The development and assessment of an efficient parallelization method for the evaluation of reaction rates in combustion simulations is presented. Combustion simulations where the finite-rate chemistry model is employed are computationally expensive. In such simulations, a transport equation for each species in the chemical reaction mechanism has to be solved, and the resulting system of equations is typically stiff. As a result, advanced implicit methods must be applied to obtain accurate solutions using reasonable time-steps at expenses of higher computational resources than explicit or classical implicit methods.

Summary Unstructured meshes allow easily representing complex geometries and to refine in regions of interest without adding control volumes in unnecessary regions. However, numerical schemes used on unstructured grids have to be properly defined in order to minimise numerical errors. An assessment of a low Mach algorithm for laminar and turbulent flows on unstructured meshes using collocated and staggered formulations is presented. For staggered formulations using cell‐centred velocity reconstructions, the standard first‐order method is shown to be inaccurate in low Mach flows on unstructured grids. A recently proposed least squares procedure for incompressible flows is extended to the low Mach regime and shown to significantly improve the behaviour of the algorithm. Regarding collocated discretisations, the odd–even pressure decoupling is handled through a kinetic energy conserving flux interpolation scheme. This approach is shown to efficiently handle variable‐density flows. Besides, different face interpolations schemes for unstructured meshes are analysed. A kinetic energy‐preserving scheme is applied to the momentum equations, namely, the symmetry‐preserving scheme. Furthermore, a new approach to define the far‐neighbouring nodes of the quadratic upstream interpolation for convective kinematics scheme is presented and analysed. The method is suitable for both structured and unstructured grids, either uniform or not. The proposed algorithm and the spatial schemes are assessed against a function reconstruction, a differentially heated cavity and a turbulent self‐igniting diffusion flame. It is shown that the proposed algorithm accurately represents unsteady variable‐density flows. Furthermore, the quadratic upstream interpolation for convective kinematics scheme shows close to second‐order behaviour on unstructured meshes, and the symmetry‐preserving is reliably used in all computations. Copyright © 2016 John Wiley & Sons, Ltd.

Linear cascades are commonly used as surrogate geometries when performing fundamental studies of turbomachinery blading. Several effects are not accounted for in linear cascades, among them the relative motion between blade and endwall. In this study three different relative endwall velocities are analysed. The effect of the relative motion between endwall and blade in a linear compressor cascade is studied through Direct Numerical Simulations. Results show a significant change in the secondary flow structure within the passage. Most notably, the tip leakage vortex is displaced away from the blade. Still, the blade spanwise range affected by the secondary flow field is similar to the case without relative endwall motion. At the outlet plane, a stratification of the total pressure losses and the exit flow angle is found, which overshadows any blade wake effects near the endwall.

Linear cascades are commonly used as surrogate geometries when performing fundamental studies of turbomachinery blading. Several effects are not accounted for in linear cascades, among them the relative motion between blade and endwall. In this study three different relative endwall velocities are analysed. The effect of the relative motion between endwall and blade in a linear compressor cascade is studied through Direct Numerical Simulations. Results show a significant change in the secondary flow structure within the passage. Most notably, the tip leakage vortex is displaced away from the blade. Still, the blade spanwise range affected by the secondary flow field is similar to the case without relative endwall motion. At the outlet plane, a stratification of the total pressure losses and the exit flow angle is found, which overshadows any blade wake effects near the endwall.