Noise generated by cavitating single-hole and multi-hole orifices in ...

ARTICLE IN PRESSP. Testud et al. / Journal of Fluids and Structures 23 (2007) 163–189 175320300280∆P measured / (0.5ρ w U 2 )260240220200180160multi-hole experimentsthick-hole developed-cavitation model: α=0.65thin-hole developed-cavitation model: α=0.65thick-hole super-cavitation model: α=0.65single-hole experiments1401 2 3 4 5 6 7 8U (m.s -1 )Fig. 11. Evaluation of the multi-hole orifice model and comparison between the single-hole orifice measurements.Table 4Conditions at the jet using the Borda–Carnot model for the multi-hole orificeDeveloped cavitationSuper cavitationU ðms 1 Þ 2.08 2.45 2.94 3.65 4.18 4.43U j ðms 1 Þ 36 43 51 63 73 77c min ðms 1 Þ 20 — 27 — — —P j ð10 5 PaÞ 0.7 — 1.3 — —example in Fig. 14). The higher harmonics are typical of steady whistling stabilized by a nonlinear feedback effect as forall self-sustained oscillations (Fletcher, 1979; Rockwell and Naudascher, 1979).Scant literature has been found on whistling of cavitating orifices in pipes. A vortex shedding phenomenon inpresence of cavitation has been investigated by Sato and Saito (2001), but in the particular case of thick orificesðt=d\2Þ. On thin orifices, some visualizations (Moussou et al., 2003) made on other EDF experiments have shown thepossibility of the presence of vortex-shedding in cavitation regime, as can be seen in Fig. 15, from Archer et al. (2002).The whistling frequencies are given in Table 5. They do not increase continuously with the flow velocity, as one wouldexpect for a hydrodynamic oscillation edge-tone like (Blake and Powell, 1983). The stable frequency is typical of anacoustic feedback which creates and maintains the acoustic oscillation close to a resonance frequency. This is alsorevealed by the locking of the phase of the time pressure signals on successive sensors, which indicates a standing wavepattern.Upstream of the orifice, the level of whistling is higher than downstream: hence the acoustic feedback is suspected tohappen predominantly upstream. The upstream reflection coefficient, see Fig. 5, is reflecting but irregular: no clearacoustic reflection point can be identified (as it can be for the cavity of a valve downstream, see Section 2.6.2). Thisirregular shape is due to the intricacy of the upstream rig design, with a succession of elbows, slight restrictions ofsections and some open valves.It is also worth mentioning that the whistling frequency does not coincide with any downstream natural acousticfrequency. This is coherent with the acoustic uncoupling observed from both sides of the orifice.The single-hole orifice has a ratio t=d ¼ 0:6, inferior to 2, so that it is considered as a thin orifice. We assume that thewhistling phenomenon is influenced by the thickness of the orifice t, rather than its diameter. It is also natural to use the