Computation of Hypersonic Flow of a Diatomic Gas in Rotational Nonequilibrium Past a Blunt Body Using the Generalized Boltzmann Equation

Chen, R.; Agarwal, R. K.; Tcheremissine, F. G.; Abe, Takashi

doi:10.1063/1.3076525

Cited by 2 publications

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“…To improve the computational efficiency, the asymptotic preserving (AP) schemes have been proposed and developed [14]. Based on the DVM framework, many kinetic solvers have been developed for diatomic gas as well [15,16].…”

Section: Introductionmentioning

confidence: 99%

Unified gas-kinetic wave-particle methods V: diatomic molecular flow

Xu,

Chen,

Liu

et al. 2020

Preprint

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In this paper, the unified gas-kinetic wave-particle (UGKWP) method is further developed for diatomic gas with the energy exchange between translational and rotational modes for flow study in all regimes. The multiscale transport mechanism in UGKWP is coming from the direct modeling in a discretized space, where the cell's Knudsen number, defined by the ratio of particle mean free path over the numerical cell size, determines the flow physics simulated by the wave particle formulation. The non-equilibrium distribution function in UGKWP is tracked by the discrete particle and analytical wave. The weights of distributed particle and wave in different regimes are controlled by the accumulating evolution solution of particle transport and collision within a time step, where distinguishable macroscopic flow variables of particle and wave are updated inside each control volume. With the variation of local cell's Knudsen number, the UGKWP becomes a particle method in the highly rarefied flow regime and converges to the gas-kinetic scheme (GKS) for the Navier-Stokes solution in the continuum flow regime without particles. Even targeting on the same solution as the discrete velocity method (DVM)-based unified gas-kinetic scheme (UGKS), the computational cost and memory requirement in UGKWP could be reduced by several orders of magnitude for the high speed and high temperature flow simulation, where the translational and rotational nonequilibrium becomes important in the transition and rarefied regime. As a result, 3D hypersonic computations around a flying vehicle in all regimes can be conducted using a personal computer.The UGKWP method for diatomic gas will be validated in various cases from one dimensional shock structure to three dimensional flow over a sphere, and the numerical solutions will be compared with the reference DSMC results and experimental measurements.

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Section: Introductionmentioning

confidence: 99%

Unified gas-kinetic wave-particle methods V: diatomic molecular flow

Xu,

Chen,

Liu

et al. 2020

Preprint

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“…This method has been developed by Professor Cheremisin of the Computing Center of the Russian Academy of Science [12][13][14][15]. It has been extensively applied by him and many other researchers [16] including the second author of this paper [17][18][19][20][21]. The key numerical features of this method are: (a) it is fully conservative, (b) it preserves the positiveness of the solution, (c) it does not disturb the thermodynamic equilibrium and therefore can be applied for computing flows approaching continuum regime, (d) it is essentially deterministic and therefore does not produce statistical noise, (e) it employs numerically efficient integration grids that make it very efficient, (f) it can employ a variable mesh that may exceed the local mean free path in the regions of low gradients, and (g) the method can be easily parallelized.…”

Section: Introductionmentioning

confidence: 99%

A Conservative Numerical Method for Solving the Generalized Boltzmann Equation for an Inert Mixture of Diatomic Gases

TCheremisine

Agarwal

2009

47th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition

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This paper describes the computational methodology for computing hypersonic nonequilibrium shock wave (SW) flows in a mixture of non reacting diatomic gases such as Nitrogen and Oxygen using the Generalized Boltzmann Equation (GBE) at Knudsen numbers in transitional and rarefied flow regimes. In the GBE, the internal and translational degrees of freedom are considered in the framework of quantum and classical mechanics respectively. The computational framework available for the standard Boltzmann equation (for a monoatomic gas with translational degrees of freedom) is extended by including both the rotational and vibrational degrees of freedom in the GBE. The solution of GBE requires modeling of transition probabilities, elastic and inelastic cross-sections etc. of a diatomic gas molecule, needed for the solution of the collision integral. The whole problem that includes both the vibrational-translational (VT) and rotational-translational (RT) energy transfers is solved by applying a three-stage splitting procedure to the GBE. The three stages consist of free molecular transport, VT relaxation, and RT relaxation. For computation of shock structure in a mixture of gases, the GBE needs to be formulated in impulse space instead of the standard velocity space. Furthermore, till now, the computations of SW in neutral gas mixtures have been performed only for 1D problem and they assume cylindrical symmetry of the solution in the velocity space. In this paper, we describe the development of a general numerical method for multicomponent neutral mixtures applicable to 2D and 3D flows. A 3D code has been developed and applied to compute the SW in neutral binary mixture.

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Computation of Hypersonic Flow of a Diatomic Gas in Rotational Nonequilibrium Past a Blunt Body Using the Generalized Boltzmann Equation

Cited by 2 publications

References 0 publications

Unified gas-kinetic wave-particle methods V: diatomic molecular flow

Unified gas-kinetic wave-particle methods V: diatomic molecular flow

A Conservative Numerical Method for Solving the Generalized Boltzmann Equation for an Inert Mixture of Diatomic Gases

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