A new scattering kernel in kinetic theory of gases

Cercignani, Carlo; Lampis, Maria; Lentati, A.M.

doi:10.1080/00411459508206026

Cited by 20 publications

(12 citation statements)

References 7 publications

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“…The CL model involves the tangential momentum and normal kinetic energy accommodation coefficients and performs respectably against laboratory results under certain high-speed rarefied flow conditions [20,21]. Because the CL model has well-defined interaction parameters and compares well in a limited range of laboratory conditions, it remains the preferred scattering-kernel interaction model for engineering analysis and theoretical studies [22], despite efforts to improve the model [23,24].…”

Section: Developments In Gas-surface Interaction Modelingmentioning

confidence: 99%

Assessment of Gas-Surface Interaction Models for Computation of Rarefied Hypersonic Flow

Padilla

Boyd

2009

Journal of Thermophysics and Heat Transfer

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Among the few classes of computational approaches for examining rarefied gas dynamics, the most widely used technique for spatial scales relevant to suborbital spaceflight is the direct simulation Monte Carlo method. One area in which the direct simulation Monte Carlo method can be improved is the numerical modeling of the interactions between gas molecules and solid surfaces. Gas-surface interactions are not well understood for rarefied hypersonic conditions, although various models have been developed. The goal of this study is the assessment of gas-surface interaction models in use with the direct simulation Monte Carlo method. Assessment is made of the two most common gas-surface interaction models in use with direct simulation Monte Carlo: the Maxwell model and the Cercignani, Lampis, and Lord model. The assessment is performed by simulations of flat-plate wind-tunnel tests. Boundary-layer profiles are compared with existing wind-tunnel data. At about 90% accommodation, both models match the wind-tunnel profiles. Parametric studies demonstrate differences between the model predictions of scattering distributions, boundary-layer profiles, and surface-property distributions. The two models offer similar performance for computing flat-plate aerodynamics.= total enthalpy I 0 = modified Bessel function of the first kind and zeroth order K = scattering kernel Kn = global Knudsen number Kn DGL = density-gradient-length local Knudsen number m = mass of one molecule n = number density n = local normal unit vector of the solid surface P, P max = probability, maximum probability p = pressure q 1 = dynamic pressure, 0:5 1 V 2 1 R G = particular gas constant R u = universal gas constant St = Stanton number, (heat flux at the solid surface divided by q 1 V 1 ) T = temperature T = characteristic temperature of intermolecular potential T VHS = reference temperature for the variable-hard-sphere collision model t = local resultant tangent unit vector of the solid surface [t 1 t 2 =jt 1 t 2 j, t 1 and t 2 are orthonormal] V = magnitude of velocity jVj V = mass velocity, bulk velocity, or mean molecular velocity W p = reference particle weight, n=n simulation particles x, y = computational domain coordinates relative to the flat-plate leading edge Z rot;1 = maximum rotational collision number = energy accommodation coefficient VSS = deflection angle exponent of variable-soft-sphere collision model = Dirac delta function diameter = reference collision cross-sectional diameter = number of internal energy degrees of freedom vib = characteristic temperature of vibration = mean free path = absolute viscosity = absolute molecular velocity, V 0 0 = random molecular velocity = mass density = momentum accommodation coefficient = flux ! = viscosity index for the variable-hard-sphere collision model Subscripts E int = internal energy e = at the edge of the boundary layer i = incident M = Maxwell mp = most probable n = relative to surface normal vector Q = physical property r = reflected rot = rotational internal energy mode t = relative t...

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Section: Developments In Gas-surface Interaction Modelingmentioning

confidence: 99%

Assessment of Gas-Surface Interaction Models for Computation of Rarefied Hypersonic Flow

Padilla

Boyd

2009

Journal of Thermophysics and Heat Transfer

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“…Then we introduce the boundary conditions for the distribution functions. As in Cercignani's work [14][15][16] (see also [6,53]), we define the sets of outgoing (Σ x + ) and incoming (Σ x − ) velocities at point x ∈ ∂Ω such that Σ x ± := {v ∈ R d : ±v · n(x) > 0} and denote the boundary sets…”

Section: Preliminaries and Main Results 21 Boundary And Initial Condimentioning

confidence: 99%

Diffusion Limit of Kinetic Equations for Multiple Species Charged Particles

Lin

Chun

2014

Arch Rational Mech Anal

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In ionic solutions, there are multi-species charged particles (ions) with different properties like mass, charge etc. Macroscopic continuum models like the Poisson-Nernst-Planck (PNP) systems have been extensively used to describe the transport and distribution of ionic species in the solvent. Starting from the kinetic theory for the ion transport, we study a Vlasov-Poisson-Fokker-Planck (VPFP) system in a bounded domain with reflection boundary conditions for charge distributions and prove that the global renormalized solutions of the VPFP system converge to the global weak solutions of the PNP system, as the small parameter related to the scaled thermal velocity and mean free path tends to zero. Our results may justify the PNP system as a macroscopic model for the transport of multi-species ions in dilute solutions.

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“…In fact, the criticisms opposed to the Maxwell scattering kernel [6,[16][17][18] suggest to take into account the case when more than one accommodation coefficient is present (see the Cercignani-Lampis model [6][7][8], and the anisotropic scattering kernel [9]). This will be the subject of a subsequent work.…”

Section: Discussionmentioning

confidence: 99%

Asymptotic Analysis of a Slightly Rarefied Gas with Nonlocal Boundary Conditions

Caflisch¹,

Lombardo

Sammartino

2011

J Stat Phys

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In this paper nonlocal boundary conditions for the Navier-Stokes equations are derived, starting from the Boltzmann equation in the limit for the Knudsen number being vanishingly small. In the same spirit of (Lombardo et al. in J. Stat. Phys. 130:69-82, 2008) where a nonlocal Poisson scattering kernel was introduced, a gaussian scattering kernel which models nonlocal interactions between the gas molecules and the wall boundary is proposed. It is proved to satisfy the global mass conservation and a generalized reciprocity relation. The asymptotic expansion of the boundary-value problem for the Boltzmann equation, provides, in the continuum limit, the Navier-Stokes equations associated with a class of nonlocal boundary conditions of the type used in turbulence modeling.

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A new scattering kernel in kinetic theory of gases

Cited by 20 publications

References 7 publications

Assessment of Gas-Surface Interaction Models for Computation of Rarefied Hypersonic Flow

Assessment of Gas-Surface Interaction Models for Computation of Rarefied Hypersonic Flow

Diffusion Limit of Kinetic Equations for Multiple Species Charged Particles

Asymptotic Analysis of a Slightly Rarefied Gas with Nonlocal Boundary Conditions

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