Investigation on the Effects of Atwood Number on the Combustion Performance of Hydrogen-Oxygen Supersonic Mixing Layer

Conference paper
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 680)


Combustion enhancement strategies are needed to improve the combustion efficiency of the supersonic shear layer. A 2D hydrogen-air supersonic shear layer with central jet filled of hydrogen and inert gas mixture under different Atwood (At) numbers is simulated, based on Navier-Stokes equations. The main purpose is to study whether optimal combustion enhancement can be obtained by changing fluid properties (At number). The Euler method cannot effectively identify the hidden flow field structure. Thus, the Lagrangian coherent structure method (LCS) is adopted to visualize the evolution process of vortex. Different Atwood numbers are adjusted by different inert gas (\(\mathrm {N}_{2}\), \(\mathrm {Ar}\), and \(\mathrm {He}\), corresponding to At = 0.14, 0.26, 0.57) with identical mass flow of hydrogen. The obtained results show that combustion efficiency of the reacting cases tends to increase and then decrease, as At number increases. At = 0.26 has the best combustion efficiency which is mainly measured by the normalized mass production of water. Combustion efficiency of At = 0.26 is higher than that of other two cases because of the shorter vortex shedding distance and resulting larger burning area. Combustion performance is controlled by the mixing process. Vortex shedding position is found to play an important role in entrainment process which directly decides the combustion efficiency. The entrained oxygen can be completely consumed because of the excess hydrogen. In conclusion, shortening vortex shedding position helps improve mixing and combustion efficiency, which can be achieved by adjusting Atwood Number.


Atwood number Supersonic shear layer Combustion efficiency Mixing enhancement Vortex shedding 



This work is partially supported by Key Research and Development project of Sichuan Province (Grant No. 2019ZYZF0002) and the National Natural Science Foundation of China (Grant No. 91741113). We thank the Center for High Performance Computing of SJTU for providing a super computer to support this research.


