High-order compressible formulation for LES/PDF simulations of turbulent reacting flows

Abstract

High-speed turbulent reacting flows are relevant to many modern engines. Large-eddy simulation (LES) is a practical and accurate approach to study such challenging flows in which the large scales of turbulence are resolved while those below a filter cut-off are modelled. In turbulent combustion, the transported probability density function (PDF) model is appealing because of its broad applicability and no modelling requirement for the reaction rate term. However, most of the progress with LES/PDF solvers has been limited to the low Mach regime. Moreover, the particle algorithms employed for solving the joint PDF equation have typically been first-order accurate in space and time. In this work, a high-order accurate compressible LES/PDF solver is developed starting with an existing direct numerical simulation (DNS) solver, S3D. Artificial fluid properties (AFP) are employed to model the sub-grid fluxes and the transport equation for the composition PDF is solved with the Lagrangian Monte Carlo approach. The governing equations are integrated in time with a new implementation of the Runge-Kutta algorithm that is fourth-order accurate for the deterministic equations and weak second-order accurate for the stochastic equations. High-order schemes are also employed for spatial discretisation, compact filter and particle interpolation and mean estimation. The newly developed solver is first studied with the Taylor-Green vortex problem to assess the capability of AFP as a sub-grid model, and then optimise its parameters with respect to the numerical dissipation from the compact filter. The optimal solver is then validated on a series of experimental non-reacting jets with and without temperature gradients. Next, a systematic validation of the PDF implementation is conducted with 1D problems and the temporal error convergence of the coupled solver is verified. Then, a temporally evolving non-premixed flame involving significant extinction and reignition is simulated at low and high convective Mach numbers and validated with DNS data. Finally, an experimental high Reynolds number supersonic lifted jet flame is simulated with the new LES/PDF capability. The predictions for the temporal and spatial jets are also compared with those from an LES employing a well-mixed model in order to highlight the importance of the PDF model.