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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
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.
Runyu TIAN , Hongming GONG , Yu CHANG , Xiaoping KONG . Calculation method for heat flow at stagnation point of spherical head based on boundary layer theory[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2025 , 46(2) : 130448 -130448 . DOI: 10.7527/S1000-6893.2024.30448
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