Abstract
Liquid centered coaxial swirl injectors are a viable replacement to shear coaxial elements in LOX/methane rocket engines, but design data is limited. This study derives the classical inviscid design theory for a liquid centered coaxial swirl element using Reynolds Transport Theorem, implements it as a MATLAB design tool, and evaluates the element studied in Bee et al. The model made is an inverse design tool. Rather than giving the geometry as an input and predicting upstream spray cone, it takes a measured spray cone and solves for the passage fullness, discharge coefficient, nozzle radius, tangential port geometry. At a 62-degree spray cone angle and 22 bar pressure drop, the model returned a nozzle radius of 1.6876e-3 m, passage fullness of 0.8471, and exit velocity of 62 m/s. The model reproduces a published swirl number and velocity ratio within 4% but independent verifications of the model's validity reveal that the Abramovich geometric constant produces the greatest difference, with the model predicting 0.2774 against the published 2.02, attributed to the failure of the inviscid assumption over a long injector post where wall shear diminishes angular momentum that the free vortex relation assumes is conserved.