scholarly journals On the Rarefied Gas Experiments

Entropy ◽  
2019 ◽  
Vol 21 (7) ◽  
pp. 718 ◽  
Author(s):  
Róbert Kovács
Keyword(s):  
Density Dependence ◽  
Stokes Equations ◽  
Rarefied Gas ◽  
Mass Density ◽  
Navier Stokes ◽  
Internal Variables ◽  
Material Structure ◽  
Rarefied Gases ◽  
Scaling Properties ◽  
Material Parameters

There are limits of validity of classical constitutive laws such as Fourier and Navier-Stokes equations. Phenomena beyond those limits have been experimentally found many decades ago. However, it is still not clear what theory would be appropriate to model different non-classical phenomena under different conditions considering either the low-temperature or composite material structure. In this paper, a modeling problem of rarefied gases is addressed. The discussion covers the mass density dependence of material parameters, the scaling properties of different theories and aspects of how to model an experiment. In the following, two frameworks and their properties are presented. One of them is the kinetic theory based Rational Extended Thermodynamics; the other one is the non-equilibrium thermodynamics with internal variables and current multipliers. In order to compare these theories, an experiment on sound speed in rarefied gases at high frequencies, performed by Rhodes, is analyzed in detail. It is shown that the density dependence of material parameters could have a severe impact on modeling capabilities and influences the scaling properties.

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.

scholarly journals Renormalisation Group Analysis of Turbulent Hydrodynamics

2013 ◽  
Vol 2013 ◽  
pp. 1-20 ◽  
Author(s):  
Dirk Barbi ◽  
Gernot Münster
Keyword(s):  
Stokes Equations ◽  
Group Analysis ◽  
Structure Functions ◽  
Renormalisation Group ◽  
Theoretical Physics ◽  
Navier Stokes ◽  
Scaling Exponents ◽  
Navier Stokes Equations ◽  
Scaling Properties ◽  
Promising Tool

Turbulent hydrodynamics is characterised by universal scaling properties of its structure functions. The basic framework for investigations of these functions has been set by Kolmogorov in 1941. His predictions for the scaling exponents, however, deviate from the numbers found in experiments and numerical simulations. It is a challenge for theoretical physics to derive these deviations on the basis of the Navier-Stokes equations. The renormalization group is believed to be a very promising tool for the analysis of turbulent systems, but a derivation of the scaling properties of the structure functions has so far not been achieved. In this work, we recall the problems involved, present an approach in the framework of the exact renormalisation group to overcome them, and present first numerical results.

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.

Two-phase filtered mass density function for LES of turbulent reacting flows

2014 ◽  
Vol 760 ◽  
pp. 243-277 ◽  
Author(s):  
Z. Li ◽  
A. Banaeizadeh ◽  
F. A. Jaberi
Keyword(s):  
Density Function ◽  
Stokes Equations ◽  
Liquid Droplet ◽  
Mass Density ◽  
Mixing Layer ◽  
Reacting Flows ◽  
Navier Stokes ◽  
Turbulent Reacting Flows ◽  
Two Phase ◽  
Filtered Mass Density Function

AbstractThis paper describes a new computational model developed based on the filtered mass density function (FMDF) for large-eddy simulation (LES) of two-phase turbulent reacting flows. The model is implemented with a unique Lagrangian–Eulerian–Lagrangian computational methodology. In this methodology, the resolved carrier gas velocity field is obtained by solving the filtered form of the compressible Navier–Stokes equations with high-order finite difference (FD) schemes. The gas scalar (temperature and species mass fractions) field and the liquid (droplet) phase are both obtained by Lagrangian methods. The two-way interactions between the phases and all the Eulerian and Lagrangian fields are included in the new two-phase LES/FMDF methodology. The results generated by LES/FMDF are compared with direct numerical simulation (DNS) data for a spatially developing non-reacting and reacting evaporating mixing layer. Results for two more complex and practical flows (a dump combustor and a double-swirl burner) are also considered. For all flows, it is shown that the two-phase LES/FMDF results are consistent and accurate.

On the thermodynamic theory of the second viscosity

1954 ◽  
Vol 226 (1164) ◽  
pp. 51-56 ◽  
Keyword(s):  
Stokes Equations ◽  
Relaxation Times ◽  
Thermodynamic Theory ◽  
Navier Stokes ◽  
Internal Variables ◽  
Usual Sense ◽  
Navier Stokes Equations ◽  
Shear Moduli ◽  
Essential Components ◽  
Positive Functions

It seems possible to reconcile the Navier-Stokes equations and the thermodynamic theory of relaxation, but a full insight into the problem of the two viscosities may be obtained by considering the liquid as a limiting case of an elastic body with ‘after-effects’. The aftereffect theory, when applied to a generalized stress-strain relation that contains temperature and entropy besides the components of the strain and stress tensors, leads to interesting results; for instance, it can be proved that the compression and shear moduli, divided by p , are positive functions in p ( = io>, where cj is the frequency), in the sense of the electric network terminology. In such materials one can define an apparent viscosity matrix; its essential components in the special case of isotropic visco-elastic substances are the first and the second viscosities, which are positive functions too. It is not possible to represent an arbitrary after-effect behaviour of a material by a thermodynamic theory of relaxation in the usual sense, except if the relaxation times are real and positive and some other conditions are fulfilled, but it seems that an appropriate extension of the thermodynamic theory can be made. In those cases that are suitable for a thermodynamic treatment, the internal variables representing the internal mechanisms divide, for isotropic substances, into two groups; the one containing invariant variables, active only in compression, the other containing sets of five variables with tensor character, and active only in shear deformation. It is essential for a thermodynamic treatment of shear relaxation to represent each molecular mechanism by such a set of five internal variables.

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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