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Ramesh K Agarwal - One of the best experts on this subject based on the ideXlab platform.

  • Computation of Hypersonic Flow of a Diatomic Gas in Rotational Nonequilibrium Past 3D Blunt Bodies Using the Generalized Boltzmann Equation
    2016
    Co-Authors: Christopher D. Wilson, Ramesh K Agarwal, Felix G Tcheremissine
    Abstract:

    The results of 3-D numerical simulations of hypersonic flow of a diatomic Gas, namely the nitrogen past 3-D blunt bodies (an axisymmetric blunt body, bicone and a hollow-cylinder-flare) at low to high Knudsen numbers Kn are presented. In a previous paper, AIAA 2007-0205, flow field simulations in a Monoatomic Gas were reported by employing several computational models namely the Navier-Stokes equations, Burnett equations, Direct Simulation Monte Carlo (DSMC), and the classical Boltzmann equation. The effect of Knudsen number Kn varying from 0.01 to 10 was investigated for Mach 3 flow past a 2D blunt body. In a follow-up paper, AIAA 2007-4550, computations for flow of nitrogen in rotational non-equilibrium past a 2D blunt body were reported by solving the Generalized Boltzmann Equation (GBE) [1]. In this paper, the hypersonic flow fields past complex axisymmetric blunt bodies at angle of attack in a diatomic Gas are computed using the 3D GBE code for Kn varying from 0.1 to 10. In the GBE (same as the Wang-Chang Uhlenbeck Equation (WC-UE) except that it includes the degenerate rotational energy states explicitly), the internal and translational degrees of freedom are considered in the framework o

  • A Conservative Numerical Method for Solving the Generalized Boltzmann Equation for an Inert Mixture of Diatomic Gases
    2016
    Co-Authors: Felix G. Tcheremisine, Ramesh K Agarwal
    Abstract:

    This paper describes the computational methodology for computing hypersonic non-equilibrium 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. Fo

  • computation of hypersonic flow past a blunt body in an inert binary Gas mixture in rotational non equilibrium using the generalized boltzmann equation
    51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, 2013
    Co-Authors: Geng Qian, Baoguo Wang, Ramesh K Agarwal
    Abstract:

    The results of 2-D numerical simulations of hypersonic flow of a single diatomic Gas, e.g., Nitrogen and a binary inert mixture of two Gases (which are constituents of air namely N2, O2, Ar) past a 2-D blunt body in rotational non-equilibrium from low to high Knudsen Numbers are obtained using the Wang-Chang Uhlenbeck equation (1) or the Generalized Boltzmann Equation (2). The computational framework available for the classical Boltzmann equation for a Monoatomic Gas with translational degrees of freedom (3) is extended by including the rotational degrees of freedom in the GBE. The general computational methodology for the solution of the GBE for a diatomic Gas is similar to that for the classical Boltzmann equation except that the evaluation of the collision integral becomes significantly more complex due to the quantization of rotational energy levels. There are two main difficulties encountered in computation of high Mach number flows of diatomic Gases with rotational degrees of freedom using the GBE: (1) a large velocity domain is needed for accurate numerical description of molecular velocity distribution function resulting in enormous computational effort in calculation of the collision integral and (2) about 50 to 70 energy levels are needed for accurate representation of the rotational spectrum of the Gas. These two problems result in very large CPU and memory requirements for shock wave computations at high Mach numbers (> 6). We employ a two level Rotational-Translational (RT) relaxation model to address this problem (4); as a result the efficiency of calculations increases by several orders of magnitude. For numerical solution of GBE for an inert binary Gas mixture, the GBE is formulated in the impulse space. The Gas mixtures may consist of both monatomic and diatomic Gases with arbitrary constituents, concentrations, and mass ratios. The method is exercised for various concentration ratios, mass ratios, and density ratios to evaluate its ability to simulate a wide range of binary Gas mixtures of Monoatomic and diatomic Gases. In particular, the method is applied to simulate two of the three primary constituents of air (N2, O2, Ar) in a binary mixture at 1:1 density ratio and air concentration ratio with Gases in translational and rotational non-equilibrium. The results of GBE are compared with DSMC calculations; a reasonably good agreement is obtained. The solutions presented in this paper can also serve as validation test cases for other methods as well as an important building block in developing complex 3D simulations for shock waves in a mixture of multiple Gases.

