COMSOL 6.4 - Acoustics in a Single-Family Home

The study of acoustics over several floors in a building can give essential information for industrial settings with machinery but also for dwellings. Especially, the noise level caused by constant sources is a valuable quantity to evaluate whether an environment is acoustically comfortable or not. Problems with such a large geometry scale are best modeled with the acoustic diffusion equation, which makes use of the high-frequency limit to assume a perfectly diffuse sound field (see Ref. 1 and Ref. 2).

This tutorial model shows the basic steps and principles used when setting up a model using the Acoustic Diffusion Equation physics interface. In the model, the acoustics of a single-family home is investigated. The model setup includes studies for steady state, eigenvalue, and transient analyses. This allows to derive the sound pressure level distribution and reverberation times in the different rooms. The sound pressure level radiated outside the house is also determined with a manual coupling to the Ray Acoustics physics interface.

Model Definition

In this model the acoustics of a generic single-family home is analyzed over broadband frequency. It is a two-story house consisting of 10 rooms, as depicted in Figure 1. The rooms are coupled with each other either by defining the transmission loss of the partition between them or by forcing continuity in the sound field. Two types of partitions are defined in this model, namely light and heavy, with transmission losses of 5 dB and 10 dB respectively. Wall boundary conditions are entered as absorption coefficients, with values assumed to be realistic for the materials in the model (Ref. 3). The acoustic mean free path in each room is also calculated with a simple equation based on the room volume and surface area from Ref. 4. For complex geometries, however, the mean free path should be measured or estimated from a separate detailed model. A monopole point source is located in the living room at the coordinates (xs, ys, zs) and radiates with a power Ps. These are parameters found under > .

Three studies with the Acoustic Diffusion Equation physics interface are performed to assess the acoustic conditions inside the house. The first one is a stationary study, returning sound field properties caused by constant emission from the source. The second study investigates the eigenvalues in the problem to analyze the modal behavior of the model. The last study looks into the transient decay of sound when the constant source is turned off. Following these, a fourth study investigates the sound field outside the house thanks

to the Ray Acoustics physics interface. The outdoor area on one side of the house adjacent to the living room is considered.

Figure 1: Geometry of the single-family home.

The coupling between the Acoustic Diffusion Equation and the Ray Acoustics interfaces is done manually. Sound is assumed to be radiated uniformly from the two windows closest to the source. The sound power incident on each window is then calculated from the stationary study and used as input to the Release from Boundary feature in Ray Acoustics. Transmission loss through the windows is also applied to obtain the correct total power radiated.

Results and Discussion

The sound pressure level (SPL) caused by a constant source is depicted in Figure 2 on slices and in Figure 3 on the boundaries of the model. It is naturally seen that the highest SPL is found in the rooms closest to the source, especially the living room and the staircase which were coupled together with a continuous sound field. The decrease in SPL as rooms get further from the source is due both to transmission loss through partitions and to absorption within rooms.

Figure 2: SPL on horizontal slices of the model.

Figure 3: SPL on the boundaries of the model.

The energy distribution in the house can also be studied by means of sound energy density as plotted in Figure 4. The linear scale of this quantity makes it more suited to analyze the direct surroundings of the source, as opposed to the logarithmic scale of the SPL. Due to its location close to a corner, the radiation pattern appears as if the source was broader than a single monopole point.

Figure 4: Sound energy density in the house with a constant source.

In addition to energy distribution, the local energy flux through the house is represented in Figure 5. The location of the point source is naturally seen as the origin of the energy flux, and the propagation to adjacent rooms and up the staircase is clearly visible. While this result could easily be anticipated given the simplicity of the study case, such an analysis can give valuable information in a more complex setting.

Figure 5: Energy flux through the house caused by a point source.

The reverberation times T60 shown in Figure 6 were obtained from Eyring–Norris formula

(1)

with V the volume of the given room, c the speed of sound, A the absorption area of the room, and ma the air absorption constant. The study was carried out for broadband frequency, resulting in one value for each room. The reverberation times found lie between 0.3 s and 0.65 s. These are coherent values given the small volumes of the rooms in the house.

Figure 6: Eyring–Norris reverberation times of the rooms.

The eigenvalue study allows to investigate the modes in the building. For example, the third sound energy density mode is displayed in Figure 7. It shows that two adjacent rooms on the first floor are excited together at the eigenvalue λ = 23.45 rad/s. The eigenvalues describe the exponential decays of the modes, they are therefore directly linked to the reverberation times of the rooms or groups of coupled rooms through the formula T60 = 55.3/4λ. The relation between the first ten eigenvalues and reverberation times is given in Table 1. Use the table in combination with the figure to identify the reverberation times of the different spaces.

