The symmetric forms of the conservation equations for mass, energy, and momentum in reactive ideal gas mixtures are presented. A modified form of the continuity equation is introduced which accounts for possible diffusion of mass under the gradient of density in simple fluids, similar to the Smoluchowski equation describing the Brownian motion of small particles suspended in a fluid subject to an external force. An intermediate statistical field called clusterdynamics is postulated and the statistically-stationary nature of the Brownian motions of small suspensions in stationary fluids is attributed to the fact that the suspensions are in equilibrium with molecular-clusters, that themselves possess Brownian motions. The Newton law of viscosity is generalized through the introduction of momentum diffusion velocity Vij and the rate of stress tensor is defined in terms of the corresponding diffusional flux of momenta. A modified form of the Navier-Stokes equation is presented that includes a source (sink) of momentum caused by heat release (absorption) associated with exothermic (endothermic) chemical reactions. The equivalence between the modified and the original forms of the Navier-Stokes equation is established. The symmetric forms of the conservation equations, in the absence of dissipations, are then used to derive four wave equations which describe the propagation of density, temperature, pressure, and velocity perturbations at the cluster-dynamic scale. The results may provide certain guidelines towards the identification of a scaleinvariant statistical theory of turbulence in chemicallyreactive hydrodynamic fields.
|Original language||English (US)|
|Number of pages||24|
|Journal||American Society of Mechanical Engineers, Heat Transfer Division, (Publication) HTD|
|State||Published - Dec 1 1996|
ASJC Scopus subject areas
- Mechanical Engineering
- Fluid Flow and Transfer Processes