ID#: Plenary 1
Abstract Title: Problems of Predicting Turbulent Burning Rates
Session Title: Monday Plenary Session
Session Date: 7/30/01
Session Start Time: 10:30 AM
Author: Bradley, Derek
Organization: School of Mechanical Engineering, University of Leeds
Country: United Kingdom
Abstract: At present there are two main approaches to the understanding and mathematical modelling of practical turbulent combustion. These involve the joint probability density function (JPDF) transport equations [1,2] and laminar flamelets [3,4]. There is no conflict in the way the complexities of turbulent-reaction interactions are handled, but each approach emphasises different aspects and the computational requirements are different. The JPDF approach is capable of exactly representing the interaction of chemical reactions and convection, although viscous dissipation and turbulent mixing of scalars must be closed by modelling. The computational demands of detailed chemistry can be excessive, but these diminish with intrinsic low-dimensional manifolds (ILDM) [5] that reduce the chemistry from that of a fully detailed scheme. The in situ adaptive tabulation, ISAT, algorithm [6] also reduces the computational effort.
Direct numerical simulations (DNS) [7] are valuable in suggesting closure procedures in moment methods, while large eddy simulations (LES) [8] give a more realistic picture of practical flows than do first and second moment models. Laminar flamelet methods computationally uncouple the chemistry from the turbulence in stretched laminar flame studies then re-couple it in the turbulent flame. The conditional moment closure (CMC) approach [9] has affinities with flamelet methods. With CMC in non-premixtures most of the scalar fluctuation can be associated with the mixture fraction, and conditional averaging with respect to it allows closure of the conditional average chemical reaction term. Normally these conditional fluctuations of the reactive scalars are smaller than the unconditional fluctuations and can be neglected. If they are not, conditioning of second moments might be employed.
The laminar flamelet approach has proved rather more robust and effective than might originally have been anticipated. One reason, revealed by direct numerical simulations, is that a continuous laminar flame structure can be thickened by small scale turbulence without invalidating the flamelet assumption [7,10]. As a result, a Karlovitz flame stretch factor can be accommodated which is 17 times that of the Klimov-Williams limit [11].
The principal parameters that express burning rate are the turbulent burning velocity and the mean volumetric heat release rate. The burning velocity is rather difficult either to define precisely or to measure rigorously. It is not a convenient parameter when there is no readily discernible propagating flame front, as in furnaces and gas turbine combustion chambers with recirculating flow, or when the front is severely disrupted at high Karlovitz stretch factors. Under such conditions, the mean volumetric heat release rate is a more convenient parameter and computation of its spatial distribution can be readily incorporated into CFD codes.
The paper attempts a unified approach, that embraces both of these parameters, and highlights some current problems. A new expression is presented for the turbulent burning velocity, based on a universal pdf of turbulent strain rates, with both flamelet burning and quenching controlled by Markstein numbers, and some fractal considerations. Different expressions for the turbulent burning velocity are compared.
Presentation Format: podium