Figure 7: Sound energy density mode at λ = 23.45 rad/s.

Table 1: First ten eigenvalues with their associated reverberation times.
Eigenvalues (rad/s)	Reverberation times (s)
21.66	0.638
22.89	0.604
23.45	0.589
26.95	0.513
28.35	0.487
31.85	0.434
32.75	0.422
35.91	0.385
36.58	0.378
46.59	0.297

The transient behavior of the house can be investigated by modeling the constant source being turned off. With this technique, the normalized SPL in a room becomes a measure of the sound energy decay, as represented in Figure 8. The decay curves appear as straight lines due to the underlying assumption of a perfectly diffuse sound field.

Figure 8: Energy decay curves from three different rooms.

The rays emitted from the two radiating windows are depicted in Figure 9 after 3 ms. This type of plot can be helpful to visually inspect radiation and reflection patterns. In the present case, the hemisphere radiated into appears to be sufficiently sampled. Moreover, the total source power of each window was calculated from the incident power on their inner surface. It is then logical to find that the window closest to the source emits the largest power. The analysis of reflections is, however, limited. The outdoor area next to the house was modeled as a domain bounded by air and without any obstacle. Therefore, only few reflections at most can happen before a ray disappears into an air boundary.

Figure 9: Ray location and power after 3 ms.

The SPL on the ground surface resulting from the window radiation is shown in Figure 10. The SPL on the inner boundaries of the house is also represented for comparison. With the lack of reflections from obstacles, the highest SPL is found in front of the house at 87 dB. The effect of the transmission loss through the windows is also clearly seen from the large drop between the interior and the exterior of the living room.

Figure 10: SPL on the house boundaries and on the ground surface outside the house.

Notes About the COMSOL Implementation

The studies in this tutorial were performed for broadband frequency. Nevertheless, the Acoustic Diffusion Equation interface allows to set up models in octave bands, 1/3 octave bands, as well as custom bands defined by the user.

The stationary solution computed first was later used as input to a time dependent study and to a ray tracing study. This process is done under > in the study steps by selecting > , > , and > . Remember to disable all sources in the time-dependent study step by enabling the option, and to disable the Acoustic Diffusion Equation interface in the ray tracing study step.

The Release from Boundary feature requires two numbers to determine the emission of rays. The controls the number of points created to discretize the radiating surface. Rays are released from every of these points. Then, the dictates the number of rays released by each point. As a consequence, the total number of rays in the feature is the product of these two numbers. For a detailed guide on how to set up the Ray Acoustics physics interface in the context of room acoustics see the Small Concert Hall Acoustics model, also included in the Acoustics Module Application Library.

References

1. R. Schroeder, “New method of measuring reverberation time,” J. Acoust. Soc. Am., vol. 37, pp. 409–412, 1965.

2. V. Valeau, J. Picaut, and M. Hodgson, “On the use of a diffusion equation for room acoustic prediction,” J. Acoust. Soc. Am., vol. 119, p. 1504, 2006.

3. T.J. Cox and P. D’Antonio, Acoustic Absorbers and Diffusers: Theory, design and application, 2nd ed., Taylor and Francis, 2009.

4. J. Pujolle, “Les différentes définitions du libre parcours moyen du son dans une salle,” Revue d’Acoustique, vol. 36, pp. 44–50, 1976 (in French).

Acoustics_Module/Building_and_Room_Acoustics/one_family_house

Modeling Instructions

This section contains the modeling instructions for the model. They are followed by the Geometry Modeling Instructions section.

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

The geometry is set up by importing a geometry sequence. The sequence imports the one-family house geometry, including parameters for source location and power, and sets up several selections. The predefined selections simplify the rest of the model setup.

Geometry 1

In the toolbar, click and choose .

Browse to the model’s Application Libraries folder and double-click the file one_family_house_geom_sequence.mph.

Import 1 (imp1)

In the window, under > click .

In the window for , click

Click the

button in the toolbar.

In the toolbar, click

Click the

button in the toolbar.

Global Definitions

Import the model parameters from text files. The parameters include the source location and power, as well as boundary conditions for the surfaces and partitions.

Parameters 1 - Source

The parameters for the source location were defined in the geometry-sequence file. Add a parameter for the source power.

In the window, under click .

In the window for , type Parameters 1 - Source in the text field.

Locate the section. In the table, enter the following settings:


Name	Expression	Value	Description
P_s	0.1[W]	0.1 W	Source power

Parameters 2 - Indoor Boundaries

In the toolbar, click

and choose > .

