# Mitigating the Piston Effect in High-Speed Hyperloop Transportation: A Study on the Use of Aerofoils

^{*}

## Abstract

**:**

## 1. Introduction

#### 1.1. Studies on Airflow around High-Speed Systems

#### 1.2. Kantrowitz Limit

#### 1.3. Aerodynamic Studies on the Hyperloop

#### 1.4. Research Questions

- How does the piston effect influence the performance of a Hyperloop pod in a partially vacuum tunnel?
- Does the addition of aerofoil-shaped fins improve the aerodynamic performance of a Hyperloop pod?

## 2. Method

#### 2.1. Model Dimensions

#### 2.2. Computational Modeling

- k-ω closure: σ
_{k1}= 0.85, σ_{ω1}= 0.65, β_{1}= 0.075 - k-ε closure: σ
_{k2}= 1.00, σ_{ω2}= 0.85, β_{2}= 0.082 - SST closure: β
^{*}= 0.09, a_{1}= 0.31

#### 2.3. Materials

^{3}and thermal conductivity of 8.5 W/mk, and the specific heat can be found using the following expression [46]. The constants in this equation are obtained by curve-fitting the experimental data, as reported in [46], and are applicable only in the temperature range of 340 to 3000 K.

_{P}) of air at this temperature is 1006.17 J/kgK, the thermal conductivity being 0.028389 W/m K. The viscosity of the air is 1.948 × 10

^{−7}kg/m s. The material for the tube is assumed to be structural steel.

#### 2.4. Phase I Model—Investigation of the Plunger Effect

_{max}represents the maximum radius of the body, x represents the space coordinate, and the V represents the volume. The volume is given by:

^{2}, respectively. After the models were made, the computational domain was created along with models. Both the models have the same computational domain. The computational domain has been given the shape of the tube in which the pod will be operating. The dimensions of the computational domain are 5.2 m diameter for the upper wall and 4.5 m height of the whole tube while the length is 304.8 m (1000 ft.). The distance between the nose of the pods and the inlet boundary is 152.4 m.

#### 2.5. Mesh Generation and Grid Convergence

#### 2.6. Phase II Model—With Aerofoils to Mitigate the Plunger Effect

## 3. Results

#### 3.1. Verification and Validation of the Model Used

#### 3.2. Drag Coefficient

#### 3.3. Lift Coefficient

#### 3.4. Formation of Eddy Currents

#### 3.5. Velocity Contours

#### 3.6. Pressure Contours

## 4. Discussion

#### 4.1. Plunger Effect inside the Vacuum Tube

#### 4.2. Use of Aerofoil Fins on Hyperloop Pods

#### 4.3. Limitations of the Study

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**The modular aeroshell design of the Spartan Hyperloop competition team. The design uses a modular concept to account for the design for manufacturability and assembly considerations.

**Figure 10.**Comparison of the stream lines around the two pods. It was observed that the phase 2 pod led to fewer eddy currents compared to the phase 1 pod.

**Figure 12.**A comparison of the pressure contours around the two pods. The pressure in all the cases is maximum at the front of the pod, especially around the nose.

Case | Number of Elements | Drag (n) (Relative Error) | Lift (n) (Relative Error) | Pressure (pa) (Relative Error) | Velocity (m/s) (Relative Error) |
---|---|---|---|---|---|

Type 1 | 3,081,385 | 2793.89 (34.95%) | −185.27 (0%) | 227.81 (27.05%) | 1374.77 (19.55%) |

Type 2 | 2,236,054 | 2070.32 (180.95%) | −185.27 (5.29%) | 179.31 (15.88%) | 1149.87 (14.70%) |

Type 3 * | 1,601,627 | 736.9 | −195.07 | 207.8 | 1319 |

Material of the pod | 3k Twill weave carbon fiber |

Material of the tube | Steel |

Material for the fluid | Air |

Speeds considered (m/s) | 112, 154, 241, 309 |

Tube pressure (Pa) | 25 |

Tube temperature (°C) | 49 |

Density of fluid (kg/m^{3}) | 0.000270 |

Density of the pod material (kg/m^{3}) | 1760 |

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**MDPI and ACS Style**

Bose, A.; Viswanathan, V.K. Mitigating the Piston Effect in High-Speed Hyperloop Transportation: A Study on the Use of Aerofoils. *Energies* **2021**, *14*, 464.
https://doi.org/10.3390/en14020464

**AMA Style**

Bose A, Viswanathan VK. Mitigating the Piston Effect in High-Speed Hyperloop Transportation: A Study on the Use of Aerofoils. *Energies*. 2021; 14(2):464.
https://doi.org/10.3390/en14020464

**Chicago/Turabian Style**

Bose, Aditya, and Vimal K. Viswanathan. 2021. "Mitigating the Piston Effect in High-Speed Hyperloop Transportation: A Study on the Use of Aerofoils" *Energies* 14, no. 2: 464.
https://doi.org/10.3390/en14020464