DID YOU KNOW? DTIC has over 3.5 million final reports on DoD funded research, development, test, and evaluation activities available to our registered users. Click HERE
to register or log in.
Numerical Simulation of BGK-Burnett Equations.
Final rept. 1 Feb 95-30 Nov 96,
WICHITA STATE UNIV KS
Pagination or Media Count:
Recently it has been shown using Boltzmanns 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 Boltnmanns 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.
APPROVED FOR PUBLIC RELEASE