Shock Waves

pp 1–15 | Cite as

Numerical investigation of a chemically reacting and rarefied hypersonic flow field

  • H. Gijare
  • A. Bhagat
  • N. Dongari
Original Article


Numerical simulations are carried out in the non-continuum flow regime to analyze flow features in the shock layer of a reentry vehicle. A new solver, rarefiedHypersonicFoam, has been developed based on the OpenFOAM platform, which can simulate the intermediate hypersonic reacting flow regime, where chemical non-equilibrium effects are imperative. The solver accommodates features to model air chemistry, multispecies transport, thermodynamic properties of high-temperature air, and non-equilibrium boundary conditions. The solver is validated with ballistic range experimental data for shock standoff distance and heat flux values over a conical reentry vehicle. Results have exhibited good agreement with the experimental data and show significant improvement when compared with the conventional high-speed compressible flow solver. The modified solver is used to analyze hypersonic flow over a bi-conic reentry capsule at different altitudes and velocities in the rarefied hypersonic flow regime. The results show that at lower altitude, chemical reactions absorb a considerable amount of heat compared to higher altitude. The rate of reaction reduces with the decrease in the flow velocity, which results in reduced heat flux values. It is observed that, if only rarefaction effects are considered in the solver, it overpredicts the heat flux values. Therefore, incorporation of chemical reactions while analyzing rarefied hypersonic flow fields is imperative.


Hypersonic flows Rarefied gas dynamics Reentry Shock layer Computational fluid dynamics Air chemistry OpenFOAM 



The research was supported by the Department of Science and Technology (DST): SERB/F/2684/2014-15 and Ministry of Human Resource Development (MHRD) fellowship. We would like to acknowledge V. K. Saraswat for his valuable suggestions.


