Blade Passage Frequency Research Articles

Acoustic characteristics of water-jet propulsion with screw mixed-flow pump under quasi-submerged state

As a key point of the stealth performance, acoustic characteristics of a screw mixed water-jet pump were investigated under the quasi-submerged state. The relationships between thrust and rotation speed of screw-mixed pump, drag, and submerged velocity of water-jet propulsion were obtained from the flume tests and numerical simulation. Based on the results of the unsteady flow field calculation with the detached eddy simulation (DES), the sound radiation fields of the screw mixed water-jet propulsion at different rotation speeds were investigated by the finite element method (FEM) coupled with the vibro-acoustic method. The flow-induced dipole source noise of every flow passage component increases with the increasing of rotation speed. The mathematical relations of the flow-induced noise at impeller between different rotation speeds were established. The maximum sound pressure level (SPL) of every flow passage component appears at the impeller blade-passing frequency (BPF). In the medium-high frequency domain, dipole source induced noise from the impeller is the main external noise field during the propulsion process. At the first-order BPF, the ratio of SPL of the impeller is equal to the 0.5 power of the rotation speed in the phase of [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text]. At the sixth-order BPF, the ratio of SPL of the impeller is directly proportional to the reciprocal power of rotation speed ratio in the phase of [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text].

Effect of Blade Outlet Angle on Acoustics of Marine Centrifugal Pump

To research the effect of blade outlet angle on acoustics of marine centrifugal pump, the unsteady numerical simulation analysis of the four models is carried out and the dipole source of pump shell is extracted. The constraint modal of pump, interior sound pressure level (SPL), exterior acoustic directivity and sound power level are obtained. The results show that five and six SPL peaks appear at BPF and blade frequency multiplier in the pump inlet and outlet, respectively, the SPL peak value is the largest at blade passing frequency (BPF), and the interior acoustics propagates to inlet and outlet directions, and to outlet more significantly. The exterior acoustic directivity in the four models is the same in all directions, and the blade outlet angle has little influence on the changes of exterior acoustic directivity. The SPL at BPF and 2BPF in Y = 0 plane is significantly smaller than that in X = 0 and Z = 0 planes, and the difference of maximum SPL at BPF is 7.2 dB and 8.0 dB and that at 2BPF is 7.6 dB and 6.4 dB, respectively. The sound power level is maximum at 2BPF, and that at the BPF and 2BPF increases first and then decreases with the blade outlet angle increases. When the blade outlet angle is 40o, the interior and exterior acoustic performances are better. The experimental value of the SPL in model 35 is basically consistent with the simulated value, which fully indicates that the numerical simulation analysis has high accuracy and provides support for the credibility of the acoustic simulation results.

Experimental Study of Pressure Pulsation in a Mixed-Flow Pump with Different Tip Clearances Based on Wavelet Analysis

In order to investigate the effect of various impeller tip clearances on the pressure pulsation in a mixed-flow pump, the energy performance test and pressure pulsation experiment of a mixed-flow pump with different tip clearances are studied simultaneously. The pressure pulsation signals at impeller inlet, middle, and oulet are processed and analyzed by the wavelet transform. The results show that the change of tip clearance can affect the head and efficiency of mixed-flow pump. Under designed flow rate, when the tip clearance increases from 0.2 mm to 1.1 mm, the head and efficiency decrease by 18.1% and 11.6%, respectively. Due to the strong influence of blade passing frequency (BPF) at impeller middle, the period of pressure pulsation curve is about 1/4 of impeller rotation period. At impeller inlet, the low-frequency pulsation with energy concentration is the main disturbance frequency, and, with the increase of tip clearance, not only does the high-value region of wavelet spectrum expand to low-frequency direction but also it is easy to form second-order peaks in the time-averaged wavelet curve. At impeller outlet, affected by BPF and rotor-stator interaction (RSI), the high-frequency disturbance in RSI area decreases first and then increases. The wavelet coherence demonstrates the stable low-frequency disturbances in comparison to others and it will affect the flow field at impeller middle.

