# Coupled Fluid-Thermal Investigation on Drag and Heat Reduction of a Hypersonic Spiked Blunt Body with an Aerodisk

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Coupled Fluid-Thermal Numerical Method

#### 2.1. Coupling Strategy

#### 2.2. Validation Example

^{−5}m for meeting the requirement of the Menter’s SST k-ω turbulent model and obtaining wall heat flux independent of the grid height (y + <1). The parameters of hypersonic flow are shown in Table 2. In the numerical simulation, the AUSM + spatial discretization scheme with second-order accuracy [31], Menter’s SST k-ω turbulent model [32] and LU-SGS time marching scheme [33] were adopted. The gas model was calorically perfect gas. Because the thermal conductivity and dynamic viscosity of the air are important for the calculation of aeroheating, the above two parameters were obtained by the corresponding Sutherland’s models. The structural temperature was calculated by the ABAQUS software. The coupling analysis was transient, in which the coupled time step Δt was set to be 1 × 10

^{−3}s and 1 × 10

^{−4}s, and the total time of coupling analysis was 2 s. The steady flow field was taken as the initial condition for the coupling analysis, and the initial structural temperature was set as 294.4 K.

^{−3}s. Therefore, the coupled time step of 1 × 10

^{−3}s was adopted in the subsequent analysis. The calculated dimensionless results of the outer wall are shown in Figure 4. The calculated results are in good agreement with the experimental results. Table 3 lists the calculated and experimental results of the stagnation point; the relative errors of the stagnation heat flux and stagnation temperature were 1.34% and 4.95% respectively. The above comparisons validate the accuracy of the loosely coupled method.

## 3. Geometric and Numerical Models

_{w}are shown in Table 4. This paper established the axisymmetric numerical model. Figure 7 presents the computational grids and boundary conditions, and the grid height near wall was 1 × 10

^{−5}m in the fluid grid for obtaining wall heat flux independent of the grid height. The AUSM+ spatial discretization scheme with second-order accuracy, Menter’s SST k-ω turbulent model, and the LU-SGS time marching scheme were adopted. The gas model was calorically perfect gas. The thermal conductivity and dynamic viscosity of the air were obtained by Sutherland’s models. The thickness of the forebody was 15 mm, and the temperature of inner wall remained constant (300 K). Table 5 lists the corresponding material properties. The structural temperature was calculated by the ABAQUS software.

## 4. Results and Discussion

#### 4.1. Comparison of Initial Results

_{d}) and the peak heat flux of forebody (Q

_{max}). The drag coefficients of Models 2, 3, and 4 were 5.70%, 42.26% and 48.59%, respectively, which are lower than that in Model 1. The peak heat fluxes of Models 3 and 4 were 37.80% and 46.79%, respectively, which are lower than that of Model 1, while the peak heat flux of Model 2 was 25.73% higher than that of Model 1. Therefore, the drag was reduced in Models 2, 3, and 4, and Models 3 and 4 had better drag reduction performance than Model 2. Models 3 and 4 significantly reduced the aeroheating of forebody, while Model 2 enhanced the aeroheating, which is detrimental to the thermal protection. The function of the aerodisk is enhancing the compression to hypersonic flow.

#### 4.2. Evolution of Analysis Results

^{−3}s based on the conclusion drawn in Section 2.2, and the total analysis time was 20 s. The steady flow field was taken as the initial condition for coupling analysis, and the initial temperature of the structure was 300 K. The calculated results at different times are shown in Figure 11 and Figure 12. When the coupling analysis began, the aeroheating caused the wall temperature to increase gradually, resulting in the decrease of the aeroheating according to Fourier’s law. The coupled method considers the influence of wall temperature on aeroheating. The wall heat flux is always maintained at the initial value in traditional uncoupling analysis, which will cause the structural temperature to be higher than actual value. In addition, with the progress of calculation, the changing rates of the above-calculated results gradually decreased. The stationary solution will be reached when the computational time approaches infinity.

#### 4.3. Effects of the Spike and Aerodisk

## 5. Conclusions

- (1)
- The coupling analysis of the hypersonic circular tube was carried out. The relative errors of the stagnation heat flux and stagnation temperature between calculated and experimental results were 1.34% and 4.95%, respectively, thus verifying the calculation effectiveness of the proposed loosely coupled method in this paper.
- (2)
- The coupling analysis had little influence on the drag coefficient. In all spiked models, more than 87% of the drag was caused by pressure, and only a small part was caused by the viscosity effect. With the progress of calculation, the changing rates of the coupled calculated results gradually decreased. The spiked model with the planar aerodisk had the least drag and the lowest temperature of the forebody; besides, the planar aerodisk also had the lowest temperature and the best non-ablative property. Influenced by the recirculation zone and reattached shock wave, the maximum temperature of the forebody in Model 4 was the closest to the downstream, at the position of 49.11°.
- (3)
- With the increase of the length of the spike, the decrease rates of drag, pressure, heat flux, and temperature decreased gradually. Increasing the diameter of the aerodisk also reduced the temperature of the forebody, while the drag reduction efficiency increased at first and then decreased. Therefore, the heat and drag reduction must be considered comprehensively for the optimal design of the spike.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**Dimensionless heat flux and dimensionless temperature distributions of the outer wall at 2 s: (

