A High Order Theory for an Isothermal Rarefied Gas Flow in Micro Channels

2003 ◽  
Author(s):  
Nevena D. Stevanovic
Keyword(s):  
Small Parameter ◽  
Gas Flow ◽  
Rarefied Gas ◽  
Reynolds Numbers ◽  
Order Theory ◽  
Gas Flows ◽  
Regular Perturbation ◽  
Micro Electro Mechanical Systems ◽  
Slip Boundary ◽  
Micro Channels

Gas flows take place in a number of micro-electro-mechanical systems (MEMS). Since the dimensions of the MEMS are within μm range, it is necessary to take into account the gas rarefaction effects in investigations of these flows. This paper presents the solution and analysis of isothermal compressible gas flow through micro channels with slow varying cross section under low Mach number conditions. The problem is solved by the introduction of the small parameter ε that presents the square of the Mach and Reynolds numbers ratio. Small parameter ε is used in a regular perturbation analysis of the problem. The exact dependence among Mach, Reynolds and Knudsen number is utilized, which leads to accurate prediction of the influence of the inertia forces and the slip boundary conditions.

scholarly journals New exact solutions for microscale gas flows

2021 ◽  
Vol 128 (1) ◽  
Author(s):  
Hollis Williams
Keyword(s):  
Heat Source ◽  
Exact Solutions ◽  
Gas Flow ◽  
Rarefied Gas ◽  
Gas Flows ◽  
Point Heat Source ◽  
Slip Boundary ◽  
Rarefied Gas Flows ◽  
New Exact Solutions ◽  
Dependent Point

AbstractWe present a number of exact solutions to the linearised Grad equations for non-equilibrium rarefied gas flows and heat flows. The solutions include the flow and pressure fields associated to a point force placed in a rarefied gas flow close to a no-slip boundary and the temperature field for a point heat source placed in a heat flow close to a temperature jump boundary. We also derive the solution of the unsteady Grad equations in one dimension with a time-dependent point heat source term and the Grad analogue of the rotlet, a well-known singularity of Stokes flow which corresponds to a point torque.

scholarly journals Pressure-Driven Gas Flows in Micro Channels with a Slip Boundary: A Numerical Investigation

2020 ◽  
Vol 16 (2) ◽  
pp. 147-159
Author(s):  
A. Aissa ◽  
M. E. A. Slimani ◽  
F. Mebarek-Oudina ◽  
R. Fares ◽  
A. Zaim ◽  
...  
Keyword(s):  
Numerical Investigation ◽  
Gas Flows ◽  
Slip Boundary ◽  
Micro Channels ◽  
Pressure Driven

DSMC Simulation of Rarefied Gas Flow Over a Wall Mounted Cube

2019 ◽  
Author(s):  
Deepak Nabapure ◽  
Ram Chandra Murthy
Keyword(s):  
Gas Flow ◽  
Rarefied Gas ◽  
Flow Behavior ◽  
Direct Simulation Monte Carlo ◽  
Temperature Fields ◽  
Gas Flows ◽  
Rarefied Gas Flows ◽  
Dsmc Simulation ◽  
Recirculation Length ◽  
Velocity Pressure

Abstract The present study investigates the flow behavior of the rarefied gas over a wall-mounted cube. The problem is studied for different cube heights (h) of 9mm and 18mm in the slip and transition regimes. The Direct Simulation Monte Carlo (DSMC) method is employed to evaluate the properties such as velocity, pressure and temperature fields. The Reynolds number (Re) ranges from 403 to 807, and the Knudsen number (Kn) is in the range from 0.05 to 0.103. A typical shock wave is formed in front of the cube. The recirculation length of the vortices normalized with respect to the respective cube heights for Kn = 0.05 and Kn = 0.103 are about 1.11 and 1.95 respectively. Similarly, the center of the vortices is located at about 3.33 and 6.11 times the respective cube heights upstream, for Kn = 0.05 and Kn = 0.103. The local temperature and pressure variations observed upstream of the cube are two orders higher in magnitude and are primarily attributed to strong compressibility effects. The present study paves the way for benchmarking, and forms a basis for understanding the rarefied gas flows over complex geometries.

Effect of Manifold Design on Flow Distribution in Parallel Micro-Channels

2003 ◽  
Author(s):  
Ralph L. Webb
Keyword(s):  
Flow Distribution ◽  
Reynolds Numbers ◽  
Published Data ◽  
Micro Electro Mechanical Systems ◽  
Micro Channels ◽  
Significant Disagreement ◽  
Manufacturing Tolerances ◽  
Header Design ◽  
Laminar And Turbulent Regimes ◽  
Good Agreement

Gas or liquid flow in multiple, parallel micro-channels is of interest for Micro-Electro-Mechanical Systems (MEMS) cooling applications. The published data for friction in 10-to-400μm hydraulic diameter, single micro-channels show good agreement with the conventional equations in the laminar and turbulent regimes. However, investigators of flow in multiple, parallel micro-channels in the same range of channel sizes report significantly different results. They report significant disagreement with the conventional equations and argue that transition occurs at Reynolds numbers as small as 200, dependent on the channel shape. This paper proposes that the apparent discrepancies of friction in multiple micro-channels can be attributed to flow mal-distribution. Flow mal-distribution is expected in multi-channels, because of manufacturing tolerances and poor manifold design. It can be minimized by proper header design and better manufacturing tolerances.