In the window for , type Parameters 2 - Indoor Boundaries in the text field.

Locate the section. Click

Browse to the model’s Application Libraries folder and double-click the file one_family_house_parameters_indoor.txt.

Add Material

In the toolbar, click

to open the window.

Go to the window.

In the tree, select > .

Click the right end of the split button in the window toolbar.

From the menu, choose .

In the toolbar, click

to close the window.

Proceed to set up the physics of the model. Broadband frequency is considered in this case, which is also equivalent to single frequency. Each room is defined with absorption coefficients on its boundaries and a mean free path. The rooms are then coupled with each other by applying transmission loss or sound field continuity on the partitions they have in common.

Acoustic Diffusion Equation (ade)

Select Domains 2–12 only.

Room 1

In the window, expand the node, then click .

In the window for , locate the section.

Click

Select Domain 5 only.

Wall 1

In the window, expand the node, then click .

In the window for , locate the section.

From the list, choose .

Locate the section. In the α text field, type a_wall.

Room 1

In the window, click .

Wall 2

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. In the α text field, type a_window.

Room 1

In the window, click .

Wall 3

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. In the α text field, type a_floor.

Room 1

In the window, click .

Wall 4

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. In the α text field, type a_ceiling.

Room 2

Right-click and choose .

In the window for , locate the section.

Click

Select Domain 8 only.

Room 3

Right-click and choose .

In the window for , locate the section.

Click

Select Domain 7 only.

Wall 3

In the window, expand the node, then click .

In the window for , locate the section.

From the list, choose .

Locate the section. In the α text field, type a_stairs.

Room 4

In the window, under > right-click and choose .

In the window for , locate the section.

Click

Select Domain 9 only.

Room 5

Right-click and choose .

In the window for , locate the section.

Click

Select Domain 4 only.

Room 6

Right-click and choose .

In the window for , locate the section.

Click

Select Domains 3 and 10 only.

Room 7

Right-click and choose .

In the window for , locate the section.

Click

Select Domain 2 only.

Room 8

Right-click and choose .

In the window for , locate the section.

Click

Select Domain 6 only.

Room 9

Right-click and choose .

In the window for , locate the section.

Click

Select Domain 12 only.

Room 10

Right-click and choose .

In the window for , locate the section.

Click

Select Domain 11 only.

Mapped Room Coupling 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. In the TL text field, type TL_heavy.

Mapped Room Coupling 2

Right-click and choose .

In the window for , locate the section.

From the list, choose .

Mapped Room Coupling 3

Right-click and choose .

In the window for , locate the section.

From the list, choose .

Mapped Room Coupling 4

Right-click and choose .

In the window for , locate the section.

From the list, choose .

Mapped Room Coupling 5

Right-click and choose .

In the window for , locate the section.

From the list, choose .

Mapped Room Coupling 6

Right-click and choose .

In the window for , locate the section.

From the list, choose .

Mapped Room Coupling 7

Right-click and choose .

In the window for , locate the section.

From the list, choose .

Mapped Room Coupling 8

Right-click and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. In the TL text field, type TL_light.

Mapped Room Coupling 9

Right-click and choose .

In the window for , locate the section.

From the list, choose .

Room Coupling 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Locate the section. In the TL text field, type TL_light.

Click to expand the section. Select the checkbox.

Point Source 1

In the toolbar, click

and choose .

Select Point 49 only.

In the window for , locate the section.

In the qp text field, type P_s.

Now create a mesh for the model. Geometrical acoustics methods do not require a fine mesh to perform accurately; however, in order to study the sound-pressure level on the different surfaces the element sizes should remain reasonably small.

Mesh 1

In the window, under right-click and choose .

Proceed to compute the stationary study. Solving the model takes a few seconds.

Study 1 - Stationary

In the window, click .

In the window for , type Study 1 - Stationary in the text field.

In the toolbar, click

Results

Sound Pressure Level (ade) - Slices

In the window for , type Sound Pressure Level (ade) - Slices in the text field.

Multislice

In the window, expand the node, then click .

In the window for , locate the section.

Find the subsection. In the text field, type 0.

Find the subsection. In the text field, type 4.

In the toolbar, click

Sound Pressure Level (ade) - Boundaries

In the toolbar, click

In the window for , type Sound Pressure Level (ade) - Boundaries in the text field.

Locate the section. Select the checkbox.

Surface 1

Right-click and choose .

In the window for , locate the section.

In the text field, type ade.Lp.

In the toolbar, click

Multislice

In the window, expand the node, then click .

In the window for , locate the section.

Find the subsection. In the text field, type 0.

