Compressibility effects in supersonic and hypersonic turbulent boundary layers subject to wall disturbances. (English) Zbl 07747585
Summary: In the present study, we investigate the compressibility effects in supersonic and hypersonic turbulent boundary layers under the influence of wall disturbances by exploiting direct numerical simulation databases at Mach numbers up to 6. Such wall disturbances enforce extra Reynolds shear stress on the wall and induce mean streamline curvature in rough wall turbulence that leads to the intensification of turbulent motions in the outer region. The turbulent and fluctuating Mach numbers, the density and the velocity divergence fluctuation intensities suggest that the compressibility effects are enhanced by the increment of the free-stream Mach number and the implementation of the wall disturbances. The differences between the Reynolds and Favre average due to the density fluctuations constitute approximately 9% of the mean velocity close to the wall and 30% of the Reynolds stress near the edge of the boundary layer, indicating their non-negligibility in turbulent modelling strategies. The comparatively strong compressive events behaving as eddy shocklets are observed at the free-stream Mach number of 6 only in the cases with wall disturbances. By further splitting the velocity into the solenoidal and dilatational components with the Helmholtz decomposition, we found that the dilatational motions are organized as travelling wave packets in the wall-parallel planes close to the wall and as forward inclined structures in the form of radiated waves in the vertical planes. Despite their increased magnitudes and higher portion in the Reynolds normal and shear stresses, the dilatational motions show no tendency of contributing significantly to the skin friction and the production of turbulent kinetic energy due to their mitigation by the cross-correlation between the solenoidal and dilatational velocity components.
MSC:
| 76N20 | Boundary-layer theory for compressible fluids and gas dynamics |
| 76F40 | Turbulent boundary layers |
| 76F50 | Compressibility effects in turbulence |
| 76F65 | Direct numerical and large eddy simulation of turbulence |
| 76M20 | Finite difference methods applied to problems in fluid mechanics |
| 76J20 | Supersonic flows |
| 76K05 | Hypersonic flows |
Keywords:
compressible turbulent boundary layer; Navier-Stokes equations; direct numerical simulation; finite difference method; fluctuating Mach number; Reynolds/Favre average; eddy shockletReferences:
| [1] | Alvarez, M.2017 Mach number effects on rough-wall turbulent boundary layers. PhD thesis, UCLA. |
| [2] | Bernardini, M., Modesti, D., Salvadore, F. & Pirozzoli, S.2021STREAmS: a high-fidelity accelerated solver for direct numerical simulation of compressible turbulent flows. Comput. Phys. Commun.263, 107906. · Zbl 1539.76002 |
| [3] | Bernardini, M. & Pirozzoli, S.2011Wall pressure fluctuations beneath supersonic turbulent boundary layers. Phys. Fluids23 (8), 085102. · Zbl 1241.76286 |
| [4] | Bowersox, R.2007 Survey of high-speed rough wall boundary layers: invited presentation. In 37th AIAA Fluid Dynamics Conference and Exhibit, p. 3998. |
| [5] | Ceci, A., Palumbo, A., Larsson, J. & Pirozzoli, S.2022Numerical tripping of high-speed turbulent boundary layers. Theor. Comput. Fluid Dyn.36, 865-886. |
| [6] | Chan, L., Macdonald, M., Chung, D., Hutchins, N. & Ooi, A.2015A systematic investigation of roughness height and wavelength in turbulent pipe flow in the transitionally rough regime. J. Fluid Mech.771, 743-777. |
| [7] | Chan, L., Macdonald, M., Chung, D., Hutchins, N. & Ooi, A.2018Secondary motion in turbulent pipe flow with three-dimensional roughness. J. Fluid Mech.854, 5-33. · Zbl 1415.76326 |
