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This study experimentally investigates the statistics of wall-pressure fluctuations and their source inside attached cavitation under different cavity regimes. Experiments were conducted in the divergent section of a convergent-divergent channel at a constant Reynolds number of Re = 7.8 × 105 based on throat height, and different cavitation numbers σ = 1.18, 0.92, 0.82 and 0.78. Four high-frequency unsteady pressure transducers were flushed-mounted in the divergent section downstream the throat where cavitation develops to sample the unsteady pressure signals induced by cavity behaviors. Flow visualization and wall-pressure measurement in high frequency on the order of MHz were employed using a synchronizing sampling technique. Results are presented for sheet/cloud cavitating flows. Specifically, sheet cavitation with both inception shear layer and fully cavitated shear layer and cloud cavitation under re-entrant jet dominated shedding and shock wave dominated shedding are studied. Compared with re-entrant jet, the interactions between shock wave and cavity could induce pressure peaks with high magnitude within cavity, which will collapse the local vapor along its propagating path and reduce local void fraction. Furthermore, statistics analysis shows that within the cavity, wall-pressure fluctuations increase with the distance to cavity leading edge increase in the first half of cavity length, and the moments of the probability density distribution skewness and kurtosis factor decrease, indicating the asymmetry and intermittency of wall-pressure fluctuation signals decrease. In shock wave dominated cavity shedding condition, the skewness and kurtosis factor increase. These results can provide data to improve the accuracy of turbulence modeling in numerical simulation of turbulent cavitating flow.

Cavitation is a complex multiphase flow phenomenon with an abrupt transient phase change between the liquid and the vapor, including multiscale vortical motions. The transient cavitation dynamics is closely associated with the evolution of the cavitation vortex structures. The present paper investigates the cavitation vortex dynamics using different vortex identification methods, including the vorticity method, the Q criterion method, the Omega method (Ω), the λ2 method and the Rortex method. The Q criterion is an eigenvalue-based criterion, and in the Omega method, the parameter is normalized, is independent of the threshold value and in most conditions Ω=0.52. The Rortex method is based on an eigenvector-based criterion. Numerical simulations are conducted using the implemented compressible cavitation solver in the open source software OpenFOAM for the sheet/cloud cavitating flows around a NACA66 (mod) hydrofoil fixed at α=6°, σ=1.25 and Re=7.96×105. The flow is characterized by the alternate interactions of the re-entrant flow and the collapse induced shock wave. Results include the vapor structures and the vortex dynamics in the unsteady sheet/cloud cavitating flows, with emphasis on the vortex structures in the cavitation region, the cavity interface, the cavity closure, the cavity wakes, and the foil wakes with the shedding cavity. The comparisons of the various methods, including that the vorticity method, the Q criterion method, the Omega method, the λ2 method and the Rortex method, show the performances of different methods in identifying the cavitation vortex structures. Generally, during the attached cavity growth stage, the Q criteria can well predict the vortex structures in the cavitation region and at the foil trailing edge in the pure liquid region, while with the Omega method and the Rortex method, the vortex structures outside the attached cavity and on the foil pressure side can also be predicted. The λ2 method can well predict the vortex structures in the cavity closure region. During the re-entrant jet development stage, the vortex structures in the re-entrant jet region is weak. During the cavity cloud shedding stage, the vortex dynamics at the foil leading edge covered by newly grown cavity sheet is different from that during the attached cavity sheet growth stage. During the shock wave formation and propagation stage, strong vortex structures with both the size and the strength are observed owing to the cavity cloud shedding and collapse behavior. The influence of the small parameter e in the Omega method on the cavitation vortex identification is discussed.