Influence of axial skewed slots on the rotating instability of a low-speed axial compressor

Experimental and numerical analyses were performed on a low-speed axial compressor rotor to investigate the aerodynamic and acoustic effects of axial skewed slots casing treatment on the rotating instability. The experimental results showed that the stall margin could be improved by 8.0% and the frequency broadband hump owing to the rotating instability was suppressed effectively. In the noise spectra, the two dominant broadband humps on both sides of the blade-passing frequency also reduced in amplitude. Full-annulus unsteady computational fluid dynamics simulations were performed near the design condition. Time- and frequency-domain analyses as well as a proper orthogonal decomposition method were applied to obtain the oscillation, frequency, energy and flow characteristics of the rotating instability. Axial skewed slots casing treatment causes a distinct reduction in the amplitude of the pressure fluctuations and frequency spectra with a decrease in the energy of the rotating instability modes. The slots alleviated the tip flow blockage by the periodic injection and removal of the fluid from the passage, which enabled a high tip clearance flow downstream with little impingement on the neighbouring blade tip.

Effects of Engine Acoustic Waves on Aerooptical Environment in Subsonic Flight

Spatially and temporally resolved wave fronts were collected in flight using Airborne Aero-Optics Laboratory at varying subsonic Mach numbers through both the naturally developing boundary layer and an artificially generated shear layer. Dispersion analysis was used to separate the wave fronts into the downstream and upstream-traveling components. The upstream propagating component was associated with sound waves, originating from the aircraft’s engine, located downstream of the measurement location, with convective speeds that are consistent with theoretical predictions. The spectra of the acoustic-related component were dominated by the tonal frequency associated with the engine’s fan blade pass frequency. Modal analysis also revealed the streamwise spatially periodic nature of the acoustic component of the wave fronts, further confirming the acoustic nature of these distortions. An analytical model was derived which established the relationship between overall levels of acoustic-related optical distortions and the acoustic pressure fluctuations. The model was used to estimate the acoustic pressure spectra and sound pressure levels at the measurement location.

Stall inception in a contra-rotating fan under radially distorted inflows

The fan of a gas turbine engine is often subject to distortion due to non-uniformities in the incoming flow which could eventually result in an early stall of the fan. Contra-rotating fans have potential aerodynamic advantages and could replace the conventional fan configurations of gas turbine engines. Understanding the phenomenon prior to stall is important to characterise the behaviour of the stage at low mass flow rates. This paper investigates the phenomena leading to stall in a low-aspect ratio contra-rotating fan stage operating at different speed combinations under radially distorted inflows. Unsteady casing static pressure measurements obtained at a location upstream of rotor-1 leading edge are analysed using wavelet and Fourier analysis techniques. The results primarily concluded that a higher speed of rotation of rotor-2 could possibly suppress the pre-stall disturbances. The fluid structures leading to stall are initially associated with the blade passing frequency (BPF). These frequencies stretch to lower frequencies during the onset of fully developed stall and fully developed stall finally occurs at low frequencies.

Ship Airwakes in Waves and Motions and Effects on Helicopter Operation

Insight into the effects of motions and waves on a ship airwake can be used to provide information regarding safe conditions for at sea flight operations and pilot training. We present a study on the effects of waves and motions on a ship's airwake and a helicopter operating above the flight deck using full scale computational fluid dynamics simulations. The ONR Tumblehome Ship (ONRT) geometry is analyzed in wind and regular head waves corresponding to nominal sea states 3 and 6. In order to separate the effects of waves and motions, simulations are conducted for both sea states with combinations of: waves and motions, waves and no motions, no waves with motions, and no motions or waves. A triple velocity decomposition is conducted in order to quantify changes in the airwake due to motions and waves. The aerodynamic loads on a helicopter hovering in the airwake are studied with one-way and two-way coupling approaches. The one-way coupled analysis uses the velocity field data from the full scale airwake simulations along with disk actuator theory to calculate thrust fluctuations for three different rotor sizes operating above the flight deck. In the two-way coupled study a helicopter loosely based on the Sikorsky SH-60 Seahawk hovering above the flight deck of the ONRT is simulated, including dynamic overset grids of the main rotor, tail rotor and fuselage. This approach captures the interaction between the rotor downwash and the ONRT airwake. The study shows that for the lower sea state 3 the motions and waves have little effect on the airwake behavior, exhibiting little change with respect to the baseline case without motions and waves. At sea state 6 the flow field is modified significantly, which also affects the forces on the helicopter. Force fluctuations show main peaks at the wave encounter frequency and the blade passage frequency, as well as higher harmonics. The one-way coupling approach shows that larger rotors effectively filter out small scale fluctuations while smaller diameter rotors are affected by smaller flow structures.

