Our method of choosing our simulation model
Based on our literature review, many of the papers utilised a Large Eddy Simulation (LES) model. This is more performant than a direct numerical simulation as it takes approximations on a small scale at the element level while resolving the larger eddies in the mesh via solving the Navier-Stokes equation. This provides more accurate results than the Reynolds-Averaged Navier Stokes, which can only provide a time-averaged velocity for each mesh polygon. As such, we also used LES models in our simulations.
The simulations we settled on
Our simulations are run on COMSOL Version 5.4 using the Large Eddy Simulation Model Residual Based Variational Multiscale with Viscosity (LES-RBVMWV) which is designed to solve for large turbulent eddies and modelling the effects of smaller eddies.
In our simulations, a riblet surface is placed in an air tunnel that is long and comparatively wide. This allows us to minimise the wall effects experienced by the riblets and thus, makes our virtual drag measurements more accurate and similar to those we expect to see in real life.
For the velocity of air flowing over the riblets, this speed was chosen to be approximately 80 m/s. This is to simulate the type of air that is likely to flow over the surface of a bullet train, which has a high Reynolds number – this means that the air flow is very likely to be turbulent and therefore, the riblets would have a much better effect. We opted to make the tunnel symmetrical over the four faces of the “wind tunnel”. This was possible using the boundary conditions available in COMSOL v5.4!
Our studies were chosen to be time-dependent due to the transient nature of the vortices that are observed. This also allowed us to observe how flow over our riblets would develop over time and would also give us clues as to how we could better modify the shape of our riblets for drag reduction.
For post-processing, we chose streamlines which best allow us to visualise the flow of fluid over the riblets. Using derived values, we used surface integration of total stress in the X direction as a means to calculate drag force acting on the riblet surface. This values could be calculated to determine which surface best reduces drag.
The simulations we have run so far
While we run our simulations to optimise the riblet geometry, we also aim for the resultant geometry to be feasible to manufacture. Hence, we restricted our feature size to have a minimum resolution of 60 micrometers, as that is what is achievable by the CNC milling machines available to us. We did this to see how drag would act over riblets of those dimensions in simulations.
As you can see in the above picture, the wind tunnel is represented by an “air box” with air entering from one end and out the other along the x-axis (which is indicated in the photo). The streamlines correspond to the magnitude of the velocity, which can be compared to the legend on the right. As you can see, most air sweeps through at a speed of about 70 to 80 m/s but some slower velocity streamlines can still be seen in the photo above. We can zoom in in COMSOL to get a better look!
Here the velocity streamlines are going into the page. It can be seen that most of the streamlines pass above the riblets at 80 m/s. However, nearer to the riblets, the air is slowed down to due to the riblets, apparent from the blue streamlines nearer to each riblet. In the above photo, it can even be seen that high-velocity air can pass through easily between the riblets, interacting with the surface and increasing drag.
Simulations indicated that the drag actually worsens at this length scale by more than 800%, which is in line with theoretical predictions, as the calculated dimensionless length for the riblets is significantly longer than the length typically reported as optimal. While the vortices cannot be observed in the above photo (likely due to the transient nature of the vortices and the mesh fineness), the increase in drag is likely due to the fact that any vortices formed can’t be lifted above the riblets and as a result, high-speed air that forms the vortices interacts with the surface anyways. This means that the riblets lose their drag reducing effects. Furthermore, the riblets even increased the surface area interacting with the air above it as compared to the flat plate, this means that overall drag acting on the whole riblet surface increased. Thus, explaining why drag increased so significantly over the 60x60x1000 riblet surface!
We then started looking into running additional simulations at resolutions higher than that of the CNC machines, in the hopes of finding an optimal geometry, leaving the practicality of manufacturing as a secondary consideration. This caused simulation times to go up significantly, as the mesh resolution required for simulation increased significantly. As such, we started running simulations on SimScale, a cloud CFD simulation platform, which allows us to use multiple parallel cores.
As we continue to run the simulations and try to attempt even greater accuracy and similarity to real life, computational intensity becomes a major concern. This means that we are looking towards other software that might be able to meet the requirements of what we have run so far. This software would also need to run faster than typical educational licenses and COMSOL v5.4! Perhaps simulation cloud computing services like Simscale may serve our purposes better.
Attempts at using SIMSCAle
While attempts at running Simscale did initially prove to be meaningful, with our simulations running smoothly and the cloud computing service proving to be much more convenient and less computationally intensive, we realised that the mesh size could not be reduced in a way that would ensure that our optimal geometry riblets could be covered modelled by our mesh. This is likely because at an optimal geometry, with a thickness of only 6 micrometers, our riblets are simply much too small to mesh without extensive computational power. In Simscale, this meant that our riblet surface seemed to disappear into a flat plate under the mesh. After many attempts, we realised that using other computational platforms to run optimal riblet geometries may be less meaningful given that it would be next to impossible to manufacture those riblets anyway.
With that, we have been looking into other shapes that may function better in air and have more realistic geometries to manufacture. This would mean more literature review into other geometries such as those of the golf ball!
DImpled surface simulations
Dimpled surface simulations were run to observe how the dimples help reduce drag. According to theories, there should be a layer of slow-moving air immediately above the surface, followed by a layer of fast-moving air. This layer separation helps to reduce drag and thus, should be observed in the simulations!
In the photo above, it can be seen that there is indeed a layer of air above the plate that passes at a lower velocity. On the other hand, on the non-dimpled plate, the air simply passes over at 40 m/s, as seen in the image below. The lower velocity air over the plate should mean a reduction in drag. Now, all there is left to do is to calculate the drag reduction in numbers.
