Towards the Direct Numerical Simulation of Fuel Droplet Combustion in Detonation Waves
Franz O'Meally, California Institute of Technology
Detonation waves are a complex physical phenomenon coupling shock waves and combustion. These waves implemented in jet engines have been theorized to improve the efficiency of hypersonic aircraft. However, such engines have not been realized due to the unstable nature of the waves. While it is impossible to directly numerically simulate an entire detonation wave engine, simulating a few droplets is not only feasible, but would allow us to develop models that will remove the need to resolve the small scales. Our code, Multi-component Flow Code (MFC), uses an interface-capturing scheme via a non-conservative volume fraction advection equation to resolve interfaces. This scheme has been shown to accurately simulate shock-bubble interactions similar in nature to fuel droplets in a detonation wave. The simulation of the evolution of individual droplets in detonation waves in this framework, however, requires the addition of source terms in our species continuity and volume fraction equations that are consistent in mixture regions. The difficulty with implementing a source term in the volume fraction equation lies in the non-conservative nature of the equation. This work highlights one method for deriving such source terms. By invoking assumptions of the equation state, one can combine total and species continuity to derive consistent source terms for our interface-capturing scheme. The method is tested with mass transfer problems via binary diffusion, which gives symmetric solutions in self-diffusion and correctly induces a velocity when ideal gases of different densities diffuse.