COMSOL 6.4 - Submarine High-Frequency Asymptotic Scattering

Submarine High-Frequency
Asymptotic Scattering

The primary defense of a submarine lies in its capacity to remain hidden during operation. As radio waves are strongly absorbed by sea water, sound navigation and ranging, or SONAR, is one of the main methods used for the detection of submarines. SONAR systems are also used for underwater exploration as well as in the fishing industry.

Designers analyze the way acoustic waves are reflected in order to minimize the equivalent reflecting area of the submarine. This tutorial studies the scattering off the BeTTSi benchmark submarine (Benchmark Target Echo Strength Simulation).

This model uses the high-frequency approximation of the Pressure Acoustics, Asymptotic Scattering interface. The analysis is fast and a good approximation at high frequencies, where the wavelength is much smaller than the scattering object.

Figure 1: BeTSSi submarine geometry.

Model Definition

The target strength, or TS, is a measure of the area of a sonar target. In most submarines, reduction of the backscatter signal is achieved through the application of absorbing materials to the outer surfaces of the submarine. In this model, the target strength is computed for a single angle of incidence and frequency. The model can be readily extended with a sweep over frequencies and source locations.

The tutorial is based on the BeTTSi benchmark submarine (Benchmark Target Echo Strength Simulation) presented in Ref. 1 and Ref. 2. The geometry, shown in Figure 1, is also used and discussed in detail the Submarine Target Strength tutorial model in the Acoustics Module Application Library.

In the present tutorial, the scattering problem is solved with the Pressure Acoustics, Asymptotic Scattering physics interface. The interface relies on a high-frequency approximation where the sound field is assumed to be locally plane. This is valid as long as the wavelength is much smaller than the important geometry details as well as the radius of curvature of important surfaces. Reflections are treated analytically at surfaces and the radiated/scattered field is computed using the Kirchhoff–Helmholtz integral. This approach is also sometimes referred to as high-frequency BEM or HFB.

In this model, the surface properties of the submarine are defined through an angle dependent absorption coefficient α(θ). The angle dependency is included using the built-in variable paas.thetai. The absorption data is generic and is here given in an interpolation function. The absorption data can be based on measurements or computed using a submodel. An example of the submodel approach is given in the Application Gallery tutorial Anechoic Coating:

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www.comsol.com/model/anechoic-coating-44201

Results and Discussion

The full 3D radiation pattern, evaluated at 100 m is depicted in Figure 2. Notice the main lobe corresponding to the specular reflection on the main part of the submarine body. The corresponding radiation pattern in the xy-plane, evaluated at a source distance of 1000 m is depicted in Figure 3. The near-field total pressure and the near-field scattered sound pressure level is depicted in Figure 4 and Figure 7, respectively.

The asymptotic scattering approach relies on a visibility computation, that is, the portion of the scattering object surfaces that have a directly incident background field. The visibility for the current configuration is depicted in Figure 5 (top left). For the visible surfaces, the angle of incidence of the incident field as well as the corresponding absorption coefficient is depicted in the top right and the bottom figures, respectively.

Finally, the ballistic target strength (TS) for the current configuration of source and scatterer is depicted in Figure 6.

Figure 2: Radiation pattern evaluated at 100 m from the submarine.

Figure 3: Radiation pattern in the xy-plane, evaluated at the source distance (1 km).

Figure 4: Total acoustic pressure (incident and scattered) evaluated at the submarine surface and in the z = 0 plane. The evaluation grid is slightly under resolving the pattern.

Figure 5: The surface visibility (top left); the angle of incidence of the incident acoustic field on the visible surfaces (top right); and the absorption including the angle dependency (bottom).

Figure 6: The plot shows the target strength TS.

Figure 7: The scattered SPL in the z = 0 plane in the region around the submarine.

Notes About the COMSOL Implementation

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The walls (visible) of the scattering object can be characterized in terms of a reflection coefficient R (complex valued), a normal impedance Zn (complex valued), or an absorption coefficient α and phase. The reflection coefficient and the absorption coefficient can have a dependency on the angle of incidence using the built-in variable paas.theta. If multiple sources are defined, the variable will automatically take the differences into account. Variables also exist for the source defined by the individual background pressure field features, for example, for the first feature paas.bpf1.theta (using the item scope).

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When results processing using either a grid dataset or a radiation patter plot, it is important to resolve the wave pattern. This is particularly so since the method is used for high-frequency problems where the wavelength is much smaller than the scattering objects. The spatial resolution can be set on the grid dataset as well as in the radiation pattern plot. Remember that rendering each data point is time consuming.

References

1. B. Nolte, I. Schäfer, C. de Jong, and L. Gilroy, “BeTSSi II benchmark on target strength simulation,” Proceedings of Forum Acusticum, 2014.

2. J.V. Venås and T. Kvamsdal, “Isogeometric boundary element method for acoustic scattering by a submarine,” Comp. Meth. Appl. Mech. Eng., vol. 359, p. 112670, 2020, doi.org/10.1016/j.cma.2019.112670.

Acoustics_Module/Underwater_Acoustics/submarine_asymptotic_scattering

Modeling Instructions

From the menu, choose .

New

In the window, click

Model Wizard

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In the tree, select > > .

