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Numerical study of instabilities and compressibility effects on supersonic jet over a convex wall

Published online by Cambridge University Press:  23 December 2022

Qing Wang ,
Feng Qu Open the ORCID record for Feng Qu [Opens in a new window] ,
Di Sun  and
Junqiang Bai
Qing Wang
Affiliation:
School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, PR China
Feng Qu*
Affiliation:
School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, PR China
Di Sun
Affiliation:
School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, PR China
Junqiang Bai
Affiliation:
School of Aeronautics, Northwestern Polytechnical University, Xi'an 710072, PR China
*
†Email address for correspondence: qufeng@nwpu.edu.cn
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Abstract

The supersonic jet over a convex wall is numerically investigated using the delayed detached-eddy simulation method based on the two-equation shear-stress transport model. The current study focuses on instabilities, turbulent statistics and the influence of compressibility effects. A widely applicable data-driven modal decomposition approach, called dynamic mode decomposition is used to gain further insight into the dynamical behaviours of the flow. The results demonstrate that streamwise vortices caused by the centrifugal force play significant roles in shear layer instabilities. The spanwise modulation of the streamwise vortices induces inflection points in the flow, resulting in secondary shear layer instability. This instability, which is sustained by the side-to-side sway of the streamwise vortices to obtain energy from the mean flow, dominates the rapid growth of the shear layer and turbulent stresses in the growth region. In the self-similar region, there is not only self-similarity of velocity profiles, but also self-similarity of normalized turbulent stresses. The compressibility effect significantly inhibits the growth of the shear layer and the formation of large-scale streamwise vortices. The investigation of turbulent stresses in the self-similar region with increasing convective Mach number indicates that the compressibility effect enhances turbulence anisotropy.

JFM classification

Aerodynamics: High-speed flow Boundary Layers: Boundary layer separation Compressible Flows: Supersonic flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 954 , 10 January 2023 , A6
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

