HEAT TRANSFER to a FULL-COVERAGE FILM-COOLED SURFACE with 3O” SLANT-HOLE INJECTION
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~NASACONTRACTOR ic REPORT HEAT TRANSFER TO A FULL-COVERAGE FILM-COOLED SURFACE WITH 3o” SLANT-HOLE INJECTION M. E. Crawford, W. M. Kuys, ., I and R. J. Moffut -: / ” Prepared by STANFORD UNIVERSITY Stanford, Calif. 94305 for Lewis Research Center NATIONAL AERONAUTICSAND SPACE ADMINISTRATION l WASHINGTON, D. C. l DECEMBER1976 - 1. Report No. 1 2. G overnment Accession No. I 3. IbL.. r NASA CR -2786 4. Title and Subtitle 5. Report Date HEAT TRANSFER TO A FULL-COVERAGE FILM-COOLED Dx.emhPr 1976 SURFACE WITH 30’ SLANT-HOLE INJECTION 6. Performing Organization Code 7. Author(s) 8. Performing Organization Report No. M. ,E. Crawford, W. M. Kays, and R. J. Moffat HMT-25 10. Work Unit No. 4. Performing Organization Name and Address Stanford University 11. Contract or Grant No. Stanford, California 94305 NAS3-14336 13. Type of Report and Period Covered 12. Sponsoring Agency Name and Address Contractor Report National Aeronautics and Space Administration 14. Sponsoring Agency Code Washington, D.C. 20546 15. Supplementary Notes Final Report. Project Manager, Raymond S. Colladay, Fluid System Components Division, NASA Lewis Research Center, Cleveland, Ohio 16. Abstract Heat transfer behavior was studied in a turbulent, boundary layer with full-coverage film cooling through an array of discrete holes and with injection 30’ to the wall surface in the downstream direction. Stanton numbers were measured for a staggered hole pattern with pitch-to-diameter ratios of 5 and 10, an injection mass flux ratio range of 0.1 to 1.3, and a range of Reynolds num- ber Re, of 1. 5X105 to 5X106. Air was used as the working fluid, and the mainstream velocity varied from 9.8 to 34.2 m/set (32 to 112 ft/sec). The data were taken for secondary injection temperatures equal to the wall temperature and also equal to the mainstream temperature. The data may be used to obtain Stanton number as a continuous function of the injectant temperature by use of linear superposition theory. The heat transfer coefficient is defined on the basis of a mainstream-to-wall temperature difference. This definition permits direct comparison of per- formance between film cooling and transpiration cooling. A differential prediction method was developed to predict the film cooling data base. The method utilizes a two-dimensional boundary layer program with routines to model the injection process and turbulence augmentation. The program marches in the streamwise direction, and when a row of holes is encountered, it stops and injects fluid into the boundary layer. The turbulence level is modeled by algebraically augmenting the mixing length, with the augmentation keyed to a penetration distance for the in- jected fluid. Most of the five-hole diameter data were successfully predicted. 17. Key Words (Suggested by Author(s) ) 18. Distribution Statement Boundary layer Unclassified - unlimited Film cooling STAR category 34 Heat transfer .: Turbulence 19. Security Classif. (of this report) 20. Security Classif. (of this page) 21. No. of Pages 22. Price’ Unclassified Unclassified 245 $8.00 _. --. *.For sale by the National Technical Information Service, Springfield, Virginia 22161 - . ‘:. Table of Contents Page Chapter 1. INTRODUCTION ..................... 1 1.1 Background for the Problem .............. 1 1.2 Full-Coverage Film Cooling .............. 2 1.3 Heat Transfer with Film Cooling ........... .5 1.4 Literature Review .................. 7 1.4.1 Experimental Works .............. 7 1.4.2 Analytical Works ............... 9 1.5 Objectives for the Present Research ......... 11 Chapter 2. EXPERIMENTAL FACILITY AND METHODOLOGY ........ 13 2.1 Discrete Hole Rig .................. 13 2.1.1 Primary Air Supply System ........... 13 2.1.2 Secondary Air Supply System .......... 14 2.1.3 Test Plate Electrical Power System ...... 14 2.1.4 Preplate/Afterplate Heating System ...... 14 2.1.5 Heat Exchanger Cooling Water System ...... 15 2.2 The Test Surface ................... 15 2.2.1 Discrete Hole Test Section .......... 15 2.2.2 Preplate and Afterplate ............ 16 2.3 Rig Instrumentation and Measurement ......... 17 2.3.1 Temperature .................. 17 2.3.2 Pressure ................... 18 2.3.3 Test Plate Power ............... 18 2.3.4 Afterplate Heat Flux ............. 18 2.3.5 Secondary Air Flow Rate ............ 18 2.3.6 Velocity and Temperature Profiles ....... 19 2.4 Formulation of the Heat Transfer Data ........ 19 2.4.1 Radiation'Loss ................ 20 2.4.2 Conduction Loss ................ 21 2.4.3 Secondary Air Exit Temperature ........ 22 2.4.4 Convection Between Plate and Secondary Air . 23 2.4.5 Energy Balance Closure ............ 24 iii - .-- _... - __.. Page 2.5 Rig Qualification . 2.6 2.5.1 Hydrodynamics . , . t . 26 2.5.2 Heat Transfer . .'. .' . 27 Chapter 3. EXPERIMENTAL DATA . 34 3.1 Types of Data. 34 3.2 Description of the Stanton Number Data . 34 3.3 Stanton Number Data . 