# The Rapid Data-Driven Prediction Method of Coupled Fluid–Thermal–Structure for Hypersonic Vehicles

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## Abstract

**:**

## 1. Introduction

## 2. Rapid Data-Driven Prediction Method

#### 2.1. Proper Orthogonal Decomposition

#### 2.2. Radial Basis Function Interpolation

**.**

#### 2.3. Rapid Prediction Method Based on Data-Driven

**.**The pulsation value ${\mathit{Y}}^{\prime}$ is used to construct matrix $\mathit{M}$:

## 3. Numerical Simulation

## 4. Result of Prediction

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A

${\mathit{P}}_{\mathit{\infty}}$$\left(\mathbf{P}\mathbf{a}\right)$ | ${\mathit{T}}_{\mathit{\infty}}\left(\mathbf{K}\right)$ | $\mathit{M}\mathit{a}$ | $\mathit{R}{\mathit{e}}_{\mathit{\infty}}$ |
---|---|---|---|

$648.1$ | $241.5$ | $6.47$ | $1.31\times {10}^{6}$ |

Elastic Modulus $\left(\mathbf{G}\mathbf{P}\mathbf{a}\right)$ | Poisson’s Ratio | Density $\left(\mathbf{K}\mathbf{g}/{\mathbf{m}}^{3}\right)$ | Coefficient of Linear Expansion $\times {10}^{-6}\left({\mathbf{K}}^{-1}\right)$ | Thermal Conductivity $\left(\mathbf{W}/\left(\mathbf{m}\mathit{\xb7}\mathbf{K}\right)\right)$ | Specific Heat Capacity $\left(\mathbf{J}/\left(\mathbf{k}\mathbf{g}\mathit{\xb7}\mathbf{K}\right)\right)$ |
---|---|---|---|---|---|

206 | 0.3 | 8030 | 17.5 | 16.27 | 502.48 |

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**Figure 9.**Relative error contour of the structural temperature and stress: (

**a**) temperature; (

**b**) stress.

$\mathbf{Mach}\mathbf{Number}\left(\mathbf{M}\mathbf{a}\right)$ | $\mathbf{Altitude}\left(H/km\right)$ | $\mathbf{Angle}\mathbf{of}\mathbf{Attack}\left(\alpha /\xb0\right)$ |
---|---|---|

$3\le Ma\le 8$ | $20\le \mathrm{H}\le 40$ | $-8\le \mathsf{\alpha}\le 8$ |

Method | Maximum Temperature of Structure/K | $\mathbf{Maximum}\mathbf{Heat}\mathbf{Flux}/\left(\mathbf{k}\mathbf{W}/{\mathbf{m}}^{2}\right)$ | Maximum Pressure of Flow Field/Pa |
---|---|---|---|

Numerical Simulation in this paper | 436 | 663 | 35,386 |

Experiment [10] | 465 | 670 | 37,815 |

Test Condition | $\mathbf{Altitude}\left(\mathbf{H}/\mathbf{k}\mathbf{m}\right)$ | $\mathbf{Mach}\mathbf{Number}\left(\mathbf{M}\mathbf{a}\right)$ | $\mathbf{Angle}\mathbf{of}\mathbf{Attack}\left(\mathbf{\alpha}/\xb0\right)$ |
---|---|---|---|

1 | 38 | 4.2 | −3.2 |

2 | 26 | 5 | −6.4 |

3 | 30 | 3.4 | 3.2 |

4 | 34 | 6.6 | 0 |

5 | 22 | 5.8 | 6.4 |

Method | Number of Snapshots | CPU Time for One Snapshot/h | CPU Time for Predicting one Test Condition/s |
---|---|---|---|

Prediction method | 5 | $\approx 12$ | 0.14 |

Numerical simulation | 60 | $\approx 12$ | $-$ |

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**MDPI and ACS Style**

Liu, J.; Wang, M.; Li, S.
The Rapid Data-Driven Prediction Method of Coupled Fluid–Thermal–Structure for Hypersonic Vehicles. *Aerospace* **2021**, *8*, 265.
https://doi.org/10.3390/aerospace8090265

**AMA Style**

Liu J, Wang M, Li S.
The Rapid Data-Driven Prediction Method of Coupled Fluid–Thermal–Structure for Hypersonic Vehicles. *Aerospace*. 2021; 8(9):265.
https://doi.org/10.3390/aerospace8090265

**Chicago/Turabian Style**

Liu, Jing, Meng Wang, and Shu Li.
2021. "The Rapid Data-Driven Prediction Method of Coupled Fluid–Thermal–Structure for Hypersonic Vehicles" *Aerospace* 8, no. 9: 265.
https://doi.org/10.3390/aerospace8090265