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Evolution of tornado-like vortices in three-dimensional compressible rectangular cavity flows

Published online by Cambridge University Press:  13 January 2023

Yong Luo ,
Hao Tian ,
Conghai Wu ,
Hu Li ,
Yimin Wang Open the ORCID record for Yimin Wang [Opens in a new window]  and
Shuhai Zhang Open the ORCID record for Shuhai Zhang [Opens in a new window]
Yong Luo
Affiliation:
State Key Laboratory of Aerodynamics, China Aerodynamics Research and Development Center, Mianyang, Sichuan 621000, PR China
Hao Tian
Affiliation:
State Key Laboratory of Aerodynamics, China Aerodynamics Research and Development Center, Mianyang, Sichuan 621000, PR China
Conghai Wu
Affiliation:
State Key Laboratory of Aerodynamics, China Aerodynamics Research and Development Center, Mianyang, Sichuan 621000, PR China
Hu Li
Affiliation:
State Key Laboratory of Aerodynamics, China Aerodynamics Research and Development Center, Mianyang, Sichuan 621000, PR China
Yimin Wang
Affiliation:
State Key Laboratory of Aerodynamics, China Aerodynamics Research and Development Center, Mianyang, Sichuan 621000, PR China
Shuhai Zhang*
Affiliation:
State Key Laboratory of Aerodynamics, China Aerodynamics Research and Development Center, Mianyang, Sichuan 621000, PR China
*
†Email address for correspondence: shuhai_zhang@163.com
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Abstract

The spatial structure and time evolution of tornado-like vortices in a three-dimensional cavity are studied by topological analysis and numerical simulation. The topology theory of the unsteady vortex in the rectangular coordinate system (Zhang, Zhang & Shu, J. Fluid Mech., vol. 639, 2009, pp. 343–372) is generalized to the curvilinear coordinate system. Two functions $\lambda (q_1,t)$ and $q(q_1,t)$ are obtained to determine the topology structure of the sectional streamline pattern in the cross-section perpendicular to the vortex axis and the meridional plane, respectively. The spiral direction of the sectional streamlines in the cross-section perpendicular to the vortex axis depends on the sign of $\lambda (q_1,t)$. The types of critical points in the meridional plane depend on the sign of $q(q_1,t)$. The relation between the critical points of the streamline pattern in the meridional plane and that in the cross-section perpendicular to the vortex axis is set up. The flow in a three-dimensional rectangular cavity is numerically simulated by solving the three-dimensional Navier–Stokes equations using high-order numerical methods. The spatial structures and the time evolutions of the tornado-like vortices in the cavity are analysed with our topology theory. Both the bubble type and spiral type of vortex breakdown are observed. They have a close relationship with the vortex structure in the cross-section perpendicular to the vortex axis. The bubble-type breakdown has a conical core and the core is non-axisymmetric in the sense of topology. A criterion for the bubble type and the spiral type based on the spatial structure characteristic of the two breakdown types is provided.

JFM classification

Vortex Flows: Vortex breakdown Wakes/Jets: Separated flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 955 , 25 January 2023 , A9
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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References

