In this paper the pressure distribution of the gaseous flow in a microchannel is studied via a lattice Boltzmann equation(LBE)method.With effective relaxation times and a generalized second order slip boundary condition,the LBE can be used to simulate rarefied gas flows from slip to transition regimes.The Knudsen minimum phenomena of mass flow rate in the pressure driven flow is also investigated.The effects of Knudsen number(rarefaction effect),pressure ratio and aspect ratio(compression effect)on the pressure distribution are analyzed.It is found the rarefaction effect tends to the curvature of the nonlinear pressure distribution,while the compression effect tends to enhance its nonlinearity.The combined effects lead to a local minimum of the pressure deviation.Furthermore,it is also found that the relationship between the pressure deviation and the aspect ratio follows a pow-law.
In this paper,the power-law fluid flows in a two-dimensional square cavity are investigated in detail with multi-relaxation-time lattice Boltzmann method(MRTLBM).The influence of the Reynolds number(Re)and the power-law index(n)on the vortex strength,vortex position and velocity distribution are extensively studied.In our numerical simulations,Re is varied from 100 to 10000,and n is ranged from 0.25 to 1.75,covering both cases of shear-thinning and shear-thickening.Compared with the Newtonian fluid,numerical results show that the flow structure and number of vortex of power-law fluid are not only dependent on the Reynolds number,but also related to power-law index.
