Cylindrical Tube With N Segments

R2026b

Acoustic propagation in a cylindrical tube with lossy segments

Since R2026b

• 

Cylindrical Tube With N Segments 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 the transmission line of a segmented, cylindrical tube. For a tube with one lossy segment, the model implements an equivalent T-network circuit of two Acoustic Inertance blocks in series, with one Acoustic Compliance block in parallel. For a tube with N lossy segments, the block cascades the equivalent circuit N times, forming a ladder network. The diagram shows an equivalent circuit for N=3.

The inertance value for each inertance component is

$$M=\frac{\rho L}{N\pi R^2},$$

where:

• ρ is the density of the fluid.

• L is the length of the tube.

• N is the number of segments.

• R is the radius of the circular opening.

The two inertance components at the beginning and end of the ladder network have an inertance value of M / 2.

The compliance value for each Acoustic Compliance block is

$$C=\frac{\pi R^{2}L}{N\rho c^2},$$

where c is the sound speed in the fluid.

Ports

Conserving

P1 — Left terminal of the network circuit

acoustic

Acoustic conserving port associated with the left terminal of network circuit. The pressure at the input of the tube is measured across P1 and P3, and the volume velocity at the tube input is the volume velocity flowing out of P1.

P2 — Right terminal of the network circuit

acoustic

Acoustic conserving port associated with the right terminal of T-network circuit. The pressure at the output of the tube is measured across P2 and P3, and the volume velocity at the tube output is the volume velocity flowing out of P2.

P3 — Bottom terminal of the T-network circuit

acoustic

Acoustic conserving port associated with the bottom terminal of network circuit. The pressure at the input of the tube is measured across P1 and P3, and the pressure at the output of the tube is measured across P2 and P3.

Parameters

Number of tube segments — Number of tube segments

40 (default) | positive integer

Number of tube segments, specified as a positive integer.

Tube length — Length of the tube

0.35 m (default) | positive scalar

Length of the tube in meters.

Tube radius — Radius of the tube

0.0075 m (default) | positive scalar

Radius of the tube in meters.

Inertance series resistance — Series resistance of inertance components

0 (Pa*s)/m³ (default) | nonnegative scalar

Series resistance of inertance components. It may be beneficial for numerical stability to specify a small, nonnegative resistance value.

Compliance parallel conductance — Parallel conductance of compliance components

0 m³/(Pa*s) (default) | nonnegative scalar

Parallel conductance of compliance components. It may be beneficial for numerical stability to specify a small, nonnegative conductance value.

Include additional tube load — Option to include additional tube load

off (default) | on

Select this parameter to include an additional tube load, which introduces a minimum damping ratio to provide resistive damping that reduces artifacts in the linearized frequency response.

Minimum damping ratio — Minimum damping ratio

0.1 (default) | positive scalar

Minimum damping ratio introduced when you include an additional tube load. Enabling this parameter sets the minimum value of the series resistance at each end of the circuit to M_d / 2, where

$$M_d=2d_r\sqrt{\frac{M}{2C},}$$

and d_r is the minimum damping ratio. The minimum parallel conductance at the beginning of the circuit is set to 1 / M_d.

Dependencies

To enable this parameter, select the Include additional tube load parameter.

Version History

Introduced in R2026b