Effects of blade surface roughness on compressor performance and tonal noise emission in a marine diesel engine turbocharger

A numerical study was conducted to investigate the effects of blade surface roughness on compressor performance and tonal noise emission. The equivalent sand-grain roughness model was used to account for blade surface roughness, and a hybrid method that combines computational fluid dynamics and boundary element method was used to predict compressor performance and tonal noise. The numerical approach was validated against experimental data for a baseline compressor. Nine different cases with different blade surface roughness were studied in this paper, the global performance was analyzed under compressor design speed, and the tonal noise level was predicted under the design condition. The results indicate that compressor total-to-total pressure ratio and isentropic efficiency were gradually decreased with the increasing blade surface roughness. Besides, the blade total pressure loss coefficient and the efficiency loss coefficient were also increased. It was found that the reverse flow at the leading edge of compressor rotor blades reduced blade loading. The pressure fluctuation at the leading edge showed that the peak of pressure fluctuations increased as the blade surface roughness was increased. The sound pressure level at blade-passing frequency shows a significant change with variation in blade surface roughness, which results in an increased total noise level. Furthermore, it was shown that the blade surface roughness had nearly no influence on acoustic directivity, but the sound pressure level increased with the increase in roughness, especially at blade-passing frequency.

Field monitoring of the ground vibrations adjacent to an onshore wind turbine foundation

Investigations of the soil–foundation interaction behaviour of wind turbine foundations and transfer of energy from the wind to the ground have not been reported in Canada. Indeed, very few vibration monitoring studies have been conducted globally around wind farms. It has been found that turbines predominantly produce vibrations related to structural resonances and blade-passing frequencies. Energy is found to be modified with distance and is dominated by surface waves. This paper describes a study of the effect of wind–structure interaction on the behaviour of a turbine foundation and the generation of ground-based vibrations around a working commercial wind turbine in Ontario. The field monitoring system and meteorological instrumentation are described in this paper and the responses of the structure and surrounding ground due to the fluctuating wind-field are discussed. The spectral analysis shows that the higher frequency vibrations attenuate more rapidly than the lower frequency vibrations. The tilted elliptical particle motions are found to be non-Gaussian because of the non-Gaussian wind conditions. The response attenuation with distance indicates that both geometric and material attenuation may dominate the vibration attenuation in the near field and only geometric attenuation occurs in the far field.

Investigation on RANS prediction of propeller induced pressure pulses and sheet-tip cavitation interactions in behind hull condition

This paper investigates the numerical prediction of cavitation and hull pressure pulses induced by a marine propeller operating in behind-hull conditions of a container vessel in model scale. Simulations are performed using commercial package Star-CCM+ and opensource package OpenFOAM using RANS approach and predictions are compared with experimental measurements. A mesh dependency study with respect to wake prediction is also presented. Operating conditions scaled to two different Reynolds numbers with the same propulsion characteristics and cavitation number are considered to study scaling effect. Simulations using tip refined mesh are performed and compared with using base mesh to study the tip vortex generation, tip vortex cavitation, its interaction with sheet cavity and induced pressure pulses. The influence of time step length is also investigated.Star-CCM+ and OpenFOAM predict consistent results. The predicted cavitation patterns agree well compared to experimental measurements as well as pressure pulse levels up to 3~4 times blade passing frequency (BPF) especially for the predictions with tip refined mesh. The sheet cavitation is the major contribution to 1st and 2nd order BPF pressure pulses and its closure has significant contributions to higher-order pressure pulses. Deduced pressure pulses by tip vortex cavitation (TVC) are significant ranging from 3rd order to 10th order of BPFs. The TVC induced pressure pulses are related to its violent bursting behavior which is influenced by the closure of the sheet cavity.

