[SanFer]

Hello,

I have been experiencing some problems concerning the stability of the solution of an external flow (Mach=0.6) in both steady and transient case solution. The geometry is (nearly) an ellipse revolved around a vertical axis in its middle chord, so that its planform is circular and its relative thickness is 0.2 approximately. Hence, the body does not possess a sharp trailing edge.

I want to obtain a transient solution for a lateral periodic movement (small displacements) of the body, initializing the case with the steady solution.

For the steady solution, once the case reaches convergence, the force monitor in the vertical direction shows an erratic oscillation (approximately 10% of the mean force). That could be reasonable considering the small value of the force (the order of magnitude of the lift coefficient is 1e-3 based on the planform surface), but the oscillation are then also present in the transient simulation. The lateral force shows the expected behaviour (pure sine wave), but since the perturbation are small, the oscillations in the vertical force and the lateral force are of the same order of magnitude.

I am trying to solve the problem using the inviscid equations, density based implicit solved with a second order upwind discretisation method, having tried with different Courant numbers and relaxation factors. I have tried to remesh the trailing and leading edge to capture the stagnation point, and to adapt the mesh based on pressure and Mach number gradients, but the oscillations continue. I do not know if introducing a BL and a turbulence model could alleviate the problem.

If anybody can give me some guidance to get a more stable solution, or knows the reason for this behaviour, I would sincerely appreciate it.

Best regards,

Emilio