Dear all,

I have a question concerning noise-production due to turbulence: How can I calculate Noise from turbulence (esp. turbulent fluctuations)? I can write delta p ~ C rho (u_i)'*(u_j)' (just by dimensionless analysis). But how can I get the frequencies and other values (supposed I have the Reynolds stress tensor eg. from DNS)

Can somebody recommend some literature.

Many thaks for your help

Matthias

To get the corrct frequencey, you need DNS data. Then you may use FFT.

Thanks for the answer, can you recommend some books concerning the theoery and numerical solitions of this problem.

Matthias

If you are solving the compressible Navier-Stokes equations, you have to compute the thermodynamic pressure and hence acoustics are a part of the solution. The accuracy of the acoustic solution depends on the closure model used in case of turbulent flows. If are using a DNS approach, closure is a non-issue and the acoustic solution should be very accurate. You can look into the CTR homepage for some papers (especially those by Prof. Lele).

However, DNS using the compressible Navier-Stokes equations can be very expensive and has to be used only in case of highly compressible (Mach number, M > 0.5) flows. At low Mach numbers, flow dynamics (velocity fields) affect the acoustics but not vice-versa. So the acoustics can be decoupled from the velocity fields and can be computed separately. Also, at low M, acoustics are weak and have a relatively low amplitude. Then a linear solution should be sufficient in most cases.

If a linear acoustic solution suffices, you can use the classical Lighthill approximation discussed in many fluid mechanics books. The source term for the acoustic equation (for the acoustics waves) should include a component arising from turbulent fluctuations of velocity in case of turbulent flows. This is the sequence of steps in this method.

* Compute the velocity and density (or temperature) fields using the incompressible N-S equations.

* Compute the source terms for the acoustic equations.

* Solve the acoustic equations.

There is a paper by Karen Pao and Phil Collela that discusses this approach. I am not sure where it is published but you can find it in Pao's homepage (which has a link from Collela's homepage at LBNL). Note that the pressure waves have very high speeds (relative to fluid velocities) and have to integrated using small time-steps. The above approach circumvents this problem by using a mesh coarser than one used to compute velocities for the pressure. Grid spacing for pressure equations, in general, should depend on the highest acoustic wavenumber that needs to be resolved.

I am not sure you can use dimensional arguments here since acoustics are associated with compressible flows which is not necessarily the case with turbulence. If you use dimensional analysis, any dependence on \gamma (ratio of specific heats) and Mach number, quantities that relate to the compressibility of the medium, can not be captured. This is due to the fact that both quantities are non-dimensional.

Thanks for your good ideas,but I want to ask that can you give me the whole website of CTR homepage and Pao's homepage and Collela's homepage.Thanks again!

Hi Aim

CTR-URL is: http://ctr.stanford.edu/

The following is Karen Pao's web page. The papers you need are available in PDF and postscripts formats.

http://www.c3.lanl.gov/~kip/

Thanks a lot

Thanks

Can you tell me the detail about the source term of acoutics equations, and where can I find some infomations about the acoustics equations.