Thermal field structures in low Damkôhler reacting flows

Abstract

This paper is mainly concerned with the regime of distributed reaction zones of a wellstirred reactor, where the Damköhler number is below unity. It is an original study compared with the majority of work done in the eld of the interaction between combustion and turbulence in premixed ames. The turbulent structures are subjected to opposing effects, i.e. reduction induced by chemical effects and expansion induced by the increase in mean temperature due to exothermic reactions. When Da >1, the rst effect due to the chemistry can scarcely outweigh the expansion of the turbulent structures caused by the exothermic effect. This result is the major contribution of the present study. This phenomenon is not suf ciently known, both in terms of mechanism and quantitative effects. The rst objective of this work is to try to provide a qualitative explanation, using an experimental and computational analysis based on certain hypotheses. These assumptions will then explain the difference observed between the behaviour of the temperature uctuations in the case of reacting and non-reacting turbulent ow in low Damköhler number situations, where the exothermic effect is negligible. The present paper analyses and compares the uctuating temperature structures inside this reactor for various mean temperature situations. The experimental study is conducted using ne-wire thermoanemometry. The results of numerical simulations obtained using the Navier-Stokes energy equations and the chemical species transport equations associated with a turbulence model are compared with available measurements. The predictions were within engineering accuracy of experimental data. NOTATIONB f ratio of turbulence time to auto-ignition delay c sound velocity (m/s) Da 1 Damköhler number, ratio of dynamic turbulence to chemical time scales Da 2 Damköhler number, ratio of thermal turbulence to chemical time scales E y ( f ) frequential spectrum of temperature f frequency (s ¡1 ) f e y characteristic frequency of energetic eddies (s ¡1 ) f lim limit frequency (s ¡1 ) F y atness factor of the thermal probability density function k turbulent kinetic energy (m 2 /s 2 ) l e y energetic length scale of the velocity eld (m) L reactor diameter (m) L u integral length scale of the velocity eld (m) L y integral length scale of the thermal eld (m) p pressure inside the reactor (bar) P production term due to mean strain P r Prandtl number R t ratio of thermal to dynamic turbulence time scales Re t turbulent Reynolds number S y skewness factor for the probability density functions of the temperature uctuations A01300 Ó IMechE 2001 Proc Instn Mech Engrs Vol 215 Part A 245 The MS was Downloaded from t e y characteristic time for energetic thermal eddies (s) t R mean residence time (s) t y dissipation time of temperature uctuations (s) T mean temperature inside the reactor (K) u i velocity component in the x,y and z directions in the Cartesian coordinate system (m/s) U i volume-weighted contravariant velocity component in the x,Z and z directions (m/s) U 0 jet velocity at ...