figure 5: Test Blade Setup ............................................................................. .. 8
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`Figure 6: Grid of 2 3/8 in Diameter Bars ..................................................... .. 9
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`Figure 7: Gird of 1/2 in Diameter Bars ...................................................... .. 10
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`Figure 8: Uncertainty Analysis ................................................................... .. 13
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`Figure 9: Stagnation Point comparison ...................................................... .. 15
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`Figure 10:Clean Tunnel Comparison .......................................................... .. 16
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`Figure 11:Heat Transfer Comparison .......................................................... .. 17
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`Figure 12:Grid Comparison ......................................................................... .. 19
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`Table 1: List of Equipment ........................................................................ .. 10
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`Table 2: Clean Tunnel Flow Comparison................................................. .. 14
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`Table 3:
`2 3/8 in Grid Comparison ........................................................... .. 16
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`Table 4: 1/2 in Grid Comparison .............................................................. .. 18
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`Page 8 of 54
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`B1
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`Nomenclature List
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`- air inlet angle, degrees
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`- air exit angle, degrees
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`- axial chord length, in
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`- degrees Celsius
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`- voltage
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`- zero velocity voltage
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`- heat transfer coeflicient, W/m2K
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`- electric current, amps
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`- degrees Kelvin
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`- thermal coefficient for air, W/mK
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`- kilogram
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`- length of gold sheet, in
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`- Newton, kg m/52
`- Nusselt number
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`- measure of resistance
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`— resistance per square
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`- pitch distance between turbine blades, in
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`- atmospheric pressure, psi
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`- pounds per square inch
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`- heat transfer flux, W/m2
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`- convective heat transfer flux, W/m2
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`- conductive heat transfer flux, W/m2
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`- autocorrelation function
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`- resistance per square of gold at 357° C, Ohm/SQ
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`- Reynolds number
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`— surface arc length, in
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`- fi'ee-stream air temperature
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`- surface temperature of yellow liquid crystal band, C
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`- longitudinal turbulence intensity (See Equation ?)
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`- local velocity fluctuation
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`- Watts
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`- width of gold film, in
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`— emmissivity
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`- Stefan-Boltzman constant, W/m2K4
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`— viscosity of air, Ns/m2
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`-=;qm'ov><g€(:c‘>=-§5*l_>:-lg‘-]_r/’1m="(7§I‘v<30 N
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`Page 9 of 54
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`- dynamic pressure, torr
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`- microscale turbulent length scale, m
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`— experimental uncertainty in parameter x
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`Page 10 of 54
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`Introduction
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`Theoretical Background
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`The heat transfer on turbine blades directly affects the way engine designers can develop
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`new turbines to allow for higher turbine inlet temperatures in engines. A better understanding of
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`turbine blade heat transfer allows for better and more efficient cooling techniques to be
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`developed. With more eflicient cooling, increases in the turbine inlet temperature can be made
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`without advances in materials technology. Since this has a direct and beneficial effect on the
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`engine cycle design, reflected in greater specific thrust and lower thrust specific fiiel consumption,
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`this area is of great interest to the gas turbine engine industry. If a greater understanding of the
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`heat transfer on such blades can be reached, new and better designs can be made.
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`The efiect of turbulence on heat transfer has been known for some time but has yet to be
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`physically modeled with great success. There are several parameters to describe the turbulent
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`flow that are used in this study. The first of which is turbulence intensity. Turbulence intensity in
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`the axial direction, noted as T“, is one ofthe parameters of interest in this investigation.
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`Turbulence intensity is a method of measuring non-dimensional turbulence in a single direction. It
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`is the fluctuating velocity expressed as a percentage of the non-fluctuating velocity. This is
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`142
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`7L= U
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`[1]
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`Roach developed correlations for predicting turbulence intensity generated by passive
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`grids (Roach 82-92). For a square mesh of square grids this correlation is Reynolds number
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`independent. This correlation is given as:
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`Page 11 of 54
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`[2]
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`ise heat
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`These may be
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`ignation point
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`iter-rotating
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`1 impinging
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`vortices bring
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`igers of
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`such vortices
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`ur at low
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`from forming.
