Micro-gas Surface Roughness Effects Of The Lattice Boltzmann Simulation

Surface roughness is identified as an important factor in Knudsen flows of liquid or gas.As the development of Micro-Electro-Mechanical Systems(MEMS) and micro fabrication,micro flows have been receiving more and more attention.Liquid flows in microchannels are most concentrated on the effects of surface tension and wall wettability,and their experiments and theoretical analyses have made considerable successes.However,the way to study the roughness effect of micro gas flows(also rarefied gas flows) is quite different from that of micro liquid flows.Since the result based on the Navier-Stokes equation(NSE) is highly dubitable due to the invalidation of the continuum hypothesis in micro gas flows,the molecular-based models including molecular dynamics(MD) simulations,Boltzmann equation(BE) simulations,direct simulations Monte-Carlo(DSMC) and information preservation (IP) simulations have to be employed for numerical studies.Recently,the lattice Boltzmann method(LBM) provides a new effective way to study the micro flow systems.The researches indicate that the results by lattice Boltzmann method are consistent with the theoretical analyses and experiments. Compared with molecular dynamics simulations,direct simulations Monte-Carlo simulations and other related methods,the lattice Boltzmann method gains the advantages of computational efficiency and flexibility for complex boundary geometries.However,few studies up to now present a deep understanding of the effects of surface roughness on the micro gas flow systems at high Knudsen numbers. To understand the effect of various roughnesses and different geometries on the micro gas flow systems,we here design a lattice Boltzmann model and a microchannel with various roughness boundaries,and then a series of numerical simulations are taken. The surface roughness of the microchannel is modeled to be square,sinusoidal, triangular and fractal,respectively.By this model,the roughness effect combining with the effects of rarefaction and compressibility in different boundaries on the micro gas flows of nitrogen and helium are studied and analyzed.The main contents of this paper are as follows: 1) The relaxation time and its relationship with the Knudsen number are re-deduced from gas dynamics.The relaxation time is determined from the physical properties of the investigated gas and cannot be freetly adjusted.The expression of the Knudsen number is independent of the grid size by setting a certain relaxation time. Compared with theoretical and experimental studies the effectiveness of the lattice Boltzmann model is validated.It is shown that the modified relaxation time is able to eliminate the unrealistically high value of the bulk viscosity and is in good agreement with experiments.2) The surface roughness is modeled by a self-affine fractal which is a reasonable tool to produce suitable surface of controlled roughness to describe the wall boundary of the microchannel.The height of the rough microchannel is H=1.2μm and the length is L=5H or L=10H.Correspondly,the Knudsen numbers of nitrogen and helium are Kn_N2=0.055 and Kn_He=0.16.Importantly,the thoee boundary conditions are discussed and the influence of the tangential momentum accommodation coefficient(TMAC) on the slip velocity near the rough boundary is measured.3) The effects of relative roughness and Knudsen number in the micro flows of nitrogen and helium are studied and analyzed.Numerical simulations show that the surface roughness influences not only velocity distribution but also pressure distribution.In addition,the relative mass flow rate decreases greatly and the relative resistance coefficient rises rapidly as the relative roughness increases.The effects of rarefaction,compressibility and roughness are strongly coupled.To measure the effect of roughness geometry,the result of fractal roughness is also compared with that of square,sinusoidal,triangular roughness.The comparisons and analyses of velocity and resistance coefficient show that the roughness geometry is an important factor besides the relative roughness in studying the effects of surface roughness.These phenomena above different from macroscopic flows are of great importance in understanding the characteristics of micro gas flows.