Grad's distribution functions-based gas kinetic scheme for simulation of flows beyond Navier–Stokes level

2021 ◽  
Vol 33 (12) ◽  
pp. 122007
Author(s):  
Z. Y. Yuan ◽  
C. Shu ◽  
Z. J. Liu
Keyword(s):  
Kinetic Scheme ◽  
Distribution Functions ◽  
Navier Stokes

scholarly journals Turbulence through the Spyglass of Bilocal Kinetics

Entropy ◽  
2018 ◽  
Vol 20 (7) ◽  
pp. 539 ◽  
Author(s):  
Gregor Chliamovitch ◽  
Yann Thorimbert
Keyword(s):  
Turbulent Flows ◽  
Kinetic Scheme ◽  
Navier Stokes ◽  
Pressure Tensor ◽  
Kinetic Description ◽  
Balance Equations ◽  
Coupling Term ◽  
Navier Stokes Equation ◽  
Local Character ◽  
Non Local

In two recent papers we introduced a generalization of Boltzmann’s assumption of molecular chaos based on a criterion of maximum entropy, which allowed setting up a bilocal version of Boltzmann’s kinetic equation. The present paper aims to investigate how the essentially non-local character of turbulent flows can be addressed through this bilocal kinetic description, instead of the more standard approach through the local Euler/Navier–Stokes equation. Balance equations appropriate to this kinetic scheme are derived and closed so as to provide bilocal hydrodynamical equations at the non-viscous order. These equations essentially consist of two copies of the usual local equations, but coupled through a bilocal pressure tensor. Interestingly, our formalism automatically produces a closed transport equation for this coupling term.

scholarly journals A Modified Gas-Kinetic Scheme for Turbulent Flow

2014 ◽  
Vol 16 (1) ◽  
pp. 239-263 ◽  
Author(s):  
Marcello Righi
Keyword(s):  
Boundary Layer ◽  
Shock Wave ◽  
Kinetic Energy ◽  
Turbulent Boundary Layer ◽  
Numerical Scheme ◽  
Stokes Equations ◽  
Kinetic Scheme ◽  
Navier Stokes ◽  
Turbulent Stress ◽  
Navier Stokes Equations

AbstractThe implementation of a turbulent gas-kinetic scheme into a finite-volume RANS solver is put forward, with two turbulent quantities, kinetic energy and dissipation, supplied by an allied turbulence model. This paper shows a number of numerical simulations of flow cases including an interaction between a shock wave and a turbulent boundary layer, where the shock-turbulent boundary layer is captured in a much more convincing way than it normally is by conventional schemes based on the Navier-Stokes equations. In the gas-kinetic scheme, the modeling of turbulence is part of the numerical scheme, which adjusts as a function of the ratio of resolved to unresolved scales of motion. In so doing, the turbulent stress tensor is not constrained into a linear relation with the strain rate. Instead it is modeled on the basis of the analogy between particles and eddies, without any assumptions on the type of turbulence or flow class. Conventional schemes lack multiscale mechanisms: the ratio of unresolved to resolved scales – very much like a degree of rarefaction – is not taken into account even if it may grow to non-negligible values in flow regions such as shocklayers. It is precisely in these flow regions, that the turbulent gas-kinetic scheme seems to provide more accurate predictions than conventional schemes.

EQUILIBRIUM VELOCITY DISTRIBUTION FUNCTIONS FOR A KINETIC MODEL OF TWO-PHASE FLOWS

1995 ◽  
Vol 05 (02) ◽  
pp. 191-211 ◽  
Author(s):  
LIONEL SAINSAULIEU
Keyword(s):  
Velocity Distribution ◽  
Gas Flow ◽  
Stokes Equations ◽  
Volume Fraction ◽  
Velocity Distribution Function ◽  
Distribution Functions ◽  
Solid Particles ◽  
Navier Stokes ◽  
Two Phase ◽  
Entropy Balance

We consider a cloud of solid particles in a gas flow. The cloud is described by a probability density function which satisfies a kinetic equation. The gas flow is modeled by Navier-Stokes equations. The two phases exchange momentum and energy. We obtain the entropy balance of the gas flow and deduce some bounds for the volume fraction of the gas phase. Writing the entropy balance for the dispersed phase enables one to determine the particles equilibrium velocity distribution function when the gas flow is known.

