Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-28T21:32:38.715Z Has data issue: false hasContentIssue false
  • English
  • Français

Turbulent kinetic energy decay in supersonic streamwise interacting vortices

Published online by Cambridge University Press:  19 October 2016

Fabrizio Vergine ,
Cody Ground  and
Luca Maddalena
Fabrizio Vergine*
Affiliation:
Aerodynamics Research Center, University of Texas at Arlington, Arlington, TX 76019, USA
Cody Ground
Affiliation:
Aerodynamics Research Center, University of Texas at Arlington, Arlington, TX 76019, USA
Luca Maddalena
Affiliation:
Aerodynamics Research Center, University of Texas at Arlington, Arlington, TX 76019, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

Only a few fundamental studies on the dynamics and interactions of supersonic streamwise vortices have been conducted so far despite the recognized potential of these structures to enhance supersonic mixing. In an effort to shed light on this largely unexplored field, multiple experimental campaigns were conducted in a Mach 2.5 flow to probe the dynamics of turbulence decay in complex flows originating from selected modes of supersonic streamwise vortex interaction. The first part of the manuscript presents the detailed study of two vortex interaction scenarios: one selected to obtain merging of co-rotating vortices and the other to prevent vorticity amalgamation. In the second part, data from three additional vortex merging cases are used to substantiate the findings of the first part of the study and characterize the decay of turbulence. Stereoscopic particle image velocimetry was employed to probe the resulting flow fields at different downstream stations. It was found that these complex vortex interactions measurably affect both the morphology and the magnitude of the streamwise vorticity and turbulent kinetic energy as well as the associated decays. Particularly, while the turbulent kinetic energy across each vorticity patch undergoes an initial production before decreasing monotonically in both scenarios, its content in the coalesced structure is roughly double that of the isolated vortices. The manuscript also presents the analysis of the turbulence data from 27 supersonic vortical structures differing in shape, strength and modes of interaction, acquired within a range of vortex Reynolds numbers of almost one order of magnitude. Dimensional analysis was then used to correlate the spatial decay of turbulent kinetic energy with the vortex Reynolds number. For all the cases considered here, where the fluctuating Mach number was found to be subsonic, the form of the resulting law was similar to that reported in previous scholarly publications, despite the complexity of the vortex dynamics considered in this work.

