Multiplicity for idealized rotational detonation waves

Abstract

Simulations of three-dimensional rotational detonation waves are conducted to understand the mechanisms of wave bifurcation. A compressible reacting Euler solver is developed within the framework of OpenFOAM, and a fixed mass flux boundary condition is developed to avoid complex injector dynamics. Influences of inflow mass flow rates and initiations of ignition spots are studied. As the inflow mass flow rate increases, one detonation wave is maintained. Constrained by the circumference of the combustor, the maximum fill height is achieved when the maximum post-shock pressure expansion is reached. Further increasing mass flow rates does not lead to wave bifurcation or higher mean fill height. By introducing multiple ignition regions, an identical number of stable waves are ignited and maintained, which signifies that wave numbers are not uniquely determined by the inlet boundary conditions. The minimum fill height (or largest velocity deficit) owing to either the lowest mass flow rate or the maximum wave number is obtained when the pressure expansion distance is comparable to the hydrodynamic thickness. The scaling of fill height is subsequently explained through a theoretical relation based on mass conservation. It is shown that neither increasing mass flow rates nor existence of multiple waves is a sufficient condition for wave bifurcation. The fill height is intrinsically connected with wave numbers, and both cannot be predicted solely based on boundary conditions. Future work will relax some idealizations in this work to further quantify the limit for the fill height.