REFERENCES

Baca, B.K. 1982 An experimental study of the reattachment of a free shear layer in compressible turbulent flow. PhD thesis, Princeton University.Google Scholar
Bogdanoff, D.W. 1983 Compressibility effects in turbulent shear layers. AIAA J. 21 (6), 926–927.CrossRefGoogle Scholar
Clemens, N.T. & Mungal, M.G. 1992 Two- and three-dimensional effects in the supersonic mixing layer. AIAA J. 30 (4), 973–981.CrossRefGoogle Scholar
Crowther, W.J., Wilde, P.I.A., Gill, K. & Michie, S.M. 2009 Towards integrated design of fluidic flight controls for a flapless aircraft. Aeronaut. J. 113 (1149), 699–713.CrossRefGoogle Scholar
Cunff, C.L. & Zebib, A. 1996 Nonlinear spatially developing görtler vortices in curved wall jet flow. Phys. Fluids 8 (9), 2375–2384.CrossRefGoogle Scholar
Dunaevich, L. & Greenblatt, D. 2020 Stability and transition on a coand cylinder. Phys. Fluids 32 (8), 084106.CrossRefGoogle Scholar
Elliott, G.S., Mo, S. & Arnette, S.A. 1995 The characteristics and evolution of large-scale structures in compressible mixing layers. Phys. Fluids 7 (4), 864–876.CrossRefGoogle Scholar
Englar, R.J., Hemmerly, R.A., Taylor, D.W., Moore, W.H., Seredinsky, V., Valckenaere, W. & Jackson, J.A. 1981 Design of the circulation control wing stol demonstrator aircraft. J. Aircraft 18 (1), 51–58.CrossRefGoogle Scholar
Fan, C.C., Xiao, X., Edwards, J.R., Hassan, H.A. & Baurle, R.A. 2004 Hybrid large-eddy / reynolds-averaged navier-stokes simulation of shock-separated flows. J. Spacecr. Rockets 41 (6), 897–906.CrossRefGoogle Scholar
Ferlauto, M. & Marsilio, R. 2017 Numerical investigation of the dynamic characteristics of a dual-throat-nozzle for fluidic thrust-vectoring. AIAA J. 55 (1), 86–98.CrossRefGoogle Scholar
Flamm, J.D., Deere, K.A., Mason, M.L., Berrier, B.L. & Johnson, S.K. 2006 Design enhancements of the two-dimensional, dual throat fluidic thrust vectoring nozzle concept. In 3rd AIAA Flow Control Conference, AIAA Paper 2006-3701.Google Scholar
Fu, D., Ma, Y. & Zhang, L. 2000 Direct numerical simulation of transition and turbulence in compressible mixing layer. Sci. China Ser. A: Math. 43 (4), 421–429.CrossRefGoogle Scholar
Fujisawa, N. & Kobayashi, R. 1987 Turbulence characteristics of wall jets along strong convex surfaces. Intl J. Mech. Sci. 29 (5), 311–320.CrossRefGoogle Scholar
Gnanamanickam, E.P., Bhatt, S., Artham, S. & Zhang, Z. 2019 Large-scale motions in a plane wall jet. J. Fluid Mech. 877, 239–281.CrossRefGoogle Scholar
Goebel, S.G. & Dutton, J.C. 2015 Experimental study of compressible turbulent mixing layers. AIAA J. 29 (4), 538–546.CrossRefGoogle Scholar
Görtler, H. 1941 Instabilitat laminarer grenzchichten an konkaven wanden gengenuber gewissen deeidimensionalen storungen. Z. Angew. Math. Mech. 21 (4), 250–252.CrossRefGoogle Scholar
Gregory-Smith, D.G. & Gilchrist, A.R. 1987 The compressible coanda wall jet—an experimental study of jet structure and breakaway. Intl J. Heat Fluid Flow 8 (2), 156–164.CrossRefGoogle Scholar
Gregory-Smith, D.G. & Senior, P. 1994 The effects of base steps and axisymmetry on supersonic jets over coanda surfaces. Intl J. Heat Fluid Flow 15 (4), 291–298.CrossRefGoogle Scholar
Hall, J.L., Dimotakis, P.E. & Rosemann, H. 1993 Experiments in nonreacting compressible shear layers. AIAA J. 31 (12), 2247–2254.CrossRefGoogle Scholar
Han, G., de Zhou, M. & Wygnanski, I. 2006 On streamwise vortices and their role in the development of a curved wall jet. Phys. Fluids 18 (9), 1.CrossRefGoogle Scholar
Harley, C., Wilde, P. & Crowther, W. 2009 Application of circulation control manoeuvre effectors for three axis control of a tailless flight vehicle. In 47th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition, AIAA Paper 146.Google Scholar
Hayakawa, K., Smits, A.J. & Bogdonoff, S.M. 1984 Turbulence measurements in a compressible reattaching shear layer. AIAA J. 22 (7), 889–895.CrossRefGoogle Scholar
Henri, C. 1936 Device for deflecting a stream of elastic fluid projected into an elastic fluid. US Patent 2, 052, 869. Google Patents.Google Scholar
