I thank Steve for the facilities and advice that enabled the speedy completion of the experimental part of this thesis. The first part models some nonlinear interactive effects in bubbly mixtures generated in cavitating flow, and the second part focuses on an acoustic study of the collapse process of a single bubble in moving bubble cavitation. First, a Fourier analysis of the Rayleigh-Plesset equation is used to obtain an approximate solution for the nonlinear response of a single bubble in an infinite liquid.
The final thickness of the layer results in characteristic natural frequencies of the bubble mixture, all of which are smaller than the natural frequency of the bubbles. These characteristic natural frequencies are functions of the void fraction and the ratio of layer thickness to bubble radius. The amplitude of the response increases as the excitation frequency, wf, is reduced from wb to about 0.5wb and decreases with further decreases in excitation frequency.
The effect manifests as an increase in the ratio of the second harmonic to the first harmonic as the number of small-radius bubbles becomes larger compared to the number of large-radius bubbles. The occurrence of reverberation and reverberation and their effects on some characteristic measures of the acoustic signal such as power spectra are reviewed in this chapter.
Chapter 1 INTRODUCTION
These studies have reported the formation of a jet and a counterjet during bubble collapse and have increased our understanding of the bubble collapse process. Much of the theoretical research does not take into account the effect of various fluid dynamic factors, such as eddies, flow separation and turbulence. Experimental measurements by Ceccio and Brenner (1991) suggest some measurements to characterize the bubble cavitation noise.
Tangren, Dodge and Seifert (1949) and van Wijngaarden made the first attempts to model these interactions in bubbling mixtures. 1988a and 1988b) have modeled bubbly mixtures as continuum, and Chahine (1982) has modeled bubbly mixtures by summing the effects of individual bubbles in the presence of other bubbles. The experimental component of the study involves an acoustic investigation of the bubble collapse process by characterizing the main features of the acoustic signal generated by a collapsing bubble and relating these properties and the flow variables to other measures of the acoustic signal such as spectra and peak amplitudes.
It is hoped that such a study will reveal some ways to characterize the sound emission of a single bell through experimental measurements. The results from single bubble measurements can be combined with interactive effects in bubble mixtures to enable a qualitative understanding of sound emission in bubble clouds.
Chapter 2
Note that the radius oscillations occur at harmonics of the frequency of the pressure oscillation, wf. The compressibility of the fluid and the relative motion allow for the energy dissipation in the flow. Significant amplitude of the second harmonic is one of the main results of the nonlinear analysis.
It is also known that the lowest characteristic natural frequency of the cloud dominates the frequency response. To investigate this, consider the response of the fundamental harmonic shown in Fig. Equation (84) is similar in structure to equations (5) and (37), and the solution is zero only at the harmonic of the excitation frequency.
We can see that the amplitude of the first harmonic pressure oscillation increases with increasing excitation frequency. The number of bubbles is greater at a smaller size, where the natural frequency of the bubble is higher. Increasing the value of m seems to decrease the amplitude of the first harmonic.
The influence of environmental conditions on the frequency response of the bubble layer is shown in fig. The effect of changes in void fraction on the frequency response of the layer is shown in fig. The effect of changing the wall oscillation amplitude is shown in fig.
The natural frequencies are mainly determined by the proportion of voids and the ratio between the thickness of the layer and the radius of the bubble. The amplitude of the response increases as the lowest natural frequency approaches about 0. Larger values of the void fraction result in a decrease in the amplitude of the pressure oscillation and the radius in all cases.
Therefore, the distance between the bubbles must be much smaller than the thickness of the bubble layer. In light of the discussion given above (section 2.8), the current theory is valid for small excitations.
Chapter 3
Harrison (1952) traced the origin of the return to the presence of permanent gas in the bubble. This allows relatively anechoic recording of the initial part of the acoustic signal generated by cavitation on the surface of the headform. Obviously, the two head shapes produce different characteristic events due to differences in the interaction between bubble dynamics and flow structure.
The bubble may break up during the collapse due to shear in the flow or as a result of the onset of higher order oscillations. We now turn to other statistical features of the acoustic signal by first examining the mean value of the measured quantities. First, the ratio of the maximum amplitude in the main pulse to the maximum amplitude in the rebound pulse, r, is shown in Fig.
A somewhat similar behavior was observed to occur in the results for the pulse width ratio. Then the dependence of the average value of the above characteristics on the flow rate, the type of event and the shape of the head will be examined. It is seen that most of the experimental values for cavitation numbers of 0.55 and 0.50 lie in
Changes in the nondimensional power spectra were examined to understand the redistribution of spectral energy that was due to the changes. Details of changes in spectral energy distribution in other cases are listed in Table 3.2. Details of the effect of varying flow rate on the nondimensional spectral density are summarized in Table 3.4.
In the case of the Schiebe head shape, most rebound events produced single-peak acoustic pulses, while in the case of the I.T.T.C. This appears to be correlated with an increase in the eflective width of the pulse, represented by peak separation, r, in the case of the I.T.T.C. A similar reduction in the fraction of spectral energy in high frequencies occurs in the Schiebe head shape due to multipeaking.
This may also be due to an increase in the effective width of the acoustic signal caused by multipeaking. The numbers indicate the frequency range (in kHz) in which the spectral energy content increases (decreases) as a result of change in the flow state indicated at the top of the bars.
Chapter 4 CONCLUSIONS
Each of the pulses may contain more than one peak - a phenomenon referred to as multipeaking. However, multipeaks decrease and rebound increases with reduction in the cavitation number for the Schiebe head shape. The peak amplitude of the acoustic pulse from the first collapse is always twice the peak amplitude of the second collapse.
Characteristic measures of the acoustic signal, such as peak amplitude and acoustic impulse, increased with decreasing cavitation number. The characteristic measures of the acoustic signal have a higher value at a lower flow rate at a cavitation number of 0.45. It appears that the theoretical model based on the Rayleigh-Plesset equation predicts the correct order of magnitude for the characteristic measures of the audio signal, but does not correctly predict the dependence of the pulse width on the cavitation number.
The fraction of spectral energy in high frequencies (30 kHz-80 kHz) is significantly reduced as cavitation decreases. In the case of the Schiebe head shape, the fraction of the spectral energy between 50 kHz and 75 kHz is significantly reduced due to multipeaking. This may be caused by an increase in the eflective width of the acoustic pulse due to multipeaking.
However, in the case of the Schiebe head shape, the fraction of the spectral energy in the low frequency range increases with the increase in the flow rate. Clearly, many of the observations from the acoustic study of bubble collapse are not well understood in terms of physical mechanisms of bubble collapse. However, these observations can be used in a statistical model (Baiter (1986)) to describe the cavitation noise of single bubbles.
The results of modeling the non-linear effects in bubble mixtures, combined with a statistical description obtained from acoustic study of single bubble cavitation noise, can be used to qualitatively describe the noise generated by bubble mixtures. The nonlinear effects must also be modeled differently to allow for large oscillations in bubble radius amplitude, which will give us a detailed and more realistic understanding of the interactive effects in bubble clouds. Application to subharmonic threshold for measuring the damping of oscillating gas bubbles in liquids.