37 3.3.1 Thick Initial Boundary Layer with Heated Starting Length . 38 3.3.2 Thick Initial Boundary Layer with Unheated Starting Length . 40 3.3.3 Thick Initial Boundary Layer with Change in Mainstream Velocity . '. 43 3.3.4 Thin Initial Boundary Layer with Heated Starting Length . 45 3.4 Spanwise Velocity and Temperature Profiles . 47 Chapter 4. ANALYSIS OF THE DATA ................ 78 4.1 Effects of Full-Coverage Film Cooling on Stanton Number ....................... 78 4.1.1 Injectant Temperature and Blowing Ratio ... 78 4.1.2 Upstream Initial Conditions ......... 80 4.1.3 Hole Spacing ................. 81 4.2 Correlation of the Stanton Number Data ....... 81 4.3 Development of a Prediction Model ........... 83 4.3.1 Injection Model ............... 85 4.3.2 Turbulence-Augmentation Model ........ 89 4.4 Numerical Prediction of the Data .......... 93 iV Page Chapter 5. SUMMARYAND RECOMMENDATIONS. .......... 109 Appendik I. STANTON NUMBER DATA ............... 112 II. SPANWISE PROFILE DATA .............. 181 III. STANTON NUMBER DATA REDUCTION PROGRAM. 206 IV. ON THE HEAT TRANSFER BEHAVIOR FOR THE INITIAL FILM-COOLING ROWS . 223 v. ON AN ASYMPTOTIC STANTON NUMBER AND JET COALESCENCE . 226 VI. SHEAR STRESS AND MIXING-LENGTH PROFILES . 228 References........................... 230 List of Figures Figure Page 1.1 Full-coverage film-cooled turbine blade and blade cavity . 2 1.2 Hole-pattern and heat transfer area for slant-hole in- jection test surface . 4 2.1 Flow schematic of wind tunnel facility, the Discrete Hole Rig . 29 2.2 Photograph of Discrete Hole Rig . 30 2.3 Photograph of slant-hole injection test surface, showing staggered hole array . 30 2.4 Cross-sectional drawing of the discrete hole test sec- tion........................... 31 2.5 Close-up photograph of discrete hole test surface . 32 2.6 Photograph of test section cavity showing secondary air delivery tubes . 32 2.7 Configurations for tunnel topwall and boundary layer trip: #l is for thick initial boundary layer; 82 is for thin initial boundary layer . 33 3.1 Upstream velocity profile for initially high Re62 , heated starting length runs (see Section 3.3.1). 50 3.2 Upstream temperature profile for initially high Re62 , heated starting length runs (see Section 3.3.1). 51 3.3 Stanton number data versus non-dimensional distance along surface for initial conditions in Figures 3.1 and 3.2, to study effects of heated starting length . 52 3.4 Data fromFigure 3.3, replotted versus enthalpy thickness Reynolds number . 53 3.5 Upstream velocity profiles (P/D = 5, 10) for initially high Re62 s unheated starting length runs (see Section 3.3.2).......................... 54 3.6 Stanton number data (P/D = 5) versus non-dimensional dis- tance along surface for initial conditions in Figure 3.5, to study effects of blowing ratio . , . 55 Vi Figure Page 3.7 8 = 1 data from Figure 3.6, replotted versus enthalpy thickness Reynolds number . , . , . ,.. 56.. 3.8 8 = 0 data from Figure 3.6, replotted versus enthalpy thickness Reynolds number . 57‘ 3.9 Stanton number data (P/D = 10) versus non-dimensional .dis- tance along surface for initial conditions in Figure 3.5, to study effects of change in hole spacing . + . 58; 3.10 Data from Figure 3.9, replotted versus enthalpy thickness Reynolds number . ..59 3.11 Upstream,velocity profile for initially high Re62 , un- heated starting length runs (see Section 3.3.3) . 6d 3.12 Stanton number data versus non-dimensional distance .along -, surface for initial conditions in Figure 3.11, to study effects of change in U,. , . , . , . , , 61 3.13 Data from Figure 3.12, replotted versus enthalpy thickness Reynolds number . , . , . 62 3.14 Upstream velocity profile for initially high Re62 , un- ,heated starting length runs (see Section 3.3.3) . 63 3.15 Stanton number data versus non-dimensional distance along surface for initial conditions in Figure 3.14, to study effects of change in U, . , . , . , . 64 3.16 Data for Figure 3.15, replotted versus enthalpy thickness Reynolds number , . , . , , . , . , . 65: 3.17 Upstream velocity profiles (P/D = 5, 10) for initially low Reg2 , heated starting length runs (see Section 3.3.4).,. , . , . ? . 66 3.18 Upstream temperature profiles (P/D = 5, 10) for initially low Reg2 , heated starting length runs (see Section 3.3.4)........................... 67 3.19 Stanton number data (P/D = 5) versus non-dimensional,dis- ..I tance along surface for initial conditions in Figures 3.17 and 3.18, to study effects of thin initial momentum boundary layer , . , . , , . , . 68 3.20 Data from Figure 3.19, replotted,versus enthalpy thick- '.' ness Reynolds number . .,. .. 69 Vii Figure Page 3.21 Stanton number data (P/D = 10) versus non-dimensional distance along surface for initial conditions in Fig- ures 3.17 and 3.18, to study effects of change in hole spacing..........................70 3.22 Data from Figure 3.21, replotted versus enthalpy thick- ness Reynolds number . 71 3.23 Velocity profiles downstream of ninth blowing row (see Figure 3.1 for boundary layer initial conditions) .