×

Trapped waves in supersonic and hypersonic turbulent channel flow over porous walls. (English) Zbl 1495.76047

Summary: 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.

MSC:

76F10 Shear flows and turbulence
76F50 Compressibility effects in turbulence
76F70 Control of turbulent flows
76E05 Parallel shear flows in hydrodynamic stability
76S05 Flows in porous media; filtration; seepage
76J20 Supersonic flows
76K05 Hypersonic flows
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Abderrahaman-Elena, N. & García-Mayoral, R.2017Analysis of anisotropically permeable surfaces for turbulent drag reduction. Phys. Rev. Fluids2 (11), 114609.
[2] 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.
[3] Aurégan, Y. & Leroux, M.2008Experimental evidence of an instability over an impedance wall in a duct with flow. J. Sound Vib.317 (3-5), 432-439.
[4] Aurégan, Y., Leroux, M. & Pagneux, V.2005 Abnormal behavior of an acoustical liner with flow. In Forum Acusticum 2005, Budapest.
[5] Beam, R.M. & Warming, R.F.1978An implicit factored scheme for the compressible Navier-Stokes equations. AIAA J.16 (4), 393-402. · Zbl 0374.76025
[6] Beam, R.M. & Warming, R.F1976An implicit finite-difference algorithm for hyperbolic systems in conservation-law form. J. Comput. Phys.22 (1), 87-110. · Zbl 0336.76021
[7] Brambley, E.J.2009Fundamental problems with the model of uniform flow over acoustic linings. J. Sound Vib.322 (4-5), 1026-1037.
[8] 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.
[9] Cess, R.D.1958 A survey of the literature on heat transfer in turbulent tube flow. Res. Rep. pp. 8-0529.
[10] Chapelier, J.-B., Wasistho, B. & Scalo, C.2018A coherent vorticity preserving eddy-viscosity correction for large-eddy simulation. J. Comput. Phys.359, 164-182. · Zbl 1383.76279
[11] Chapelier, J.-B., Wasistho, B. & Scalo, C.2019Large-eddy simulation of temporally developing double helical vortices. J. Fluid Mech.863, 79-113. · Zbl 1415.76392
[12] Del Alamo, J.C. & Jimenez, J.2006Linear energy amplification in turbulent channels. J. Fluid Mech.559, 205-213. · Zbl 1095.76021
[13] Douasbin, Q., Scalo, C., Selle, L. & Poinsot, T.2018Delayed-time domain impedance boundary conditions (D-TDIBC). J. Comput. Phys.371, 50-66. · Zbl 1415.76558
[14] Dragna, D., Pineau, P. & Blanc-Benon, P.2015A generalized recursive convolution method for time-domain propagation in porous media. J. Acoust. Soc. Am.138 (2), 1030-1042.
[15] Duan, L., Beekman, I. & Martin, M.P.2010Direct numerical simulation of hypersonic turbulent boundary layers. Part 2. Effect of wall temperature. J. Fluid Mech.655, 419-445. · Zbl 1197.76078
[16] Fedorov, A.2011Transition and stability of high-speed boundary layers. Annu. Rev. Fluid Mech.43, 79-95. · Zbl 1299.76054
[17] Fedorov, A., Shiplyuk, A., Maslov, A., Burov, E. & Malmuth, N.2003Stabilization of a hypersonic boundary layer using an ultrasonically absorptive coating. J. Fluid Mech.479, 99-124. · Zbl 1141.76304
[18] Fedorov, A.V., Kozlov, V.F., Shiplyuk, A.N., Maslov, A.A. & Malmuth, N.D.2006Stability of hypersonic boundary layer on porous wall with regular microstructure. AIAA J.44 (8), 1866-1871.
[19] Friedrich, R. & Bertolotti, F.P.1997Compressibility effects due to turbulent fluctuations. Appl. Sci. Res.57, 165-194. · Zbl 0911.76027
[20] Fung, K.Y. & Ju, H.2001Broadband time-domain impedance models. AIAA J.39 (8), 1449-1454.
