scholarly journals Validation of a Second-Order Slip Model for Transition-Regime, Gaseous Flows

2004 ◽  
Author(s):  
Nicolas G. Hadjiconstantinou
Keyword(s):  
Second Order ◽  
Stress Fields ◽  
Gas Flows ◽  
Transition Regime ◽  
Slip Model ◽  
Dilute Gas ◽  
Transient Problems ◽  
Model Predictions ◽  
Gaseous Flows ◽  
Related Stress

We discuss and validate a recently proposed second-order slip model for dilute gas flows. Our discussion focuses on the importance of quantitatively accounting for the effect of Knudsen layers close to the walls. This is important, not only for obtaining an accurate slip model but also for interpreting the results of the latter since in transition-regime flows the Knudsen layers penetrate large parts of the flow. Our extensive validation illustrates the above points by comparing direct Monte Carlo solutions to the slip model predictions for an unsteady flow. Excellent agreement is found between simulation and the slip model predictions up to Kn = 0.4, for both the velocity profile and stress at the wall. This demonstrates that the proposed second-order slip model reliably describes arbitrary flowfields (and related stress fields) in a predictive manner at least up to Kn = 0.4 for both steady and transient problems.

scholarly journals Highly dilute gas flows over an ellipse

2020 ◽  
Vol 32 (9) ◽  
pp. 097104
Author(s):  
Shiying Cai ◽  
Chunpei Cai ◽  
Jun Li
Keyword(s):  
Gas Flows ◽  
Dilute Gas

scholarly journals On the second-order temperature jump coefficient of a dilute gas

2012 ◽  
Vol 707 ◽  
pp. 331-341 ◽  
Author(s):  
Gregg A. Radtke ◽  
N. G. Hadjiconstantinou ◽  
S. Takata ◽  
K. Aoki
Keyword(s):  
Hard Sphere ◽  
Temperature Jump ◽  
Second Order ◽  
Bgk Model ◽  
Volumetric Heating ◽  
Dilute Gas ◽  
The Poisson Equation ◽  
Jump Relation ◽  
Temperature Jump Coefficient ◽  
Time Dependent Problems

AbstractWe use LVDSMC (low-variance deviational Monte Carlo) simulations to calculate, under linearized conditions, the second-order temperature jump coefficient for a dilute gas whose temperature is governed by the Poisson equation with a constant forcing term, as in the case of homogeneous volumetric heating. Both the hard-sphere gas and the BGK model of the Boltzmann equation, for which slip/jump coefficients are not functions of temperature, are considered. The temperature jump relation and jump coefficient determined here are closely linked to the general jump relations for time-dependent problems that have yet to be systematically treated in the literature; as a result, they are different from those corresponding to the well-known linear and steady case where the temperature is governed by the homogeneous heat conduction (Laplace) equation.

Review—Numerical Models for Dilute Gas-Particle Flows

1982 ◽  
Vol 104 (3) ◽  
pp. 297-303 ◽  
Author(s):  
C. T. Crowe
Keyword(s):  
Numerical Models ◽  
Model Development ◽  
Point Of View ◽  
One Dimensional ◽  
Advantages And Disadvantages ◽  
Dilute Gas ◽  
Particle Flows ◽  
Gaseous Flows ◽  
Droplet Flows ◽  
Two Fluid

The rapidly increasing capability of computers has led to the development of numerical models for gaseous flows and, in turn, gas-particle and gas-droplet flows. This paper reviews the essential features of gas-particle flows from the point of view of model development. Various models that have appeared for one-dimensional and two-dimensional flows are discussed. The advantages and disadvantages of the trajectory and two-fluid models are noted.

