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And Three-Dimensional Disturbances in a Blasius Boundary Layer 0 7 2000 Receptivity and Growth of Two- and Three-Dimensional Disturbances in a Blasius Boundary Layer by Rudolph A. King B.S.M.E., Old Dominion University (1987) M.S., Old Dominion University (1991) Submitted to the Department of Aeronautics and Astronautics in partial fulfillment of the requirements for the degree of Doctor of Philosophy MASSACHUSETTSINSTITUTE OF TECHNOLOGY at theI 0 7 2000 MASSACHUSETTS INSTITUTE OF TECHNOLOGY 2 February 2000 © Rudolph A. King, 1999. All rights reserved. The author hereby grants to MIT permission to reproduce and distribute publicly paper and electronic copies of this thesis document in whole or in part. Author. Department of Aeronautics and Astronautics November 18, 1999 Certified by: Kenneth S. Breuer Visiting Associate Professor Thesis Supervisor Certified by. Mark Drela A7 Associate Professor Committee Member Certified by Ian A. Waitz EZ Associate Professor Committee Member Certified by Richard W. Wlezien Program Manager, Tactical Technology Office, DARPA Committee Member Accepted by Professor Nesbitt' W. Hagood IV Chairman, Department Committee on Graduate Students Receptivity and Growth of Two- and Three-Dimensional Disturbances in a Blasius Boundary Layer by Rudolph A. King Submitted to the Department of Aeronautics and Astronautics on November 18, 1999, in partial fulfillment of the requirements for the degree of Doctor of Philosophy Abstract In this experimental study, acoustic receptivity was examined for a Blasius bound- ary layer formed on a flat plate. Non-localized surface roughness, 2-D and oblique, were considered for various roughness heights and acoustic wave amplitudes. The receptivity sites (surface roughness) had a well defined wavenumber spectrum with a fundamental wavenumber of km. A planar downstream-traveling acoustic wave was created to temporally excite the flow near the resonance frequency, wis, of an unsta- ble eigenmode corresponding to kt, = km. Branch I was selected to occur near the streamwise center of the roughness to maximize the receptivity. The range of acoustic forcing levels c and roughness heights Ah examined resulted in a linear dependence of receptivity coefficients; however, the larger values of the combination C - Ah resulted in subsequent nonlinear development of the Tollmien-Schlichting (T-S) wave. The measured receptivity was seen to increase markedly with increasing obliqueness of the surface roughness patterns. Detuning of the 2-D and oblique disturbances was investigated by varying the streamwise wall-roughness wavenumber a, and measur- ing the T-S response. Oblique transition was also investigated by exciting a pair of oppositely-oriented oblique Orr-Sommerfeld modes (w/wts, ±/#3//3) = (1, ±1). For small values of e-Ah, a peak-valley structure corresponding to a spanwise wavenumber of 20,, was observed. The maximum streamwise velocity fluctuations, ut(fo), occur at peak locations as expected. For the largest value of c - Ah, significant mean-flow distortion was observed in the mean streamwise velocity. Large spanwise velocity gradients, IdU/d(I, exist between peaks and valleys and appear to generate a sec- ondary instability. The maximum values of ut no longer occur at peak locations of the stationary structure but at locations of spanwise inflection points. The magnitude of Ut scales with |dU/d(|. A nonlinear interaction of two nonstationary modes was conjectured as a possible mechanism for the enhancement of the streak amplification rate. Thesis Supervisor: Kenneth S. Breuer Title: Visiting Associate Professor 3 MMR111111P - MMI RN."PRM- M 011'"11Rims" 'I M1I M"IPW Acknowledgments The author is sincerely grateful to Professor Kenneth S. Breuer for the technical support and guidance he provided as thesis supervisor. The technical discussions with researchers in the Flow Physics and Control Branch at NASA Langley Research Center contributed significantly to the work. I would like to thank Jerome Harris for providing wind-tunnel technician support throughout the experimental study. The support of Gregory K. Draughon of the Microelectronics & Technical Support Section in the manufacturing of the roughness patterns was greatly appreciated. The author is also thankful to local management, William L. Sellers III and Michael J. Walsh, for providing the resources necessary to complete the study I am forever grateful to my parents, Clifford and Christophine King, and my brothers and sisters for their continual support and encouragement during my grad- uate study. 4 M" -, Rim m Contents 1 Introduction 23 1.1 Background .... ........ ......... ........ ... 23 1.1.1 Brief historical overview of boundary-layer transition .... 23 1.1.2 Boundary-layer transition overview .. ....... ...... 