The Boundary Condition Of The Discrete Velocity Direction Model And Its Application In Wavy Channel

With the rapid development of MEMS,the micro-scale flow and heat transfer have been paid increasingly attention.The characteristic length of the internal flow of MEMS varies greatly,and the gas flow covers several flow regimes.Such flow always meets rarefied effect,such as the velocity slip,temperature jump and thermal creep.In addition,the micro flow is always with the characteristics of low Reynolds number,viscous effect,and so on,which pose a great challenge for the numerical study.The discrete velocity direction(DVD)model is a simplified method for the Boltzmann equation,which can simulate the gas flow of low Reynolds number accurately and efficiently in all flow regimes.However the model cannot be directly applied to the curved surface.To solve this problem,this paper improved the DVD model to any curved surface channel by presenting a new boundary condition,then developed parallel programs of the DVD model based on the new boundary condition.Finally,the flow characteristics of gas in micro scale sinusoidal corrugated channels are simulated.This paper mainly contains the following contents:Firstly,the boundary condition for the DVD model on the curved wall is established,which extended the model from the straight wall surface to the arbitrary curved wall surface.This work include two aspects,one is to obtain the governing equations of the DVD model in curvilinear coordinates by coordinate transformation,the other is to propose a molecule reflection form in the curved wall surface,where the number proportion of the reflecting molecules from the wall in each direction is no longer equal,but determined by the wall angle.Based on this,a general expression of the number density of reflecting molecules from the curved wall is derived.Secondly,based on the serial program of the DVD model,the parallel programming is realized by FORTEAN+MPI method.By fully considering the fact that the discrete directions are independent of each other,the program is realized on the discrete directions,not the geometric blocks,which differs from the traditional parallel CFD programs.There are several advantages:the first one is that it can achieve the programs with less modification,and the second one is it can improve the maintainability of the program,when the computational scheme for the governing equations is changed,it is not necessary to redesign the parallel program,the third one is that all threads are carried out in the same geometric region,so the threads cost almost the same computation time,which can further improve the computational efficiency.The number of participating processors can be given arbitrarily,and the higher performance of the processor,the greater the workload,which can reduce the influence of the poor performance of the processor to improve the calculation efficiency.Finally,based on the parallel program,the flow characteristics of gas in sinusoidal corrugated channels are calculated and analyzed systematically.Two different types of wavy channels were employed:one with crests and troughs facing each other alternately by a phase of 180°,i.e.,symmetric channel,and the other with crests and troughs facing each other by a phase of 0°,i.e.,serpentine channel.This paper presents the effect of variation of Kn number,range from 0.02 to 2.26,the change of amplitude ratio,ranges from 0 to 0.2,and wavelength ratio on the slip velocity,friction factor,Po number and mass flux in above channels.The study in the symmetric channel found that with the increase of Kn number the slip velocity and the friction factor increases,while the Po number decreases slightly,and the mass flow rate increases firstly and then decreases,which exists a minimum mass in the vicinity of Kn=1.What's more with the increase of the amplitude and the decreases of wavelength,the average slip velocity and flow rate decreases,while the Po number increases.The study in the serpentine channel found that the influence of Kn number on these parameters is consistent with that of the symmetric channel,under the same amplitude,the friction factor is larger,the Po number is smaller,and the flow rate is almost the same.The influence of amplitude and wavelength on all these parameters is very small,although the increase of the amplitude will increase the flow,but the increment is less than 6%.