  • computation of hypersonic flow of a diatomic Gas in rotational nonequilibrium past a blunt body using the generalized boltzmann equation
    RAREFIED GAS DYNAMICS: Proceedings of the 26th International Symposium on#N#Rarefied Gas Dynamics, 2011
    Co-Authors: Christopher Wilson, Ramesh K Agarwal, Felix G Tcheremissine
    Abstract:

    The results of 2-D numerical simulations of non-equilibrium hypersonic flow of a diatomic Gas, e.g., nitrogen past a 2-D blunt body at low to high Knudsen Numbers are presented. The flow field is computed using the Generalized Boltzmann (or the Wang-Chang Uhlenbeck [1]) Equation (GBE) for Kn varying from 0.1 to 10. In the GBE [2], the internal and translational degrees of freedom are considered in the framework of quantum and classical mechanics respectively. The computational framework available for the classical Boltzmann equation (for a Monoatomic Gas with translational degrees of freedom) [3] is extended by including the rotational degrees of freedom in the GBE. The general computational methodology for the solution of the GBE for a diatomic Gas is similar to that for the classical BE except that the evaluation of the collision integral becomes significantly more complex due to the quantization of rotational energy levels. 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. An efficient computational methodology has been developed for the solution of GBE for computing the flow field in diatomic Gases at high Mach numbers. There are two main difficulties encountered in computation of high Mach number flows of diatomic Gases with rotational degrees of freedom using the GBE: (1) a large velocity domain is needed for accurate numerical description of molecular velocity distribution function resulting in enormous computational effort in calculation of the collision integral, and (2) about 50 to 70 energy levels are needed for accurate representation of the rotational spectrum of the Gas. These two problems result in very large CPU and memory requirements for shock wave computations at high Mach numbers (> 6). Our computational methodology has addressed these problems, and as a result efficiency of calculations has increased by several orders of magnitude. The code has been parallelized on a SGI Origin 2000, 64 R12000 MIPS processor supercomputer.

  • computations of hypersonic flow of a diatomic Gas in rotational non equilibrium past 3d blunt bodies using the generalized boltzmann equation
    RAREFIED GAS DYNAMICS: Proceedings of the 26th International Symposium on#N#Rarefied Gas Dynamics, 2011
    Co-Authors: Christopher Wilson, Ramesh K Agarwal, Felix G Tcheremissine
    Abstract:

    The results of 2-D numerical simulations of non-equilibrium hypersonic flow of a diatomic Gas, e.g., nitrogen past a 2-D blunt body at low to high Knudsen Numbers are presented. The flow field is computed using the Generalized Boltzmann (or the Wang-Chang Uhlenbeck [1]) Equation (GBE) for Kn varying from 0.1 to 10. In the GBE [2], the internal and translational degrees of freedom are considered in the framework of quantum and classical mechanics respectively. The computational framework available for the classical Boltzmann equation (for a Monoatomic Gas with translational degrees of freedom) [3] is extended by including the rotational degrees of freedom in the GBE. The general computational methodology for the solution of the GBE for a diatomic Gas is similar to that for the classical BE except that the evaluation of the collision integral becomes significantly more complex due to the quantization of rotational energy levels. 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. An efficient computational methodology has been developed for the solution of GBE for computing the flow field in diatomic Gases at high Mach numbers. There are two main difficulties encountered in computation of high Mach number flows of diatomic Gases with rotational degrees of freedom using the GBE: (1) a large velocity domain is needed for accurate numerical description of molecular velocity distribution function resulting in enormous computational effort in calculation of the collision integral, and (2) about 50 to 70 energy levels are needed for accurate representation of the rotational spectrum of the Gas. These two problems result in very large CPU and memory requirements for shock wave computations at high Mach numbers (> 6). Our computational methodology has addressed these problems, and as a result efficiency of calculations has increased by several orders of magnitude. The code has been parallelized on a SGI Origin 2000, 64 R12000 MIPS processor supercomputer.

M Chrysos - One of the best experts on this subject based on the ideXlab platform.

