DSMC simulation of gas mixing in T-shape micromixer

Gas mixing in a T-shape micromixer has been simulated using the direct simulation Monte Carlo (DSMC) method in the present paper. The adequate mixing is considered to be obtained when the mass composition of the species, CO or N₂, deviates by not more than ±1% from its equilibrium composition. The mixing coefficient was defined as the ratio of the mixing length to the main channel height. It was observed that the two gas streams started to diffuse at the inlet of the T junction before subsequent mixing. This phenomenon is quite distinguished from what have been observed in their macro counterparts. The simulation results show that with a certain inlet Knudsen number (Kn), maintaining the scale of the geometry, no difference occurs in the mixing process along the channel. As the inlet Kn increases, while the diffusion of the molecules behaves more active, the mixing coefficient decreases. Furthermore, increasing the inlet pressure will cause the mixing length to increase, since the convection effect of the gas stream is more pronounced compared with the diffusion effect. Increasing the gas flow temperature or the wall temperature can both enhance the mixing performance, while the effect of increasing the wall temperature is more significant.     

Fluid Dynamics and Heat Transfer Analysis of Three Dimensional Microchannel Flows with Microstructures

The subsonic gas flows through straight rectangular cross-sectional microchannel with patterned microstructures was simulated using the direct simulation Monte Carlo (DSMC) method. An implicit treatment for low-speed inflow and outflow boundaries for the DSMC of the flows in microelectromechanical systems (MEMS) is employed. The 3-D microchannel flows are simulated with the cross-section aspect ratio ranging between 1 and 5. The comparison between 3-D cases and 2-D case shows that when the aspect ratio < 3, the two extra side-walls in the 3-D case have significant effects on the heat transfer and flow properties. When the aspect ratio increases, the flow pattern and heat transfer characteristics tend to approach those of 2-D results. The 2-D simplification is found to be reasonable when the cross-section aspect ratio is larger than 5. The microchannel flows with microstructures are also calculated with three different Knudsen numbers regime cases, and each case is calculated with three different microstructure temperatures, 273 K, 323 K, and 373 K. One Knudsen numbers regime ranges between 0.72 and 1.8, another regime ranges between 0.24 and 0.6 and the other regime ranges between 0.08 and 0.2. The computations show that the cooling and heating effects of the microstructure temperature on flow properties are enhanced with decreasing Knudsen number, and the higher microstructure temperature accelerates the velocity of the flow at the locations above the microstructures.     

Continuum Simulation of the Microscale Backward-Facing Step Flow in a Transition Regime

Microscale backward-facing step flows in transition regime are investigated in the present study using continuum-based Burnett equations. A relaxation method on the Burnett terms is proposed here, and convergent results at Knudsen number up to 0.5 are achieved. The results of Burnett equations agree very well with experimental data and direct simulation Monte Carlo (DSMC) results. The detailed flow characteristics of backward-facing step flow in transition regime are presented, and the difference from macro flow is analyzed. The effects of pressure ratio, Kn, and step ratio are discussed.     

A UNIFIED ENGINEERING MODEL FOR STEADY AND QUASI-STEADY SHEAR-DRIVEN GAS MICROFLOWS

We analyze one-dimensional plane Couette flows in the entire Knudsen regime with the objective of modeling shear-driven rarefied gas flows encountered in various microelectromechanical system (MEMS) components. Using the linearized Boltzmann solutions available in the literature and hard sphere direct simulation Monte Carlo (DSMC) results, we develop a unified empirical model that includes analytical expressions for the velocity distribution and shear stress for steady plane Couette flows. We also present extension of this model to time-periodic oscillatory Couette flows. Comparisons between the extended model and ensemble averaged unsteady DSMC computations show good agreements in the quasi-steady flow limit, where the Stokes number (β) based on the plate separation distance and oscillation frequency is ≤ 0.25. Overall, the new model accurately predicts the velocity distribution and shear stress for steady and quasi-steady (β ≤ 0.25) flows in a wide Knudsen number range (K_n ≤ 12), and it is strictly valid for low subsonic flows with Mach number ≤ 0.3.     

