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Experimental validation of inviscid linear stability theory applied to an axisymmetric jet

Published online by Cambridge University Press:  11 January 2022

L.R. Gareev Open the ORCID record for L.R. Gareev [Opens in a new window] ,
J.S. Zayko Open the ORCID record for J.S. Zayko [Opens in a new window] ,
A.D. Chicherina Open the ORCID record for A.D. Chicherina [Opens in a new window] ,
V.V. Trifonov Open the ORCID record for V.V. Trifonov [Opens in a new window] ,
A.I. Reshmin Open the ORCID record for A.I. Reshmin [Opens in a new window]  and
V.V. Vedeneev Open the ORCID record for V.V. Vedeneev [Opens in a new window]
L.R. Gareev
Affiliation:
Institute of Mechanics, Lomonosov Moscow State University, Moscow 119192, Russia
J.S. Zayko*
Affiliation:
Institute of Mechanics, Lomonosov Moscow State University, Moscow 119192, Russia
A.D. Chicherina
Affiliation:
Institute of Mechanics, Lomonosov Moscow State University, Moscow 119192, Russia
V.V. Trifonov
Affiliation:
Institute of Mechanics, Lomonosov Moscow State University, Moscow 119192, Russia
A.I. Reshmin
Affiliation:
Institute of Mechanics, Lomonosov Moscow State University, Moscow 119192, Russia
V.V. Vedeneev
Affiliation:
Institute of Mechanics, Lomonosov Moscow State University, Moscow 119192, Russia Department of Mechanics and Mathematics, Lomonosov Moscow State University, Moscow 119991, Russia
*
†Email address for correspondence: [email protected]
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Abstract

We study the development of perturbations in a submerged air jet with a round cross-section and a long laminar region (five jet diameters) at a Reynolds number of 5400 by both inviscid linear stability theory and experiments. The theoretical analysis shows that there are two modes of growing axisymmetric perturbations, which are generated by three generalized inflection points of the jet's velocity profile. To validate the results of linear stability theory, we conduct experiments with controlled axisymmetric perturbations to the jet. The characteristics of growing waves are obtained by visualization, thermoanemometer measurements and correlation analysis. Experimentally measured wavelengths, growth rates and spatial distributions of velocity fluctuations for both growing modes are in good agreement with theoretical calculations. Therefore, it is demonstrated that small perturbations to the laminar jet closely follow the predictions of inviscid linear stability theory.

JFM classification

Instability: Shear-flow instability Wakes/Jets: Jets
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 934 , 10 March 2022 , A3
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

