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Pressure fluctuations induced by a hypersonic turbulent boundary layer

  • Lian Duan (a1), Meelan M. Choudhari (a2) and Chao Zhang (a1)

Abstract

Direct numerical simulations (DNS) are used to examine the pressure fluctuations generated by a spatially developed Mach 5.86 turbulent boundary layer. The unsteady pressure field is analysed at multiple wall-normal locations, including those at the wall, within the boundary layer (including inner layer, the log layer, and the outer layer), and in the free stream. The statistical and structural variations of pressure fluctuations as a function of wall-normal distance are highlighted. Computational predictions for mean-velocity profiles and surface pressure spectrum are in good agreement with experimental measurements, providing a first ever comparison of this type at hypersonic Mach numbers. The simulation shows that the dominant frequency of boundary-layer-induced pressure fluctuations shifts to lower frequencies as the location of interest moves away from the wall. The pressure wave propagates with a speed nearly equal to the local mean velocity within the boundary layer (except in the immediate vicinity of the wall) while the propagation speed deviates from Taylor’s hypothesis in the free stream. Compared with the surface pressure fluctuations, which are primarily vortical, the acoustic pressure fluctuations in the free stream exhibit a significantly lower dominant frequency, a greater spatial extent, and a smaller bulk propagation speed. The free-stream pressure structures are found to have similar Lagrangian time and spatial scales as the acoustic sources near the wall. As the Mach number increases, the free-stream acoustic fluctuations exhibit increased radiation intensity, enhanced energy content at high frequencies, shallower orientation of wave fronts with respect to the flow direction, and larger propagation velocity.

