Microscale Gas Flows Research Articles

Non-Maxwell slippage induced by surface roughness for microscale gas flow: a molecular dynamics simulation

Rarefied gas flows in rough microchannels are investigated by non-equilibrium molecular dynamics simulations. The surface roughness is modelled by an array of triangular modules. The Maxwell slip model is found to break down due to the surface roughness for gas flows in microchannels with large surface roughness. Non-Maxwell slippage shows that the slip length is smaller than that predicted by the Maxwell model and is nonlinearly related to the mean free path. For larger surface roughness and smaller Knudsen number, the non-Maxwell effect becomes more pronounced. The boundary conditions, generally including velocity slip, no-slip and negative slip, depend not only on the Knudsen number but also on the surface roughness. Simulation results show that A/λ ≈ 1 is a good criterion to validate the no-slip boundary condition and A/λ > 0.3 can be a criterion to judge the occurrence of non-Maxwell slippage, where A is the surface roughness size and λ is the mean free path of gas molecules. The permeability enhanced by the surface roughness may be responsible for the roughness-induced non-Maxwell slippage.

Modeling of Microscale Gas Flows in Transition Regime Part I: Flow over Backward Facing Steps

Design of thermal management solutions for future nanoscale electronics or photonics devices will require knowledge of flow and transport through micron-scale ducts. This article concentrates on a typical flow process, namely flow over a backward-facing step with pressure boundary conditions at inlet and exit. Discrete simulation Monte Carlo (DSMC) is used as the simulation tool. An IP method is used to separate the macroscopic velocity from the molecular velocity, thus reducing statistical noise as typical in DSMC calculation of low-speed flows. Simulation is conducted for Re of 0.03 to 0.64, Ma of 0.013 to 0.083, and Kn of 0.24 to 4.81. For these parameter values no recirculating region is observed, and the high heat flux associated with reattachment is also absent.

Gas-kinetic numerical method for solving mesoscopic velocity distribution function equation

A gas-kinetic numerical method for directly solving the mesoscopic velocity distribution function equation is presented and applied to the study of three-dimensional complex flows and micro-channel flows covering various flow regimes. The unified velocity distribution function equation describing gas transport phenomena from rarefied transition to continuum flow regimes can be presented on the basis of the kinetic Boltzmann–Shakhov model equation. The gas-kinetic finite-difference schemes for the velocity distribution function are constructed by developing a discrete velocity ordinate method of gas kinetic theory and an unsteady time-splitting technique from computational fluid dynamics. Gas-kinetic boundary conditions and numerical modeling can be established by directly manipulating on the mesoscopic velocity distribution function. A new Gauss-type discrete velocity numerical integration method can be developed and adopted to attack complex flows with different Mach numbers. HPF parallel strategy suitable for the gas-kinetic numerical method is investigated and adopted to solve three-dimensional complex problems. High Mach number flows around three-dimensional bodies are computed preliminarily with massive scale parallel. It is noteworthy and of practical importance that the HPF parallel algorithm for solving three-dimensional complex problems can be effectively developed to cover various flow regimes. On the other hand, the gas-kinetic numerical method is extended and used to study micro-channel gas flows including the classical Couette flow, the Poiseuille- channel flow and pressure-driven gas flows in two-dimensional short micro-channels. The numerical experience shows that the gas-kinetic algorithm may be a powerful tool in the numerical simulation of micro-scale gas flows occuring in the Micro-Electro-Mechanical System (MEMS).

Gaseous slip flow analysis of a micromachined flow sensor for ultra small flow applications

The velocity slip of a fluid at a wall is one of the most typical phenomena in microscale gas flows. This paper presents a flow analysis considering the velocity slip in a capacitive micro gas flow sensor based on pressure difference measurements along a microchannel. The tangential momentum accommodation coefficient (TMAC) measurements of a particular channel wall in planar microchannels will be presented while the previous micro gas flow studies have been based on the same TMACs on both walls. The sensors consist of a pair of capacitive pressure sensors, inlet/outlet and a microchannel. The main microchannel is 128.0 µm wide, 4.64 µm deep and 5680 µm long, and operated under nearly atmospheric conditions where the outlet Knudsen number is 0.0137. The sensor was fabricated using silicon wet etching, ultrasonic drilling, deep reactive ion etching (DRIE) and anodic bonding. The capacitance change of the sensor and the mass flow rate of nitrogen were measured as the inlet-to-outlet pressure ratio was varied from 1.00 to 1.24. The measured maximum mass flow rate was 3.86 × 10−10 kg s−1 (0.019 sccm) at the highest pressure ratio tested. As the pressure difference increased, both the capacitance of the differential pressure sensor and the flow rate through the main microchannel increased. The laminar friction constant f ⋅ Re, an important consideration in sensor design, varied from the incompressible no-slip case and the mass sensitivity and resolution of this sensor were discussed. Using the current slip flow formulae, a microchannel with much smaller mass flow rates can be designed at the same pressure ratios.