| [8] | Chen, S., Wang, J., Li, H., Wan, M. & Chen, S.2018Spectra and mach number scaling in compressible homogeneous shear turbulence. Phys. Fluids30 (6), 065109. |
| [9] | Chen, S., Wang, J., Li, H., Wan, M. & Chen, S.2019Effect of compressibility on small scale statistics in homogeneous shear turbulence. Phys. Fluids31 (2), 025107. |
| [10] | Chung, D., Chan, L., Macdonald, M., Hutchins, N. & Ooi, A.2015A fast direct numerical simulation method for characterising hydraulic roughness. J. Fluid Mech.773, 418-431. |
| [11] | Chung, D., Hutchins, N., Schultz, M.P. & Flack, K.A.2021Predicting the drag of rough surfaces. Annu. Rev. Fluid Mech.53, 439-471. · Zbl 1459.76060 |
| [12] | Coleman, G.N., Kim, J. & Moser, R.D.1995A numerical study of turbulent supersonic isothermal-wall channel flow. J. Fluid Mech.305, 159-183. · Zbl 0960.76517 |
| [13] | Czarnecki, K.R.1966 The problem of roughness drag at supersonic speeds. NASA Tech. Rep. TN D-3589. |
| [14] | Di Giovanni, A. & Stemmer, C.2018Cross-flow-type breakdown induced by distributed roughness in the boundary layer of a hypersonic capsule configuration. J. Fluid Mech.856, 470-503. · Zbl 1415.76268 |
| [15] | Duan, L., Beekman, I. & Martin, M.2010Direct numerical simulation of hypersonic turbulent boundary layers. Part 2. Effect of wall temperature. J. Fluid Mech.655, 419-445. · Zbl 1197.76078 |
| [16] | Duan, L., Beekman, I. & Martin, M.P.2011Direct numerical simulation of hypersonic turbulent boundary layers. Part 3. Effect of Mach number. J. Fluid Mech.672, 245-267. · Zbl 1225.76160 |
| [17] | Duan, L., Choudhari, M.M. & Wu, M.2014Numerical study of acoustic radiation due to a supersonic turbulent boundary layer. J. Fluid Mech.746, 165-192. |
| [18] | Duan, L., Choudhari, M.M. & Zhang, C.2016Pressure fluctuations induced by a hypersonic turbulent boundary layer. J. Fluid Mech.804, 578-607. |
| [19] | Ducros, F., Ferrand, V., Nicoud, F., Weber, C., Darracq, D., Gacherieu, C. & Poinsot, T.1999Large-eddy simulation of the shock/turbulence interaction. J. Comput. Phys.152 (2), 517-549. · Zbl 0955.76045 |
| [20] | Ekoto, I.W., Bowersox, R.D.W., Beutner, T. & Goss, L.2008Supersonic boundary layers with periodic surface roughness. AIAA J.46 (2), 486-497. |
| [21] | Ekoto, I.W., Bowersox, R.D.W., Beutner, T. & Goss, L.2009Response of supersonic turbulent boundary layers to local and global mechanical distortions. J. Fluid Mech.630, 225-265. · Zbl 1181.76006 |
| [22] | Flack, K.A. & Schultz, M.P.2010Review of hydraulic roughness scales in the fully rough regime. Trans. ASME J. Fluids Engng132 (4), 041203. |
| [23] | Flack, K.A. & Schultz, M.P.2014Roughness effects on wall-bounded turbulent flows. Phys. Fluids26 (10), 101305. |
| [24] | Flack, K.A., Schultz, M.P. & Shapiro, T.A.2005Experimental support for Townsend’s Reynolds number similarity hypothesis on rough walls. Phys. Fluids17 (3), 035102. · Zbl 1187.76157 |
| [25] | Flores, O. & Jimenez, J.2006Effect of wall-boundary disturbances on turbulent channel flows. J. Fluid Mech.566, 357-376. · Zbl 1275.76146 |
| [26] | Fukagata, K., Iwamoto, K. & Kasagi, N.2002Contribution of Reynolds stress distribution to the skin friction in wall-bounded flows. Phys. Fluids14 (11), L73-L76. · Zbl 1185.76134 |
| [27] | Gatski, T.B. & Bonnet, J.P.2013Compressibility, Turbulence and High Speed Flow. Academic. |
| [28] | Gomez, T., Flutet, V. & Sagaut, P.2009Contribution of Reynolds stress distribution to the skin friction in compressible turbulent channel flows. Phys. Rev. E79 (3), 035301. |
| [29] | Griffin, K.P., Fu, L. & Moin, P.2021Velocity transformation for compressible wall-bounded turbulent flows with and without heat transfer. PNAS118 (34), e2111144118. |
| [30] | Hama, F.R.1954Boundary-layer characteristics for smooth and rough surfaces. Trans. Soc. Nav. Archit. Mar. Engrs62, 333-358. |