[21] Fung, K.-Y. & Ju, H.2004Time-domain impedance boundary conditions for computational acoustics and aeroacoustics. Intl J. Comput. Fluid Dyn.18 (6), 503-511. · Zbl 1065.76589
[22] Fung, K.-Y., Ju, H. & Tallapragada, B.2000Impedance and its time-domain extensions. AIAA J.38 (1), 30-38.
[23] 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.
[24] Huang, P.G., Coleman, G.N. & Bradshaw, P.1995Compressible turbulent channel flows: DNS results and modelling. J. Fluid Mech.305 (1), 185-218. · Zbl 0857.76036
[25] 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.
[26] Ingard, U.1959Influence of fluid motion past a plane boundary on sound reflection, absorption, and transmission. J. Acoust. Soc. Am.31 (7), 1035-1036.
[27] Jiménez, J., Uhlmann, M., Pinelli, A. & Kawahara, G.2001Turbulent shear flow over active and passive porous surfaces. J. Fluid Mech.442, 89-117. · Zbl 1014.76027
[28] Joseph, R.M., Hagness, S.C. & Taflove, A.1991Direct 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.
[29] Kinsler, L.E., Frey, A.R., Coppens, A.B. & Sanders, J.V.1999Fundamentals of Acoustics, 4th edn. Wiley.
[30] Lee, M. & Moser, R.D.2015Direct numerical simulation of turbulent channel flow up to \(Re_\tau = 5200\). J. Fluid Mech.774, 395-415.
[31] Lin, J., Scalo, C. & Hesselink, L.2016High-fidelity simulation of a standing-wave thermoacoustic– piezoelectric engine. J. Fluid Mech.808, 19-60. · Zbl 1383.76081
[32] Malik, M.L.1990Numerical methods for hypersonic boundary layer stability. J. Comput. Phys.86, 376-413. · Zbl 0682.76043
[33] Marx, D., Aurégan, Y., Bailliet, H. & Valière, J.-C.2010PIV and LDV evidence of hydrodynamic instability over a liner in a duct with flow. J. Sound Vib.329 (18), 3798-3812.
[34] Myers, M.K.1980On the acoustic boundary condition in the presence of flow. J. Sound Vib.71 (3), 429-434. · Zbl 0448.76065
[35] Nagarajan, S.2004 Leading edge effects in bypass transition. PhD thesis, Stanford University. · Zbl 1145.76025
[36] Nagarajan, S., Lele, S.K. & Ferziger, J.H.2003A robust high-order compact method for large eddy simulation. J. Comput. Phys.191, 392-419. · Zbl 1051.76030
[37] Olivetti, S., Sandberg, R.D. & Tester, B.J.2015Direct numerical simulation of turbulent flow with an impedance condition. J. Sound Vib.344, 28-37.
[38] Özyörük, Y. & Long, L.N.1997A time-domain implementation of surface acoustic impedance condition with and without flow. J. Comput. Acoust.5 (3), 277-296.
[39] Özyörük, Y., Long, L.N. & Jones, M.G.1998Time-domain numerical simulation of a flow-impedance tube. J. Comput. Phys.146, 29-57. · Zbl 0932.76055
[40] 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.
[41] Pope, S.B.2000Turbulent Flows. Cambridge University Press. · Zbl 0966.76002
[42] Pujals, G., García-Villalba, M., Cossu, C. & Depardon, S.2009A note on optimal transient growth in turbulent channel flows. Phys. Fluids21 (1), 015109. · Zbl 1183.76425
[43] Pulliam, T.H. & Chaussee, D.S.1981A diagonal form of an implicit approximate-factorization algorithm. J. Comput. Phys.39 (2), 347-363. · Zbl 0472.76068
[44] 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.
[45] Rasheed, A., Hornung, H.G., Fedorov, A.V. & Malmuth, N.D.2002Experiments on passive hypervelocity boundary-layer control using an ultrasonically absorptive surface. AIAA J.40 (3), 481-489.
