A Constrained Control Approach for the Automated Choice of an Optimal Progress Variable for Chemistry Tabulation

Abstract

Flame structure look-up table generating strategies, e.g. the flamelet-progress variable approach, are based on the definition of a suitable progress variable. This variable is usually obtained from a linear combination of the species’ mass fractions contained in the system. The most important issue is the unique mapping between the progress variable and the independent variable, e.g. space or time. This is ensured by claiming the monotonicity of the progress variable. For simple fuel-oxidiser compositions, this can be performed by analysing the flame structure. However, in the case of complex chemical systems, finding such a progress variable is a non-trivial task, since a lack of monotonicity in the main species mass fractions often exists. In this article it is investigated how a valid progress variable can be found by an automated procedure. Some recent investigations use the fact that finding a monotonous progress variable is equivalent to solving a constrained optimisation problem. The new approach is to construct an algorithm to find a valid progress variable, which is also optimal in the sense that the gradients of the tabulated quantities are minimized. This leads to smoother data and reduces the interpolation effort when reading from the table. The method solves a nonlinear optimal control problem, where the monotonicity of the progress variable is ensured as an inequality constraint by using a genetic algorithm. Finally the performance of the new algorithm is evaluated for homogeneous reactor calculations and laminar diffusion flamelet look-up tables.