Rotating detonation engine injector and method of designing

A method of designing a propellant injector for a rotating detonation engine (RDE), comprising:

• identifying a preferred fuel propellant and a preferred oxidizer propellant;
• acquiring initial flow conditions for the preferred fuel propellant through a fuel injector nozzle and the preferred oxidizer propellant through an oxidizer injector nozzle, wherein the initial flow conditions of each preferred propellant include:
• an initial mass flow rate;
• an initial upstream pressure, wherein the initial upstream pressure is upstream relative to an outlet aperture of a corresponding injector nozzle;
• identifying a temperature for each preferred propellant;
• calculating an initial cross-sectional area of the fuel injector nozzle using Equation 1:
• m
• ˙
• =
• A
• ⁢
• P
• T
• ⁢
• γ
• R
• ⁢
• (
• 1
• +
• γ
• -
• 1
• 2
• )
• γ
• +
• 1
• 2
• ⁢
• (
• γ
• -
• 1
• )
• (
• 1
• )
• where {dot over (m)} is the initial mass flow rate of the preferred fuel propellant, A is the initial cross-sectional area of the fuel injector nozzle, P is the initial upstream pressure of the fuel propellant, T is the temperature of the fuel propellant, R is the gas specific constant of the preferred fuel propellant, and γ is the specific heat ratio of the preferred fuel propellant;
• calculating an initial cross-sectional area of the oxidizer injector nozzle using Equation 1, where {dot over (m)} is the mass flow rate of the preferred oxidizer propellant, A is the initial cross-sectional area of the oxidizer injector nozzle, P is the initial upstream pressure of the preferred oxidizer propellant, T is the temperature of the preferred oxidizer propellant, R is the gas specific constant of the preferred oxidizer propellant, and γ is the specific heat ratio of the preferred oxidizer propellant;
• calculating an updated upstream pressure of the preferred fuel propellant using Equation 1 with the calculated initial cross-sectional area for the preferred fuel propellant and calculating an updated upstream pressure of the preferred oxidizer propellant using Equation 1 with the calculated initial cross-sectional area for the preferred oxidizer propellant;
• if a fuel-oxidizer pressure ratio for the updated upstream pressures is outside of a range of 0.8775 to 1.4917, adjusting the initial cross-sectional area for one or both of the fuel injector nozzle and the oxidizer injector nozzle and recalculating the updated upstream pressure until the fuel-oxidizer pressure ratio is in a range of 0.8775 to 1.4917;
• and
• manufacturing the propellant injector with one or more fuel injector nozzles and one or more oxidizer injector nozzles having particular cross-sectional areas that result in the fuel-oxidizer pressure ratio being in the range of 0.8775 to 1.4917.