| [31] | Hirasaki, G.J. & Hellums, J.D.1970Boundary conditions on the vector and scalar potentials in viscous three-dimensional hydrodynamics. Q. Appl. Math.28 (2), 293-296. · Zbl 0229.76031 |
| [32] | Huang, J., Duan, L. & Choudhari, M.M.2022Direct numerical simulation of hypersonic turbulent boundary layers: effect of spatial evolution and Reynolds number. J. Fluid Mech.937, A3. · Zbl 07482837 |
| [33] | Huang, P.G., Coleman, G.N. & Bradshaw, P.1995Compressible turbulent channel flows: DNS results and modelling. J. Fluid Mech.305, 185-218. · Zbl 0857.76036 |
| [34] | Jiménez, J.2004Turbulent flows over rough walls. Annu. Rev. Fluid Mech.36, 173-196. · Zbl 1125.76348 |
| [35] | Jouybari, M.A., Yuan, J., Brereton, G.J. & Jaberi, F.A.2020 Supersonic turbulent channel flows over two and three dimensional sinusoidal rough walls. arXiv:2012.02852 · Zbl 1531.76056 |
| [36] | Kadivar, M., Tormey, D. & Mcgranaghan, G.2021A review on turbulent flow over rough surfaces: fundamentals and theories. Intl J. Thermofluids10, 100077. |
| [37] | Kempf, A.M., Wysocki, S. & Pettit, M.2012An efficient, parallel low-storage implementation of Klein’s turbulence generator for LES and DNS. Comput. Fluids60, 58-60. · Zbl 1365.76088 |
| [38] | Klein, M., Sadiki, A. & Janicka, J.2003A digital filter based generation of inflow data for spatially developing direct numerical or large eddy simulations. J. Comput. Phys.186 (2), 652-665. · Zbl 1047.76522 |
| [39] | Kuya, Y., Totani, K. & Kawai, S.2018Kinetic energy and entropy preserving schemes for compressible flows by split convective forms. J. Comput. Phys.375, 823-853. · Zbl 1416.76182 |
| [40] | Latin, R.M. & Bowersox, R.D.W.2000Flow properties of a supersonic turbulent boundary layer with wall roughness. AIAA J.38 (10), 1804-1821. |
| [41] | Lee, H., Williams, O. & Martin, P.2023 Compressible boundary layer velocity transformation based on a generalized form of the total stress. arXiv:2112.13818. |
| [42] | Lee, J.H., Sung, H.J. & Krogstad, P.2011Direct numerical simulation of the turbulent boundary layer over a cube-roughened wall. J. Fluid Mech.669, 397-431. · Zbl 1225.76163 |
| [43] | Lee, S., Lele, S.K. & Moin, P.1991Eddy shocklets in decaying compressible turbulence. Phys. Fluids3 (4), 657-664. |
| [44] | Leonardi, S., Orlandi, P. & Antonia, R.A.2007Properties of d- and k-type roughness in a turbulent channel flow. Phys. Fluids19 (12), 125101. · Zbl 1182.76449 |
| [45] | Liepman, H.W. & Goddard, F.E.1957Note on the mach number effect upon the skin friction of rough surfaces. J. Aeronaut. Sci.23 (10), 784. |
| [46] | Liu, Y., Yang, Q., Tu, G., Li, X., Guo, Q. & Wan, B.2023Hypersonic boundary-layer instability suppression by transverse microgrooves with machining flaw. AIAA J.61 (3), 1021-1031. |
| [47] | Ma, G.Z., Xu, C.X., Sung, H.J. & Huang, W.X.2020Scaling of rough-wall turbulence by the roughness height and steepness. J. Fluid Mech.900, R7. · Zbl 1460.76482 |
| [48] | Macdonald, M., Chan, L., Chung, D., Hutchins, N. & Ooi, A.2016Turbulent flow over transitionally rough surfaces with varying roughness densities. J. Fluid Mech.804, 130-161. |
| [49] | Modesti, D. & Pirozzoli, S.2016Reynolds and Mach number effects in compressible turbulent channel flow. Intl J. Heat Fluid Flow59, 33-49. |
| [50] | Modesti, D. & Pirozzoli, S.2019Direct numerical simulation of supersonic pipe flow at moderate Reynolds number. Intl J. Heat Fluid Flow76, 100-112. |
| [51] | Modesti, D., Sathyanarayana, S., Salvadore, F. & Bernardini, M.2022Direct numerical simulation of supersonic turbulent flows over rough surfaces. J. Fluid Mech.942, A44. |
| [52] | Morinishi, Y., Tamano, S. & Nakabayashi, K.2004Direct numerical simulation of compressible turbulent channel flow between adiabatic and isothermal walls. J. Fluid Mech.502, 273-308. · Zbl 1134.76363 |
| [53] | Morkovin, M.1962Effects of compressibility on turbulent flows. Mécanique Turbul.367 (380), 26. |
