Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-18T03:35:02.008Z Has data issue: false hasContentIssue false
  • English
  • Français

Wall-cooling effects on pressure fluctuations in compressible turbulent boundary layers from subsonic to hypersonic regimes

Published online by Cambridge University Press:  02 August 2022

Peng-Jun-Yi Zhang Open the ORCID record for Peng-Jun-Yi Zhang [Opens in a new window] ,
Zhen-Hua Wan Open the ORCID record for Zhen-Hua Wan [Opens in a new window] ,
Nan-Sheng Liu Open the ORCID record for Nan-Sheng Liu [Opens in a new window] ,
De-Jun Sun  and
Xi-Yun Lu Open the ORCID record for Xi-Yun Lu [Opens in a new window]
Peng-Jun-Yi Zhang
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027, PR China
Zhen-Hua Wan*
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027, PR China
Nan-Sheng Liu
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027, PR China
De-Jun Sun
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027, PR China
Xi-Yun Lu
Affiliation:
Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027, PR China
*
†Email address for correspondence: wanzh@ustc.edu.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

Pressure fluctuations play an essential role in the transport of turbulent kinetic energy and vibrational loading. This study focuses on examining the effect of wall cooling on pressure fluctuations in compressible turbulent boundary layers by high-fidelity direct numerical simulations. Pressure fluctuations result from the vorticity mode and the acoustic mode that are both closely dependent on compressibility. To demonstrate the effects of wall cooling at various compressibility intensities, three free-stream Mach numbers are investigated, i.e. $M_\infty =0.5$, 2.0 and 8.0, with real gas effects being absent for $M_\infty =8.0$ due to a low enthalpy inflow. Overall, opposite effects of wall cooling on pressure fluctuations are found between the subsonic/supersonic cases and the hypersonic case. Specifically, the pressure fluctuations normalized by wall shear stress $p^\prime _{rms}/\tau _w$ are suppressed in the subsonic and supersonic cases, while enhanced in the hypersonic case near the wall. Importantly, travelling-wave-like alternating positive and negative structures (APNS), which greatly contribute to pressure fluctuations, are identified within the viscous sublayer and buffer layer in the hypersonic cases. Furthermore, generating mechanisms of pressure fluctuations are explored by extending the decomposition based on the fluctuating pressure equation to compressible turbulent boundary layers. Pressure fluctuations are decomposed into five components, in which rapid pressure, slow pressure and compressible pressure are dominant. The suppression of pressure fluctuations in the subsonic and supersonic cases is due to both rapid pressure and slow pressure being suppressed by wall cooling. In contrast, wall cooling strengthens compressible pressure for all Mach numbers, especially in the hypersonic case, resulting in increased wall pressure fluctuations. Compressible pressure plays a leading role in the hypersonic case, mainly due to the APNS. Essentially, the main effects of wall cooling can be interpreted by the suppression of the vorticity mode and the enhancement of the acoustic mode.