scholarly journals Development of an Efficient Particle Approach for Micro-Scale Gas Flow Simulations

2009 ◽  
Author(s):  
Quanhua Sun ◽  
Feng Li ◽  
Jing Fan ◽  
Chunpei Cai
Keyword(s):  
Cell Size ◽  
Gas Flow ◽  
Rarefied Gas ◽  
Direct Simulation Monte Carlo ◽  
Gas Flows ◽  
Dsmc Method ◽  
Low Speed ◽  
Micro Scale ◽  
Information Preservation ◽  
Cfd Method

The micro-scale gas flows are usually low-speed flows and exhibit rarefied gas effects. It is challenging to simulate these flows because traditional CFD method is unable to capture the rarefied gas effects and the direct simulation Monte Carlo (DSMC) method is very inefficient for low-speed flows. In this study we combine two techniques to improve the efficiency of the DSMC method. The information preservation technique is used to reduce the statistical noise and the cell-size relaxed technique is employed to increase the effective cell size. The new cell-size relaxed IP method is found capable of simulating micro-scale gas flows as shown by the 2D lid-driven cavity flows.

Experiments on the Resistance Law for Non-Darcy Compressible Gas Flows in Porous Media

1974 ◽  
Vol 96 (4) ◽  
pp. 353-357 ◽  
Author(s):  
B. A. Masha ◽  
G. S. Beavers ◽  
E. M. Sparrow
Keyword(s):  
Reynolds Number ◽  
Porous Material ◽  
Incompressible Flow ◽  
Gas Flow ◽  
Strong Support ◽  
Reynolds Numbers ◽  
Gas Flows ◽  
Pressure Distributions ◽  
Flow Through ◽  
Compressible Gas

Experiments were performed to examine the resistance law for non-Darcy compressible gas flow through a porous material. A particular objective of the investigation was to determine whether a resistance law deduced from incompressible flow experiments could be applied to flows with significant density changes. To this end, the coefficients appearing in the Forchheimer resistance law were first determined from experiments in the incompressible flow regime. These values were then used in an analytical model employing the Forchheimer resistance law to predict streamwise pressure distributions for subsonic compressible flow through the porous material. Corresponding experimental pressure distributions were measured for flow Reynolds numbers up to 81.6. At the highest Reynolds number of the tests the density changed by about a factor of two along the length of the porous medium. The greatest discrepancy between experimental and predicted pressures at any Reynolds number was 2 percent. This agreement lends strong support to the validity of using the incompressible Forchheimer resistance law for subsonic flows in which density changes are significant.

Simulation of Rarefied Gas Flow in Microchannel Based on Vorticity-Stream Function Method

2007 ◽  
Author(s):  
Xueyong Wei ◽  
Mike C. L. Ward ◽  
Dejiang Lu ◽  
Zhuangde Jiang
Keyword(s):  
Stream Function ◽  
Function Method ◽  
Gas Flow ◽  
Rarefied Gas ◽  
Taylor Series Expansion ◽  
Accommodation Coefficient ◽  
Parallel Plates ◽  
Slip Boundary ◽  
Tangential Momentum ◽  
New Formula

Vorticity-stream function method is successfully used to solve an incompressible gas flow in the parallel-plates micro-channel. A new formula in finite difference scheme is developed to describe the boundary vorticity based on the slip boundary theory and Taylor series expansion. Results show that the boundary vorticity are not only influenced by the Knudsen number (Kn) but also influenced by the tangential momentum accommodation coefficient (TMAC).

scholarly journals Effect of viscosity on slip boundary conditions in rarefied gas flows

2019 ◽  
Author(s):  
Nam T. P. Le
Keyword(s):  
Slip Velocity ◽  
Rarefied Gas ◽  
Cross Flow ◽  
Navier Stokes ◽  
Gas Flows ◽  
Gas Temperature ◽  
Slip Boundary ◽  
Rarefied Gas Flows ◽  
Viscosity Models ◽  
Simulation Results

The viscosity of gases plays an important role in the kinetic theory of gases and in the continuum-fluid modeling of the rarefied gas flows. In this paper we investigate the effect of the gas viscosity on the surface properties as surface gas temperature and slip velocity in rarefied gas simulations. Three various viscosity models in the literature such as the Maxwell, Power Law and Sutherland models are evaluated. They are implemented into OpenFOAM to work with the solver “rhoCentralFoam” that solves the Navier-Stokes-Fourier equations. Four test cases such as the pressure driven backward facing step nanochannel, lid-driven micro-cavity, hypersonic gas flows past the sharp 25-55-deg. biconic and the circular cylinder in cross-flow cases are considered for evaluating three viscosity models. The simulation results show that, whichever the first-order or second-order slip and jump conditions are adopted, the simulation results of the surface temperature and slip velocity using the Maxwell viscosity model give good agreement with DSMC data for all cases studied.

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