Finite Volume Simulation of Supersonic to Hypersonic Gas Flow and Heat Transfer through Microchannels

AbstractThe heat transfer characteristics of supersonic to hypersonic gas flow in microchannels are numerically studied by solving a two‐dimensional Navier‐Stokes (NS) system of equations utilizing Maxwell's velocity slip with thermal creep, and a corresponding temperature jump relationship derived by von Smoluchowski. An explicit Finite Volume (FV) solver has been developed using modified advection upwind splitting methods (AUSM+) to simulate the high speed microscale gas flow. The influence of the inlet Mach number on overall hydrodynamics and heat transfer is also studied. The supersonic test case has been compared with the Direct Solution Monte Carlo (DSMC) and Finite Element (FE) results available in the literature. The study of high speed flow through microchannels demonstrates an increase in temperature due to the wall friction and that fluid flow decelerates throughout the microchannels. The wall temperature jump and the centerline temperature are higher for larger inlet Mach numbers.

Numerical study of micro-scale gas flow using finite volume method

Numerical studies of subsonic gas flow through micro-thruster as no-slip benchmark problem and high speed gas flow through short micro-channel with slip and temperature jump correction have been carried out by solving two dimensional compressible Navier-Stokes (NS) system of equations. A 2-D explicit finite volume (FV) flow solver has been developed using modified advection upwind splitting methods (AUSM+) to achieve the solution of micro-scale gas flow having high resolution shock capturing ability. The results obtained are compared with published 1-D numerical, Direct Simulation Monte Carlo (DSMC) and 2-D Finite element (FEM) results. This study utilizes the robustness and accuracy of AUSM+ and FVM to predict the micro-scale gas flows with simple explicit time marching, ranging from subsonic to supersonic flow.

Gas mixing in microchannels using the direct simulation Monte Carlo method

Mixing in microchannels is an important problem because the flow is always laminar flow even though the velocity may be high. The present paper analyzes the inherent factors affecting micro gas mixing using the direct simulation Monte Carlo (DSMC) method at high Knudsen numbers. The discretization errors in the DSMC method were analyzed to ensure numerical accuracy. The simulation results show that the wall characteristics have little effect on the mixing length when the main gas flow velocities for different wall characteristics were the same. The mixing length is nearly inversely proportional to the gas temperature. The dimensionless mixing coefficient, which is the ratio of the mixing length to the channel height, is proportional to the Mach number and inversely proportional to the Knudsen number. This conclusion was validated for microscale gas flows, but is expected to apply to all laminar gas flows at all scales.

Complex Microscale Flow Simulations Using Langmuir Slip Condition

ABSTRACT Langmuir slip boundary condition combined with macroscopic governing equations is suggested to simulate microscale gas flows. The concept is numerically implemented and verified, with the focus on analyzing complex gaseous flows involving separation. Compressible backward-facing step flow is compared to other analysis results with the purpose of diatomic gas Langmuir slip condition validation. Numerical analysis is performed for Reynolds number from 10 to 60 for a prediction of separation at a T-shaped micromanifold. The numerical solutions of velocity and shear stress distributions at walls are in good agreement with other numerical results. Nonlinear behavior is clearly present in several parameter studies, including reattachment length at the wall of side branch. It is substantiated from these results that the Langmuir slip condition predicts appropriately the physics in complex microscale gas flows even with separation.

Gas kinetic algorithm for flows in Poiseuille-like microchannels using Boltzmann model equation

The gas-kinetic unified algorithm using Boltzmann model equation have been extended and developed to solve the micro-scale gas flows in Poiseuille-like micro-channels from Micro-Electro-Mechanical Systems (MEMS). The numerical modeling of the gas kinetic boundary conditions suitable for micro-scale gas flows is presented. To test the present method, the classical Couette flows with various Knudsen numbers, the gas flows from short microchannels like plane Poiseuille and the pressure-driven gas flows in two-dimensional short microchannels have been simulated and compared with the approximate solutions of the Boltzmann equation, the related DSMC results, the modified N-S solutions with slip-flow boundary theory, the gas-kinetic BGK-Burnett solutions and the experimental data. The comparisons show that the present gas-kinetic numerical algorithm using the mesoscopic Boltzmann simplified velocity distribution function equation can effectively simulate and reveal the gas flows in microchannels. The numerical experience indicates that this method may be a powerful tool in the numerical simulation of micro-scale gas flows from MEMS.

