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Mach number effects on the global mixing modes induced by ramp injectors in supersonic flows

Published online by Cambridge University Press:  19 September 2014

Luca Massa
Luca Massa*
Affiliation:
Department of Mechanical and Aerospace Engineering, University of Texas at Arlington, Arlington, TX 76019, USA
*
†Email address for correspondence: massa@uta.edu
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Abstract

Modern injectors for supersonic combustors (hypermixers) augment the fuel–air mixing rate by energizing the perturbation in the mixing layer. From an instability point of view, the increased perturbation growth is linked to the increased complexity of the equilibrium base flow when compared to the axisymmetric mixing layer. Common added features are streamwise vortex streaks, oblique recompression shocks and Prandtl–Meyer expansions. One of the main effects of such distortions of the mean flow is to transform the instability responsible for the creation of fine scales from a local amplified mode to a global self-sustained fluctuation. The focus of the present research is on the flow distortion induced by flushed ramps for free-stream Mach numbers in the range 2.5–3.5. The principal mean flow features are the recirculation region due to the recompression of the flow after the ramp, the shear layer over the recirculation region and the vortex streaks propagating from the ramp corners. A global three-dimensional stability analysis and three-dimensional direct numerical simulations of small perturbations of the mean flow are performed. The growth and energy distribution of the dominant and subdominant fluctuations supported by the three-dimensional steady laminar base flow are computed. The main results are the growth rates of the self-sustained varicose and sinuous modes and their correlation to the variation in the free-stream Mach number. The complex three-dimensional wavemaker is investigated by evaluating the three-dimensional eigenfunctions of the direct and adjoint modes, and the effects of the axial vorticity generated by the ramp corners are discussed.

JFM classification

Instability: Absolute/convective instability Compressible Flows: Compressible Flows Flow Control: Mixing enhancement
Type
Papers
Information
Journal of Fluid Mechanics , Volume 757 , 25 October 2014 , pp. 403 - 431
Copyright
© 2014 Cambridge University Press 

