Boundary conditions for gas flow problems from anisotropic scattering kernels

2015 ◽  
Vol 56 (10) ◽  
pp. 103101 ◽  
Author(s):  
Quy-Dong To ◽  
Van-Huyen Vu ◽  
Guy Lauriat ◽  
Céline Léonard
Keyword(s):  
Boundary Conditions ◽  
Gas Flow ◽  
Anisotropic Scattering ◽  
Flow Problems

Study on the Deposition Profile Characteristics in the Micron-Scale Trench Using Direct Simulation Monte Carlo Method

1998 ◽  
Vol 120 (2) ◽  
pp. 296-302 ◽  
Author(s):  
Masato Ikegawa ◽  
Jun’ichi Kobayashi ◽  
Morihisa Maruko
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Boundary Conditions ◽  
Gas Flow ◽  
Direct Simulation Monte Carlo ◽  
Low Pressure ◽  
Sputter Deposition ◽  
Direct Simulation ◽  
Simulation Monte Carlo ◽  
Profile Characteristics

As integrated circuits are advancing toward smaller device features, step-coverage in submicron trenches and holes in thin film deposition are becoming of concern. Deposition consists of gas flow in the vapor phase and film growth in the solid phase. A deposition profile simulator using the direct simulation Monte Carlo method has been developed to investigate deposition profile characteristics on small trenches which have nearly the same dimension as the mean free path of molecules. This simulator can be applied to several deposition processes such as sputter deposition, and atmospheric- or low-pressure chemical vapor deposition. In the case of low-pressure processes such as sputter deposition, upstream boundary conditions of the trenches can be calculated by means of rarefied gas flow analysis in the reactor. The effects of upstream boundary conditions, molecular collisions, sticking coefficients, and surface migration on deposition profiles in the trenches were clarified.

Laminar Forced Convection in Annular Microchannels With Slip Flow Regime

2009 ◽  
Author(s):  
Arman Sadeghi ◽  
Abolhassan Asgarshamsi ◽  
Mohammad Hassan Saidi
Keyword(s):  
Nusselt Number ◽  
Fluid Flow ◽  
Aspect Ratio ◽  
Boundary Conditions ◽  
Knudsen Number ◽  
Gas Flow ◽  
Slip Flow ◽  
Outer Wall ◽  
Graphical Form ◽  
Uniform Temperature

Fluid flow and heat transfer at microscale have attracted an important research interest in recent years due to the rapid development of microelectromechanical systems (MEMS). Fluid flow in microdevices has some characteristics which one of them is rarefaction effect related with gas flow. In this research, hydrodynamically and thermally fully developed laminar rarefied gas flow in annular microducts is studied using slip flow boundary conditions. Two different cases of the thermal boundary conditions are considered, namely: uniform temperature at the outer wall and adiabatic inner wall (Case A) and uniform temperature at the inner wall and adiabatic outer wall (Case B). Using the previously obtained velocity distribution, energy conservation equation subjected to relevant boundary conditions is numerically solved using fourth order Runge-Kutta method. The Nusselt number values are presented in graphical form as well as tabular form. It is realized that for the case A increasing aspect ratio results in increasing the Nusselt number, while the opposite is true for the case B. The effect of aspect ratio on Nusselt number is more notable at smaller values of Knudsen number, while its effect becomes slighter at large Knudsen numbers. Also increasing Knudsen number leads to smaller values of Nusselt number for the both cases.

Unsteady Flow Calculations by Numerical Methods

1972 ◽  
Vol 94 (2) ◽  
pp. 457-465 ◽  
Author(s):  
V. L. Streeter
Keyword(s):  
Numerical Methods ◽  
Boundary Conditions ◽  
Unsteady Flow ◽  
Various Boundary Conditions ◽  
Flow Problems ◽  
Velocity Flow ◽  
Compressed Gas ◽  
Order Of Magnitude ◽  
Metal Pipes ◽  
Complex Boundary

A review of methods of handling unsteady flow problems in metal pipes by numerical methods is undertaken. The characteristic method, typifying explicit methods, and the centered implicit method are developed, including the manner various boundary conditions are introduced into the solutions. High velocity flow is briefly reviewed, i.e., flow cases with the velocity of flow of the same order of magnitude as the pulse wave speed. Three complex boundary conditions are examined: turbomachinery, column separation, and the compressed gas accumulator.

scholarly journals Convergence Analysis on Unstructured Meshes of a DDFV Method for Flow Problems with Full Neumann Boundary Conditions

2016 ◽  
Vol 2016 ◽  
pp. 1-22
Author(s):  
A. Kinfack Jeutsa ◽  
A. Njifenjou ◽  
J. Nganhou
Keyword(s):  
Boundary Conditions ◽  
Numerical Test ◽  
Neumann Boundary ◽  
Unstructured Meshes ◽  
Neumann Boundary Conditions ◽  
Discrete Problem ◽  
Discrete Energy ◽  
Flow Problems ◽  
Associated Matrix ◽  
Uniqueness Of A Solution

