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

Journal Article · Tue Dec 09 00:00:00 EST 2014 · AIP Conference Proceedings

DOI:https://doi.org/10.1063/1.4902679· OSTI ID:22390583

Aksenova, Olga A. ^[1]; Khalidov, Iskander A. ^[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)

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 attractors 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.

• OSTI ID: 22390583
• Journal Information: AIP Conference Proceedings, Vol. 1628, 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); ISSN 0094-243X
• Country of Publication: United States
• Language: English

Related Subjects

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