The cavitation instability induced by the development of a re-entrant jet
Authors: CALLENAERE MATHIEU , FRANC JEAN-PIERRE , MICHEL JEAN-MARIE , RIONDET MICHEL 
Published: July 2002

The instability of a partial cavity induced by the development of a re-entrant jet
is investigated on the basis of experiments conducted on a diverging step. Detailed
visualizations of the cavity behaviour allowed us to identify the domain of the
re-entrant jet instability which leads to classical cloud cavitation. The surrounding
regimes are also investigated, in particular the special case of thin cavities which do
not oscillate in length but surprisingly exhibit a re-entrant jet of periodical behaviour.
The velocity of the re-entrant jet is measured from visualizations, in the case of
both cloud cavitation and thin cavities. The limits of the domain of the re-entrant
jet instability are corroborated by velocity fluctuation measurements. By varying the
divergence and the confinement of the channel, it is shown that the extent of the auto-oscillation
domain primarily depends upon the average adverse pressure gradient in
the channel. This conclusion is corroborated by the determination of the pressure
gradient on the basis of LDV measurements which shows a good correlation between
the domain of the cloud cavitation instability and the region of high adverse pressure
gradient. A simple phenomenological model of the development of the re-entrant jet in
an adverse pressure gradient confirms the strong influence of the pressure gradient on
the development of the re-entrant jet and particularly on its thickness. An ultrasonic
technique is developed to measure the re-entrant jet thickness, which allowed us to
compare it with the cavity thickness. By considering an estimate of the characteristic
height of the perturbations developing on the interface of the cavity and of the
re-entrant jet, it is shown that cloud cavitation requires negligible interaction between
both interfaces, i.e. a thick enough cavity. In the case of thin cavities, this interaction
becomes predominant; the cavity interface breaks at many points, giving birth to
small-scale vapour structures unlike the large-scale clouds which are periodically shed
in the case of cloud cavitation. The low-frequency content of the cloud cavitation
instability is investigated using spectral analysis of wall pressure signals. It is shown
that the characteristic frequency of cloud cavitation corresponds to a Strouhal number
of about 0.2 whatever the operating conditions and the cavity length may be, provided
the Strouhal number is computed on the basis of the maximum cavity length. For
long enough cavities, another peak is observed in the spectra, at lower frequency,
which is interpreted as a surge-type instability. The present investigations give insight
into the instabilities that a partial cavity may undergo, and particularly the re-entrant
jet instability. Two parameters are shown to be of most importance in the analysis of
the re-entrant jet instability: the adverse pressure gradient and the cavity thickness
compared to the re-entrant jet thickness. The present results allowed us to conduct a
qualitative phenomenological analysis of the stability of partial cavities on cavitating
hydrofoils. It is conjectured that cloud cavitation should occur for short enough
cavities, of the order of half the chordlength, whereas the instability often observed
at the limit between partial cavitation and super-cavitation is here interpreted as a
cavitation surge-type instability.