Direct numerical test of the B-G-K model equation by the DSMC method

In the present paper the rarefied gas how caused by the sudden change of the wall temperature and the Rayleigh problem are simulated by the DSMC method which has been validated by experiments both in global flour field and velocity distribution function level. The comparison of the simulated results with the accurate numerical solutions of the B-G-K model equation shows that near equilibrium the BG-K equation with corrected collision frequency can give accurate result but as farther away from equilibrium the B-G-K equation is not accurate. This is for the first time that the error caused by the B-G-K model equation has been revealed.

Information Preservation (IP) Method in Simulation

This paper reviews firstly methods for treating low speed rarefied gas flows: the linearised Boltzmann equation, the Lattice Boltzmann method (LBM), the Navier-Stokes equation plus slip boundary conditions and the DSMC method, and discusses the difficulties in simulating low speed transitional MEMS flows, especially the internal flows. In particular, the present version of the LBM is shown unfeasible for simulation of MEMS flow in transitional regime. The information preservation (IP) method overcomes the difficulty of the statistical simulation caused by the small information to noise ratio for low speed flows by preserving the average information of the enormous number of molecules a simulated molecule represents. A kind of validation of the method is given in this paper. The specificities of the internal flows in MEMS, i.e. the low speed and the large length to width ratio, result in the problem of elliptic nature of the necessity to regulate the inlet and outlet boundary conditions that influence each other. Through the example of the IP calculation of the microchannel (thousands long) flow it is shown that the adoption of the conservative scheme of the mass conservation equation and the super relaxation method resolves this problem successfully. With employment of the same measures the IP method solves the thin film air bearing problem in transitional regime for authentic hard disc write/read head length ( ) and provides pressure distribution in full agreement with the generalized Reynolds equation, while before this the DSMC check of the validity of the Reynolds equation was done only for short ( ) drive head. The author suggests degenerate the Reynolds equation to solve the microchannel flow problem in transitional regime, thus provides a means with merit of strict kinetic theory for testing various methods intending to treat the internal MEMS flows.

Information preservation (IP) method in simulation of internal rarefied gas flows in MEMS

This paper reviews firstly methods for treating low speed rarefied gas flows: the linearised Boltzmann equation, the Lattice Boltzmann method (LBM), the Navier-Stokes equation plus slip boundary conditions and the DSMC method, and discusses the difficulties in simulating low speed transitional MEMS flows, especially the internal flows. In particular, the present version of the LBM is shown unfeasible for simulation of MEMS flow in transitional regime. The information preservation (IP) method overcomes the difficulty of the statistical simulation caused by the small information to noise ratio for low speed flows by preserving the average information of the enormous number of molecules a simulated molecule represents. A kind of validation of the method is given in this paper. The specificities of the internal flows in MEMS, i.e. the low speed and the large length to width ratio, result in the problem of elliptic nature of the necessity to regulate the inlet and outlet boundary conditions that influence each other. Through the example of the IP calculation of the microchannel (thousands m ? long) flow it is shown that the adoption of the conservative scheme of the mass conservation equation and the super relaxation method resolves this problem successfully. With employment of the same measures the IP method solves the thin film air bearing problem in transitional regime for authentic hard disc write/read head length ( 1000 L m ? = ) and provides pressure distribution in full agreement with the generalized Reynolds equation, while before this the DSMC check of the validity of the Reynolds equation was done only for short ( 5 L m ? = ) drive head. The author suggests degenerate the Reynolds equation to solve the microchannel flow problem in transitional regime, thus provides a means with merit of strict kinetic theory for testing various methods intending to treat the internal MEMS flows.

Development of a Cell Size Relaxed Scheme for the Direct Simulation Monte Carlo Method

The conventional direct simulation Monte Carlo (DSMC) method has a strong restriction on the cell size because simulated particles are selected randomly within the cell for collisions. Cells with size larger than the molecular mean free path are generally not allowed in correct DSMC simulations. However, the cell-size induced numerical error can be controlled if the gradients of flow properties are properly involved during collisions. In this study, a large cell DSMC scheme is proposed to relax the cell size restriction. The scheme is applied to simulate several test problems and promising results are obtained even when the cell size is greater than 10 mean free paths of gas molecules. However, it is still necessary, of course, that the cell size be small with respect to the flow field structures that must be resolved.