NUMERICAL SIMULATION OF GAS FLOW AND MIXING IN A MICROCHANNEL USING THE DIRECT SIMULATION MONTE CARLO METHOD

The direct simulation Monte Carlo (DSMC) method was employed to investigate gas flow and mixing in a microchannel at near-atmospheric pressure conditions. Simulations for pressure-driven flows were first carried out for a single-component gas flow in a microchannel. Mixing of two parallel gas streams (H 2 and O 2 ), separated by a splitter plate and then entering a microchannel, was considered. The effects of the inlet velocities, the inlet-outlet pressure difference, and the pressure ratio of the incoming streams (H 2 and O 2 ) on the mixing behavior were considered. The effect of the "accommodation coefficient" of the solid wall of the microchannel on the mixing behavior was also examined. The simulation results indicate that mixing decreases with the increase of inlet-outlet pressure difference. When the two streams enter the microchannel with different inlet pressures, mixing is found to decrease with the increase of the pressure ratio. The mixing process is found to be much slower for nearly specularly reflected walls compared to the mixing in a microchannel with completely diffuse walls.     

Calibration of low-pressure MEMS gas sensor for detection of hydrogen gas

Detection of hydrogen by sensors are significant for improvement and safe usage of hydrogen gas as an energy source. In this paper, the application of the MEMS gas sensor for detection of hydrogen gas is numerically studied to develop the application of this device in different industrial applications. The flow feature and force generation mechanism inside a rectangular enclosure with heat and cold arms as the non-isothermal walls are inclusively discussed. In this study, the pressure of hydrogen is varied from 62 to 1500 pa correspond to Knudsen number from 0.1 to 4.5 to investigate all characteristics of the thermal-driven force inside the MEMS sensor. In order to simulate a rarefied gas inside the micro gas detector, Boltzmann equations are applied to obtain high precision results. To solve these equations, Direct Simulation Monte Carlo (DSMC) approach is used as a robust method for the non-equilibrium flow field. The effects of length, thickness and temperature of arms are comprehensively investigated in different ambient pressures. In addition, the effect of various hydrogen concentrations on the Knudsen force is studied. Our findings show that maximum Knudsen force occurs at P = 387 pressure and intensifies when the length of the arms is increased from 50 μm to 150 μm. In addition, the obtained results demonstrate that the generated force is highly sensitive to hydrogen gas species and this enables device for detection of hydrogen gas.     

Nonequilibrium Gas Flow and Heat Transfer in a Heated Square Microcavity

The flow of a rarefied gas in a square enclosure with one wall at high temperature and the other three walls at the same low temperature is investigated. The flow, characterized by the reference Knudsen number and ratio of the cold over the hot temperatures, is simulated both deterministically, using the nonlinear Shakhov kinetic model, and stochastically, using the DSMC method. Excellent agreement between the two approaches is obtained. It is found that along the side walls the gas velocity, depending on the flow parameters, may be either from cold to hot or from hot to cold regions. Furthermore, it is confirmed that the average heat flux departing from the hot plate exhibits a nonmonotonic behavior with regard to the temperature ratio, deducing a maximum heat flux at a temperature ratio of about 0.3. The flow and heat transfer characteristics are explained by computing the ballistic and collision parts of the total bulk quantities and by investigating the contribution of each part to the overall solution.     

ANALYSIS OF THERMAL SLIP IN OSCILLATING RAREFIED FLOW USING DSMC

In this study, the nonequilibrium effects at the stagnation wall in one-dimensional unsteady microflow responding to the external sinusoidal oscillation are investigated. The fluctuating behavior of the rarefied medium is simulated by employing the unsteady DSMC method under various conditions with different acoustic Reynolds and Knudsen numbers. As a result, it is found that the nonequilibrium effect exists at the stagnation wall, especially when the gas density number is small. Due to such a nonequilibrium effect found in a fluctuating medium, the Knudsen number representing system size becomes a more important system parameter than the acoustic Reynolds number even for the constant excitation frequency. Also, the validity of the well-known Maxwell-Smoluchowski relation and its higher-order modifications are tested by comparing the heat fluxes from these relations with the direct DSMC result.     

EFFECTS OF RAREFACTION AND COMPRESSIBILITY OF GASEOUS FLOW IN MICROCHANNEL USING DSMC

The direct simulation Monte Carlo (DSMC) is performed for two-dimensional gaseous flow through a microchannel in both slip and transition regimes to understand the effects of compressibility and rarefaction. Results are presented in the form of axial pressure distribution, velocity profile, local friction coefficient, and local Mach number (Ma) and are compared with the available analytical and experimental results. The effect of compressibility is examined for the inlet to outlet pressure ratios ranging from 1.38 to 4.5. Low-pressure drop simulations with Knudsen numbers (Kn) ranging from 0.03 to 0.11 are performed to identify the effect of rarefaction. It was found that compressibility makes the axial pressure variation nonlinear and enhances the local friction coefficient. On the other hand, rarefaction does not affect pressure distribution but causes the flow to slip at the wall and reduces the local friction coefficient. In addition, it was found that the locally fully developed (LFD) assumption is valid for low Ma flows by comparison with DSMC results.     

