Simulation of Gas Flow in Channels with Variable Cross-Section at Different Flow Modes using Lattice Boltzmann Method (LBM)

2019 ◽  
pp. 105-115
Author(s):  
A.V. Burmistrov ◽  
S.I. Salikeev ◽  
A.A. Raykov
Keyword(s):  
Lattice Boltzmann Method ◽  
Cross Section ◽  
Lattice Boltzmann ◽  
Gas Flow ◽  
Stokes Equations ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Wide Range ◽  
Boltzmann Method ◽  
Contact Free

All contact-free vacuum pumps operate in a very wide pressure range. Therefore, the calculation of flows through the slot channels is associated with the need to take into account the laws of all three modes of gas flow: viscous, transitional and molecular. Most of channels of contact-free pumps are formed by curved walls, which are slits of variable cross-section in the direction of gas flow, having a minimum gap in some place. The paper considers the basic methods of calculating flows in channels of variable cross-section: the Monte Carlo method for molecular mode, the numerical solution of Navier --- Stokes equations for viscous mode and the Lattice Boltzmann method (LBM) for a wide range of pressures. The results of gas flow simulation calculated in COMSOL Multiphysics with LBM method are presented. The influence of the gas flow mode on the velocity profile in the channel is discussed. Based on the simulation results, the conductivity of channels of different geometries was calculated at various pressures at the inlet and outlet of the channel. The graphs of conductivity dependence on the Knudsen number for the method of angular coefficients, the model of lattice Boltzmann equations and experimental data are presented. It is shown that for slit channels of variable cross-section, the LBM model agrees well with the experiment under any gas flow modes.

SIMULATION OF AN AXISYMMETRIC RISING BUBBLE BY A MULTIPLE RELAXATION TIME LATTICE BOLTZMANN METHOD

2009 ◽  
Vol 23 (24) ◽  
pp. 4907-4932 ◽  
Author(s):  
ABBAS FAKHARI ◽  
MOHAMMAD HASSAN RAHIMIAN
Keyword(s):  
Free Surface ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Rise Velocity ◽  
Rising Bubble ◽  
Wide Range ◽  
Theoretical Predictions ◽  
Multiple Relaxation Time ◽  
Bubble Rising ◽  
Boltzmann Method

In this paper, the lattice Boltzmann method is employed to simulate buoyancy-driven motion of a single bubble. First, an axisymmetric bubble motion under buoyancy force in an enclosed duct is investigated for some range of Eötvös number and a wide range of Archimedes and Morton numbers. Numerical results are compared with experimental data and theoretical predictions, and satisfactory agreement is shown. It is seen that increase of Eötvös or Archimedes number increases the rate of deformation of the bubble. At a high enough Archimedes value and low Morton numbers breakup of the bubble is observed. Then, a bubble rising and finally bursting at a free surface is simulated. It is seen that at higher Archimedes numbers the rise velocity of the bubble is greater and the center of the free interface rises further. On the other hand, at high Eötvös values the bubble deforms more and becomes more stretched in the radial direction, which in turn results in lower rise velocity and, hence, lower elevations for the center of the free surface.

scholarly journals A Multiple-Grid Lattice Boltzmann Method for Natural Convection under Low and High Prandtl Numbers

Fluids ◽  
2021 ◽  
Vol 6 (4) ◽  
pp. 148
Author(s):  
Seyed Amin Nabavizadeh ◽  
Himel Barua ◽  
Mohsen Eshraghi ◽  
Sergio D. Felicelli
Keyword(s):  
Natural Convection ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Large Scale ◽  
Bgk Model ◽  
Flow Equations ◽  
Wide Range ◽  
Prandtl Numbers ◽  
Boltzmann Method ◽  
Benchmark Solutions

A multi-distribution lattice Boltzmann Bhatnagar–Gross–Krook (BGK) model with a multiple-grid lattice Boltzmann (MGLB) model is proposed to efficiently simulate natural convection over a wide range of Prandtl numbers. In this method, different grid sizes and time steps for heat transfer and fluid flow equations are chosen. The model is validated against natural convection in a square cavity, since extensive benchmark solutions are available for that problem. The proposed method can resolve the computational difficulty in simulating problems with very different time scales, in particular, when using extremely low or high Prandtl numbers. The technique can also enhance computational speed and stability while keeping the simplicity of the BGK method. Compared with the conventional lattice Boltzmann method, the simulation time can be reduced up to one-tenth of the time while maintaining the accuracy in an acceptable range. The proposed model can be extended to other lattice Boltzmann collision models and three-dimensional cases, making it a great candidate for large-scale simulations.

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.

