On the role of back-propagating pressure suppression in enhancing the pressure-gain performance of quasi-2D rotating detonation engines

TL;DR

This work addresses the contested question of achieving positive pressure gain in rotating detonation engines by introducing an abstract check valve model to suppress back-propagating pressure and coupling it with a quasi-2D flow framework. Using a quasi-1D axial simplification, the authors derive quasi-2D governing equations and perform parametric simulations over expansion ratio $A_e$ and backflow strength $α_b$, revealing that stronger backflow suppression modestly improves $PG$ but cannot eliminate back-propagating disturbances due to valve-induced flow perturbations. The study identifies a critical region in the $A_e$–$α_b$ space where positive $PG$ is possible, with a maximum exit recovery coefficient $η_4$ around 1.21 at $A_e=2.83$ as $α_b o ext{∞}$, and provides a general PG criterion via normalization to an equivalent inlet Mach number $M_1$, yielding $M_{1,cr1}=0.177$ and $M_{1,cr2}=2.749$ for stoichiometric hydrogen/air mixtures. Overall, the paper offers theoretical guidance for flow-channel design to suppress back-propagating pressure and enhance PG in RDEs, highlighting the remaining aerodynamic challenges and trade-offs inherent to non-ideal valve behavior.

Abstract

The total pressure gain (PG) characteristics of the quasi-2D rotating detonation engine (RDE) are numerically investigated in this study, based on an abstract check valve model and the quasi-1D assumption. The influence of back-propagating pressure suppression on PG and its underlying mechanism are examined. An abstract check valve model is established to simulate various flow channel configurations, with backflow check strength $α_b$ defined, where a larger $α_b$ corresponds to a stronger backflow blocking effect. The quasi-1D assumption is applied along the axial direction to simplify the radial features of the annular RDE. The quasi-2D governing equations for RDE flow are derived. Simulations are conducted for varying expansion ratios $A_e$ and values of $α_b$. The results indicate that increasing $α_b$ effectively suppresses back-propagating pressure and slightly improves PG; however, it cannot fully eliminate the back-propagating pressure, as the check valve itself introduces flow disturbances. Increasing $A_e$ also suppresses back-propagating pressure but significantly reduces PG. Achieving positive PG requires reducing $A_e$ below a critical value. However, this reduction is limited by $α_b$; further reduction in $A_e$ leads to forward propagation of back-propagating pressure to the engine inlet, resulting in inlet blocking. Therefore, a sufficiently large $α_b$ is essential for the required reduction in $A_e$. The key aerodynamic challenge for achieving positive PG lies in optimizing flow channels to suppress back-propagating pressure efficiently. Finally, a general PG criterion is proposed by normalizing the quasi-2D RDE with stoichiometric hydrogen/air mixtures. This study provides theoretical guidance for enhancing PG in RDEs.

Figures (21)

• Figure 1: Schematic diagram of the check valve model Wen22: (a) forward flow schematic, (b) backflow schematic.
• Figure 2: Control volume of the check valve model.
• Figure 3: Variations of entropy change $\Delta s$ and PG with respect to the density ratio $x$ under the condition where the backflow check strength $\alpha_b \in (-1, \alpha_1)$: (a) for $x \in (x_{f1}, x_{f2})$, and (b) for $x \in (1, x_{g2})$.
• Figure 4: Variations of entropy change $\Delta s$ and PG with respect to the density ratio $x$ under the condition where the backflow check strength $\alpha_b \in (\alpha_1, \infty)$ for $x \in (1, x_{g2})$.
• Figure 5: Variation of PG with dimensionless outlet pressure $p^*$ for the check valve model and the sudden expansion model: (a) the backflow check strength $\alpha_b$ takes values of 41, 80, 200, and 860, corresponding to area ratios $A^* = 0.2, 0.15, 0.1, 0.05$, respectively; (b) by selecting several additional values of $A^*$, the corresponding $\alpha_b$ values are calculated based on the mapping relationship in (a).