REFERENCES

Ashrafi, A., Romanic, D., Kassab, A., Hangan, H. & Ezami, N. 2021 Experimental investigation of large-scale tornado-like vortices. J. Wind Engng Ind. Aerodyn. 208, 104449.CrossRefGoogle Scholar
Ashton, R., Refan, M., Iungo, G.V. & Hangan, H. 2019 Wandering corrections from PIV measurements of tornado-like vortices. J. Wind Engng Ind. Aerodyn. 189, 163–172.CrossRefGoogle Scholar
Atvars, K., Knowles, K., Ritchie, S.A. & Lawson, N.J. 2009 Experimental and computational investigation of an ‘open’ transonic cavity flow. Proc. Inst. Mech. Engrs G: J. Aerosp. Engng 223 (4), 357–368.Google Scholar
Benjamin, T.B. 1962 Theory of the vortex breakdown phenomenon. J. Fluid Mech. 14 (4), 593–629.CrossRefGoogle Scholar
Beresh, S.J., Wagner, J.L. & Casper, K.M. 2016 Compressibility effects in the shear layer over a rectangular cavity. J. Fluid Mech. 808, 116–152.CrossRefGoogle Scholar
Beresh, S.J., Wagner, J.L., Henfling, J.F., Spillers, R.W. & Pruett, B.O.M. 2015 a Width effects in transonic flow over a rectangular cavity. AIAA J. 53 (12), 3831–3835.Google Scholar
Beresh, S.J., Wagner, J.L., Pruett, B.O.M., Henfling, J.F. & Spillers, R.W. 2015 b Supersonic flow over a finite-width rectangular cavity. AIAA J. 53 (2), 296–310.CrossRefGoogle Scholar
Bossel, H.H. 1969 Vortex breakdown flowfield. Phys. Fluids 12 (3), 498–508.CrossRefGoogle Scholar
Brockwell, P.J. & Davis, R.A. 1991 Time Series: Theory and Methods, 2nd edn, pp. 239–241. Springer Press.CrossRefGoogle Scholar
Chen, L., Zhu, T., Xu, J. & Jiang, T. 2017 Applications of fluorescence-oil-flow visualization technique in hypersonic wind tunnel test (in Chinese). Acta Aerodyn. Sin. 35 (6), 817–822.Google Scholar
Chong, M.S., Perry, A.E. & Cantwell, B.J. 1990 A general classification of three-dimensional flow fields. Phys. Fluids A: Fluid Dyn. 2 (5), 765–777.CrossRefGoogle Scholar
Church, C.R., Snow, J.T., Baker, G.L. & Agee, E.M. 1979 Characteristics of tornado-like vortices as a function of swirl ratio: A laboratory investigation. J. Atmos. Sci. 36, 1755–1776.2.0.CO;2>CrossRefGoogle Scholar
Citro, V., Giannetti, F., Brandt, L. & Luchini, P. 2015 Linear three-dimensional global and asymptotic stability analysis of incompressible open cavity flow. J. Fluid Mech. 768, 113–140.Google Scholar
Crook, S.D., Lau, T.C.W. & Kelso, R.M. 2013 Three-dimensional flow within shallow, narrow cavities. J. Fluid Mech. 735, 587–612.CrossRefGoogle Scholar
Délery, J.M. 1994 Aspects of vortex breakdown. Prog. Aerosp. Sci. 30 (1), 1–59.Google Scholar
Délery, J.M. 2001 Robert Legendre and Henri Werlé: toward the elucidation of three-dimensional separation. Annu. Rev. Fluid Mech. 33 (1), 129–154.CrossRefGoogle Scholar
Dix, R.E. & Bauer, R.C. 2000 Experimental and predicted acoustic amplitudes in a rectangular cavity. AIAA Paper 2000-0472.Google Scholar
Dolling, D.S., Perng, S.W. & Leu, Y.L. 1997 An experimental study of passive control of hypersonic cavity flow oscillations. Tech. Rep. AFRL-SR-BL-TR-98-0240. Center for Aeromechanical Research, University of Texas.Google Scholar
Gloerfelt, X., Bogey, C. & Bailly, C. 2007 Cavity noise, pp. 4–6, 46–47. Arts et Métiers ParisTech.Google Scholar