Hoholis, G., Steijl, R. & Badcock, K. 2016 Circulation control as a roll effector for unmanned combat aerial vehicles. J. Aircraft 53 (6), 1875–1889.CrossRefGoogle Scholar
Johnson, A.D. & Papamoschou, D. 2010 Instability of shock-induced nozzle flow separation. Phys. Fluids 22 (1), 143–865.CrossRefGoogle Scholar
Kim, K.U., Elliott, G.S. & Dutton, J.C. 2020 Three-dimensional experimental study of compressibility effects on turbulent free shear layers. AIAA J. 58 (1), 133–147.CrossRefGoogle Scholar
Li, L., Hirota, M., Ouchi, K. & Saito, T. 2017 Evaluation of fluidic thrust vectoring nozzle via thrust pitching angle and thrust pitching moment. Shock Waves 27 (1), 53–61.CrossRefGoogle Scholar
Likhachev, O., Neuendorf, R. & Wygnanski, I. 2001 On streamwise vortices in a turbulent wall jet that flows over a convex surface. Phys. Fluids 13 (6), 1822–1825.CrossRefGoogle Scholar
Liu, X.D., Osher, S. & Chan, T. 1994 Weighted essentially non-oscillatory schemes. J. Comput. Phys. 115 (1), 200–212.CrossRefGoogle Scholar
Llopis-Pascual, A. 2017 Supercritical coanda jets for flight control effectors. PhD thesis, Manchester University, Manchester.Google Scholar
Mason, M. & Crowther, W. 2004 Fluidic thrust vectoring for low observable air vehicles. In 2nd AIAA Flow Control Conference, AIAA Paper 2004-2210.Google Scholar
Matsson, O. & John, E. 1998 Görtler vortices in wall jet flow on a rotating cylinder. Phys. Fluids 10 (9), 2238–2238.CrossRefGoogle Scholar
Menter, F.R. 1994 Two-equation eddy-viscosity turbulence models for engineering applications. AIAA J. 32, 1598–1605.CrossRefGoogle Scholar
Moin, P. & Mahesh, K. 1998 Direct numerical simulation: a tool in turbulence research. Annu. Rev. Fluid Mech. 30 (1), 539–578.CrossRefGoogle Scholar
Nagata, R., Watanabe, T. & Nagata, K. 2018 Turbulent/non-turbulent interfaces in temporally evolving compressible planar jets. Phys. Fluids 30 (10), 105109.CrossRefGoogle Scholar
Naqavi, I.Z., Tyacke, J.C. & Tucker, P.G. 2018 Direct numerical simulation of a wall jet: flow physics. J. Fluid Mech. 852, 507–542.CrossRefGoogle Scholar
Neuendorf, R., Lourenco, L. & Wygnanski, I. 2004 On large streamwise structures in a wall jet flowing over a circular cylinder. Phys. Fluids 16 (7), 2158–2158.CrossRefGoogle Scholar
Neuendorf, R. & Wygnanski, I. 1999 On a turbulent wall jet flowing over a circular cylinder. J. Fluid Mech. 381, 1–25.CrossRefGoogle Scholar
Pandey, A. & Gregory, J.W. 2020 Instabilities and turbulence in a forced turbulent convex wall jet. Phys. Fluids 32 (9), 095111.CrossRefGoogle Scholar
Pandey, A. & Gregory, J.W. 2021 Spanwise wavelength of streamwise vortices in a forced turbulent convex wall jet. AIAA J. 58 (1), 1–6.Google Scholar
Papamoschou, D. & Roshko, A. 1988 The compressible turbulent shear layer: an experimental study. J. Fluid Mech. 197 (1), 453–477.CrossRefGoogle Scholar
Qu, F., Chen, J., Sun, D., Bai, J. & Zuo, G. 2019 a A grid strategy for predicting the space plane's hypersonic aerodynamic heating loads. Aerosp. Sci. Technol. 86, 659–670.CrossRefGoogle Scholar
Qu, F. & Sun, D. 2017 Investigation into the influences of the low-speed flows’ accuracy on rans simulations. Aerosp. Sci. Technol. 70, 578–589.CrossRefGoogle Scholar
Qu, F., Sun, D., Han, K., Bai, J., Zuo, G. & Yan, C. 2019 b Numerical investigation of the supersonic stabilizing parachute's heating loads. Aerosp. Sci. Technol. 87, 89–97.CrossRefGoogle Scholar
Rowley, C.W. & Dawson, S.T.M. 2017 Model reduction for flow analysis and control. Annu. Rev. Fluid Mech. 49 (1), 387–417.CrossRefGoogle Scholar
Sandham, N.D. & Reynolds, W.C. 1991 Three-dimensional simulations of large-eddies in the compressible mixing layer. J. Fluid Mech. 224 (2), 133–158.CrossRefGoogle Scholar
Schmid, P. & Sesterhenn, J. 2010 Dynamic mode decomposition of numerical and experimental data. J. Fluid Mech. 656 (10), 5–28.CrossRefGoogle Scholar
Smith, D.R. & Warsop, C. 2019 Nato avt-239 task group: ‘innovative control effectors for manoeuvring of air vehicles’–introduction and overview. In AIAA Scitech 2019 Forum, AIAA Paper 2019-0041.Google Scholar
