Extension of a Compressible Pressure-Based Solver for Reacting Flows

Abstract

Within the last decade innovative combustion technologies have been developed to reduce environmental pollution. For instance, lean premixed combustion results in a lower flame temperature, and hence in less thermal nitric oxide. However, lean combustion increases the susceptibility to thermoacoustic instabilities. These instabilities can cause operational difficulties or even destroy the combustor. Therefore, the suppression of thermoacoustic instabilities is of growing importance for the design process of combustion chambers. Since a full scale experimental analysis of instabilities is very expensive, computational fluid dynamics (CFD) has become a promising tool to predict thermoacoustic instabilities. The solving strategy pursued within CFD codes for combustion prediction is mostly driven by two key aspects. Firstly, the flow speed within industrially applied combustion chambers is usually within the incompressible regime, i.e. the Mach number is low. These low Mach number flows are traditionally simulated by preconditioned density-based or pressure-based solvers. Secondly, combustion simulation is remarkably more expensive than cold flow computation due to a higher number of transport equations which have to be solved for accurate combustion predictions. Since pressure-based solvers commonly require lower computational effort than preconditioned density-based solvers, the majority of CFD codes used for combustion simulations invoke a pressure-based solver. Pressure-based solvers have been developed initially with the assumption of an incompressible flow where pressure and density variations are decoupled. This decoupling results in infinite propagation speed of pressure oscillations which eventually precludes the computation of thermoacoustic instabilities. Many extensions of pressure-based implicit solvers towards compressible flows have been developed. However, most of these extensions suffer from low temporal order of accuracy or require costly inner loop iterations to converge to a time-accurate solution. Moureau et al. proposed a pressure-based method, which is second order accurate for linear acoustics and low Mach advection without inner loop iterations. The semi-implicit compressible solver invokes a fractional step method based on characteristic splitting of acoustic and advective modes. The corrector step solves a Helmholtz equation and contains purely the acoustic modes of the flow. Advective modes are solved within the predictor step. This allows for adapted numerical treatments of the different modes. Since the semi-implicit characteristic splitting (SICS) solver is a promising algorithm for thermoacoustic computations due to its low computational costs and high accuracy, it has been implemented in the DLR CFD code THETA. The main topic of this work is the extension of the SICS solver for reacting flows, i.e. transport equations for mass fractions are incorporated in the original solution algorithm. Furthermore,