Multifrequency Instability of Cavitating Inducers

Recent testing of high-speed cavitating turbopump inducers has revealed the existence of more complex instabilities than the previously recognized cavitating surge and rotating cavitation. This paper explores one such instability that is uncovered by considering the effect of a downstream asymmetry, such as a volute on a rotating disturbance similar to (but not identical to) that which occurs in rotating cavitation. The analysis uncovers a new instability that may be of particular concern because it occurs at cavitation numbers well above those at which conventional surge and rotating cavitation occur. This means that it will not necessarily be avoided by the conventional strategy of maintaining a cavitation number well above the performance degradation level. The analysis considers a general surge component at an arbitrary frequency $ω$ present in a pump rotating at frequency $Ω$ and shows that the existence of a discharge asymmetry gives rise not only to beat components at frequencies, $Ω−ω$ and $Ω+ω$ (as well as higher harmonics), but also to rotating as well as surge components at all these frequencies. In addition, these interactions between the frequencies and the surge and rotating modes lead to “coupling impedances” that effect the dynamics of each of the basic frequencies. We evaluate these coupling impedances and show not only that they can be negative (and thus promote instability) but also are most negative for surge frequencies just a little below $Ω$⁠. This implies potential for an instability involving the coupling of a surge mode with a frequency around $0.9Ω$ and a low-frequency rotating mode about $0.1Ω$⁠. We also examine how such an instability would be manifest in unsteady pressure measurements at the inlet to and discharge from a cavitating pump and establish a “footprint” for the recognition of such an instability.