This set of OpenFOAM simulations concerns laminar flows around a sphere at various values of Reynold's numbers. This case has been done with air as a working fluid and around a sphere with a diameter of 1 meter. For validation on the simulations I kept track of the drag coefficients and compared them to experimental values.
The scope of this set of simulations is just the laminar range of flows, so no turbulence modelling is needed. Thus, I only completed simulations in which the Reynold's number dosen't exceed more than a couple of hundreds.
A great way of validating simulations is measuring a certain flow value of intrest, which in this case is the drag coefficient, and comparing those values to experimental ones.
The drag coefficient commonly denoted as
It is mathematically defined as:
The picture below represents the relationship of the drag coefficient and the Reynold's number.
The region of intrest for this project is up to about the Reynold's number of 300. The rest will be the topic of a different project available here.
The geometry consists of a sphere with a diameter of 1 meter in the centre of a square with sides of 10 meters. I created this simple geometry in Blender and exported it as a set of .STL files. Each .STL file coresponds to a patch with distinct boundary conditions, and this format is very well optimized for work with OpenFOAM and particularly with the snappyHexMesh meshing tool it provides.
I made the mesh with the snappyHexMesh utilitty, and all of the parameters i used can be found in the Mesh folder.
In short, I added a bit of refinement to the walls and more refinement to the region close to the sphere, and on top of that added some inflation layers to the sphere (this will be more usefull in the turbulent set of simulations). Here's a view of a slice of the mesh in the proximity of the sphere:
The mesh consists of 173368 hexahedral cells, 6488 polyhedral cells and 72 prismatic cells. The average and maximum non-orthogonality values of the mesh are 6.53 and 41.58 respectfully, so there will be no need to use non-orthogonal correctors while solving the simulations. The maximum skewness is 0.49, which is completely fine.
For each case, I first did a simulation with the potentialFoam solver to obtain a solution that will be used as an initial field in the other part of the simulation. This solver is only suitable for inviscid, irrotational and incompressible flows, but it is still very usefull for a giving us a decenst first estimate of the flow fields.
After that i used the pisoFoam solver with two corrector loops and zero non-orthogonal correctors. For the discretization schemes i focused on accuracy by using limited linear divergence schemes and least squares for the gradient schemes. All of these details can be found in the proper system directory.
For tracking the values of the drag coefficient I used runtime postprocessing with a function object forceCoeffs (can be found in the system folder). I used a jupyter notebook (also available in this repo) to plot theese values.
All of the values are very close to the experimental values and thus I conclude that the simulations are accurate.