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Numerical study of acoustic radiation due to a supersonic turbulent boundary layer

  • Lian Duan (a1), Meelan M. Choudhari (a2) and Minwei Wu (a3)
Abstract

Direct numerical simulations are used to examine the pressure fluctuations generated by fully developed turbulence in a Mach 2.5 turbulent boundary layer, with an emphasis on the acoustic fluctuations radiated into the free stream. Single- and multi-point statistics of computed surface pressure fluctuations show good agreement with measurements and numerical simulations at similar flow conditions. Consistent with spark shadowgraphs obtained in free flight, the quasi-homogeneous acoustic near field in the free-stream region consists of randomly spaced wavepackets with a finite spatial coherence. The free-stream pressure fluctuations exhibit important differences from the surface pressure fluctuations in amplitude, frequency content and convection speeds. Such information can be applied towards improved modelling of boundary layer receptivity in conventional supersonic facilities and, hence, enable a better utilization of transition data acquired in such wind tunnels. The predicted acoustic characteristics are compared with the limited available measurements. Finally, the numerical database is used to understand the acoustic source mechanisms, with the finding that the supersonically convecting eddies that can directly radiate to the free stream are confined to the buffer zone within the boundary layer.

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Corresponding author
Email address for correspondence: duanl@mst.edu
References
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Beresh, S. J., Henfling, J. F., Spillers, R. W. & Pruett, B. O. M. 2011 Fluctuating wall pressures measured beneath a supersonic turbulent boundary layer. Phys. Fluids 23 (7), 075110.
Bernardini, M. & Pirozzoli, S. 2011 Wall pressure fluctuations beneath supersonic turbulent boundary layers. Phys. Fluids 23, 085102.
Bies, D. W.1966 A review of flight and wind tunnel measurements of boundary layer pressure fluctuations and induced structure response. Tech. Rep. NASA CR-626.
Blake, W. K. 1986 Mechanics of Flow-Induced Sound and Vibration. Academic Press.
Bookey, P., Wyckham, C., Smits, A. J. & Martin, M. P.2005 New experimental data of STBLI at DNS/LES accessible Reynolds numbers. AIAA Paper 2005-309.
Borg, M. P. & Schneider, S. P. 2008 Effect of free-stream noise on roughness-induced transition for the X-51A forebody. J. Spacecr. Rockets 45 (6), 11061116.
Bull, M. K. 1967 Wall-pressure fluctuations associated with subsonic turbulent boundary layer flow. J. Fluid Mech. 28, 719754.
Bushnell, D. M. 1990 Notes on initial disturbance fields for the transition problem. In Instability and Transition (ed. Hussaini, M. Y. & Voigt, R. G.), vol. 1, pp. 217232. Springer.
Choi, H. & Moin, P. 1990 On the space–time characteristics of wall-pressure fluctuations. Phys. Fluids 2 (8), 14501460.
Coleman, G. N., Kim, J. & Moser, R. D. 1995 A numerical study of turbulent supersonic isothermal-wall channel flow. J. Fluid Mech. 305, 159183.
Del Alamo, J. C. & Jimenez, J. 2009 Estimation of turbulent convection velocities and corrections to Taylor’s approximation. J. Fluid Mech. 640, 526.
Dolling, D. S. & Dussauge, J. P. 1989 A survey of measurements and measuring techniques in rapidly distorted compressible turbulent boundary layers. AGARDograph 315, 118.
Donaldson, J. & Coulter, S.1995 A review of free-stream flow fluctuation and steady-state flow quality measurements in the AEDC/VKF supersonic tunnel A and hypersonic tunnel B. AIAA Paper 95-6137.
Duan, L., Beekman, I. & Martín, M. P. 2010 Direct numerical simulation of hypersonic turbulent boundary layers. Part 2. Effect of wall temperature. J. Fluid Mech. 655, 419445.
