基于边界层理论的球头驻点热流计算方法

doi:10.7527/S1000-6893.2024.30448

Abstract

Abstract:

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.

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

CLC Number:

V211.19

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 Aeronautica et Astronautica Sinica, 2025, 46(2): 130448.

Figures/Tables 13

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References 28

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步长	壁面温度760 K工况			11个工况
步长	迭代启动次数	平均迭代步数	耗时/s	总耗时/s
0.005	123	1 060.21	92	906
0.01	123	535.20	46	476
0.02	122	264.72	23	249
0.04	151	130.65	15	123

风洞	速度u_∞/（m·s^-1）	静压p_∞/Pa	密度ρ_∞/ （10^-3kg·m³）	壁温T_w/K	球头直径D/cm	试验值/（W·cm^-2）	BLES热流/（W·cm^-2）	相对试验值偏差/%	FR热流/（W·cm^-2）	相对试验值偏差/%
IITB-ST激波风洞^［26］	1 828.00	79.0	2.572	300.00	5	31.8	26.92	-15.35	26.68	-16.10
Calspan 96英寸激波风洞^［27］	1 922.43	47.66	4.619	296.22	1.27	85.99	81.40	-5.34	80.67	-6.19
					1.905	70.01	66.46	-5.07	65.87	-5.91
					3.175	59.58	51.48	-13.60	51.02	-14.37
					7.62	41.09	33.23	-19.13	33.93	-17.43
	2 150.21	369.92	15.055	296.11	1.27	232.24	222.50	-4.19	222.78	-4.07
	2 306.82	1 036.76	28.29	295.83	1.27	400.09	394.30	-1.45	393.98	-1.53
	3 565.86	40.80	0.840	294.78	1.27	291.41	288.48	-1.01	282.64	-3.01
CARDC2 m激波风洞B	2 623.14	959.0	15.062	286.88	3	290.66	295.96	1.82	295.82	1.78
	2 980.00	538.0	7.013	298.00	3	304.25	309.63	1.77	302.64	-0.53
	3 118.67	703.0	8.743	287.69	3	409.40	403.16	-1.52	390.96	-4.50
LENS XX^［28］	5 732.00	180.155	1.16	300.00	7.62	651.00	648.96	-0.31	639.21	-1.81
CARDC高焓膨胀风洞^［11］	6 260.00	18.4	0.44	282.1	5	659.70	638.83	-3.16	613.98	-6.93
	7 750.00	14.3	0.221	281.0	2	1 525.10	1 368.06	-10.30	1 347.06	-11.67
	7 990.00	17.5	0.177	290.0	2	1 574.60	1 340.51	-14.87	1 337.27	-15.07

拟合式	3	4	5	6
P₁	0~2	0~2	0~1	0.7~0.9
P₂	无	无	无	-0.5~0
P₃	-2~2	-2~2	-1~1	0.4~1
P₄	-2~2	-2~2	-1~1	0~0.5
P₅	无	无	-1~1	-0.5~0
P₆	无	-2~2	-1~1	0~0.45

拟合式	FR公式	3参数	4参数	5参数	6参数
总偏差	7.173 16	2.989 87	2.984 06	2.672 90	2.365 93
P₁	0.76	0.87	0.89	0.91	0.77
P₂	无	无	无	无	-0.26
P₃	0.4	0.68	0.72	0.77	0.68
P₄	0.4	0.14	0.17	0.14	0.15
P₅	无	无	无	-0.23	-0.13
P₆	0.4	无	0.04	0.31	0.19

拟合式	FR公式	3参数	4参数	5参数	6参数
总偏差	10.940 1	5.536 83	5.663 09	5.207 14	4.432 80
P₁	0.76	0.87	0.89	0.91	0.77
P₂	无	无	无	无	-0.26
P₃	0.4	0.68	0.72	0.77	0.68
P₄	0.4	0.14	0.17	0.14	0.15
P₅	无	无	无	-0.23	-0.13
P₆	0.4	无	0.04	0.31	0.19

Calculation method for heat flow at stagnation point of spherical head based on boundary layer theory

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