Modeling of Cavity Residence Time via Modeled Lagrangian Particle Tracking

One of the critical components in a scramjet is the cavity flame holder. In evaluating the sizing of this component, the residence time of the fuel in the cavity is a common parameter used. However, to obtain the residence time via CFD is an expensive undertaking. One method is to perform an LES simulation of the cavity and use Lagrangian particle tracking to obtain both the mean and probability density function of the time that the particles remain in the cavity. While this method affords a significant amount of information, it is very costly in CPU run time. A simpler method involves performing a time accurate RANS simulation of the cavity, and when converged, overlay a traceable scalar in the cavity region, and then record the decay of this scalar’s flux at a downstream location. The time scale of the decay rate can then be estimated and a residence time inferred. This method is less computationally expensive than the LES approach, but still requires a time-accurate solution while only providing a mean cavity residence time evaluation.

In this paper a method of determining the mean cavity residence time as well as the Probability Density Function (PDF) of the residence time is proposed and demonstrated. This method is based on Lagrangian particle tracking modeled by the Generalized Langevin Equation and is implemented as a post-processing step for a steady RANS solution. Computational cost is on the order of minutes and the results are in agreement with values obtained by the LES and scalar decay methods.