Skip to main content
Log in

Direct Numerical Simulation of a Square Jet Ejected Transversely into an Accelerating, Laminar Main Flow

  • Published:
Flow, Turbulence and Combustion Aims and scope Submit manuscript

Abstract

A numerical simulation of a square jet ejected transversely into a laminar boundary-layer flow was performed at a jet-to-main-flow velocity ratio of 9.78 and jet Reynolds number of 6330. The jet consisted of a single pulse with a duration equal to the time required for the jet fluid to travel 173 jet widths. A strongly-favourable streamwise pressure gradient was applied to the boundary layer and produced a freestream acceleration that is above the typical threshold required for relaminarization. The results of the simulation illustrate the effect of the favourable streamwise pressure gradient on the flowfield created by the transverse jet. Notably, the horseshoe vortex system created upwind of the jet remains steady in time and does not induce noticeable fluctuations in the jet flow. The upwind and downwind shear layers of the jet roll-up through a Kelvin–Helmholtz-like instability into discrete shear-layer vortices. Jet vorticity in the upwind and downwind shear layers accumulates near the corners of the jet and produces two sets of vortex pairs, the former of which couple with the shear-layer vortices to produce large, counter-rotating vortices in the freestream, while the latter are unstable and periodically produce hairpin vortices in the main-flow boundary layer and elongated vortices in the freestream behind the jet. The departure of the jet flowfield from the vortical structures typically observed in transverse jets illustrates the substantive effect of the favourable streamwise pressure gradient on the flowfield created by the jet.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Azih, C., Brinkerhoff, J.R., Yaras, M.I.: Direct numerical simulation of convective heat transfer in a zero-pressure-gradient boundary layer with supercritical water. J. Therm. Sci. 21, 49–59 (2012)

    Article  Google Scholar 

  2. Baker, C.J.: The laminar horseshoe vortex. J. Fluid Mech. 95, 347–367 (1979)

    Article  Google Scholar 

  3. Bowman, C.T.: Control of combustion-generated nitrogen oxide emissions: technology driven by regulation. In: Proceedings of the Combustion Institute, vol. 24, pp. 859–878 (1992)

  4. Brinkerhoff, J.R., Yaras, M.I.: Interaction of viscous and inviscid instability modes in separation–bubble transition. Phys. Fluids 23, 124102 (2011)

    Article  Google Scholar 

  5. Broadwell, J.E., Breidenthal, R.E.: Structure and mixing of a transverse jet in incompressible flow. J. Fluid Mech. 148, 405–412 (1984)

    Article  Google Scholar 

  6. Cortelezzi, L., Karagozian, A.R.: On the formation of the counter-rotating vortex pair in transverse jets. J. Fluid Mech. 446, 347–373 (2001)

    MathSciNet  MATH  Google Scholar 

  7. de B. Alves, L.S., Kelly, R.E., Karagozian, A.R.: Transverse-jet shear-layer instabilities. Part 2. Linear analysis for large jet-to-crossflow velocity ratio. J. Fluid Mech. 602, 383–401 (2008)

    MathSciNet  MATH  Google Scholar 

  8. Djenidi, L., Antonia, R.A.: LDA measurements in low Reynolds number turbulent boundary layer. Exp. Fluids 14, 280–288 (1993)

    Article  Google Scholar 

  9. Eroglu, A., Breidenthal, R.E.: Structure, penetration, and mixing of pulsed jets in crossflow. AIAA J. 39, 417–423 (2001)

    Article  Google Scholar 

  10. Escudier, M.P., Abdel-Hameed, A., Johnson, M.W., Sutcliffe, C.J.: Laminarization and retransition of a turbulent boundary layer subjected to a favourable pressure gradient. Exp. Fluids 25, 491–502 (1998)