JFM classification

Compressible Flows: Compressible boundary layers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 946 , 10 September 2022 , A14
Check for updates
Copyright
© The Author(s), 2022. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Adams, N.A. 1998 Direct numerical simulation of turbulent compression ramp flow. Theor. Comput. Fluid Dyn. 12 (2), 109–129.CrossRefGoogle Scholar
Adrian, R.J., Meinhart, C.D. & Tomkins, C.D. 2000 Vortex organization in the outer region of the turbulent boundary layer. J. Fluid Mech. 422, 1–54.CrossRefGoogle Scholar
Anantharamu, S. & Mahesh, K. 2020 Analysis of wall-pressure fluctuation sources from direct numerical simulation of turbulent channel flow. J. Fluid Mech. 898, A17.Google Scholar
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.CrossRefGoogle Scholar
Bernardini, M., Modesti, D., Salvadore, F. & Pirozzoli, S. 2021 Streams: a high-fidelity accelerated solver for direct numerical simulation of compressible turbulent flows. Comput. Phys. Commun. 263, 107906.CrossRefGoogle Scholar
Bernardini, M. & Pirozzoli, S. 2011 Wall pressure fluctuations beneath supersonic turbulent boundary layers. Phys. Fluids 23 (8), 085102.CrossRefGoogle Scholar
Bernardini, M., Pirozzoli, S. & Grasso, F. 2011 The wall pressure signature of transonic shock/boundary layer interaction. J. Fluid Mech. 671, 288–312.CrossRefGoogle Scholar
Bull, M.K. 1996 Wall-pressure fluctuations beneath turbulent boundary layers: some reflections on forty years of research. J. Sound Vib. 190 (3), 299–315.CrossRefGoogle Scholar
Chang, P.A. III, Piomelli, U. & Blake, W.K. 1999 Relationship between wall pressure and velocity-field sources. Phys. Fluids 11 (11), 3434–3448.CrossRefGoogle Scholar
Chu, Y.-B., Zhuang, Y.-Q. & Lu, X.-Y. 2013 Effect of wall temperature on hypersonic turbulent boundary layer. J. Turbul. 14 (12), 37–57.CrossRefGoogle Scholar
Coleman, G.N., Kim, J. & Moser, R.D. 1995 A numerical study of turbulent supersonic isothermal-wall channel flow. J. Fluid Mech. 305, 159–183.CrossRefGoogle Scholar
Dolling, D.S. & Dussauge, J.P. 1989 A survey of measurements and measuring techniques in rapidly distorted compressible turbulent boundary layers. AGARDograph 315, 1–18.Google Scholar
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, 419–445.CrossRefGoogle Scholar
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, 245–267.Google Scholar
Duan, L., Choudhari, M.M. & Wu, M. 2014 Numerical study of acoustic radiation due to a supersonic turbulent boundary layer. J. Fluid Mech. 746, 165–192.Google Scholar
Duan, L., Choudhari, M.M. & Zhang, C. 2016 Pressure fluctuations induced by a hypersonic turbulent boundary layer. J. Fluid Mech. 804, 578–607.CrossRefGoogle ScholarPubMed
Ducros, F., Ferrand, V., Nicoud, F., Weber, C., Darracq, D., Gacherieu, C. & Poinsot, T. 1999 Large-eddy simulation of the shock/turbulence interaction. J. Comput. Phys. 152 (2), 517–549.CrossRefGoogle Scholar
Foysi, H., Sarkar, S. & Friedrich, R. 2004 Compressibility effects and turbulence scalings in supersonic channel flow. J. Fluid Mech. 509, 207–216.CrossRefGoogle Scholar
Gerolymos, G.A., Sénéchal, D. & Vallet, I. 2013 Wall effects on pressure fluctuations in turbulent channel flow. J. Fluid Mech. 720, 15–65.CrossRefGoogle Scholar
Gloerfelt, X. & Berland, J. 2013 Turbulent boundary-layer noise: direct radiation at Mach number 0.5. J. Fluid Mech. 723, 318–351.CrossRefGoogle Scholar
