Skip to main content
SpringerLink
Log in

Saddle point of attachment in jet–crossflow interaction

  • Original Article
  • Published:
Theoretical and Computational Fluid Dynamics Aims and scope Submit manuscript

Abstract

Numerical simulation and theoretical analysis were performed to investigate the upstream topology of a jet–crossflow interaction. The numerical results were validated with mathematical theory as well as a juncture flow structure. The upstream critical point satisfies the condition of occurrence for a saddle point of attachment in the horseshoe vortex system. In addition to the classical topology led by a saddle point of separation, a new topology led by a saddle point of attachment was found for the first time in a jet–crossflow interaction. The degeneration of the critical point from separation to attachment is determined by the velocity ratio of the jet over the crossflow, and the boundary layer thickness of the flat plate. When the boundary layer thickness at the upstream edge of the jet is close to one diameter of the jet, the flow topology is led by a saddle point of attachment. Variation of the velocity ratio does not change the topology but the location of the saddle point. When the boundary layer thickness is less than 0.255 of the jet flow diameter, large velocity ratio can generate a saddle point of attachment without spiral horseshoe vortex; continuously decreasing the velocity ratio will change the flow topology to saddle point of the separation. The degeneration of the critical point from attachment to separation was observed.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Sabatino, D.R., Smith, C.R.: Boundary layer influence on the unsteady horseshoe vortex flow and surface heat transfer. J. Turbomach. 131(1), 011015 (2009)

    Article  Google Scholar 

  2. Perry, A.E., Fairlie, B.D.: Critical points in flow patterns. Adv. Geophys. 18, 299–315 (1975)

    Article  Google Scholar 

  3. Agui, J.H., Andreopoulos, J.: Experimental investigation of a three-dimensional boundary layer flow in the vicinity of an upright wall mounted cylinder. J. Fluids Eng. 114(4), 566–576 (1992)

    Article  Google Scholar 

  4. Thompson, M.C., Hourigan, K., Co Commonwealth Scientific and Industrial Research Organization, Division of Building, and Engineering: Prediction of the Vortex Junction Flow Upstream of a Surface Mounted Obstacle. CSIRO. Division of Building, Construction and Engineering (1992)

  5. Visbal, M.R.: Numerical investigation of laminar juncture flows. In: 20th, AIAA, Fluid Dynamics, Plasma Dynamics and Lasers Conference, Buffalo, NY, June 12–14, 12 p (1989)

  6. Visbal, M.R.: Structure of laminar juncture flows. AIAA J. 29(8), 1273–1282 (1991)

    Article  Google Scholar 

  7. Chen, C.-L., Hung, C.-M.: Numerical study of juncture flows. AIAA J. 30(7), 1800–1807 (1992)

    Article  MATH  Google Scholar 

  8. Hung, C.-M., Sung, C.-H., Chen, C.-L.: Computation of saddle point of attachment. AIAA J. 30(6), 1561–1569 (1992)

    Article  MATH  Google Scholar 

  9. Coon, M.D., Tobak, M.: Experimental study of saddle point of attachment in laminar juncture flow. AIAA J. 33(12), 2288–2292 (1995)

    Article  Google Scholar 

  10. Younis, M.Y., Zhang, H., Hu, B., Mehmood, S.: Topological evolution of laminar juncture flows under different critical parameters. Sci. China Technol. Sci. 57(7), 1342–1351 (2014)

    Article  Google Scholar 

  11. Zhang, H., Younis, M.Y., Hu, B., Wang, H., Wang, X.: Investigation of attachment saddle point structure of 3-D steady separation in laminar juncture flow using PIV. J. Vis. 15(3), 241–252 (2012)

    Article  Google Scholar 

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

    Article  Google Scholar 

  13. Schlegel, F., Wee, D., Marzouk, Y.M., Ghoniem, A.F.: Contributions of the wall boundary layer to the formation of the counter-rotating vortex pair in transverse jets. J. Fluid Mech. 676, 461–490 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  14. Bagheri, S., Schlatter, P., Schmid, P.J., Henningson, D.S.: Global stability of a jet in cross-flow. J. Fluid Mech. 624, 33–44 (2009)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  16. Mahesh, K.: The interaction of jets with crossflow. Annu. Rev. Fluid Mech. 45, 397–407 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  17. 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. R. Soc. 460(2051), 3339–3368 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  18. Sau, A., Sheu, T.W., Hwang, R.R., Yang, W.: Three-dimensional simulation of square jets in cross-flow. Phys. Rev. E 69(6), 066302 (2004)