REFERENCES

Batchelor, G.K. & Gill, A.E. 1962 Analysis of the stability of axisymmetric jets. J. Fluid Mech. 14 (4), 529–551.CrossRefGoogle Scholar
Belyaev, I.V., Bychkov, O.P., Zaitsev, M.Y., Kopiev, V.A., Kopiev, V.F., Ostrikov, N.N., Faranosov, G.A. & Chernyshev, S.A. 2018 Development of the strategy of active control of instability waves in unexcited turbulent jets. Fluid Dyn. 53 (3), 347–360.CrossRefGoogle Scholar
Boguslawski, A., Wawrzak, K. & Tyliszczak, A. 2019 A new insight into understanding the Crow and Champagne preferred mode: a numerical study. J. Fluid Mech. 869, 385–416.CrossRefGoogle Scholar
Boiko, A.V., Dovgal, A.V., Grek, G.R. & Kozlov, V.V. 2012 Physics of Transitional Shear Flows. Fluid Mechanics and Its Applications, vol. 98. Springer.CrossRefGoogle Scholar
Boiko, A.V., Westin, K.J.A., Klingmann, B.G.B., Kozlov, V.V. & Alfredsson, P.H. 1994 Experiments in a boundary layer subjected to free stream turbulence. Part 2. The role of TS-waves in the transition process. J. Fluid Mech. 281, 219–245.CrossRefGoogle Scholar
Boronin, S.A., Healey, J.J. & Sazhin, S.S. 2013 Non-modal stability of round viscous jets. J. Fluid Mech. 716, 96–119.CrossRefGoogle Scholar
Burattini, P., Antonia, R.A., Rajagopalan, S. & Stephens, M. 2004 Effect of initial conditions on the near-field development of a round jet. Exp. Fluids 37, 56–64.CrossRefGoogle Scholar
Chorny, A. & Zhdanov, V. 2012 Turbulent mixing and fast chemical reaction in the confined jet flow at large Schmidt number. Chem. Engng Sci. 68, 541–554.CrossRefGoogle Scholar
Cohen, J. & Wygnanski, I. 1987 The evolution of instabilitites in the axisymmetric jet. Part 1. The linear growth of disturbances near the nozzle. J. Fluid Mech. 176, 191–219.CrossRefGoogle Scholar
Crow, S.C. & Champagne, F.H. 1971 Orderly structure of jet turbulence. J. Fluid Mech. 48, 547–591.CrossRefGoogle Scholar
Fiedler, H.E. & Fernholz, H.-H. 1990 On management and control of turbulent shear flows. Prog. Aerosp. Sci. 27, 305–387.CrossRefGoogle Scholar
Garnaud, X., Lesshat, L., Schmid, P.J. & Huerre, P. 2013 The preferred mode of incompressible jets: linear frequency response analysis. J. Fluid Mech. 716, 189–202.CrossRefGoogle Scholar
Ginevskii, A.S., Vlasov, E.V. & Karavosov, R.K. 2004 Acoustic Control of Turbulent Jets. Springer.CrossRefGoogle Scholar
Hilgers, A. & Boersma, B.J. 2001 Optimization of turbulent jet mixing. Fluid Dyn. Res. 29, 345–368.CrossRefGoogle Scholar
Jiménez-González, J.I., Brancher, P. & Martínez-Bazán, C. 2015 Modal and non-modal evolution of perturbations for parallel round jets. Phys. Fluids 27 (4), 044105.CrossRefGoogle Scholar
Jordan, P. & Colonius, T. 2013 Wave packets and turbulent jet noise. Annu. Rev. Fluid Mech. 45, 173–195.CrossRefGoogle Scholar
Jung, D., Gamard, S. & George, W.K. 2004 Downstream evolution of the most energetic modes in a turbulent axisymmetric jet at high Reynolds number. Part 1. The near-field region. J. Fluid Mech. 514, 173–204.CrossRefGoogle Scholar
Karpov, V.L., Mostinskii, I.L. & Polezhaev, Y.V. 2005 Laminar and turbulent modes of combustion of submerged hydrogen jets. High Temp. 43 (1), 119–124.CrossRefGoogle Scholar
Kozlov, V., Grek, G. & Litvinenko, Y. 2016 Visualization of Conventional and Combusting Subsonic Jet Instabilities. Springer International Publishing.CrossRefGoogle Scholar
Kozlov, V.V. & Ramazanov, M.P. 1981 An experimental investigation of the stability of Poiseuille flow. Izv. Akad. Nauk SSSR, Tech. Sci. 8, 45–48.Google Scholar
Krivokorytov, M.S., Golub, V.V., Moralev, I.A. & Volodin, V.V. 2014 Experimental study of the development of a helium jet during acoustic action. High Temp. 52, 436–440.CrossRefGoogle Scholar
Lemanov, V.V., Lukashov, V.V. & Sharov, K.A. 2020 Transition to turbulence through intermittence in inert and reacting jets. Fluid Dyn. 55 (6), 768–777.CrossRefGoogle Scholar
