Concentration probability distribution and intermittence in turbulent jets

Abstract

In a turbulent flow with mixing of the temperature and concentration, the velocities are random quantities; therefore, the appropriate probability distributions are necessary for averaging different relations. This requirement is especially strong when analyzing combustion processes, and the stabilization and propagation of flames in a turbulent flow. Under these conditions the mixing and chemical kinetics should be considered together, and since the chemical reaction rate has a nonlinear dependence on the temperature and concentration, the temperature and concentration probability distributions should be known in order to solve the problem. It is natural to attempt to obtain and solve the appropriate probability equations [1–3]. It is possible to derive these relations from the equations of motion, diffusion, and thermal conductivity [1, 2], but some assumptions are necessary in order to obtain a self-contained description. On the other hand (and this applies to the present paper), the required equation can be obtained from certain phenomenological considerations [3–6]. It follows from this equation that the concentration probability is distributed according to the normal law in regions without infermittency. The equation enables one to calculate the intensity of concentration fluctuations at the edge of a turbulent flow for a completely turbulent fluid.