A&AE 590D: Molecular Gas Dynamics

Fall 2006

Credits: 3

Day & Time: MWF 2:30-3:20 pm

Room: GRIS 274

Web page:http://roger.ecn.purdue.edu/~aae590d

Instructor:

Alina Alexeenko, E-mail: aae590d@roger.ecn.purdue.edu

Required Text

· G.A. Bird, Molecular Gas Dynamics and Direct Simulation of Gas Flows. Oxford Science Publications, 2000.

Recommended Texts

· J. M. Haile, Molecular Dynamics Simulation. Wiley, 1997.

· E.H. Kennard, Kinetic Theory of Gases: With an Introduction to Statistical Mechanics. McGraw-Hill, 1938.

Grading:

Homeworks/Computer Assignments 40%

2 Midterms 30 %

Final Project 30%

Course description:

Introduction to basic concepts and numerical methods of molecular gas dynamics. Elements of the kinetic theory of gases. Review of probability and statistics. Distribution of molecular velocities. Fluctuations and brownian motion. Potential energy functions for molecular interaction. Binary collision dynamics. The Boltzmann equation (BE). Transport properties: viscosity, thermal conductivity and diffusivity. Connection between BE and Euler and Navier-Stokes equations. The molecular dynamics (MD) method: theory and numerical recipes. The direct simulation Monte Carlo (DSMC) method: general procedure and implementations. DSMC models of chemical reaction and internal energy relaxation. DSMC applications to high-altitude aerothermodynamics. Shock wave structure. Thruster exhaust plumes and satellite contamination.  Discrete ordinate method for model kinetic equations and applications to MEMS flows.

Tentative Schedule

Week	Topics
1	Molecular hypothesis. Elementary gas kinetic theory. Pressure and temperature.
2	Molecular collisions and scattering. Binary collision dynamics. Collision frequency and mean free path.
3	Velocity distribution function. The Boltzmann Equation: assumptions, derivation, non-dimensional form
4	Summational invariants. H-theorem and equilibrium. Maxwell velocity distribution function. Boltzmann H-function and entropy.
5	Moment transfer equation. Conservation equations.  Connection between BE and Euler, Navier-Stokes equations.
6	Transport properties: viscosity, thermal conductivity, diffusivity.
7	Midterm I
8	Molecular dynamics: overview of theory; potential energy functions
9	Molecular dynamics: numerical recipes and examples. Matlab refresher, MD demo codes (computer lab)
10	Introduction to DSMC. Review of relevant probability and statistics. Fluctuations.
11	Pseudo random number generators. Inverse-cumulative and acceptance-rejection sampling from a prescribed distribution. DSMC procedure, requirements and algorithms.
12	Collisional schemes, models for internal energy relaxation and chemical reactions. Gas-surface interaction. Midterm II
13	Discrete ordinate method. Quadratures. Numerical solution of linearized Boltzmann, BGK/ES model kinetic equations.
14	DSMC applications to high-altitude aerothermodynamics.  Shock wave structure. Expansion into vacuum. Thruster exhaust plumes and satellite contamination.
15	Couette flow: free molecular, ES model equation and Navier-Stokes solutions. Poiseuille and thermal transpiration flows. Applications of kinetic methods to microflows.