Hello,

I'm an engineering student involed with a CFD project. In this project I use a code that performs the simulation of external, viscous, compressible flow at low Mach numbers. Now I'm interested in calculating the acoustic field using my output pressure field but I don't know how! Maybe it can be a very basic question, but I could not found how to do it.

Thanks for the attention.

You want to use the velocity, pressure and density distribution on a closed surface surrounding your object, there are 2 methods, onr called the Kirchhoff, the other Ffowcs Williams - Hawkings. They allow you to calculate the pressure perturbation anywhere outside the above-mentioned closed surface, even outside your computational surface. You should find plenty of info on the WEB about it, or in that new journal called IJA or International Journal of Aeroacoustics

Fred

The alternative to Ffowcs-Williams or similar is direct calculation of the acoustic signal. Find the time averaged mean pressure level at the observer's position (inside the computational domain), then the fluctuation around that mean with time is your 'signal'. Transform this pressure v. time signal into the frequency domain via a Fourier transform to extract the amplitudes of the component frequencies.

The drawback with this method is that it takes a lot of mesh to resolve the acoustic waves.The rule of thumb is cell size=lambda/6 (some say lambda/10), where lambda is the wavelength of the highest frequency you want to resolve.

Smith, Is lambda=speed of sound/highest frequency ?

Yep,and remember you have to keep (at least) this cell size at every point between the source and the observer,otherwise you loose information

any advics book which involves this calculations student

Perhaps not only that, you need also a code that doesn't eat all your pressure waves for dinner within a couple of wavelengths (like most commercial FV codes do) when the amplitudes of the perturbations are so small that they usually are in acoustic applications. In other words, you need high-order discretization to track the waves.

Interesting comments!

Our experience with RADIOSS-CFD is that provided you have 10 elements per wavelength, the code is able to propagate acoustic pressure waves without significant damping. Our Finite Element which is 2nd order accurate.

This is now substantiated by quite a few results, some of them being posted on our web site www.mcube.fr under the M3/publication and under the M-Explicit example section.

Dimitri

I have seen the results on the homepage earlier, and it is probably true that FEM is better suited for wave propagation problems even using lower-order schemes (2nd). At the same time, 2nd order discretisation in itself may not be sharp enough to extract the correct aeroacoustic SOURCES, especially not the broadband ones, unless you use LES or DNS. In other words, whatever the code spits out in terms of noise sources, you will be able to track fairly - but what really DID you track? But then again, tonal noise generation may the the code be well suited for.

Anders,

Yes indeed, we use LES turbulence scheme which is very well suited to our explicit time integrator. We agree with you that this is much better than a RANS scheme that would propably damp out quite a few frequencies.

One of the code main interest is the capability to visualize sources. This is key to the success of numerical simulation in this field in our opinion.

Dimitri

The calculation of the acoustic waves is not easy like what you said. In fact, comutational aeroacoustics is becoming a new, challenging research field currently. Please note computational aeroacoustics is not fully the same as CFD!!!!