TRANSITION IN BOUNDARY LAYER FLOWS by IAIN D GARDINER, BSc (Hons) Department of Mechanical and Industrial Engineering Thesis submitted to the C.N.A.A. for the Degree of Doctor of Philosophy March 1987 o 4' Dundee College of Technology Boundary Layer Wind Tunnel Facility DECLARATION I hereby declare that the following work has been composed by myself and that this dissertation has not been presented for any previous award of the C.N.A.A. or any other University. Iain D Gardiner 11 Transition in Boundary Layer Flows by Iain D Gardiner Abstract An experimental investigation of transition in boundary layer flows under the influence of various freestream conditions is described. Velocity profiles are obtained automatically by means of a stepper- motor driven traverse mechanism which carries a hot wire probe connected to a constant temperature anemometer and associated instrumentation. This was achieved by use of a data acquisition and control facility centred around a microcomputer with a Eurocard rack mounted extension. The automatic boundary layer traverse is software controlled and the data obtained is stored in a disc file for subsequent analysis and graphical display. As an integral part of this facility a successful method of obtaining reliable intermittency values from a hot wire signal was developed. The influence of freestream turbulence and pressure gradient upon transition within a boundary layer developing on a flat plate is elucidated by a series of controlled experiments. From the data accumulated, the concept of statistical similarity in transition regions is extended to include moderate non-zero pressure gradients, with the streamwise mean intermittency distribution described by the normal distribution function. An original correlation which accounts for the influence of freestream turbulence in zero pressure gradient flows, and the combined influence of freestream turbulence and pressure gradient in adverse pressure gradient flows, on the transition length Reynolds number Rg, is presented. (The limited amount of favourable pressure gradient data precluded the extension of the correlation to include favourable pressure gradient flows). A further original contribution was the derivation of an intermittency weighted function which describes the development of the boundary layer energy thickness through the transition region. A general boundary layer integral prediction scheme based on existing established integral techniques for the laminar and turbulent boundary layers with an intermittency modelled transition region, has been developed and applied successfully to a range of test data. iii COURSES & CONFERENCES ATTENDED DATE TITLE & LOCATION CONTENT 11-13 April 1984 "Hot Wire Anemometry" A series of lectures and Cranfield Institute of 'hands on' experiments Technology giving valuable experience on both practical and theoretical aspects of hot wire anemometry techniques. 2-30 May 1984 "New Technology Applications A series of evening in Manufacturing Industry" lectures and Dundee College of demonstrations relating Technology to principles of digital control. 11-13 Sept 1985 Conference on "Developments The paper "A low cost in measurements and data acquisition instrumentation in system based on a BBC Engineering" Hatfield microcomputer" by Polytechnic Milne, J S, Fraser, C J and Gardiner, I D was presented by J S Milne. 7-10 April 1986 Second International The paper "Application Conference on of a microcomputer for "Micro-computers in control, data Engineering: Development acquisition and and Application of Software" modelling in University College of transitional boundary Swansea layer studies" by Fraser C J , Milne J S and Gardiner, I D was presented by C J Fraser. IV ACKNOWLEDGEMENTS I wish to thank my supervisors, Mr J S Milne and Dr C J Fraser, who at all times throughout the duration of this project have willingly proferred their advice upon every aspect of the work described herein. My gratitude extends to the technical and secretarial staff of the Department of Mechanical Engineering for their valuable friendship over the past three years and also to Liz for her efforts in the typing of this thesis. Finally, the financial support of the Scottish Education Department during the period 1983-86 is acknowledged. v NOMENCLATURE Symbol Function Connotation Units a - Tani’s profile parameter - C - constant in the law of the wall - Cf - local skin friction coefficient - Cp - Pressure coefficient - < o CD H 12 or H Shape factor - h 32 6* % Shape factor - k - Von Karman constant in law of the wall - 0.41 - Rx X Uoo Length Reynolds Number - \) G 8 R a Q Transition length Reynolds Number - A Uoo Transition length Reynolds RA Number - V Re 0 Uoo Momentum thickness Reynolds - V Number R6* 6 * Uoo displacement thickness Reynolds V Number Tu x 100 freestream turbulence intensity % 'U o o u local mean velocity m/s U co freestream velocity m/s freestream velocity at leading u0 edge m/s Wall friction velocity m/s UT + dimensionless