The objective of this paper is to investigate the unsteady cavitation behaviors and the corresponding cavitating flow-induced vibrations. Results are presented for the modified NACA66 hydrofoils made of stainless steel and POM Polyacetate respectively at Re = 6.0×105 for various cavitation regimes. The high-speed camera and the single point laser Doppler vibrometer (LDV) are used to observe the transient cavitating flow patterns and measure the vibration velocities. The results showed that the vibration amplitude increases dramatically for the cloud cavitation due to the development of large-scale cloud cavity. The main flow-induced frequencies, which are in accordance with the cavity shedding frequency, decrease with the decrease of the cavitation number. As for the effect of the hydroelastic response on the vibration behavior, the lift coefficient for the POM Polyacetate hydrofoil fluctuates more significantly with a larger mean value than that for the stainless steel hydrofoil. Compared with the vaporous cavity along the suction side of the stainless steel hydrofoil, the cavity for POM Polyacetate hydrofoil appears to be fragmentized. The main vibration frequencies for the POM Polyacetate hydrofoil are larger than that for the stainless steel hydrofoil, with the chaotic hydroelastic response with high frequency.

The objective of this paper is to investigate the effects of air injection on the characteristics of two different unsteady sheet/cloud cavitation shedding mechanisms, namely re-entrant flow mechanism and bubbly shock propagation mechanism, in the convergent-divergent channel. Experiments were conducted in the 10° divergent section with a ventilation slit near the throat, using a simultaneous sampling technique to synchronize the transient cavity behaviors with wall-pressure signals. Results are presented at a Reynolds number 9.33 × 105 and Froude number 10.24 for (1) under re-entrant flow mechanism (σ = 0.81) characterized by the intermittent shedding of small-scale cavities, and (2) under bubbly shock propagation mechanism (σ = 0.70) characterized by periodic large-scale cavity cloud shedding, with three non-dimensional air injection volumetric flow rates, namely 0, 1.135 × 10−3 and 2.270 × 10−3. The results show that air injection from the throat into the shear layer can significantly suppress cavitation induced unsteady pressure fluctuations. With the increasing of air flow rate, the size of the attached sheet cavity and the shedding cavity clusters grows larger, and the distance between the new attached sheet cavity and the shedding cavity cloud decreases, resulting in the cavitation region misty. The cavitation evolution tends to be stable, indicating the increase in the cavitation cycle, and the FFT analysis of the unsteady pressure fluctuations shows the decrease in dominant frequency. For the re-entrant flow mechanism condition, air injection rate at 1.135 × 10−3 will cause the transition from small-scale cavity clusters shedding to large-scale cavity cloud shedding, accompanying with pressure fluctuations increasing. With the air injection rate further increase, the pressure fluctuations decrease. Air injection can significantly reduce the unsteady pressure fluctuations spectral content in the frequency range of 1 kHz to 10 kHz. For the bubbly shock propagation mechanism condition, air injection can avoid the formation and propagation of the bubbly shock and suppress both the pressure peaks and pressure fluctuations. With the increase in the air injection rate, the unsteady pressure fluctuations are further suppressed. The unsteady pressure spectral content between 0.2 kHz and 10 kHz is effectively reduced.

The objective of this paper is to investigate the compressible turbulent cavitating flows with special emphasis on shock wave dynamics, with the water/vapor compressibility taken into account. The simulations are performed by solving the compressible, multiphase unsteady Reynolds-averaged Navier-Stokes equations with Saito cavitation model and SST-SAS turbulence model. The compressibility of both the pure water and vapor is considered by employment of the Tait equation of state for water and ideal gas equation of state for vapor. Results are presented for a 3-D NACA66 hydrofoil fixed at α = 6° and σ =1.25 in partial cavitating flows. Cavity collapse induced shock wave formation and propagation, which is closely related to the compressibility characteristics of cavitating flows, are well predicted. Good performance has been obtained for both the cavity evolution process and cavitation induced pressure signals, especially the cavity collapse induced shock wave emission and its interaction with the attached cavity sheet. The pressure peaks in microseconds accompanying the shock wave are captured. The typical quasi-periodic sheet/cloud cavitation evolution is characterized by the following four stages: (1) the growth of the attached cavity sheet, (2) development of re-entrant flow and attached cavity sheet breakup, (3) attached cavity sheet rolling up and cavity cloud shedding, and (4) cloud cavity collapse, shock wave emission and propagation. The cloud cavity collapse induced shock wave dynamics is supposed to be the major origin of cavitation instabilities.

