Friction Coefficient Calculation in Stepped Micro-channel for Wide Range of KnudsenNumber by LBM Method

With the rapid development of fabrication technologiesin micro electro mechanical systems (MEMS), microscale gas flows has attracted significant research interestin the last two decades. In this research, the pressuredriven fluid flow of rarefied gases in the stepped microchannelover a wide range of Knudsen number has beenanalyzed with using the isothermal two-dimensionalLattice Boltzmann Multiple Relaxation Time (MRT)method. In the model, a modified second-order slipboundary condition and a Bosanquet-type effectiveviscosity are used to consider the velocity slip at theboundaries and to cover the slip and transition regimesof flow and to gain an accurate simulation of rarefiedgases. LBM method is used owing to its kinetic natureand computational features of the Boltzmann equation.Firstly, the LBM code is verified by comparing thecomputed centerline pressure distribution and crosssectional velocity profile with the solution of thelinearized Boltzmann equation and experimental resultsmeasured by others. The verified code is then used tostudy the streamline and friction coefficient at differentconditions. The results are discussed in the way toexplore effects of outlet Knudsen on the flow patterns.The calculation shows that the friction coefficientdecreases with increasing the Knudsen number andstepping the micro-channel has an inverse effect on thefriction coefficient. Furthermore, a new correlation issuggested for calculation of the friction coefficient inthe stepped micro-channel for slip and transition flowregimes.

کلیدواژه ها:

Micro-channel ، Lattice Boltzmann ، FrictionCoefficient ، Knudsen Number ، Gas Flow