Copyright

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, 075110.
Bernardini, M. & Pirozzoli, S. 2011 Wall pressure fluctuations beneath supersonic turbulent boundary layers. Phys. Fluids 23, 085102.
Bernardini, M., Pirozzoli, S. & Grasso, F. 2011 The wall pressure signature of transonic shock/boundary layer interaction. J. Fluid Mech. 671, 288312.
Bies, D. W.1966 A review of flight and wind tunnel measurements of boundary layer pressure fluctuations and induced structure reponse. NASA Tech. Rep. CR-626.
Blake, W. K. 1986 Mechanics of Flow-Induced Sound and Vibration. Academic.
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.
Bounitch, A., Lewis, D. R. & Lafety, J. F.2011 Experimental study of second-mode instabilities on a 7-degree cone at Mach 6. AIAA Paper 2011-1200.
Bradshaw, P. 1967 Inactive motion and pressure fluctuations in turbulent boundary layers. J. Fluid Mech. 30, 241258.
Bull, M. K. 1996 Wall-pressure fluctuations beneath turbulent boundary layers: some reflection on forty years of research. J. Sound Vib. 190 (3), 299315.
Cadot, O., Douady, S. & Couder, Y. 1995 Characterization of the low-pressure filaments in a three-dimensional turbulent shear flow. Phys. Fluids 7, 630646.
Casper, K. M.2011 Turbulent pressure fluctuations in a hypersonic boundary layer. Final Project Rep. AAE 626, Purdue University, West Lafayette, IN, USA, 2011.
Choi, H. & Moin, P. 1990 On the space–time characteristics of wall-pressure fluctuations. Phys. Fluids 2 (8), 14501460.
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., Choudhari, M. M. & Wu, M. 2014 Numerical study of pressure fluctuations due to a supersonic turbulent boundary layer. J. Fluid Mech. 746, 165192.
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.
Eléna, M. & Lacharme, J. P. 1988 Experimental study of a supersonic turbulent boundary layer using a laser doppler anemometer. J. Méc. Théor. Appl. 7 (2), 175190.
Ffowcs-Williams, J. E. & Maidanik, G. 1965 The Mach wave field radiated by supersonic turbulent shear flows. J. Fluid Mech. 21, 641657.
Ganapathisubramani, B., Clemens, N., Hambleton, W. T., Longmire, E. K. & Marusic, I. 2005 Investigation of large-scale coherence in a turbulent boundary layer uisng two-point correlations. J. Fluid Mech. 524, 5780.
Ganapathisubramani, B., Clemens, N. T. & Dolling, D. S. 2006 Large-scale motions in a supersonic turbulent boundary layer. J. Fluid Mech. 556, 271282.
Gloerfelt, X. & Berland, J. 2013 Turbulent boundary-layer noise: direct radiation at Mach number 0.5. J. Fluid Mech. 723, 318351.
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.
Harris, J. & Blanchard, D.1982 Computer program for solving laminar, transitional, or turbulent compressible boundary-layer equations for two-dimensional and axisymmetric flow. NASA-TM-83207.
Jiang, G. S. & Shu, C. W. 1996 Efficient implementation of weighted ENO schemes. J. Comput. Phys. 126 (1), 202228.
Kat, R. De & Oudheusden, B. W. Van 2012 Instantaneous planar pressure determination from PIV in turbulent flows. Exp. Fluids 52 (5), 10891106.
Kendall, J. M. 1970 Supersonic boundary layer transition studies. Space Program Summary 3, 4347.
Kida, S. & Miura, H. 1998 Identification and analysis of vortical structures. Eur. J. Mech. (B/Fluids) 17 (4), 471488.
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.
Kim, K. C. & Adrian, R. J. 1999 Very large-scale motion in the outer layer. Phys. Fluids 11, 417422.
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. 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.
Maestrello, L. 1969 Radiation from and panel response to a supersonic turbulent boundary layer. J. Sound Vib. 10 (2), 261262.
Marco, A. D., Camussi, R., Bernardini, M. & Pirozzoli, S. 2013 Wall pressure coherence in supersonic turbulent boundary layers. J. Fluid Mech. 732, 445456.
Martín, M. P. 2007 DNS of hypersonic turbulent boundary layers. Part 1. Initialization and comparison with experiments. J. Fluid Mech. 570, 347364.
Masutti, M., Chazot, E. & Carbonaro, M. 2012 Disturbance level characterization of a hypersonic blowdown facility. AIAA J. 50 (12).
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.
Naka, Y., Stanislas, M., Foucaut, J. M., Coudert, S., Laval, J. P. & Obi, S. 2015 Space–time pressure–velocity correlations in a turbulent boundary layer. J. Fluid Mech. 771, 624675.
Pate, S. R.1978 Dominance of radiated aerodynamic noise on boundary-layer transition in supersonic-hypersonic wind tunnels. Tech. Rep. AEDC-TR-77-107. Arnold Engineering Development Center.
Peltier, S. J., Humble, R. A. & Bowersox, R. D. W.2012 PIV of a Mach 5 turbulent boundary layer over diamond roughness elements. AIAA Paper 2012-3061.
Phillips, O. M. 1960 On the generation of sound by supersonic turbulent shear layers. J. Fluid Mech. 9, 128.
Piponniau, S., Dussauge, J. P., Debieve, J. F. & Dupont, P. 2009 A simple model for low-frequency unsteadiness in shock-induced separation. J. Fluid Mech. 629, 87108.
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.
Schlatter, P. & Örlü, R. 2010 Assessment of direct numerical simulation data of turbulent boundary layers. J. Fluid Mech. 659, 116126.
Schneider, S. P. 2001 Effects of high-speed tunnel noise on laminar-turbulent transition. J. Spacecr. Rockets 38 (3), 323333.
Schneider, S. P. 2008 Development of hypersonic quiet tunnels. J. Spacecr. Rockets 45 (4), 641664.
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 Re 𝜃 = 1410. J. Fluid Mech. 187, 6198.
Stainback, P. C. 1971 Hypersonic boundary-layer transition in the presence of wind tunnel noise. AIAA J. 9 (12), 24752476.
Steen, L. E.2010 Characterization and development of nozzles for a hypersonic quiet wind tunnel. Master’s thesis, Purdue University, West Lafayette, IN, USA.
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.
Tomkins, C. D. & Adrian, R. J. 2003 Spanwise structure and scale growth in turbulent boundary layers. J. Fluid Mech. 490, 3774.
Tsuji, Y., Fransson, J. H. M., Alferdsson, P. H. & Johansson, A. V. 2007 Pressure statistics and their scaling in high-Reynolds-number turbulent boundary layers. J. Fluid Mech. 585, 140.
Tsuji, Y., Imayama, S., Schlatter, P., Alfredsson, P. H., Johansson, A. V., Marusic, I., Hutchins, N. & Monty, J. 2012 Pressure fluctuation in high-Reynolds-number turbulent boundary layer: results from experiments and dns. J. Turbul. 13 (50), 119.
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, 7073.
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.
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.
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