skip to main content

Title: Comparison of analytic models of instability of rarefied gas flow in a channel

Numerical and analytical results are compared concerning the limit properties of the trajectories, attractors and bifurcations of rarefied gas flows in channels. The cascade of bifurcations obtained in our previous analytical and numerical investigations is simulated numerically for different scattering functions V generalizing the ray-diffuse reflection of gas particles from the surface. The main purpose of numerical simulation by Monte Carlo method is the investigation of the properties of different analytic nonlinear dynamic systems corresponding to rarefied gas flow in a channel. The results are compared as well for the models suggested originally by R. N. Miroshin, as for the approximations considered for the first time or for studied in our subsequent papers. Analytical solutions we obtained earlier for the ray reflection which means only one determined velocity of scattered from the walls gas atoms, generally different from the specular reflection. The nonlinear iterative equation describing a rarefied gas flow in a long channel becomes unstable in some regions of corresponding parameters of V (it means the sensitivity to boundary conditions). The values of the parameters are found from analytical approximations in these regions. Numerical results show that the chaotic behavior of the nonlinear dynamic system corresponds to strange attractorsmore » and distinguishes clearly from Maxwellian distribution and from the equilibrium on the whole. In the regions of instability (as the dimension of the attractor increases) the search for a corresponding state requires a lot more computation time and a lot of data (the amount of data required increases exponentially with embedding dimension). Therefore the main complication in the computation is reducing as well the computing time as the amount of data to find a suitably close solution. To reduce the computing time our analytical results are applied. Flow conditions satisfying the requirements to the experiment are indicated where the instability of considered type can be detected. The advantages and the drawbacks of considered approximations are detected and the features of obtained solutions are indicated. The recommendations are given for applying the results in practical applications and in numerical calculations of rarefied gas flows.« less
Authors:
 [1] ;  [2]
  1. St.-Petersburg State University, Department of Mathematics and Mechanics, 198504, Universitetskiy pr., 28, Peterhof, St.-Petersburg (Russian Federation)
  2. St.-Petersburg State Polytechnic University, Department of Mathematics and Mechanics, 195251, Polytechnicheskaya ul., 29, St.-Petersburg (Russian Federation)
Publication Date:
OSTI Identifier:
22390583
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; ANALYTICAL SOLUTION; APPROXIMATIONS; ATOMS; ATTRACTORS; BIFURCATION; BOUNDARY CONDITIONS; CHAOS THEORY; COMPARATIVE EVALUATIONS; COMPUTERIZED SIMULATION; EQUILIBRIUM; GAS FLOW; INSTABILITY; ITERATIVE METHODS; MONTE CARLO METHOD; NONLINEAR PROBLEMS; REFLECTION; SCATTERING; SENSITIVITY