Theory

The model and the duct of the compressor that feeds it form a compression system: the duct (area $A_c$ , equivalent length $L_c$ ) holds the moving mass of gas, the volume behind it the compressible gas. Like a Helmholtz resonator, the system oscillates at $\omega_H$ . The card is shown only when its toggle on the Run Settings step is on (it is meant for a model fed by a compressor or turbocharger). Greitzer (1976) showed that one non-dimensional number, $B$ , decides whether a disturbance at the stall line of the compressor grows into surge (an oscillation of the whole system) or settles into rotating stall; a larger $B$ moves the system towards surge. The paper's own cases, from $B = 0.45$ to $B = 5$ , show that the value at which this happens depends on the compressor: there is no universal limit, so the card shows $B$ as an indicator, without a pass or fail. The model was derived for axial compressors; Fink, Cumpsty & Greitzer (1992) extended it to a centrifugal compressor with a free spool, and Haeckel et al. (2023) use it for the surge limit of a turbocharger compressor, so the card applies to both.

The plenum volume is the fluid volume of the model (the closed skin of the exported geometry, packing regions included) plus the extra volume entered here. The speed of sound is that of the gas at the operating state. None of these numbers is used by a solver; they can be changed before or after a run.

Equations

\omega_H = c\,\sqrt{\frac{A_c}{V_p\,L_c}}, \qquad f_H = \frac{\omega_H}{2\pi}, \qquad B = \frac{U}{2\,\omega_H\,L_c}

(1)

where	meaning	unit
$\omega_H$	Helmholtz angular frequency of the compression system	rad/s
$c$	Speed of sound at the operating state	m/s
$A_c$	Compressor duct area	m²
$V_p$	Plenum volume: model fluid volume + extra volume	m³
$L_c$	Equivalent compressor duct length	m
$U$	Impeller tip speed, $\pi D n/60$	m/s

Default and rule

Default: π D n / 60 from the speed and the tip diameter
Rule: Π D n / 60 from the speed and the tip diameter.
Source: Greitzer (1976), eqs. 9 and 15.

Valid range > 0

Indicator

The card reports B; the paper gives no universal limit for it.

Theory

Equations

Default and rule

Valid range > 0

Related 6

References 3