  • collision induced raman scattering from a pair of dissimilar particles an intriguing mathematical model predicting the suppression of the odd numbered partial waves
    Journal of Chemical Physics, 2016
    Co-Authors: M Chrysos
    Abstract:

    Relying on a simple analytic two-atom model in which the anisotropy of the interaction dipole polarizability obeys an inverse power law as a function of separation, we offer mathematical and numerical evidence that, in a Monoatomic Gas, the free-free Raman spectrum for a collisional pair of two different isotopes, a-a', may vastly differ from that for a-a. This result is obtained even if a and a' are assumed to have the same mass and zero nuclear spin and even if a-a and a-a' are subject to the same interaction polarizability and potential. The mechanism responsible for this effect is inherent in the parity of the partial-wave rotational quantum number J: given that the contribution of each partial wave to the Raman cross section is controlled by a polarizability-transition matrix-element and that each of those matrix-elements has a radial component with a magnitude slightly smaller than that of the preceding partial wave, a deficit which disfavors the odd-numbered waves is accumulated upon summing over J. In the far high-frequency wing, this deficit tends to generate spectral intensities for a-a' about half as great as the a-a ones, a tendency which becomes all the more effective as temperature is decreased. We show for instance that, for the spectral branch ΔJ = 2, the fractional difference between the free-free differential cross sections for a-a and a-a' is 12(1-x(2))(3)1+3x(4), with x=√[E/E(')] (E (E') being the initial (final) state energy of the pair and E' - E = hcν (ν > 0)). Remarkably, this quantity is zero at ν ≈ 0 but goes to 12 for ν ≫ 0. For ΔJ = 0, analogous conclusions may be drawn from the expression (1+ln(1+x1-x)2arctanx)(-1).

  • Collision-induced Raman scattering from a pair of dissimilar particles: An intriguing mathematical model predicting the suppression of the odd-numbered partial waves
    Journal of Chemical Physics, 2016
    Co-Authors: M Chrysos
    Abstract:

    Relying on a simple analytic two-atom model in which the anisotropy of the interaction dipole polarizability obeys an inverse power law as a function of separation, we offer mathematical and numerical evidence that, in a Monoatomic Gas, the free-free Raman spectrum for a collisional pair of two different isotopes,a–a′, may vastly differ from that for a–a. This result is obtained even if a and a′ are assumed to have the same mass and zero nuclear spin and even if a–a and a–a′ are subject to the same interaction polarizability and potential. The mechanism responsible for this effect is inherent in the parity of the partial-wave rotational quantum number J: given that the contribution of each partial wave to the Raman cross section is controlled by a polarizability-transition matrix-element and that each of those matrix-elements has a radial component with a magnitude slightly smaller than that of the preceding partial wave, a deficit which disfavors the odd-numbered waves is accumulated upon summing over J. In the far high-frequency wing, this deficit tends to generate spectral intensities for a–a′ about half as great as the a–a ones, a tendency which becomes all the more effective as temperature is decreased. We show for instance that, for the spectral branch ΔJ = 2, the fractional difference between the free-free differential cross sections for a–a and a–a′ is 12(1−x2)31+3x412(1−x2)31+3x4, with x=E/E′−−−−−√x=E/E′ (E (E′) being the initial (final) state energy of the pair and E′ − E = hcν (ν > 0)). Remarkably, this quantity is zero at ν ≈ 0 but goes to 1212 for ν ≫ 0. For ΔJ = 0, analogous conclusions may be drawn from the expression (1+ln(1+x1−x)2arctanx)−1(1+ln(1+x1−x)2arctanx)−1.

Felix G Tcheremissine - One of the best experts on this subject based on the ideXlab platform.