Burnett Simulations of Gaseous Flows in Transition Regime

2011 ◽  
Author(s):  
J. X. Wang ◽  
F. B. Bao ◽  
J. Z. Lin ◽  
Jiachun Li ◽  
Song Fu
Keyword(s):  
Transition Regime ◽  
Gaseous Flows

Strength Homogenization of Double-Porosity Cohesive-Frictional Solids

2013 ◽  
Vol 80 (2) ◽  
Author(s):  
J. Alberto Ortega ◽  
Franz-Josef Ulm
Keyword(s):  
Effective Stress ◽  
Double Porosity ◽  
Second Order ◽  
Porous Solids ◽  
Strength Development ◽  
Strength Criteria ◽  
Model Predictions ◽  
Strength Behavior ◽  
Homogenization Model ◽  
The Mean

The strength homogenization of cohesive-frictional solids influenced by the presence of two pressurized pore spaces of different characteristic sizes is addressed in this study. A two-scale homogenization model is developed based on limit analysis and the second-order method (SOM) in linear comparison composite theory, which resolves the nonlinear strength behavior through the use of linear comparison composites with optimally chosen properties. For the scale of the classical configuration of a porous solid, the formulation employs a compressible thermoelastic comparison composite to deliver closed-form expressions of strength criteria. Comparisons with numerical results reveal that the proposed homogenization estimates for drained conditions are adequate except for high triaxialities in the mean compressive strength regime. At the macroscopic scale of the double-porosity material, the SOM results are in agreement with strength criteria predicted by alternative micromechanics solutions for materials with purely cohesive solid matrices and drained conditions. The model predictions for the cohesive-frictional case show that drained strength development in granularlike composites is affected by the partitioning of porosity between micro- and macropores. In contrast, the drained strength is virtually equivalent for single- and double-porosity materials with matrix-inclusion morphologies. Finally, the second-order linear comparison composite approach confirms the applicability of an effective stress concept, previously proposed in the literature of homogenization of cohesive-frictional porous solids, for double-porosity materials subjected to similar pressures in the two pore spaces. For dissimilar pore pressures, the model analytically resolves the complex interplays of microstructure, solid properties, and volume fractions of phases, which cannot be recapitulated by the effective stress concept.

Effect of Velocity-Slip Boundary Conditions on Jeffery–Hamel Flow Solutions

2010 ◽  
Vol 77 (4) ◽  
Author(s):  
M. A. Al-Nimr ◽  
Vladimir A. Hammoudeh ◽  
M. A. Hamdan
Keyword(s):  
Friction Coefficient ◽  
Skin Friction ◽  
Flow Direction ◽  
Velocity Slip ◽  
Skin Friction Coefficient ◽  
Second Order ◽  
Slip Model ◽  
Wall Angle ◽  
First Order ◽  
Slip Boundary

In the present work, the Jeffery–Hamel flow problem has been studied using both first- and second-order velocity-slip models, and then compared with the no-slip model. The objectives are to observe the behavior of the flow predicted by the two slip models and to establish criteria for using the two velocity-slip models. The study concentrates on examining the effect of the change in the Knudsen number (Kn) on the velocity profiles, magnitude of slip at the wall, and skin friction coefficient. Assuming that a difference between the two slip models of the order of 10% or less justifies the use of the simple first-order model, the transitional Kn numbers have been found. These Kn numbers depend on the flow direction, being either inflow or outflow. Also, there are three distinct regions that specify where to use each of the no-slip, first-order, and second-order slip models. Further, the reversal of the flow has been investigated as a function of the Kn number and for different Re⋅α, where Re is Reynolds number and α is the wall angle. Using the second-order slip models, it is found that as the Kn number increases, reversal occurs at Re⋅α smaller than the 10.31 value at which flow reversal happens in the no-slip model, and increasing the Kn number leads to a reduction in the skin friction coefficient in all cases except when reversal occurs.

scholarly journals A slip model for micro/nano gas flows induced by body forces

2009 ◽  
Vol 8 (3) ◽  
pp. 417-422 ◽  
Author(s):  
Q. D. To ◽  
C. Bercegeay ◽  
G. Lauriat ◽  
C. Léonard ◽  
G. Bonnet
Keyword(s):  
Gas Flows ◽  
Slip Model ◽  
Body Forces
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