  1. 1.
    Bertin, J.J.: Hypersonic Aerothermodynamics. AIAA, Washington (1994)Google Scholar
  2. 2.
    Gupta, R.N., Jerrold M.Y., Richard A.T., Lee K.: A review of reaction rates and thermodynamic and transport properties for an 11-species air model for chemical and thermal nonequilibrium calculations to 30000 K. NASA Technical Memorandum 1232 (1990)Google Scholar
  3. 3.
    Anderson Jr., J.D.: Modern Compressible Flow: With Historical Perspective, vol. 12. McGraw-Hill, New York (1990)Google Scholar
  4. 4.
    Anderson Jr., J.D.: Hypersonic and High Temperature Gas Dynamics. AIAA, Washington (2006)CrossRefGoogle Scholar
  5. 5.
    Furudate, M., Satoshi, N., Keisuke, S.: Behavior of two-temperature model in intermediate hypersonic regime. J. Thermophys. Heat Transf. 13(4), 424–430 (1999). CrossRefGoogle Scholar
  6. 6.
    Park, C., Park, C.: Validation of CFD codes for real-gas regime. 32nd Thermophysics Conference, AIAA 1997–2530 (1997).
  7. 7.
    OpenFoam.: OpenFOAM v2.3.0. The Open Source CFD Toolbox. Free Software Foundation, Inc. (2014). Accessed 2 Nov 2018Google Scholar
  8. 8.
    Kurganov, A., Noelle, S., Petrova, G.: Semidiscrete central-upwind schemes for hyperbolic conservation laws and Hamilton–Jacobi equations. SIAM J. Sci. Comput. 23(3), 707–740 (2001). MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Greenshields, C.J., Weller, H.G., Gasparini, L., Reese, J.M.: Implementation of semi-discrete, non-staggered central schemes in a colocated, polyhedral, finite volume framework, for high-speed viscous flows. Int. J. Numer. Methods Fluids 63(1), 1–21 (2010). MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Maxwell, J.C.: On stresses in rarefied gases arising from inequalities of temperature. Proc. R. Soc. Lond. 27(185–189), 304–308 (1878). CrossRefzbMATHGoogle Scholar
  11. 11.
    Smoluchowski von Smolan, M.: Über wärmeleitung in verdünnten gasen. Ann. Phys. 300(1), 101–130 (1898). CrossRefzbMATHGoogle Scholar
  12. 12.
    Le, N.T.P., Greenshields, C.J., Reese, J.M.: Evaluation of nonequilibrium boundary conditions for hypersonic rarefied gas flows. Progr. Flight Phys. 3, 217–230 (2012). CrossRefGoogle Scholar
  13. 13.
    Le, N.T., Shoja-Sani, A., Roohi, E.: Rarefied gas flow simulations of NACA 0012 airfoil and sharp 25–55-deg biconic subject to high order nonequilibrium boundary conditions in CFD. Aerosp. Sci. Technol. 41, 274–288 (2015). CrossRefGoogle Scholar
  14. 14.
    Shoja-Sani, A., Roohi, E., Kahrom, M., Stefanov, S.: Investigation of aerodynamic characteristics of rarefied flow around NACA 0012 airfoil using DSMC and NS solvers. Eur. J. Mech. B Fluids 48, 59–74 (2014). MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Lofthouse, A.J.: Nonequilibrium Hypersonic Aerothermodynamics Using the Direct Simulation Monte Carlo and Navier–Stokes Models (No. CIO8-0001). Michigan University, Ann Arbor (2008)Google Scholar
  16. 16.
    Lofthouse, A.J., Scalabrin, L.C., Boyd, I.D.: Velocity slip and temperature jump in hypersonic aerothermodynamics. J. Thermophys. Heat Transf. 22(1), 38–49 (2008). CrossRefGoogle Scholar
  17. 17.
    Gijare, H., Assam, A., Dongari, N.: Aero-thermodynamics optimization of re-entry capsule in the slip flow regime. 1st International ISHMT-ASTFE Heat and Mass Transfer Conference (2015)Google Scholar
  18. 18.
    Bhagat, A. Mopuru, D.R., Dongari, N., Saraswat, V.K.: Effect of nozzle divergence angle on plume expansion in outer-space conditions. 1st International ISHMT-ASTFE Heat and Mass Transfer Conference (2015)Google Scholar
  19. 19.
    Bansal, A., Feldick, A., Modest, M.: Simulation of hypersonic flow and radiation over a mars reentry vehicle using OpenFOAM. 50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, Nashville, TN, USA, AIAA Paper 2012-650 (2012).
  20. 20.
    Casseau, V., Espinoza, D.E., Scanlon, T.J., Brown, R.E.: A two-temperature open-source CFD model for hypersonic reacting flows, part two: multi-dimensional analysis. Aerospace 3(4), 45 (2016). CrossRefGoogle Scholar
  21. 21.
    Casseau, V., Palharini, R.C., Scanlon, T.J., Brown, R.E.: A two-temperature open-source CFD model for hypersonic reacting flows, part one: zero-dimensional analysis. Aerospace 3(4), 34 (2016). CrossRefGoogle Scholar
  22. 22.
    McBride, B.J., Gordon, S., Reno, M.A.: Coefficients for calculating thermodynamic and transport properties of individual species. NASA Technical Memorandum 4513 (1993)Google Scholar
  23. 23.
    Gnoffo, P.A., Gupta, R.N., Shinn, J.L.: Conservation equations and physical models for hypersonic air flows in thermal and chemical nonequilibrium. NASA Technical Memorandum 2867 (1989)Google Scholar
  24. 24.
    Bird, R.B.: Transport phenomena. Appl. Mech. Rev. 55(1), R1–R4 (2002). CrossRefGoogle Scholar
  25. 25.
    Vincenti, W.G., Kruger, C.H.: Introduction to Physical Gas Dynamics. Wiley, New York (1965)Google Scholar
  26. 26.
    Muylaert, J., Walpot, L., Vennemann, D.: A review of European code-validation studies in high-enthalpy flow. Philos. Trans. R. Soc. Lond. A Math. Phys. Eng. Sci. 357(1759), 2249–2278 (1999). CrossRefGoogle Scholar
  27. 27.
    Billig, F.S.: Shock-wave shapes around spherical- and cylindrical-nosed bodies. J. Spacecr. Rockets 4(6), 822–823 (1967). CrossRefGoogle Scholar
  28. 28.
    Nonaka, S., Mizuno, H., Takayama, K., Park, C.: Measurement of shock standoff distance for sphere in ballistic range. J. Thermophys. Heat Transf. 14(2), 225–229 (2000). CrossRefGoogle Scholar
  29. 29.
    Nagdewe, S.P., Shevare, G.R., Kim, H.D.: Study on the numerical schemes for hypersonic flow simulation. Shock Waves 19(5), 433–442 (2009). CrossRefzbMATHGoogle Scholar
  30. 30.
    Kennard, E.H.: Kinetic Theory of Gases, with an Introduction to Statistical Mechanics. McGraw-Hill, New York (1938)Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Mechanical and Aerospace DepartmentIndian Institute of Technology, HyderabadHyderabadIndia

Personalised recommendations