A Discrete Duality Finite Volume (DDFV) method to solve on unstructured meshes the flow problems in anisotropic nonhomogeneous porous media with full Neumann boundary conditions is proposed in the present work. We start with the derivation of the discrete problem. A result of existence and uniqueness of a solution for that problem is given thanks to the properties of its associated matrix combined with adequate assumptions on data. Their theoretical properties, namely, stability and error estimates (in discrete energy norms andL2-norm), are investigated. Numerical test is provided.

A New Formulation for Computational Fluid Dynamics

1979 ◽  
Vol 101 (4) ◽  
pp. 453-460
Author(s):  
D. B. Reed ◽  
W. L. Oberkampf
Keyword(s):  
Fluid Dynamics ◽  
Boundary Conditions ◽  
Transport Equation ◽  
Mesh Size ◽  
Channel Length ◽  
Test Case ◽  
Parallel Plates ◽  
Flow Problems ◽  
Vector Quantity ◽  
New Formulation

A new vector quantity in fluid dynamics is defined and a vector transport equation for the quantity is derived. The new vector quantity is defined as the curl of the vorticity and is referred to as the angular vorticity. The transport equation for the new quantity is derived by taking the curl of the vorticity transport equation. The new transport equation combined with Poisson type velocity equations comprises the new angular vorticity-velocity formulation. The major advantage of the new formulaton is that computational boundary conditions for through-flow problems may be significantly relaxed. Boundary conditions for the newly defined variable are derived. A simple test case of laminar incompressible planar flow between parallel plates was executed to determine if the new formulation would produce results comparable to previous solutions. Numerical experiments were conducted using channel length, mesh size, and Reynolds number as parameters. The results are compared to values obtained by other investigators. The results show that the angular vorticity formulation is a feasible method for solution of fluid flow problems where fully developed flow is not attained.

Generalized Couette Flow of a Third-Grade Fluid with Slip: The Exact Solutions

2010 ◽  
Vol 65 (12) ◽  
pp. 1071-1076 ◽  
Author(s):  
Rahmat Ellahi ◽  
Tasawar Hayat ◽  
Fazal Mahmood Mahomed
Keyword(s):  
Boundary Conditions ◽  
Exact Solutions ◽  
Closed Form ◽  
Analytical Solutions ◽  
Present Note ◽  
Nonlinear Problems ◽  
Third Grade ◽  
Third Grade Fluid ◽  
Flow Problems ◽  
Grade Fluid

The present note investigates the influence of slip on the generalized Couette flows of a third-grade fluid. Two flow problems are considered. The resulting equations and the boundary conditions are nonlinear. Analytical solutions of the governing nonlinear problems are found in closed form.

Poiseuille Number Correlations of Gas Flow in Concentric Micro Annular Tubes

2008 ◽  
Author(s):  
Chungpyo Hong ◽  
Yutaka Asako ◽  
Koichi Suzuki
Keyword(s):  
Boundary Conditions ◽  
Gas Flow ◽  
Slip Flow ◽  
Tube Length ◽  
Slip Boundary Conditions ◽  
Slip Boundary ◽  
Rarefaction Effect ◽  
Wide Range ◽  
Poiseuille Number ◽  
Fast Flow

Poiseuille number, the product of friction factor and Reynolds number (f · Re) for quasi-fully developed concentric micro annular tube flow was obtained for both no-slip and slip boundary conditions. The numerical methodology is based on the Arbitrary-Lagrangian-Eulerian (ALE) method. The compressible momentum and energy equations were solved for a wide range of Reynolds and Mach numbers for both isothermal flow and no heat conduction flow conditions. The detail of the incompressible slip Poiseuille number is kindly documented and its value defined as a function of r* and Kn is represented. The outer tube radius ranges from 50 to 150μm with the radius ratios of 0.2, 0.5 and 0.8 and selected tube length is 0.02m. The stagnation pressure, pstg is chosen in such away that the exit Mach number ranges from 0.1 to 0.7. The outlet pressure is fixed at the atmospheric pressure. In the case of fast flow, the value of f · Re is higher than that of incompressible slip flow theory due to the compressibility effect. However in the case of slow flow the value of f · Re is slightly lower than that of incompressible slip flow due to the rarefaction effect, even the flow is accelerated. The value of f · Re obtained for no-slip boundary conditions is compared with that of obtained for slip boundary conditions. The values of f · Re obtained for slip boundary conditions are predicted by f · Re correlations obtained for no-slip boundary conditions since rarefaction effect is relatively small for the fast flow.

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