The objective of this paper is to study the cavitation vortex dynamics in compressible turbulent cavitating flow, around a NACA66 hydrofoil. The simulations are conducted based on the open source software OpenFOAM, solving the compressible governing equations together with the Tait state equation for water and ideal gas state equation for vapor. The Saito cavitation model is used to model the cavitation phase change process and SAS SST turbulence model is adopted to account for the turbulence effects. The numerical results showed a good agreement with the experiments. The cavity evolution presents quasi-periodic behaviors, and the alternative re-entrant flow movement and shock wave dynamics play an important role in cavitation vortex dynamics. Strong coherent relationship between cavitation behaviors and vortex dynamics is illustrated. Based on the budget analysis of vorticity transport equation, it shows that during the attached cavity growth, the re-entrant flow development and the cloud cavity being shed stages, the baroclinic torque term dominates the vorticity transport process. During the shock wave propagation stage, the vortex dilatation term dominates in the attached cavity sheet region. Besides, the baroclinic torque term has strong influence on vorticity transport characteristics.

The objective of this paper is to investigate the unsteady pressure fluctuation characteristics in the process of breakup and shedding of unsteady sheet/cloud cavitating flows via combined experimental and computational methods. Experiments are conducted in the divergent section of a convergent-divergent channel using a simultaneous sampling technique to synchronize the transient cavitation behaviors and wall-pressure signals. In the numerical simulations, the Zwart cavitation model and the modified RNG k-e turbulence model are solved, with the compressibility effects of both water and vapor considered. In addition, one-dimensional bubbly shock wave relationship is applied to analyze the process of the vapor fraction discontinuity propagation. Two different types of cavity breakup and shedding existing in the unsteady sheet/cloud cavitating flows are observed, which is induced by re-entrant flow and vapor fraction discontinuity propagation mechanism, respectively. The re-entrant flow generates at the rear of the cavity, moving forward along the wall. When it arrives at the throat, it breaks up the attached cavity, resulting in the cloud cavity shedding. During the process, the wall pressure fluctuation is relatively small. The vapor fraction discontinuity propagation is resulted from the bubbly shock in water/vapor mixture of the sheet/cloud cavity. There is a significant difference of vapor fraction between the pre- and post of the discontinuity. The pre-discontinuity area is almost pure vapor, and the post-discontinuity area consists of water/vapor mixtures with relatively low vapor fraction. During the discontinuity propagation, the pressure peak exists at shock wave front. When the discontinuity arrives at the throat, the void fraction will suddenly decrease, which indicates the low vapor generation rate. Under the convection of the main flow, the attached cavity will be separated from the newly generated vapor, resulting in the attached cavity breaking up and the cavity cloud shedding.

The objective of this paper is to address the simulation of supercavitating flows around a slender body projectile at the sub-, trans- and supersonic speeds with the water compressibility effects considered. Based on the slender body theory (SBT) and the matched asymptotic expansion method (MAEM), the integro-differential equations for the cases of M a M a >1 are derived and solved. The results show that there is a good agreement of the supercavity shape for both the cases of M a M a >1 between the numerical simulation and the experimental results. The influence of Mach number on the supercavity length L , maximum radius R , slenderness λ , the corresponding growth rate of the supercavity length L ˜ , the growth rate of the maximum supercavity radius R ˜ , and the position of the supercavity maximum section (PSMS) are discussed. It can be found that L ˜ is much bigger than R ˜ , due to the large λ . It also concludes that the front part of the supercavity is thicker than the rear part, and the PSMS moves forward further at supersonic speed. Finally, the reason for the supercavity shape transition around M a = 1 is illustrated and it may be the c a use of the extension of perturbation zones at transonic speed.

