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AlbertoArtoni October 22, 2021 05:33

Curle Analogy Function object
I was trying to understand why the Curle analogy is implement as it has been implemented:

p' = \frac{1}{4\pi} \frac{\mathbf{r}}{|\mathbf{r}|^2}\large( \frac{\mathbf{F}}{|\mathbf{r}|}   + \frac{1}{c_0}\frac{d\mathbf{F}}{dt} \large) .

The actual formulation by Curle can be seen as:

p' = \frac{1}{4\pi}\nabla\cdot\nabla\cdot \int_{V} \frac{\mathbf{T}}{r} dV - \frac{1}{4\pi}\nabla\cdot \int_{\partial V} (\frac{p'\mathbf{I}}{r}) \cdot \mathbf{n} d\partial V

I can see that if we are far enough, we can replace the divergence with -\frac{1}{c_0}\frac{\mathbf{r}}{|\mathbf{r}|}\frac{\partial}{\partial t}.

I don't understand:
1) why was the volume term omitted
2) from where the term \frac{\mathbf{F}}{|\mathbf{r}|} comes from.


cmiked June 15, 2022 04:21

OpenFOAM Curle Analogy
1 Attachment(s)
The derivation of the OpenFOAM formulation can be found in the book "Aeroacoustics of Low Mach Number Flows" by Glegg et. al. pg 83.
OpenFOAM accounts only for the dipoles in this formulation.

Furthermore, when calculating the force, OpenFOAM uses only the pressure at given input surfaces since, by default, the convection term is zero at walls for viscous flows. (see attached).

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