[46] Raupach, M.R., Antonia, R.A. & Rajagopalan, S.1991Rough-wall turbulent boundary layers. Appl. Mech. Rev.40 (1), 1-25.
[47] Reynolds, W.C. & Hussain, A.K.M.F.1972The mechanics of an organized wave in turbulent shear flow. Part 3. Theoretical models and comparisons with experiments. J. Fluid Mech.54 (2), 263-288.
[48] Reynolds, W.C. & Tiederman, W.G.1967Stability of turbulent channel flow, with application to Malkus’s theory. J. Fluid Mech.27 (2), 253-272.
[49] 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.
[50] Rienstra, S.W. & Darau, M.2011Boundary-layer thickness effects of the hydrodynamic instabilty along an impedance wall. J. Fluid Mech.671, 559-573. · Zbl 1225.76117
[51] Rinaldi, E., Patel, A., Schlatter, P. & Pecnik, R.2017Linear stability of buffer layer streaks in turbulent channels with variable density and viscosity. Phys. Rev. Fluids2 (11), 113903.
[52] Rosti, M.E., Brandt, L. & Pinelli, A.2018Turbulent channel flow over an anisotropic porous wall – drag increase and reduction. J. Fluid Mech.842, 381-394. · Zbl 1419.76374
[53] Rotta, J.C.1960Turbulent Boundary Layers with Heat Transfer in Compressible Flow. Advisory Group for Aeronautical Research and Development.
[54] Scalo, C., Bodart, J. & Lele, S.K.2015Compressible turbulent channel flow with impedance boundary conditions. Phys. Fluids27, 035107.
[55] Sebastian, R., Marx, D. & Fortuné, V.2019Numerical simulation of a turbulent channel flow with an acoustic liner. J. Sound Vib.456, 306-330.
[56] Sousa, V.C.B., Patel, D., Chapelier, J.-B., Wartemann, V., Wagner, A. & Scalo, C.2019Numerical investigation of second-mode attenuation over carbon/carbon porous surfaces. J. Spacecr. Rockets56 (2), 319-332.
[57] Squire, D.T., Morrill-Winter, C., Hutchins, N., Schultz, M.P., Klewicki, J.C. & Marusic, I.2016Comparison of turbulent boundary layers over smooth and rough surfaces up to high Reynolds numbers. J. Fluid Mech.795, 210-240. · Zbl 1359.76146
[58] Tam, C.K.W. & Auriault, L.1996Time-domain impedance boundary conditions for computational aeroacoustics. AIAA J.34 (5), 917-923. · Zbl 0904.76079
[59] Tester, B.J.1973The propagation and attenuation of sound in lined ducts containing uniform or ‘plug’ flow. J. Sound Vib.28 (2), 151-203. · Zbl 0258.76057
[60] Trettel, A. & Larsson, J.2016Mean velocity scaling for compressible wall turbulence with heat transfer. Phys. Fluids28, 026102.
[61] Troian, R., Dragna, D., Bailly, C. & Galland, M.-A.2017Broadband liner impedance eduction for multimodal acoustic propagation in the presence of a mean flow. J. Sound Vib.392, 200-216.
[62] 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.
[63] Vreman, A.W.2004An eddy-viscosity subgrid-scale model for turbulent shear flow: algebraic theory and applications. Phys. Fluids16 (10), 3670. · Zbl 1187.76543
[64] Wagner, A.2014 Passive hypersonic boundary layer transition control using ultrasonically absorptive carbon-carbon ceramic with random microstructure. PhD thesis, Katholieke Universiteit, Leuven.
[65] Wilcox, D.C.1998Turbulence Modeling for CFD, 3rd edn. DCW Industries.
[66] Zhao, R., Liu, T., Wen, C.Y., Zhu, J. & Cheng, L.2018Theoretical modeling and optimization of porous coating for hypersonic laminar flow control. AIAA J.56 (8), 2942-2946.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.