Hostname: page-component-77f85d65b8-7lfxl Total loading time: 0 Render date: 2026-04-22T12:08:29.883Z Has data issue: false hasContentIssue false
  • English
  • Français

Trapped waves in supersonic and hypersonic turbulent channel flow over porous walls

Published online by Cambridge University Press:  11 June 2021

Yongkai Chen Open the ORCID record for Yongkai Chen [Opens in a new window]  and
Carlo Scalo Open the ORCID record for Carlo Scalo [Opens in a new window]
Yongkai Chen*
Affiliation:
School of Mechanical Engineering, Purdue University, West Lafayette, IN 47906, USA
Carlo Scalo
Affiliation:
School of Mechanical Engineering, Purdue University, West Lafayette, IN 47906, USA School of Aeronautics and Astronautics, Purdue University, West Lafayette, IN 47906, USA*
*
†Email address for correspondence: chen1305@purdue.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

This study investigates the effect of an isothermal wall with complex impedance on compressible turbulent channel flow up to bulk Mach numbers of $6.00$. Such investigation is carried out via the time-domain impedance boundary conditions based on auxiliary differential equations method. A three-parameter complex impedance, modelling a frequency-selective porous wall, with tuneable resonating frequency $\omega _{res}$ and variable resistance $R \in [0.10, 1.0]$ is employed. Higher resistance leads to lower wall permeability with $R \rightarrow \infty$ representing the impermeable limit. Three bulk Mach numbers $M_b = \{1.50, 3.50, 6.00\}$ are investigated with a semi-local Reynolds number $Re_\tau ^{*} \approx 220$. It is found that a sufficiently low $R$ could trigger flow instabilities, which comprise streamwise-travelling waves in the near-wall region, akin to spanwise rollers at low subsonic flow conditions and second-mode waves at hypersonic conditions. The probability density function of instantaneous wall-shear stress shows an enhancement in extreme positive cases of wall-shear stress fluctuations, leading to an increase in the mean wall-shear stress due to porous walls. The wave dynamically affects the turbulence, yielding a local peak near the wall in the pre-multiplied spectrum of the production term of turbulence kinetic energy. Linear stability analysis using the turbulent base flow profile confirmed that the finite wall permeability triggers the instability when $R$ is below a threshold $R_{{cr}}$, which shows a sub-linear proportionality on the bulk Mach number $M_b$. The perturbed field exhibits more dilatational nature in high Mach number flows with low permeability.

JFM classification

Aerodynamics: High-speed flow Turbulent Flows: Compressible turbulence Flow Control: Instability control

Information

Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 920 , 10 August 2021 , A24
Check for updates
Copyright
© The Author(s), 2021. 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.)

Article purchase

Temporarily unavailable

Footnotes

*

The online version of this article has been updated since original publication. A notice detailing the change has also been published