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`‘ransfer
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`is a correlation constant which for square mesh of square bars is 1.13, cl is the
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`ance or bar diameter, and x is the distance downstream of the grid (Roach 84-
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`ion allows for the prediction of turbulence intensity or for this study the distance
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`JCS a desired turbulence intensity.
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`iarameters of interest are the micro and macro or integral length scales. The
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`It may be considered a measure of the average length
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`:h are primarily the method in which turbulence energy is dissipated (Roach 85).
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`described by the equation:
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`.1_:-_1 “(Tl
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`2U
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`(Roach, 85) [3]
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`.(T) represents the autocorrelation function, a correlation of each point to all
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`time. The second derivative of this correlation is used to determine the
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`301156 of this function.
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`‘al length or macro scale may be considered to be a measure of the largest eddy
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`.-nt field (Roach, 85). This is found by determining the area under the
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`Jrve as it goes from 1 to 0. This area is determined by integrating this curve as
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`re macro length scale is defined as:
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`A, = UJ’ R( T)dT
`0
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`mination of the free stream velocity by the pitot probe is done via the
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`Page 12 of 54
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`10
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`The heat transfer coefficients are of direct interest to this investigation. For this study the
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`blade will be heated by resistance heating to provide a surface temperature higher than the
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`surrounding air temperature. This temperature difference will in turn drive convective heat
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`transfer to occur. The amount of resistance heating can be calculated as follows:
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`q =
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`I ZR"
`[61
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`W
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`In this equation q” is the heat transfer from the blade, I is the current applied to the blade, R”35.7 is
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`the resistance per square of the gold, and w is the width of the gold layer. This represents the
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`total heat transfer from the blade.
`In order to determine the convective heat transfer which is the
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`target of this investigation the conductive and radiative nodes of heat transfer must be accounted
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`for. Since, the construction of the turbine blade is designed to minimize conduction by using a
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`highly insulative closed-cell foam core, that mode is assumed to be negligible. The radiative mode
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`is calculated by the following equation:
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`qR = w(T;L — 1:)
`[7]
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`where T is the absolute temperature in Kelvin for both cases. By subtracting these modes from
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`the total heat transfer the conductive heat transfer can be determined.
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`612 = 9" - 60(T£‘c - T..;‘)— (IL
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`Once the conductive heat flux is determined the conductive heat transfer coefficient can be
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`Page 13 of 54
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`The next step in the process is to non-dimensionalize this coefiicient. This can be reduced
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`to either the Stanton number or Nusselt number for reporting. These two are determined as
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`follows:
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`11
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`it
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`St =
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`pVmc,,
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`[10]
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`hB
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`Nu: k ”
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`[11]
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`The Nusselt number can be divided fiirther by the square root of Reynolds number to remove any
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`Reynolds number dependency in laminar flow regions.
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`Experimental Background
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`This investigation builds on work previously performed at both the United States Air
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`Force Academy and the University of California at Davis. This work includes investigating the
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`effects of turbulence intensity on heat transfer as well as mapping the turbulence generated by
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`grids. Baughn et al investigated the effect of turbulence intensity in a simultaneous study at
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`UCDavis and USAFA. Their results can be summarized as the turbulence intensity is increased
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`from 1% to 10% the heat transfer level increases, the suction side boundary layer transition moves
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`upstream and the spanwise variation on the pressure side disappears (Baughn, et al 12). Baughn
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`et al also note that these results compare favorably to rotating tests performed. This helps
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`address the concern that cascade tunnels do not address rotational effects (Baughn, et al l2).
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`The study of turbulent flow quality produced by grids conducted last semester by Duncan
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`and Peterson confinned that the work done by Roach held true for the Cascade Wind Tunnel.
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`The results of that investigation concluded that the correlation given by Roach worked well for
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`passive generation such as will be used in this investigation.
`It also noted that the use of a grid
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`Page 14 of 54
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`passive generation such as will be used in this investigation.
