Accession Number : ADA326201

Title :   Numerical Simulation of BGK-Burnett Equations.

Descriptive Note : Final rept. 1 Feb 95-30 Nov 96,

Corporate Author : WICHITA STATE UNIV KS

Personal Author(s) : Agarwal, Ramesh K. ; Balakrishnan, Ramesh

PDF Url : ADA326201

Report Date : 15 AUG 1996

Pagination or Media Count : 73

Abstract : Recently it has been shown using Boltzmann's H-Theorem that the conventional Burnett equations violate the second law of thermodynamics, and hence must not be employed for fluid dynamic simulations. To overcome this difficulty, a new set of equations, designated the BGK-Burnett equations was derived recently by the authors. A second-order distribution function was derived by employing the Chapman-Enskog expansion on the BGK-Boltzmann equation. Moments of the BGK-Boltzmann equation with the collision invariant vector using the second-order distribution function yield the BGK-Burnett equations. It has been shown by the authors that the BGK-Burnett equations are stable to small wavelength disturbances and that they yield results consistent with the second law of thermodynamics. In order to prove that these equations are indeed entropy consistent, it is shown that the second-order distribution function does not violate Boltnmann's H-Theorem. This new set of equations must be used for computing hypersonic flows at moderate Knudsen numbers. The BGK-Burnett equations are employed to compute the hypersonic shock structure. The results of the computations show that under certain flow conditions, the conventional Burnett equations violate the second law of thermodynamics while the BGK-Burnett equations provide entropy consistent results.

Descriptors :   *COMPUTATIONAL FLUID DYNAMICS, *HYPERSONIC FLOW, HEAT TRANSFER, COMPUTERIZED SIMULATION, STRESS ANALYSIS, SHOCK WAVES, FINITE DIFFERENCE THEORY, FLOW FIELDS, PARTIAL DIFFERENTIAL EQUATIONS, TWO DIMENSIONAL FLOW, MAXWELLS EQUATIONS, HYPERSONIC CHARACTERISTICS, HEAT FLUX, BOLTZMANN EQUATION, ENTROPY, KNUDSEN NUMBER.

Subject Categories : Fluid Mechanics

Distribution Statement : APPROVED FOR PUBLIC RELEASE