24 1.1.3 Receptivity ..... ..... ...... ...... ...... 29 1.1.4 Oblique transition .... ...... ...... ..... .... 40 1.2 Objectives ... ..... ..... ..... ..... ..... ..... 44 1.3 Road map . ..... ..... ..... ..... ..... ..... .. 45 1.4 Summary of contributions .... ...... ...... ...... .. 46 2 Experimental Hardware 47 2.1 Wind tunnel facility ....... ...... ...... ...... .. 47 2.2 Flat plate model .... ......... ........ ........ 49 2.3 Instrumentation .. ...... ....... ...... ...... ... 51 2.4 Test configuration ..... ...... ...... ....... ..... 52 2.4.1 Surface roughness ..... ........ ........ .... 52 2.4.2 Acoustic excitation .. ...... ..... ...... ..... 54 3 Experimental Procedure 57 3.1 Overview .... ......... ........ ........ ..... 57 3.2 Pressure gradient assessment ..... ........ ......... 59 3.3 Acoustic field generation ..... ..... ..... ..... ..... 61 3.4 Mean-flow measurements ......... ........ ........ 65 3.5 Hot-wire measurements . ...... ..... ...... ...... .. 67 3.5.1 Calibration procedure and analysis . .... .... .... .. 68 3.5.2 Freestream measurements . ..... .... ..... ..... 72 3.5.3 Boundary-layer measurements ... .... ..... ..... 72 3.6 Data reduction .... ..... ..... ...... ..... ..... 74 3.6.1 T-S wave decomposition .... ..... .... ..... ... 74 3.6.2 Computation of receptivity coefficient .... ...... .... 4 Results and Discussions: Mean Flow 79 4.1 Boundary-layer characterization ............. ........ 79 4.2 Freestream characteristics ... ........ ........ ..... 83 4.3 Acoustic-field characterization . ...... ...... ...... ... 86 4.4 Sum m ary ... ......... ........ ........ ..... 87 5 Results and Discussions: Two-Dimensional Disturbances 89 5.1 Influence of acoustic forcing level and roughness height ...... .. 89 5.2 The effect of detuning ..... ........ ........ ..... 95 5.3 Broadband disturbance evolution ...... ........ ...... 98 5.4 Sum m ary ... ......... ........ ........ ..... 105 6 Results and Discussions: Oblique Disturbances 107 6.1 Influence of obliqueness ... ....... ...... ...... .... 108 6.2 The effect of detuning .......... ............. ... 111 6.3 Broadband disturbance evolution .. ............ ...... 113 6.4 Sum m ary .... ..... ...... ..... .... ..... .... 115 7 Results and Discussions: Three-Dimensional Disturbances (Oblique Transition) 119 7.1 Peak-valley structure of disturbance field ........ ........ 120 7.2 Disturbance evolution .... ......... ........ ...... 130 7.3 Sum m ary ..... ....... ...... ...... ...... ... 141 6 ............ 8 Concluding Remarks and Future Work 143 8.1 Contributions ......... ............................... 144 8.2 Recommendation for future work ... .... ..... .... .... 146 A Error Analysis 149 B Fluctuating Pressure Measurements on Test-Section Walls 159 B.1 Rotor-stator interaction .... ..... ..... ..... ..... 160 B.2 Results of dynamic pressure measurements ..... ..... ..... 163 7 s MII liinimiumnlinimmillisimp ilii List of Figures 1-1 Schematic depicting a typical transition process in the absence of a bypass m echanism ... ...... ...... ...... ...... .. 25 1-2 Nondimensional spatial growth rates, a*, for a. two-dimensional T-S wave computed using LST. The growth rate is nondimensionalized by Jr.. .... ...... ...... ...... ...... ..... 26 1-3 Schematic depicting the receptivity process resulting from the interac- tion of freestream acoustic and/or convected gust and a surface inho- m ogeneity. .. ........ ........ ........ ....... 28 2-1 Top and side views of wind tunnel. ..... ...... ...... .. 48 2-2 End view of spanwise traverse. ..... ..... ..... ..... .. 49 2-3 Top and side views of flat plate model. .... ...... ....... 50 2-4 The three types of receptivity sites investigated: (a) two dimensional, (b) oblique, and (c) three dimensional. Flow is from top to bottom and shaded areas represent raised regions. .. ....... ...... 54 3-1 Schematic of experimental setup. ...... ...... ....... 58 3-2 Neutral stability curve for a Blasius boundary layer with 2-D distur- bances. ...... ........ ........ ....... ...... 58 3-3 Examples of possible (a) amplitude and (b) phase distributions when a. downstream- and upstream-traveling wave coexist in test section. 62 3-4 Plot of percent difference between tunnel velocities measured using static pressure tabs and pitot-static probe versus tunnel speed. .... 68 9 3-5 Typical hot-wire calibration curve with calibration coefficients and m ean square error. .... ............ ........... 70 3-6 Example of decomposition method obtained from short streamwise sur- veys. Part (c) shows a vector diagram depicting Equation 3.16 used to extract T-S wave from measured disturbance field. ........... 75 3-7 Graphical representation of decomposition method used for wall-normal surveys. ... ........ ........ ........ ....... 77 4-1 Freestream velocity measurements along
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