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Assessment of continuum breakdown for chemically reacting wake flows

Sharanya Subramaniam* and Kelly A. Stephani†

  • Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Champaign, Illinois 61820, USA

  • *Ph.D. candidate, Department of Mechanical Science and Engineering.
  • †Assistant Professor, Department of Mechanical Science and Engineering. Corresponding author: ksteph@illinois.edu
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Phys. Rev. Fluids 3, 123401 – Published 10 December, 2018

DOI: https://doi.org/10.1103/PhysRevFluids.3.123401

Abstract

This work aims at predicting continuum breakdown in high-speed, chemically reacting wake flows using breakdown parameters obtained from the generalized Champan-Enskog (GCE) theory. Previous efforts have addressed the mathematical development of these mechanism driven breakdown parameters and their utility in predicting continuum breakdown in high Mach number compressing flows. Here we present a specieswise perturbation parameter, based on the 2-norm in Hilbert space of the first-order GCE perturbation, which can be used to assess the extent to which the underlying equilibrium Maxwell-Boltzmann (MB) distribution of a given species has been perturbed. This parameter is derived for the one-, two-, and three-temperature models, and is applicable to multicomponent, chemically reacting flowfields. All transport mechanisms that can lead to distortion of the specieswise equilibrium MB distribution function—translational, rotational and vibrational heat fluxes, mass and thermal diffusion fluxes, and stress tensor components including bulk viscosity and relaxation pressure terms—are simultaneously incorporated into this perturbation parameter that can be computed for each species. This parameter and the mechanism-based GCE breakdown parameters are used to assess continuum breakdown in the forebody and wake region of a cylinder subjected to hypersonic flow. The influence of altitude, freestream velocity, and cylinder surface reactions on continuum breakdown is analyzed. Regions of continuum breakdown are observed in the shock, boundary layer, as well as in the wake. Most notably, the surface chemistry at the cylinder wall forebody can lead to the formation of breakdown regions in the wake that are detached from the cylinder surface.

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References (38)

