skip to main content

Title: Use of finite volume radiation for predicting the Knudsen minimum in 2D channel flow

In an earlier paper we employed an analogy between surface-to-surface radiation and free-molecular flow to model Knudsen flow through tubes and onto planes. In the current paper we extend the analogy between thermal radiation and molecular flow to model the flow of a gas in a 2D channel across all regimes of rarefaction. To accomplish this, we break down the problem of gaseous flow into three sub-problems (self-diffusion, mass-motion and generation of pressure gradient) and use the finite volume method for modeling radiation through participating media to model the transport in each sub-problem as a radiation problem. We first model molecular self-diffusion in the stationary gas by modeling the transport of the molecular number density through the gas starting from the analytical asymptote for free-molecular flow to the kinetic theory limit of gaseous self-diffusion. We then model the transport of momentum through the gas at unit pressure gradient to predict Poiseuille flow and slip flow in the 2D gas. Lastly, we predict the generation of pressure gradient within the gas due to molecular collisions by modeling the transport of the forces generated due to collisions per unit volume of gas. We then proceed to combine the three radiation problems tomore » predict flow of the gas over the entire Knudsen number regime from free-molecular to transition to continuum flow and successfully capture the Knudsen minimum at Kn ∼ 1.« less
Authors:
 [1] ;  [2]
  1. TCS Innovation Labs - TRDDC, 54 Hadapsar Industrial Estate, Pune 411013 (India)
  2. ICTAS, College of Engineering, Virginia Polytechnic Institute, VA 24061 (United States)
Publication Date:
OSTI Identifier:
22390576
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 1628; Journal Issue: 1; Conference: 29. International Symposium on Rarefied Gas Dynamics, Xi'an (China), 13-18 Jul 2014; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CAPTURE; COLLISIONS; COMPUTERIZED SIMULATION; DENSITY; KNUDSEN FLOW; LAMINAR FLOW; MASS; PRESSURE GRADIENTS; SELF-DIFFUSION; SLIP FLOW; SURFACES; THERMAL RADIATION; TUBES