Cavitation phenomenon happens when a liquid is subjected to fast changes in local pressure and speed, and the local liquid pressure becomes lower than its saturated vapor pressure. In most situations, it is not favorable and damaged equipment, and also reduce system efficiency and make noises and vibrations. There are several cavitation regimes depending on the cavitation number such as incipient cavitation, shear cavitation, sheet/cloud cavitation, and supercavitation. Diagnosing different phenomena such as shedding and collapsing in different cavitation regimes can help to find out what is happening in the considered fluid. Signal processing is one of the most important ways to analyze the fluctuations and changes of unsteady systems or processes. Therefore, it can be useful in detection of cavitation phenomena.
Many different experimental and numerical investigations have been done in cavitation flow over various cases such as blunt body, disk and sphere. Achenbach (Achenbach, 1972) measured the total drag experimentally, local static pressure and local skin friction distribution of the flow past sphere in a broad range of Reynolds numbers (5×104 < Re < 6×106). Marston et al. (Marston, Yong, Ng, Tan, & Thoroddsen, 2011) considered the dynamics of cavitation over a sphere to investigate the difference of cavitation structures between Newtonian and non-Newtonian liquids by increasing viscosity. They used high-speed cameras to observe the dynamics of cavitation. Different turbulence and mass transfer models have been used in different cases to investigate cavitation. Shang et al. (SHANG, EMERSON, & GU, 2012) investigated numerically cavitation over a submarine using LES turbulence models under the framework of openFOAM. They validated their data with experiments and found that how cavitation numbers affected the circumfluence of the tail regions. They also found that in small cavitation numbers (0.1<0.4), the cavity cloud lasted continuously. Gnanaskandan and Mahesh (Gnanaskandan & Mahesh, 2016) studied cavitation numerically over a circular cylinder at Reynolds numbers between 200 and 3900 for different cavitation numbers (2, 1, 0.7 and 0.5) by a homogeneous mixture model. They captured the dynamics of cavity formation and collapse leading to pressure waves in their simulations. They investigated that when ?=1.0, the cavity detaches from the body itself at the shedding frequency. Despite, in the transitory regime of cavitation (?=0.7 and 0.5), there was a low-frequency cavity detachment phenomenon in addition to the shedding frequency. Pendar and Roohi (Pendar & Roohi, 2016) simulated cavitation and supercavitation regimes and they compared large eddy simulation and k-? SST turbulence models and Kunz, Sauer and Zwart mass transfer models around 3D hemispherical head-form body and a conical cavitator. In another study (Roohi, Pendar, & Rahimi, 2016), they compared these models to capture unsteady cavitation and supercavitation flow behind a 3-D disk cavitator? precisely. Pendar and Roohi (Pendar & Roohi, 2018) simulated partial and supercavitation over a sphere at a constant Reynolds number of 1.5 × 106 and the broad range of cavitation numbers (0.36 < 1) and compared the results with experimental data. They reported detailed analyses of the instantaneous cavity leading edge and separation point location, vortex shedding, streamwise velocity fluctuation and evolution of the cavity. In the following, we carry on many experimental researches have been done on signal processing in different cavitation regimes and cavitation detection of different geometries. Cudina (?DINA, 2003) used the audible sound of a centrifugal pump to detect cavitation phenomenon. He did experiments to detect the incipient and development of cavitation and its development of cavity cloud. Experimental results illustrate that there is a discrete frequency tone within the audible noise spectra which is strongly dependent on the cavitation process and its development. Escaler et al. (Escaler, Egusquiza, Farhat, Avellan, & Coussirat, 2006) evaluate the detection of cavitation in actual hydraulic turbines? experimentally. They analyzed measuring of the structural vibrations, acoustic emissions and hydrodynamic pressures in the especial machine. They found that by increasing the cavitation severity, the amplitude of the entire spectrum increases without any significant change in its shape. They computed the amplitude envelope of the filtered signal by using an algorithm based on the Hilbert transform. He and Liu (He & Liu, 2011) used the wavelet scalogram analysis to understand the characteristics of the cavitation