# Simcenter 3D Solutions Verifying analytical results of Transmission Loss of a Simple Expansion Chamber from text book problem with Simcenter 3D Acoustics results

2024-06-25T10:25:02.000-0400
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## Summary

An example problem from well known book from Munjal is solved using Simcenter 3D Acoustics and TL curve is compared. It is observed that both the results of TL curve very well match and the analytical results are verified.

## Details

Below text book is referred -

Noise and Vibration Control by M L Munjal, IISc Lecture Note Series, IISc press

Example 5.1 on Pg 170 in above Text book.

This example  contains geometry of a simple expansion chamber with all the geometric dimensions such as exhaust and tail pipe length, radius and length of expansion chamber etc. are defined. The solution contains Transmission Loss (TL) formula with which one can evaluate frequency at known TL value. The TL curve in frequency range of 0 to 1200 Hz is shown on Pg 169. It is required to find out lowest frequency range in which the TL is at least 10 dB.

It is intended to verify the TL result with that from Simcenter 3D Acoustics.

Problem:

Verifying Transmission Loss results of a Simple Expansion Chamber from text book problem with Simcenter 3D Acoustics results.

Solution

The geometry of the simple expansion chamber is built with exact dimension given in Simcenter 3D Modelling application.

The geometry is used to create fem and sim file and meshed with hexahedral elements with appropriate element size. Air is used as material for the fluid domain. Three microphone point locations are created, two at inlet and one at outlet in the fluid domain.

Solver is Nastran FEM and analysis type is Acoustic.

Following boundary conditions and loads are used –

Load at Inlet: Unit panel normal velocity (-1 m/s)

Outlet: Automatically matched layer (AML)

All other walls of the muffler are assumed as reflective. SOL 108 Direct  frequency response is created with frequency range of 0 to 1200 Hz and output is requested for acoustic pressure in SORT 2 format. Since three mic points are created in the mesh, the solver automatically gives TL function plot in the results.

The model is solved with 4 processors in parallel and results are postprocessed as shown below.

TL is 10 dB or more in the frequency range 137 and 445 Hz as seen in above plot.

From above we see that the results from Simcenter 3D Acoustics are matching very well with the text book problem and the TL equation is verified.

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