Hall, M.G. 1961 A theory for the core of a leading-edge vortex. J. Fluid Mech. 11 (2), 209–228.CrossRefGoogle Scholar
Hall, M.G. 1972 Vortex breakdown. Annu. Rev. Fluid Mech. 4, 195–218.Google Scholar
Heller, H.H. & Bliss, D.B. 1975 The physical mechanism of flow-induced pressure fluctuations in cavities and concepts for their suppression. AIAA Paper 1975-491.Google Scholar
Jameson, A. & Yoon, S. 1987 Lower-upper implicit schemes with multiple grids for the Euler equations. AIAA J. 25, 929–935.CrossRefGoogle Scholar
Jordan, D.W. & Smith, P. 1977 Nonlinear Ordinary Differential Equations. Oxford University Press.Google Scholar
Karami, M., Hangan, H., Carassale, L. & Peerhossaini, H. 2019 Coherent structures in tornado-like vortices. Phys. Fluids 31 (8), 085118.Google Scholar
Lambourne, N.C. & Bryer, D.W. 1962 The bursting of leading-edge vortices-some observations and discussion of the phenomenon. Tech. Rep. 3282. Aeronautical Research Council.Google Scholar
Lawson, S.J. & Barakos, G.N. 2011 Review of numerical simulations for high-speed, turbulent cavity flows. Prog. Aerosp. Sci. 47 (3), 186–216.CrossRefGoogle Scholar
Legendre, R. 1956 Séparation de l’écoulement laminaire tridimensionnel. La Rech. Aéronaut. 54, 3–8.Google Scholar
Legendre, R. 1977 Lignes de courant d'un écoulement permanent. La Rech. Aéronaut. 6, 327–335.Google Scholar
Leibovich, S. 1978 The structure of vortex breakdown. Annu. Rev. Fluid Mech. 10 (1), 221–246.CrossRefGoogle Scholar
Leibovich, S. 1984 Vortex stability and breakdown: survey and extension. AIAA J. 22 (9), 1192–1206.Google Scholar
Lessen, M., Singh, P.J. & Paillet, F. 1974 The stability of a trailing line vortex. Part 1. Inviscid theory. J. Fluid Mech. 63 (4), 753–763.CrossRefGoogle Scholar
Lugt, H.J. 1989 Vortex breakdown in atmospheric columnar vortices. Bull. Am. Meteorol. Soc. 70, 1526–1537.2.0.CO;2>CrossRefGoogle Scholar
Meseguer-Garrido, F., de Vicente, J., Valero, E. & Theofilis, V. 2014 On linear instability mechanisms in incompressible open cavity flow. J. Fluid Mech. 752, 219–236.CrossRefGoogle Scholar
Morton, M.H. 2007 Certification of the F-22 advanced tactical fighter for high cycle and sonic fatigue. AIAA Paper 2007-1766.Google Scholar
Natarajan, D. & Hangan, H. 2012 Large eddy simulations of translation and surface roughness effects on tornado-like vortices. J. Wind Engng Ind. Aerodyn. 104–106, 577–584.CrossRefGoogle Scholar
Nolan, D.S. 2012 Three-dimensional instabilities in tornado-like vortices with secondary circulations. J. Fluid Mech. 711, 61–100.Google Scholar
Perry, A. & Chong, M. 1987 A description of eddying motions and flow patterns using critical-point concepts. Annu. Rev. Fluid Mech. 19, 125–155.Google Scholar
Picella, F., Loiseau, J.-C., Lusseyran, F., Robinet, J.-C., Cherubini, S. & Pastur, L. 2018 Successive bifurcations in a fully three-dimensional open cavity flow. J. Fluid Mech. 844, 855–877.Google Scholar
Plentovich, E.B., Stallings, R.L. & Tracy, M.B. 1993 Experimental cavity pressure measurements at subsonic and transonic speeds. Tech. Rep. 3358. Langley Research Center.Google Scholar
Pope, S.B. 2000 Turbulent Flows, 1st edn, p. 270. Cambridge University Press.CrossRefGoogle Scholar