noise deeply. They investigated the time-frequency characteristics of the cavitation noise in various cavitation states and process experimentally by recording audible sounds. Their results showed that the cavitation noise could be distinguished from the background noise because of their different frequency characteristic. Also, they mentioned wavelet scalogram method is very potent for the time-frequency analysis of the cavitation noise. Lee et al. (LEE, HAN, PARK, & SEO, 2013) expressed application of signal processing techniques to detection the tip vortex and cavitation noise in marine propeller based on acoustical measurements. In their study, the Short-Time Fourier Transform (STFT) analysis and the Detection of Envelope Modulation on Noise (DEMON) spectrum analysis were employed, they illustrated that these two techniques are appropriate for finding such a repeating frequency. Also, they observed that these two techniques had been successfully employed for identifying the tip vortex when the cavitation phenomenon generated. Giorgi et al. (Giorgi, Ficarella, & Lay-Ekuakille, 2015) implement an experimental study of a cavitating flow of water inside a restricted nozzle. The cavitation phenomena were characterized by four different flow regimes at the variation of the pressure and temperature inside the orifice. They analyzed signals with the wavelet transform to highlight the influence of temperature. Data is acquired by pressure signals and images of the cavitating flow-field. Kang et al. (Kang, Feng, Liu, Cang, & Gao, 2017) employed wavelet transform for their experiments on hydro turbine to diagnose whether the cavitation occurs. The results of this paper illustrated that the characteristics of incipient cavitation could be detected in the audible frequency band. They found that the wavelet analysis of noise signals can distinguish different of operating conditions, also can discriminate between the incipient cavitation and the other regimes of cavitation by visual observation. In this section, we consider experimental studies on signal processing of cavitation over sphere precisely. Brandner et al. (Brandner, Walker, Niekamp, & Anderson, 2010) investigated cloud cavitation over a sphere experimentally and took the photo of the sphere in water tunnel in constant Reynolds number (1.5×106) and various cavitation numbers (0.6<1.0) in different regimes of cavitation from inception to supercavitation. They investigated instantaneous cavity leading edge location, separating laminar boundary layer, Shedding phenomena and frequency content. Pixel intensity of photos was used as an input value of wavelet transform and contour plot from power spectra at discrete cavitation number increments of 0.1 between 0.4 to 0.9, and 0.95 was derived. They mentioned because of the data gathered limitations in the present work, higher spatial and temporal resolutions are required. Graaf et al. (de Graaf, Brandner, & Pearce, 2017) investigated the physics and spectral content of cloud cavitation about a sphere experimentally in a water tunnel by high-speed imaging and surface pressure measurement. The power spectral densities of the long sampled normalized pressure signals were analyzed by using the Welch and wavelet methods. For the Welch method, these were derived by using a Hamming window length of 1024 and 50% overlap. The power spectrogram for the same data using a Morlet-6 wavelet is acquired using the smallest wavelet scale of 2dt and a scale spacing of 0.25, where dt=1/1024s is the sample period. They identified three distinct shedding regimes: a uni-modal regime for ? >0.9 and two bi-modal regimes for 0.9>? >0.675 and 0.675>? >0.3. They found that at high cavitation numbers (? >0.9), where cavity lengths are small, the breakup is driven by small-scale instabilities in the overlying boundary layer. But in cavitation numbers below 0.9, greater cavity lengths allow large-scale shedding to develop driven by coupled re-entrant jet formation and shockwave propagation.
As expressed in the literature, the small amount of research on the wavelet transform of cases with cavitation especially in the sphere are available. Most of signal processing research on sphere cavitation are experimentally, and there is no wavelet analysis of numerical investigation. The experimental data in this model types were analyzed by capturing an image or acoustic data of the model. In this work, the exact values of flow properties points are captured during the time in different cavitation numbers. The data is analyzed by wavelet transform, and it is discussed on regimes and phenomena in flow depending on its frequencies.?