Simulation of Gas Flow in a Microchannel by Lattice Boltzmann Method

2009 ◽  
pp. 195-200 ◽  
Author(s):  
In-Won Park ◽  
Myung-Seob Shin ◽  
Sung-Joon Byun ◽  
Joon-Yong Yoon
Keyword(s):  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Gas Flow ◽  
Boltzmann Method

Parallelization of the Lattice Boltzmann Method in Simulating Buoyancy-Driven Convection Heat Transfer

2004 ◽  
Author(s):  
Anoosheh Niavarani-Kheirier ◽  
Masoud Darbandi ◽  
Gerry E. Schneider
Keyword(s):  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Message Passing ◽  
Large Scale ◽  
Message Passing Interface ◽  
Parallel Machines ◽  
Convection Heat Transfer ◽  
Wide Range ◽  
Buoyancy Driven Convection ◽  
Boltzmann Method

The main objective of the current work is to utilize Lattice Boltzmann Method (LBM) for simulating buoyancy-driven flow considering the hybrid thermal lattice Boltzmann equation (HTLBE). After deriving the required formulations, they are validated against a wide range of Rayleigh numbers in buoyancy-driven square cavity problem. The performance of the method is investigated on parallel machines using Message Passing Interface (MPI) library and implementing domain decomposition technique to solve problems with large order of computations. The achieved results show that the code is highly efficient to solve large scale problems with excellent speedup.

Gas Flow in Microchannels and Nanochannels With Variable Cross Section for All Knudsen and All Mach Number Values

2020 ◽  
Vol 143 (2) ◽  
Author(s):  
Snežana S. Milićev ◽  
Nevena D. Stevanović
Keyword(s):  
Mach Number ◽  
Friction Factor ◽  
Cross Section ◽  
Gas Flow ◽  
Variable Cross Section ◽  
Molecular Flow ◽  
Variable Cross ◽  
General Boundary Condition ◽  
Poiseuille Number ◽  
Isothermal Gas

Abstract The analytical solution for steady viscous pressure-driven compressible isothermal gas flow through micro- and nanochannels with variable cross section for all Knudsen and all Mach number values is presented in this paper. The continuum one-dimensional governing equations are solved using the friction factor that is established in a special way to provide solutions for mass flow rate, pressure, and velocity distribution through the microchannels and nanochannels in the entire rarefaction regime. The friction factor, defined by the general boundary condition and generalized diffusion coefficient proposed by Beskok and Karniadakis (1999, “A Model for Flows in Channels, Pipes, and Ducts at Micro and Nano Scales,” J. Microscale Thermophys. Eng., 3, pp. 43–77), spreads the solution application to all rarefaction regimes from continuum to free molecular flow. The correlation between the product of friction factor and Reynolds number (Poiseuille number) and Knudsen number is established explicitly in the paper. Moreover, the obtained solution includes the inertia effect, which allows the application of the solution to both subsonic and supersonic gas flows, which was not shown earlier. The presented solution confirms the existence of the Knudsen minimum in the diverging, converging, and microchannels and nanochannels with constant cross section. The proposed solution is verified by comparison with experimental, analytical, and numerical results available in literature.

scholarly journals Simulation of gas flow in micro-porous media with the regularized lattice Boltzmann method

Fuel ◽  
2017 ◽  
Vol 205 ◽  
pp. 232-246 ◽  
Author(s):  
Junjian Wang ◽  
Qinjun Kang ◽  
Yuzhu Wang ◽  
Rajesh Pawar ◽  
Sheik S. Rahman
Keyword(s):  
Porous Media ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Gas Flow ◽  
Boltzmann Method

Consistent subgrid scale modelling for lattice Boltzmann methods

2012 ◽  
Vol 700 ◽  
pp. 514-542 ◽  
Author(s):  
Orestis Malaspinas ◽  
Pierre Sagaut
Keyword(s):  
Lattice Boltzmann Method ◽  
Turbulent Flows ◽  
Lattice Boltzmann ◽  
Stokes Equations ◽  
Mixing Layer ◽  
Velocity Distribution Function ◽  
Theoretical Point ◽  
Subgrid Scale ◽  
Hermite Expansion ◽  
Boltzmann Method

AbstractThe lattice Boltzmann method has become a widely used tool for the numerical simulation of fluid flows and in particular of turbulent flows. In this frame the inclusion of subgrid scale closures is of crucial importance and is not completely understood from the theoretical point of view. Here, we propose a consistent way of introducing subgrid closures in the BGK Boltzmann equation for large eddy simulations of turbulent flows. Based on the Hermite expansion of the velocity distribution function, we construct a hierarchy of subgrid scale terms, which are similar to those obtained for the Navier–Stokes equations, and discuss their inclusion in the lattice Boltzmann method scheme. A link between our approach and the standard way on including eddy viscosity models in the lattice Boltzmann method is established. It is shown that the use of a single modified scalar relaxation time to account for subgrid viscosity effects is not consistent in the compressible case. Finally, we validate the approach in the weakly compressible case by simulating the time developing mixing layer and comparing with experimental results and direct numerical simulations.

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