Improved sampling techniques for the direct simulation Monte Carlo method

The direct simulation Monte Carlo (DSMC) method is a widely used approach for flow simulations having rarefied or nonequilibrium effects. It involves heavily to sample instantaneous values from prescribed distributions using random numbers. In this note, we briefly review the sampling techniques typically employed in the DSMC method and present two techniques to speedup related sampling processes. One technique is very efficient for sampling geometric locations of new particles and the other is useful for the Larsen-Borgnakke energy distribution.

Characteristics of Micronozzle Gas Flows

The fluid characteristics of gas flows in the micronozzle whose throat height is 20 μm were investigated by the direct simulation Monte Carlo (DSMC) method. In a series of cases, the dependence of mass flux on the pressure difference was gained, and the DSMC's results show good agreement with the experimental data. The comparison of mass flux and the Mach number contours between the DSMC and Navier-Stokes equations adding slip boundary also reveals quantitatively that the continuum model will be invalid gradually even when the average Knudsen number is smaller than 0.01. As one focus of the present paper, the phenomenon of the multiple expansion-compression waves that comes from the nozzle's divergent part was analyzed in detailed.

Statistical Simulation of Rarefied Gas Flows in Micro-Channels

Rarefied gas flows through micro-channels are simulated using particle approaches, named as the information preservation (IP) method and the direct simulation Monte Carlo (DSMC) method. In simulating the low speed flows in long micro-channels the DSMC method encounters the problem of large sample size demand and the difficulty of regulating boundary conditions at the inlet and outlet. Some important computational issues in the calculation of long micro-channel flows by using the IP method, such as the use the conservative form of the mass conservation equation to guarantee the adjustment of the inlet and outlet boundary conditions and the super-relaxation scheme to accelerate the convergence process, are addressed. Stream-wise pressure distributions and mass fluxes through micro-channels given by the IP method agree well with experimental data measured in long micro-channels by Pong et al. (with a height to length ratio of 1.2:3000), Shih et al. (l.2:4800), Arkilic et al. and Arkilic (l.3:7500), respectively. The famous Knudsen minimum of normalized mass flux is observed in IP and DSMC calculations of a short micro-channel over the entire flow regime from continuum to free molecular, whereas the slip Navier-Stokes solution fails to predict it.

Thickness And Component Distributions Of Yttrium-Titanium Alloy Films In Electron-Beam Physical Vapor Deposition

Thickness and component distributions of large-area thin films are an issue of international concern in the field of material processing. The present work employs experiments and direct simulation Monte Carlo (DSMC) method to investigate three-dimensional low-density, non-equilibrium jets of yttrium and titanium vapor atoms in an electron-beams physical vapor deposition (EBPVD) system furnished with two or three electron-beams, and obtains their deposition thickness and component distributions onto 4-inch and 6-inch mono-crystal silicon wafers. The DSMC results are found in excellent agreement with our measurements, such as evaporation rates of yttrium and titanium measured in-situ by quartz crystal resonators, deposited film thickness distribution measured by Rutherford backscattering spectrometer (RBS) and surface profilometer and deposited film molar ratio distribution measured by RBS and inductively coupled plasma atomic emission spectrometer (ICP-AES). This can be taken as an indication that a combination of DSMC method with elaborate measurements may be satisfactory for predicting and designing accurately the transport process of EBPVD at the atomic level.