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References

Åkervik, E., Brandt, L., Henningson, D. S., Hœpffner, J., Marxen, O. & Schlatter, P. 2006 Steady solutions of the Navier–Stokes equations by selective frequency damping. Phys. Fluids 18, 068102.CrossRefGoogle Scholar
Bagheri, S., Schlatter, P., Schmid, P. J. & Henningson, D. S. 2009 Global stability of a jet in crossflow. J. Fluid Mech. 624, 33–44.CrossRefGoogle Scholar
Baker, A. H., Jessup, E. R. & Manteuffel, T. 2005 A technique for accelerating the convergence of restarted GMRES. SIAM J. Matrix Anal. Applics. 26 (4), 962–984.CrossRefGoogle Scholar
Balay, S., Adams, M. F., Brown, J., Brune, P., Buschelman, K., Eijkhout, V., Gropp, W. D., Kaushik, D., Knepley, M. G., McInnes, L. C., Rupp, K., Smith, B. F. & Zhang, H.2013 PETSc Users Manual. Tech. Rep. ANL-95/11 – Revision 3.4. Argonne National Laboratory.CrossRefGoogle Scholar
Berger, M. & Rigoutsos, I. 1991 An algorithm for point clustering and grid generation. IEEE Trans. Syst. Man Cybern. 21 (5), 1278–1286.CrossRefGoogle Scholar
Bjorstad, P. & Gropp, W. 2004 Domain Decomposition: Parallel Multilevel Methods for Elliptic Partial Differential Equations. Cambridge University Press.Google Scholar
Buckmaster, J. D. & Ludford, G. S. S. 1988 The effect of structure on the stability of detonations I. Role of the induction zone. In Symposium (International) on Combustion, vol. 21, pp. 1669–1676. Elsevier.Google Scholar
Chomaz, J.-M. 2005 Global instabilities in spatially developing flows: non-normality and nonlinearity. Annu. Rev. Fluid Mech. 37, 357–392.CrossRefGoogle Scholar
Colella, P., Graves, D. T., Keen, B. J. & Modiano, D. 2006 A Cartesian grid embedded boundary method for hyperbolic conservation laws. J. Comput. Phys. 211, 347–366.CrossRefGoogle Scholar
Criminale, W. O., Jackson, T. L. & Joslin, R. D. 2003 Theory and Computation in Hydrodynamic Stability. Cambridge University Press.CrossRefGoogle Scholar
Curran, E. T., Heiser, W. H. & Pratt, D. T. 1996 Fluid phenomena in scramjet combustion systems. Annu. Rev. Fluid Mech. 28, 323–360.CrossRefGoogle Scholar
Giannetti, F. & Luchini, P. 2007 Structural sensitivity of the first instability of the cylinder wake. J. Fluid Mech. 581, 167–197.CrossRefGoogle Scholar
Gudmundsson, K. & Colonius, T. 2011 Instability wave models for the near-field fluctuations of turbulent jets. J. Fluid Mech. 689, 97–128.CrossRefGoogle Scholar
Gutmark, E. J., Schadow, K. C. & Yu, K. H. 1995 Mixing enhancement in supersonic free shear flows. Annu. Rev. Fluid Mech. 27, 375–417.CrossRefGoogle Scholar
Hallberg, M. P. & Strykowski, P. J. 2006 On the universality of global modes in low-density axisymmetric jets. J. Fluid Mech. 569, 493–507.CrossRefGoogle Scholar
Huerre, P. & Monkewitz, P. A. 1990 Local and global instabilities in spatially developing flows. Annu. Rev. Fluid Mech. 22, 473–537.CrossRefGoogle Scholar
Jackson, T. L. & Grosch, C. E. 1990 Absolute/convective instabilities and the convective Mach number in a compressible mixing layer. Phys. Fluids A 2 (6), 949–954.CrossRefGoogle Scholar
Koike, S., Suzuki, K., Kitamura, E., Hirota, M., Takita, K., Masuya, G. & Matsumoto, M. 2006 Measurement of vortices and shock waves produced by ramp and twin jets. J. Propul. Power 22 (5), 1059–1067.CrossRefGoogle Scholar
Lehoucq, R. B., Sorensen, D. C. & Yang, C. 1998 ARPACK Users’ Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods. SIAM.CrossRefGoogle Scholar
Lin, S. P. & Reitz, R. D. 1998 Drop and spray formation from a liquid jet. Annu. Rev. Fluid Mech. 30, 85–105.CrossRefGoogle Scholar
Lingwood, R. J. 1996 An experimental study of absolute instability of the rotating-disk boundary-layer flow. J. Fluid Mech. 314 (1), 373–405.CrossRefGoogle Scholar
Massa, L. 2012 Effect of carbon content on supersonic shear layer instability. J. Fluid Mech. 693, 261–296.CrossRefGoogle Scholar
Massa, L. & Ravindran, P. 2012 On the effects of finite rate carbon/oxygen chemistry on supersonic jet instability. J. Fluid Mech. 713, 330–361.CrossRefGoogle Scholar
Megerian, S., Davitian, J., Alves, L. S. de B. & Karagozian, A. R. 2007 Transverse-jet shear-layer instabilities. Part 1. Experimental studies. J. Fluid Mech. 593, 93–129.CrossRefGoogle Scholar
Morrison, G. L. & McLaughlin, D. K. 1980 Instability process in low Reynolds number supersonic jets. AIAA J. 18, 793–800.CrossRefGoogle Scholar
Nakagawa, M. & Dahm, W. J. A.2000 Mach number effects on entrainment and mixing in supersonic planar turbulent wakes. In Proceedings of the 38th Aerospace Sciences Meeting and Exhibit 10–13 January 2000, Reno, NV, AIAA-2000-0664.Google Scholar
Nicoud, F. & Poinsot, T. 2005 Thermoacoustic instabilities: should the Rayleigh criterion be extended to include entropy changes? Combust. Flame 142, 153–159.CrossRefGoogle Scholar
Reynolds, W. C. & Hussain, A. 1972 The mechanics of an organized wave in turbulent shear flow. Part 3. Theoretical models and comparisons with experiments. J. Fluid Mech. 54, 263–288.CrossRefGoogle Scholar
Sandberg, R. D. 2012 Numerical investigation of turbulent supersonic axisymmetric wakes. J. Fluid Mech. 702, 488–520.CrossRefGoogle Scholar
Shan, J. W. & Dimotakis, P. E. 2006 Reynolds-number effects and anisotropy in transverse-jet mixing. J. Fluid Mech. 566, 47–96.CrossRefGoogle Scholar
Sivashinsky, G. I. 1979 On self-turbulization of a laminar flame. Acta Astronaut. 6 (5–6), 569–591.CrossRefGoogle Scholar
Spalart, P. R. 2000 Strategies for turbulence modelling and simulations. Intl J. Heat Fluid Flow 21 (3), 252–263.CrossRefGoogle Scholar
Strykowski, P. J., Krothapalli, A. & Jendoubi, S. 1996 The effect of counterflow on the development of compressible shear layers. J. Fluid Mech. 308, 63–96.CrossRefGoogle Scholar
Theofilis, V. 2003 Advances in global linear instability analysis of non-parallel and three-dimensional flows. Prog. Aerosp. Sci. 39 (4), 249–315.CrossRefGoogle Scholar
Van Leer, B. 1977 Towards the ultimate conservative difference scheme. IV. A new approach to numerical convection. J. Comput. Phys. 23 (3), 276–299.CrossRefGoogle Scholar
Vergine, F., Crisanti, M. & Maddalena, L. 2013 Investigation of the merging process and dynamics of streamwise vortices generated by a flow-mixing device in a Mach 2.5 flow. In Proceedings of the 51st AIAA Aerospace Sciences Meeting, including the New Horizons Forum and Aerospace Exposition, 7–10 January 2013, Grapevine, TX.Google Scholar