STUDY OF 2 – D NON CONTINUUM GAS FLOWS USING DIRECT SIMULATION MONTE CARLO (DSMC) ALGORITHM

Abstract

Continuum mechanics is a branch of mechanics that deals with the analysis of the kinematics (flow) and the mechanical behavior (deformation) of materials modeled as a continuum. In doing so, this fact is ignored that all matter is composed of atoms and molecules. Fundamental physical concepts such as conservation of energy, conservation of momentum and conservation of mass can be used to form differential equations which model the behavior of such material. Fluid Mechanics is a sub discipline of continuum mechanics, in which fluid is treated as a continuum. Here, Continuity equation and Navier-Stokes equations are used to analyze the flow variables. Although traditional CFD methods can be effectively used to study various fluid flow related phenomena ranging from turbo machinery, compressor designs and analysis, drag reduction of motor vehicles and so on, they also have a few limitations. The concept of continuum mechanics is quite accurate in the cases where the inter-atomic and/or inter-molecular distance is negligible as compared to the characteristic length of the domain of study. However, continuum analysis is not able to provide accurate results when this is not the case. To address this issue, fluid flows can also be studied by taking into account that matter is composed of very large number of atoms and molecules. Though fundamental physical laws can be applied to individual entities (atoms and/or molecules), however, to model real world problems, which would mean simulating hundreds of millions of particles, it is almost impossible to do so. Statistical Mechanics (or Statistical Thermodynamics) is the application of probability theory and statistics to the field of mechanics. Using statistical mechanics, the microscopic properties of molecules and atoms can be related with the bulk properties of the matter. Using this model for fluids, information about the position, velocity and state of molecules at any instant can be extracted. One of the major mathematical models is constructed by using Boltzmann equation; however, analytical solution of Boltzmann equation is rather complicated. Direct Simulation Monte Carlo (DSMC) technique is a numerical method which employs the concepts of probability theory and statistics to analyze non continuum gas flows. The gas is modeled as a collection of numerous particles and position and velocity of every particle is determined during each time step The present study is concerned with the flow behavior of rarefied gas over a circular cylinder. In present study, CFD analysis and well as DSMC analysis of external flow over a circular cylinder is performed. A computer code based upon Direct Simulation Monte Carlo (DSMC) technique is developed in Mathematica 7.0 as well as in C++. Comparison of CFD analysis for same geometry as modeled for DSMC technique was performed which indicated significant agreement between the two approaches, hence cementing the fact that traditional CFD techniques are in fact a generalized form of microscopic model of fluids. After validation of developed C++ computer code, it was applied to study 2 – D non continuum flow over a circular cylinder. DSMC method is employed for predicting the flow behavior. Results for various parameter combinations are presented here.