[wc3speler]

Dear forum,


I'm trying to find the acoustic field induced by a pair of co-rotating vortices. This should be a spiral pattern, like in the attachment. To test things I use Lighthill's classical analogy.

Set-up
The velocity and pressure fields are governed by the unsteady bernouilli equation. For this case an analytical expression for the flow field exists [1,2]:

U - i*V = gamma*z / ( i * pi * (z^2 - b^2) )

with z = x + i*y and b = r0*e^(i*angularSpeed*t) where r0 is the half distance between two vortex cores = 1 meter. The flow pressure is not needed for Lighthill so I've omitted it here. I have implemented this and set the parameters as in the references (speed of sound = 1 m/s, core radius = 0.1m, rho = 1 etc). Within a distance of 0.15 m of the center of each core the velocity field is replaced by the Scully vortex core model. This prevents the velocity from becoming very large in a core's center (the case has very steep gradients) and should allow one to use a very fine grid to accurately represent the acoustic source (e.g. page 90 of [1]).

Problem
I observe an odd behaviour of the acoustic source term and resulting acoustic field when I refine the mesh.

• Mesh 1: 162 x 162 (uniform) cells on a rectangular domain of 200 x 200 m. Result: spiral pattern, pretty close to exact wavelength, but wrong amplitudes and phase.
• Mesh 2: 324 x 324 (uniform) cells on the same domain. Result: spiral pattern is gone, the source term grows bigger. Further refining to 500 cells makes it even worse.
• Mesh 3: When the source region is made very fine (the inner 6 x 6 meter) as suggested in [1], my source term has blown up (values of ~100, while it should be << 1)

When I used my LEE solver, I found the same behaviour of fine mesh = bad results. How can I prevent the above from happing? Or did I implement something incorrectly?

For convience, I've uploaded my case here: https://www.dropbox.com/sh/5qthfm2dp...raFqAXvCa?dl=0
cvLighthill.C is the solver, which includes at each time step corotatingVortices.H to generate the flow field. Suggestions are more than welcome!


Jurriaan

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[1] Phd dissertation of M. Escobar: Finite Element Simulation of Flow-Induced Noise using Lighthill’s Acoustic Analogy
[2] Phd dissertation of W.J. Zhu: Aero-Acoustic Computations of Wind Turbines

[Esmaeelef]

Dear Jurriaan,

I know that it is a long time since you have posted this issue for modelling co-rotating vertices with OpenFOAM. I am now trying to model the same co-rotating vortices with OpenFOAM solvers. I am observing the spiral pattern, however there is some difference in the amplitude of acoustic wave of my result and that of analytic solution, regardless of the mesh size I use. I was wondering if you could solve this issue and if so could kindly give me some suggestions to resolve this issue.

Thank you in advance
Kind Regards
Esmaeel