First principle basis of the direct numerical simulation for turbulence of inert and reactive gases

First principle basis of the direct numerical simulation
for turbulence of inert and reactive gases

by Shunichi Tsuge

TARA Center, University of Tsukuba, Japan

An open question of whether phenomenological fluid equations to be used for direct numerical simulation of turbulence are warranted on `first principles' is addressed, and the problem is posed using Klimontovich microscopic density to replace the Boltzmann function of the classical statistical mechanics. For inert monatomic gases, it is shown that all the gasdynamic equations, namely, the three conservation equations plus the Navier-Stokes stress law and the Fourier heat conduction law are retrieved as governing instantaneous quantities, without having recourse to any concepts of averaging or statistical equilibrium. For reactive gases, however, the Arrhenius reaction rate law written in terms of the fluctuating temperature is not justified, reflecting the fact that this rate law hinges crucially on these concepts.

Full Paper at: http://xxx.lanl.gov/abs/chao-dyn/9712020

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Author E-mail: shunt@tara.tsukuba.ac.jp

Past contributions of microscopic
methodology to phenomenologies
1. concept of entropy and the second law of thermodynamics (Boltzmann)
2. derivation of the Navier-Stokes equation from Boltzmann equation (Chapman, Enskog-1917, Grad-1949)
3. region of validity of 'equilibrium' thermodynamics; the same as Navier-Stokes eq., not Euler eq. (Prigogine, 1949)
4. derivation of the Arrhenius' law of chemical reaction rate using inelastic collision model with threshold potential
(Present, 1955)
WARRANTED ON "FIRST PRINCIPLES"!

Are these assertions also correct for turbulence?
Does the Navier-Stokes eq. for turbulence DNS have first principle basis?

Turbulence:
1. stochastic
2. fractal (Sreenivasan, 1986)

Other abstracts available on the Internet - Click to see any of the followings:

Solitary-wave Solution of Turbulence with Application to Benard Convection
First principle basis of the direct numerical simulation for turbulence of inert and reactive gases
A solitary-wave representation of turbulence in the physical-plus-eddy space
Coherent solitary-wave of mixing layer turbulence in the physical-plus-eddy space
A New Hierarchy System on the Basis of a Master Boltzmann Equation for Microscopic Density
Molecular and turbulent transports competing in premixed flames

Or directly obtain the sources by visiting the following URLs:

FOR Title : First principle basis of the direct numerical simulation for turbulence of inert and reactive gases
Location : http://xxx.lanl.gov/abs/chao-dyn/9712020

FOR Title : A solitary-wave representation of turbulence in the physical-plus-eddy space
Location : http://xxx.lanl.gov/abs/chao-dyn/9803013

FOR Title : Coherent solitary-wave of mixing layer turbulence in the physical-plus-eddy space
Location : http://xxx.lanl.gov/abs/chao-dyn/9803035

For further information: shunt@tara.tsukuba.ac.jp