Some Effects of Density Variations in Turbulent Flows with Pressure Fluctuations

Abstract

To analyse the possible effects of density variations, which are induced by combustion and heat exchange processes, on turbulent flows with varying pressure field it is proposed to employ the balance equation for conditional probability density function (PDF) of velocity at concentration value fixed. The latter is derived from the governing set of Langevin’s type equations which replaces the commonly used Navier-tocks and molecular diffusion equations set. By using it the balance equations for conditionally averaged velocity and fluctuation intensity are obtained and these values have been shown to depend upon density and turbulent Schmidt number for uniform homogeneous turbulence, even when there is no pressure wave. And, naturally, lighter gas volumes have greater velocity fluctuation intensity.

Also in the acoustic wave an amplitude of the velocity fluctuations depends on density and Schmidt number, that leads to the additional velocity shear between the lighter and heavier gas moles in the wave. The latter due to the turbulent friction, Causes the acoustic energy dissipation to increase. It was found that conditionally averaged velocity fluctuations intensity is function on frequency in acoustic wave, if the latter is greater than some threshold value. It is worth noting that similar behaviour of Nusselt number has been found in experiments of Keller (1993). The turbulence time scale should be greater than half a period of the acoustic oscillations for acoustics to affect a turbulence. That fact may be employed to explain the existence of the lowest frequency threshold after attaining of which the acoustic oscillations commence to affect the heat and mass transfer processes. Besides, it was supposed that velocity shear in acoustic wave decreases the characteristic non-uniformity length scale, and qualitative picture of turbulent scales evolution is presented.