PIV experimental study on flow structure and dynamics of square stirred tank using modal decomposition

Stirred mixing is one of the important unit operations in the chemical, petroleum, pharmaceutical and food industries. The mixing of liquids is achieved by a rotating shear flow field formed by a periodic jet flow from the impeller. In this work, we investigated the flow structure in a square stirred tank without baffles and with a Rushton impeller (RT) using particle image velocimetry (PIV) technique. The instantaneous flow fields were obtained as a function of various rotations per minute (rpm) for the impeller (N=120, 150, 180, 210 and 240 rpm), while phase-resolved velocity information was obtained for N=150 rpm. The proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) methods were applied to analyze the velocity fields, flow structure and dynamic information in the absence of impeller area. As demonstrated by the results, there is a wide range of spatial and temporal scales throughout the process. The high energy parts exist in two kinds of structures except for the average fluid flow. The instability phenomenon results from the cyclic shear flow and the trailing vortices structure caused by the periodic jet near the blade passage frequency. As the Reynolds number is on the rise, the periodic flow increases, the random turbulence is reduced, and the flow tends to the ultimate stable state. The square section acts like baffles to change the direction of the fluid circumferential velocity while increasing the radial and tangential flow, which is conducive to mixing. This study provides a basis for understanding the flow structure and unsteady characteristics in a square stirred mixing tank.

Numerical simulation of transient flow in a shaft extension tubular pump unit during runaway process caused by power failure

To explore the load impact and instantaneous flow characteristics of a tubular pump under unconventional operating conditions, the runaway condition caused by the unit power failure are investigated. Unsteady three-dimensional (3D) numerical simulation and model test were executed on whole flow system of the pump, where a 3D VOF method was specifically adopted to simulate water surfaces of the upstream and downstream reservoirs. The results of numerical simulation in terms of system performance parameters and runaway speed presented a quite good agreement with the experimental data. During the transient process, both the rotational speed and flow rate of the pump unit were found to rapidly decrease with time until maximum runaway speed (1.51n0) was reached, where however, a time lag of 0.7s between the rotational speed and flow rate has been noticed. The explored increase of pressure pulsations is generally believed to have taken source from incurred water shock waves, where the main pulsation frequencies throughout the whole flow passage were the blade passing frequency (BPF) and its harmonics. Large flow vortical structures immerged within the rear guide vanes when the flow rate decreased to zero, while the same flow vortices appeared within the front guide vanes when the impeller rotational speed gradually fell to zero. This study’s results provide a meaningful reference about pump transient operations, leading to the prevention of associated structural vibrations and possible blade cracks, for safe operations of the pumping stations.

Fansmitter: Acoustic data exfiltration from air-Gapped computers via fans noise

Computers that contain sensitive information are often maintained in air-gapped isolation. In this defensive measure, a computer is disconnected from the Internet - logically and physically - preventing accidental or intentional leakage of sensitive information outward. In recent years it has been shown that malware can leak data over an air-gap by transmitting sonic and ultrasonic signals from a computer speaker. In order to eliminate such acoustic covert channels, current best practice recommends the elimination of speakers in secured computers, thereby creating a so-called ‘audio-gapped’ system.In this paper, we present ‘Fansmitter,’ a malware that can acoustically exfiltrate data from air-gapped computers, even when audio hardware and speakers are not present. Our method utilizes the noise emitted from the CPU, GPU, and chassis fans. We show that a software can regulate the internal fans’ rotation speed in order to control their acoustic signal, known as blade pass frequency (BPF). Binary data can be modulated and transmitted over these audio signals to a remote microphone (e.g., a nearby smartphone). We present design considerations, including acoustic waveform analysis, data modulation and demodulation, and data transmission and reception. We evaluate the acoustic covert channel with various fans at different distances and present the results. We also discuss issues such as stealth, interference, and countermeasures. Using our method we successfully transmitted data from audio-less, air-gapped computers, to a mobile phone in the same room. We demonstrated an effective transmission at distances of 1–8 m, with a maximum bit rate of 60 bit/min per fan.

Resonance Investigation and its Effects on Weight Optimization of Tubular Steel Wind Turbine Towers

The dynamic behavior of tubular steel wind turbine towers is investigated, with emphasis on discussing how the effort to avoid resonance of the soil-foundation-tower system, by keeping its eigenfrequencies outside specific ranges around the rotor (1P) and blade-passing (3P) frequencies, influences tower optimization. For modern, tall towers avoidance of resonance becomes critical compared to other structural design checks, such as buckling and fatigue. Considering that the rotor and blades have predefined mass and rotation frequencies, the tower’s fundamental frequencies should be controlled considering the cross-sectional properties of the tower as well as the flexibility of its foundation. The objective of the optimization problem formulated in this work is to reduce tower weight, while satisfying the resonance and buckling criteria and considering restrictions pertaining to fabrication, transportation and erection. The vibration modes and frequencies of a 120m tall tower are determined via detailed as well as simplified finite element models, with the latter proving to be sufficiently accurate. The dependence of the tower’s vibration frequencies on the soil and foundation is also investigated. The numerical models are introduced into the high performance optimization computing platform (HP-OCP), to obtain an optimum distribution of tower shell thickness over the height.