**a**) heat flux; (

**b**) temperature.

**Figure 11.**Evolution of wall heat flux of the forebody: (

**a**) Model 1; (

**b**) Model 2; (

**c**) Model 3; (

**d**) Model 4.

**Figure 12.**Evolution of wall temperature of the forebody: (

**a**) Model 1; (

**b**) Model 2; (

**c**) Model 3; (

**d**) Model 4.

**Figure 13.**Comparison of structural temperature field of the forebody at 20 s: (

**a**) Model 1; (

**b**) Model 2; (

**c**) Model 3; (

**d**) Model 4.

**Figure 16.**Initial pressure and heat flux of the forebodies with different lengths L: (

**a**) pressure; (

**b**) heat flux.

**Figure 17.**Comparison of the structural temperature field of the forebody at 20 s: (

**a**) L/D = 0.5; (

**b**) L/D = 1; (

**c**) L/D = 1.5; (

**d**) L/D = 2.

**Figure 19.**Initial pressure and heat flux of forebodies with different diameters d: (

**a**) pressure; (

**b**) heat flux.

**Figure 20.**Comparison of the structural temperature field of the forebody at 20 s: (

**a**) d = 24 mm; (

**b**) d = 28 mm; (

**c**) d = 32 mm; (

**d**) d = 36 mm.

Parameter | Value | Parameter Description |
---|---|---|

k (W/(m·K)) | 16.72 | Thermal conductivity |

c (J/(kg·K)) | 502.48 | Specific heat |

ρ (kg/m^{3}) | 8030 | Density |

Parameter | Value | Parameter Description |
---|---|---|

Ma_{∞} | 6.47 | Mach number |

α (°) | 0 | Angle of attack |

T_{∞} (K) | 241.5 | Static temperature |

p_{∞} (Pa) | 648.1 | Static pressure |

Results | Quantity | Calculation | Experiment |
---|---|---|---|

Q_{s} (kW/m^{2}) | Stagnation heat flux | 661 | 670 |

T_{s} (K) | Stagnation temperature | 442 | 465 |

Parameter | Value | Parameter Description |
---|---|---|

Ma_{∞} | 8 | Mach number |

α (°) | 0 | Angle of attack |

T_{∞} (K) | 247.02 | Static temperature |

p_{∞} (Pa) | 21.96 | Static pressure |

T_{w} (K) | 300 | Wall temperature |

Parameter | Value | Parameter Description |
---|---|---|

k (W/(m·K)) | 2 | Thermal conductivity |

c (J/(kg·K)) | 1000 | Specific heat |

ρ (kg/m^{3}) | 1500 | Density |

Model | C_{d} | Q_{max} (kW/m^{2}) |
---|---|---|

1 | 0.966172 | 263.56 |

2 | 0.911118 | 331.37 |

3 | 0.557827 | 163.94 |

4 | 0.496696 | 140.25 |

Model | Forebody | Spike |
---|---|---|

1 | 0.966172 | 0 |

2 | 0.901042 | 0.010076 |

3 | 0.502472 | 0.055355 |

4 | 0.427148 | 0.069549 |

Model | Pressure | Viscosity |
---|---|---|

1 | 0.900701 | 0.065471 |

2 | 0.820853 | 0.090265 |

3 | 0.486492 | 0.071335 |

4 | 0.434233 | 0.062463 |

Model | 1 | 2 | 3 | 4 |
---|---|---|---|---|

t = 0 s | 0.966172 | 0.911118 | 0.557827 | 0.496696 |

t = 5 s | 0.968403 | 0.889627 | 0.544266 | 0.487179 |

t = 10 s | 0.969502 | 0.879822 | 0.538436 | 0.483491 |

t = 15 s | 0.970382 | 0.872595 | 0.533643 | 0.480497 |

t = 20 s | 0.971165 | 0.866611 | 0.529479 | 0.477855 |

L/D | C_{d} | Q_{max} (kW/m^{2}) |
---|---|---|

0.5 | 0.741191 | 205.21 |

1 | 0.572515 | 157.36 |

1.5 | 0.496696 | 140.25 |

2 | 0.455366 | 130.63 |

d (mm) | C_{d} | Q_{max} (kW/m^{2}) |
---|---|---|

24 | 0.448826 | 113.95 |

28 | 0.434467 | 97.71 |

32 | 0.442206 | 87.26 |

36 | 0.464701 | 79.67 |

d (mm) | Spike | Forebody |
---|---|---|

24 | 0.098819 | 0.350007 |

28 | 0.133358 | 0.301109 |

32 | 0.173247 | 0.268960 |

36 | 0.218722 | 0.245978 |

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**MDPI and ACS Style**

Fan, B.; Huang, J.
Coupled Fluid-Thermal Investigation on Drag and Heat Reduction of a Hypersonic Spiked Blunt Body with an Aerodisk. *Aerospace* **2022**, *9*, 19.
https://doi.org/10.3390/aerospace9010019

**AMA Style**

Fan B, Huang J.
Coupled Fluid-Thermal Investigation on Drag and Heat Reduction of a Hypersonic Spiked Blunt Body with an Aerodisk. *Aerospace*. 2022; 9(1):19.
https://doi.org/10.3390/aerospace9010019

**Chicago/Turabian Style**

Fan, Bing, and Jie Huang.
2022. "Coupled Fluid-Thermal Investigation on Drag and Heat Reduction of a Hypersonic Spiked Blunt Body with an Aerodisk" *Aerospace* 9, no. 1: 19.
https://doi.org/10.3390/aerospace9010019