Computational Modeling of Molecular Gas Convection With a c²-z² Model

Modelling micro channel flows momentum and heat diffusion / convection are recent parameters modelling the molecule velocity distribution. Macroscopic models describe velocity and energy / enthalpie with integrals of mass increments. Using microscopic models motion and forces of a molecular flow have to be computed by models of physical properties, whose are described by statistical power moments of the molecule velocity. Therefore dilute flows have to be investigated in small channels with a mean free path length of molecules higher than the channel width of the the micro channel itself (λ₀ ≥ H₀). Modelling this process by a continuous flow the boundary conditions have to be modified (e.g. [9]). Instead of a simple Dirichlet boundary condition with a neglecting velocity directly at the channel wall, given slip models define a slip velocity of the ducted fluid depending on the shear stress at the wall. The present model uses the statistical approximation of the molecule velocity distribution to simulate the behaviour of this discrete flow with a weighted averaged molecule velocity ξ˜_i, its standard deviation σ and the characterisic molecule collision rate z. The number density n of molecules N per volume V near one position is used for the weighting factor averaging method describing the mean molecule velocity. The present model is validated computing Poiseuille and Couette flows with different Knudsen numbers. Showing the advantages of the present model the simulation results are compared with simulation results of the wall-distance depending diffusivity model of Lockerby and Reese [5] and BGK results of a Lattice-Boltzmann simulation.