COMSOL 6.4 - Test Bench Car Interior

In this application, a point source generates a pressure wave in the Sound Brick, a test bench car interior (Ref. 1). The sound pressure level is measured at another point and at a range of frequencies high enough that a good mesh resolution is required to properly resolve the wave. To get an idea of the accuracy of the model, the sound pressure level response is studied using four different mesh resolutions.

Model Definition

The geometrical and material parameters in this model come from Ref. 2. The geometry of the Sound Brick is shown in Figure 1. The model solves for the acoustic pressure p in the frequency domain using the Pressure Acoustics, Frequency Domain interface.

A monopole point flow source of strength Q S = 10−5 m3/s located at the point R0 = (0.21, 0, 1.28) drives the system. The walls of the Sound Brick are assumed to be perfectly reflecting and have the default sound hard boundary condition. The sound pressure level is measured at the point R1 = (1.34, 1.22, 0.8) at a range of frequencies from 743 Hz to 745 Hz.

Figure 1: The geometry of the test bench car interior.

The dimensions of the test bench car are length × height × depth = 3.0 m × 1.4 m × 1.7 m. The windshield has its lower end 0.8 m above the floor and with an inclination such that the entire volume of the geometry is 6.5 m3.

Results and Discussion

Figure 2 shows the instantaneous pressure distribution in the car interior at 745 Hz.

Figure 2: Isosurface plot of the pressure distribution at 745 Hz, for the coarsest one of the 4 meshes used in the model.

A direct comparison of the computational results with those published in Ref. 2 is difficult for two reasons:

•

The sampling frequency is too small to resolve some of the resonances at the higher frequencies

•

The amplitude for the point source is not given

Nevertheless, it is possible to examine the accuracy of the results by studying how they converge when using successively greater mesh resolutions.

To provide an idea of the accuracy of the various solutions, Figure 3 shows the measured sound pressure level between 743 Hz and 745 Hz, computed at 0.005 Hz intervals for the listed mesh resolutions. The plot can be reproduced by changing the frequency resolution from 0.05 Hz to 0.005 Hz when following the Modeling Instructions. As you can see in the plot, all the curves follow each other except at the dips and peaks, where the curves predict slightly different frequencies for the resonances. This is an idealized setup where there is no sources of damping, so a perfect resolution in space and time would result in infinite sound levels in the peaks and absolutely no sound in the dips. In real-life applications, the extremes would be much less pronounced than in the plot because the sound sources are rarely point-like and the walls are usually not perfectly reflecting. In such cases, you can expect a similar solution accuracy at the peaks and the dips as in between them.

Figure 3: Sound pressure level (dB) at the point of measurement as a function of frequency (Hz) for a few different mesh densities. The legend shows the maximum mesh element size in fractions of the wavelength L.

Notes about Modeling in COMSOL Multiphysics

In general, 5 to 6 second-order elements per wavelength are needed to resolve the waves. In the case treated in the step-by-step instructions, you generate the initial mesh by specifying a maximum element size of λ/5, where λ = c/f is the free-space wavelength of the sound waves at 745 Hz. After showing how you to set up, run, and analyze the model with this mesh, the instructions take you through the mesh convergence study. As it is seen from this model, depending on the level of accuracy desired, 5 second-order elements per wavelength is not always fine enough to get accurate resonances. When a model has sharp resonances or it has small geometry details, the mesh should be finer. Therefore it is always recommended to do a mesh convergence study when performing simulations, as is done in this model. Moreover, as it is clear from this model, having a fine enough frequency resolution is also important as it is clear that the two solutions match well between the resonances.

It is good simulation practice to perform a mesh convergence analysis to be sure that the obtained results have converged.

