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Research Papers: Multiphase Flows

# Cavitation Resonance

[+] Author and Article Information
S. C. Li1

School of Engineering, University of Warwick, Coventry CV4 7AL, UK; State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, P.R.C.scl@eng.warwick.ac.uk

Z. G. Zuo, S. Li

School of Engineering, University of Warwick, Coventry CV4 7AL, UK

S. H. Liu, Y. L. Wu

State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing, 100084, P.R.C.

The University of Michigan, USA.

That is, in contrast to the natural (high) frequencies of individual bubbles, a low-frequency noise component is always observed. It is believed to be generated by the bubble cloud oscillating at its characteristic frequency.

First, with an assumption of $σf=0$, it finds a number of minima of impedance $(Z12)$ at the exit of the low-pressure tank. The results are then represented as a graph of modulus $∣Z12∣$ against $ω$, as shown in Fig. 4. Second, Newton’s method is used to determine the exact values of $s=σf+iω$ to satisfy $Z12=0$.

The impedance is defined as $Z(X)=H(X)∕Q(X)$. The large value of $Z(x)$ indicates that a small flow-rate perturbation can trigger large pressure oscillation.

By cross reference to Fig. 1, the corresponding component in the venture system can be identified. Here, sections 5–9 in Fig. 5 correspond to the sections 5–9 (divisions of venture section) in Fig. 1.

From the definition of impedance, it is readily seen that a high impedance (say, at the throat) indicates a low flow-rate fluctuation $Q(x)$ and high-pressure fluctuation $H(x)$. In other words, any small flow-rate variation will trigger high-pressure fluctuations.

Note: The value of impedance $Z$ is not plotted in the figure. However, since $Z(x)=H(x)∕Q(x)$, it is readily to see that $Z(12−14)S2>Z(12−14)S1$.

This work was based on the true unsteadiness of rotor-stator interaction, enabling the propagation of pressure fluctuations throughout the entire flow system.

The advance in high-speed photography has facilitated the observation of individual bubble behavior in cavitation cloud (17).

And also numerical results shown in the plot but nothing mentioned.

That is, the cloud itself is a complete oscillating system rather than a simply lumped-capacitive element in an oscillating system. Apart from compliance, it possesses, at least, the inertial mass, elasticity, and viscous resistance. For some cases, these parameters have a rather discrete nature than lumped parameters, subject to the geometric shape and properties of the cloud.

One is the cloud; the other is the liquidphase in the system.

That is, a small perturbation of flow rate (such as the cavity unsteadiness in this case) will trigger huge pressure fluctuations.

Or local systems such as a water plug in a draft tube.

See Ref. 18.

For example, The Mechanics of Nonlinear Systems With Internal Resonances by A. I. Manevich and L. I. Manevich.

One is the initial pressure propagation wave caused by a step pressure rise at the one end of a bubble column, and the other is the initially nonexisting volumetric oscillation (in-phase) of bubbles.

1

Corresponding author.

J. Fluids Eng 130(3), 031302 (Mar 03, 2008) (7 pages) doi:10.1115/1.2842149 History: Received December 20, 2006; Revised December 21, 2007; Published March 03, 2008

## Abstract

This article deals with a phenomenon named as cavitation resonance. Cavitation-associated pressure fluctuations in hydraulic systems affect their design, operation, and safety. Under certain conditions, the amplitude of a particular component of these fluctuations will be significantly magnified, causing a resonance. Here, the observed phenomenon from three different flow systems is briefly introduced. Based on the coupling of two subsystems, a hypothesis of (macroscopic) mechanism reduced from these experimental observations is presented.

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## Figures

Figure 1

(a) Schematic of the UM Venturi. (b) Details of the Venturi section.

Figure 2

FFT results of fluctuations for (a) σ=0.84, (b) σ=0.74, and (c) σ=0.69

Figure 3

Amplitude variation of the particular fluctuation-component with cavitation number

Figure 4

Frequency scan of UM Venturi, with an assumption of σf=0. These results are to be fed as input to Newton’s method for finding exact values of the natural frequencies of the noncavitated system.

Figure 5

Mode shape of UM Venturi for s=−1.03+i385.16

Figure 6

(a) Schematic of Francis turbine model HL-169-25 and its cavitation test rig. (b) Low-frequency fluctuations from HL-169-25 turbine: mode shape analysis.

Figure 7

(a) The particular fluctuation component f2 (with frequency f0=52–88Hz) against the guide-vane openings a0 measured in the cone (No. 11 transducer) and elbow (No. 56 transducer) of the draft tube and in the spiral case (No. 1 transducer), respectively: The same variation pattern with guide-vane opening for these three different locations indicates the propagation of the f2 component in the system under initial cavitation conditions. (b) The locations of the pressure transducer Nos. 1, 11, and 52 on the model turbine (distance unit: mm).

Figure 8

The spectra at the inlet of spiral case and at the inlet of the draft tube, both showing a distinguishing component (around 10Hz), indicate the propagation of this component throughout the system. (a) Pressure fluctuations at the inlet of the spiral case. (b) Pressure fluctuations at the inlet of the draft tube.

Figure 9

Schematic of Warwick Venturi

Figure 10

Frequency scanning result showing the first harmonic frequency of f0=5.4Hz (i.e., ω=33.93rad∕s).

Figure 11

Mode shapes of Warwick Venturi (hydraulic impedance)

Figure 12

Pressure fluctuations for σ=0.79. (a) The recorded pressure signals. (b) FFT analysis: The scale of the ordinate is a normalized amplitude in the FFT analysis.

Figure 13

Amplitude variation of the particular fluctuation-component with cavitation number

Figure 14

Frequency variations of pressure fluctuations against cavitation number (Reboud (7))

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