  1. 1.
    Abarzhi SI (2010) Review of theoretical modelling approaches of Rayleigh–Taylor instabilities and turbulent mixing. Philos Trans Roy Soc Math Phys Eng Sci 368(1916):1809-1828.
  2. 2.
    Brouillette M (2002) The richtmyer-meshkov instability. Ann Rev Fluid Mech 34(1):445–468.
  3. 3.
    Gan Y, Xu A, Zhang G et al (2011) Lattice Boltzmann study on Kelvin-Helmholtz instability: roles of velocity and density gradients. Phys Rev E 83(5):056704.
  4. 4.
    Zhou Y (2017) Rayleigh–Taylor and Richtmyer–Meshkov instability induced flow, turbulence, and mixing. II. Phys Rep 723:1–160.
  5. 5.
    Goncharov VN (2002) Analytical model of nonlinear, single-mode, classical Rayleigh-Taylor instability at arbitrary Atwood numbers. Phys Rev Lett 88(13):134502.
  6. 6.
    Li-Feng W, Wen-Hua Y, Ying-Jun L (2010) Two-dimensional Rayleigh-Taylor instability in incompressible fluids at arbitrary Atwood numbers. Chin Phys Lett 27(2):025203CrossRefGoogle Scholar
  7. 7.
    Ding J, Si T, Yang J et al (2017) Measurement of a Richtmyer-Meshkov instability at an air-SF 6 interface in a semiannular shock tube. Phys Rev Lett 119(1):014501.
  8. 8.
    Lombardini M, Hill D J, Pullin DI et al (2011) Atwood ratio dependence of Richtmyer–Meshkov flows under reshock conditions using large-eddy simulations. J Fluid Mech 670:439–480.
  9. 9.
    Pantano C, Sarkar S (2002) A study of compressibility effects in the high-speed turbulent shear layer using direct simulation. J Fluid Mech 451:329-371.
  10. 10.
    Soteriou MC, Ghoniem AF (1995) Effects of the free-stream density ratio on free and forced spatially developing shear layers. Phys Fluids 7(8):2036–2051.
  11. 11.
    Lesshafft L, Marquet O (2010) Optimal velocity and density profiles for the onset of absolute instability in jets. J Fluid Mech 662:398–408.
  12. 12.
    Milton BE, Pianthong K (2005) Pulsed, supersonic fuel jets—a review of their characteristics and potential for fuel injection. Int J Heat Fluid Flow 26(4):656–671.
  13. 13.
    Haller G, Yuan G (2000) Lagrangian coherent structures and mixing in two-dimensional turbulence. Phys D Nonlinear Phenom 147(3–4):352–370.
  14. 14.
    Peacock T, Haller G (2013) Lagrangian coherent structures: The hidden skeleton of fluid flows. Phys Today 66(2):41–47.
  15. 15.
    Liang G, Yu B, Zhang B et al (2019) Hidden flow structures in compressible mixing layer and a quantitative analysis of entrainment based on Lagrangian method. J Hydrodyn 31(2):256–265.
  16. 16.
    Qian C, Bing W, Huiqiang Z et al (2016) Numerical investigation of H2/air combustion instability driven by large scale vortex in supersonic mixing layers. Int J Hydrogen Energy 41(4):3171–3184.
  17. 17.
    Gupta RN, Yos JM, Thompson RA et al (1990) A review of reaction rates and thermodynamic and transport properties for an 11-species air model for chemical and thermal nonequilibrium calculations to 30000 KGoogle Scholar
  18. 18.
    Houim RW, Kuo KK (2011) A low-dissipation and time-accurate method for compressible multi-component flow with variable specific heat ratios. J Comput Phys 230(23):8527–8553.
  19. 19.
    Yuan L, Tang T (2007) Resolving the shock-induced combustion by an adaptive mesh redistribution method. J Computat Phys 224(2):587–600.
  20. 20.
    McBride BJ (2002) NASA Glenn coefficients for calculating thermodynamic properties of individual species. John H. Glenn Research Center at Lewis Field, National Aeronautics and Space AdministrationGoogle Scholar
  21. 21.
    Zhong X (1996) Additive semi-implicit Runge–Kutta methods for computing high-speed nonequilibrium reactive flows. J Comput Phys 128(1):19–31.
  22. 22.
    Rosenbrock HH (1963) Some general implicit processes for the numerical solution of differential equations. Comput J 5(4):329–330.
  23. 23.
    Kim SL, Choi JY, Jeung IS et al (2001) Application of approximate chemical Jacobians for constant volume reaction and shock-induced combustion. Appl Numer Math 39(1):87–104.
  24. 24.
    Liu XD, Osher S, Chan T (1994) Weighted essentially non-oscillatory schemes. J Comput Phys 115(1):200–212.
  25. 25.
    Wang Z, Yu B, Chen H et al (2018) Scaling vortex breakdown mechanism based on viscous effect in shock cylindrical bubble interaction. Phys Fluids 30(12):126103.
  26. 26.
    Goebel SG, Dutton JC, Krier H et al (1994) Mean and turbulent velocity measurements of supersonic mixing layers. Miner Deposita 29(1):263–272.
  27. 27.
    Choi JY, Jeung IS, Yoon Y (2000) Computational fluid dynamics algorithms for unsteady shock-induced combustion, part 1: validation. AIAA J 38(7):1179–1187.
  28. 28.
    Clutter J, Mikolaitis D, Shyy W (1998) Effect of reaction mechanism in shock-induced combustion simulations. In: 36th AIAA aerospace sciences meeting and exhibit p 274.
  29. 29.
    Gerlinger P, Stoll P, Kindler M et al (2008) Numerical investigation of mixing and combustion enhancement in supersonic combustors by strut induced streamwise vorticity. Aerosp Sci Technol 12(2):159–168.
  30. 30.
    Li L, Huang W, Yan L et al (2017) Mixing enhancement and penetration improvement induced by pulsed gaseous jet and a vortex generator in supersonic flows. Int J Hydrogen Energy 42(30):19318–19330.
  31. 31.
    Gong C, Jangi M, Bai XS et al (2017) Large eddy simulation of hydrogen combustion in supersonic flows using an Eulerian stochastic fields method. Int J Hydrogen Energy 42(2):1264–1275.

Copyright information

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2021

Authors and Affiliations

  1. 1.School of Aeronautics and AstronauticsShanghai Jiao Tong UniversityShanghaiChina
  2. 2.Sichuan Research InstituteShanghai Jiao Tong UniversityChengduChina

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