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Efficient Prediction of the Temperature History of a Hypersonic Vehicle Throughout the Mission Trajectory with an Aerodynamic Thermal Load Element

  • Gyubin Kim
  • Yeon Cheol Kang
  • Jeongmin Woo
  • Jeong Ho Kim
  • Jin Yeon ChoEmail author
Original Paper
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Abstract

This work introduces an efficient approach for aero-thermo-mechanical analysis to predict the temperature history of a hypersonic vehicle during its full mission trajectory. The approach uses a recently proposed aerodynamic thermal load element, in which the effects of aerodynamic pressure and aerodynamic heating are efficiently considered using local piston theory and the Eckert reference temperature method, respectively. This element is implemented as a user-subroutine in commercial software to handle realistic models for the aero-thermo-mechanical analysis, such as the X-43A. A finite element model of the X-43A is constructed for a benchmark test. Using the model, an aero-thermo-mechanical analysis is carried out while considering the full mission trajectory of the X-43A. The predicted temperature results are compared with recorded flight test data from the X-43A. Additionally, the aero-thermo-mechanical behavior of the hypersonic vehicle is investigated according to various parameters. The investigation confirms that the approach can be efficiently used in the design of hypersonic vehicles with considerable savings in computational cost.

Keywords

Hypersonic vehicle Aero-thermo-mechanical analysis Piston theory Eckert reference temperature Aerodynamic thermal load element X-43A 

List of Symbols

\( a_{( \bullet )} \)

Speed of sound, \( {\text{m/s}} \)

\( C_{1} \)

Coefficient of Sutherland’s law, \( \text{kg} /\left( {m\,{\text{s}}\sqrt {\text{K}} } \right) \)

\( c_{\text{f}}^{*} \)

Skin friction coefficient at reference temperature

\( c_{p} \)

Specific heat at constant pressure, \( {\text{J/K/kg}} \)

\( {\mathbf{F}}_{I}^{\text{ATL}} \)

Aerodynamic thermal load element for node I

\( h \)

Convective heat transfer coefficient, \( {\text{W/m}}^{ 2} / {\text{K}} \)

\( M_{( \bullet )} \)

Mach number

\( {\mathbf{n}}_{{\mathbf{0}}} \)

The outward normal unit vector of the surface of the initial configuration

\( {\mathbf{n}}_{\text{t}} \)

The outward unit normal vector of the surface of the deformed configuration

\( p_{( \bullet )} \)

Pressure, \( \text{Pa} \)

\( { \Pr } \)

Prandtl number

\( q_{\text{aero}} \)

Aerodynamic heat flux, \( {\text{W/m}}^{ 2} \)

\( R \)

Ideal gas constant, \( {\text{J/K/kg}} \)

\( \text{Re}_{\text{cr}} \)

Critical Reynold’s number

\( \text{Re}^{*} \)

Reynold’s number at reference temperature

\( r \)

Recovery factor

\( S \)

Coefficient of Sutherland’s law, \( {\rm K} \)

\( {\text{St}}^{*} \)

Stanton number at reference temperature

\( T_{\text{aw}} \)

Adiabatic wall temperature, \( {\rm K} \)

\( T_{\text{w}} \)

Wall temperature, \( {\rm K} \)

\( T^{*} \)

Reference temperature, \( {\rm K} \)

\( T_{( \bullet )} \)

Temperature, \( {\rm K} \)

\( {\mathbf{V}}_{\text{L}} \)

Velocity vector of flow, \( {\text{m/s}} \)

\( {\mathbf{V}}_{\text{S}} \)

Velocity vector of structure, \( {\text{m/s}} \)

\( V_{( \bullet )} \)

Velocity, \( {\text{m/s}} \)

\( W \)

Downwash at each point, \( {\text{m/s}} \)

\( x \)

Distance from leading edge to location of interest, \( \text{m} \)

\( \phi_{I} \)

Shape function for node I

\( \gamma \, \)

Specific heat ratio

\( \mu^{*} \)

Coefficient of viscosity at reference temperature, \( {\text{kg/m/s}} \)

\( \rho_{( \bullet )} \)

Density, \( {\text{kg/m}}^{ 3} \)

\( \rho^{*} \)

Density at reference temperature, \( {\text{kg/m}}^{ 3} \)

Subscripts

\( ( \bullet ) \)

Subscripts such as \( {\text{L}} \), \( {\text{LPT}} \), t or \( \infty \)

\( {\text{L}} \)

Steady-state physical quantity at each local position

\( {\text{LPT}} \)

Updated physical quantity through the local piston theory

t

Total or stagnation property

\( \infty \)

Physical quantity of freestream

Notes

Acknowledgements

This work was conducted at the High-Speed Vehicle Research Center of KAIST with the support of the Defense Acquisition Program Administration and the Agency for Defense Development under Contract UD170018CD.

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Copyright information

© The Korean Society for Aeronautical & Space Sciences 2019

Authors and Affiliations

  1. 1.Department of Aerospace EngineeringInha UniversityIncheonRepublic of Korea

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