Goody, M.C. & Simpson, R.L. 2000 Surface pressure fluctuations beneath two- and three-dimensional turbulent boundary layers. AIAA J. 38 (10), 1822–1831.CrossRefGoogle Scholar
Griffin, K.P., Fu, L. & Moin, P. 2021 Velocity transformation for compressible wall-bounded turbulent flows with and without heat transfer. Proc. Natl Acad. Sci. USA 118 (34), e2111144118.CrossRefGoogle ScholarPubMed
Hadjadj, A., Ben-Nasr, O., Shadloo, M.S. & Chaudhuri, A. 2015 Effect of wall temperature in supersonic turbulent boundary layers: a numerical study. Intl J. Heat Mass Transfer 81, 426–438.CrossRefGoogle Scholar
Hopkins, E.J. & Inouye, M. 1971 An evaluation of theories for predicting turbulent skin friction and heat transfer on flat plates at supersonic and hypersonic Mach numbers. AIAA J. 9 (6), 993–1003.CrossRefGoogle Scholar
Hoyas, S. & Jiménez, J. 2008 Reynolds number effects on the Reynolds-stress budgets in turbulent channels. Phys. Fluids 20 (10), 101511.CrossRefGoogle Scholar
Huang, J., Duan, L. & Choudhari, M.M. 2022 Direct numerical simulation of hypersonic turbulent boundary layers: effect of spatial evolution and Reynolds number. J. Fluid Mech. 937, A3.CrossRefGoogle Scholar
Huang, P.G., Coleman, G.N. & Bradshaw, P. 1995 Compressible turbulent channel flows: DNS results and modelling. J. Fluid Mech. 305, 185–218.CrossRefGoogle Scholar
Jiang, G.-S. & Shu, C.-W. 1996 Efficient implementation of weighted ENO schemes. J. Comput. Phys. 126 (1), 202–228.CrossRefGoogle Scholar
Kim, J. 1989 On the structure of pressure fluctuations in simulated turbulent channel flow. J. Fluid Mech. 205, 421–451.CrossRefGoogle Scholar
Kistler, A.L. & Chen, W.S. 1963 The fluctuating pressure field in a supersonic turbulent boundary layer. J. Fluid Mech. 16 (1), 41–64.CrossRefGoogle Scholar
Laganelli, A.L., Martellucci, A. & Shaw, L.L. 1983 Wall pressure fluctuations in attached boundary-layer flow. AIAA J. 21 (4), 495–502.CrossRefGoogle Scholar
Laufer, J. 1964 Some statistical properties of the pressure field radiated by a turbulent boundary layer. Phys. Fluids 7 (8), 1191–1197.CrossRefGoogle Scholar
Lele, S.K. 1994 Compressibility effects on turbulence. Annu. Rev. Fluid Mech. 26 (1), 211–254.CrossRefGoogle Scholar
Lilley, G.M. 1963 Wall pressure fluctuations under turbulent boundary layers at subsonic and supersonic speeds. Tech. Rep. 454. AGARD.Google Scholar
Maestrello, L. 1969 Radiation from and panel response to a supersonic turbulent boundary layer. J. Sound Vib. 10 (2), 261–295.CrossRefGoogle Scholar
Mansour, N.N., Kim, J. & Moin, P. 1988 Reynolds-stress and dissipation-rate budgets in a turbulent channel flow. J. Fluid Mech. 194, 15–44.CrossRefGoogle Scholar
Morkovin, M.V. 1962 Effects of compressibility on turbulent flows. Mécanique de la Turbulence 367 (380), 26.Google Scholar
Patel, A., Peeters, J.W.R., Boersma, B.J. & Pecnik, R. 2015 Semi-local scaling and turbulence modulation in variable property turbulent channel flows. Phys. Fluids 27 (9), 095101.CrossRefGoogle Scholar
Phillips, O.M. 1960 On the generation of sound by supersonic turbulent shear layers. J. Fluid Mech. 9 (1), 1–28.CrossRefGoogle Scholar
Pirozzoli, S. 2010 Generalized conservative approximations of split convective derivative operators. J. Comput. Phys. 229 (19), 7180–7190.CrossRefGoogle Scholar