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`It also noted that the use of a grid
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`perpendicular to the flow instead of parallel to the cascade had negligible effects on the turbulence
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`generated (Duncan and Peterson 18-l9). That research used a round bar generation grid and thus
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`the correlation coefficient is Reynolds number dependent as shown in Roach (Roach 86). This
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`research tests a square mesh of square bars which Roach found to be Reynolds number
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`independent in the range of interest (Roach 87).
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`With the effect of turbulence intensity investigated by Baughn et al and the effectiveness of
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`generating turbulence by grids established by Roach and confirmed for the USAFA tunnel by
`Duncan and Peterson, this investigation establishes a relationship between length scales and heat
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`transfer. By using a turbulence intensity level of 10%, the results of this investigation can be
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`compared to Baughn et al, to analyze the effects of length scales. The objective of this project is
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`to determine if a relationship exists between turbulent heat transfer and micro and macro length
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`scales. Heat transfer is tested at 10% turbulence intensity. Additionally, a clean tunnel test is
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`performed for comparison. Length scale comparisons will allow for a better understanding of
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`turbulent heat transfer. Length scale investigations will provide data for updating turbulent CFD
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`codes to include length scale eifects. The investigation also looks at passive turbulence
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`generation, comparing the results to the correlations reported by Roach (Roach 82-92).
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`Experimental Methods
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`Experiment Setup
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`The experiment takes place in the USAF Academy Aeronautics Lab Cascade Wind
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`Tunnel. The Cascade Wind Tunnel is designed to place a linear cascade of turbine blades in a
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`flow which will simulate the flow over the normally rotating turbine blades. The turbines in the
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`Page 15 of 54
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`turbine around the 3rd or 4th stage with Reynolds numbers around 80,000. The tunnel is a closed
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`loop system with a heat exchanger to provide for temperature control.
`In the test section are
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`seven test blades with the end walls simulating two more blade surfaces. This setup is shown in
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`Figure 1. The blades in the test section very closely match the Langston geometry. This
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`geometry can be seen in Langston et al, 1977 (Langston 23).
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`The test section has a test probe which traverses parallel to the blade plane. This probe
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`contains a hot film sensor, pitot-static probe and a wedge probe, which is not used in this study.
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`The pitot-static probe is connected to a pressure transducer which outputs to a torr meter as well
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`as the IPA 100. The hot film anemometer outputs to the [FA 100 and HP 3852A. Additionally a
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`K type thermocouple outputs to the IFA 100 allowing for temperature measurements. Data from
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`the [FA 100 and HP 3852A are input to the P90 computer which is controlled by TV3 software,
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`which was written in the Aero Department. This setup is designed to collect the flow data. This
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`can be seen in Figure 2 and Figure 3.
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`Page 16 of 54
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`Constant Speed Fan
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`Heat Exchanger
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`Rolator Blades
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`Settling Chamber
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`Turbulence G rid
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`Test Blades
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`Test Section
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`Hot Film Anemometer
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`Pitot-static Probe
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`K-type Thermocouple
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`Turbine Blade
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`Assembly
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`Figure 3: Test Section Diagram
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`Turbulenca
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`G”‘‘
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`IFA 100
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`HP 3352A
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`Page 17 of 54
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`Outputs: HP JISZA undll-‘A100
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`Figure 4: Traversable Test Probe
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`The setup for collecting heat transfer data centers on the test blade. The test blade is
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`located in the center of the cascade.
`It is made of closed cell polystyrene, which is covered with
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`Super 77 aerosol adhesive and a thin gold film with a resistance per square of 2.512 ohm/sq. This
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`gold film is then covered with black paint and sprayed with 35W1 liquid crystals. The liquid
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`crystals are active in the 35-3 6° Celsius range, with the yellow band indicating 35.7° Celsius. The
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`gold acts as a conductor and provides resistance heating to the blade. Two electrodes at the
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`trailing edge are connected to a DC power supply providing up to 5 amps. A multimeter is placed
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`in series with the power supply and the blade to provide current readings. The entire test blade
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`setup can be seen in Figure 4. This test blade allows for surface temperature a current readings to
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`be taken which then allo