The objective of the paper is to investigate the physics involved in the compressible cavitating flows, with emphasis on the compressibility effects. 3-D numerical simulations were conducted on the open source software platform OpenFOAM, using both the native incompressible cavitation solver interPhaseChangeFOAM and implemented compressible cavitation solver, where the cavitation model and turbulence model are kept the same and differences of the two approaches mainly root in the density variances of pure liquid and pure vapor. Results are presented for the transient sheet/cloud cavitating flows around a Clark-Y hydrofoil fixed at attack of angle α=8° at inlet velocity U=10m/s and cavitation number σ=0.8, where both ensemble averaged statistics and transient characteristics are analyzed. Good agreement can be obtained using both the incompressible and compressible approaches when compared with the experiment data. While it is found that compared with the incompressible approach, the compressible approach can predict the unsteady cavitation evolution and cavity shedding frequency better. With the compressibility effects considered, the time averaged void fraction distribution decreases, and the cavity size (i.e. cavitation area) becomes smaller. The re-entrant flow thickness normalized by local cavity thickness predicted by the compressible approach is larger than that by the incompressible approach, indicating that the compressible approach can predict the re-entrant jet dynamics well. The velocity divergence analysis show that compared with that in incompressible approach, where velocity divergence mainly comes from the mass transfer between phases, in compressible approach, the velocity divergence originates from both the cavitation two-phase fluid compressibility and mass transfer, and the fluid density variance dominates in compressible results. Following, the budget analysis of vorticity transport equation (VTE) show that the vortex stretching term dominates the cavitation vortex dynamics. Compressibility effects will significantly increase the dilatation term and decrease baroclinic term by decreasing the misalignment between density gradient and pressure gradient. Finally, the temperature and density variance in different cavitation structures are presented.

The main purpose of this work is to shed light on the physics involved in the two distinct cavity cloud shedding mechanisms in cloud cavitating flows, namely re-entrant jet mechanism (RJM) and shock wave propagation mechanism (SWM). A compressible cavitating flow solver, which considers the compressibility effects of both liquid and vapor, is used to account for the wave dynamics in cavitating flows. The compressible Navier-Stokes equations, coupling the mass, momentum energy equations, and phase fraction transport equation, along with the thermodynamic equations of state for both liquid and vapor, Saito cavitation model and the SST-SAS turbulence model, are solved. Numerical results are presented for the conditions of both the re-entrant jet mechanism and shock wave mechanism around a NACA66 (mod) hydrofoil (Leroux et al., 2005), respectively, with emphasis on the process of re-entrant jet development and shock wave formation and propagation. The results show that the re-entrant jet can cause the attached cavity sheet breakup for both the two cavity cloud shedding mechanisms in both high and low angle of attack, while the shock wave formation and propagation process only occurs under shock wave mechanism at low angles of attack. Pressure evolution illustrates that in the re-entrant jet mechanism, cavity cloud collapse will induce high pressure load, while no shock wave and thus the corresponding rebound phenomenon are observed. In shock wave mechanism, during the whole process of the shock wave dynamics, namely generation, propagation and rebound process, pressure fluctuations increase sharply along with the generation of the pressure peaks with large amplitude and short time interval. Further study on the compressible characteristics involved in the two cavity shedding mechanisms illustrates that vapor fraction and mass transfer have a significant effect in sonic speed and Mach number characteristics. The average and standard derivation of maximum Mach number (Mamax) in shock wave mechanism is lower than that in re-entrant jet mechanism. Cavitating flows are characterized by low sonic speed value in the cavitation region and high sonic speed value in the pure liquid region and a sonic speed boundary layer exists between the two regions, the thickness of which is about the size of the local attached cavity sheet on foil surface. In the process of shock wave generation and rebound, cavity volume and cavity volume rate experience large fluctuations, showing strong cavitation instabilities in shock wave mechanism.

The three kinds of vortex identification methods, namely, [Formula: see text] criterion, [Formula: see text] criterion and [Formula: see text] method, are then employed to investigate the physical interactions between the cavitation and vortex dynamics around two-dimensional Clark-Y hydrofoil. The results show that compared to the [Formula: see text] and [Formula: see text] criterion, the [Formula: see text] method can capture the vortex structures with both strong and weak vortices, especially for the weak vortices located in the boundary of the cavity and the back region of the re-entrant flow. A proper value of [Formula: see text] in [Formula: see text] method based on the previous studies is then suggested to avoid the pseudo-vortex structure in cavitating flow field due to division by zero. The modified [Formula: see text] method with a proper [Formula: see text] is then applied to analyze the details of vortical structures in the growth of attached cavity, the re-entrant flow development stage and the cloud cavity shedding stage. The results show that the vortical structures are captured in the boundary and rear region of the attached cavity, the intensity and complexity of strong vortices in the rear boundary region of re-entrant flow increased with its development, and the strength and area of vortical structures at the trailing edge of hydrofoil increased with propulsion of cloud cavity before it sheds completely.