  1. S. Chapman and T. G. Cowling, The Mathematical Theory of Nonuniform Gases: An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases (Cambridge University Press, Cambridge, 1970).
  2. G. A. Bird, The DSMC Method (CreateSpace Independent Publishing Platform, 2013).
  3. R. Roveda, D. B. Goldstein, and P. L. Varghese, Hybrid Euler/particle approach for continuum/rarefied flows, J. Spacecr. Rockets 35, 258 (1998).
  4. J. M. Burt and I. D. Boyd, A hybrid particle approach for continuum and rarefied flow simulation, J. Comput. Phys. 228, 460 (2009).
  5. T. E. Schwartzentruber and I. D. Boyd, A hybrid particle-continuum method applied to shock waves, J. Comput. Phys. 215, 402 (2006).
  6. T. E. Schwartzentruber, L. C. Scalabrin, and I. D. Boyd, A modular particle–continuum numerical method for hypersonic nonequilibrium gas flows, J. Comput. Phys. 225, 1159 (2007).
  7. V. I. Kolobov, R. R. Arslanbekov, V. V. Aristov, A. A. Frolova, and S. A. Zabelok, Unified solver for rarefied and continuum flows with adaptive mesh and algorithm refinement, J. Comput. Phys. 223, 589 (2007).
  8. I. D. Boyd, G. Chen, and G. V. Candler, Predicting failure of the continuum fluid equations in transitional hypersonic flows, Phys. Fluids 7, 210 (1995).
  9. T. R. Deschenes, T. D. Holman, and I. D. Boyd, Effects of rotational energy relaxation in a modular particle-continuum method, J. Thermophys. Heat Transfer 25, 218 (2011).
  10. T. R. Deschenes and I. Boyd, Extension of a modular particle-continuum method to vibrationally excited, hypersonic flows, AIAA J. 49, 1951 (2011).
  11. A. L. Garcia and B. J. Alder, Generation of the Chapman–Enskog distribution, J. Comput. Phys. 140, 66 (1998).
  12. G. A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows (Clarendon, Oxford, 1994).
  13. W.-L. Wang and I. D. Boyd, Predicting continuum breakdown in hypersonic viscous flows, Phys. Fluids 15, 91 (2003).
  14. T. E. Schwartzentruber, L. C. Scalabrin, and I. D. Boyd, Hybrid particle-continuum simulations of nonequilibrium hypersonic blunt-body flowfields, J. Thermophys. Heat Transfer 22, 29 (2008).
  15. C. Schrock, R. McMullan, and J. Camberos, Continuum onset parameter based on entropy gradients using Boltzmann's H-theorem, in 43rd AIAA Aerospace Sciences Meeting and Exhibit (Reno, Nevada, 2005), p. 967.
  16. C. Schrock, R. McMullan, and J. Camberos, Calculation of entropy generation rates via DSMC with application to continuum/equilibrium onset, in 38th AIAA Thermophysics Conference (Toronto, Ontario Canada, 2005), p. 4830.
  17. S. Chigullapalli, A. Venkattraman, M. S. Ivanov, and A. A. Alexeenko, Entropy considerations in numerical simulations of nonequilibrium rarefied flows, J. Comput. Phys. 229, 2139 (2010).
  18. J. Meng, N. Dongari, J. M. Reese, and Y. Zhang, Breakdown parameter for kinetic modeling of multiscale gas flows, Phys. Rev. E 89, 063305 (2014).
  19. J. H. Ferziger and H. G. Kaper, Mathematical Theory of Transport Processes in Gases (North-Holland Publishing Company, Amsterdam, Netherlands, 1972).
  20. A. M. Verhoff and I. D. Boyd, Consistent modeling of rotational nonequilibrium in a hybrid particle-continuum method, in 44th AIAA Thermophysics Conference (San Diego, CA, 2013), p. 3145.
  21. T. D. Holman and I. D. Boyd, Effects of continuum breakdown on hypersonic aerothermodynamics for reacting flow, Phys. Fluids 23, 027101 (2011).
  22. E. Nagnibeda and E. Kustova, Non-Equilibrium Reacting Gas Flows: Kinetic Theory of Transport and Relaxation Processes (Springer Science & Business Media, 2009).
  23. K. A. Stephani, D. B. Goldstein, and P. L. Varghese, A nonequilibrium surface reservoir approach for hybrid DSMC/Navier–Stokes particle generation, J. Comput. Phys. 232, 468 (2013).
  24. K. Swaminathan-Gopalan, S. Subramaniam, and K. A. Stephani, Generalized Chapman-Enskog continuum breakdown parameters for chemically reacting flows, Phys. Rev. Fluids 1, 083402 (2016).
  25. S. Tiwari, Coupling of the Boltzmann and Euler equations with automatic domain decomposition, J. Comput. Phys. 144, 710 (1998).
  26. M. J. Wright, G. V. Candler, and D. Bose, Data-parallel line relaxation method for the Navier-Stokes equations, AIAA J. 36, 1603 (1998).
  27. J. L. Steger and R. F. Warming, Flux vector splitting of the inviscid gasdynamic equations with application to finite-difference methods, J. Comput. Phys. 40, 263 (1981).
  28. B. Van Leer, Toward the ultimate conservative difference scheme, J. Comput. Phys. 135, 229 (1997).
  29. C. Park, Review of chemical-kinetic problems of future NASA missions. I-Earth entries, J. Thermophys. Heat Transfer 7, 385 (1993).
  30. D. Bose and G. V. Candler, Thermal rate constants of the N2+O→NO+N reaction using ab initio A″3 and A′3 potential energy surfaces, J. Chem. Phys. 104, 2825 (1996).
  31. D. Bose and G. V. Candler, Thermal rate constants of the O2+N→ NO+O reaction based on A2′ and the A4′ potential-energy surfaces, J. Chem. Phys. 107, 6136 (1997).
  32. B. J. Mcbride, M. J. Zehe, and S. Gordon, NASA Glenn coefficients for calculating thermodynamic properties of individual species, Tech. Rep. (NASA TP-2002-211556, 2002).
  33. J. G. Parker, Rotational and vibrational relaxation in diatomic gases, Phys. Fluids 2, 449 (1959).
  34. R. C. Millikan and D. R. White, Systematics of vibrational relaxation, J. Chem. Phys. 39, 3209 (1963).
  35. J. D. Ramshaw, Self-consistent effective binary diffusion in multicomponent gas mixtures, J. Non-Equilib. Thermodyn. 15, 295 (1990).
  36. R. N. Gupta, J. M. Yos, R. A. Thompson, and K.-P. Lee, A review of reaction rates and thermodynamic and transport properties for the 11-species air model for chemical and thermal nonequilibrium calculations to 30000 K, Tech. Rep. (NASA-RP-1232, 1990).
  37. M. MacLean, J. Marschall, and D. Driver, Finite-rate surface chemistry model, II: Coupling to viscous Navier-Stokes code, in 42nd AIAA Thermophysics Conference (Honolulu, Hawaii, 2011), p. 3784.
  38. A. J. Lofthouse, I. D. Boyd, and M. J. Wright, Effects of continuum breakdown on hypersonic aerothermodynamics, Phys. Fluids 19, 027105 (2007).

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Phys. Rev. Fluids 3, 123401– Published 10 December, 2018
  • Received 9 May 2018
Article part of CHORUS
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