Exploring the aerothermal characteristic of a flight body has great military applications in tracking, locating, thermal protection, and infrared stealth technologies. Available studies are mostly focused on the transient aerothermal characteristics of vehicles in some specific flight datum, which are not able to satisfy the requirements in real-time tracking for an infrared system. This paper probes into a method of dynamic thermal analysis of a cone-cylinder flight body with a high spinning speed. Firstly, a theoretical model for analyzing the dynamic aerothermal characteristics is established using the thermal node-network method. Then, trajectory datum and the convective heat-transfer coefficients are solved simultaneously. Besides, the trajectory datum in supersonic, transonic, and subsonic regimes is separately defined as the boundary conditions, and fluid-thermal analysis methods are implemented by a combination of sliding mesh and multicoordinate approaches. Finally, the flow characteristics are analyzed and compared with disregarding the rotational speed. The results demonstrate that there are significant differences between the two cases, especially at the high-speed regimes. This study further confirms that it is essential to conduct the aerothermal analysis from a dynamic point of view, and taking the impacts of coupling motion into account is also of vital importance.

For flight vehicles, aerothermal responses are crucial in the testing of flight parameters for an infrared radiation tracking measurement system, such as coordinate, attitude, and yaw [

Unfortunately, researchers have mainly focused on the transient aerodynamic heating of vehicle in some specific flight states [

Additionally, high-speed spinning is the major mode to maintain flying stability for some vehicles, but related to the aeroheating characteristics for a flight body with coupling motion of precession, spinning, and pitching is limited. Particularly, the effects of spinning are often neglected. For example, Silton [

Therefore, the dynamic aerothermal characteristics of the flight body in coupled motions of precession, spinning, and pitching are necessary studies. In this article, dynamic aerothermal related to the surface of a cone-cylinder spinning flight body is reconstructed using updated modeling approaches. Firstly, the six degrees of freedom (6-DOF) trajectory model is established, and the motion characteristics are analyzed at different launch conditions. Then, the trajectory datum and the convective heat-transfer coefficients are simultaneously solved by the Runge-Kutta method, and the influencing factors are also analyzed.

A kind of spinning projectile is taken as the research object to investigate the continuous aeroheating characteristics on the surface of a flight body in the coupled motions of precession, spinning, and pitching. The simplified structural model is depicted in Figure

Geometric model.

The 6-DOF kinetic model is established by the exterior ballistic theory to describe the movement regularities of the cone-cylinder spinning flight body. The modeling procedures are listed below: Firstly, the reference coordinate systems are created, including the ground coordinate, datum coordinate, ballistic coordinate, body coordinate, and body-axis coordinate systems. Then, the dynamic loads are analyzed, including the gravity, drag, lift, Magnus force, static moment, equatorial and polar damping moment, and Magnus moment.

Based on the general theoretical analysis above, the kinematic equations and the kinetic equations are derived according to the momentum theorem and mass center motion theorem in the ballistic coordinate system.

Similarly, the kinetic equations and kinematic equations are derived in accordance with the theorem of momentum moment in the body-axis coordinate system.

Accordingly, the 6-DOF trajectory model can be obtained by simultaneous equations (

The domain decomposition and surface element division are essential to derive the theoretical model. In this paper, the node-network method is proposed to generate the surface elements and take the center of each element as a compute node. The cone-shaped angle

The cylindrical surface is evenly divided into

In the body coordinate system, column coordinates of node (

Similarly, the column coordinates of node (

In this section, a theoretical model for solving the convective heat transfer coefficient on the surface of the flight body will be constructed from the theory of heat transmission. For taking the impacts of spinning speed into account, the absolute velocity in the rotating coordinate system is assumed to be the flight velocity; then, according to the velocity synthesis theorem,

If the standard-sea-level atmospheric parameters are regarded as the airflow parameters of the projectile at the launch position, and the relations between temperature, density, and pressure of the freestream can be, respectively, expressed as

The adiabatic wall temperature

According to the fluid mechanics and heat-transfer theories, the local Nusselt number can be approximately substituted for calculating the forced convection heat transfer on a flat plate, when the high-speed airflow is passing over the cylindrical surface longitudinally.

