Additional acoustic results: receivers, section power, dissipation, flow effect

Four results that the program computes during the frequency sweep, because they need the pressure inside the model at every frequency: the pressure at receiver points, the sound power through section planes, the power dissipated in every perforate and packing, and the transmission loss without the mean flow. They are switched on in Run Settings, panel "Additional acoustic results", before the run.

Last updated 2026-11-11

Theory

The sweep keeps only the scattering matrix of the ports; the pressure inside is not stored, because it would take gigabytes on a large model. At every frequency the system is factorised anyway. With any of these results switched on, each sweep worker also solves the nodal pressure $p$ for the run's own excitation (every excited inlet at its entered amplitude or power and phase, as the transmission loss), reduces it to a few numbers, and discards it. That costs one more back-substitution per frequency.

Receivers: the pressure at a point is interpolated with the P2 shape functions of the tetrahedron that contains it. The magnitude is the peak amplitude; the SPL is that of the RMS value.

Sections: a plane normal to x, y or z is sampled on a regular grid of spacing $h$ (1/90 of the model's longest size) inside the gas. At every sample the pressure and its normal derivative are interpolated, the particle velocity follows from the momentum equation, and the active intensity is summed with an area weight $w_q$ . Samples inside a packing are left out, because there the density is that of the equivalent fluid; the area left out is reported. The weights are scaled so that they add up to the exact area of the plane through the gas elements; the grid alone is staircased (2.4 % low on a 57 mm pipe). On a packed resonator the power through the inlet pipe equals the net input power from the scattering matrix, and the power through the outlet pipe the transmitted power, within 2 %.

Dissipation: every perforate and packing enters the system as a complex coefficient $c_i(\omega)$ times a real matrix $T_i$ . The time-averaged power each one absorbs is equation (3). The sum over all absorbers equals the incident power minus the power leaving through all ports, which the scattering matrix gives independently; on a packed resonator the two agree to 1e-3.

Flow effect: with mean-flow convection on (Mean-flow convection), a second sweep solves the same mesh and frequencies without the convection terms and without the ports' Mach numbers. The file gives both transmission losses and their difference.

Equations

p_r = \sum_{a=1}^{10} N_a(\xi_r)\, p_a

(1)

where	meaning	unit
$p_r$	Pressure at the receiver	Pa
$N_a$	P2 shape functions of the containing tetrahedron	-
$p_a$	Nodal pressures	Pa

W = \sum_q w_q\, \tfrac12 \mathrm{Re}\left(p_q\, v_{n,q}^*\right), \qquad v_n = -\frac{1}{i\omega\rho} \frac{\partial p}{\partial n}

(2)

where	meaning	unit
$W$	Net sound power through the section, positive along the plane normal	W
$w_q$	Area weight of a sample: the exact gas area of the plane divided by the number of samples	m²
$v_n$	Particle velocity normal to the plane	m/s
$\rho$	Gas density at the sample	kg/m³

P_i = \frac{1}{2\omega}\,\mathrm{Im}(c_i)\; p^H T_i\, p

(3)

where	meaning	unit
$P_i$	Time-averaged power absorbed by perforate or packing term $i$	W
$c_i$	Its frequency-dependent coefficient in the system	various
$T_i$	Its real matrix (jump matrix of a perforate, stiffness or mass of the packed elements)	various

Source

The relations are the program's own finite-element quantities. A receiver in an anechoic duct reads 1 Pa for a 1 Pa plane wave; the section power equals $|A|^2 S/(2\rho c)$ .

Valid range

Sections

Leave packings out of a section, or expect the packed area to be missing from the power.

Receivers

A point outside the acoustic model has no value; the log lists it.

Theory

Equations

Source

Valid range

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