Find the subsection. In the text field, type 2.

Find the subsection. In the text field, type 3.

In the toolbar, click

Arrow Volume

In the window, expand the node.

Right-click and choose .

Streamline 1

In the window, right-click and choose .

In the window for , locate the section.

In the text field, type 100.

Select Boundaries 66, 68, 133, and 139 only.

Locate the section. Find the subsection. From the list, choose .

Color Expression 1

Right-click and choose .

In the window for , locate the section.

In the text field, type sqrt(ade.Jx^2+ade.Jy^2+ade.Jz^2).

Locate the section. From the list, choose .

In the toolbar, click

Reverberation Time

In the toolbar, click

and choose .

In the window for , type Reverberation Time in the text field.

Volume 1

Right-click and choose .

In the window for , locate the section.

In the text field, type ade.T60_EN.

Locate the section. From the list, choose .

In the toolbar, click

Model Thumbnail

In the toolbar, click

In the window for , type Model Thumbnail in the text field.

Streamline 1

In the window, under > right-click and choose .

Streamline 1

In the window, right-click and choose .

In the window for , locate the section.

In the text field, type 50.

Color Expression 1

In the window, expand the node, then click .

In the window for , locate the section.

Clear the checkbox.

Slice 1

In the window, right-click and choose .

In the window for , locate the section.

In the text field, type ade.Lp.

Locate the section. From the list, choose .

From the list, choose .

In the text field, type 0.3.

Locate the section. Clear the checkbox.

Surface 1

Right-click and choose .

Selection 1

In the window, right-click and choose .

In the window for , locate the section.

From the list, choose .

Surface 1

In the window, click .

In the window for , locate the section.

In the text field, type 1.

Locate the section. Clear the checkbox.

From the list, choose .

Surface 2

Right-click > > and choose .

Selection 1

In the window, expand the node, then click .

In the window for , locate the section.

Click

In the dialog, type 16, 17, 20, 21, 23, 25, 29, 32, 45, 61, 123, 201 in the text field.

Click .

In the toolbar, click

Add and compute an eigenvalue study to investigate the modes in the house and derive associated reverberation times.

Add Study

In the toolbar, click

to open the window.

Go to the window.

Find the subsection. In the tree, select > .

Click the button in the window toolbar.

In the toolbar, click

to close the window.

Study 2

Step 1: Eigenvalue

In the window for , locate the section.

Select the checkbox. In the associated text field, type 10.

Select the checkbox.

From the list, choose .

In the window, click .

In the window for , type Study 2 - Eigenvalue in the text field.

In the toolbar, click

Results

Sound Energy Density Modes (ade)

In the window for , locate the section.

From the list, choose .

Multislice

In the window, expand the node, then click .

In the window for , locate the section.

Find the subsection. In the text field, type 0.

Find the subsection. In the text field, type 2.

In the toolbar, click

Reverberation Time

In the window, under click .

In the window for , type Reverberation Time in the text field.

In the toolbar, click

Add a transient study to calculate the energy decay in the different rooms. The solution from Study 1 serves as input to represent a stationary source being turned off at the initial time of the transient study.

Add Study

In the toolbar, click

to open the window.

Go to the window.

Find the subsection. In the tree, select > .

Click the button in the window toolbar.

In the toolbar, click

to close the window.

Study 3

Step 1: Time Dependent

In the window for , locate the section.

In the text field, type range(0,0.01,1).

Locate the section. Select the checkbox.

In the tree, select > > .

Right-click and choose .

Click to expand the section. Find the subsection. From the list, choose .

From the list, choose .

In the window, click .

In the window for , type Study 3 - Transient in the text field.

Locate the section. Clear the checkbox.

In the toolbar, click

Results

Energy Decay Curves (normalized)

In the toolbar, click

In the window for , type Energy Decay Curves (normalized) in the text field.

Locate the section. From the list, choose .

Click to expand the section. From the list, choose .

In the text area, type Energy Decay Curves.

Locate the section.

Select the checkbox. In the associated text field, type Level (dB).

Point Graph 1

Right-click and choose .

Select Points 100, 377, and 415 only.

In the window for , locate the section.

In the text field, type ade.Lp-with('first',ade.Lp).

Click to expand the section. From the list, choose .

Click to expand the section. Select the checkbox.

Find the subsection. In the text field, type Point .

In the toolbar, click

The sound field radiated outside the house can be investigated with the Ray Acoustics interface. Start by importing parameters to represent absorption and scattering coefficients in the outdoor domain.

Global Definitions

Parameters 3 - Outdoor Boundaries

In the toolbar, click