    Article  Google Scholar 

  11. Fric, T.F., Roshko, A.: Vortical structure in the wake of a transverse jet. J. Fluid Mech. 279, 1–47 (1994)

    Article  Google Scholar 

  12. Gutmark, E.J., Grinstein, F.F.: Flow control with noncircular jets. Annu. Rev. Fluid Mech. 31, 239–272 (1999)

    Article  Google Scholar 

  13. Haven, B.A., Kurosaka, M.: Kidney and anti-kidney vortices in crossflow jets. J. Fluid Mech. 352, 27–64 (1997)

    Article  Google Scholar 

  14. Ho, C.M., Huerre, P.: Perturbed free shear layers. Annu. Rev. Fluid Mech. 16, 365–424 (1984)

    Article  Google Scholar 

  15. Johari, H.: Scaling of fully pulsed jets in crossflow. AIAA J. 44, 2719–2725 (2006)

    Article  Google Scholar 

  16. Jones, V.P., Launder, B.E.: Some properties of sink-flow turbulent boundary layers. J. Fluid Mech. 56, 337–351 (1972)

    Article  Google Scholar 

  17. Kamotani, Y., Greber, I.: Experiments on a turbulent jet in a cross flow. AIAA J. 10, 1425–1429 (1972)

    Article  Google Scholar 

  18. Karagozian, A.R.: Transverse jets and their control. Pror. Energy Combust. Sci. 36, 531–553 (2010)

    Article  Google Scholar 

  19. Keffer, J.F., Baines, W.D.: The round turbulent jet in a cross-wind. J. Fluid Mech. 15, 481–496 (1963)

    Article  MATH  Google Scholar 

  20. Kelso, R.M., Lim, T.T., Perry, A.E.: An experimental study of round jets in cross-flow. J. Fluid Mech. 306, 111–144 (1996)

    Article  Google Scholar 

  21. Kelso, R.M., Smits, A.J.: Horseshoe vortex systems resulting from the interaction between a laminar boundary layer and a transverse jet. Phys. Fluids 7, 153–158 (1995)

    Article  Google Scholar 

  22. Kim, H.T., Kline, S.J., Reynolds, W.C.: The production of turbulence near a smooth wall in a turbulent boundary layer. J. Fluid Mech. 50, 133–160 (1971)

    Article  Google Scholar 

  23. Krothapalli, A., Lourenco, L., Buchlin, J.M.: Separated flow upstream of a jet in crossflow. AIAA J. 28, 414–420 (1990)

    Article  Google Scholar 

  24. Lim, T.T., New, T.H., Luo, S.C.: On the development of large-scale structures of a jet normal to a cross flow. Phys. Fluids 13, 770–775 (2001)

    Article  MathSciNet  Google Scholar 

  25. Liscinsky, D.S., True, B., Holdeman, J.D.: Crossflow mixing of noncircular jets. J. Propuls. Power 12, 225–236 (1996)

    Article  Google Scholar 

  26. Margason, R.J.: Fifty years of jet in crossflow research. In: Computational and Experimental Assessment of Jets in Cross Flow, CP-539. AGARD Rept CP-539 (1993)

  27. McMahon, H.M., Hester, D.D., Palfery, J.G.: Vortex shedding from a turbulent jet in a cross-wind. J. Fluid Mech. 48, 73–80 (1971)

    Article  Google Scholar 

  28. Megerian, S., Davitian, J., de B. Alves, L.S., Karagozian, A.R.: Transverse-jet shear-layer instabilities. Part 1. Experimental studies. J. Fluid Mech. 593, 93–129 (2007)

    Article  MATH  Google Scholar 

  29. Moretti, P.H., Kay, V.M.: Heat transfer in turbulent boundary layer with varying free-stream velocity and varying surface temperature—an experimental study. Int. J. Heat Mass Transfer 8, 1187–1202 (1965)