Spalart, P.R., Deck, S., Shur, M.L., Squires, K.D., Strelets, M.K. & Travin, A. 2006 A new version of detached-eddy simulation, resistant to ambiguous grid densities. Theor. Comput. Fluid Dyn. 20, 181–195.CrossRefGoogle Scholar
Sun, D., Qu, F., Liu, C., Yao, F. & Bai, J. 2020 Numerical study of the suction flow control of the supersonic boundary layer transition in a framework of gas-kinetic scheme. Aerosp. Sci. Technol. 109 (2), 106397.CrossRefGoogle Scholar
Sun, D., Qu, F. & Yan, C. 2018 An effective flux scheme for hypersonic heating prediction of re-entry vehicles. Comput. Fluids 176, 109–116.CrossRefGoogle Scholar
Sun, M., Sandham, N.D. & Hu, Z. 2019 Turbulence structures and statistics of a supersonic turbulent boundary layer subjected to concave surface curvature. J. Fluid Mech. 865, 60–99.CrossRefGoogle Scholar
Taira, K., Brunton, S.L., Dawson, S.T., Rowley, C.W., Colonius, T., Mckeon, B.J., Schmidt, O.T., Gordeyev, S., Theofilis, V. & Ukeiley, L.S. 2017 Modal analysis of fluid flows: an overview. AIAA J. 55 (12), 4013–4041.CrossRefGoogle Scholar
Taira, K., Hemati, M.S., Brunton, S.L., Sun, Y. & Yeh, C.A. 2020 Modal analysis of fluid flows: applications and outlook. AIAA J. 58 (3), 998–1022.CrossRefGoogle Scholar
Tsuji, Y., Morikawa, Y., Nagatani, T. & Sakou, M. 1977 The stability of a two-dimensional wall jet. Aeronaut. Q. 28 (4), 235–246.CrossRefGoogle Scholar
Tu, J.H., Rowley, C.W., Luchtenburg, D.M., Brunton, S.L. & Kutz, J.N. 2014 On dynamic mode decomposition: theory and applications. J. Comput. Dyn. 1 (2), 391–421.CrossRefGoogle Scholar
Urban, W.D. & Mungal, M.G. 2001 Planar velocity measurements in compressible mixing layers. J. Fluid Mech. 431, 189–222.CrossRefGoogle Scholar
Wang, Q.C., Wang, Z.G., Sun, M.B., Yang, R., Zhao, Y.X. & Hu, Z. 2019 The amplification of large-scale motion in a supersonic concave turbulent boundary layer and its impact on the mean and statistical properties. J. Fluid Mech. 863, 454–493.CrossRefGoogle Scholar
Wang, Q.C., Wang, Z.G. & Zhao, Y.X. 2017 The impact of streamwise convex curvature on the supersonic turbulent boundary layer. Phys. Fluids 29 (11), 116106.CrossRefGoogle Scholar
Warsop, C., Crowther, W. & Forster, M. 2019 Nato avt-239 task group: supercritical coanda based circulation control and fluidic thrust vectoring. In AIAA Scitech 2019 Forum, AIAA Paper 2019-0044.Google Scholar
Watanabe, T. & Nagata, K. 2021 Large-scale characteristics of a stably stratified turbulent shear layer. J. Fluid Mech. 927, A27.CrossRefGoogle Scholar
Wernz, S. & Fasel, H.F. 2007 Nonlinear resonances in a laminar wall jet: ejection of dipolar vortices. J. Fluid Mech. 588, 279–308.CrossRefGoogle Scholar
Wilde, P., Buonanno, A., Crowther, W. & Savvaris, A. 2008 Aircraft control using fluidic maneuver effectors. In 26th AIAA Applied Aerodynamics Conference, AIAA Paper 2008-6406.Google Scholar
Williams, F.A. 2003 Mixing of a conserved scalar in a turbulent reacting shear layer. J. Fluid Mech. 481, 291–328.Google Scholar
Yoon, S. & Jameson, A. 1988 Lower-upper symmetric-gauss-seidel method for the euler and navier-stokes equations. AIAA J. 26 (9), 1025–1026.CrossRefGoogle Scholar
Yubiao, J., Liu, Z., Yong, H., Lihua, G. & Hong, C., 2018 Lift response characteristics of a circulation control airfoil with internally blown flap. Acta Aeronaut. Astronaut. Sinica 39 (7), 64–72.Google Scholar
Zhang, D., Tan, J. & Li, H. 2017 Structural characteristics of supersonic mixing enhanced by introducing streamwise vortices. Appl. Phys. Lett. 111 (11), 114103.CrossRefGoogle Scholar
Zhang, D., Tan, J. & Yao, X. 2019 Direct numerical simulation of spatially developing highly compressible mixing layer: structural evolution and turbulent statistics. Phys. Fluids 31 (3), 036102.CrossRefGoogle Scholar
Zhou, Q., He, F. & Shen, M.Y. 2012 Direct numerical simulation of a spatially developing compressible plane mixing layer: flow structures and mean flow properties. J. Fluid Mech. 711, 437–468.CrossRefGoogle Scholar