Analysis of vibration monitoring data of an onshore wind turbine under different operational conditions

A wind turbine structure works under the complicated environment and its operational state is complex. In this study, the operational state of a 1.5 MW wind turbine and the vibration response of the tower have been monitored for a long time. The vibration characteristic of the wind turbine under different operational conditions is discussed in detail, and it was observed that the rated rotation speed condition has the highest vibration level. The Campbell diagrams of wind turbine both in the FA direction and SS direction are drawn based on the natural frequencies results, which are identified by data-driven stochastic subspace identification method. It was observed from the Campbell diagrams that when the rotation speed is close to the grid-connected rotation speed, the blade-passing frequency 3f (0.43 Hz) is equal to the fundamental frequency of wind turbine which will easily lead to the resonance. This phenomenon is confirmed by the time history diagrams of the operational condition and vibration speed of a certain startup process. Lastly, the relationship between first-order, second-order modal parameters and operational conditions of the wind turbine are discussed in detail respectively. The mean value of first-order natural frequency is affected slightly by the different operational conditions while the value of second-order natural frequency increases significantly with the increase of rotation speed. The work in this paper can help us to better understand the response of the wind turbine under different operational conditions, which can also lay the foundation for the structure design, modal validation and damage diagnosis of wind turbine.

Investigating the In-Flow Characteristics of Multi-Operation Conditions of Cross-Flow Fan in Air Conditioning Systems

Cross-flow fans are widely used in numerous applications such as low-pressure ventilation, household appliances, laser instruments, and air-conditioning equipment. Cross-flow fans have superior characteristics, including simple structure, small size, stable airflow, high dynamic pressure coefficient, and low noise. In the present study, numerical simulation and experimental research were carried out to study the unique secondary flow and eccentric vortex flow characteristics of the internal flow field in multi-operating conditions. To this end the vorticity and the circumferential pressure distribution in the air duct are obtained based on the performed experiments and the correlation between spectral characteristics of multiple operating conditions and the inflow state is established. The obtained results show that when the area of the airflow passage decreases while the area of the eccentric vortex area gradually increases, then the airflow of the cross-flow fan decreases, the outlet expands, and the flow pattern uniformity reduces. It was found that wakes form in the vicinity of the blade and the tail of the volute tongue, which generate pressure pulsation, and aerodynamic noise. The pressure distribution along the inner circumference shows that the total minimum pressure appears in the eccentric vortex near the volute tongue and the volute returns near the zone. Moreover, it was found that the total pressure near the eccentric vortex is significantly smaller than that of the main flow zone. As the flow rate decreases, the pressure pulsation amplitude of the eccentric vortex region significantly increases, while the static and total pressure pulsation amplitudes are gradually increased. Close to the eccentric vortex on the inner side of the blade in the volute tongue area, total pressure is low, total pressure on the outside of the blade is not affected, and pressure difference between the inner and outer sides is large. When the flow rate of the cross-flow fan is 0.4 Qd, there is no obvious peak at the harmonic frequency of the blade passage frequency. This shows that the aerodynamic noise is caused by the main unstable flow.

Research of transient rotor–stator interaction effect in a mixed-flow pump under part-load conditions

