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Hello to all!

I am trying to simulate the pressure attenuation in cylindical pipes. I was expecting to get results similar to the analytical expression, but they are way too different.

The analytical expression for the attenuation coefficient is

,

where is the angular frequency of the wave, and are the viscosity and density of the fluid inside the pipe, is the speed of sound in the fluid, is the specific heat ratio and denotes the Prandtl number.

To calculate the value of the final pressure, it is used the analytical expression

,

where is the attenuation coefficient, is the lenght of the pipe in which the pressure is wanted to be calculated and is the reference pressure.

I ran the simulations using 4 different interfaces with 2D Axyssimetric geometry in COMSOL 5.5

• Pressure acoustics, Transient (with viscous fluid model)
• Pressure acoustics, Transient (with thermally conducting and viscous model)
• Linearized Navier-Stokes, Transient
• Thermoviscous Acoustics, Transient

For a pipe filled with air (at atmospheric pressure) with a diameter excited with a single gaussian pressure pulse with a peak of and a standard deviation of , the analytical pressure, in is .

The results in the simulations were

• Pressure acoustics, Transient (with viscous fluid model) -
• Pressure acoustics, Transient (with thermally conducting and viscous model) -
• Linearized Navier-Stokes, Transient -
• Thermoviscous Acoustics, Transient -

I do not know why the numerical results are so different from the analytical. The mesh is already very fine.

Does someone have any idea of what can be causing this difference, or if I am missing something?

Sincerely thanks,

Bruno