Skip to main content Accessibility help

Numerical study of high speed jets in crossflow

  • Xiaochuan Chai (a1), Prahladh S. Iyer (a1) and Krishnan Mahesh (a1)


Large-eddy simulation (LES) and dynamic mode decomposition (DMD) are used to study an underexpanded sonic jet injected into a supersonic crossflow and an overexpanded supersonic jet injected into a subsonic crossflow, where the flow conditions are based on the experiments of Santiago & Dutton (J. Propul. Power, vol. 13 (2), 1997, pp. 264–273) and Beresh et al. (AIAA J., vol. 43, 2005a, pp. 379–389), respectively. The simulations successfully reproduce experimentally observed shock systems and vortical structures. The time averaged flow fields are compared to the experimental results, and good agreement is observed. The behaviour of the flow is discussed, and the similarities and differences between the two regimes are studied. The trajectory of the transverse jet is investigated. A modification to Schetz et al.’s theory is proposed (Schetz & Billig, J. Spacecr. Rockets, vol. 3, 1996, pp. 1658–1665), which yields good prediction of the jet trajectories in the current simulations in the near field. Point spectra taken at various locations in the flowfield indicate a global oscillation for the sonic jet flow, wherein different regions in the flow oscillate with a frequency of $St=fD/u_{\infty }=0.3$ . For supersonic jet flow, no such global frequency is observed. Dynamic mode decomposition of the three-dimensional pressure field obtained from LES is performed and shows the same behaviour. The DMD results indicate that the $St=0.3$ mode is dominant between the upstream barrel shock and the bow shock for the sonic jet, while the roll up of the upstream shear layer is dominant for the supersonic jet.


Corresponding author

Email address for correspondence:


