Prediction model for wall energy exchange in solid rocket motor nozzles based on coupled heat transfer
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摘要:
固体火箭发动机喷管内部热环境预示影响热防护结构的优化设计，为实现喷管内强迫对流换热的快速预测，建立了喷管壁面能量交换预示模型，并采用隐式有限差分格式求解，其中耦合传热通过热流密度相等与温度连续的条件实现，同时引入无量纲壁面距离表征湍流边界层速度分布，并将其转化为热边界层参数参与传热。计算得到了壁面的表面传热系数、热流密度以及热防护结构温度变化历程，并与传统数值模拟方法、Bartz经验公式的计算结果进行了对比验证。结果表明：快速预示模型计算获得的喷管热防护结构内部监测点温度变化历程与数值模拟方法相比最大误差为5.63%，预示的表面传热系数均值与热流密度均值精度相比Bartz公式分别提高了3.56倍和3.04倍，在强迫对流换热最为剧烈的喷管喉部，预示结果相对数值模拟方法的平均误差为9.19%；在相同计算资源条件下，预示模型的计算效率相比数值模拟方法提高了两个数量级。
Abstract:The internal thermal environment of solid rocket engine nozzles plays a critical role in optimizing the design of thermal protection structures. To rapidly predict forced convection heat transfer in the nozzle, an energy exchange prediction model for the nozzle wall was established and solved using an implicit finite difference method. The coupling of heat transfer was achieved through the conditions of equal heat flux density and continuous temperature. A dimensionless wall distance was introduced to characterize the velocity distribution of the turbulent boundary layer, which was then converted into thermal boundary layer parameters to participate in the heat transfer calculations. The convective heat transfer coefficient, heat flux density, and temperature variations of the thermal protection structure were computed and compared with the results from traditional numerical simulation methods and Bartz’s empirical formula. The results showed that the temperature variation at the monitoring points in the nozzle’s thermal protection structure calculated by the rapid prediction model deviated by a maximum of 5.63% from the numerical simulation results. The predicted average convective heat transfer coefficient and heat flux density were 3.56 and 3.04 times more accurate than those obtained using Bartz’s formula. At the nozzle throat, where forced convection heat transfer was most intense, the average error of the predicted results compared with the numerical simulation method was 9.19%. Under the same computational resource conditions, the prediction model’s computational efficiency was two orders of magnitude higher than that of the numerical simulation method.
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Key words:
- composite nozzle /
- solid rocket motor /
- Bartz formula /
- coupled heat transfer /
- prediction model
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图 1 复合材料喷管结构示意图（单位：mm）
Figure 1. Schematic diagram of the composite nozzle structure （unit：mm）
图 4 不同时刻喷管温度分布云图
Figure 4. Temperature distribution contours of the nozzle at different time instances
图 5 快速预示模型网格离散示意图
Figure 5. Schematic diagram of mesh discretization in the rapid prediction model
图 6 平板湍流边界层的速度分布
Figure 6. Velocity distribution in turbulent boundary layers on a flat plate
图 10 不同方法计算8 mm监测点处温度-时间变化曲线
Figure 10. Comparison of temperature-time histories at the 8 mm measurement point using different computational methods
图 11 不同扩张段面积比在8 mm监测点处温度-时间变化曲线
Figure 11. Temperature-time variation at the 8 mm measurement point for different area ratios in the expansion section
图 12 喷管喉部不同径向深度监测点温度-时间变化曲线
Figure 12. Temperature-time variation at different radial depth measurement points in nozzle throat
图 13 不同时刻快速预示模型相对CFD方法的全路径温度误差对比
Figure 13. Comparison of full-path temperature errors of the rapid prediction model relative to CFD at different times
图 14 不同方法计算所得平均结果对比
Figure 14. Comparison of mean results calculated by different methods
参数 数值 密度/（kg/m3） 1 800 比定压热容/（J/（kg·K）） −77.91 + 2.11T−5.1×10−4T 2 热导率/（W/（m·K）） 312.44−0.28T + 6.97×10−5T 2 
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参数 数值 密度/（kg/m3） 2 200 比定压热容/（J/（kg·K）） 716.181 8 + 0.532 7T 热导率/（W/（m·K）） $ \begin{cases} -4.21+5.71\times {10}^{-2}T-5.59\times {10}^{-5}{T}^{2}\quad\quad\quad\;\; \text{300 K \lt }T\leqslant \text{700 K}\\-4.21+5.71\times {10}^{-2}T-4.39\times {10}^{-5}{T}^{2}\quad\quad\quad\;\; \text{700 K \lt }T\leqslant \text{1 100 K}\\106.09-\text{1.004 8}\times {10}^{-1}T+2.39\times {10}^{-5}{T}^{2}\quad\quad T \gt \text{1 100 K}\end{cases} $
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