It is known that the compressible flow theory cannot be used in predicating the aerodynamic heat flux using an implicit function with the given physical quantity. In order to solve the problem, a reference temperature method that calculates the boundary-layer parameters in the flow field is proposed. The transport and thermodynamic properties are evaluated at the reference temperature (

According to the theory of heat transmission, a relation between the local Nusselt number and the heat-transfer coefficient is defined as

Then, the coefficient of convection heat transfer on the cylindrical surface can be expressed as

The coefficient of convection heat transfer on the conical surface can be approximately calculated by the circle theorem of hydrodynamics [

The primary data for trajectory calculation is shown below: the lengths of conical and cylindrical sections are 400 mm and 500 mm. The cylindrical diameter is 155 mm, and the mass is 46.5 kg. The distance from the center of mass to the warhead is 550 mm. The launch velocity, shot angle, and flight time are 1030 m/s, 45°, and 80 s, respectively. The equatorial moment of inertia is 1.814 kg∙m^{2}, and the pole moment of inertia is 0.163 kg∙m^{2}. The Runge-Kutta method is adopted to simultaneously solve the 6-DOF trajectory model and the aerodynamic heat transfer model, and the ballistic parameters and the heat-transfer coefficients with flight time can be obtained synchronously. Figure

Trajectory curves at different initial velocities.

Figures

Velocity at different initial velocities.

Angular speed at different initial velocities.

Figure

3-D distribution of the Reynolds number.

Average reference temperatures.

From the results, each compute node corresponds to a Reynolds number and a reference temperature, and the maximum Re is about

Figure

Adiabatic wall, recovery, and airflow temperature.

Transient heat transfer coefficients.

Figure

Convection heat transfer coefficient.

To get the effects of launch conditions on the coefficient of convection heat transfer, the influencing factors which include the launching velocity, spinning speed, and launching angle are analyzed, as shown in Figures

Average coefficients at different launch velocities.

Average coefficients of convection heat transfer at different initial rotational speeds.

Average coefficients of convection heat transfer at different launch angles.

In this article, dynamic aerothermal characteristics on the surface of a cone-cylinder spinning flight body are reconstructed using updated modeling approaches, and the thermal node-network method is successfully applied for predicting the aerothermal environment of the body coupling motion of precession, spinning, and pitching. The exterior trajectory datum and the coefficient of convection heat transfer during the flight are synchronously obtained. The main results of this work are as follows:

The flight velocity is decreasing exponentially in the ascending period of the trajectory, and the attenuation rates are quicker with the initial velocities. The exponential attenuation rate of angular speed in the ascending period is faster than in the descending. Besides, the average reference temperature on the surface of the conical part is significantly higher than that of the cylindrical part in the first 20 seconds of the trajectory, especially in a short time after launching. After 20 seconds, the average reference temperature on the conical surface is lower than that of the cylindrical part

The average coefficient of convection heat transfer is increasing with the initial velocity and rotational speed, and the attenuation rates are growing rapidly at the ascending stage during the flight, whereas the coefficient is inversely proportional to the initial velocity at the descending stage, and the shot angle is changed similarly. Additionally, the transient coefficient of convection heat transfer is dropping sharply at the beginning, and rising dramatically before a slow attenuation

Aerothermal characteristic is determined not only by the current flight state but also by the heat transfer environment during the flight, which is a progressive, lasting, and dynamic process. In consideration of the spinning speed, the coefficient of convection heat transfer is obviously too high to disregard, especially in supersonic regimes

Diameter, m

Mass, kg

Time, s

Area of surface panel, m^{2}

Density, kg/m^{3}

Specific heat capacity, J/(kg·K)

Cone-shaped angle, rad

Thermal conductivity, W/(m·K)

Adiabatic index

Normal vector of surface panel

Equatorial moment of inertia

Polar moment of inertia

Velocity, m/s

Angular speed, rad/s

Dynamic viscosity, (N·s)/m^{2}

Rifling angle, rad

Heat transfer coefficient, W/(m^{2}·K)

Elevation attack angle, rad

Azimuth attack angle, rad

Elevation angle in the

Azimuth angle in the

Elevation angle in the velocity direction

Azimuth angle in the velocity direction, rad

Temperature, K

Pressure, Pa

Total enthalpy, J

Nusselt number

Reynolds number

Prandtl number.

Wall

Compute node

Axial direction

Relative values

Freestream condition

Flow parameter at reference temperature condition.

The [MATLAB calculation procedures] data used to support the findings of this study are available from the corresponding author upon request.

The authors declare that there is no conflict of interest regarding the publication of this paper.

This work was supported by the Natural Science Foundation of China (NSFC) under the Grant Number of 11372136, the Shanghai Municipal Science and Technology Commission of China (SMSTCC) under the Grant Number of 17050502000, and the Shanghai Ocean University under the Grant Number of A2-2006-20-200210.