Duct mode load

You can apply a rectangular, cylindrical, or annular duct mode load at the inlet of a duct that is modeled with fluid elements. Duct mode loads are supported in an uncoupled acoustics solution running Simcenter Nastran Direct Frequency Response (SOL108) with FEMAO.

In duct acoustics, duct modes are important in applications such as HVAC and automotive exhaust systems (generally, applications in which you need to reduce exhaust noise).

In long ducts, each acoustic mode can be expressed as the product of standing waves with a propagating component. A specific duct mode is characterized by the mode orders and the amplitude.

The general solution for a duct mode propagating in a duct with an infinite length (z-direction) is expressed as:

S\left( {x,y,z,\omega} \right) = \sum\limits_m^\infty {\sum\limits_n^\infty {{A_{m,n}}} } \left( \omega \right)\cos \left( {\frac{{n\pi }}{{{L_x}x}}} \right)\cos \left( {\frac{{m\pi }}{{{L_y}y}}} \right){e^{ \pm ,i,{k_{m,n}}z}}

where,

\cos \left( {\frac{{n\pi }}{{{L_x}x}}} \right)\cos \left( {\frac{{m\pi }}{{{L_y}y}}} \right)

describes the standing wave in x and y,

{e^{ \pm ,i,{k_{m,n}}z}}

describes the propagating wave on the duct axis (z-direction),

{A_{m,n}}

is the amplitude,

m,n

are the mode orders relative to the two directions in the duct cross section,

{L_x},{L_y}

are dimensions of the duct cross section, and

{k_{m,n}}

is the wave number.

Each duct mode has a characteristic cut-on frequency. As a result, specific duct modes propagate only from a certain frequency onwards. This is demonstrated in the amplitude response plot below, where ω1, ω2, and ω3 correspond to the cut-on frequencies of three duct modes, each with unique mode orders (m,n).

The software considers the boundaries on which you apply duct mode loads as reflectionless. That is, wave components that are reflected back to the duct mode boundary are completely absorbed.

There are two options for defining duct mode loads on an inlet boundary:

• Define a specific duct mode load with given phase and amplitude.The specific duct mode load is useful when you understand the amplitude and the frequency range associated with the incoming noise. For example, you could know the amplitude of the incident modes from previous experiments. You can define specific duct modes that have a corresponding cut-on frequency within this range.

• Define a distributed duct mode load. The distributed duct mode load is useful when your noise source encompasses a broadband of frequencies or you do not have experimental data for the incoming noise source.With the distributed duct mode load, you define the acoustic amplitude that is applied to all modes. For each solution frequency, the software applies all possible cut-on modes as incoherent sources with equal acoustic power. The software computes the response of each mode separately, and then sums them to compute the total response.

Two subcase types are available, and are required to include a duct mode load in your solution.

• Subcase - Specific Duct ModesYou can include only specific duct mode loads in this subcase type.

• Subcase - Distributed Duct ModesYou can include only distributed duct mode loads in this subcase type.

Multiple duct mode loads can be defined in the same model, but only one definition can exist at a specific fluid boundary. For example, you could model a system of ducts that includes multiple inlets. A unique duct mode load could be defined on each inlet.

Duct outlet boundary

To allow the acoustic waves to exit a duct system without reflections, you have two options.

• You can define the Anechoic End Duct (AED) Simulation Object on a duct outlet. The AED is a reflectionless boundary on a duct outlet. You can use this option when you are only interested in results within the duct system, and not exterior acoustic radiation.

• You can define the Automatically Matched Layer (AML) at the outlet. When the AML is defined, the acoustic energy at the outlet can radiate to exterior microphone locations. You can use this option when you are interested in results within the duct system, and exterior acoustic radiation.

Duct mode output

When a duct mode load is defined on a duct inlet, and either an anechoic end duct boundary or an AML is defined on a duct outlet, two additional output options are available in the Acoustic Output Requests Modeling Object.

• Transmission loss is computed as the power introduced by the duct mode boundary conditions divided by the sum of the modal transmitted power coefficients at the anechoic end duct boundary or the power at the AML radiation surface. Mathematically, it is written as:{\rm{Transmission,Loss = }}\frac{{{\rm{Power,In}}}}{{{\rm{Power,Out}}}}

• Transmission Coefficients represent the amplitude of the output modes expressed in terms of pressure, intensity, or power.

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Duct mode load, Simcenter 3D 2021.1 Series

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