velocity - U u / /UT vi Symbol Function Connotation Units ✓ U , V , w fluctuating Velocity components in x, y, z directions respectively m/s X location of the 50% intermittency point mm X streamwise co-ordinate mm y transverse co-ordinate mm z spanwise co-ordinate mm y+ dimensionless y co-ordinate - local intermittency - Y mean 'near wall' intermittency - Y 6 boundary layer thickness at u = 0.995 Uoo mm CO displacement thickness mm 6* /(- u/u„) 0 (i - u/u^ ay momentum thickness mm j k < oo 6** Energy thickness mm X U/Uoo X transition normalising length 62 dUco Pohlhausen pressure parameter - xp V dx xe e2 dUoo modified Pohlhausen/Thwaites V dx parameter V fluid dynamic viscosity kg/ms V fluid kinematic viscosity m 2/s p air density kg/m3 TT Coles "wake" profile parameter - Q Standard deviation of mean intermittency distribution mm vii Symbol Function Connotation Units To Wall shear stress transition normalising r x~xs co-ordinate X X - X transition normalising c ----- co-ordinate a X - xs transition normalising n xe - XS co-ordinate Thwaites relationships ^ 1 ( ^ 0) between £1 and Aq Subscripts e - related to the end of transition i - denoting initial conditions l - relating to transition length L - related to the laminar region o - denoting conditions at the leading edge s - related to the start of transition t - related to the transition region T - related to the turbulent region Other symbols, not noted here, are defined within the text. viii CONTENTS Page No Frontispiece i Declaration ii Abstract iii List of Courses and Conferences attended iv Acknowledgements v Nomenclature vi Contents ix Statement of Objectives xiii Chapter 1 Introduction 1.1 Early experiments 1 1.2 Stability of laminar flow 2 1.3 Transition to turbulence 3 1.4 Practical significance of transition 6 1.5 Prediction of transition onset 7 1.6 Boundary layer development through transition (present investigation) 11 1.7 Microcomputer involvement 15 Chapter 2 Experimental Facilities 2.1 Wind tunnel test facility 16 2.2 The boundary layer plate 10 2.3 Preliminary tests and tunnel modifications 19 2.4 Turbulence generating grids 21 2.5 Freestream pressure gradients 22 2.6 Hot wire instrumentation 23 2.7 Probe linearisation 25 2.8 Intermittency Measurement 25 2.9 Measurement of Cf using a Preston tube 29 IX Page No Chapter 3 Microcomputer Data Acquisition & Control 3.1 Introduction 49 3.2 Transmission of data 50 3.3 Data acquisition 51 3.4 Choice of Microcomputer 55 3.5 Accessing signals on the BBC micro 57 3.6 Accessing singal using the Beebex Eurocard Extension 60 3.7 Control of the hot wire probe position 62 3.8 Conditioning of signals to suit the Beebex system 64 3.9 Development of Data Acquisition and Control software 68 Chapter 4 Data Reduction and Theoretical Considerations 4.1 Introduction 81 4.2 Reduction of Laminar Mean velocity profiles 81 4.3 Reduction of Turbulent mean velocity profiles 82 4.4 Estimation of errors in boundary layer integral thicknesses 88 4.5 Approach to equilibrium and low Reynolds number effects 90 4.6 Transitional mean velocity profiles 93 4.7 Determination of start and end of transition 95 4.8 Flow two dimensionality 96 Chapter 5 Development of Data Acquisition, Control and Data Reduction Package 5.1 Introduction 104 5.2 Running the software package 105 5.3 Special features of the package 107 x Page No Chapter 6 Details of Experiments and Discussion of Results 6.1 Introduction 111 6.2 Description of experimental flows 111 6.3 Flow measurements 117 6.4 Description of transition process 118 6.5 Start of transition - Correlations 120 6.6 Statistical similarity of transition regions 124 6.7 The effect of freestream turbulence on transition length (zero pressure gradient) 127 6.8 Combined effect of freestream turbulence and adverse pressure gradient on transition length 131 6.9 The effect of favourable pressure gradient on transition length 133 6.10 Correlating the combined influence of freestream turbulence and pressure gradient on transition length 134 Chapter 7 Prediction of the Transition Boundary Layer Development 7.1 Introduction 170 7.2 Transition model 172 7.3 The computational model 175 7.4 Model performance 179 Conclusions 180 Suggestions :for future work 184 Bibliography 186 xi APPENDICES APPENDIX 1 - Experimental uncertainty in boundary layer integral thicknesses 195 APPENDIX 2 - Microcomputer based system for setting up the DISA 55M25 Lineariser 202 APPENDIX 3 - Derivation of 8^* 208 APPENDIX 4 - Integral prediction methods for laminar and turbulent boundary layers 212 APPENDIX 5 - Software listings 224 xii STATEMENT OF OBJECTIVES 1) To review the literature on the current conceptional understanding of the transition process. 2) To improve the flow in the existing boundary layer wind tunnel test facility. 3) To investigate the suitability of a microcomputer based system with analogue-to-digital conversion facilities for the acquisition of data, from a hot wire signal, in laminar, turbulent and transitional boundary layers.