scholarly journals Angular moments models for rarefied gas dynamics. Numerical comparisons with kinetic and Navier-Stokes equations

2020 ◽  
Vol 13 (4) ◽  
pp. 739-758
Author(s):  
Sébastien Guisset ◽  
Keyword(s):  
Gas Dynamics ◽  
Stokes Equations ◽  
Rarefied Gas ◽  
Rarefied Gas Dynamics ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Numerical Comparisons

Status of the Navier–Stokes Equations in Gas Dynamics. A Review

2018 ◽  
Vol 53 (1) ◽  
pp. 152-168
Author(s):  
V. S. Galkin ◽  
S. V. Rusakov
Keyword(s):  
Gas Dynamics ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations

An analytically predictive model for moderately rarefied gas flow

2012 ◽  
Vol 698 ◽  
pp. 406-422 ◽  
Author(s):  
Thomas Veltzke ◽  
Jorg Thöming
Keyword(s):  
Mass Flow ◽  
Flow Rate ◽  
Stokes Equations ◽  
Rarefied Gas ◽  
Knudsen Diffusion ◽  
Convective Transport ◽  
Surface Topology ◽  
Fickian Diffusion ◽  
Navier Stokes ◽  
Navier Stokes Equations

AbstractIn microducts deviation from continuum flow behaviour of a gas increases with rarefaction. When using Navier–Stokes equations to calculate a flow under slightly and moderately rarefied conditions, slip boundary conditions are used which in turn refer to the tangential momentum accommodation coefficient (TMAC). Here we demonstrate that, in the so-called slip and transition regime, the flow in microducts can be reliably described by a consistently non-empirical model without considering the TMAC. We obtain this equation by superposition of convective transport and Fickian diffusion using two-dimensional solutions of Navier–Stokes equations and a description for the Knudsen diffusion coefficient as derived from kinetic theory respectively. For a wide variety of measurement series found in the literature the calculation predicts the data accurately. Surprisingly only size of the duct, temperature, gas properties and inlet and outlet pressure are necessary to calculate the resulting mass flow by means of a single algebraic equation. From this, and taking the discrepancies of the TMAC concerning surface roughness and nature of the gases into account, we could conclude that neither the diffusive proportions nor the total mass flow rates are influenced by surface topology and chemistry at Knudsen numbers below unity. Compared to the tube geometry, the model slightly underestimates the flow rate in rectangular channels when rarefaction increases. Likewise, the dimensionless mass flow rate and the diffusive proportion of the total flow are distinctly higher in a tube. Thus the cross-sectional geometry has a significant influence on the transport mechanisms under rarefied conditions.

Rarefied Gas Flow Analysis of a Suborbital Shuttle With the Academic CFD Code Galatea

2017 ◽  
Author(s):  
Angelos G. Klothakis ◽  
Georgios N. Lygidakis ◽  
Ioannis K. Nikolos
Keyword(s):  
Gas Flow ◽  
Microelectromechanical Systems ◽  
Stokes Equations ◽  
Rarefied Gas ◽  
Flow Analysis ◽  
Velocity Slip ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Rarefied Gas Flows ◽  
Wide Range

During the past decade considerable efforts have been exerted for the simulation of rarefied gas flows in a wide range of applications, like the flow over suborbital vehicles, in microelectromechanical systems, etc. Such flows appear to be significantly different from those at the continuum regime, making the Navier-Stokes equations to fail without further amendment. In this study an in-house academic CFD solver, named Galatea, is modified appropriately to account for rarefied gases. The no-slip condition on solid walls is no longer valid, hence, velocity slip and temperature jump boundary conditions are applied instead. Additionally, a second-order accurate slip model has been incorporated, namely, this of Beskok and Karniadakis, increasing the accuracy in the same area but avoiding simultaneously the numerical difficulties, entailed by the computation of the second derivative of slip velocity when complex geometries and unstructured grids are coupled. The proposed solver is validated against rarefied laminar flow over a suborbital shuttle, designed by the Azim’UTBM team. The obtained results are compared with those extracted with the parallel open-source kernel SPARTA, which is based on the DSMC method. A satisfactory agreement is reported between the two methodologies, demonstrating the potential of the modified solver to simulate effectively such flows.

Numerical Simulation and Modeling of Laminar Developing Flow in Channels and Tubes With Slip

2013 ◽  
Vol 135 (10) ◽  
Author(s):  
Y. S. Muzychka ◽  
R. Enright
Keyword(s):  
Stokes Equations ◽  
Rarefied Gas ◽  
Slip Boundary Condition ◽  
Momentum Equation ◽  
Navier Stokes ◽  
Cfd Simulations ◽  
Navier Stokes Equations ◽  
Navier Slip ◽  
Slip Boundary ◽  
Rarefied Gas Flows

Analytical solutions for slip flows in the hydrodynamic entrance region of tubes and channels are examined. These solutions employ a linearized axial momentum equation using Targ's method. The momentum equation is subjected to a first order Navier slip boundary condition. The accuracy of these solutions is examined using computational fluid dynamics (CFD) simulations. CFD simulations utilized the full Navier–Stokes equations, so that the implications of the approximate linearized axial momentum equation could be fully assessed. Results are presented in terms of the dimensionless mean wall shear stress, τ⋆, as a function of local dimensionless axial coordinate, ξ, and relative slip parameter, β. These solutions can be applied to either rarefied gas flows when compressibility effects are small or apparent liquid slip over hydrophobic and superhydrophobic surfaces. It has been found that, under slip conditions, the minimum Reynolds number should be ReDh>100 in order for the approximate linearized solution to remain valid.

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