Mechanics of Rarefied Gases

Schaaf, S. A.

doi:10.1007/978-3-662-10109-4_5

Cited by 52 publications

(25 citation statements)

References 118 publications

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“…Contrary to the expected distributions given by the Maxwell model, high-speed molecular-beam experiments [14][15][16] showed scattering distributions to be petal-shaped and not centered about the mean specular angle, rather than a composition of a circle and a sharp oval. Partly because of molecular-beam experimental findings, various models were developed to match the observed scattering distributions.…”

Section: Developments In Gas-surface Interaction Modelingmentioning

confidence: 94%

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: 94%

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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“…For example, in the minimum mass solar nebula (MMSN, hereafter;Hayashi 1981), the mean free path is >1 cm for distances >1 au from the central star (Nakagawa et al 1986); the dust grains we consider here are smaller than this value. Then, the drag force is written as (Schaaf 1963)…”

Section: Dust Componentmentioning

confidence: 99%

Dust Dynamics in Protoplanetary Disk Winds Driven by Magnetorotational Turbulence: A Mechanism for Floating Dust Grains With Characteristic Sizes

Miyake

Suzuki

Inutsuka

2016

ApJ

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We investigate the dynamics of dust grains of various sizes in protoplanetary disk winds driven by magnetorotational turbulence, by simulating the time evolution of the dust grain distribution in the vertical direction. Small dust grains, which are well-coupled to the gas, are dragged upward with the upflowing gas, while large grains remain near the midplane of a disk. Intermediate-size grains float near the sonic point of the disk wind located at several scale heights from the midplane, where the grains are loosely coupled to the background gas. For the minimum mass solar nebula at 1 au, dust grains with size of 25-45 μm float around 4 scale heights from the midplane. Considering the dependence on the distance from the central star, smaller-size grains remain only in an outer region of the disk, while larger-size grains are distributed in a broader region. We also discuss the implications of our result for observations of dusty material around young stellar objects.

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“…For a complete derivation of this term see e.g. Schaaf (1963, and the equations leading to Eq. (7)); KGS94 (Eq.…”

Section: Treatment Of the Gas-dust Interactionmentioning

confidence: 99%

Three-component modeling of C-rich AGB star winds

Sandín

Höfner

2003

A&A

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Abstract. We present three-component wind models for carbon-rich pulsating AGB stars. In particular we study the effects of drift in models of long-period variables, meaning that the dust is allowed to move relative to the gas (drift models). In addition we investigate the importance of the degree of variability of the wind structures. The wind model contains separate conservation laws for each of the three components of gas, dust and the radiation field. We use two different representations for the gas opacity, resulting in models with different gas densities in the wind. The effects which we investigate here are important for the understanding of the wind mechanism and mass loss of AGB stars. This study is hereby a necessary step towards more reliable interpretations of observations. We find that the effects of drift generally are significant. They cannot be predicted from models calculated without drift. Moreover, the non-drift models showing the lowest mass loss rates, outflow velocities, and the smallest variability in the degree of condensation do not form drift model winds. The wind formation in drift models is, except for a few cases, generally less efficient and the mass loss consequently lower than in the corresponding non-drift models. The effects of drift are generally larger in the more realistic models using that representation of the gas opacity which results in lower densities. The outflow properties of these models are also -for all cases we have studied -sensitive to the period of the stellar pulsations. A check of the mass loss rates against a (recent) fit formula shows systematically lower values, in particular in the more realistic models with a low density. The fit is in its current form inapplicable to the new models presented here.

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Mechanics of Rarefied Gases

Cited by 52 publications

References 118 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

Dust Dynamics in Protoplanetary Disk Winds Driven by Magnetorotational Turbulence: A Mechanism for Floating Dust Grains With Characteristic Sizes

Three-component modeling of C-rich AGB star winds

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