Duan, L., Beekman, I. & Martín, M. P. 2011 Direct numerical simulation of hypersonic turbulent boundary layers. Part 3. Effect of Mach number. J. Fluid Mech. 672, 245267.
Duan, L. & Martín, M. P. 2011 Direct numerical simulation of hypersonic turbulent boundary layers. Part 4. Effect of high enthalpy. J. Fluid Mech. 684, 2559.
Farabee, T. & Casarella, M. J. 1991 Spectral features of wall pressure fluctuations beneath turbulent boundary layers. Phys. Fluids 3, 24102420.
Fedorov, A. V. 2003 Receptivity of a high-speed boundary layer to acoustic disturbances. J. Fluid Mech. 491, 101129.
Fedorov, A. V. 2011 Transition and stability of high-speed boundary layers. Annu. Rev. Fluid Mech. 43, 7995.
Ffowcs Williams, J. E. 1963 The noise from turbulence convected at high speed. Phil. Trans. R. Soc. Lond. A 255 (1061), 453469.
Ffowcs Williams, J. E. & Maidanik, G. 1965 The Mach wavefield radiated by supersonic turbulent shear flows. J. Fluid Mech. 21, 641657.
George, W. K., Beuther, P. D. & Arndt, R. E. A. 1984 Pressure spectra in turbulent free shear flows. J. Fluid Mech. 148, 155191.
Goldstein, M. E. 2001 An exact form of Lilley’s equation with a velocity quadrupole/temperature dipole source term. J. Fluid Mech. 443, 231236.
Guarini, S. E., Moser, R. D., Shariff, K. & Wray, A. 2000 Direct numerical simulation of a supersonic turbulent boundary layer at Mach 2.5. J. Fluid Mech. 414, 133.
Jiang, G. S. & Shu, C. W. 1996 Efficient implementation of weighted ENO schemes. J. Comput. Phys. 126 (1), 202228.
Kendall, J. M.1970 Supersonic boundary layer transition studies. JPL Space Programs Summary, vol. 3, pp. 43–47.
Kim, J. 1989 On the structure of pressure fluctuations in simulated turbulent channel flow. J. Fluid Mech. 205, 421451.
Kim, J. & Hussain, F. 1993 Propagation velocity of perturbations in turbulent channel flow. Phys. Fluids 5 (3), 695706.
Kistler, A. L. & Chen, W. S. 1963 The fluctuating pressure field in a supersonic turbulent boundary layer. J. Fluid Mech. 16, 4164.
Kovasznay, L. S. G. 1953 Turbulence in supersonic flow. J. Aeronaut. Sci. 20, 657674.
Laufer, J.1962 Sound radiation from a turbulent boundary layer. In Proceedings of the Marseille Conference on Turbulence. CNRS Report 108.
Laufer, J. 1964 Some statistical properties of the pressure field radiated by a turbulent boundary layer. Phys. Fluids 7 (8), 11911197.
Liepmann, H. W. & Roshko, A. 1957 Elements of Gasdynamics. John Wiley & Sons.
Lighthill, M. J. 1952 On sound generated aerodynamically: I. General theory. Proc. R. Soc. Lond. A 211, 564587.
Lighthill, M. J. 1954 On sound generated aerodynamically: II. Turbulence as a source of sound. Proc. R. Soc. Lond. A 222, 132.
Logan, P.1988 Modal analysis of hot-wire measurements in supersonic turbulence. AIAA Paper 88-423.
Maestrello, L. 1969 Radiation from and panel response to a supersonic turbulent boundary layer. J. Sound Vib. 10 (2), 261262.
Martín, M. P. 2007 DNS of hypersonic turbulent boundary layers. Part I: Initialization and comparison with experiments. J. Fluid Mech. 570, 347364.
Masutti, M., Spinosa, E., Chazot, O. & Carbonaro, M. 2012 Disturbance level characterization of a hypersonic blowdown facility. AIAA J. 50 (12), 27202730.