Hide All
Abramovich, G. N. 1963 The Theory of Turbulent Jets. chap. 12, §  4. Massachusetts Institute of Technology Press.
Arunajatesan, S.2012 Evaluation of two-equation RANS models for simulation of jet-in-cross-flow problems. AIAA Paper 2012-1199.
Arunajatesan, S. & McWherter-Payne, M. A.2013 Unsteady modeling of jet-in-crossflow problems. AIAA Paper 2013-3099.
Ben-Yakar, A., Mungal, M. G. & Hanson, R. K. 2006 Time evolution and mixing characteristics of hydrogen and ethylene transverse jets in supersonic crossflows. Phys. Fluids 18 (2), 026101.
Beresh, S., Erven, R., Henfling, J. & Spillers, R. 2005a Penetration of a transverse supersonic jet into a subsonic compressible crossflow. AIAA J. 43, 379389.
Beresh, S., Erven, R., Henfling, J. & Spillers, R. 2005b Turbulent characteristics of a transverse supersonic jet in a subsonic compressible crossflow. AIAA J. 43, 23852394.
Beresh, S. J., Henfling, J. F. & Erven, R. J.2002 Surface measurements of a supersonic jet in subsonic compressible crossflow for the validation of computational models. Sandia Report SAND2002-1890.
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, 30513061.
Chai, X. & Mahesh, K. 2010 Simulations of high speed turbulent jets in crossflow. AIAA Paper 20104603.
Chai, X. & Mahesh, K.2011 Simulations of high speed turbulent jets in crossflows. AIAA Paper. 2011–650.
Chai, X. & Mahesh, K. 2012 Dynamic-equation model for large-eddy simulation of compressible flows. J. Fluid Mech. 699, 385413.
Cubbison, R. W., Anderson, B. H. & Ward, J. J.1961 Surface pressure distributions with a sonic jet normal to adjacent flat surfaces at Mach 2.92–6.4. NASA-TN-D-580, E-1025.
Elena, M., Lacharme, J. P. & Gaviglio, J. 1985 Comparison of hot-wire and laser Doppler anemometry methods in supersonic turbulent boundary layers. Proc. Intl Symp. Laser Anemometry 1, 151157.
Everett, D. E. & Morris, M. J. 1998 Wall pressure measurements for a sonic jet injected transversely into a supersonic crossflow. J. Propul. Power 14 (6), 861868.
Fric, T. F. & Roshko, A. 1994 Vortical structure in the wake of a transverse jet. J. Fluid Mech. 279, 147.
Génin, F. & Menon, S. 2010 Dynamics of sonic jet injection into supersonic crossflow. J. Turbul. 11, N4.
Germano, M., Piomelli, U., Moin, P. & Cabot, M. 1991 A dynamic subgrid-scale eddy viscosity model. Phys. Fluids 3, 1760.
Gruber, M. R., Nejadt, A. S. & Chen, T. H. 1995 Mixing and penetration studies of sonic jets in a Mach 2 freestream. J. Propul. Power 11 (2), 315323.
Gruber, M. R., Nejad, A. S., Chen, T. H. & Dutton, J. C. 1997 Compressibility effects in supersonic transverse injection flowfields. Phys. Fluids 9 (5), 14481461.
Iyer, P. S. & Mahesh, K. 2013 High-speed boundary-layer transition induced by a discrete roughness element. J. Fluid Mech. 729, 524562.
Jovanovic, M. R., Schmid, P. J. & Nichols, J. W. 2014 Sparsity-promoting dynamic mode decomposition. Phys. Fluids 26 (2), 024143.
Kamotani, Y. & Greber, I. 1972 Experiments on a turbulent jet in a cross flow. AIAA J. 10, 14251429.
Kawai, S. & Lele, S. K. 2010 Large-eddy simulation of jet mixing in supersonic crossflows. AIAA J. 48, 20632083.
Lazar, E., Elliott, G. & Glumac, N. 2010 Energy deposition applied to a transverse jet in a supersonic crossflow. AIAA J. 48 (8), 16621672.
Mahesh, K. 2013 The interaction of jets with crossflow. Annu. Rev. Fluid Mech. 45 (1), 379407.
McAulay, J. E. & Pavli, A. J.1960 Cold-flow performance of thrust-vector control by secondary injection. NASA-TM-X-416.
McDaniel, J. C. & Graves, J. 1986 A laser-induced-fluorescence visualization study of transverse, sonic fuel injection in a nonreacting supersonic combustor. J. Propul. 4 (6), 591597.
McMillin, B. K., Seitzman, J. M. & Hanson, R. K. 1994 Comparison of NO and OH planar fluorescence temperature measurements in scramjet model flowfields. AIAA J. 32, 19451952.
Moin, P., Squires, K., Cabot, W. & Lee, S. 1991 A dynamic subgrid-scale model for compressible turbulence and scalar transport. Phys. Fluids A 3 (11), 27462757.
Morkovin, M. V., Pierce, C. A. Jr & Craven, C. E. 1952 Interaction of a side jets with a supersonic main stream. In Bull. 35, Engineering Research Institute, University of Michigan, No. UM-N-11701.
Muppidi, S. & Mahesh, K. 2005 Study of trajectories of jets in crossflow using direct numerical simulations. J. Fluid Mech. 530, 81100.
Muppidi, S. & Mahesh, K. 2008 Direct numerical simulation of passive scalar transport in transverse jets. J. Fluid Mech. 598, 335360.
Muppidi, S. & Mahesh, K. 2010 DNS of transition in supersonic boundary layers. AIAA Paper 20104440.
Muppidi, S. & Mahesh, K.2011 DNS of unsteady shock boundary layer interaction. AIAA Paper 2011–724.
Muppidi, S. & Mahesh, K. 2012 Direct numerical simulations of roughness-induced transition in supersonic boundary layers. J. Fluid Mech. 693, 2856.
New, T. H., Lim, T. T. & Luo, S. C. 2003 Elliptic jets in cross-flow. J. Fluid Mech. 494, 119140.
Papamoschou, D. & Hubbard, D. G. 1993 Visual observations of supersonic transverse jets. Exp. Fluids 14, 468476.
Park, N. & Mahesh, K.2007 Numerical and modeling issues in les of compressible turbulent flows on unstructured grids. AIAA Paper 2007–0722.
Peterson, D. P. & Candler, G. V. 2010 Hybrid Reynolds-averaged and large-eddy simulation of normal injection into a supersonic crossflow. J. Propul. Power 26 (3), 533544.
Pirozzoli, S., Grasso, F. & Gatski, T. B. 2004 Direct numerical simulation and analysis of a spatially evolving supersonic turbulent boundary layer at $M=2.25$ . Phys. Fluids 16 (3), 530545.
Rana, Z. A., Thornber, B. & Drikakis, D. 2011 Transverse jet injection into a supersonic turbulent cross-flow. Phys. Fluids 23 (4), 046103.
Rogers, R. C.1971 A study of the mixing of hydrogen injected normal to a supersonic airstream. NASA-TN-D-6114.
Rothstein, A. D. & Wantuck, P. J.(Eds) 1992 A Study of the Normal Injection of Hydrogen into a Heated Supersonic Flow Using Planar Laser-Induced Fluorescence, AIAA Paper 92-3423.
Rowley, C. W., Mezic, I., Bagheri, S., Schlatter, P. & Henningson, D. S. 2009 Spectral analysis of nonlinear flows. J. Fluid Mech. 641, 115127.
Santiago, J. G. & Dutton, J. C. 1997 Velocity measurements of a jet injected into a supersonic crossflow. J. Propul. Power 13 (2), 264273.
Schetz, J. A. & Billig, F. S. 1966 Penetration of gaseous jets injected into a supersonic stream. J. Spacecr. Rockets 3, 16581665.
Schmid, P. J. 2010 Dynamic mode decomposition of numerical and experimental data. J. Fluid Mech. 656, 528.
Schmid, P. J., Li, L., Juniper, M. P. & Pust, O. 2011 Applications of the dynamic mode decomposition. Theor. Comput. Fluid Dyn. 25 (1–4), 249259.
Smith, S. H. & Mungal, M. G. 1998 Mixing, structure and scaling of the jet in crossflow. J. Fluid Mech. 357, 83122.
Vanlerberghe, W. M., Santiago, J. G., Dutton, J. C. & Lucht, R. P. 2000 Mixing of a sonic transverse jet injected into a supersonic flow. AIAA J. 38 (3), 470479.
Walker, R. E., Stone, A. R. & Shandor, M. 1963 Secondary gas injection in a conical rocket nozzle. AIAA J. 1, 334338.
Yee, H. C., Sandham, N. D. & Djomehri, M. J. 1999 Low-dissipative high-order shock-capturing methods using characteristic-based filters. J. Comput. Phys. 150 (1), 199238.
Yuan, L. L. & Street, R. L. 1998 Trajectory and entrainment of a round jet in crossflow. Phys. Fluids 10 (9), 23232335.
Zukoski, E. E. & Spaid, F. W. 1964 Secondary injection of gases into a supersonic flow. AIAA J. 2, 16891696.
MathJax is a JavaScript display engine for mathematics. For more information see

JFM classification


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed