Navier-Stokes computation of some gas mixture problems in the slip ow regime (original) (raw)
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Navier-Stokes Computation of Some Gas Mixture Problems in the Slip Flow Regime
Scientia Iranica
Several kinetic descriptions have already been utilized for the simulation of rarefied gas mixture flows. Although such developments are important, Navier-Stokes computation can find extended use in engineering applications. Recently, the authors have derived new velocity-slip and temperature-jump boundary conditions for slip flows of gas mixtures. Appealing to these new boundary conditions, Navier-Stokes computation of rarefied gas mixture problems has become feasible. In the present contribution, the proposed conditions in conjunction with the Navier-Stokes equations and an equation for the conservation of species are solved for some binary gas mixture problems in the slip flow regime. Applications include low pressure flow in a converging-diverging nozzle, wall-cooling of a nozzle under rarefied condition, and parallel mixing in a microchannel. Simulation results are presented in terms of the distributions of overall Knudsen number, Mach number, pressure, temperature, and concent...
Mechanics Research Communications, 2011
Recently, several kinetic descriptions have been utilized for the simulation of gas mixture flows in microgeometries. Although such developments are important, Navier-Stokes computation can find extended use in engineering applications. In the present contribution, a rarefied flow of a gas mixture in the vicinity of a wall is concerned and new velocity-slip and temperature-jump boundary conditions are derived for the whole mixture. Appealing to these new boundary conditions, Navier-Stokes computation of microscale gas mixture flows becomes feasible. Consequently, the proposed conditions in conjunction with the Navier-Stokes equations and an equation for the conservation of species are solved for a He-Ne flow in a microchannel and suitability of the derived boundary conditions is demonstrated in the slip flow regime.
Aerospace Science and Technology, 2019
In this paper we numerically evaluate the recently developed Aoki et al. slip and jump conditions in high-speed rarefied gas flows for the first time. These slip and jump conditions are developed to be employed with the Navier-Stokes-Fourier equations. They were derived based on the Boltzmann equation with the first order Chapman-Enskog solution, and the analysis of the Knudsen layer. Four aerodynamic configurations are selected for a comprehensive evaluation of these conditions such as sharp-leading-edge flat plate, vertical plate, wedge and circular cylinder in cross-flow with the Knudsen number varying from 0.004 to 0.07, and argon as the working gas. The simulation results using the Aoki et al. boundary conditions show suitable agreement with the DSMC data for slip velocity and surface gas temperature. The accuracy of these boundary conditions is superior to the conventional Maxwell, Smoluchowski and Le boundary conditions.
Multifluid Description of Rarefied Gas Mixture Flows
Journal of Thermal Engineering
In the present contribution attention is focused to extend the application of multifluid descriptions to rarefied conditions for the first time. To this aim, a multifluid Maxwell model and a multifluid Smoluchowski model are proposed for near wall behavior of the constituents of a rarefied gas mixture. Afterwards, multifluid balance equations in conjunction with these boundary conditions are solved for some slip flows of binary gas mixtures between parallel plates. The corresponding results are compared with those of a previously developed Navier-Stokes solver. Inspection of the results indicates that while the Navier-Stokes equations may lose their accuracy under high rarefaction, non-equilibrium features are properly captured by developed multifluid description. This successful method is thereafter utilized to discuss the consequences of velocity-slip, the tangential-momentum-accommodation coefficient, and mass disparity of the mixture constituents on the degree of non-equilibrium between the constituents of the gas mixtures between parallel plates.
Viscous velocity, diffusion and thermal slip coefficients for ternary gas mixtures
European Journal of Mechanics - B/Fluids, 2015
An approach is presented to determine the viscous velocity, diffusion and thermal slip coefficients for three-component gaseous mixtures. The gas is described by the McCormack linearized kinetic model. It is shown that two diffusion slip coefficients exist for a ternary mixture. The boundary problem is solved by the discrete velocity method. The slip coefficients are calculated and tabulated for HeAr -Xe mixture at various values of the mole fractions for the hard-sphere and experimental potentials. It has been found that the diffusion and thermal slip coefficients are more sensitive to the interaction potential than the viscous one. Representative velocity profiles of the Knudsen layer are also shown. Furthermore, a test calculation is presented for pressure and mole fraction driven flows in a tube. The flow rates obtained by the slip solution are compared to the kinetic results. It is revealed that the slip flow approximation provides a relatively good estimation of the flow rates at higher rarefaction parameters. The present methodology and the tabulated data can be useful to determine the gaseous flow in the slip region for the ternary mixture.
International Journal of Heat and Mass Transfer, 2005
Modeling microfluidics it is necessary to calculate gas flows through micropumps, microvalves and other elements. A heat transfer through a gas in microscales must be also known for modeling of microsystems. Since the size of microsystems is close to the molecular mean free path, the gas rarefaction must be taken into account. If the Knudsen number is moderately small then gas flows and heat transfer can be calculated applying the continuum mechanics equations with the velocity slip and temperature jump boundary conditions. In the present work, a critical review of the theoretical results on the slip and jump coefficients and their recommended data are given.
Microfluidics and Nanofluidics, 2010
A comparative study between computational and experimental results for pressure-driven binary gas flows through long microchannels is performed. The theoretical formulation is based on the McCormack kinetic model and the computational results are valid in the whole range of the Knudsen number. Diffusion effects are taken into consideration. The experimental work is based on the Constant Volume Method, and the results are in the slip and transition regime. Using both approaches, the molar flow rates of the He–Ar gas mixture flowing through a rectangular microchannel are estimated for a wide range of pressure drops between the upstream and downstream reservoirs and several mixture concentrations varying from pure He to pure Ar. In all cases, a very good agreement is found, within the margins of the introduced modeling and measurement uncertainties. In addition, computational results for the pressure and concentration distributions along the channel are provided. As far as the authors are aware of, this is the first detailed and complete comparative study between theory and experiment for gaseous flows through long microchannels in the case of binary mixtures.
Microfluidics and Nanofluidics, 2010
The flow of binary gas mixtures through long micro-channels with triangular and trapezoidal cross sections is investigated in the whole range of the Knudsen number. The flow is driven by pressure and concentration gradients. The McCormack kinetic model is utilized to simulate the rarefied flow of the gas mixture, and the kinetic equations are solved by an upgraded discrete velocity algorithm. The kinetic dimensionless flow rates are tabulated for selected noble gas mixtures flowing through micro-channels etched by KOH in silicon (triangular and trapezoidal channels with acute angle of 54.74°). Furthermore, the complete procedure to obtain the mass flow rate for a gas mixture flowing through a channel, based on the dimensionless kinetic results, which are valid in each cross section of the channel, is presented. The study includes the effect of the separation phenomenon. It is shown that gas separation may change significantly the estimated mass flow rate. The presented methodology can be used for engineering purposes and for the accurate comparison with experimental results.
Discrete velocity modelling of gaseous mixture flows in MEMS
Superlattices and Microstructures, 2004
The need of developing advanced micro-electro-mechanical systems (MEMS) has motivated the study of fluid-thermal flows in devices with micro-scale geometries. In many MEMS applications the Knudsen number varies in the range from 10 −2 to 10 2 . This flow regime can be treated neither as a continuum nor as a free molecular flow. In order to describe these flows it is necessary to implement the Boltzmann equation (BE) or simplified kinetic model equations.
Shear Driven Micro-Flows of Gaseous Mixtures
Sensor Letters, 2006
A mesoscale kinetic-type approach is proposed to solve shear driven micro flows of binary gas mixtures in MEMS. The coupled linear integro-differential equations, which formally describe the flow, are solved using the discrete velocity method. The complicated collision integral term is approximated by the McCormack model. The proposed approach is applied in one and two dimensions, solving the Couette and the driven cavity problems respectively, for two binary gas mixtures (Ne-Ar and He-Xe). Numerical results are presented for a wide range of the rarefaction and for various molar concentrations. It is demonstrated that the formulation is very efficient and can be implemented as an alternative to classical approaches, such as Navier Stokes solvers with slip boundary conditions.