Operator splitting versus source linearization for the reaction-(advection)-diffusion equation in OpenFOAM®

Abstract

Novel combustion technologies like MILD or (ultra-)lean combustion aim to reduce pollutant emissions and increase process efficiency. Pollutants are reduced by distributing the reaction zone over large regions and keeping the combustion temperature low. Lower temperatures also reduce heat loss and increase combustion efficiency. These combustion conditions can come at the cost of unstable operation caused by frequent near-extinction or near-ignition states in the flame. These unstable states must be captured when modeling MILD or (ultra-)lean flames. Solving the reaction-advection-diffusion fully coupled is often prohibitive because of the numerical effort and the memory requirements. Common Computational Fluid Dynamics (CFD) codes use operator splitting (OS) schemes to overcome this issue. OS divides the reaction-diffusion problem into sub-problems and provides an algorithm to recover the original problem’s solution by combining the sub-problems. The advantage of OS is that the individual sub-problems, e.g., transport and chemistry, can be solved with specialized solvers. The main drawback of using OS schemes is a loss of accuracy when recovering the original problem. Near-ignition or near-extinction states pose a peculiar problem for OS schemes, and the predicted results can deviate significantly from the actual one; furthermore, they can introduce a time step size dependence of the steady-state solution. OpenFOAM® uses a particular OS; the chemistry sub-problem is linearized and added as an explicit source to the transport problem. Technically speaking, this approach is not an OS but a source term linearization. As the open-source CFD toolbox OpenFOAM® is increasingly used for combustion simulations, understanding the accuracy, the steady-state consistency and the temporal evolution of the linearization approach is essential. In this work, the performance of the OpenFOAM® source linearization is evaluated and compared to OS schemes. The accuracy and steady-state consistency are evaluated by scalar linear stability analysis, while the temporal evolution is evaluated using near-ignition and near-extinction perfectly-stirred reactor test cases.