Study of Convergence Time for Rarefied Gas Simulations Using an Unstructured DSMC Solver

This article studies the required convergence time for direct-simulation Monte Carlo (DSMC) simulations of rarefied gas flows. An arbitrary-geometry DSMC solver (RGS2D) with an efficient particle-tracking algorithm is introduced and employed for macro-/micro-scale flow applications. Convergence time study is performed by tracing different heat and flow parameters such as intermolecular collision rate, number of particles, drag coefficient, inlet/outlet mass flow rate, and distributions over the wall, i.e., pressure coefficient, skin friction coefficient, heat transfer coefficient, and wall collision rate. The results indicate that the required simulation time depends on the capturing parameter.     

A Model for Predicting Laminar Gas Flow Through Micropassages

INTRODUCTIONModerntechnologieshavedevelopedrapidlyinfab-ricatingmicroelectronics,miniaturizedmanufacturingandbiomedicalengineeringetc.Thefiuidflowandheattransferinmicropassageshasbecomeoneofthemostimportantresearchfieldsofheatandmasstrans-fer.Thepioneerexperimentsearliestinvestigationsonthefluidflowandheattransferinmicromachinedstructurewithplate-finandpin-finheatsinkwerereportedbyTuckermanandPeasein1984l1].WuandLittle(1984)[2'3]measuredthefrictionfactorforgasflowandheattransferinthemicr…     

UNIQUE BEHAVIORS OF A BACKWARD-FACINGSTEP FLOW AT MICROSCALE

ABSTRACT

The direct simulation Monte Carlo (DSMC) method is used to simulate micro backward-facing step flows in both slip and transition flow regimes. The effects of rarefaction on flow characteristics are analyzed and discussed. It is found that flow separation, recirculation, and reattachment will disappear as Knudsen number Kn exceeds 0.1. The stability of the vortex behind the step relies on the magnitudes of mean and thermal velocities in the region, which are closely related to the Kn number, local temperature, and driving pressure ratio. A highly intensified pressure and velocity region behind the step is identified in the transition flow regime. The mechanism leading to the significant increase of velocity and pressure is discussed. The effect of rarefaction on the surface shear stress and friction coefficient is also studied.     

Three-dimensional laminar slip-flow and heat transfer in a rectangular microchannel with constant wall temperature

Three-dimensional laminar slip-flow and heat transfer in rectangular microchannels having constant temperature walls are studied numerically using the finite-volume method for thermally and simultaneously developing flows. The Navier–Stokes and energy equations are solved with velocity slip and temperature jump at the wall. A modified convection–diffusion coefficient at the wall–fluid interface is defined to incorporate the temperature-jump boundary condition. Validity of the numerical simulation procedure is established and the effect of rarefaction on hydrodynamicaly developing flow field, pressure gradient and entrance length is analyzed. A correlation for the fully developed friction factor is presented as a function of Knudsen number (Kn) and aspect ratio (α). The influence of rarefaction on the Nusselt (Nu) number is investigated for thermally and simultaneously developing flows. The effect of velocity slip is found to increase the Nu number, while the temperature-jump tends to decrease it, and the combined effect could result in an increase or a decrease in the Nu number. In the fully developed region, there could be high as 15% increase or low as 50% decrease in Nu number is plausible for the range of parameters considered in this work.     

DSMC SIMULATION OF MICROSCALE BACKWARD-FACING STEP FLOW

The direct simulation Monte Carlo (DSMC) method was used to simulate microbackward-facing step flows in both slip and transition flow regimes. A DSMC code was developed and validated with microchannel flows. The effects of Kn number in flow characteristics were analyzed in detail. It was found that the phenomena of flow separation, recirculation, and reattachment will disappear as Kn number exceeds 0.1. A significant jump of pressure and velocity behind the step was observed in the transition flow regime. The effect of the compressibility is also discussed. The compressibility has significant effect on flow characteristics in the slip flow regime but would be negated by the rarefaction in the transition flow regime.     

