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A numerical study of shear layer characteristics of low-speed transverse jets

Published online by Cambridge University Press:  03 February 2016

Prahladh S. Iyer  and
Krishnan Mahesh
Prahladh S. Iyer
Affiliation:
Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN 55455, USA
Krishnan Mahesh
Affiliation:
Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN 55455, USA
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Abstract

Direct numerical simulation (DNS) and dynamic mode decomposition (DMD) are used to study the shear layer characteristics of a jet in a crossflow. Experimental observations by Megerian et al. (J. Fluid Mech., vol. 593, 2007, pp. 93–129) at velocity ratios ($R=\overline{v}_{j}/u_{\infty }$) of 2 and 4 and Reynolds number ($Re=\overline{v}_{j}D/{\it\nu}$) of 2000 on the transition from absolute to convective instability of the upstream shear layer are reproduced. Point velocity spectra at different points along the shear layer show excellent agreement with experiments. The same frequency ($St=0.65$) is dominant along the length of the shear layer for $R=2$, whereas the dominant frequencies change along the shear layer for $R=4$. DMD of the full three-dimensional flow field is able to reproduce the dominant frequencies observed from DNS and shows that the shear layer modes are dominant for both the conditions simulated. The spatial modes obtained from DMD are used to study the nature of the shear layer instability. It is found that a counter-current mixing layer is obtained in the upstream shear layer. The corresponding mixing velocity ratio is obtained, and seen to delineate the two regimes of absolute or convective instability. The effect of the nozzle is evaluated by performing simulations without the nozzle while requiring the jet to have the same inlet velocity profile as that obtained at the nozzle exit in the simulations including the nozzle. The shear layer spectra show good agreement with the simulations including the nozzle. The effect of shear layer thickness is studied at a velocity ratio of 2 based on peak and mean jet velocity. The dominant frequencies and spatial shear layer modes from DNS/DMD are significantly altered by the jet exit velocity profile.

JFM classification

Turbulent Flows: Turbulence simulation Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 790 , 10 March 2016 , pp. 275 - 307
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Copyright
© 2016 Cambridge University Press 