Examination of the LBM in simulation of microchannel flow in transitional regime

The gas flows in micro-electro-mechanical systems possess relatively large Knudsen number and usually belong to the slip flow and transitional flow regimes. Recently the lattice Boltzmann method (LBM) was proposed by Nie et al. in Journal of Statistical Physics, vol. 107, pp. 279-289, in 2002 to simulate the microchannel and microcavity flows in the transitional flow regime. The present article intends to test the feasibility of doing so. The results of using the lattice Boltzmann method and the direct simulation Monte Carlo method show good agreement between them for small Kn (Kn = 0.0194), poor agreement for Kn = 0.194, and large deviation for Kn = 0.388 in simulating microchannel flows. This suggests that the present version of the lattice Boltzmann method is not feasible to simulate the transitional channel flow.

Statistical Simulation of Thin-Film Bearings

The information preservation (IP) method and the direct simulation Monte Carlo (DSMC) method are used to simulate the gas flows between the write/read head and the platter of the disk drive (the slider bearing problem). The results of both methods are in good agreement with numerical solution of the Reynolds equation in the cases studied. However, the DSMC method owing to the problem of large sample size demand and the difficulty in regulating boundary conditions at the inlet and outlet was able to simulate only short bearings, while IP simulates the bearing of authentic length ~1000 m ? and can provide more detailed flow information.

Monte Carlo Modeling of Micro Scale Gas Flows

An information preservation (IP) method has been used to simulate many micro scale gas flows. It may efficiently reduce the statistical scatter inherent in conventional particle approaches such as the direct simulation Monte Carlo (DSMC) method. This paper reviews applications of IP to some benchmark problems. Comparison of the IP results with those given by experiment, DSMC, and the linearized Boltzmann equation, as well as the Navier-Stokes equations with a slip boundary condition, and the lattice Boltzmann equation, shows that the IP method is applicable to micro scale gas flows over the entire flow regime from continuum to free molecular.

Information Preservation Modeling of Rayleigh-Benard Transition from Thermal Conduction to Convection

Onset and evolution of the Rayleigh-Benard (R-B) convection are investigated using the Information Preservation (IP) method. The information velocity and temperature are updated using the Octant Flux Splitting (OFS) model developed by Masters & Ye based on the Maxwell transport equation suggested by Sun & Boyd. Statistical noise inherent in particle approaches such as the direct simulation Monte Carlo (DSMC) method is effectively reduced by the IP method, and therefore the evolutions from an initial quiescent fluid to a final steady state are shown clearly. An interesting phenomenon is observed: when the Rayleigh number (Ra) exceeds its critical value, there exists an obvious incubation stage. During the incubation stage, the vortex structure clearly appears and evolves, whereas the Nusselt number (Nu) of the lower plate is close to unity. After the incubation stage, the vortex velocity and Nu rapidly increase, and the flow field quickly reaches a steady, convective state. A relation of Nu to Ra given by IP agrees with those given by DSMC, the classical theory and experimental data.

IP Simulation of Micro Gas Flows under 3-D Head Sliders

Gas film lubrication of a three-dimensional flat read-write head slider is calculated using the information preservation (IP) method and the direct simulation Monte Carlo (DSMC) method, respectively. The pressure distributions on the head slider surface at different velocities and flying heights obtained by the two methods are in excellent agreement. IP method is also employed to deal with head slider with three-dimensional complex configuration. The pressure distribution on the head slider surface and the net lifting force obtained by the IP method also agree well with those of DSMC method. Much less (of the order about 10(2) less) computational time (the sum of the time used to reach a steady stage and the time used in sampling process) is needed by the IP method than the DSMC method and such an advantage is more remarkable as the gas velocity decreases.

Rarefied gas dynamics: fundamentals, simulations and micro flows

Kinetic Study Of The Rayleigh-Benard Flows

The present paper employs the direct simulation Monte Carlo (DSMC) method to study the Rayleigh-Benard flows, where the temperature ratio of the upper to lower plate is fixed to 0.1. For a Knudsen number (Kn) of 0.01, as the Rayleigh number (Ra) increases, the flow changes from the thermal conductive state to the convective state at about Ra=1700, and the calculated relation of heat flux through the lower plate versus Ra is in good agreement with classical experimental and theoretical results. For Kn=0.05, the thermal conductive state remains stable, and the increase of Ra cannot trigger thermal instability.