Liepmann, D. & Gharib, M. 1992 The role of streamwise vorticity in the near-field entrainment of round jets. J. Fluid Mech. 245, 643–668.CrossRefGoogle Scholar
Mair, M., Bacic, M., Chakravarthy, K. & Williams, B. 2020 Jet preferred mode vs shear layer mode. Phys. Fluids 32, 064106.CrossRefGoogle Scholar
Morris, P.J. 1976 The spatial viscous instability of axisymmetric jets. J. Fluid Mech. 77 (3), 511–526.CrossRefGoogle Scholar
Mullyadzhanov, R.I., Sandberg, R.D., Abdurakipov, S.S., George, W.K. & Hanjalić, K. 2018 Propagating helical waves as a building block of round turbulent jets. Phys. Rev. Fluids 3, 062601.CrossRefGoogle Scholar
Mullyadzhanov, R.I. & Yavorsky, N.I. 2018 The far field of a submerged laminar jet: linear hydrodynamic stability. St. Petersburg State Polytech. Univ. J. Phys. Math. 11 (3), 84–94.Google Scholar
Nastro, G., Fontane, J. & Joly, L. 2020 Optimal perturbations in viscous round jets subject to Kelvin–Helmholtz instability. J. Fluid Mech. 900, A13.CrossRefGoogle Scholar
Nishioka, M., Iida, S. & Ichikawa, Y. 1975 An experimental investigation of the stability of plane Poiseuille flow. J. Fluid Mech. 72 (4), 731–751.CrossRefGoogle Scholar
Ortiz, S. & Chomaz, J.M. 2011 Transient growth of secondary instabilities in parallel wakes: anti lift-up mechanism and hyperbolic instability. Phys. Fluids 23, 114106.CrossRefGoogle Scholar
Petersen, R.A. & Samet, M.M. 1988 On the preffered mode of jet instability. J. Fluid Mech. 194, 153–173.CrossRefGoogle Scholar
Pfenniger, W. 1961 Transition in the inlet length of tubes at high Reynolds numbers. In Boundary Layer and Flow Control (ed. G. Lachman), pp. 970–980. Pergamon.Google Scholar
Pickering, E., Rigas, G., Nogueira, P.A.S., Cavalieri, A.V.G., Schmidt, O.T. & Colonius, T. 2020 Lift-up, Kelvin–Helmholtz and Orr mechanisms in turbulent jets. J. Fluid Mech. 896, A2.CrossRefGoogle Scholar
Pickering, E., Rigas, G., Schmidt, O.T., Sipp, D. & Colonius, T. 2021 Optimal eddy viscosity for resolvent-based models of coherent structures in turbulent jets. J. Fluid Mech. 917, A29.CrossRefGoogle Scholar
Rayleigh, J. 1892 Scientific Papers, vol. 3, p. 575. Cambridge University Press.Google Scholar
Roshko, A. 1954 On the development of turbulent wakes from vortex streets. NACA Tech. Rep. 1191.Google Scholar
Sadeghi, H. & Pollard, A. 2012 Effects of passive control rings positioned in the shear layer and potential core of a turbulent round jet. Phys. Fluids 24, 115103.CrossRefGoogle Scholar
Samimy, M., Webb, N. & Crawley, M. 2018 Excitation of free shear-layer instabilities for high-speed flow control. AIAA J. 56 (5), 1770–1791.CrossRefGoogle Scholar
Sazhin, S. 2014 Droplets and Sprays. Springer.CrossRefGoogle Scholar
Schubauer, G.B. & Skramstad, H.K. 1947 Laminar boundary-layer oscillations and transition on a flat plate. J. Res. Natl Bur. Stand. 38, 251–292.CrossRefGoogle Scholar
Semeraro, O., Lesshafft, L., Jaunet, V. & Jordan, P. 2016 Modeling of coherent structures in a turbulent jet as global linear instability wavepackets: theory and experiment. Intl J. Heat Fluid Flow 62, 24–32.CrossRefGoogle Scholar
Shtern, V. & Hussain, F. 2003 Effect of deceleration on jet instability. J. Fluid Mech. 480, 283–309.CrossRefGoogle Scholar
Trefethen, L.N., Trefethen, A.E., Reddy, S.C. & Driscoll, T.A. 1993 Hydrodynamic stability without eigenvalues. Science 261, 578–584.CrossRefGoogle ScholarPubMed
Vlasov, E.V. & Ginevskii, A.S. 1967 Acoustic modification of the aerodynamic characteristics of a turbulent jet. Fluid Dyn. 2, 93–96.CrossRefGoogle Scholar
Zaman, K.B.M.Q. & Hussain, A.K.M.F. 1980 Vortex pairing in a circular jet under controlled excitation. Part 1. General jet response. J. Fluid Mech. 101 (3), 449–491.CrossRefGoogle Scholar
Zayko, J., Teplovodskii, S., Chicherina, A., Vedeneev, V. & Reshmin, A. 2018 Formation of free round jets with long laminar regions at large Reynolds numbers. Phys. Fluids 30, 043603.CrossRefGoogle Scholar