Pirozzoli, S. & Bernardini, M. 2011 Turbulence in supersonic boundary layers at moderate Reynolds number. J. Fluid Mech. 688, 120–168.CrossRefGoogle Scholar
Pirozzoli, S., Bernardini, M. & Grasso, F. 2010 Direct numerical simulation of transonic shock/boundary layer interaction under conditions of incipient separation. J. Fluid Mech. 657, 361–393.CrossRefGoogle Scholar
Poinsot, T.J. & Lele, S.K. 1992 Boundary conditions for direct simulations of compressible viscous flows. J. Comput. Phys. 101 (1), 104–129.CrossRefGoogle Scholar
Pope, S.B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Ritos, K., Drikakis, D. & Kokkinakis, I.W. 2019 Acoustic loading beneath hypersonic transitional and turbulent boundary layers. J. Sound Vib. 441, 50–62.CrossRefGoogle Scholar
Sarkar, S. 1992 The pressure–dilatation correlation in compressible flows. Phys. Fluids A 4 (12), 2674–2682.CrossRefGoogle Scholar
Schewe, G. 1983 On the structure and resolution of wall-pressure fluctuations associated with turbulent boundary-layer flow. J. Fluid Mech. 134, 311–328.CrossRefGoogle Scholar
Schlatter, P. & Örlü, R. 2010 Assessment of direct numerical simulation data of turbulent boundary layers. J. Fluid Mech. 659, 116–126.CrossRefGoogle Scholar
Smits, A.J. & Dussauge, J.-P. 2006 Turbulent Shear Layers in Supersonic Flow. Springer.Google Scholar
Spalart, P.R., Moser, R.D. & Rogers, M.M. 1991 Spectral methods for the Navier–Stokes equations with one infinite and two periodic directions. J. Comput. Phys. 96 (2), 297–324.CrossRefGoogle Scholar
Tan, D.K.M., Tran, T.T. & Bogdonoff, S.M. 1987 Wall pressure fluctuations in a three-dimensional shock-wave/turbulent boundary interaction. AIAA J. 25 (1), 14–21.CrossRefGoogle Scholar
Tang, J., Zhao, Z., Wan, Z.-H. & Liu, N.-S. 2020 On the near-wall structures and statistics of fluctuating pressure in compressible turbulent channel flows. Phys. Fluids 32 (11), 115121.CrossRefGoogle Scholar
Trettel, A. & Larsson, J. 2016 Mean velocity scaling for compressible wall turbulence with heat transfer. Phys. Fluids 28 (2), 026102.CrossRefGoogle Scholar
Walz, A. 1969 Boundary Layers of Flow and Temperature. MIT.Google Scholar
Xu, D., Wang, J., Wan, M., Yu, C., Li, X. & Chen, S. 2021 Effect of wall temperature on the kinetic energy transfer in a hypersonic turbulent boundary layer. J. Fluid Mech. 929, A33.CrossRefGoogle Scholar
Yu, M., Xu, C.-X. & Pirozzoli, S. 2019 Genuine compressibility effects in wall-bounded turbulence. Phys. Rev. Fluids 4 (12), 123402.CrossRefGoogle Scholar
Yu, M., Xu, C.-X. & Pirozzoli, S. 2020 Compressibility effects on pressure fluctuation in compressible turbulent channel flows. Phys. Rev. Fluids 5 (11), 113401.CrossRefGoogle Scholar
Zhang, C., Duan, L. & Choudhari, M.M. 2017 Effect of wall cooling on boundary-layer-induced pressure fluctuations at Mach 6. J. Fluid Mech. 822, 5–30.CrossRefGoogle Scholar
Zhang, C., Duan, L. & Choudhari, M.M. 2018 Direct numerical simulation database for supersonic and hypersonic turbulent boundary layers. AIAA J. 56 (11), 4297–4311.CrossRefGoogle Scholar
Zhang, Y.-S., Bi, W.-T., Hussain, F., Li, X.-L. & She, Z.-S. 2012 Mach-number-invariant mean-velocity profile of compressible turbulent boundary layers. Phys. Rev. Lett. 109 (5), 054502.CrossRefGoogle ScholarPubMed
Zhang, Y.-S., Bi, W.-T., Hussain, F. & She, Z.-S. 2014 A generalized Reynolds analogy for compressible wall-bounded turbulent flows. J. Fluid Mech. 739, 392–420.CrossRefGoogle Scholar