Hyperloop

Project Aim

The aim of this project is to analyse the aerodynamic aspects of a hyperloop pod and develop a suitable design for the same. Hyperloop is a proposed mode of passenger and freight transportation, in a sealed system of tubes maintained under low pressure resulting in less air resistance than conventional mode of transportation, leading to better fuel efficiency and higher speeds.

The project focuses on analysing and selecting different design aspects such as the pod diameter, tube diameter, shape of pod and speed of pod.

Members

• Bikram Sarkar
• BSR Karthik Varma
• Jagadish BC
• Abhishek Choudhary

Work done

We have considered the tube to be maintained at a pressure of 100 Pa at 298 K, which gives us a density of 0.00116843 kg/m3 inside the pod in normal conditions.

The diameter of pod is kept as 3m, somewhat similar to the diameter of the fuselage of small private jets. The length of the pod is kept as 20 m, taking into consideration that it can house at least 20 passengers with a seat pitch of 36 inches.

For analysis, Ansys 18.1 Fluent was used. Initially 2D analysis was performed using the transition shear stress transport (SST) viscous model since its more accurate than fully turbulent k-ω model. A velocity inlet and pressure outlet boundary condition was imposed on the tube. The reference frame moved with the pod, thus, no-slip tube wall moved with the same velocity as inlet flow.

For the initial phase, the velocity of pod (Vpod or Vinlet) is selected as 160 m/s , comparable to high speed rail systems present currently. The diameter of tube is varied and checked for the drag force values.

The Reynold’s number (Re) was calculated for the hydraulic diameter in the blockage region using the formula Re = ρVpodDh/μ. We can see that the drag force reduces, as we increase the tube diameter, due to lower blockage ratio. The tube diameter is limited to 6m, since larger tube would also lead to a greater material and financial expense.

The maximum speed the pod can travel within the tube without choking the flow, is known as the Kantrowitz limit. This happens when the velocity of flow in the partially blocked region near the pod reaches the speed of sound, resulting in a choked flow and high drag force. Due to this we need to limit the velocity of the pod to a value such that the maximum velocity inside the tube remains less than mach 1.

We have considered the speed of sound (c = √γRT ) to be constant at 343 m/s since γ=1.4 and R=287.058 J/kg K remains independent of the pressure. Thus, for further analysis, we considered an inlet velocity of 120 m/s.

The drag force values for a few basic shapes were tabulated and compared.

Fixing circular section for the front, more shapes were analysed for the rear profile.

We can clearly see that a circular front profile and an elongated elliptical rear profile (semi-major axis = 6m ; semi-minor axis =1.5m) experiences the least drag force.

Then the same profiles are analysed for a symmetrical 3D model, one being cylindrical and the other being cuboidal.

Thus the basic shape of the pod being finalised, it can be noticed that the current drag force is considerably less than the 2-D cuboid profile we began with. This also means that the maximum velocity of air inside the tube is much less than mach 1, in this case. Due to smooth edges of the present pod design, the inlet velocity can be increased, without the maximum velocity inside the tube exceeding mach 1.

It’s safe to keep the limit the maximum speed of air inside the tube below 300 m/s. Thus the pod is capable of travelling at 200 m/s without choking the flow. The maximum velocity of 298.199 m/s for an inlet velocity of 200 m/s is fairly close to the value obtained by the incompressible flow continuity equation:

AtubeVinlet = AbypassVmax ; where Vmax comes out to be 288 m/s.

It is known that the Cd of a simple long cylinder with its axis in direction of the fluid flow is 0.8. The Cd of the pod is 0.675 which is fairly close to the standard case, since the pod design has an added aerodynamic benefit of the spherical and spheroid ends.

Future Scope

The Hyperloop concept is surely different from conventional transportation modes. The concept of using low pressure tubes eradicates a lot of constraints which modern modes of transportation usually face, for example: travelling through a partial vacuum decreases the loss in thrust due to aerodynamic drag, thus making hyperloop much more energy efficient. Moreover, it will allow us to travel among cities much quicker. The hyperloop pods are also capable of travelling near sonic speed, if a well-designed compressor is used to prevent choking even at sonic speeds. Companies like Tesla and SpaceX have already contributed to the growth of the hyperloop concept, which confirms that it has a lot of scope in the near future.