Entropy considerations in numerical simulations of non-equilibrium rarefied flows

Chigullapalli, Sruti; Venkattraman, Ayyaswamy; Иванов, М. С.; Alexeenko, Alina

doi:10.1016/j.jcp.2009.11.027

Cited by 29 publications

(10 citation statements)

References 25 publications

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“…Finally, the collision integrals involved in computing (5) and (9) and the ratio of collision integrals in (12) can be expressed in terms of the VHS parameters as follows:…”

Section: Consistent Treatment Of Transport Propertiesmentioning

confidence: 99%

Generation of a Hybrid DSMC/CFD Solution for Gas Mixtures with Internal Degrees of Freedom

Stephani

Goldstein²,

Varghese³

2012

50th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition

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A consistent approach for generating a hybrid DSMC/CFD solution is presented for re-entry applications involving neutral gas mixtures with internal energy. A quality hybrid solution requires consistency in the thermo-chemical models employed by the particle (DSMC) and continuum (CFD) solvers, as well as an appropriate boundary condition for the transfer of flux information across the hybrid interface. The first half of this work focuses on achieving consistency in the transport properties obtained by particle and continuum solvers, including species diffusion, viscosity and translational and internal thermal conductivities for a five-species air mixture. In the second portion, a new approach for the generation of particles at a hybrid interface is presented for gas mixtures with internal degrees of freedom. Particle thermal velocities and internal energies are prescribed from the appropriate non-equilibrium (perturbed) distribution, in which diffusion, shear stress and heat flux terms are included in the Generalized Chapman-Enskog formulation of the perturbation. The significance of the contributions from these terms on the perturbation are examined at a hybrid interface within non-equilibrium boundary layer flow, as well as within the breakdown region near a normal shock, in a five-species air gas mixture. The validity of the Chapman-Enskog perturbation at each of these hybrid interfaces is assessed by comparison with the Generalized Chapman-Enskog perturbations. Nomenclature α VSS exponent D i scaled diffusion flux τ ij,s scaled shear stress q i,s scaled translational heat flux q i,s scaled internal heat flux d ref reference diameter T ref reference temperature ω temperature exponent α VSS scattering exponent g relative molecular collision speed D s effective diffusion coefficient D st binary diffusion coefficient χ mole fraction Y mass fraction

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“…Finally, the collision integrals involved in computing (5) and (9) and the ratio of collision integrals in (12) can be expressed in terms of the VHS parameters as follows:…”

Section: Consistent Treatment Of Transport Propertiesmentioning

confidence: 99%

Generation of a Hybrid DSMC/CFD Solution for Gas Mixtures with Internal Degrees of Freedom

Stephani

Goldstein²,

Varghese³

2012

50th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition

View full text Add to dashboard Cite

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“…2 In discretized form, ν j (f j −f γ,j )w j = 0 from conservation of mass and entropy generation rate readṡ Entropy can be a powerful parameter in verification of numerical solution to non-equilibrium flows. In this 0-D problem, non-dimensional entropy starts from an initial value of 31.25 and increases with time till equilibrium is reached at 31.85.…”

Section: Iiia Verification -Space Homogeneous Relaxationmentioning

confidence: 99%

Unsteady 3D Rarefied Flow Solver Based on Boltzmann-ESBGK Model Kinetic Equations

Chigullapalli

Alexeenko

2011

41st AIAA Fluid Dynamics Conference and Exhibit

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Formulation and verification of unsteady rarefied flow solver based on Boltzmann-ESBGK equations in arbitrary three-dimensional geometries is presented. The solver is based on the finite volume method in physical space and the discrete ordinate method in velocity space with an implicit time discretization. Verification is carried out for an unsteady approach to equilibrium, a steady one-dimensional Couette flow and a two-dimensional quasi-steady gas damping problem. Finally, the application of the full 3D parallel solver is considered to simulate unsteady microscale gas damping in a micro-electro-mechanical system switch.

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“…Numerical & Visualization Methods A finite volume scheme with third order accurate WENO scheme for spatial fluxes [9] is used to solve the ES-BGK model kinetic equations. The DSMC solutions were obtained using Bird's fortran code DSMC1S.f that is specialized to solve the problem of a one-dimensional stationary shock wave.…”

Section: Bi-modal Distribution Function : Mott-smith Theorymentioning

confidence: 99%

Visualizing Non-Equilibrium Flow Simulations using 3-D Velocity Distribution Functions

Venkattraman

Alexeenko

2011

AIP Conference Proceedings

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Abstract. Scientific visualization techniques have been used to probe and understand better the physics of non-equilibrium flows. A visualization methodology for non-equilibrium flow simulations using 3-D velocity distribution functions(VDFs) is illustrated in application to various non-equilibrium flow problems. A one-dimensional normal shock wave problem is considered for two different upstream Mach numbers corresponding to weak and strong non-equilibrium flow conditions. The iso-surfaces of 3-D VDFs inside the shock wave obtained using various solution techniques including the ES-BGK method, DSMC technique, Mott-Smith solution, and the Navier-Stokes(NS) distribution functions using Chapman-Enskog theory are compared and contrasted. The visualization technique is extended to two-dimensional hypersonic flow at M = 10 past a flat plate with sharp leading edge by comparing the isosurfaces of 3-D NS VDFs obtained at three different locations in the flowfield. The visualization of 3-D VDFs is shown to provide valuable information about the degree and direction of non-equilibrium for both 1-D and 2-D flows.

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Entropy considerations in numerical simulations of non-equilibrium rarefied flows

Cited by 29 publications

References 25 publications

Generation of a Hybrid DSMC/CFD Solution for Gas Mixtures with Internal Degrees of Freedom

Generation of a Hybrid DSMC/CFD Solution for Gas Mixtures with Internal Degrees of Freedom

Unsteady 3D Rarefied Flow Solver Based on Boltzmann-ESBGK Model Kinetic Equations

Visualizing Non-Equilibrium Flow Simulations using 3-D Velocity Distribution Functions

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