Refan, M. & Hangan, H. 2016 Characterization of tornado-like flow fields in a new model scale wind testing chamber. J. Wind Engng Ind. Aerodyn. 151, 107–121.CrossRefGoogle Scholar
Refan, M. & Hangan, H. 2018 Near surface experimental exploration of tornado vortices. J. Wind Engng Ind. Aerodyn. 175, 120–135.CrossRefGoogle Scholar
Rossiter, J.E. 1964 Wind-tunnel experiments on the flow over rectangular cavities at subsonic and transonic speeds. Aeronautical Research Council Reports and Memoranda, no. 3438.Google Scholar
Rotunno, R. 2013 The fluid dynamics of tornadoes. Annu. Rev. Fluid Mech. 45 (1), 59–84.CrossRefGoogle Scholar
Rowley, C.W., Colonius, T. & Basu, A.J. 2002 On self-sustained oscillations in two-dimensional compressible flow over rectangular cavities. J. Fluid Mech. 455 (455), 315–346.CrossRefGoogle Scholar
Rowley, C.W. & Williams, D.R. 2006 Dynamics and control of high-Reynolds-number flow over open cavities. Annu. Rev. Fluid Mech. 38 (1), 251–276.Google Scholar
Sarpkaya, T. 1971 a On stationary and travelling vortex breakdowns. J. Fluid Mech. 45 (3), 545–559.CrossRefGoogle Scholar
Sarpkaya, T. 1971 b Vortex breakdown in swirling conical flows. AIAA J. 9 (9), 1792–1799.CrossRefGoogle Scholar
Shur, M.L., Spalart, P.R., Strelets, M.K. & Travin, A.K. 2008 A hybrid RANS-LES approach with delayed-DES and wall-modelled LES capabilities. Intl J. Heat Fluid Flow 29 (6), 1638–1649.Google Scholar
Spalart, P.R. & Allmaras, S.R. 1994 A one-equation turbulence model for aerodynamic flows. AIAA Paper 92-0439.Google Scholar
Stallings, R.L. & Wilcox, F.J. 1987 Experimental cavity pressure distributions at supersonic speeds. Tech. Rep. 2683. Langley Research Center.Google Scholar
Woodiga, S. & Liu, T. 2009 Skin friction fields on delta wings. Exp. Fluids 47, 897–911.Google Scholar
Yang, D.G., Liu, J., Wang, X.S., Shi, A., Zhou, F.Q. & Zheng, X.D. 2018 Analysis of design method and aeroacoustics characteristics inside typical cavity. Acta Aerodyn. Sin. 36 (3), 432–439, 448.Google Scholar
Yeom, H.-W., Seo, B.-G. & Sung, H.-G. 2013 Numerical analysis of a scramjet engine with intake sidewalls and cavity flameholder. AIAA J. 51 (7), 1566–1575.CrossRefGoogle Scholar
Zhang, H. 1995 Analytical analysis of subsonic and supersonic vortex motion. Acta Aerodyn. Sin. 13 (3), 259–264.Google Scholar
Zhang, H. 2005 Structural Analysis of Separated Flows and Vortex Motion (in Chinese). National Defense Industry Press.Google Scholar
Zhang, S. 2018 Tubular limiting stream surface: tornado in three-dimensional vortical flow. Appl. Maths Mech. 39 (11), 1631–1642.Google Scholar
Zhang, S., Jiang, S. & Shu, C.-W. 2008 Development of nonlinear weighted compact schemes with increasingly higher order accuracy. J. Comput. Phys. 227 (15), 7294–7321.CrossRefGoogle Scholar
Zhang, S., Zhang, H. & Shu, C.-W. 2009 Topological structure of shock induced vortex breakdown. J. Fluid Mech. 639, 343–372.CrossRefGoogle Scholar
Zhou, F.Q., Yang, D.G., Wang, X.S., Liu, J. & Shi, A. 2018 Effect of leading edge plate on high speed cavity noise control. Acta Aeronaut. Astronaut. Sin. 39 (4), 121812.Google Scholar
Zhou, J., Adrian, R.J., Balachandar, S. & Kendall, T.M. 1999 Mechanisms for generating coherent packets of hairpin vortices in channel flow. J. Fluid Mech. 387, 353–396.CrossRefGoogle Scholar