An optimization-based approach to injector element design

An injector optimization methodology, method i, is used to investigate optimal design points for gaseous oxygen/gaseous hydrogen (GO₂/GH₂) injector elements. A swirl coaxial element and an unlike impinging element (a fuel-oxidizer-fuel triplet) are used to facilitate the study. The elements are optimized in terms of design variables such as fuel pressure drop, ΔP_f, oxidizer pressure drop, ΔP₀, combustor length, L_comb, and full cone swirl angle, Θ, (for the swirl element) or impingement half-angle, α, (for the impinging element) at a given mixture ratio and chamber pressure. Dependent variables such as energy release efficiency, ERE, wall heat flux, Q_w, injector heat flux, Q_inj, relative combustor weight, W_rel, and relative injector cost, C_rel, are calculated and then correlated with the design variables. An empirical design methodology is used to generate these responses for both element types. Method i is then used to generate response surfaces for each dependent variable for both types of elements. Desirability functions based on dependent variable constraints are created and used to facilitate development of composite response surfaces representing the five dependent variables in terms of the input variables. Three examples illustrating the utility and flexibility of method i are discussed in detail for each element type. First, joint response surfaces are constructed by sequentially adding dependent variables. Optimum designs are identified after addition of each variable and the effect each variable has on the element design is illustrated. This stepwise demonstration also highlights the importance of including variables such as weight and cost early in the design process. Secondly, using the composite response surface that includes all five dependent variables, unequal weights are assigned to emphasize certain variables relative to others. Method i is used here to enable objective trade studies on design issues such as component life and thrust to weight ratio. Finally, combining results from both elements to simulate a trade study, thrustto- weight trends are illustrated and examined in detail.