Arabian Journal for Science and Engineering

, Volume 43, Issue 9, pp 4879–4888 | Cite as

Three-Dimensional Modeling Shock-Wave Interaction with a Fin at Mach 5

  • Amjad A. Pasha
Research Article - Mechanical Engineering


The three-dimensional single-fin configuration finds application in an intake geometry where the cowl-shock wave interacts with the side-wall boundary layer. Accurate numerical simulation of such three-dimensional shock/turbulent boundary-layer interaction flows, which are characterized by the appearance of strong crossflow separation, is a challenging task. Reynolds-averaged Navier–Stokes computations using the shock-unsteadiness modified Spalart–Allmaras model is carried out at Mach of 5 at large fin angle of \(23^{\circ }\). The computed results using the modified model are compared to the standard Spalart–Allmaras model and validated against the experimental data. The focus of the work is to implement the modified model and to study the flow physics in detail in the complex region of swept-shock-wave turbulent boundary-layer interaction in terms of the shock structure, expansion fan, shear layer and the surface streamlines. The flow structure is correlated with the wall pressure and skin friction in detail. It is observed that the standard model predicts an initial pressure location downstream of the experiments. The modified model reduces the eddy viscosity at the shock and predicts close to the experiments. Overall, the surface pressure using modified model has predicted accurately at all the locations. The skin friction is under-predicted by both the models in the reattachment region and is attributed to the poor performance of turbulence models due to flow laminarization.


High-speed flows Shock wave Turbulent boundary layer Shock-unsteadiness Separation bubble Turbulence modeling Single fin Compressible flows Computational fluid dynamics 

List of symbols


Shock-unsteadiness damping parameter


Skin friction coefficient


Shock-unsteadiness parameter


Upstream Mach number normal to shock


Wall-normal distance to the nearest point in wall coordinates

\(\delta _0\)

Boundary-layer thickness upstream of interaction

\(\mu _T\)

Eddy viscosity

\(\nu \)

Kinematic molecular viscosity

\(\tilde{\nu }\)

Modified turbulent kinematic viscosity



Stagnation condition


Normal to shock wave


Wall condition

\(\infty \)