JFM classification

Compressible Flows: Compressible Flows Turbulent Flows: Shear layer turbulence Vortex Flows: Vortex dynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 807 , 25 November 2016 , pp. 353 - 385
Check for updates
Copyright
© 2016 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Arai, T., Sakaue, S., Hayase, H., Hiejima, T., Sunami, T. & Nishioka, M.2011 Streamwise vortices introduced by hyper mixer on supersonic mixing. AIAA Paper 2011–2342.CrossRefGoogle Scholar
Aso, S., Yamane, Y., Ando, Y., Umii, K., Tokunaga, K. & Sakata, K.1997 A study on supersonic mixing flowfield with swept ramp injectors. AIAA Paper 97-0397.CrossRefGoogle Scholar
Batchelor, G. K. 1959 The Theory of Homogeneous Turbulence. Cambridge University Press.Google Scholar
Benedict, L. H. & Gould, R. D. 1996 Towards better uncertainty estimates for turbulence statistics. Exp. Fluids 22, 129–136.CrossRefGoogle Scholar
Beresh, S. J., Henfling, J. F., Erven, R. J. & Spillers, R. W. 2005 Turbulent characteristics of a transverse supersonic jet in a subsonic sompressible crossflow. AIAA J. 43, 2385–2394.CrossRefGoogle Scholar
Beresh, S. J., Henfling, J. F., Erven, R. J. & Spillers, R. W. 2006 Crossplane velocimetry of a transverse supersonic jet in a transonic crossflow. AIAA J. 44, 3051–3061.CrossRefGoogle Scholar
Billig, F. & Schetz, J. A.1992 Analysis of penetration and mixing of gas jets in supersonic cross flow. AIAA Paper 92-5061.CrossRefGoogle Scholar
Cerretelli, C. & Williamson, C. H. K. 2003 The physical mechanism for vortex merging. J. Fluid Mech. 475, 41–77.CrossRefGoogle Scholar
Chigier, N. A. & Chervinsky, A. 1967 Experimental investigation of swirling vortex motion in jets. Trans. ASME J. Appl. Mech. 34, 443–451.CrossRefGoogle Scholar
Donohue, J. M. & McDaniel, J. C. 1996 Complete three-dimensional multiparameter mapping of a supersonic ramp fuel injector flowfield. AIAA J. 34, 455–462.CrossRefGoogle Scholar
George, W. K. & Wang, H. 2009 The exponential decay of homogeneous turbulence. Phys. Fluids 21, 025108.CrossRefGoogle Scholar
Hearst, R. J. & Lavoie, P. 2014 Decay of turbulence generated by a square-fractal-element grid. J. Fluid Mech. 741, 567–584.CrossRefGoogle Scholar
Inoue, K. & Aso, S.2004. A study on new ramp injectors with slotted nozzle for improvement of supersonic mixing. AIAA Paper 2004–4208.CrossRefGoogle Scholar
Isaza, J. C., Salazar, R. & Warhaft, Z. 2014 On grid-generated turbulence in the near-and far field regions. J. Fluid Mech. 753, 402–426.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, 1059–1067.CrossRefGoogle Scholar
Kondo, A., Hayase, H., Sakaue, S. & Arai, T.2009 Effect of expansion ramp angle on supersonic mixing using streamwise vortices. AIAA Paper 2009–7314.CrossRefGoogle Scholar
Kondo, A., Sakaue, S. & Arai, T.2008 Fluctuation of mass flux and concentration on supersonic mixing using streamwise vortices. AIAA Paper 2008–2535.CrossRefGoogle Scholar
Maddalena, L., Vergine, F. & Crisanti, M. 2014 Vortex dynamics studies in supersonic flow: merging of co-rotating streamwise vortices. Phys. Fluids 26, 046101.CrossRefGoogle Scholar
Marble, F. E. 1985 Growth of a diffusion flame in the field of a vortex. In Recent Advances in the Aerospace Sciences, pp. 395–413. Plenum.CrossRefGoogle Scholar
Meunier, P., Dizs, S. L. & Leweke, T. 2005 Physics of vortex merging. C. R. Phys. 6, 431–450.CrossRefGoogle Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Schumacher, J.2000 Numerical simulation of cantilevered ramp injector flow fields for hypervelocity fuel/air mixing enhancement. PhD thesis, University of Toronto.Google Scholar
Sinhuber, M., Bodenschatz, E. & Bewley, G. P. 2015 Decay of turbulence at high Reynolds numbers. Phys. Rev. Lett. 114, 034501.CrossRefGoogle ScholarPubMed
Smith, C. T. & Goyne, C. P. 2011 Application of stereoscopic particle image velocimetry to a dual-mode scramjet. J. Propul. Power 27, 1178–1185.CrossRefGoogle Scholar
Swithenbank, J. & Chigier, N. A. 1969 Vortex mixing for supersonic combustion. Symposium (International) on Combustion 12, 1153–1162.CrossRefGoogle Scholar
Taylor, G. I. 1935 Statistical theory of turbulence II. Proc. R. Soc. Lond. A 151, 444–454.CrossRefGoogle Scholar
Valente, P. C. & Vassilicos, J. C. 2011 The decay of turbulence generated by a class of multiscale grids. J. Fluid Mech. 687, 300–340.CrossRefGoogle Scholar
Vergine, F. & Maddalena, L.2012 Evolution of large-scale structures generated by a strut injector in a mach 2.5 flow. AIAA Paper 2012–0332.CrossRefGoogle Scholar
Vergine, F. & Maddalena, L. 2014 Stereoscopic particle image velocimetry measurements of supersonic, turbulent, and interacting streamwise vortices: challenges and application. Prog. Aerosp. Sci. 66, 1–16.CrossRefGoogle Scholar
Vergine, F. & Maddalena, L. 2015 Study of two supersonic streamwise vortex interactions in a mach 2.5 flow: merging and no merging configurations. Phys. Fluids 27, 076102.CrossRefGoogle Scholar
Waitz, I. A., Qiu, Y. J., Manning, T. A., Fung, A. K. S., Elliot, J. K., Kerwin, J. M., Krasnodebski, J. K., O’Sullivan, M. N., Tew, D. E., Greitzer, E. M. et al. 1997 Enhanced mixing with streamwise vorticity. Prog. Aerosp. Sci. 33, 323–351.CrossRefGoogle Scholar