On 21st November 2019, Tesla launched a new electric pickup truck: Cybertruck. Everyone must have been gobsmacked by its polygonal body rather than its impressive specs such as 0-60 in 2.9 sec, 500-mile range, etc.
It is a norm that the surface of a car needs to be smooth to achieve better efficiency and higher speed. But Elon Musk’s firm has gone for the other route.
In my opinion, it cannot be aerodynamic given that the car mainly consists of straight lines and sharp edges. But the American genius must have thought about it too. So I thought it would be interesting to visualise the flow around the vehicle.
The objectives of this simulation are the following:
- Visualisation of streamlines
- Calculation of Cd [-] (Coefficient of drag)
Coefficient of drag is a dimensionless number often used in Automotive/Aerospace engineering to determine whether the object is aerodynamic or not.
There are quite a few CAD models of the Cybertruck on GrabCAD, but most of them are too detailed, and it will make the meshing quite tough, so I decided to create one myself. I downloaded a couple of reference images and inserted in Solidworks. It is almost impossible to make a perfect 1:1 scale model, so I’ve set the wheelbase (3,807mm) and modelled the rest. The CAD model is available here.
Mesh and Conditions
I have used cloud-based simulation service called simscale. The calculation itself is done using OpenFOAM, but on the server.
Since the model is symmetrical, only half of it has been assigned inside of the calculation area, and symmetry wall has been applied to reduce the calculation time and load.
In terms of meshing, two cartesian boxes are set around the truck to increase the calculation accuracy. Surface refinement and boundary inflation have been applied as well.
- Velocity inlet: 27.8 [m/s]
- Pressure outlet: 101.325 [KPa]
- Symmetry wall
- Ground: Moving wall 27.8[m/s]
- Model surface: No-slip wall
- Outer walls: Slip wall
- Front tyre (d=900mm): Rotating wall 61.8 [rad/s]
- Rear tyre (d=850mm): Rotating wall 65.4 [rad/s]
The calculation took 161 minutes with 42.9 CPUh.
So here are the results. The image below illustrates the pressure applied to the surface of the vehicle and the velocity magnitude around it at the centre.
As expected, massive vortices are generated at the back of the vehicle (Fig.6 and 7), which is one of the ordinary things to happen for automobiles. It could be reduced slightly by rounding the edges at the rear but considering this is a pickup truck; it may not be too bad. The diffuser-ish shape and the closed hatch seem to be effective in reducing wake.
Fig.8 indicates vorticity (Z normal). Strong vortices on the bonnet can be observed. When vortices are generated, vorticity around the edge becomes significant, just like the tip of the bonnet and the rear end. This tendency cannot be seen on the summit of the roof, which means the sharp edge on top does not create vortices.
If you have a look at streamlines on top, it is more obvious that the airflow is not disturbed by the top (Fig.9).
Fig.9 shows the vorticity around Cybertruck. The red area indicates vortices rotating clockwise while the blue area shows counter-clockwise vortices.
As shown in the clip and Fig.10, edge between the roof and the side creates a vortex. Because of the angled sides, the direction of rotation differs in front and rear. The air hitting the front extends across the front face and tries to flow into sides, but the sharp edge does not allow it to do so smoothly; instead, it separates the airflow from the surface, which ultimately creates vortex. The complete opposite thing occurs in the rear, behind the peak of the roof. A vortex circulating counter-clockwise can be observed (blue) beneath the vortex generated in front (red). Since the blue vortex has counter-clockwise rotation, the red vortex is pulled back onto the rooftop, over the blue vortex and eventually progresses towards the centre (0:02-0:05 in the clip).
The leading cause of drag force is pressure difference; if there is a high-pressure region in front and low-pressure region at the back, a greater force applies to the frontal surface, then it pushes the object backwards. We call this drag. Fluid’s viscosity creates drag too, but in general, it is negligible so it will be ignored here.
In Paraview, I’ve calculated each cell’s area normal to each axis, then used an equation: Pressure times area normal to X-axis, to calculate drag force generated by pressure differences. Fig.12 shows the drag force applied to the vehicle. It is obvious that the front-face generates the majority of drag.
If you get a closer look (Fig.13), you see slightly more drag is generated by the rear wheel arch than the one in front (yellow circles). You may be wondering ‘Why is that? The air should be hitting the frontal surface area more, shouldn’t it?’
Fig.14 displays the velocity magnitude viewed from above (normal to Y). As you can see, velocity magnitudes in front of the front wheel arch is significantly higher compared to the rear (yellow circles). The wheel arch avoids airflow’s direct hit due to turbulence generated at the corner it seems.
The pressure difference is apparent in Fig.15 with the contour’s scale of 0-500 [Pa].
Fig.16 illustrates streamlines around the front and rear wheel arch. Flow separation at the front left corner creates strong vortices which have higher velocity whereas the air directly hits the rear wheel arch without any vortices; the direct hit results in low-speed/high-pressure.
Coefficient of Drag, Cd, can be calculated by the equation below.
The each value is the following:
- D: 591.8 [N]
- A: 3.3097 [㎡]
- ρ: 1.1965 [kg/㎥]
- U: 27.8 [m/s]
- No obvious flow separation on the roof.
- Cd = 0.387 [-]
I had run another simulation with no rotational wheels before this one to make sure the mesh size is acceptable. Although the tyres are simple cylinders in my model, taking rotations into account reduced the Cd value from 0.427 to 0.387.
Plans for next
I may try modifying Cybertruck until I achieve Cd=0.25 which is equivalent to that of Tesla Model X. Let’s see how it goes…
A transient simulation didn’t run successfully this time so I may try that again in the future.
In case you are interested in this project, click here to have a look, edit and setup a simulation.