| [54] | Musker, A.J.1979Explicit expression for the smooth wall velocity distribution in a turbulent boundary layer. AIAA J.17 (6), 655-657. · Zbl 0397.76053 |
| [55] | Nikuradse, J.1933Stromungsgesetze in rauhen rohren. VDI-Forschungsheft361, 1. · JFM 59.1462.02 |
| [56] | Orlandi, P. & Leonardi, S.2006DNS of turbulent channel flows with two-and three-dimensional roughness. J. Turbul.7, N73. |
| [57] | Orlandi, P. & Pirozzoli, S.2021Secondary flow in smooth and rough turbulent circular pipes: turbulence kinetic energy budgets. Fluids6 (12), 448. |
| [58] | Patel, A., Boersma, B. & Pecnik, R.2016The influence of near-wall density and viscosity gradients on turbulence in channel flows. J. Fluid Mech.809, 793-820. · Zbl 1383.76244 |
| [59] | Peltier, S.J.2013 Behavior of turbulent structures within a Mach 5 mechanically distorted boundary layer. PhD thesis, Texas A&M University. |
| [60] | Peltier, S.J., Humble, R.A. & Bowersox, R.D.W.2016Crosshatch roughness distortions on a hypersonic turbulent boundary layer. Phys. Fluids28 (4), 045105. |
| [61] | Pirozzoli, S.2010Generalized conservative approximations of split convective derivative operators. J. Comput. Phys.229 (19), 7180-7190. · Zbl 1426.76485 |
| [62] | Pirozzoli, S.2011Numerical methods for high-speed flows. Annu. Rev. Fluid Mech.43, 163-194. · Zbl 1299.76103 |
| [63] | Pirozzoli, S. & Bernardini, M.2011Turbulence in supersonic boundary layers at moderate Reynolds number. J. Fluid Mech.688, 120-168. · Zbl 1241.76286 |
| [64] | Pirozzoli, S., Bernardini, M. & Grasso, F.2010On the dynamical relevance of coherent vortical structures in turbulent boundary layers. J. Fluid Mech.648, 325-349. · Zbl 1189.76290 |
| [65] | Pirozzoli, S., Bernardini, M. & Orlandi, P.2016Passive scalars in turbulent channel flow at high Reynolds number. J. Fluid Mech.788, 614-639. · Zbl 1381.76109 |
| [66] | Pirozzoli, S., Grasso, F. & Gatski, T.B.2004Direct numerical simulation and analysis of a spatially evolving supersonic turbulent boundary layer at \(M= 2.25\). Phys. Fluids16 (3), 530-545. · Zbl 1186.76423 |
| [67] | Poggie, J., Bisek, N.J. & Gosse, R.2015Resolution effects in compressible, turbulent boundary layer simulations. Comput. Fluids120, 57-69. · Zbl 1390.76207 |
| [68] | Samtaney, R., Pullin, D.I. & Kosović, B.2001Direct numerical simulation of decaying compressible turbulence and shocklet statistics. Phys. Fluids13 (5), 1415-1430. · Zbl 1184.76474 |
| [69] | Shima, N., Kuya, Y., Tamaki, Y. & Kawai, S.2021Preventing spurious pressure oscillations in split convective form discretization for compressible flows. J. Comput. Phys.427, 110060. · Zbl 07510246 |
| [70] | Smits, A.J. & Dussauge, J.P.2006Turbulent Shear Layers in Supersonic Flow. Springer. |
| [71] | Sun, D., Guo, Q., Li, C. & Liu, P.2019Direct numerical simulation of effects of a micro-ramp on a hypersonic shock wave/boundary layer interaction. Phys. Fluids31 (12), 126101. |
| [72] | Sun, Z.S., Zhu, Y.J., Hu, Y. & Zhang, S.Y.2018Direct numerical simulation of a fully developed compressible wall turbulence over a wavy wall. J. Turbul.19 (1), 72-105. |
| [73] | Tao, J.J.2009Critical instability and friction scaling of fluid flows through pipes with rough inner surfaces. Phys. Rev. Lett.103 (26), 264502. |
| [74] | Townsend, A.A.1976The Structure of Turbulent Shear Flow. Cambridge University Press. · Zbl 0325.76063 |
| [75] | Trettel, A. & Larsson, J.2016Mean velocity scaling for compressible wall turbulence with heat transfer. Phys. Fluids28 (2), 026102. |
| [76] | Tyson, C.J. & Sandham, N.D.2013Numerical simulation of fully-developed compressible flows over wavy surfaces. Intl J. Heat Fluid Flow41, 2-15. |
| [77] | Van Driest, E.1951Turbulent boundary layer in compressible fluids. Intl J. Aeronaut. Space Sci.18 (3), 145-160. · Zbl 0045.12903 |
