THE TURBULENT BOUNDARY LAYER: EXPERIMENTAL HEAT TRANSFER WITH STRONG FAVORABLE PRESSURE GRADIENTS AND BLOWING By D. W. Kearney, R. J. Moffat and W. M. Kays Report No. HTMT-12 Prepared Under Grant NASA JGi--0"5-020-134 for The National Aeronautics and Space Administration (ACCESSION NUMBER) T RU) (CDE) V 0 ' (NASA c1 OR TMX OR NUMBER) 4pY Thermpsciences Division Deparime tof Mechanical Engineering vStanford University Stanford, California April 1970 Reproduced by NATIONAL TECHNICAL I INFORMATION SERVICE U S Departmnt f Commerce -- - - Springfield-- VA 22151 THE TURBULENT BOUNDARY LAYER: EXPERIMENTAL HEAT TRANSFER WITH STRONG FAVORABLE PRESSURE GRADIENTS AND BLOWING By D. W. Kearney, R. J. Moffat and W. M. Kays Report No. HMT-12 Prepared Under Grant NASA NGL-05-020-134 for The National Aeronautics and Space Administration Thermosciences Division Department of Mechanical Engineering Stanford University Stanford,California April 1970 fBgE0IOPAGE .- BSANK NOT FILMED. ACKNOWLEDGMENTS This research was made possible through grants from the National Science Foundation, NSF GK 2201, and the National Aeronautics and Space Administration, NGL 0,5-020-134. The authors wish to express appreciation for the interest of Dr. Royal E. Rostenbach of NSF, and Dr. Robert W. Graham of NASA Lewis Laboratories. The cooperation of R. J. Loyd throughout the experi­ mental program was a necessary factor in its success. The assistance of B. Blackwell and P. Andersen in part of the testing is appreciated. Special credit is due Miss Jan Elliott for her timely and competent handling of the publi­ cation process. iii ABSTRACT Heat transfer experiments have been carried out in air on a turbulent boundary layer subjected to a strongly accelerated free-stream flow, with and without surface transpiration. Stanton number, mean temperature and mean velocity profiles, and turbulence intensity profiles were measured along the accelerated region. The tests were conducted with favorable pressure gradients denoted by values of the acceleration dU -6 6 - parameter K( = -) of 2.0 x 10 and 2.5 x 10 . The %2dx blowing fraction, F( = PoV.PpU 0 ), ranged from 0.0 to 0.004. The flow was incompressible (U,max = 86 fps) with a moderate temperature difference, 25 F, across the boundary layer. One objective of the program was to obtain detailed heat transfer data in strong accelerations, to both increase understanding in this area and to provide a base for future prediction procedures. A second, and equally important, objective was to determine whether or not relaminarization of the boundary layer occurs at K = 2.5 x 1076 . The experimental results demonstrate that the Stanton number, as a function of enthalpy thickness Reynolds number, falls increasingly below the behavior observed in unaccelerated flows as K is increased, with or without blowing. The profile traverses show that, at the end of acceleration, the boundary layer is still fully turbulent. Further heat transfer results are presented which il­ lustrate the effects of various conditions at the start of acceleration (notably the thicknesses of the thermal and hydrodynamic layers); step-changes in blowing within the accelerated region; and an increase in the free-stream turbulence intensity. The experimental results reported here, as well as data taken by other experimenters at lower values of K , have iv been used to calculate the distribution of turbulent Prandtl number across the boundary layer. These calculations suggest­ that a correlation of turbulent Prandtl number which is use­ ful for flow over a flat plate is equally valid in accelerated flows. Using a numerical solution of the appropriate boundary layer equations, the experimental results are predicted with reasonable accuracy, including the effects of various initial conditions and free-stream turbulence intensities. v TABLE OF CONTENTS Page Acknowledgments .......... ............... iii Abstract.............. .... .... ... iv Table of Contents............... ..... vi List of Figures................ ..... viii List of Tables xi Nomenclature xii Chapter One. INTRODUCTION........ ..... .. I A. General background........ ..... .. 1 B. Report organization •.3 ........... C. Laminarization............ .... 5 D. Constant-K boundary layers. ......... 7 Chapter Two. EXPERIMENTAL SURFACE HEAT TRANSFER TO STRONGLY ACCELERATED TURBULENT BOUNDARY LAYERS .l................. 11 A. Previous experimental findings .l........ 11 B. Objectives ................. ... 14 C. Experimental program . ............. 15 C.1 Test apparatus ............... 15 C.2 Test plan ................. 16 D. Experimental results .............. 17 D.1 Effects of strong acceleration, with and without blowing . ............ 17 D.2 Response to changes in initial conditions . 