Empirical slip and viscosity model performance for microscale gas flow

For the simple geometries of Couette and Poiseuille flows, the velocity profile maintains a similar shape from continuum to free molecular flow. Therefore, modifications to the fluid viscosity and slip boundary conditions can improve the continuum based Navier–Stokes solution in the non-continuum non-equilibrium regime. In this investigation, the optimal modifications are found by a linear least-squares fit of the Navier–Stokes solution to the non-equilibrium solution obtained using the direct simulation Monte Carlo (DSMC) method. Models are then constructed for the Knudsen number dependence of the viscosity correction and the slip model from a database of DSMC solutions for Couette and Poiseuille flows of argon and nitrogen gas, with Knudsen numbers ranging from 0.01 to 10. Finally, the accuracy of the models is measured for non-equilibrium cases both in and outside the DSMC database. Flows outside the database include: combined Couette and Poiseuille flow, partial wall accommodation, helium gas, and non-zero convective acceleration. The models reproduce the velocity profiles in the DSMC database within an L2 error norm of 3% for Couette flows and 7% for Poiseuille flows. However, the errors in the model predictions outside the database are up to five times larger. Copyright © 2005 John Wiley & Sons, Ltd.

New directions in fluid dynamics: non-equilibrium aerodynamic and microsystem flows.

Fluid flows that do not have local equilibrium are characteristic of some of the new frontiers in engineering and technology, for example, high-speed high-altitude aerodynamics and the development of micrometre-sized fluid pumps, turbines and other devices. However, this area of fluid dynamics is poorly understood from both the experimental and simulation perspectives, which hampers the progress of these technologies. This paper reviews some of the recent developments in experimental techniques and modelling methods for non-equilibrium gas flows, examining their advantages and drawbacks. We also present new results from our computational investigations into both hypersonic and microsystem flows using two distinct numerical methodologies: the direct simulation Monte Carlo method and extended hydrodynamics. While the direct simulation approach produces excellent results and is used widely, extended hydrodynamics is not as well developed but is a promising candidate for future more complex simulations. Finally, we discuss some of the other situations where these simulation methods could be usefully applied, and look to the future of numerical tools for non-equilibrium flows.

A Direct Simulation Method for Subsonic, Microscale Gas Flows

Microscale gas flows are the subject of increasingly active research due to the rapid advances in micro-electro-mechanical systems (MEMS). The rarefied phenomena in MEMS gas flows make molecular-based simulations desirable. However, it is necessary to reduce the statistical scatter in particle methods for microscale gas flows. In this paper, the development of an information preservation (IP) method is described. The IP method reduces the statistical scatter by preserving macroscopic information of the flow in the particles and the computational cells simulated in the direct simulation Monte Carlo (DSMC) method. The preserved macroscopic information of particles is updated during collisions and is then modified to include the pressure field effects excluded in the collisions. An additional energy transfer model is proposed to describe the energy flux across an interface, and a collision model is used to redistribute the information after both particle–particle and particle–surface collisions. To validate the IP method, four different flows are simulated and the solutions are compared against DSMC results. The results from the IP method generally agree very well with the DSMC results for steady flows and low frequency unsteady flows ranging from the near-continuum regime to the free-molecular regime.

Discussion about the Similarity of Micro-scale Gas Flows

Article Discussion about the Similarity of Micro-scale Gas Flows was published on December 1, 2002 in the journal International Journal of Nonlinear Sciences and Numerical Simulation (volume 3, issue 3-4).

Analysis of micro-scale gas flows with pressure boundaries using direct simulation Monte Carlo method

The development of a two-dimensional direct simulation Monte Carlo program for pressure boundaries using unstructured cells and its applications to typical micro-scale gas flows are described. For the molecular collision kinetics, variable hard sphere molecular model and no time counter collision sampling scheme are used, while the cell-by-cell particle tracing technique is implemented for particle movement. The program has been verified by comparison of simulated equilibrium collision frequency with theoretical value and by comparison of simulated non-equilibrium profiles of one-dimensional normal shock with previous reported work. Applications to micro-scale gas flows includes micro-manifold, micro-nozzle and slider air bearing. The aim is to further test the treatment of pressure boundaries, developed previously by the first author, by particle flux conservation for gas flows involving many exits, complicated geometries and moving boundaries. For micro-manifold gas flows, excellent mass flow conservation between the inlet and two exits is obtained at low subsonic flows. For micro-nozzle gas flows, with fixed inlet pressure, the mass flow rate increases with decreasing pressure ratio (exit to inlet), but remains essentially the same at pressure ratios much lower than that obtained by continuum inviscid analysis. For higher specified pressure ratios, the locations of maximum Mach number moves further downstream as the pressure ratio decreases; while, for lower specified pressure ratios, the Mach number increases all the way through the nozzle to the exit. Eventually, supersonic speed is observed at the exit for pressure ratios equal to or less than 0.143. Finally, for slider air bearing gas flows of the computer hard drive, the simulated gas pressures, at different rotating speeds, agree very well with previous studies. However, there exists strong translational non-equilibrium in the gas flows at the high rotating speeds. The applicability of the treatment of pressure boundaries using the equilibrium Maxwell–Boltzmann distribution function is discussed in terms of the magnitude of the local Knudsen number at the pressure boundary for micro-nozzles and slider air bearing applications.