Numerically gas radiation heat transfer modeling in chemically nonequilibrium reactive flow

Abstract

A numerical method for calculation of strong radiation for 2D reactive air is developed. Governing equations are taken to be 2D, compressible Reynolds-average Navier–Stokes and species transport equations. Also, radiation heat flux is evaluated using a model of discrete ordinate method. A multiband model is used to construct absorption coefficients. Tangent slab approximation is assumed to determine the characteristic parameters needed in the Discrete Ordinates Method.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

References

  1. 1.

    Anderson JD Jr (1986) Hypersonic and high temperature gas dynamics. McGraw-Hill Book Company, New York

    Google Scholar 

  2. 2.

    Hartung LC, Hassan HA (1993) Radiation transport around axisymmetric blunt body vehicle using a modified differential approximation. AIAA paper, no. 90-1864

  3. 3.

    Hartung LC (1991) Nonequilibrium radiative heating prediction method for areoassist flowfield with coupling to flowfield solvers, Thesis for degree of doctor of philosophy, Department of Mechanical and Aerospace Engineering, North Carolina State University

  4. 4.

    Rakiich JV, Bailey HE, Park C (1983) Computation of nonequilibrium supersonic tree-dimensional inviscid flow over blunt-nosed bodies. AIAA J 21(6):834–841

    Article  Google Scholar 

  5. 5.

    Sakai T, Sawada K, Park C (1997) Assessment of Planck—Roseland—gray model for radiating shock layer. AIAA paper 97-2560

  6. 6.

    Sakai T, Sawada K, Park C (1999) Calculation of radiating flowfield behind a reflected shock wave in air. J Thermo Phys Heat Transf 13(1):42–49

    Article  Google Scholar 

  7. 7.

    Tauber ME, Sutton K (1991) Stagnation point radiative heating relations for earth and mars entries. J Spacecraft Rockets 28(1):40–42

    Article  Google Scholar 

  8. 8.

    Kuo KK (1986) Principle of combustion. Willey, New York

    Google Scholar 

  9. 9.

    Wright MJ, Bose D, Olejniczak J (2005) The impact of flowfield-radiation coupling on aero heating for TITAN Aerocapture. AIAA 2004-0484

  10. 10.

    Vincenti WG, Kruger CJ (1965) Introduction to physical gas dynamics. Wiley, New York

    Google Scholar 

  11. 11.

    Tsai YLP, Hsieh KC (1990) Comparative study of computational efficiency of two Lu Schemes for non-equilibrium reacting flows. AIAA paper no. 90-0396

  12. 12.

    Palmer G (1987) An implicit flux-split algorithm to calculate hypersonic flowfield in chemical equilibrium. AIAA paper, no. 87-1580

  13. 13.

    Li CP (1972) Time dependent solution of nonequilibrium dissociating gas past a blunt body. J Spacecr Rocket 9(8):571–582

    Article  Google Scholar 

  14. 14.

    Sakai T, Tsuru T, Sawada K (2001) Computation hypersonic radiating flow field over a blunt body. J Thermophys Heat Transf 15:1

    Google Scholar 

  15. 15.

    Baldwin B, Lomax H (1978) Thin layer approximation and algebraic model for separated turbulent flows. AIAA paper 78-257

  16. 16.

    Rahmanpour M, Ebrahimi R, Shams M (2007) Numerical study of nonequilibrium air dissociation for calculation of electron density in hypersonic flow. J Aerospace Sci Technol (JAST) 4(4):2007–532

    Google Scholar 

  17. 17.

    Rahmanpour M (2006) Aerodynamic heating with nonequilibrium reactions and gas radiation from flow field over a blunt body. MSc. thesis, K.N. Toosi University of Technology, Iran

  18. 18.

    Esch D, Siripong A, Pike R (1970) Thermodynamic properties in polynomial form carbon, hydrogen, and oxygen systems from 300–15,000 K, NASA-RFL-TR-70-3

  19. 19.

    Siegel R, Howell JR (2002) Thermal radiation heat transfer, 4th edn. Taylor and Francis, New York

    Google Scholar 

  20. 20.

