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Grid criteria for numerical simulation of hypersonic aerothermodynamics in transition regime. (English) Zbl 1430.76354
Summary: Grid is an important factor in numerical simulation of hypersonic aerothermodynamics. This paper introduces three criteria for determining grid size in the transition flow regime when using the computational fluid dynamics (CFD) method or the direct simulation Monte Carlo (DSMC) method. The numerical relationship between these three criteria sizes is deduced according to the one-dimensional fluid theory. Then, the relationship is verified using the CFD method to simulate the flow around a two-dimensional cylinder. At the same time, the dependence of simulation accuracy on grid size in the CFD and DSMC methods is studied and the mechanism is given. The result shows that the simulation accuracy of heat flux especially depends on the normal grid size next to surfaces, where the $$Re_{\mathrm{cell},w}$$ criterion and the $$\lambda_w$$ criterion based on local parameters are applicable and equivalent, while the $$Re_{\mathrm{cell},\infty}$$ criterion based on the free-stream parameter is only applicable under the assumption of constant viscosity coefficient and constant temperature wall conditions. On the other hand, the trend of the heat flux changing with grid size obtained by CFD and DSMC is exactly the opposite. Therefore, the grid size must be strictly satisfied with the grid criteria when comparing CFD with DSMC and even the hybrid DSMC with Navier-Stokes method.

##### MSC:
 76K05 Hypersonic flows 76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
##### Keywords:
high-speed flow; plumes/thermals
dsmcFoam
Full Text:
##### References:
 [1] Anderson, J. D.Jr.2010Fundamentals of Aerodynamics. Tata McGraw-Hill Education. [2] Berger, A. E., Solomon, J. M., Ciment, M., Leventhal, S. H. & Weinberg, B. C.1980Generalized OCI schemes for boundary layer problems. Math. Comput.35 (151), 695-731. [3] Bird, G. A.1994 Molecular Gas Dynamics and the Direct Simulation of Gas Flows. (Oxford Engineering Science Series, 42). Clarendon Press; Oxford University Press. [4] Bird, G. A.2013The DSMC Method. CreateSpace Independent Publishing Platform. [5] Brandis, A. M. & Johnston, C. O.2014Characterization of stagnation-point heat flux for earth entry. In 45th AIAA Plasmadynamics and Lasers Conference, p. 2374. AIAA. [6] Cercignani, C.1988The Boltzmann equation. In The Boltzmann Equation and Its Applications, pp. 40-103. Springer. [7] Ciment, M., Leventhal, S. H. & Weinberg, B. C.1978The operator compact implicit method for parabolic equations. J. Comput. Phys.28 (2), 135-166. · Zbl 0393.65038 [8] Dilley, A. D. & McClinton, C. R.2001 Evaluation of CFD turbulent heating prediction techniques and comparison with hypersonic experimental data. NASA Tech. Rep. 2001-210837. [9] Fay, J. A.1958Theory of stagnation point heat transfer in dissociated air. J. Aerosp. Sci.25 (2), 73-85. [10] Hoffmann, K., Siddiqui, M. & Chiang, S.1991Difficulties associated with the heat flux computations of high speed flows by the Navier-Stokes equations. In 29th Aerospace Sciences Meeting, p. 467. [11] Jasak, H.1996 Error analysis and estimation for the finite volume method with applications to fluid flows. PhD thesis, University of London Imperial College. [12] Kellogg, R., Shubin, G. & Stephens, A.1980Uniqueness and the cell Reynolds number. SIAM J. Numer. Anal.17 (6), 733-739. · Zbl 0463.76069 [13] Klopfer, G. & Yee, H.1988Viscous hypersonic shock-on-shock interaction on blunt cowl lips. In 26th Aerospace Sciences Meeting, p. 233. AIAA. [14] Lofthouse, A. J., Scalabrin, L. C. & Boyd, I. D.2008Velocity slip and temperature jump in hypersonic aerothermodynamics. J. Thermophys. Heat Transfer22, 38-49. [15] Maxwell, J. C.III1878On stresses in rarefied gases arising from inequalities of temperature. Proc. R. Soc. Lond.27 (185-189), 304-308. · JFM 10.0756.01 [16] Men’shov, I. S. & Nakamura, Y.2000Numerical simulations and experimental comparisons for high-speed nonequilibrium air flows. Fluid Dyn. Res.27 (5), 305-334. [17] Myong, R. S.2011Impact of computational physics on multi-scale CFD and related numerical algorithms. Comput. Fluids45 (1), 64-69. · Zbl 1429.76017 [18] Papadopoulos, P., Venkatapathy, E., Prabhu, D., Loomis, M. P. & Olynick, D.1999Current grid-generation strategies and future requirements in hypersonic vehicle design, analysis and testing. Appl. Math. Modell.23 (9), 705-735. · Zbl 0956.76077 [19] Scanlon, T. J., Roohi, E., White, C., Darbandi, M. & Reese, J. M.2010An open source, parallel DSMC code for rarefied gas flows in arbitrary geometries. Comput. Fluids39 (10), 2078-2089. · Zbl 1245.76127 [20] Siddiqui, M. S., Hoffmann, K. A., Chiang, S. T. & Rutledge, W. H.1992A comparative study of the Navier Stokes solvers with emphasis on the heat transfer computations of high speed flows. In 30th Aerospace Sciences Meeting and Exhibit. AIAA. [21] Singh, N. & Schwartzentruber, T. E.2016Heat flux correlation for high-speed flow in the transitional regime. J. Fluid Mech.792, 981-996. · Zbl 1381.76322 [22] Singh, N. & Schwartzentruber, T. E.2017Aerothermodynamic correlations for high-speed flow. J. Fluid Mech.821, 421-439. · Zbl 1383.76413 [23] Smoluchowski von Smolan, M.1898Über Wärmeleitung in verdünnten Gasen. Ann. Phys.300 (1), 101-130. [24] Sutton, K. & Graves, R. A.Jr. 1971 A general stagnation-point convective heating equation for arbitrary gas mixtures. NASA Tech. Rep. R-376t. [25] Tsien, H. S.1946Superaerodynamics, mechanics of rarefied gases. J. Aeronaut. Sci.13 (12), 653-664. [26] Xiang, Z., Wei, Y. & Haibo, H.2017Computational grid dependency in CFD simulation for heat transfer. In 2017 8th International Conference on Mechanical and Aerospace Engineering (ICMAE), pp. 193-197. IEEE. [27] Yang, J. & Liu, M.2017A wall grid scale criterion for hypersonic aerodynamic heating calculation. Acta Astron.136, 137-143. [28] Zel’Dovich, Y. B. & Raizer, Y. P.2012Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena. Courier Corporation.
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