How can we use CFD to help in making acoustic design change for automotive exhaust system?

(1). There are two areas: (a). the engine exhaust pipe system for 4-stroke engine,to reduce the exhaust pressure by fine tuning of the waves in pipe system, (b). the muffler system to even out the pressure waves. (2). I think, both have been studied by 1-D wave equations. You could make it more complicated by studying 2-D or 3-D unsteady, compressible flow solutions. (3). I am not sure that 2-D, or 3-D will make the study of the flow behavior more accurate or realistic. The primary feature is the wave propagation and the wave interaction.(the pressure waves)

Do the normal CFD codes like FLUENT have the wave equation in them?

(1). It has a 3-D transient compressible Navier-Stokes code,which I think, is required to do the pressure wave simulation.

Use of CFD codes for acoustic wave propagation can be carried out succesfully. However, a very fine grid and timestep are required. Typically, with a second order code like Fluent you require at least 50 gridpoints per acoustic wavelength. This is due to the excessive dispersion and dissipation characteristics of the scheme used. Upwind differencing schemes are inherently dissipative, so very efficient at damping out acoustic waves. Not good if that's what you're trying to capture.

Also, in order to obtain a reasonable spectrum you will need to run the unsteady simulation for long enough to be able to capture several periods of the oscillation.

A MAJOR problem is that of non-reflecting boundary conditions. For an internal flow this isn't really a problem, but if any of the grid extends to freespace you will require a special non-reflecting condition. Otherwise acoustic waves will reflect from the boundary. You will not see these waves when plotting pressure contours, as acoustic waves are up to 5 orders of magnitude less than hydrodynamic pressuures. To try and get around this without specifically writing a new boundary condition, you can just put a stretched block at the outer boundary that goes to a very coarse resolution at the far edge. This will then use artificial viscosity to damp out any outgoing waves. The symptoms for this not working are that the simulation works for a transient period but then blows up.

You will only see the acoustic waves if you plot around +/-100 Pa of the mean pressure, so you'll have to reset the contour levels for pressure when visualising the results.

Good luck, hope this is of use. Cheers, Dr Kenji Takeda University of Southampton www.soton.ac.uk/~ktakeda

(1). If one starts the modeling from the exhaust valve side of the engine, the pressure wave is likely to be somewhat stronger than the "acoustic" waves as the exhaust gas leaves the exhaust valve into the exhaust pipe. (2). If one removes the muffler from the exhaust pipe, that pressure wave will create very loud noise, much higher than the "acoustic" waves. (3). Well, you are right to point out that numerical scheme used can affect the accuracy of the transient solution. The low Mach number can also pose another problem for transient compressible flow formulation.