Lattice Boltzmann Simulation of Micro Gas Flows Over a Wide Range of Knudsen Numbers

2019 ◽  
Vol 141 (9) ◽  
Author(s):  
Yan-Long Zhao ◽  
Zhi-Ming Wang
Keyword(s):  
Kinetic Equation ◽  
Knudsen Number ◽  
Lattice Boltzmann ◽  
Present Model ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Gas Flows ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Knudsen Numbers

To characterize the microflow over a larger range of Knudsen numbers, an improved kinetic equation considering the volume diffusion effect for nonideal gases was presented based on Klimontovich's kinetic equation and Enskog equation-based lattice Boltzmann Bhatnagar–Gross–Krook (LBGK) model. Then, with the modified effective viscosity and the second-order slip boundary condition, a series of numerical simulations of gas flows with different mean Knudsen numbers were carried out based on the proposed model. Compared with the solutions of Navier–Stokes equations, Navier–Stokes equations with different slip boundary conditions, bivelocity hydrodynetics, and experimental data, we found that the present model can be valid up to a Knudsen number of 30. It is also shown that the present model furnishes a better solution in the transitional flow regime (0.1 < Kn < 10). The results not only illustrate that the present model could offer a satisfactory solution to a wider range of mean Knudsen number, but also show the importance of the compressibility and surface-dominated effects in micro gas flows. The improved model provides a promising tool for handling the micro gas flows with complex geometries and boundaries.

scholarly journals Involving the Navier–Stokes equations in the derivation of boundary conditions for the lattice Boltzmann method

2011 ◽  
Vol 369 (1944) ◽  
pp. 2184-2192 ◽  
Author(s):  
Joris C. G. Verschaeve
Keyword(s):  
Boundary Condition ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Grid Spacing ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Boltzmann Method

By means of the continuity equation of the incompressible Navier–Stokes equations, additional physical arguments for the derivation of a formulation of the no-slip boundary condition for the lattice Boltzmann method for straight walls at rest are obtained. This leads to a boundary condition that is second-order accurate with respect to the grid spacing and conserves mass. In addition, the boundary condition is stable for relaxation frequencies close to two.

A New Partial Slip Boundary Condition for the Lattice-Boltzmann Method

2013 ◽  
Author(s):  
Marc-Florian Uth ◽  
Alf Crüger ◽  
Heinz Herwig
Keyword(s):  
Boundary Condition ◽  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Slip Boundary Condition ◽  
Navier Stokes ◽  
Slip Model ◽  
Navier Stokes Equations ◽  
Navier Slip ◽  
Slip Boundary ◽  
Boltzmann Method

In micro or nano flows a slip boundary condition is often needed to account for the special flow situation that occurs at this level of refinement. A common model used in the Finite Volume Method (FVM) is the Navier-Slip model which is based on the velocity gradient at the wall. It can be implemented very easily for a Navier-Stokes (NS) Solver. Instead of directly solving the Navier-Stokes equations, the Lattice-Boltzmann method (LBM) models the fluid on a particle basis. It models the streaming and interaction of particles statistically. The pressure and the velocity can be calculated at every time step from the current particle distribution functions. The resulting fields are solutions of the Navier-Stokes equations. Boundary conditions in LBM always not only have to define values for the macroscopic variables but also for the particle distribution function. Therefore a slip model cannot be implemented in the same way as in a FVM-NS solver. An additional problem is the structure of the grid. Curved boundaries or boundaries that are non-parallel to the grid have to be approximated by a stair-like step profile. While this is no problem for no-slip boundaries, any other velocity boundary condition such as a slip condition is difficult to implement. In this paper we will present two different implementations of slip boundary conditions for the Lattice-Boltzmann approach. One will be an implementation that takes advantage of the microscopic nature of the method as it works on a particle basis. The other one is based on the Navier-Slip model. We will compare their applicability for different amounts of slip and different shapes of walls relative to the numerical grid. We will also show what limits the slip rate and give an outlook of how this can be avoided.

