Rayleigh Streaming Simulation Using The Vorticity Transport Equation
Open Access
- Author:
- Sastrapradja, Debbie
- Graduate Program:
- Acoustics
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- October 06, 2004
- Committee Members:
- Victor Ward Sparrow, Committee Chair/Co-Chair
Anthony A Atchley, Committee Member
Philip John Morris, Committee Member
Cengiz Camci, Committee Member - Keywords:
- Rayleigh streaming
acoustic streaming
nonlinear acoustics
vorticity transport equation
stream function - Abstract:
- One part of understanding thermoacoustic devices involves studying a physical phenomenon called acoustic streaming, a steady fluid flow induced by oscillating acoustic waves. Current numerical calculation of acoustic streaming can involve major computing time and resources. In order to develop a quicker model, the vorticity transport equation (VTE) is used. The goal of using the VTE is to obtain a relatively fast solution with minimal computational resources, which in this case is a single PC. The intent of this method is that it is used in the early design stage of thermoacoustic devices where preliminary (although less detailed) fast results are desired. It is also preferred that the computing power be minimized as not to tie up other resources for the optimized design of thermoacoustic devices. The most well known type of acoustic streaming, Rayleigh streaming, is simulated using the VTE method. A clustered grid is utilized to capture the boundary layer effect on the acoustic streaming. The governing equations used are the VTE, Poisson's equation, and an equation that relates the stream function with the velocity. The outline of the method of calculation involves (i) generating a clustered grid and ensuring there are enough points in the boundary layer, (ii) transforming the clustered grid into the uniform computational grid, (iii) transforming the governing equations to account for the clustering, (iv) calculating the vorticity and the stream function at each grid point using a Direct Method, and (v) calculating the acoustic streaming velocity using the stream function. Steps (iv) through (v) are repeated until the solution converges. It is demonstrated that the VTE method to calculate Rayleigh streaming works well. There are two cases being simulated in the research, a parallel plate case and a cylindrical tube case. The numerical results agree with the analytical results for both cases, although there are some discrepancies in the cylindrical tube case. At this time, no numerical reason can be given to explain the discrepancies. The goal to perform the simulation fairly quickly with a single PC has been achieved.