Click .

Click

In the tree, select > .

Click

Global Definitions

Parameters 1

In the window, under click .

In the window for , locate the section.

Click

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

Interpolation 1 (int1)

In the toolbar, click

and choose > .

In the window for , locate the section.

From the list, choose .

Click

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

Click

In the text field, type alpha.

Locate the section. From the list, choose .

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


Function	Unit
alpha	1

In the table, enter the following settings:


Argument	Unit
t	deg

Geometry 1

The model uses an external mphbin file with the geometry. The instructions for building the submarine geometry can be found in the Submarine Target Strength tutorial.

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 submarine_asymptotic_scattering.mphbin.

Click

Use to simplify the geometry for meshing.

Form Composite Faces 1 (cmf1)

In the toolbar, click

and choose .

On the object , select Boundaries 1–10, 69–73, and 79–83 only.

In the window for , click

Form Composite Faces 2 (cmf2)

In the toolbar, click

and choose .

On the object , select Boundaries 4–7, 13–16, 24–27, 49, 50, 62, 63, 65, 66, and 84–87 only.

In the window for , click

The geometry should look like this.

Disable the analysis of the geometry as the remaining small geometric details can be kept.

In the window, click .

In the window for , locate the section.

Clear the checkbox.

In the toolbar, click

Definitions

Variables 1

In the window, expand the > node.

Right-click and choose .

In the window for , locate the section.

Click

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

Average 1 (aveop1)

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Add Material

In the toolbar, click

to open the window.

Go to the window.

In the tree, select > .

Click the button in the window toolbar.

In the toolbar, click

to close the window.

Materials

Water, liquid (mat1)

In the window for , locate the section.

From the list, choose .

Pressure Acoustics, Asymptotic Scattering (paas)

In the window, under click .

In the window for , locate the section.

From the list, choose .

Pressure Acoustics 1

In the window, under > click .

In the window for , locate the section.

From the list, choose .

Note that material properties cannot be space dependent when used in the Pressure Acoustics, Asymptotic Scattering interface.

Background Pressure Field 1

In the window, click .

In the window for , locate the section.

From the list, choose .

In the p0 text field, type p_ref.

Specify the x0 vector as


-d_source*cos(phi)+L/2	x
-d_source*sin(phi)	y
0	z

The boundary conditions applicable to the scattering object are added as subfeatures to the . Modify the default condition to include an angle dependent surface absorption.

Wall 1

In the window, expand the node, then click .

In the window for , locate the section.

From the list, choose .

In the αn text field, type alpha(paas.theta).

Note the use of the general paas.theta variable that defines the angle of incidence. When plotting the angle in postprocessing, the item scope of the has to be added (each background field defines its associated angle of incidence). This is shown when analyzing the results.

In this model, the mesh is set up manually. Proceed by directly adding the desired mesh component. Four elements per wavelength is adequate for the formulation in this model.

Mesh 1

As the scattering characteristics are largely influenced by the sail, rudder and bow plane, create a finer mesh around the leading edge of these surfaces. This is achieved by first meshing the necessary edges.

Edge 1

In the toolbar, click

and choose .

Select Edges 50–53, 143, 144, 146, 147, 149, 150, and 152–161 only.

Distribution 1

Right-click and choose .

In the window for , locate the section.

In the text field, type 18.

Size 1

In the window, right-click and choose .

In the window for , locate the section.

Click the button.

Locate the section.

Select the checkbox. In the associated text field, type 0.2.

Size

In the window, under > click .

In the window for , locate the section.

Click the button.

Locate the section. In the text field, type lam0/4.

In the text field, type 50[mm].

Mapped 1

In the toolbar, click

and choose .

Select Boundaries 8–19, 24–27, 32–35, 38, 39, 42, 43, 46–55, and 62–69 only.

In the window for , click

Free Triangular 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Click

Finally, use the feature, from the list, to get a more uniform triangular mesh at the front of the submarine.

Adapt 1

In the toolbar, click

and choose .

In the window for , locate the section.

From the list, choose .

Select Boundaries 1–7 only.

Locate the section. In the text field, type lam0/4.

Click

The mesh should look like this.

In the window, click .

Study 1

Step 1: Frequency Domain

In the window, under click .

In the window for , locate the section.

In the text field, type f0.

In the toolbar, click

Results

In Pressure Acoustics, Asymptotic Scattering models, the time consuming computations are not to solve the model. The actual solution time lies in evaluating the results in postprocessing (through the exterior field feature). To get information about the rendering/plotting time turn on the . On each plot, an section will appear where the data is displayed (expand the section). This option applies to the whole COMSOL installation; if selected, the will also appear in other models opened at a later stage.

Click the

button in the toolbar.

In the dialog, select > in the tree.

In the tree, select the checkbox for the node > .

Click .

It can be useful to select the option on the node when working with the plots, since the rendering times can be large. Also, on the node, turning on is recommended; the plots will be saved rendered in the file.

In the window, click .

In the window for , locate the section.

Select the checkbox.

Locate the section. From the list, choose .

3D Scattered SPL Radiation Pattern at 100 m

Proceed by modifying the default plots, then add some additional plots.

In the window, under click .