Mixing length scale of Bi-propellant thrusters for characteristic velocity formulation

Bi-propellant thrusters in space propulsion systems often utilize unlike-doublet or triplet injectors as the hypergolic propellant injection device. The impingement of liquid jet streams of fuel and oxidizer involves sheet expansion, droplet fragmentation, mixing, evaporation, and chemical reactions in liquid and gas phases. In the sequential reactive, multiphase, thermo-fluid dynamics, the rate controlling phenomenon is the mixing step. In this study, a defined length scale demonstrates the distribution of fuel and oxidizer and thus represents their mixing states, facilitating the straightforward formulation of characteristic velocity in a consistent manner for doublet and triplet injectors as a function of propellant injection conditions with a film cooling effect. The validity of the present modeling framework is confirmed by a good agreement with characteristic velocity measured by hot firing tests covering a wide range of the mixture ratio. We also clarify the meaning of a widely accepted practical indicator, the so-called Rupe factor, over half a century of injector design history.