  • Computation of Hypersonic Flow of a Diatomic Gas in Rotational Nonequilibrium Past 3D Blunt Bodies Using the Generalized Boltzmann Equation
    2016
    Co-Authors: Christopher D. Wilson, Ramesh K Agarwal, Felix G Tcheremissine
    Abstract:

    The results of 3-D numerical simulations of hypersonic flow of a diatomic Gas, namely the nitrogen past 3-D blunt bodies (an axisymmetric blunt body, bicone and a hollow-cylinder-flare) at low to high Knudsen numbers Kn are presented. In a previous paper, AIAA 2007-0205, flow field simulations in a Monoatomic Gas were reported by employing several computational models namely the Navier-Stokes equations, Burnett equations, Direct Simulation Monte Carlo (DSMC), and the classical Boltzmann equation. The effect of Knudsen number Kn varying from 0.01 to 10 was investigated for Mach 3 flow past a 2D blunt body. In a follow-up paper, AIAA 2007-4550, computations for flow of nitrogen in rotational non-equilibrium past a 2D blunt body were reported by solving the Generalized Boltzmann Equation (GBE) [1]. In this paper, the hypersonic flow fields past complex axisymmetric blunt bodies at angle of attack in a diatomic Gas are computed using the 3D GBE code for Kn varying from 0.1 to 10. In the GBE (same as the Wang-Chang Uhlenbeck Equation (WC-UE) except that it includes the degenerate rotational energy states explicitly), the internal and translational degrees of freedom are considered in the framework o

  • computation of hypersonic flow of a diatomic Gas in rotational nonequilibrium past a blunt body using the generalized boltzmann equation
    RAREFIED GAS DYNAMICS: Proceedings of the 26th International Symposium on#N#Rarefied Gas Dynamics, 2011
    Co-Authors: Christopher Wilson, Ramesh K Agarwal, Felix G Tcheremissine
    Abstract:

    The results of 2-D numerical simulations of non-equilibrium hypersonic flow of a diatomic Gas, e.g., nitrogen past a 2-D blunt body at low to high Knudsen Numbers are presented. The flow field is computed using the Generalized Boltzmann (or the Wang-Chang Uhlenbeck [1]) Equation (GBE) for Kn varying from 0.1 to 10. In the GBE [2], the internal and translational degrees of freedom are considered in the framework of quantum and classical mechanics respectively. The computational framework available for the classical Boltzmann equation (for a Monoatomic Gas with translational degrees of freedom) [3] is extended by including the rotational degrees of freedom in the GBE. The general computational methodology for the solution of the GBE for a diatomic Gas is similar to that for the classical BE except that the evaluation of the collision integral becomes significantly more complex due to the quantization of rotational energy levels. 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. An efficient computational methodology has been developed for the solution of GBE for computing the flow field in diatomic Gases at high Mach numbers. There are two main difficulties encountered in computation of high Mach number flows of diatomic Gases with rotational degrees of freedom using the GBE: (1) a large velocity domain is needed for accurate numerical description of molecular velocity distribution function resulting in enormous computational effort in calculation of the collision integral, and (2) about 50 to 70 energy levels are needed for accurate representation of the rotational spectrum of the Gas. These two problems result in very large CPU and memory requirements for shock wave computations at high Mach numbers (> 6). Our computational methodology has addressed these problems, and as a result efficiency of calculations has increased by several orders of magnitude. The code has been parallelized on a SGI Origin 2000, 64 R12000 MIPS processor supercomputer.

  • computations of hypersonic flow of a diatomic Gas in rotational non equilibrium past 3d blunt bodies using the generalized boltzmann equation
    RAREFIED GAS DYNAMICS: Proceedings of the 26th International Symposium on#N#Rarefied Gas Dynamics, 2011
    Co-Authors: Christopher Wilson, Ramesh K Agarwal, Felix G Tcheremissine
    Abstract:

    The results of 2-D numerical simulations of non-equilibrium hypersonic flow of a diatomic Gas, e.g., nitrogen past a 2-D blunt body at low to high Knudsen Numbers are presented. The flow field is computed using the Generalized Boltzmann (or the Wang-Chang Uhlenbeck [1]) Equation (GBE) for Kn varying from 0.1 to 10. In the GBE [2], the internal and translational degrees of freedom are considered in the framework of quantum and classical mechanics respectively. The computational framework available for the classical Boltzmann equation (for a Monoatomic Gas with translational degrees of freedom) [3] is extended by including the rotational degrees of freedom in the GBE. The general computational methodology for the solution of the GBE for a diatomic Gas is similar to that for the classical BE except that the evaluation of the collision integral becomes significantly more complex due to the quantization of rotational energy levels. 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. An efficient computational methodology has been developed for the solution of GBE for computing the flow field in diatomic Gases at high Mach numbers. There are two main difficulties encountered in computation of high Mach number flows of diatomic Gases with rotational degrees of freedom using the GBE: (1) a large velocity domain is needed for accurate numerical description of molecular velocity distribution function resulting in enormous computational effort in calculation of the collision integral, and (2) about 50 to 70 energy levels are needed for accurate representation of the rotational spectrum of the Gas. These two problems result in very large CPU and memory requirements for shock wave computations at high Mach numbers (> 6). Our computational methodology has addressed these problems, and as a result efficiency of calculations has increased by several orders of magnitude. The code has been parallelized on a SGI Origin 2000, 64 R12000 MIPS processor supercomputer.

