The characteristics of flow and thrust evolution of an annular Expansion-Deflection (ED) nozzle are numerically investigated under varying backpressure changing rates during ascending and descending trajectories. The objective is to test the sensitivity of unsteady behaviors of shock waves in the ED nozzle to backpressure changing rate, and to further elucidate the thrust evolution mechanism and mode transition hysteresis. The movement of shock reflection points on the nozzle wall follows two flow mechanisms, namely, shock self-excited oscillations and rapid backpressure changes. A low backpressure changing rate enables shock self-excited oscillations, leading to a reciprocating motion of the shock waves accompanied by thrust oscillations, while a high backpressure changing rate suppresses the shock self-excited oscillations, leading to a unidirectional motion of the wave system on the nozzle shroud wall. A criterion for distinguishing ED nozzle operation modes is proposed, which relies on the loading inflection points of the nozzle pintle base and exhibits a fast and user-friendly feature. A dual-wake mode hysteresis region is defined to quantify the hysteresis in nozzle mode transition, with the span of the region decreasing as the backpressure changing rate slows down. The present work helps in understanding the unsteady flow mechanism and thrust evolution in ED nozzles.

A predictive unsteady quasi-one-dimensional internal ballistic numerical model and a set of performance regulation mechanism formulas are established for throttling segregated fuel-oxidizer systems. The numerical model considers combustion gas injection, wall friction, and propellant surface regression, using a finite-rate chemical reaction model to describe the non-equilibrium process. With this model, performance parameters and internal flow parameter distributions of the throttling segregated fuel-oxidizer system can be well demonstrated.Results show that, adjustment of the throat radius of the throttle valve from 2.89 mm to 1.65 mm increases the thrust of the system from 105.09 N to 432.18 N, by 411.25% from the original thrust, verifying the regulation capability of the throttling segregated fuel-oxidizer system. During the dynamic operation of the throttle valve, the system experiences anti-regulations. Faster actuation of the valve leads to larger anti-regulation amplitude and shorter response period of the performance parameters. Analysis of the influencing factors of performance regulation reveals that the increase of propellant pressure index and the decrease of nozzle throat radius both contribute to the improvement in performance regulation ability of the throttling segregated fuel-oxidizer system. Accordingly, a new arrangement of throttling segregated fuel-oxidizer system with an adjustable nozzle is proposed. Simulation of this arrangement suggests that, for a specified thrust adjustment ratio, reducing the nozzle throat radius can effectively alleviate the pressure level of the fuel-rich combustion chamber of the system, thus providing more feasible performance regulation schemes for the system operation.