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References

Babu, P. & Mahesh, K. 2004 Upstream entrainment in numerical simulation of spatially evolving round jets. Phys. Fluids 16, 3699–3705.CrossRefGoogle Scholar
Bagheri, S. 2013 Koopman-mode decomposition of the cylinder wake. J. Fluid Mech. 726, 596–623.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, C. J. 1979 The laminar horseshoe vortex. J. Fluid Mech. 95, 347–367.CrossRefGoogle Scholar
Chen, K. K., Tu, J. K. & Rowley, C. W. 2012 Variants of dynamic mode decomposition: boundary condition, Koopman, and Fourier analyses. J. Nonlinear Sci. 22, 887–915.CrossRefGoogle Scholar
Davitian, J., Getsinger, D., Hendrickson, C. & Karagozian, A. R. 2010 Transition to global instability in transverse jet shear layers. J. Fluid Mech. 661, 294–315.CrossRefGoogle Scholar
Fric, T. F. & Roshko, A. 1994 Vortical structure in the wake of a transverse jet. J. Fluid Mech. 279, 1–47.CrossRefGoogle Scholar
Getsinger, D. R.2012 Shear layer instabilities and mixing in variable density transverse jet flows. UCLA Doctoral Dissertation.Google Scholar
Getsinger, D. R., Gevorkyan, L., Smith, O. I. & Karagozian, A. R. 2014 Structural and stability characteristics of jets in crossflow. J. Fluid Mech. 760, 342–367.CrossRefGoogle Scholar
Huerre, P. & Monkewitz, P. A. 1985 Absolute and convective instabilities in free shear layers. J. Fluid Mech. 159, 151–168.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
Hunt, J. C. R., Wray, A. A. & Moin, P.1988 Eddies, stream, and convergence zones in turbulent flows. Tech. Rep. CTR-S88, Center for Turbulence Research.Google Scholar
Ilak, M., Schlatter, P., Bagheri, S. & Henningson, D. S. 2012 Bifurcation and stability analysis of a jet in cross-flow: onset of global instability at a low velocity ratio. J. Fluid Mech. 696, 94–121.CrossRefGoogle Scholar
Jang, H. & Mahesh, K. 2013 Large eddy simulation of flow around a reverse rotating propeller. J. Fluid Mech. 729, 151–179.CrossRefGoogle Scholar
Kamotani, Y. & Greber, I. 1972 Experiments on a turbulent jet in a cross flow. AIAA J. 10, 1425–1429.CrossRefGoogle Scholar
Karagozian, A. R. 2010 Transverse jets and their control. Prog. Energy Combust. Sci. 36 (5), 531–553.CrossRefGoogle Scholar
Kelso, R. & Smits, A. 1995 Horseshoe vortex systems resulting from the interaction between a laminar boundary layer and a transverse jet. Phys. Fluids 7, 153–158.CrossRefGoogle Scholar
Kelso, R. M., Lim, T. T. & Perry, A. E. 1996 An experimental study of round jets in crossflow. J. Fluid Mech. 306, 111–144.CrossRefGoogle Scholar
Mahesh, K. 2013 The interaction of jets with crossflow. Annu. Rev. Fluid Mech. 45, 379–407.CrossRefGoogle Scholar
Mahesh, K., Constantinescu, G. & Moin, P. 2004 A numerical method for large-eddy simulation in complex geometries. J. Comput. Phys. 197, 215–240.CrossRefGoogle Scholar
Margason, R. J. 1993 Fifty years of jet in cross flow research. AGARD-CP-534 1, 1–141.Google Scholar
Megerian, S., Davitian, J., Alves, L. S. B. & Karagozian, A. R. 2007 Transverse-jet shear-layer instabilities. Part 1. Experimental studies. J. Fluid Mech. 593, 93–129.CrossRefGoogle Scholar
Muppidi, S. & Mahesh, K. 2005 Study of trajectories of jets in crossflow using direct numerical simulations. J. Fluid Mech. 530, 81–100.CrossRefGoogle Scholar
Muppidi, S. & Mahesh, K. 2007 Direct numerical simulation of round turbulent jets in crossflow. J. Fluid Mech. 574, 59–84.CrossRefGoogle Scholar
Muppidi, S. & Mahesh, K. 2008 Direct numerical simulation of round turbulent jets in crossflow. J. Fluid Mech. 598, 335–360.CrossRefGoogle Scholar
Rowley, C. W., Mezic, I., Bagheri, S., Schlatter, P. & Henningson, D. S. 2009 Spectral analysis of nonlinear flows. J. Fluid Mech. 641, 115–127.CrossRefGoogle Scholar
Sau, R. & Mahesh, K. 2007 Passive scalar mixing in vortex rings. J. Fluid Mech. 582, 449–461.CrossRefGoogle Scholar
Sau, R. & Mahesh, K. 2008 Dynamics and mixing of vortex rings in crossflow. J. Fluid Mech. 604, 389–409.CrossRefGoogle Scholar
Schlatter, P., Bagheri, S. & Henningson, D. S. 2011 Self-sustained global oscillations in a jet in crossflow. Theor. Comput. Fluid Dyn. 25 (1–4), 129–146.CrossRefGoogle Scholar
Schlichting, H. 1968 Boundary Layer Theory, vol. 539. McGraw-Hill.Google Scholar
Schmid, P. J. 2010 Dynamic mode decomposition of numerical and experimental data. J. Fluid Mech. 656, 5–28.CrossRefGoogle Scholar
Simpson, R. L. 2001 Junction flows. Annu. Rev. Fluid Mech. 33, 415–443.CrossRefGoogle Scholar
Smith, S. H. & Mungal, M. G. 1998 Mixing, structure and scaling of the jet in crossflow. J. Fluid Mech. 357, 83–122.CrossRefGoogle Scholar
Strykowski, P. J. & Niccum, D. L. 1991 The stability of countercurrent mixing layers in circular jets. J. Fluid Mech. 227, 309–343.CrossRefGoogle Scholar
Su, L. K. & Mungal, M. G. 2004 Simultaneous measurements of scalar and velocity field evolution in turbulent crossflowing jets. J. Fluid Mech. 513, 1–45.CrossRefGoogle Scholar
Tritton, D. J. 1959 Experiments on the flow past a circular cylinder at low Reynolds numbers. J. Fluid Mech. 6, 547–567.CrossRefGoogle Scholar
Verma, A., Jang, H. & Mahesh, K. 2012 The effect of an upstream hull on a propeller in reverse rotation. J. Fluid Mech. 704, 61–88.CrossRefGoogle Scholar