Morgan, B., Larsson, J., Kawai, S. & Lele, S. K. 2011 Improving low-frequency characteristics of recycling/rescaling inflow turbulence generation. AIAA J. 49 (3), 582597.
Morkovin, M. V. 1957 On transition experiments at moderate supersonic speeds. J. Aeronaut. Sci. 24 (7), 480486.
Pate, S. R. & Schuller, C. J. 1969 Radiated aerodynamic noise effects on boundary layer transition in supersonic and hypersonic wind tunnels. AIAA J. 7 (3), 450457.
Phillips, O. M. 1960 On the generation of sound by supersonic turbulent shear layers. J. Fluid Mech. 9, 128.
Pirozzoli, S. & Bernardini, M. 2011 Turbulence in supersonic boundary layers at moderate Reynolds numbers. J. Fluid Mech. 688, 120168.
Priebe, S. & Martín, M. P. 2012 Low-frequency unsteadiness in shock wave–turbulent boundary layer interaction. J. Fluid Mech. 699, 149.
Schneider, S. P. 2001 Effects of high-speed tunnel noise on laminar–turbulent transition. J. Spacecr. Rockets 38 (3), 323333.
Simens, M. P., Jimenez, J., Hoyas, S. & Mizuno, Y. 2009 A high-resolution code for turbulent boundary layers. J. Comput. Phys. 228 (11), 42184231.
Smits, A. J. & Dussauge, J. P. 2006 Turbulent Shear Layers in Supersonic Flow. 2nd edn. American Institute of Physics.
Spalart, P. R. 1988 Direct simulation of a turbulent boundary layer up to . J. Fluid Mech. 187, 6198.
Stetson, K. F.1983 Nosetip bluntness effects on cone frustrum boundary-layer transition in hypersonic flow. AIAA Paper 83-1763.
Taylor, E. M., Wu, M. & Martín, M. P. 2006 Optimization of nonlinear error sources for weighted non-oscillatory methods in direct numerical simulations of compressible turbulence. J. Comput. Phys. 223 (1), 384397.
Thompson, K. W. 1987 Time dependent boundary conditions for hyperbolic systems. J. Comput. Phys. 68 (1), 124.
Tsuji, Y., Fransson, J. H. M., Alfredsson, P. H. & Johansson, A. V. 2007 Pressure statistics and their scaling in high-Reynolds-number turbulent boundary layers. J. Fluid Mech. 585, 140.
Weiss, J., Knauss, H. & Wagner, S. 2003 Experimental determination of the free-stream disturbance field in a short-duration supersonic wind tunnel. Exp. Fluids 35, 291302.
Welch, P. D. 1967 The use of fast Fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms. IEEE Trans. Audio Electroacoust. AU-15, 70–73.
Williamson, J. H. 1980 Low-storage Runge–Kutta schemes. J. Comput. Phys. 35 (1), 4856.
Willmarth, W. W. 1975 Wall pressure fluctuations beneath turbulent boundary layers. Annu. Rev. Fluid Mech. 7, 1336.
Willmarth, W. W. & Wooldridge, C. E. 1962 Measurements of the fluctuating pressure at the wall beneath a thick turbulent boundary layer. J. Fluid Mech. 14, 187210.
Wu, M. & Martín, M. P. 2007 Direct numerical simulation of supersonic boundary layer over a compression ramp. AIAA J. 45 (4), 879889.
Wu, M. & Martín, M. P. 2008 Analysis of shock motion in shockwave and turbulent boundary layer interaction using direct numerical simulation data. J. Fluid Mech. 594, 7183.
Xu, S. & Martín, M. P. 2004 Assessment of inflow boundary conditions for compressible turbulent boundary layers. Phys. Fluids 16 (7), 26232639.
Zhong, X. & Wang, X. 2012 Direct numerical simulation on the receptivity, instability, and transition of hypersonic boundary layers. Annu. Rev. Fluid Mech. 44, 527561.
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