A Discrete Flux Scheme for Aerodynamic and Hydrodynamic Flows

2011 ◽  
Vol 9 (5) ◽  
pp. 1257-1283 ◽  
Author(s):  
S. C. Fu ◽  
R. M. C. So ◽  
W. W. F. Leung
Keyword(s):  
Thermal Energy ◽  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Moment Equation ◽  
Zero Order ◽  
Distribution Functions ◽  
Navier Stokes ◽  
Order Moment ◽  
Navier Stokes Equations ◽  
First Order

AbstractThe objective of this paper is to seek an alternative to the numerical simulation of the Navier-Stokes equations by a method similar to solving the BGK-type modeled lattice Boltzmann equation. The proposed method is valid for both gas and liquid flows. A discrete flux scheme (DFS) is used to derive the governing equations for two distribution functions; one for mass and another for thermal energy. These equations are derived by considering an infinitesimally small control volume with a velocity lattice representation for the distribution functions. The zero-order moment equation of the mass distribution function is used to recover the continuity equation, while the first-order moment equation recovers the linear momentum equation. The recovered equations are correct to the first order of the Knudsen number(Kn);thus, satisfying the continuum assumption. Similarly, the zero-order moment equation of the thermal energy distribution function is used to recover the thermal energy equation. For aerodynamic flows, it is shown that the finite difference solution of the DFS is equivalent to solving the lattice Boltzmann equation (LBE) with a BGK-type model and a specified equation of state. Thus formulated, the DFS can be used to simulate a variety of aerodynamic and hydrodynamic flows. Examples of classical aeroacoustics, compressible flow with shocks, incompressible isothermal and non-isothermal Couette flows, stratified flow in a cavity, and double diffusive flow inside a rectangle are used to demonstrate the validity and extent of the DFS. Very good to excellent agreement with known analytical and/or numerical solutions is obtained; thus lending evidence to the DFS approach as an alternative to solving the Navier-Stokes equations for fluid flow simulations.

The effect of high-pressure injection variations on the mixing state of underexpanded methane jets

2020 ◽  
pp. 146808742096089
Author(s):  
VD Sakellarakis ◽  
W Vera-Tudela ◽  
U Doll ◽  
D Ebi ◽  
YM Wright ◽  
...  
Keyword(s):  
High Pressure ◽  
Scaling Laws ◽  
Numerical Study ◽  
Pressure Ratio ◽  
Injection Pressure ◽  
Distribution Functions ◽  
Navier Stokes ◽  
Chamber Pressure ◽  
Gaussian Shape ◽  
Fuel Concentration

This work presents a joint experimental and numerical study of global characteristics and mixing behavior of underexpanded methane jets at high-pressure conditions in a Constant Volume Chamber. Injection pressures of 200, 250, and 300 bar and pressure ratios of 4, 5, 6, 8, and 10 at each of those pressures have been investigated. Tracer LIF with acetone as tracer has been applied to experimentally quantify the mixing of methane and quiescent air. In order to exploit the symmetry of the configuration, accompanying simulations have been carried out in Reynolds-Averaged Navier-Stokes framework with the k – w SST turbulence model and real-gas modelling based on the Soave-Redlich-Kwong Equation of State has been employed to account for high-pressure corrections in thermodynamic and caloric properties. The experiments confirm the hyperbolic decay of axial fuel concentration and the Gaussian shape of traverse concentration profiles in the self-similar region of the jets, while simulation results match well with experimentally determined fuel concentration fields. It is found that scaling laws proposed in literature for steady-state jet propagation can qualitatively interpret the effect of injection variations on jet tip penetration and volume. Increasing pressure ratio at fixed injection pressure leads to the formation of slightly richer jets, with slightly smaller mass percentage in the range of air-to-fuel ratios most favorable to autoignition. By contrast, increasing pressure ratio at fixed chamber pressure leads to virtually identical Probability Distribution Functions of local air-to-fuel ratios and the same is observed when employing a fixed pressure ratio at higher pressure levels.

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