| [78] | Volpiani, P.S., Iyer, P.S., Pirozzoli, S. & Larsson, J.2020Data-driven compressibility transformation for turbulent wall layers. Phys. Rev. Fluids5 (5), 052602. |
| [79] | Wang, J., Gotoh, T. & Watanabe, T.2017Shocklet statistics in compressible isotropic turbulence. Phys. Rev. Fluids2 (2), 023401. |
| [80] | Wang, J., Wan, M., Chen, S., Xie, C. & Chen, S.2018Effect of shock waves on the statistics and scaling in compressible isotropic turbulence. Phys. Rev. E97 (4), 043108. |
| [81] | Wang, J., Wan, M., Chen, S., Xie, C., Zheng, Q., Wang, L. & Chen, S.2020Effect of flow topology on the kinetic energy flux in compressible isotropic turbulence. J. Fluid Mech.883, A11. · Zbl 1430.76209 |
| [82] | Wang, J.C., Shi, Y.P., Wang, L.P., Xiao, Z.L., He, X.T. & Chen, S.Y.2012Effect of compressibility on the small-scale structures in isotropic turbulence. J. Fluid Mech.713, 588-631. · Zbl 1284.76214 |
| [83] | Wang, L. & Lu, X.Y.2012Flow topology in compressible turbulent boundary layer. J. Fluid Mech.703, 255-278. · Zbl 1248.76085 |
| [84] | Watanabe, T., Tanaka, K. & Nagata, K.2021Solenoidal linear forcing for compressible, statistically steady, homogeneous isotropic turbulence with reduced turbulent Mach number oscillation. Phys. Fluids33 (9), 095108. |
| [85] | Wenzel, C., Gibis, T. & Kloker, M.2022About the influences of compressibility, heat transfer and pressure gradients in compressible turbulent boundary layers. J. Fluid Mech.930, A1. · Zbl 1508.76062 |
| [86] | Wenzel, C., Selent, B., Kloker, M. & Rist, U.2018Dns of compressible turbulent boundary layers and assessment of data/scaling-law quality. J. Fluid Mech.842, 428-468. · Zbl 1419.76331 |
| [87] | Williams, O.J.H., Sahoo, D., Papageorge, M. & Smits, A.J.2021Effects of roughness on a turbulent boundary layer in hypersonic flow. Exp. Fluids62 (9), 1-13. |
| [88] | Zhu, W.K.2022Notes on the hypersonic boundary layer transition. Adv. Aerodyn.4, 23. |
| [89] | Yu, M., Liu, P.X., Fu, Y.L., Tang, Z.G. & Yuan, X.X.\(2022a\) Wall shear stress, pressure and heat flux fluctuations in compressible wall-bounded turbulence. Part I. One-point statistics. Phys. Fluids34 (6), 065139. |
| [90] | Yu, M., Liu, P.X., Fu, Y.L., Tang, Z.G. & Yuan, X.X.\(2022b\) Wall shear stress, pressure and heat flux fluctuations in compressible wall-bounded turbulence. Part II. Spectra, correlation and nonlinear interactions. Phys. Fluids34 (6), 065140. |
| [91] | Yu, M., Liu, P.X., Yuan, X.X., Tang, Z.G. & Xu, C.X.\(2023a\) Effects of wall disturbances on the statistics of supersonic turbulent boundary layers. Phys. Fluids35, 025126. |
| [92] | Yu, M. & Xu, C.X.2021Compressibility effects on hypersonic turbulent channel flow with cold walls. Phys. Fluids33 (7), 075106. |
| [93] | Yu, M., Xu, C.X. & Pirozzoli, S.2019Genuine compressibility effects in wall-bounded turbulence. Phys. Rev. Fluids4 (12), 123402. |
| [94] | Yu, M., Zhou, Q.Q., Su, H.M., Yuan, X.X. & Guo, Q.L.\(2023b\) Influences of wall disturbances on coherent structures in supersonic turbulent boundary layers. Acta Mech. Sin. (in press). |
| [95] | Yuan, X.X., Fu, Y.L., Chen, J.Q., Yu, M. & Liu, P.X.2022Supersonic turbulent channel flows over spanwise-oriented grooves. Phys. Fluids34 (1), 016109. |
| [96] | Zhang, C., Duan, L. & Choudhari, M.M.2018Direct numerical simulation database for supersonic and hypersonic turbulent boundary layers. AIAA J.56 (11), 4297-4311. |
| [97] | Zhang, Y., Bi, W., Hussain, F., Li, X. & She, Z.2012Mach-number-invariant mean-velocity profile of compressible turbulent boundary layers. Phys. Rev. Lett.109 (5), 054502. |
| [98] | Zhang, Y.S., Bi, W.T., Hussain, F. & She, Z.S.2014A generalized Reynolds analogy for compressible wall-bounded turbulent flows. J. Fluid Mech.739, 392-420. |
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