## Predicting Liquid Rocket Engine Durability: A Universal Methodology This methodology predicts liquid rocket engine durability based on operating conditions, number of missions, and operating time. It's applicable to any liquid rocket engine and uses structural analysis techniques, accounting for both low and high cycle fatigue. The Russian RD-0120 engine serves as a primary example. The core idea is to link engine durability (operating cycles and duration) to operating conditions using structural analysis and available failure data. ### Key Durability Factors Engine durability is defined by: * **Total operating duration:** Total time the engine runs. * **Duration of each mission duty cycle:** Time the engine runs during a single mission. * **Total number of operating cycles:** Number of starts/shutdowns. Two key durability margin factors are introduced: * **$q_t = T_o/t_e$**: Relates time to crack initiation ($T_o$) to required operating duration ($t_e$). * **$q_N = N_o/N_e$**: Relates cycles to crack initiation ($N_o$) to required operating cycles ($N_e$). A simplified assumption, $q_t = q_N$, is used as a first approximation, based on the observed relationship between time and cycles. ### Structural Analysis and Durability Durability analysis focuses on highly stressed components like turbine blades, impellers, and chamber walls. The approach is similar for each component, but the specific analysis techniques differ. #### Low Cycle Fatigue (LCF) and High Cycle Fatigue (HCF) Engine testing shows durability is governed by: * **LCF:** Driven by transient events (startup, throttling, shutdown). * **HCF:** Time-dependent, driven by steady-state operation. The severity of the operating environment (e.g., high-pressure hydrogen effects) must be considered. #### Stress and Strain Analysis * **Nominal thermal stress:** $\sigma_T = \alpha E (T - T_m)$, where $\alpha$ is the coefficient of thermal expansion, $E$ is the modulus of elasticity, $T$ is the local temperature, and $T_m$ is the mean temperature. * **Nominal centrifugal stress (turbine blades):** $\sigma_c = 2\rho U_o^2 L K / D$, where $\rho$ is density, $U_o$ is peripheral speed, $L$ is blade height, $K$ is a shroud geometry factor, and $D$ is rotor diameter. * **Stress concentration:** The intensity is described by a function $f(\sigma_m, \sigma_T, \alpha_m, \alpha_T)$, where $\alpha$ represents stress concentration factors. Ignoring stress concentrations can lead to significant underestimation of durability. #### Fatigue Calculation The relationship between failure stress ($\sigma_a$) and number of cycles ($N$) is crucial: $\sigma_a N^m = \text{Constant}$, where $m$ and $a$ are material constants. The fatigue limit factor ($M_k$) accounts for stress concentration, surface finish, and fatigue scale factors: $M_k = [5 + (c_i P_i)^{1/2}] / [(K_s E_s) + (1/\alpha_s) - 1]$ For electroerosive machining, $P_a = 0.75$ and $E_s = 1$. #### Damage Factor The total design damage factor ($Z$) combines steady-state thermal loads, fatigue loads, and transient loads: $Z = Z_t + Z_N + Z_{LCF}$ Failure (crack initiation) occurs when $Z = 1$. ### Durability Margin Factor ($q_N$) The paper argues against using constant, high values of $q_N$ (typically 4-10). Instead, it proposes a $q_N$ dependent on $N_e$: as $N_e$ increases, $q_N$ should decrease. A method based on the Manson model is suggested to determine $q_N$. A reduced $q_N$ (2.5-2.0 for $N_e = 10-30$) allows for better optimization of weight and performance. ### RD-0120 Engine Example The methodology is applied to the RD-0120 engine, focusing on turbine blade durability. Modifications like increasing blade thickness and removing the tip shroud significantly improve durability (up to a 13-fold increase). A characteristic parameter, $R$, describes the engine operating regime (power level). The relationship between $R$ and durability is established, showing that power level has a primary influence on durability, while cycle duration has a secondary effect. ### Conclusion This methodology provides a comprehensive approach to predicting liquid rocket engine durability, considering both time and cycle-dependent effects, operating conditions, and structural analysis. It allows for evaluating design trades and configuration modifications to enhance engine life and reusability.