References

1. The Sound Brick is located in Acoustic Competence Centre, Graz, Austria
http://portal.tugraz.at/portal/page/portal/TU_Graz

2. A. Hepberger, H. Priebsch, W. Desmet, B. Van Hal, B. Pluymers, and P. Sas, “Application of the Wave-Based Method for the Steady-state Acoustic Response Prediction of a Car Cavity in the Mid-frequency Range,” Proceedings of the International Conference on Noise and Vibration Engineering, ISMA2002, Leuven, Belgium, pp. 877–884, 2002.

Acoustics_Module/Automotive/test_bench_car_interior

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

In the window, click

In the tree, select > > .

Click .

Click

In the tree, select > .

Click

Global Definitions

Now, either enter the parameters used for the model manually or load them from the file test_bench_car_interior_parameters.txt.

Parameters 1

In the window, under click .

In the window for , locate the section.

In the table, enter the following settings:


Name	Expression	Value	Description
rho0	1.2[kg/m^3]	1.2 kg/m³	Air density
c0	343.8[m/s]	343.8 m/s	Speed of sound in air
f0	745[Hz]	745 Hz	Highest frequency used in the model
L	c0/f0	0.46148 m	Shortest wavelength
S	1e-5[m^3/s]	1E-5 m³/s	Flow source strength

You will use L, the wavelength corresponding to the highest frequency, when defining the mesh size.

Import the geometry of the test bench car interior from a file.

Geometry 1

Import 1 (imp1)

In the toolbar, click

In the window for , locate the section.

Click

Browse to the model’s Application Libraries folder and double-click the file test_bench_car_interior.mphbin.

Click

Create two points, one for the source and one for the receiver.

Point 1 (pt1)

In the toolbar, click

and choose .

In the window for , locate the section.

In the text field, type 0.21.

In the text field, type 1.28.

Point 2 (pt2)

In the toolbar, click

and choose .

In the window for , locate the section.

In the text field, type 1.34.

In the text field, type 1.22.

In the text field, type 0.8.

Form Union (fin)

In the window, click .

In the window for , click

Click the

button in the toolbar.

Materials

Material 1 (mat1)

In the window, under right-click and choose .

Select Domain 1 only.

In the window for , locate the section.

In the table, enter the following settings:


Property	Variable	Value	Unit	Property group
Density	rho	rho0	kg/m³	Basic
Speed of sound	c	c0	m/s	Basic

Pressure Acoustics, Frequency Domain (acpr)

In the window, under click .

In the window for , click to expand the section.

From the list, choose .

Monopole Point Source 1

In the toolbar, click

and choose .

Select Point 5 only.

Point 5 is the one on the geometry’s front wall.

In the window for , locate the section.

In the QS text field, type i*S.

Introducing a phase shift by multiplying the source strength with the imaginary unit gives nonzero pressure plots at the default zero value for the complex pressure variable’s phase. You can also here simply enter S in the QS text field and then enter pi/2 for the phase ϕ.

Mesh 1 - L/5

In general, 5 to 6 second-order elements per wavelength are needed to resolve the waves. For more details, see Meshing (Resolving the Waves) in the Acoustics Module User’s Guide. In this model, start by using 5 elements per wavelength and set up the mesh manually to get a structured swept mesh. This will lead to fewer degrees of freedom to be solved for. Proceed by directly adding the desired mesh component.

In the window, under click .

In the window for , type Mesh 1 - L/5 in the text field.

Swept 1

In the toolbar, click

Size

In the window, click .

In the window for , locate the section.

Click the button.

Locate the section. In the text field, type L/5.

Swept 1

In the window, click .

In the window for , click to expand the section.

Click to select the

toggle button.

Select Boundary 2 only.

Click

Study 1

Step 1: Frequency Domain

In the window, under click .

In the window for , locate the section.

In the text field, type range(f0-2,0.05,f0).

In the window, click .

In the window for , type Study 1 - L/5 - Direct Solver in the text field.

Solution 1 (sol1)

In the toolbar, click

In the window, expand the node.

Enabling the will reduce both running time and memory consumption. This option is good for pressure acoustics models that do not include nonlocal couplings.