References

REFERENCES

Abderrahaman-Elena, N. & García-Mayoral, R. 2017 Analysis of anisotropically permeable surfaces for turbulent drag reduction. Phys. Rev. Fluids 2 (11), 114609.CrossRefGoogle Scholar
Akselvoll, K. & Moin, P. 1995 Large eddy simulation of turbulent confined co-annular jets and turbulent flow over a backward facing step. Rep. TF-63, Thermo-sciences Division, Department of Mechanical Engineering, Standford University, CA 94395.Google Scholar
Aurégan, Y. & Leroux, M. 2008 Experimental evidence of an instability over an impedance wall in a duct with flow. J. Sound Vib. 317 (3–5), 432–439.CrossRefGoogle Scholar
Aurégan, Y., Leroux, M. & Pagneux, V. 2005 Abnormal behavior of an acoustical liner with flow. In Forum Acusticum 2005, Budapest.Google Scholar
Beam, R.M. & Warming, R.F. 1978 An implicit factored scheme for the compressible Navier–Stokes equations. AIAA J. 16 (4), 393–402.CrossRefGoogle Scholar
Beam, R.M. & Warming, R.F 1976 An implicit finite-difference algorithm for hyperbolic systems in conservation-law form. J. Comput. Phys. 22 (1), 87–110.CrossRefGoogle Scholar
Brambley, E.J. 2009 Fundamental problems with the model of uniform flow over acoustic linings. J. Sound Vib. 322 (4–5), 1026–1037.CrossRefGoogle Scholar
Brandes, M. & Ronneberger, D. 1995 Sound amplification in flow ducts lined with a periodic sequence of resonators. In CEAS/AIAA Joint Aeroacoustics Conference, 1st, Munich, Germany, pp. 893–901.Google Scholar
Cess, R.D. 1958 A survey of the literature on heat transfer in turbulent tube flow. Res. Rep. pp. 8–0529.Google Scholar
Chapelier, J.-B., Wasistho, B. & Scalo, C. 2018 A coherent vorticity preserving eddy-viscosity correction for large-eddy simulation. J. Comput. Phys. 359, 164–182.CrossRefGoogle Scholar
Chapelier, J.-B., Wasistho, B. & Scalo, C. 2019 Large-eddy simulation of temporally developing double helical vortices. J. Fluid Mech. 863, 79–113.CrossRefGoogle Scholar
Del Alamo, J.C. & Jimenez, J. 2006 Linear energy amplification in turbulent channels. J. Fluid Mech. 559, 205–213.CrossRefGoogle Scholar
Douasbin, Q., Scalo, C., Selle, L. & Poinsot, T. 2018 Delayed-time domain impedance boundary conditions (D-TDIBC). J. Comput. Phys. 371, 50–66.CrossRefGoogle Scholar
Dragna, D., Pineau, P. & Blanc-Benon, P. 2015 A generalized recursive convolution method for time-domain propagation in porous media. J. Acoust. Soc. Am. 138 (2), 1030–1042.CrossRefGoogle ScholarPubMed
Duan, L., Beekman, I. & Martin, 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
Fedorov, A. 2011 Transition and stability of high-speed boundary layers. Annu. Rev. Fluid Mech. 43, 79–95.CrossRefGoogle Scholar
Fedorov, A., Shiplyuk, A., Maslov, A., Burov, E. & Malmuth, N. 2003 Stabilization of a hypersonic boundary layer using an ultrasonically absorptive coating. J. Fluid Mech. 479, 99–124.CrossRefGoogle Scholar
Fedorov, A.V., Kozlov, V.F., Shiplyuk, A.N., Maslov, A.A. & Malmuth, N.D. 2006 Stability of hypersonic boundary layer on porous wall with regular microstructure. AIAA J. 44 (8), 1866–1871.CrossRefGoogle Scholar
Friedrich, R. & Bertolotti, F.P. 1997 Compressibility effects due to turbulent fluctuations. Appl. Sci. Res. 57, 165–194.CrossRefGoogle Scholar
Fung, K.Y. & Ju, H. 2001 Broadband time-domain impedance models. AIAA J. 39 (8), 1449–1454.CrossRefGoogle Scholar
Fung, K.-Y. & Ju, H. 2004 Time-domain impedance boundary conditions for computational acoustics and aeroacoustics. Intl J. Comput. Fluid Dyn. 18 (6), 503–511.CrossRefGoogle Scholar
Fung, K.-Y., Ju, H. & Tallapragada, B. 2000 Impedance and its time-domain extensions. AIAA J. 38 (1), 30–38.CrossRefGoogle Scholar
Hu, S. & Zhong, X. 1997 Linear instability of compressible plane Couette flows. In AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, AIAA Paper 1997-432.Google Scholar