Luc Mieussens - One of the best experts on this subject based on the ideXlab platform.

  • An ES-BGK model for vibrational polyatomic Gases
    2020
    Co-Authors: Y Dauvois, Julien Mathiaud, Luc Mieussens
    Abstract:

    We propose an extension of the Ellipsoidal-Statistical BGK model to account for discrete levels of vibrational energy in a rarefied polyatomic Gas. This model satisfies an H-theorem and contains parameters that allow to fit almost arbitrary values for the Prandtl number and the relaxation times of rotational and vibrational energies. With the reduced distribution technique , this model can be reduced to a three distribution system that could be used to simulate polyatomic Gases with rotational and vibrational energy for a computational cost close to that of a simple Monoatomic Gas.

  • a bgk model for high temperature rarefied Gas flows
    European Journal of Mechanics B-fluids, 2020
    Co-Authors: Celine Baranger, Jordane Mathe, Julien Mathiaud, Gentien Marois, Luc Mieussens
    Abstract:

    High temperature Gases, for instance in hypersonic reentry flows, show complex phenomena like excitation of rotational and vibrational energy modes, and even chemical reactions. For flows in the continuous regime, simulation codes use analytic or tabulated constitutive laws for pressure and temperature. In this paper, we propose a BGK model which is consistent with any arbitrary constitutive laws, and which is designed to make high temperature Gas flow simulations in the rarefied regime. A Chapman-Enskog analysis gives the corresponding transport coefficients. Our approach is illustrated by a numerical comparison with a compressible Navier-Stokes solver with rotational and vibrational non equilibrium. The BGK approach gives a deterministic solver with a computational cost which is close to that of a simple Monoatomic Gas.

Xavier, Christine Fernandes - One of the best experts on this subject based on the ideXlab platform.

  • Modelos de implosão de bolhas esféricas para sonoluminescência
    [s.n.], 2019
    Co-Authors: Xavier, Christine Fernandes
    Abstract:

    Orientador: Roberto Antonio ClementeTese (doutorado) - Universidade Estadual de Campinas, Instituto de Fisica "Gleb Wataghin"Resumo: Os processos de relaxação associados aos graus de liberdade vibracional, de dissociação e ionização em bolhas de gás diatômicos e monoatômicos em SBSL (sonoluminescência de uma única bolha) são analisados através da elaboração de modelos hidrodinâmicos apropriados onde o efeito da condução térmica na interface bolha-líquido é incluído de maneira auto-consistente. Simulações numéricas dos diversos processos de relaxação permitiram caracterizar a dinâmica de tais bolhas, além de permitir a obtenção dos valores associados às frações dissociadas e ionizadas dos Gases no interior da cavidade. Em conexão com a análise do processo de ionização, um modelo para a emissão de radiação em SBSL é construído, suas conseqüências sendo analisadas e discutidas. O efeito da condução térmica na interface bolha líquido é também consideradoAbstract: We analyze, under appropriate hydrodynamical models, the processes of relaxation associated to vibrational degrees of freedom, dissociation and ionization of diatomic and Monoatomic Gas bubbles in the sonoluminescence phenomena. Numerical simulations allowed to characterize the dynamics of such bubbles and to infer values for dissociated and ionized fractions of Gases that are present inside the cavity. In connection to an analysis of ionization process, we have constructed a model for the emission of SBSL (single bubble sonoluminescence) radiation whose main features are discussed. The effect of thermal conduction at the bubble-liquid interface is also consideredDoutoradoFísicaDoutor em Ciência