Parameter similarity method for test simulation conditions of aerodynamic heating environment

Abstract

A parameter similarity method for test simulation conditions of an aerodynamic heating environment is disclosed. With respect to the requirement that the adiabatic wall enthalpy and the cold-wall heat flux are equal in the simulation test of the aerodynamic heating environment, a method that can ensure the similarity of ground test parameters and flight parameters without the equal adiabatic wall enthalpy is proposed, and solves the problems of relying on the equal adiabatic wall enthalpy and making it difficult to accurately simulate the real aerodynamic heating environment in the current test simulation method, and provides guarantee for heat transfer and ablation test research of thermal protection/insulation material under the high temperature aerodynamic heating environment. The test conditions are not affected by the value of the adiabatic wall enthalpy. According to the method, most test devices can simulate the aerodynamic heating environment with high enthalpy.

Claims

1. A parameter similarity method for test simulation conditions of an aerodynamic heating environment, comprising the following steps: (1) assuming temperature of a free stream as T.sub.¥, free stream Mach number of the free stream as Ma.sub.¥ and free stream heat capacity ratio of air as g at flight condition; calculating recovery temperature $T_{r1}=T_{\yen }\left(1+r\frac{g-1}{2}{\mathrm{Ma}}_{\yen }^2\right)$ of the free stream, wherein r is a temperature recovery coefficient which ranges from 0.88 to 0.92; calculating adiabatic wall enthalpy h.sub.r1=∫.sub.0.sup.T.sup.r1c.sub.pdT of the free stream wherein c.sub.p is specific heat capacity of air at constant pressure and T represents the temperature; (2) calculating a first convective heat transfer coefficient a.sub.1 of the surface of a flight vehicle structure according to characteristics of the flight vehicle structure and an aerodynamic heating engineering algorithm; for a turbulent flow state of a flat surface, obtaining the first convective heat transfer coefficient
a.sub.1=0.0296(Re.sub.1*).sup.−1/2(Pr.sub.1*).sup.−2/3(rv).sub.¥c.sub.p wherein Re.sub.1* is a Reynolds number of a free stream at reference temperature; Pr.sub.1* is a Prandtl number of the free stream at reference temperature; (rv).sub.¥ is a momentum of the free stream; calculation equations of the first convective heat transfer coefficients of other geometric structural surfaces are slightly different from this, and refer to a relevant aerodynamic heating engineering algorithm; (3) calculating a cold-wall heat flux according to the first convective heat transfer coefficient obtained in the step (2);
q.sub.01=a.sub.1(T.sub.r1−T.sub.0), wherein T.sub.0 is cold-wall temperature, T.sub.0=300K; (4) calculating a wall surface temperature T.sub.w1 of the material of the flight vehicle structure under the cold-wall heat flux determined in the step (3) by using a method of computational heat transfer; (5) when an adiabatic wall enthalpy h.sub.r2 of a gas flow of a test device is less than the adiabatic wall enthalpy h.sub.r1 of the free stream, assuming a first total temperature of an initial gas flow as T.sub.2*=T.sub.w1+20K according to the geometry of the test device and the free stream condition, and calculating a second convective heat transfer coefficient α.sub.2 on the surface of a test piece in the test by using a method of computational fluid dynamics; (6) making the surface temperature of the test piece as T.sub.w2=T.sub.w1, and adjusting the recovery temperature of the gas flow in the test device according to the second convective heat transfer coefficient α.sub.2 calculated in the step (5); $T_{r2}=\frac{a_1}{a_2}\left(T_{r1}-T_{w1}\right)+T_{w2}$ calculating a second total temperature T.sub.2*=T.sub.r2/r.sub.2 of the gas flow, wherein r.sub.2 is a temperature recovery coefficient of the test condition; substituting T.sub.2* into the step (5), repeating the calculation of step (5) to step (6), and conducting a next step until T.sub.r2 and a.sub.2 tend to be stable; (7) determining the cold-wall heat flux of the test condition $q_{02}=\frac{a_2\left(T_{r2}-T_0\right)}{a_1\left(T_{r1}-T_0\right)}{q}_{01}.$

Description

DETAILED DESCRIPTION

(1) Specific embodiments of the present invention are described below in detail in combination with the technical solution.

(2) Embodiment 1: an aerodynamic heating environment with high enthalpy value and low heat flux when a certain flight vehicle flies at a high altitude of 75 km and a Mach number of 10 Ma is simulated.

(3) (1) An atmospheric parameter table is consulted to obtain the airflow temperature T.sub.¥=208.399K at high altitude of 75 km and density of ρ=3.992×10.sup.−5 kg/m.sup.3. According to the Mach number Ma.sub.¥=10, the heat capacity ratio g=1.4 of air and the temperature recovery coefficient r=0.89, the recovery temperature

(4) $T_{r1}=T_{\yen }\left(1+r\frac{g-1}{2}{\mathrm{Ma}}_{\yen }^2\right)=3667.8K$
of the airflow is calculated, and the adiabatic wall enthalpy h.sub.r1=∫.sub.0.sup.T.sup.r1c.sub.pdT=3839 kJ/kg of the airflow is calculated.

(5) (2) The convective heat transfer coefficient of the surface of the flight vehicle structure under the flight condition is calculated
a.sub.1=0.0296(Re.sub.1*).sup.−1/2(Pr.sub.1*).sup.−2/3(rv).sub.¥c.sub.p=2.8W/m.sup.2×K.

(6) (3) The cold-wall heat flux q.sub.01=a.sub.1 (T.sub.r1−T.sub.0)=9.69 kW/m.sup.2 is calculated.

(7) (4) The wall surface temperature T.sub.w1=638K of the material of the flight vehicle structure is obtained through computational heat transfer.

(8) (5) The total temperature of the gas flow is assumed as T*.sub.2=T.sub.w1+20K=658K; and the convective heat transfer coefficient α.sub.2=50 W/m.sup.2.Math.K on the surface of the test piece in the test is calculated by using a method of computational fluid dynamics.

(9) (6) The surface temperature of the test piece is made as T.sub.w2=638K and the temperature recovery coefficient under the test condition is made as r.sub.2=0.9; and the recovery temperature of the test gas flow is adjusted according to the convective heat transfer coefficient α.sub.2.

(10) $T_{r2}=\frac{a_1}{a_2}\left(T_{r1}-T_{w1}\right)+T_{w2}.$

(11) The total temperature T*.sub.2=T.sub.r2/r.sub.2 of the airflow is calculated; T*.sub.2 is changed; and calculation of step (5) to step (6) is repeated until T.sub.r2 and a.sub.2 are stable; at this moment, T.sub.r2=698.5K, a.sub.2=60 W/m.sup.2×K, T*.sub.2=776.11K.

(12) (7) The cold-wall heat flux of the test condition is determined

(13) $q_{02}=\frac{a_2\left(T_{r2}-T_{02}\right)}{a_1\left(T_{r1}-T_{01}\right)}{q}_{01}=65.14\mathrm{kW}/m^2.$