    Schuster A (1965) Radiation through a foggy atmosphere. Astrophys J. 21:315–321

    Google Scholar 

  21. 21.

    Schwarzschild K (1966) Equilibrium of the sun’s atmosphere. Ges. Wiss. Gottingen Nachr. Math-phys. Klasse 1

  22. 22.

    Chandrasekhar S (1960) Radiative transfer. Dover, New York

    Google Scholar 

  23. 23.

    Lathrop KD (1966) Use of discrete ordinate method for solution of photon transport problem. Nucl Sci Eng 24:381–388

    Google Scholar 

  24. 24.

    Fiveland WA, Jessee JP (1994) Finite element formulation of the discrete ordinate method for multidimensional geometries. J Thermo Phys Heat Transf 8(3):426–433

    Article  Google Scholar 

  25. 25.

    Viskanta R, Menguc MP (1987) Radiation heat transfer in combustion systems. Prog Energy Combust Sci 13:97–160

    Article  Google Scholar 

  26. 26.

    M Krook (1955) On the solution of equations of transfer. I. Astrophys J 122(3):488–497

    Google Scholar 

  27. 27.

    Kumar A, Tiwari SN, Graves RA, Weilmuenster KJ (1980) Laminar and turbulent flow solutions with radiation and ablation injection for jovian entry. AIAA paper 80-0288

  28. 28.

    Steger JL, Warming RF (1981) Flux vector splitting of the inviscid gas dynamic equations with application to finite difference methods. J Comp Phys 40:263–293

    MathSciNet  MATH  Article  Google Scholar 

  29. 29.

    Chul Park, Seokkwan Yoon (1989) A fully-coupled implicit method for thermo-chemical nonequilibrium air at sub-orbital flight speeds. AIAA-89-1474

  30. 30.

    Shuen JS, Yoon S (1988) Numerical study of chemically reacting flows using an LU scheme. AIAA paper no. 88-0436

  31. 31.

    Beam RM, Warming RF (1978) An implicit factored scheme for the compressible Navier_Stokes equations. Am Inst Aeronaut Astronaut J 4(16):393–402

    Google Scholar 

  32. 32.

    Steger JL, Warming RF (1981) Flux vector splitting of the inviscid gas dynamic equations with application to finite difference methods. J Comput Phys 40:263–293

    Google Scholar 

  33. 33.

    Jameson A, Yoon S (1987) Lower-upper implicit scheme with multiple grids for Euler equations. Am Inst Aeronaut Astronaut J 25(7):929–935

    Google Scholar 

  34. 34.

    Zoby EV, Lee KP, Gupra RN, Thompson RA, Simmonds AL (1989) Viscous shock-layer solutions with nonequilibrium chemistry for hypersonic flows past slender bodies. J Spacecraf Rocket 26:4

    Google Scholar 

  35. 35.

    Marrone PV (1962) Normal shock waves in air; equilibrium composition and flow parameters velocities from 26,000 to 50,000 ft/s. Cornel aeronautical libratory report no. AG-1729-A-2

  36. 36.

    Wright MJ, Deepak B, Olejniczak J (2005) The impact of flowfield-radation coupling on aeroheating for TITAN aerocapture. AIAA 2004-0484

  37. 37.

    Olsen R, Gran IR (2004) Partially-reflecting characteristic-based boundary conditions, 15th Australasian fluid mechanics conference. The University of Sydney, Sydney, Australia, 13–17 Dec

  38. 38.

    Scalabrin LC, Boyd ID (2005) Development of an unstructured Navier-Stokes solver for hypersonic nonequilibrium aerothermodynamics, 38th AIAA thermo physics conference, 6–9 June 2005, Toronto, Canada

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Morteza Rahmanpour.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Rahmanpour, M., Ebrahimi, R. & Shams, M. Numerically gas radiation heat transfer modeling in chemically nonequilibrium reactive flow. Heat Mass Transfer 47, 1659–1670 (2011). https://doi.org/10.1007/s00231-011-0828-2

Download citation

Keywords

  • Control Volume
  • Stagnation Point
  • Shock Layer
  • Fluid Element
  • Hypersonic Vehicle