In order to analyze the unsteady flow characteristic and the pressure fluctuation features of mixed-flow pump caused by the interaction between the impeller and guide vanes under part-load conditions, the unsteady flow field in the mixed-flow pump was numerically simulated based on the standard k–e turbulence model. The pressure distribution and the velocity distribution in the rotor–stator interaction (RSI) zones were acquired, and the time domain and frequency domain of the pressure fluctuation were emphatically analyzed. The results showed that the velocity within the rotor–stator interaction zones is mainly affected by the relative position of impeller and guide vane. With the decrease in flow rate condition, the flow fields become more violent and more vortexes generate in the RSI zone, which causes much energy losses. With the rotation of impeller, the vortexes generating from RSI zones move into the guide vane and dissipate in the guide vane passage in the end. The pressure pulsations at various monitoring points fluctuate periodically, and there appear four peak and four trough values with the same number of leaves. The dominant frequency of pressure pulsation was approximate to the impeller blade passing frequency (BPF). Within the rotor–stator interaction zones, the pressure pulsation coefficient in the rotor–stator interaction zone of the mixed-flow pump changes most obviously. The BPF and double and triple frequency of the pressure pulsation are dominant frequencies, and the frequency distribution range is relatively concentrated.

Study of Unforced Unsteadiness in Centrifugal Pump at Partial Flow Rates

In order to explore the unforced unsteadiness of centrifugal pumps, a 2-D frequency domain imaging display technology was used to study the development of these unsteady flow structures at partial flow conditions. The results showed that, the unsteady flow field was not only affected by rotor and stator interaction, but also appeared an unforced unsteadiness with fundamental frequency of St≈0.23 around the impeller throat area. Moreover, as the flow rates decreased, this unsteady flow structure gradually weakened and disappeared. When the flow rate was reduced to 0.6 times of design flow rate, another two unforced unsteady flow structures with characteristic frequencies of St≈0.0714 and St≈0.12 began to appear in the same area. Therefore, with the operating condition smaller than design flow rate, the internal flow became more and more complex. In addition to the forced unsteadiness, the unforced unsteadiness which is not connected with the blade passage frequency became more and more obvious.

Acoustic characterisation of a small high-speed centrifugal compressor with casing treatment: An experimental study

With the advancements in manufacturing, materials and computational methods, turbomachinery designs have become more efficient providing higher specific power and reliability with lower weight and cost. The rotational speed of turbomachines has increased while the overall machine size has decreased for a similar power output leading to the pervasive presence of small, high-speed turbomachines, specifically centrifugal compressors in helicopters, unmanned aerial vehicles (UAVs), auxiliary power units (APUs), turbochargers and micro gas turbines. In addition to superior aerodynamic performance over a wide range, increased operating speeds have made the acoustic emissions of small centrifugal compressors a critical aspect of design. Therefore, this work presents an experimental campaign to characterise the acoustic behaviour of a compressor with an intent to quantify the dominant features of the flow-induced noise for design and near surge operating conditions. Furthermore, the campaign is extended to establish the impact of the ported shroud casing treatment and operating speed on the acoustic emission of the compressor. The in-duct noise measurement method is used in this work to quantify the noise generated in the compressor by measuring pressure fluctuations near the inducer and diffuser while the propagation of the generated noise to the ducts is computed from an array of piezoelectric sensors. Spectra at the design operating point are dominated by tonal noise while broadband noise content is the dominant feature of spectra for near surge operation. Although the ported shroud cavity does not significantly alter the overall noise levels of the compressor operating at design condition, it does seem to propagate tonal noise. For near surge operation, the casing treatment positively impacts the acoustic emission with a reduction of approximately 10 dB in the range up to the blade pass frequency. Furthermore, various broadband features are also observed to be alleviated by the casing treatment.

Transient analysis of the fluid flow on a pumpjet propulsor

This work discussed the transient characteristic of PJP and gave a comparative analysis between steady and transient simulations. The simulations employed Reynolds-averaged Navier-Stokes equations (RANSE) method with a focus on the transient flow field and tip clearance effect. The mutual interference between rotor and stator does not lead to a massive difference in PJP whole open water performance. It causes remarkable changes in stator and duct, and the increasing of tip clearance enhances the changes. The exciting force on blades can not be ignored and represents a different variation between rotor and stator with the effects of advance ratio or tip clearance and possesses a characteristics frequency corresponded to blade passing frequency (BPF) and their harmonics. The exciting force intensity mainly embodies in BPF. The stator mainly has better recycling on rotor blade wake, and the recycling mainly acts on circumference velocity. Comparing with axial velocity, which shares almost the whole energy in PJP wake, both the circumference velocity and radial velocity include a little. Tip sweeping vortex and tip leakage vortex are the typical vortices in PJP. Tip leakage vortex plays a vital role in the stator flow field and PJP wake.