Large Eddy simulation of supersonic combustion using a probability density function method

Abstract

The scramjet propulsion system is regarded to be a key technology to deliver the next generation of hypersonic planes. It consists of a ramjet engine in which the combustion occurs at supersonic speed. Experiments have been used to investigate the scramjet engine, however, the high costs of gathering data is a limiting factor in its development. In this context, the numerical simulation is an affordable alternative to shed a light into supersonic combustion. The simulation of high-speed compressible and reactive flows, however, is not straightforward, including shock/boundary layer interactions and combustion. Nonetheless, most combustion models have been designed for subsonic flames and their portability to high-speed flows is non-trivial.

This work investigates the use of the Probability Density Function (PDF) method for supersonic combustion within the Large Eddy Simulation (LES) framework. Two methods are considered: one is an extension of a joint scalar PDF model (SPDF) for high speed flows and the other is a new joint velocity-scalar PDF formulation (VSPDF). The LES-PDF equations are solved using the Eulerian stochastic fields method, which is implemented into the in-house compressible code CompReal. Their performance are evaluated through a reactive shock-tube, mixing layers and a homogeneous isotropic turbulence cube simulation. Two supersonic burner configurations are simulated to validate the code against experimental data. The results show that sub-grid contributions are important at coarse meshes and the stochastic fields approach can reproduce experimental results. The University of Virginia scramjet configuration A is also simulated using the joint scalar PDF model. Results of topwall pressure, temperature and molar fractions are compared with experimental data.

Overall, the results suggest that the joint scalar PDF is the most robust and reliable formulation and the sub-grid closures for the joint velocity-scalar PDF require further investigation.