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.

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.

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.

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.

Efficient Deterministic Modelling of Three-Dimensional Rarefied Gas Flows

2012 ◽  
Vol 12 (1) ◽  
pp. 162-192 ◽  
Author(s):  
V. A. Titarev
Keyword(s):  
Gas Flow ◽  
Parallel Machines ◽  
High Efficiency ◽  
Rarefied Gas ◽  
Three Dimensional ◽  
Collision Integral ◽  
Gas Flows ◽  
Rarefied Gas Flows ◽  
Deterministic Modelling ◽  
Model Collision

AbstractThe paper is devoted to the development of an efficient deterministic framework for modelling of three-dimensional rarefied gas flows on the basis of the numerical solution of the Boltzmann kinetic equation with the model collision integrals. The framework consists of a high-order accurate implicit advection scheme on arbitrary unstructured meshes, the conservative procedure for the calculation of the model collision integral and efficient implementation on parallel machines. The main application area of the suggested methods is micro-scale flows. Performance of the proposed approach is demonstrated on a rarefied gas flow through the finite-length circular pipe. The results show good accuracy of the proposed algorithm across all flow regimes and its high efficiency and excellent parallel scalability for up to 512 cores.

scholarly journals Investigation of Subsonic and Hypersonic Rarefied Gas Flow Over a Backward Facing Step

2019 ◽  
Author(s):  
Deepak Nabapure ◽  
Jayesh Sanwal ◽  
Sreeram Rajesh ◽  
K Ram Chandra Murthy
Keyword(s):  
Mach Number ◽  
Gas Flow ◽  
Rarefied Gas ◽  
Flow Characteristics ◽  
Direct Simulation Monte Carlo ◽  
Primary Objective ◽  
Gas Flows ◽  
Backward Facing Step ◽  
Rarefied Gas Flows ◽  
Velocity Pressure

In the present study the Direct Simulation Monte Carlo (DSMC) method, which is one of most the widely used numerical methods to study the rarefied gas flows, is applied to investigate the flow characteristics of a hypersonic and subsonic flow over a backward-facing step. The work is driven by the interest in exploring the effects of the Mach number on the flow behaviour. The primary objective of this paper is to study the variation of velocity, pressure, and temperature with Mach number. The numerical tool is validated with well-established results from the literature and a good agreement is found among them. The flow is analyzed and some comments on the characteristics of the flow are also added.

Direct Simulation Monte Carlo Analysis of Rarefied Gas Flow Structures and Ventilation of Etching Gas in Magneto-Microwave Plasma Etching Reactors

2002 ◽  
Vol 124 (2) ◽  
pp. 476-482 ◽  
Author(s):  
Masato Ikegawa ◽  
Yoshihumi Ogawa ◽  
Ryoji Fukuyama ◽  
Tatehito Usui ◽  
Jun’ichi Tanaka
Keyword(s):  
Plasma Etching ◽  
Gas Flow ◽  
Microwave Plasma ◽  
Rarefied Gas ◽  
Direct Simulation Monte Carlo ◽  
Gas Flows ◽  
Direct Simulation ◽  
Rarefied Gas Flows ◽  
Simulation Monte Carlo ◽  
Gas Supply

Gas flows in plasma etching reactors for semiconductor fabrication became a chief consideration in designing second-generation reactors with higher etching rates. An axisymmetrical model based on the direct simulation Monte Carlo method has been developed for analyzing rarefied gas flows in a vacuum chamber with the conditions of downstream pressure and gas flow rate. By using this simulator, rarefied gas flows with radicals and etch-products were calculated for microwave-plasma etching reactors. The results showed that the flow patterns in the plasma chamber strongly depend on the Knudsen number and the gas-supply structure. The ventilation of the etch-products in the plasma chamber was found to be improved both for higher Knudsen numbers and for gas-supply structures of the downward-flow type, as compared with those of the radial-flow or upward-flow types.

scholarly journals Analytical models of unstable rarefied gas flow in channels and nozzles: simulation and comparison

2019 ◽  
Author(s):  
O.A. Aksenova ◽  
I.A. Khalidov
Keyword(s):  
Gas Flow ◽  
Rarefied Gas ◽  
Chaotic Behavior ◽  
Nonlinear Dynamic System ◽  
Analytical Models ◽  
Gas Flows ◽  
Flow Conditions ◽  
Practical Applications ◽  
Rarefied Gas Flows ◽  
Montecarlo Method

Three different analytical models of unstable rarefied gas flows in channels and nozzles are compared using numerical simulations by MonteCarlo method. Numerical results have demonstrated the chaotic behavior of constructed nonlinear dynamic system and the limit properties of corresponding trajectories, attractors, and bifurcations of rarefied gas flows in channels. Flow conditions satisfying the experimental requirements are indicated where the instability of considered type can be detected. The advantages and the drawbacks of the considered approximations are detected and the features of obtained solutions are indicated. Recommendations are given for applying the results in practical applications and in numerical calculations of rarefied gas flows.

Shock polar investigation in supersonic rarefied gas flows over a circular cylinder

2021 ◽  
Vol 33 (5) ◽  
pp. 052006
Author(s):  
Hassan Akhlaghi ◽  
Ehsan Roohi ◽  
Abbas Daliri ◽  
Mohammad-Reza Soltani
Keyword(s):  
Circular Cylinder ◽  
Rarefied Gas ◽  
Gas Flows ◽  
Rarefied Gas Flows
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