Theory

Besides the plane wave, a duct of radius $a$ carries transverse modes that propagate only above their cut-on frequency. For a circular duct with rigid walls the first one is the (1,0) mode, with $k_t a = 1.8412$ , the first zero of $J_1'$ , equation (1). The auto value uses the smallest port, its equivalent radius $\sqrt{A/\pi}$ and the speed of sound of the medium: that of the Material step's gas for the uniform medium, or the solved temperature at that port for the medium from the CFD fields (Acoustic medium).

The computation remains valid above that frequency: the ports are modal, every mode whose cut-on is below $f_{max}$ is included, plus Evanescent modes per port further modes, and the mode table on this step lists them. Two things change with $f_{max}$ :

the mesh: the largest element is $c/(f_{max}N_\lambda)$ , equation (2) (Elements per wavelength), so the number of unknowns grows roughly with $f_{max}^3$ where the wavelength, not the curvature, sets the size;
the insertion loss: above an outlet's first cut-on, the plane-wave radiation terminations are incomplete and the insertion loss is flagged there, unless the outlet uses the radiation-domain termination.

Equations

f_{max} = \frac{1.8412\,c}{2\pi a}, \qquad a = \sqrt{\frac{A_{min}}{\pi}}

(1)

h_{max} = \frac{c}{f_{max} N_\lambda}

(2)

where	meaning	unit
$f_{max}$	Highest frequency (auto)	Hz
$c$	Speed of sound (uniform medium, or at the smallest port)	m/s
$a$	Equivalent radius of the smallest inlet or outlet	m
$A_{min}$	Area of the smallest inlet or outlet (from the CAD)	m²
$h_{max}$	Largest element size of the acoustic mesh	m
$N_\lambda$	Elements per wavelength	-

Default and rule

Default

auto: first non-plane cut-on of the smallest portComputed by the programMeasured

Rule

Auto (equation 1). It requires the exported geometry (the port areas); until then the field reads "pending". For octave, 1/3-octave and custom spacing the field is locked and shows the upper edge of the last band or the last listed frequency.

Source

The cut-on of the (1,0) mode of a circular duct is classical duct acoustics. The program checks its numerical port modes against the zeros of $J_m'$ , computed numerically (tolerance 0.5 %; measured 0.01-0.17 % on the ports of case V2, a two-inlet single-chamber muffler with internal inlet and outlet tubes).

Cost measured on case V2 (cold air, 6 elements per wavelength, one worker, with an earlier sparse LU solver; the current solver is faster):

1.0 kHz: 39.8k unknowns, 0.9 s per frequency;
1.8 kHz: 144.6k unknowns, 11.6 s per frequency;
2.6 kHz: 381k unknowns, 141 s per frequency.

Valid range > f_min; set by the band range or the list for octave, 1/3-octave and custom spacing

Values

Above $f_{min}$ . Above the auto value, port modes beyond the plane wave are included automatically.

Cost

Doubling $f_{max}$ multiplies the number of unknowns by up to 8 on a wavelength-limited mesh, and the solve time per frequency by more.

Theory

Equations

Default and rule

Valid range > f_min; set by the band range or the list for octave, 1/3-octave and custom spacing

Related 6