Huang, P.G., Coleman, G.N. & Bradshaw, P. 1995 Compressible turbulent channel flows: DNS results and modelling. J. Fluid Mech. 305 (1), 185–218.CrossRefGoogle Scholar
Hunt, J.C.R., Wray, A.A. & Moin, P. 1988 Eddies, streams, and convergence zones in turbulent flows. In Center for Turbulence Research, Rept. CTR-S88, Stanford, CA, pp. 193–208.Google Scholar
Ingard, U. 1959 Influence of fluid motion past a plane boundary on sound reflection, absorption, and transmission. J. Acoust. Soc. Am. 31 (7), 1035–1036.CrossRefGoogle Scholar
Jiménez, J., Uhlmann, M., Pinelli, A. & Kawahara, G. 2001 Turbulent shear flow over active and passive porous surfaces. J. Fluid Mech. 442, 89–117.CrossRefGoogle Scholar
Joseph, R.M., Hagness, S.C. & Taflove, A. 1991 Direct time integration of Maxwell's equations in linear dispersive media with absorption for scattering and propagation of femtosecond electromagnetic pulses. Opt. Lett. 16 (18), 1412–1414.CrossRefGoogle ScholarPubMed
Kinsler, L.E., Frey, A.R., Coppens, A.B. & Sanders, J.V. 1999 Fundamentals of Acoustics, 4th edn. Wiley.Google Scholar
Lee, M. & Moser, R.D. 2015 Direct numerical simulation of turbulent channel flow up to $Re_\tau = 5200$. J. Fluid Mech. 774, 395–415.CrossRefGoogle Scholar
Lin, J., Scalo, C. & Hesselink, L. 2016 High-fidelity simulation of a standing-wave thermoacoustic– piezoelectric engine. J. Fluid Mech. 808, 19–60.CrossRefGoogle Scholar
Malik, M.L. 1990 Numerical methods for hypersonic boundary layer stability. J. Comput. Phys. 86, 376–413.CrossRefGoogle Scholar
Marx, D., Aurégan, Y., Bailliet, H. & Valière, J.-C. 2010 PIV and LDV evidence of hydrodynamic instability over a liner in a duct with flow. J. Sound Vib. 329 (18), 3798–3812.CrossRefGoogle Scholar
Myers, M.K. 1980 On the acoustic boundary condition in the presence of flow. J. Sound Vib. 71 (3), 429–434.CrossRefGoogle Scholar
Nagarajan, S. 2004 Leading edge effects in bypass transition. PhD thesis, Stanford University.Google Scholar
Nagarajan, S., Lele, S.K. & Ferziger, J.H. 2003 A robust high-order compact method for large eddy simulation. J. Comput. Phys. 191, 392–419.CrossRefGoogle Scholar
Olivetti, S., Sandberg, R.D. & Tester, B.J. 2015 Direct numerical simulation of turbulent flow with an impedance condition. J. Sound Vib. 344, 28–37.CrossRefGoogle Scholar
Özyörük, Y. & Long, L.N. 1997 A time-domain implementation of surface acoustic impedance condition with and without flow. J. Comput. Acoust. 5 (3), 277–296.CrossRefGoogle Scholar
Özyörük, Y., Long, L.N. & Jones, M.G. 1998 Time-domain numerical simulation of a flow-impedance tube. J. Comput. Phys. 146, 29–57.CrossRefGoogle Scholar
Patel, D.I., Gupta, P. & Scalo, C. 2017 Surface impedance determination via numerical resolution of the inverse Helmholtz problem. In 23rd AIAA/CEAS Aeroacoustics Conference, AIAA Paper 2017-3695.Google Scholar
Pope, S.B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Pujals, G., García-Villalba, M., Cossu, C. & Depardon, S. 2009 A note on optimal transient growth in turbulent channel flows. Phys. Fluids 21 (1), 015109.CrossRefGoogle Scholar
Pulliam, T.H. & Chaussee, D.S. 1981 A diagonal form of an implicit approximate-factorization algorithm. J. Comput. Phys. 39 (2), 347–363.CrossRefGoogle Scholar
Rahbari, I. & Scalo, C. 2017 Linear stability analysis of compressible channel flow over porous walls. In Whither Turbulence and Big Data in the 21st Century? (ed. A. Pollard, L. Castillo, L. Danaila & M. Glauser), pp. 451–467. Springer.CrossRefGoogle Scholar
Rasheed, A., Hornung, H.G., Fedorov, A.V. & Malmuth, N.D. 2002 Experiments on passive hypervelocity boundary-layer control using an ultrasonically absorptive surface. AIAA J. 40 (3), 481–489.CrossRefGoogle Scholar
