Conditioned moments in premixed turbulent reacting flows

Abstract

Although the rms turbulent velocity u′ is commonly considered to be the key characteristic of turbulence when studying premixed combustion, the definition of u′ in a flame is impeded by the intermittency of unburned and burned mixtures due to the random advection of the flame front by turbulent eddies. To resolve the problem, rms velocities conditioned either on unburned or burned mixture are often invoked to characterize turbulence. The goal of the present paper is to dispute this solution. To do so, balance equations for the conditioned velocities and Reynolds stresses are numerically solved in the case of a statistically planar and one-dimensional, constant-density, premixed, turbulent, reacting flow, with the turbulence being assumed to be homogeneous, isotropic, and statistically stationary. The obtained results show that the conditioned rms velocities differ substantially from u′ in such a “flame”, i.e. the above conditioned quantities are controlled not only by turbulence, but also by the aforementioned unburned-burned intermittency. Therefore, the use of the conditioned rms velocities for characterizing turbulence is not justified in premixed turbulent flames. Behaviour of various conditioned second and third moments is shown to differ substantially from the behaviour of counterpart unconditioned moments, thus calling for further research into conditioned characteristics of turbulent flames.