21 D.3 Response to changes in boundary conditions . 23 E. Prediction of selected experimental results . 24 F. Conclusions ................... 28 Chapter Three. TEE EFFECT OF FREE-STREAM TURBULENCE ON HEAT TRANSFER TO A STRONGLY ACCELERATED TURBULENT BOUNDARY LAYER . 45 A. Introduction............ .... .. 45 B. Previous experimental work. ......... .. 46 C. Experimental program . ............. 46 D. Prediction of experimental results ....... 49 vi Page E. Conclusions . 50 Chapter Four. AN EXPERIMENTAL STUDY OF TURBULENT PRANDTL NUMBER'FOR AIR IN ACCELERATED-TURBULENT BOUNDARY LAYERS ............. 57 A. Introduction .................. 57 B. Theoretical models and previous experimental results ..................... 58 C. Sources of experimental data. .......... 60 C.1 Local shear stress and heat flux profiles . 62 C.2 Selection of experimental data ....... 65 D. Turbulent Prandtl number distribution in ac­ celerated flows, with and without blowing . 66 E. Conclusions .......... .............. .. 68 References ....................... 79 Supplements: 1. EXPERIMENTAL APPARATUS AND TECHNIQUES ........ 85 A. General description ............... 85 B. Wind tunnel ................... 86 C. Test plate .................... 87 D. Transpiration system .............. 88 E. Instrumentation ................. 89 F. Qualification of the apparatus ......... 92 F.l Transpiration energy balances ....... 92 F.2 Boundary layer energy balances. ...... 96 F.3 Flat plate turbulent boundary layer . .101 F.4 Free-stream conditions...... .... .. 104 F.5 Effect of pressure gradient....... .. 105 F.6 Roughness........... .... .. 107 G. Data reduction ................ .108 G.1 Surface heat transfer. ......... .. 108 G.2 Profile data. ........... .110 G.3 Computer programs..... ..... ...111 G.4 Uncertainty analysis. .......... .. 112 H. Test procedure........... .... .. 113 2. TABULATION OF EXPERIMENTAL DATA......... ...127 A. Organization of tables and figures...... .. 127 B. Data................ .... .. 132 3. LISTINGS OF DATA REDUCTION PROGRAMS........ .. 163 vii LIST OF FIGURES Figure Page 2.1 Schematic diagram of the test apparatus... .. 30 2.2 Traverse locations and typical velocity dis­ tribution in the test apparatus for a strong acceleration .................. 31 2.3 Experimental results of surface heat transfer in a turbulent boundary layer with a strongly accelerated free-stream flow. -, Moffat and Kays [22]...... .. ............ 32 2,.4 Comparison of experimental boundary layer heat transfer in a favorable pressure gradient . 33 2.5 Traverse data for the unblown turbulent boundary­ layer with a nominal free-stream acceleration of K=2.5 x 10-6 . Traverse symbols correspond to Fig. 2.2............ .... ..... .. 34 2.6 Experimental results of surface heat transfer in a turbulent boundary layer, with and without blowing, at K-2.55 x 10-6 . -, Moffat and Kays [22] . ................... 35 2.7 Experimental results of surface heat transfer at K-2.55 x 0-6 with various initial conditions at the start of acceleration. St = 0.639/ (PrReH) is the similarity solution for laminar wedge flows with a very thick thermal boundary layer ...................... 36 2.8 Comparison of two runs of experimental heat transfer in a strong acceleration ........ 37 2.9 Experimentalheat transfer results in a strongly accelerated turbulent boundary layer with a step­ increase in blowing ............... 38 2.10 Experimental heat transfer results in a strongly accelerated turbulent boundary layer with a step­ decrease in blowing . ......... .. 39 2.11 Correlation for the Van Driest parameter in accelerating flows with blowing ......... 40 viii Figure Page 2.12 Predictions of surface heat transfer in a turbulent boundary layer with a strongly accelerated free-stream flow .......... 41 2.13 Prediction of surface heat transfer in a turbulent boundary layer with blowing and strong acceleration .................. 42 2.14 Predictions of the effect of various initial conditions at the start of acceleration on heat transfer behavior in the turbulent boundary layer ..................... 43 3.1 Experimental heat transfer for low and high initial free-stream turbulence intensities in a strongly accelerated flow. - , Moffat and Kays [22] ................... 52 3.2 Experimental turbulence intensity profiles in the constant U region prior to acceleration. Rei~f600... .... 7................ 52 3.3 Experimental turbulence intensity profiles near the end of the accelerated region. Re H 430 . 53 3.4 Experimental velocity profiles near the end of the accelerated region. Re H 430 ....... 53 3.5 Experimental temperature profiles for low and high initial free-stream turbulence ....... 54 3.6 Comparison of'predicted and experimental heat transfer results ................ 55 3.7 Effect of initial free-stream