The effects of outlet boundary conditions on simulating supersonic microchannel flows using DSMC

High speed gas flows through two-dimensional microchannels have been investigated using the Direct Simulation Monte Carlo (DSMC) method, where the pressure boundary condition has been implemented using the theory of characteristics as an alternative to the vacuum boundary. Two species, nitrogen and helium, have been used to conduct the flow simulations. It was found that the pressure boundary condition cannot only predict the flow with exit-plane pressure equal to the back pressure, which the vacuum boundary condition fails to do, but can also simulate the flow with expansion waves outside the channel. Therefore, it is considered to be more appropriate. Two inlet Mach numbers, 4.15 and 3.39, have been employed for the nitrogen flow cases with an inlet Knudsen number (Kn) of 0.062. It has been shown that for cases with an inlet Mach number equal to 4.15, the back pressure only has an effect on flow in the latter half of the microchannel, where the wall heat flux can be enhanced by increasing the back pressure. At an inlet Mach number of 3.39, the wall heat flux has the same trend as that in the higher Mach number case, though its magnitude is considerably lower. In addition, no significant effect of a step change in wall temperature distribution on the total heat exchange between the wall and the bulk flow was detected for the same inlet Mach number and back pressure.     

Analyses of gas flows in micro- and nanochannels

Micro- and nanoscale gas flows are analyzed theoretically and numerically. The analyses of gas flow similarity show that the gas flows at different scales can be similar only when the gas is treated as a prefect gas. If the gas density is so high that the density effect cannot be ignored, the three dimensionless parameters, Re, Ma, and Kn, which characterize the micro gas flow, are independent of each other and cannot be equal for flows at different scales, so the similarity breaks down. The critical density for the similarity failure can be analytically determined for each kind of gas. The analytical results were validated by numerical simulations. High density, high Knudsen number gas flows were modeled using a generalized Monte Carlo method based on the Enskog theory which considers both the density effect on the collision rate and the molecular repulsive and attractive interactions for a Lennard–Jones gas. The predicted transport coefficients agree better with experimental data than previous predictions. The simulation results show that when the gas density is higher than the critical density, the denseness effect alters the flow velocity and temperature fields from the direct simulation Monte Carlo results. Higher densities lead to greater deviation.     

DIRECT-SIMULATION MONTE CARLO MODELING ON TWO-DIMENSIONAL RAYLEIGH-BÉNARD INSTABILITIES OF RAREFIED GAS

ABSTRACT

This study investigates numerically the convective instabilities of rarefied gas in two-dimensional enclosures by the direct-simulation Monte Carlo (DSMC) method. A simulation using an enclosure with length-to-height aspect ratio AS = 2.016 is conducted to validate the value of the critical Rayleigh number on the onset of convection. Enclosures of AS = 2 and 4 are chosen to explore the influences of the Knudsen number Kn and initial wall temperatures on the flow. The results indicate that the different initial conditions may cause multiple solutions for the convection rolls and the Boussinesq approximation is no longer valid for rarefied gases of high Kn.     

跨努森数区域的微通道内流动计算模拟研究

采用一阶和修正二阶的滑移连续介质模型,对跨努森数区域的低速微通道流进行二维和三维数值模拟。用实验结果和DSMC方法验证滑移连续介质模型在跨努森数区域中的适用性,并详细讨论了微通道流的可压缩效应、稀薄效应、低雷诺数效应和三维特性。研究表明,努森数是表征稀薄效应和模型适用性的特征参数,滑移连续介质模型适用于努森数小于0.150的氮气流动;马赫数不再是微通道流可压缩效应的唯一标识参数;雷诺数是表征低雷诺数效应和三维特性的关键参数,高宽比大于20的微通道流具备良好的二维特性。     

A NEW ANALYTIC SOLUTION OF THE NAVIER-STOKES EQUATIONS FOR MICROCHANNEL FLOWS

In this article we present a new analytic solution of the Navier-Stokes equations for microchannel flows. The solution is based on the concept of the continuum approach using the Chapman-Enskog method, but built upon the proposal to introduce a hyperbolic tangent function of Kn number in the power series of the distribution function and slip boundary condition. The physics behind the mathematical modification are discussed. With the slip boundary condition accurate to O(tanh(Kn)), the solution of the Navier-Stokes equations is extended successfully to the transition flow regime. The analytic solutions are compared with results of DSMC in both slip flow and transition flow regimes. Satisfactory agreements on the velocity profiles and pressure distributions have been achieved. The extension of the upper Knudsen number limits of continuum approach is significant in molecular gas dynamics.     

Slug flow heat transfer in a semi‐infinite microtube with temperature jump wall condition

This paper presents an analytical solution of steady‐state heat transfer for laminar, two‐dimensional, and rarefied gas flow in a semi‐infinite microtube. To account for the slip‐flow characteristics of microscale heat transfer, temperature jump condition at the wall has been included in the model while the fluid velocity is assumed to be constant (slug flow). The solution yields closed form expressions for fully‐developed Nusselt numbers in terms of Knudsen number and Prandtl number under both isothermal and isoflux wall conditions. © 2009 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20263