基于边界层理论的球头驻点热流计算方法研究

doi:10.7527/S1000-6893.2024.30448

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基于边界层理论的球头驻点热流计算方法研究

田润雨¹,龚红明²,常雨³,孔小平⁴

1. 中国空气动力研究与发展中心超高速空气动力研究所
2. 中国空气动力研究与发展中心超高速空气动力研究所
3. 中国空气动力研究与发展中心超高速所
4. 中国空气动力研究与发展中心

收稿日期:2024-03-26 修回日期:2024-06-24 出版日期:2024-06-25 发布日期:2024-06-25
通讯作者: 龚红明
基金资助:
国家重点研发计划

Study on Calculation Method of Heat Flow at Stagnation Point of Spherical Head Based on Boundary Layer Theory

Received:2024-03-26 Revised:2024-06-24 Online:2024-06-25 Published:2024-06-25
Supported by:
National key research and development program

摘要/Abstract

摘要： 准确获知球头驻点热流，对于飞行器防热设计至关重要。本文基于平衡空气球头驻点层流自相似边界层假设，开展了边界层方程相关推导，采用四阶龙格-库塔法数值求解变形后的常微分边界层方程组，建立正向逼近打靶法，以寻找方程最优解，从而建立了求解边界层方程组，计算球头驻点热流的方法，在与试验值的对比中获得了较好的对比效果；以此方法为基础，针对高度10km～60km、不同速度、不同壁面温度的182个工况，开展了Fay-Riddell平衡流条件球头驻点热流公式计算偏差分析，发现在大部分工况下，壁面温度接近边界层外缘温度时，其热流计算值偏差明显增加；变形驻点热流表达式，将其中的无量纲参数拟合为多个无量纲参数组合的形式，得到了多参数拟合的新的球头驻点热流计算公式，并在多个工况下开展了热流计算效果对比研究，获得了优于Fay-Riddell平衡流条件球头驻点热流公式的应用效果。

关键词: 边界层理论, 层流自相似, 球头, 驻点热流, 平衡流, 气动热

Abstract: It is very important for aircraft thermal protection design to accurately know the heat flux at the stagnation point of spherical head. Based on the assumption of self-similar boundary layer at the stagnation point of equilibrium air, the boundary layer equations are derived. The fourth-order Runge-Kutta method is used to numerically solve the deformed ordinary differential boundary layer equations, and the forward approximation shooting method is established to find the optimal solution of the equations. Thus, the method for solving the boundary layer equations and calculating the stagnation point heat flux of the spherical head is established, and good comparison results are obtained with the experimental values. Based on this method, for 182 working conditions of height 10km ~ 60km, different velocity and different wall temperature, the calculation deviation of heat flux formula of spherical stagnation point under Fay-Riddell equilibrium flow condition is analyzed. It is found that in most working conditions, the calculation deviation of heat flux increases obviously when the wall temperature approaches the outer edge temperature of boundary layer. New heat flux formulas for spherical stagnation point are obtained by fitting the dimensionless parameters into a combination of several dimensionless parameters. The heat flux calculation results are compared under several working conditions, and the application results are better than those of the spherical stagnation point heat flux formula under Fay-Riddell equilibrium flow condition.

Key words: boundary layer theory, laminar flow self-similarity, spherical head, stagnation heat flux, equilibrium flow, Aerodynamic heat

中图分类号:

V211.19

田润雨龚红明常雨孔小平. 基于边界层理论的球头驻点热流计算方法研究[J]. 航空学报, doi: 10.7527/S1000-6893.2024.30448.

参考文献

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主管单位：中国科学技术协会主办单位：中国航空学会北京航空航天大学

基于边界层理论的球头驻点热流计算方法研究

Study on Calculation Method of Heat Flow at Stagnation Point of Spherical Head Based on Boundary Layer Theory

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