Computationally efficient tabulation of H₂-air combustion with turbulence-chemistry interaction

A reaction mapping method using multi-linear polynomials is presented, which tabulates the detailed H₂-air combustion. An assumed PDF approach is used to account for turbulence-chemistry interaction. The PDFs employed are a clipped Gaussian distribution for temperature and a joint multivariate β-PDF for species mass fractions. The objective of this work is to develop a tabulation method that overcomes one crucial problem of direct tabulation: Because the size of the table grows exponentially, the pre-processing approach often used is not feasible for higher degrees of freedom (dim≥5). The newly developed method takes advantage of the fact that the composition space required for the computation of reacting flows is always much smaller than the entire parameter space exhibiting reaction in kinetics calculations. Based on this finding an in situ structured tabulation with direct data access has been developed, which only tabulates the compositions really occurring in the calculated flow. Calculations show that the table size of this in situ method is approximately only one percent of the size of a preprocessed table. This allows to incorporate two additional dimensions in the table, the variances of temperature and species of assumed-PDFs. The result of this approach is an computationally effective code for cases with self-ignition, which is well suited for turbulent H₂-air flames in complex configurations of technical interest. In the context of the German SCRAMJET project this method will be used to design a supersonic combustion chamber.