    Article  Google Scholar 

  30. Morton, B.R., Ibbetson, A.: Jets deflected in a crossflow. Exp. Therm. Fluid Sci. 12, 112–133 (1996)

    Article  Google Scholar 

  31. Muppidi, S., Mahesh, K.: Study of trajectories of jets in crossflow using direct numerical simulations. J. Fluid Mech. 530, 81–100 (2005)

    Article  MATH  Google Scholar 

  32. Narayanan, S., Barooah, P., Cohen, J.M.: Dynamics and control of an isolated jet in crossflow. AIAA J. 41, 2316–2330 (2003)

    Article  Google Scholar 

  33. Pope, S.B.: Turbulent Flows. Cambridge University Press, New York (2000)

    Book  MATH  Google Scholar 

  34. Rivero, A., Feré, J.A., Giralt, F.: Organized motions in a jet in crossflow. J. Fluid Mech. 444, 117–149 (2001)

    Article  MATH  Google Scholar 

  35. Roberts, S.K., Yaras, M.I.: Large-eddy simulation of transition in a separation bubble. ASME J. Fluids Eng. 128, 232–238 (2006)

    Article  Google Scholar 

  36. Ruggeri, R.S., Callaghan, E.E., Bowden, D.T.: Penetration of air jets issued from circular, square and elliptical orifices directed perpendicular to an air stream. Tech. Rep. TN-2019, NACA (1950)

  37. Sau, A., Sheu, T.W.H., Tsai, S.F., Hwang, R.R., Chiang, T.P.: Structural development of vortical flows around a square jet in cross-flow. In: Proceedings: Mathematical, Physical and Engineering Sciences, vol. 460, pp. 3339–3368 (2004)

  38. Sau, R., Mahesh, K.: Dynamics and mixing of vortex rings in crossflow. J. Fluid Mech. 604, 389–409 (2008)

    Google Scholar 

  39. Sau, R., Mahesh, K.: Optimization of pulsed jets in crossflow. J. Fluid Mech. 653, 365–390 (2010)

    Article  MATH  Google Scholar 

  40. Schlichting, H.: Boundary Layer Theory. McGraw-Hill, New York (1968)

    Google Scholar 

  41. Shapiro, S.R., King, J.M., M’Closkey, R., Karagozian, A.: Optimization of controlled jets in crossflow. AIAA J. 44, 1292–1298 (2006)

    Article  Google Scholar 

  42. Spalart, P.R.: Direct simulation of a turbulent boundary layer up to Re θ  = 1410. J. Fluid Mech. 187, 61–98 (1988)

    Article  MATH  Google Scholar 

  43. Stanislas, M., Perret, L., Foucaut, J.M.: Vortical structures in the turbulent boundary layer: a possible route to a universal representation. J. Fluid Mech. 602, 327–382 (2008)

    Article  MATH  Google Scholar 

  44. Vermeulen, P.J., Grabinski, P., Ramesh, V.: Mixing of an acoustically excited air jet with a confined hot crossflow. J. Eng. Gas Turbine Power 114, 46–54 (1992)

    Article  Google Scholar 

  45. Wu, X., Moin, P.: Direct numerical simulation of turbulence in a nominally zero-pressure-gradient flat-plate boundary layer. J. Fluid Mech. 630, 5–41 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  46. Yuan, L.L., Street, R.L., Ferziger, J.H.: Large-eddy simulations of a round jet in crossflow. J. Fluid Mech. 379, 71–104 (1999)

    Article  MATH  Google Scholar 

  47. Ziefle, J., Kleiser, L.: Large-eddy simulation of a round jet in crossflow. AIAA J. 47, 1158–1172 (2009)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Metin I. Yaras.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Brinkerhoff, J.R., Yaras, M.I. Direct Numerical Simulation of a Square Jet Ejected Transversely into an Accelerating, Laminar Main Flow. Flow Turbulence Combust 89, 519–546 (2012). https://doi.org/10.1007/s10494-012-9406-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10494-012-9406-z

Keywords

Navigation