    Article  Google Scholar 

  19. Wang, X.D., Li, Z., Liang, J.Y., Kang, S.: Numerical simulations of imperfect bifurcation of jet in crossflow. Eng. Appl. Comput. Fluid Mech. 6(4), 595–607 (2012)

    Google Scholar 

  20. Cambonie, T., Aider, J.-L.: Transition scenario of the round jet in crossflow topology at low velocity ratios. Phys. Fluids 26, 084101 (2014)

    Article  Google Scholar 

  21. Erdem, E., Kontis, K., Saravanan, S.: Penetration characteristics of air, carbon dioxide and helium transverse sonic jets in mach 5 cross flow. Sensors 14(12), 23462–23489 (2014)

    Article  Google Scholar 

  22. Recker, E., Bosschaerts, W., Wagemakers, R., Hendrick, P., Funke, H., Börner, S.: Experimental study of a round jet in cross-flow at low momentum ratio. In: 15th International Symposium on Applications of Laser Techniques to Fluid Mechanics Lisbon, 05–08 July 2010

  23. Said, N.M., Mhiri, H., El Golli, S., Le Palec, G., Bournot, P.: Three-dimensional numerical calculations of a jet in an external cross flow: application to pollutant dispersion. J. Heat Transf. 125, 510–522 (2003)

    Article  Google Scholar 

  24. Sau, A., Sheu, T.W.H., Hwang, R.R., Yang, W.C.: Three-dimensional simulation of square jets in cross-flow. Am. Phys. Soc. 69(20), 066302 (2004)

    Google Scholar 

  25. Cortelezzi, L., Karagozian, A.: Three-dimensional vortex modeling of unforced transverse jets. In: Karagozian, A., Cortelezzi, L., Soldati, A. (eds.) Manipulation and Control of Jets in Crossflow, pp. 89–105. Springer, Vienna (2003)

    Google Scholar 

  26. Dickmann, D.A., Lu, F.K.: Shock/boundary layer interaction effects on transverse jets in crossflow over a flat plate. J. Spacecr. Rockets 46, 1132–1141 (2009)

    Article  Google Scholar 

  27. 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(1), 153–158 (1995)

    Article  Google Scholar 

  28. Kelso, R.M., Lim, T.T., Perry, A.E.: An experimental study of round jets in cross-flow. J. Fluid Mech. 306(1), 111–144 (1996)

    Article  Google Scholar 

  29. Krothapalli, A., Lourenco, L., Buchlin, J.: Separated flow upstream of a jet in a crossflow. AIAA J. 28(3), 414–420 (1990)

    Article  Google Scholar 

  30. Shang, J.S., McMaster, D.L., Scaggs, N., Buck, M.: Interaction of jet in hypersonic cross stream. AIAA J. 27(3), 323–329 (1989)

    Article  Google Scholar 

  31. Zhang, H., Hu, B., Younis, M.Y.: Investigation on existence and evolution of attachment saddle point structure of 3-D separation in juncture flow. In: IEEE on Applied Sciences and Technology, Islamabad, pp. 247–253 (2011)

Download references

Author information

Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, University of Missouri, Columbia, MO, USA

    Chenxing Zhang, Junxiang Shi, Zhaoqing Ke & Chung-Lung Chen

Authors
  1. Chenxing Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Junxiang Shi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhaoqing Ke
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Chung-Lung Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Chung-Lung Chen.

Additional information

Communicated by Tim Colonius.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, C., Shi, J., Ke, Z. et al. Saddle point of attachment in jet–crossflow interaction. Theor. Comput. Fluid Dyn. 31, 391–404 (2017). https://doi.org/10.1007/s00162-017-0427-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00162-017-0427-z

Keywords

Search

Navigation