This paper introduces a computerized on-line partial discharge (PD) monitoring and diagnostic system for transformers. The system, which is already in use in a power station, uses wide-band active transducers and a data acquisition unit with modularized and exchangeable components. The system software is a power equipment monitoring and diagnostic system, which is based on the component object model, and was developed for monitoring multiple parameters in multiple power supply systems. The statistical characteristics of PDs in power transformers were studied using 7 experimental models for simulating PDs in transformers and 3 models for simulating interfering discharges in air. The discharge features were analyzed using a 3-D pattern chart with a three-layer back-propagation artificial neural network used to recognize the patterns. The results show that PDs in air and oil can be distinguished. The model can be used for interference rejection on-line monitoring of partial discharge in transformers.

To suppress interference is a critical technique of online partial discharge monitoring for power equipment insulation. They can be divided into two types: periodical and impulse interference according to their signal characteristic. Different anti-interference techniques can then be chosen to suppress them separately. This paper describes various anti-interference techniques which have been developed recently and their actual effect on online partial discharge monitoring. The above techniques include a combined filter, a digital filter, a differential system and a pulse discrimination system. This paper presents some other anti-interference ideas which are satisfied for online partial discharge monitoring. >

A computer-aided online detection system of partial discharges (PDs) in power transformers is described. The impulse electrical signals of PD are detected with a current transducing unit and the acoustic emission signals of the PD are detected with acoustic transducing units. Various detected analog signals are transmitted with an optical fiber transmission system to the data-acquisition circuit and microcomputer. The frequency-division multiplexing technique is applied to transmit four channels of analog signals in one optical fiber. The amplitudes of detected electrical and acoustic signals are acquired and transmitted to the microcomputer with DMA. The microcomputer is used to store and to process the acquired signals. Two kinds of online PD calibration methods were developed, i.e. the transformer bushing method and the impulse charge couple method. With these methods various functions of this detection system are realized, such as offline and online PD detection, online PD calibration, recognition of electromagnetic interference, and location of the PD source. Onsite experiments with this system were performed in several power substations, and the test results were satisfactory. >

To analyze the statistical characteristics of partial discharges (PDs) in power transformers, 7 types of experimental models simulating PD in transformers and 3 types of models simulating interfering PD in air are designed and model experiments are conducted in a screened room. Using a digital measuring device with the sampling rate of 50 kHz, the quantity phase information of PD pulse current in models is obtained after the signal is processed by a peak-holding hardware. The PD features are extracted using the 3D pattern chart and then a group of three-layer back-propagation ANNs (artificial neural networks) is used to recognize the PD patterns. The investigation shows that ANN has enough ability to recognize different PD in oil-paper insulation of power transformers and PD interference from air can be recognized and eliminated.

This paper discusses the development of a simulation model used to study the propagation of partial discharge (PD) pulses of transformers in a 500 kV substation. The results are used to design an on-line PD monitoring system for transformers. The impedance matrix of a 500 kV single-phase transformer is computed with a special program based on geometry data and its external coupling network is calculated with EMTP. The factors that affect the coupling network (often referred to as coupling impedance) are also analyzed. It was found that the frequency characteristic of the coupling network is complex and an equivalent lumped coupling capacitance representation is only feasible below 60 kHz. The impedance varies greatly as frequency increases. The simulated PD current responses are obtained in tank grounding and 500 kV bushing tapping grounding and the optimal monitoring point is discussed. Applying resonant frequency of PD responses as monitoring frequency is suggested; this can increase the monitoring sensitivity effectively. A practical off-line PD calibration model for transformers in operation is designed according to the simulation results.