Raupach, M.R., Antonia, R.A. & Rajagopalan, S. 1991 Rough-wall turbulent boundary layers. Appl. Mech. Rev. 40 (1), 1–25.CrossRefGoogle Scholar
Reynolds, W.C. & Hussain, A.K.M.F. 1972 The mechanics of an organized wave in turbulent shear flow. Part 3. Theoretical models and comparisons with experiments. J. Fluid Mech. 54 (2), 263–288.CrossRefGoogle Scholar
Reynolds, W.C. & Tiederman, W.G. 1967 Stability of turbulent channel flow, with application to Malkus's theory. J. Fluid Mech. 27 (2), 253–272.CrossRefGoogle Scholar
Rienstra, S. 2006 Impedance models in time domain, including the extended Helmholtz resonator model. In 12th AIAA/CEAS Aeroacoustics Conference (27th AIAA Aeroacoustics Conference), AIAA Paper 2006-2686.Google Scholar
Rienstra, S.W. & Darau, M. 2011 Boundary-layer thickness effects of the hydrodynamic instabilty along an impedance wall. J. Fluid Mech. 671, 559–573.CrossRefGoogle Scholar
Rinaldi, E., Patel, A., Schlatter, P. & Pecnik, R. 2017 Linear stability of buffer layer streaks in turbulent channels with variable density and viscosity. Phys. Rev. Fluids 2 (11), 113903.CrossRefGoogle Scholar
Rosti, M.E., Brandt, L. & Pinelli, A. 2018 Turbulent channel flow over an anisotropic porous wall – drag increase and reduction. J. Fluid Mech. 842, 381–394.CrossRefGoogle Scholar
Rotta, J.C. 1960 Turbulent Boundary Layers with Heat Transfer in Compressible Flow. Advisory Group for Aeronautical Research and Development.Google Scholar
Scalo, C., Bodart, J. & Lele, S.K. 2015 Compressible turbulent channel flow with impedance boundary conditions. Phys. Fluids 27, 035107.CrossRefGoogle Scholar
Sebastian, R., Marx, D. & Fortuné, V. 2019 Numerical simulation of a turbulent channel flow with an acoustic liner. J. Sound Vib. 456, 306–330.CrossRefGoogle Scholar
Sousa, V.C.B., Patel, D., Chapelier, J.-B., Wartemann, V., Wagner, A. & Scalo, C. 2019 Numerical investigation of second-mode attenuation over carbon/carbon porous surfaces. J. Spacecr. Rockets 56 (2), 319–332.CrossRefGoogle Scholar
Squire, D.T., Morrill-Winter, C., Hutchins, N., Schultz, M.P., Klewicki, J.C. & Marusic, I. 2016 Comparison of turbulent boundary layers over smooth and rough surfaces up to high Reynolds numbers. J. Fluid Mech. 795, 210–240.CrossRefGoogle Scholar
Tam, C.K.W. & Auriault, L. 1996 Time-domain impedance boundary conditions for computational aeroacoustics. AIAA J. 34 (5), 917–923.CrossRefGoogle Scholar
Tester, B.J. 1973 The propagation and attenuation of sound in lined ducts containing uniform or ‘plug’ flow. J. Sound Vib. 28 (2), 151–203.CrossRefGoogle Scholar
Trettel, A. & Larsson, J. 2016 Mean velocity scaling for compressible wall turbulence with heat transfer. Phys. Fluids 28, 026102.CrossRefGoogle Scholar
Troian, R., Dragna, D., Bailly, C. & Galland, M.-A. 2017 Broadband liner impedance eduction for multimodal acoustic propagation in the presence of a mean flow. J. Sound Vib. 392, 200–216.CrossRefGoogle Scholar
Ulerich, R.D. 2014 Reducing turbulence-and transition-driven uncertainty in aerothermodynamic heating predictions for blunt-bodied reentry vehicles. PhD thesis, University of Texas at Austin.Google Scholar
Vreman, A.W. 2004 An eddy-viscosity subgrid-scale model for turbulent shear flow: algebraic theory and applications. Phys. Fluids 16 (10), 3670.CrossRefGoogle Scholar
Wagner, A. 2014 Passive hypersonic boundary layer transition control using ultrasonically absorptive carbon-carbon ceramic with random microstructure. PhD thesis, Katholieke Universiteit, Leuven.CrossRefGoogle Scholar
Wilcox, D.C. 1998 Turbulence Modeling for CFD, 3rd edn. DCW Industries.Google Scholar
Zhao, R., Liu, T., Wen, C.Y., Zhu, J. & Cheng, L. 2018 Theoretical modeling and optimization of porous coating for hypersonic laminar flow control. AIAA J. 56 (8), 2942–2946.CrossRefGoogle Scholar