基于边界层理论的球头驻点热流计算方法
收稿日期: 2024-03-26
修回日期: 2024-06-04
录用日期: 2024-06-21
网络出版日期: 2024-06-25
Calculation method for heat flow at stagnation point of spherical head based on boundary layer theory
Received date: 2024-03-26
Revised date: 2024-06-04
Accepted date: 2024-06-21
Online published: 2024-06-25
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-库塔法数值求解坐标变换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，从而建立了通过求解边界层方程组获得球头驻点热流的方法，将该热流简称为BLES热流，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10~60 km、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。
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[J]. 航空学报, 2025 , 46(2) : 130448 -130448 . DOI: 10.7527/S1000-6893.2024.30448
In aircraft thermal protection design， it is very important 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 ordinary differential boundary layer equations after coordinate transformation， and the forward approximation shooting method is established to find the optimal solution for the equations. Thus， by solving the boundary layer equations， a method for obtaining the heat flux at the stagnation point of the spherical head is established， which is referred to as Boundary Layer Equations Stagnation （abbreviated as BLES） heat flux in this paper. The results obtained are consistent with the experimental values. Using this method， the calculation deviation of heat flux formula of spherical stagnation point under Fay-Riddell equilibrium flow condition at 182 working conditions of 10–60 km height and different velocity and wall temperature 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 under several working conditions are compared， obtaining better results than those of the spherical stagnation point heat flux formula under the Fay-Riddell equilibrium flow condition.
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