Numerical Investigation of Combined Effects of Rarefaction and Compressibility for Gas Flow in Microchannels and Microtubes

2009 ◽  
Vol 131 (10) ◽  
Author(s):  
Xiaohong Yan ◽  
Qiuwang Wang
Keyword(s):  
Boundary Conditions ◽  
Friction Factor ◽  
Knudsen Number ◽  
Velocity Gradient ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Slip Boundary Conditions ◽  
Navier Stokes Equations ◽  
First Order ◽  
Slip Boundary

In this paper, first, the Navier–Stokes equations for incompressible fully developed flow in microchannels and microtubes with the first-order and second-order slip boundary conditions are analytically solved. Then, the compressible Navier–Stokes equations are numerically solved with slip boundary conditions. The numerical methodology is based on the control volume scheme. Numerical results reveal that the compressibility effect increases the velocity gradient near the wall and the friction factor. On the other hand, the increment of velocity gradient near the wall leads to a much larger slip velocity than that for incompressible flow with the same value of Knudsen number and results in a corresponding decrement of friction factor. General correlations for the Poiseuille number (fRe), the Knudsen number (Kn), and the Mach number (Ma) containing the first-order and second-order slip coefficients are proposed. Correlations are validated with available experimental and numerical results.

scholarly journals Simulating Turbulent Buoyant Flow by a Simple LES-Based Thermal Lattice Boltzmann Model

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Sheng Chen
Keyword(s):  
Lattice Boltzmann ◽  
Present Model ◽  
Stokes Equations ◽  
Lattice Boltzmann Model ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Buoyant Flow ◽  
Eddy Simulation ◽  
Thermal Lattice Boltzmann ◽  
Boltzmann Model

To simulate turbulent buoyant flow in geophysical science, where usually the vorticity-streamfunction equations instead of the primitive-variables Navier-Stokes equations serve as the governing equations, a novel and simple thermal lattice Boltzmann model is proposed based on large eddy simulation (LES). Thanks to its intrinsic features, the present model is efficient and simple for thermal turbulence simulation. Two-dimensional numerical simulations of natural convection in a square cavity were performed at high Rayleigh number varying from 104 to 1010 with Prandtl number at 0.7. The advantages of the present model are validated by numerical experiments.

Parallel iterative finite-element algorithms for the Navier–Stokes equations with nonlinear slip boundary conditions

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Kangrui Zhou ◽  
Yueqiang Shang
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Parallel Algorithms ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Slip Boundary Conditions ◽  
Navier Stokes Equations ◽  
Slip Boundary ◽  
Parallel Iterative ◽  
Nonlinear Slip Boundary Conditions

AbstractBased on full domain partition, three parallel iterative finite-element algorithms are proposed and analyzed for the Navier–Stokes equations with nonlinear slip boundary conditions. Since the nonlinear slip boundary conditions include the subdifferential property, the variational formulation of these equations is variational inequalities of the second kind. In these parallel algorithms, each subproblem is defined on a global composite mesh that is fine with size h on its subdomain and coarse with size H (H ≫ h) far away from the subdomain, and then we can solve it in parallel with other subproblems by using an existing sequential solver without extensive recoding. All of the subproblems are nonlinear and are independently solved by three kinds of iterative methods. Compared with the corresponding serial iterative finite-element algorithms, the parallel algorithms proposed in this paper can yield an approximate solution with a comparable accuracy and a substantial decrease in computational time. Contributions of this paper are as follows: (1) new parallel algorithms based on full domain partition are proposed for the Navier–Stokes equations with nonlinear slip boundary conditions; (2) nonlinear iterative methods are studied in the parallel algorithms; (3) new theoretical results about the stability, convergence and error estimates of the developed algorithms are obtained; (4) some numerical results are given to illustrate the promise of the developed algorithms.

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