Discussion Forum

Dear COMSOL community,

I am performing 3D external flow simulations at high Reynolds numbers (10^6 - 10^8) using RANS turbulence models such as SST. I am trying to validate the turbulence models and mesh with known published data on airship or submarine design (you can see the design of the rotationally symmetrical objects I am using in the .png file).

I am finding that my simulation results tend to underestimate the viscous component (frictional drag) and overestimate the pressure component of drag. I am performing mesh sensitivity studies, to refine its resolution and distribution. I am also trying to stick to the good practises of meshing, like using y+ values close to 1, with the purpose to achieve more accurate calculation of the shear stresses on the walls. Reducing the size of the mesh at the wall boundary and reducing the size of the boundary layer mesh increases the value of the skin friction component and also causes the pressure drag to reduce. I started with a proportion of skin friction to total drag (Cf / total Cd) of 31% and I have raised it to 71%.

From the theory, I know that a streamlined 3D object (like a submarine hull) should have a very high skin friction drag component, but I don’t really have a solid value to aim for because there is no way to measure the experimental value of the skin friction drag. Hence, my references for this value are the different formulas based on the turbulent boundary layer of a flat plate (e.g. Schoenherr) or others that include some modifications that account for experimental data (like the ITCC 57 formula). Depending on which one I use I get slightly different theoretical skin friction drag coefficients and hence the proportion of Cf / total Cd is also variable (from 82% to 89%). I have read literature reviewing this topic and I’ve read that boundary layers of 3D slender objects don’t behave like those of a flat plate, and skin friction calculated using this formulas could be underestimating this drag component. So, I am aware this formulas are only approximations.

I’m not really sure if I have to “aim for a value” of skin friction close to any of the theoretical formulas, or it is a case of refine (focusing on walls and boundary layer elements) until I reach a stable result of skin friction in my simulations (that changes less than 1% between refinements) and consider that solution mesh independent.

The limitation I am finding is that working on 3D, after certain level of refinement my simulations are taking a long time to converge or do not converge at all...so at the moment, I am stuck on that 70% of Cf / total Cd (which I know is still not mesh independent) and I am not sure if I will be able to improve it.

I have noticed in many CFD literature that results usually show only the total drag coefficient and not the skin friction / pressure components. I don’t know if it is a case of CFD calculations not being able to accurately calculate the skin friction in 3D models? (maybe because of computational demands?). I want to be able to use the program to calculate the skin friction, and not a formula, but I want my results to be consistent with the underlying physics. Therefore: I have to match the total experimental values of Cd, but at the same time the internal distribution of the drag components have to be reasonable and agree with the physics.

The validation I am doing is an starting point to test other (also slender but geometrically more complex forms) and I want to use this simple ones to “calibrate” my settings, so I can trust my results.

Is there someone working with flow over slender bodies using COMSOL CFD that could advise me on which turbulence model and mesh refinement strategy to follow to better reproduce the physics, please? Is it possible to accurately predict the skin friction drag in 3D objects? Any advice or comments will be much appreciated!

Thank you.