Modeling Micro Mass and Heat Transfer for Gases Using Extended Continuum Equations

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
Manuel Torrilhon ◽  
Henning Struchtrup
Keyword(s):  
Boundary Conditions ◽  
Direct Simulation Monte Carlo ◽  
Approximation Order ◽  
Gas Flows ◽  
High Approximation ◽  
Complete Set ◽  
Heat Transfers ◽  
Macroscopic Continuum ◽  
Analytical Expressions ◽  
High Approximation Order

This paper presents recent contributions to the development of macroscopic continuum transport equations for micro gas flows and heat transfers. Within the kinetic theory of gases, a combination of the Chapman–Enskog expansion and the Grad moment method yields the regularized 13-moment equations (R13 equations), which are of high approximation order. In addition, a complete set of boundary conditions can be derived from the boundary conditions of the Boltzmann equation. The R13 equations are linearly stable, and their results for moderate Knudsen numbers stand in excellent agreement with direct simulation Monte Carlo (DSMC) method simulations. We give analytical expressions for heat and mass transfer in microchannels. These expressions help to understand the complex interaction of fluid variables in microscale systems. Additionally, we compare interesting analogies such as a mass flux and energy Knudsen paradox. In particular, the R13 model is capable of predicting and explaining the detailed features of Poiseuille microflows.

HIGH APPROXIMATION ORDER BIORTHOGONAL MULTISCALING FUNCTIONS WITH DILATION FACTOR a

2010 ◽  
Vol 08 (06) ◽  
pp. 895-903 ◽  
Author(s):  
CHANGZHEN XIE
Keyword(s):  
Approximation Order ◽  
High Approximation ◽  
Dilation Factor ◽  
High Approximation Order ◽  
Special Case ◽  
Multiscaling Function

An algorithm is presented for constructing a pair of high approximation order biorthogonal multiscaling function with dilation factor a in terms of any given pair of biorthogonal multiscaling function. The special case that a = 2 is discussed. If the dilation factor a = 2, then a biorthogonal multiwavelet pair is constructed explicitly. Finally, examples are given.

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.

scholarly journals Rarefied gas flows through meshes and implications for atmospheric measurements

2001 ◽  
Vol 19 (5) ◽  
pp. 563-569 ◽  
Author(s):  
J. Gumbel
Keyword(s):  
Middle Atmosphere ◽  
Rarefied Gas ◽  
Direct Simulation Monte Carlo ◽  
Atmospheric Composition ◽  
Gas Flows ◽  
Atmospheric Measurements ◽  
Rarefied Gas Flows ◽  
Flow Disturbances ◽  
Composition And Structure ◽  
Compression Effects

Abstract. Meshes are commonly used as part of instruments for in situ atmospheric measurements. This study analyses the aerodynamic effect of meshes by means of wind tunnel experiments and numerical simulations. Based on the Direct Simulation Monte Carlo method, a simple mesh parameterisation is described and applied to a number of representative flow conditions. For open meshes freely exposed to the flow, substantial compression effects are found both upstream and downstream of the mesh. Meshes attached to close instrument structures, on the other hand, cause only minor flow disturbances. In an accompanying paper, the approach developed here is applied to the quantitative analysis of rocket-borne density measurements in the middle atmosphere.Key words. Atmospheric composition and structure (instruments and techniques; middle atmosphere – composition and chemistry)

Comparison of Various Pressure Based Boundary Conditions for Three-Dimensional Subsonic DSMC Simulation

2017 ◽  
Vol 140 (3) ◽  
Author(s):  
Niraj Shah ◽  
Abhimanyu Gavasane ◽  
Amit Agrawal ◽  
Upendra Bhandarkar
Keyword(s):  
Boundary Conditions ◽  
Cell Size ◽  
Pressure Ratio ◽  
Three Dimensional ◽  
Direct Simulation Monte Carlo ◽  
Statistical Error ◽  
Nonequilibrium Effect ◽  
Time Required ◽  
Characteristic Scheme ◽  
Simulation Time

Three-dimensional (3D) direct simulation Monte Carlo (DSMC) has been used to simulate flow in a straight microchannel using an in-house parallelized code. In the present work, a comparative study of seven boundary conditions is carried out with respect to time required for achieving steady-state, accuracy in predicting the specified pressure at the boundaries, and the total simulation time required for attaining a statistical error within one percent. The effect of changing the Knudsen number, pressure ratio (PR), and cross aspect ratio (CAR) on these parameters is also studied. The presence of a boundary is seen to affect the simulated pressure in a cell when compared to the specified pressure, the difference being highest for corner cells and least for cells away from walls. All boundary conditions tested work well at the inlet boundary; however, similar results are not obtained at the outlet boundary. For the same cell size, the schemes that employ first- and second-order corrections lead to a smaller pressure difference compared to schemes applying no corrections. The best predictions can be obtained by using first-order corrections with finer cell size close to the boundary. For most of the simulated cases, the boundary condition employing the characteristic scheme with nonequilibrium effect leads to the minimum simulation time. Considering the nonequilibrium effect, prediction of inlet and outlet pressures and the speed of simulation, the characteristic scheme with nonequilibrium effect performs better than all the other schemes, at least over the range of parameters investigated herein.

Reconsideration of the implicit boundary conditions in pressure driven rarefied gas flows through capillaries

Vacuum ◽  
2019 ◽  
Vol 160 ◽  
pp. 114-122 ◽  
Author(s):  
Giorgos Tatsios ◽  
Dimitris Valougeorgis ◽  
Stefan K. Stefanov
Keyword(s):  
Boundary Conditions ◽  
Rarefied Gas ◽  
Gas Flows ◽  
Rarefied Gas Flows ◽  
Pressure Driven

scholarly journals Investigating the Effect of Solid Boundaries on the Gas Molecular Mean-Free-Path

2009 ◽  
Author(s):  
Erik J. Arlemark ◽  
Jason M. Reese
Keyword(s):  
Molecular Dynamics ◽  
Boundary Conditions ◽  
Free Path ◽  
Mean Free Path ◽  
Gas Flows ◽  
Standard Temperature ◽  
Binary Collisions ◽  
The Mean ◽  
Temperature And Pressure ◽  
Definition Of

A key parameter for micro-gas-flows, the mean free path, is investigated in this paper. The mean free path is used in various models for predicting micro gas flows, both in the governing equations and their boundary conditions. The conventional definition of the mean free path is based on the assumption that only binary collisions occur and is commonly described using the macroscopic quantities density, viscosity and temperature. In this paper we compare the prediction by this definition of the mean free paths for helium, neon and argon gases under standard temperature and pressure conditions, with the mean free paths achieved by measurements of individual molecules using the numerical simulation technique of molecular dynamics. Our simulation using molecular dynamics consists of a cube with six periodic boundary conditions, allowing us to simulate an unconfined gas “package”. Although, the size of this package is important, since its impact on computational cost is considerable, it is also important to have enough simulated molecules to average data from. We find that the molecular dynamics method using 20520 simulated molecules yields results that are within 1% accuracy from the conventional definition of the mean free paths for neon and argon and within 2.5% for helium. We can also conclude that the normal approximation of only considering binary collisions is seemingly adequate for these gases under standard temperature and pressure conditions. We introduce a single planar wall and two parallel planar walls to the simulated gas of neon and record the mean free paths at various distances to the walls. It is found that the mean free paths affected by molecular collisions with the walls corresponds well with theoretical models up to Knudsen numbers of 0.2.

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