Freestream condition







Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Van Wie, D.M.: Scramjet inlets. In: Curran, E.T., Murthy, S.N.B. (eds.) Scramjet Propulsion, Progress in Astronautics and Aeronautics, pp. 447–511. Institute of Aeronautics and Astronautics Inc., Reston (2000)Google Scholar
  2. 2.
    Bose, D.; Brown, J.L.; Prabhu, D.K.; Gnoffo, P.; Johnston, C.O.; Hollis, B.: Uncertainty assessment of hypersonic aerothermodynamics prediction capability. J. Spacecr. Rockets 50(1), 12–18 (2003)CrossRefGoogle Scholar
  3. 3.
    Marvin, J. G.; Brown, J. L.; Gnoffo, P. A.: Experimental database with baseline CFD solutions: 2-d and axisymmetric hypersonic shock-wave/turbulent boundary-layer interactions, NASA TM2013216604 (2013)Google Scholar
  4. 4.
    Garnier, E.; Adams, N.; Sagaut, P.: Large Eddy Simulation for Compressible Flows. Springer, Berlin (2009)CrossRefzbMATHGoogle Scholar
  5. 5.
    Georgiadis, N.J.; Yoder, D.A.; Vyas, M.A.; Engblom, W.A.: Status of turbulence modeling for hypersonic propulsion flowpaths. Theor. Comput. Fluid Dyn. 28(3), 295–318 (2014)CrossRefGoogle Scholar
  6. 6.
    Yang, Z.: Large-eddy simulation: past, present and the future. Chin. J. Aeronaut. 28(1), 11–24 (2015)CrossRefGoogle Scholar
  7. 7.
    Fang, J.; Yao, Y.; Zheltovodov, A.A.; Lu, L.: Investigation of three-dimensional shock wave/turbulent-boundary-layer interaction initiated by a single fin. AIAA J. 55(2), 509–523 (2017)CrossRefGoogle Scholar
  8. 8.
    Kubota, H.; Stollery, J.: An experimental study of the interaction between a glancing shock wave and a turbulent boundary layer. J. Fluid Mech. 116, 431–58 (1982)CrossRefGoogle Scholar
  9. 9.
    Alvi, F.S.; Settles, G.: Physical model of the swept shock wave/boundary layer interaction flowfield. AIAA J. 30(9), 2252–2258 (1992)CrossRefGoogle Scholar
  10. 10.
    Edwards, J.R.; Chandra, S.: Comparison of eddy viscosity-transport turbulence models for three-dimensional shock-separated flowfields. AIAA J. 34(4), 756–763 (1996)CrossRefGoogle Scholar
  11. 11.
    Panaras, A.G.: The effect of the structure of swept-shock-wave/turbulent boundary-layer interactions on turbulence modeling. J. Fluid Mech. 338, 203–230 (1997)CrossRefzbMATHGoogle Scholar
  12. 12.
    Thivet, F.: Lessons learned from RANS simulations of shock wave/boundary layer interactions. AIAA Paper, p. 583 (2002)Google Scholar
  13. 13.
    Panaras, A.G.: Calculation of flows characterized by extensive crossflow separation. AIAA J. 42(12), 2474–2475 (2004)CrossRefGoogle Scholar
  14. 14.
    Delery, J.; Marvin, J. G.; Reshotko, E.: Shock-wave boundary layer interactions. AGARDograph No. 280. ISBN 92-835-159-6 (1996)Google Scholar
  15. 15.
    Panaras, A.G.: Review of the physics of swept-shock/boundary layer interactions. Prog. Aerosp. Sci. 32, 173–244 (1996)CrossRefGoogle Scholar
  16. 16.
    Knight, D.D.; Degrez, G.: Shock wave turbulent boundary layer interactions in high mach number flows—a critical survey of current numerical prediction capabilities. AGARD Advis. Rep. 319(2), 1.1–1.35 (1998)Google Scholar
  17. 17.
    Knight, D.; Yan, H.; Panaras, A.G.; Zheltovodov, A.: Advances in CFD prediction of shock wave turbulent boundary layer interactions. Prog. Aerosp. Sci. 39(2–3), 121–184 (2003)CrossRefGoogle Scholar
  18. 18.
    Babinsky, H.; Harvey, J.K.: Shock Wave-Boundary-Layer Interactions. Cambridge University Press, Cambridge (2011)CrossRefzbMATHGoogle Scholar
  19. 19.
    Roy, C.J.; Blottner, F.G.: Review and assessment of turbulence models for hypersonic flows. Prog. Aerosp. Sci. 42(7–8), 469–530 (2006)CrossRefGoogle Scholar
  20. 20.
    Ma, L.; Lu, L.; Fang, J.; Wang, Q.: A study on turbulence transportation and modification of Spalart–Allmaras model for shock-wave/turbulent boundary layer interaction flow. Chin. J. Aeronaut. 27(2), 200–209 (2014)CrossRefGoogle Scholar
  21. 21.
    Panaras, A.G.: Turbulence modeling of flows with extensive crossflow separation. Aerospace 2(3), 461–481 (2015)CrossRefGoogle Scholar
  22. 22.
    Gaitonde, D.V.: Progress in shock-wave/boundary-layer interactions. Prog. Aerosp. Sci. 721, 80–99 (2015)CrossRefGoogle Scholar
  23. 23.
    Sinha, K.; Mahesh, K.; Candler, G.V.: Modeling the effect of shock-unsteadiness in shock/turbulent boundary-layer interactions. AIAA J. 43(3), 586–594 (2005)CrossRefGoogle Scholar
  24. 24.
    Pasha, A.A.; Sinha, K.: Shock unsteadiness model applied to hypersonic shock wave/turbulent boundary-layer interactions. J. Propul. Power 28(1), 46–60 (2012)CrossRefGoogle Scholar
  25. 25.
    Spalart, P. R.; Allmaras, S. R.: A one-equation turbulence model for aerodynamic flows. AIAA Paper, p. 439 (1992)Google Scholar
  26. 26.
    Schulein, E.: Optical skin friction measurements in short-duration facilities. AIAA J. 44(8), 1732–1742 (2006)CrossRefGoogle Scholar
  27. 27.
    Wilcox, D.C.: Turbulence Modeling for CFD, 2nd edn, pp. 491–492. DCW Industries, La Canada (2000)Google Scholar
  28. 28.
    Catris, S.; Aupoix, B.: Density corrections for turbulence models. Aerosp. Sci. Technol. 4(1), 1–11 (2000)CrossRefzbMATHGoogle Scholar
  29. 29.
    Deck, S.; Duveau, P.; d’Espiney, P.; Guillen, P.: Development and application of Spalart–Allmaras one-equation turbulence model to three-dimensional supersonic complex configurations. Aerosp. Sci. Technol. 6(3), 171–183 (2002)CrossRefzbMATHGoogle Scholar
  30. 30.
    Sinha, K.; Candler, G. V.: Convergence improvement of two-equation turbulence model calculations. AIAA Paper p. 2649 (1998)Google Scholar
  31. 31.
    Pasha, A.A.; Sinha, K.: Shock-unsteadiness model applied to oblique shock-wave/turbulent boundary-layer interaction. Int. J. Comput. Fluid Dyn. 22(8), 569–582 (2008)CrossRefzbMATHGoogle Scholar
  32. 32.
    Pasha, A.A.: Study of parameters affecting separation bubble size in high speed flows using \(k\)-\(\omega \) turbulence model. J. Appl. Comput. Mech. 4(2), 95–104 (2018)Google Scholar
  33. 33.
    Nompelis, I.: Computational study of hypersonic double-cone experiments for code validation. Thesis (Ph.D.), University of Minnesota (2004)Google Scholar
  34. 34.
    Edney, B. E.: Anomalous heat transfer and pressure distributions on blunt bodies at hypersonic speeds in the presence of an impinging shock. FFA Rept. 115, The Aeronautical Research Institute of Sweden, Stockholm (1968)Google Scholar
  35. 35.
    Quadros, R.; Sinha, K.; Larsson, J.: Turbulent energy flux generated by shock/homogeneous turbulence interaction. J. Fluid Mech. 976, 113–157 (2016)MathSciNetCrossRefGoogle Scholar
  36. 36.
    Quadros, R.; Sinha, K.: Modelling of turbulent energy flux in canonical shock-turbulence interaction. Int. J. Heat Fluid Flow 61, 626–635 (2016)CrossRefGoogle Scholar
  37. 37.
    Roy, S.; Pathak, U.; Sinha, K.: Variable turbulent Prandtl number model for shock/boundary-layer interaction. AIAA J. 56(1), 342–355 (2018)CrossRefGoogle Scholar

Copyright information

© King Fahd University of Petroleum & Minerals 2018

Authors and Affiliations

  1. 1.Department of Aeronautical EngineeringKing Abdulaziz UniversityJeddahSaudi Arabia

Personalised recommendations