Molecular Gas Dynamics
Start Date:August 24, 2020
Learning Objective:Objectives include developing abilities to:
1) Calculate basic gas properties such as temperature, pressure, flow velocity, gas stresses and fluxes from the molecular velocity distribution function.
2) Identify gas flow regimes (continuum, slip, transitional, free molecular) and applicable governing equations.
3) Apply equilibrium fluxes to solve basic free-molecular flow problems.
4) Setup and conduct direct simulation Monte Carlo modeling for rarefied flow problems.
The course is about microscopic approach to understanding the behavior of a gas which states that all substances are composed of a large number of very small particles (molecules or atoms). The observable properties of gas are the consequence of the actions of the molecules making up the gas. We will cover gas dynamic phenomena that require the molecular description such as the structure of shock wave, high-altitude aerodynamics and expansions into vacuum, velocity slip and aerodynamic forces in nano/microsystems.
Topics Covered:Molecular hypothesis; elementary gas kinetic theory; pressure and temperature; molecular collisions and scattering; binary collision dynamics; collision frequency and mean free path; velocity distribution function; The Boltzmann Equation: assumptions, derivation, non-dimensional form; summational invariants; H-theorem and equilibrium; Maxwell velocity distribution function; experimental verification; Boltzmann H-function and entropy; moment transfer equation; conservation equations; connection between BE and Euler, Navier-Stokes equations; transport properties: viscosity, thermal conductivity, diffusivity; Kundsen layer; velocity slip and temperature jump; numerical methods of rarefied gas dynamics; intermolecular potentials and molecular models; introduction to DSMC; review of relevant probability and statistics; pseudo random number generators; inverse-cumulative and acceptance-rejection sampling; DSMC algorithms; collisional schemes; models for internal energy relaxation and chemical reactions; gas-suface interaction; discrete ordinate method; quadratures; numerical solution of linearized Boltzmann, BGK/ES model kinetic equations; free molecular flows: expansion into vacuum, low-pressure damping in MEMS; slip and transitional flows: Couette and Poiseuille problems; thermal transpiration; applications to microflows, thruster exhaust plumes; satellite contamination.
Applied / Theory:40 / 60
Homework:Assignments approximately every other week.
Projects:Yes. Select a problem that is interesting to you and requires application of molecular gas dynamics.. Written proposal, progress reports, and a final report/presentation are required.
Exams:Midterm exam. No final exam.
Textbooks:Official textbook information is now listed in the Schedule of Classes. NOTE: Textbook information is subject to be changed at any time at the discretion of the faculty member. If you have questions or concerns please contact the academic department.
1) G.A. Bird, Molecular Gas Dynamics and the Direct Simulation of Gas Flows. Oxford Science
2) Y. Sone, Molecular Gas Dynamics: Theory, Techniques, and Applications. Birkhauser, 2006.