Thin Rectangular Tube With Thermoviscous Losses
R2026bAcoustic propagation in a thin rectangular tube with thermoviscous losses
Since R2026b
Thin Rectangular Tube With Thermoviscous Losses block
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Libraries:
Simscape Acoustics /
Applications /
Tubes and Horns
Description
Add-On Required: This feature requires the Simscape Acoustics add-on.
This block models a thin rectangular tube with viscous and thermal losses at the wide walls. The model is a parallel-plate approximation, so the narrow side walls are neglected. The block implements an equivalent circuit of a continued-fraction circuit expansion [1]. The tube is divided into N segments, where each segment includes auxiliary circuit branches that approximate the frequency-dependent viscous and thermal boundary effects. For more information, see Equivalent Circuit.
Ports
Conserving
Parameters
More About
The Thin Rectangular Tube With Thermoviscous Losses block implements a continued-fraction circuit expansion with N segments. Each segment is modeled using a T-network architecture, resulting in a cascaded T-network or Cauer ladder network lumped-element model. Each component of the ladder network is a subnetwork. The figure shows the high-level architecture for an equivalent circuit with Number of differential tube lengths set to 3. The equivalent circuit is based on Figure 18 in the reference [1].
The block models viscous loss with series impedance components. Each series impedance subnetwork is an infinite network comprised of an initial Acoustic Inertance block followed by pairs of Acoustic Resistance and Acoustic Inertance blocks. The number of pairs is determined by Number of viscous loss branches. The figure shows an equivalent circuit of a series impedance component with an order of 4. The equivalent circuit is based on Figure 7 of the reference.
The block models thermal loss with shunt impedance components. Each shunt impedance subnetwork is an infinite network comprised of an initial Acoustic Compliance block followed by pairs of Acoustic Compliance and Acoustic Resistance blocks. The number of pairs is determined by Number of thermal loss branches. The figure shows the equivalent circuit of a shunt impedance component with an order of 5. The equivalent circuit is based on Figure 8 of the reference.
In practice, the Thin Rectangular Tube With Thermoviscous Losses collapses consecutive series impedance blocks from the equivalent circuits into a single block. The resulting model is numerically identical to the equivalent circuit but uses fewer components.
References
[1] Christensen, René. “Circuit Models for Thermoviscous Acoustics in Waveguides of Various Cross Sections via Continued Fractions.” The Journal of the Acoustical Society of America 156, no. 6 (2024): 3930–42. https://doi.org/10.1121/10.0034550.
Version History
Introduced in R2026b
