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A new curved boundary treatment for LBM modeling of thermal gaseous microflow in the slip regime

  • Zhenyu Liu
  • Zhiyu Mu
  • Huiying WuEmail author
Research Paper
  • 43 Downloads

Abstract

The lattice Boltzmann method (LBM) modeling shows its powerful capability in the numerical prediction of thermal gaseous fluid flow. However, the LBM simulation of gaseous microflow with complex boundaries is still challenging, in which the uniform Cartesian lattices are adopted in the numerical model. In this work, a new curved boundary treatment for LBM modeling of thermal gaseous microflow in slip regime is proposed, which is a combination of the non-equilibrium extrapolation method for curved boundary and the counter-extrapolation method for the gas velocity/temperature on the curved wall. The proposed treatment considers the effect of the offset between the physical boundary and the closest grid line and involves no specific gas–wall interaction parameters, which is proved to be more accurate and applicable. The new curved boundary treatment is utilized with the multiple-relaxation-time model and then validated for several benchmark cases, which shows its superiority in slip flow and heat transfer prediction compared with the current curved boundary schemes for gaseous microflow.

Keywords

Gaseous microflow Velocity slip Temperature jump Curved boundary treatment Lattice Boltzmann method 

List of symbols

A

Area [m2]

c

Velocity [m s−1]

cs

Pseudo sound speed [m s−1]

D

Diameter [m]

e

Particle velocity, [m s−1]

f

Particle distribution function of density

F

External forcing term

g

Particle distribution function of temperature

G

External force [N]

k

Specific heat ratio

Kn

Knudsen number

L

Characteristic length [m]

H

Height [m]

Ma

Mach number

n

Unit normal vector

P

Pressure [N m−2]

r

Radius or radial distance [m]

R

Gas constant [J mol−1 K−1] or radius [m]

Re

Reynolds number

t

Time [s]

T

Temperature [K]

u

Velocity [m s−1]

uτ

Tangential velocity [m s−1]

u

Velocity in x direction [m s−1]

v

Velocity in y direction [m s−1]

x,y

Cartesian coordinates [m]

x

Position = (x,y) [m]

Greek

δt

Time step [s]

δx

Lattice spacing [m]

θ

Angle [°]

λ

Gas molecule mean free path [m]

μ

Dynamic viscosity [kg m−1 s−1]

ρ

Density [kg m−3]

σT

Temperature accommodation coefficient

σv

Velocity accommodation coefficient

τg

Dimensionless relaxation time of temperature

τs

Dimensionless relaxation time of velocity

ν

Viscosity [Pa s]

ω

Weight coefficient or angular velocity [rad s−1]

\(\Omega\)

Collision operator

Superscripts

eq

Equilibrium

neq

Non-equilibrium

Subscripts

f

Fluid

g

Gas or temperature

int

Interface

s

Solid

slip

Slip

T

Temperature

w

Wall

Notes

Acknowledgements

This work was supported by the National Natural Science Foundation of China through Grant nos. 51536005, 51676124 and 51820105009; Shanghai International Science and Technology Cooperation Project through Grant no. 18160743900.

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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Mechanical EngineeringShanghai Jiao Tong UniversityShanghaiChina

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