PIV measurement of cavitating flow around a pitching hydrofoil

Particle Image Velocimetry (PIV) and hydrodynamic measurements were applied to investigate the cavitating flow of a pitching hydrofoil in the form of triangular wave motion (mean incidence α 0=10°, amplitude Δα=5° and pitching frequency f*=2Hz). The Reynolds number is Re=4.5×105. The cavitation number is set to σ=2.3, 1.36. Different typical cavity patterns are observed by PIV images in the whole pitching period, including sub cavitation, inception cavitation, sheet cavitation and cloud cavitation. As the σ decreases, the cavity area increases. And the the corresponding time and position of cavitation patterns also changed significantly. In the instantaneous velocity field of an oscillating hydrofoil, the low velocity zone (LVZ) and the mainstream zone (MZ) are observed. The LVZ corresponds to the cavitation region and changes with the change of cavitation morphology. Meanwhile, the LVZ has a large velocity gradient. The velocity gradient in the MZ is larger along the direction parallel to the incoming flow, and the velocity tends to increase first and then decrease gradually downstream. With the decrease of cavitation number, the area of LVZ increases. And the distribution of LVZ is more uneven, which is mainly caused by oscillation motion and uneven water vapor mixing.


Introduction
Analysis of each blade element in hydraulic machinery system have shown that foil can oscillate under some circumstances, such as propeller [1], water turbine [2], water-jet pump [3] and rudder [4].When the unsteady cavitation is formed, it will lead to system noise, erosion and structural damage.In many recent studies, researchers investigated numerically or experimentally the cavitating flows of the pitching hydrofoil [5][6][7], but all aspects of these phenomena have not been discovered yet because of many complex interactions of parameters.
Kubota [8] used laser doppler technology to study the structure of the cloud cavity and found that the cloud cavity is a large-scale turbulent vortex composed of many small-scale bubbles, revealing that the development of the reverse jet is the main factor for the shedding of the large-scale cavity.Foeth et al. [9] used time-resolved Particle Image Velocimetry(PIV) to investigate sheet cavitation of hydrofoils in the spanwise direction.The time-resolved PIV recordings can reveal the growth and shedding of attachment cavities.Franc et al. [10] studied the effect of unstable conditions on the attached cavitation around an NACA 16012 pitch hydrofoil.The findings revealed that the instability affects the cavity and boundary layer primarily by the effect of convection and delay effect.Hart et al. [11] found that the oscillations of hydrofoil led to irregular cavitation development and fall off forms, and the increase in inception cavitation number was mainly due to the increase in the effective angle of attack (AOA) caused by the oscillation movement.Kato et al. [12] used the PIV technology to study the lock-in phenomenon when the breakdown frequency synchronizes into the pitching frequency.In the subcavitation region, when the elongation of the sheet cavity does not change with the change of AOA under high reduced frequency.
In order to further explore the details of the cavitating flow, PIV and hydrodynamic measurements are used to study the transient cavitating flow around the pitching Clark-y hydrofoil and the corresponding hydrodynamic characteristics.

Cavitation tunnel
The experiments were conducted in the cavitation tunnel at the Beijing Institute of Technology.The tunnel is a looped test facility with a cuboid 0.7m×0.07m×0.19mtest section, as shown in figure 1.The 2D hydrofoil model with a Clark-y profile of chord length c=0.7 m and span s=0.69 m was used as the test model.Under the condition of a free-stream velocity of U∞=6.5 m/s (Re=4.5×10 5 ), the hydrofoil is placed in test section.A specialized oscillation mechanism ensured a triangular wave motion of the hydrofoil about its mid-chord axis with mean AOA α0=10°, amplitude Δα=5°and pitching frequency f*=2Hz, as shown in figure 2. In this study, the cavitation number σ is set to 2.3 and 1.36.Details of the configurations of the experiment can be found at reference [13].Figure 2 shows the variation of the α with time in the one pitching period.When the α increases, the hydrofoil is defined in upstroke stage.When the α drops, the hydrofoil is defined in the downstroke stage.In this paper, the symbol "+" is applied to indicate the upstroke phase and "-" is applied to indicate the downstroke phase.

PIV measurements
As shown in figure 3, the schematic of the PIV measurement system are given, and the velocity field data in the plane perpendicular to the spanwise were obtained.In this study, the laser is applied the continuous mode to form a continuous light sheet.A laser beam sheet is used to illuminate the flow area in question from the bottom window of the test section, thus capturing the structural characteristics.The cavitating flow information on the suction side of the hydrofoil were recorded using the SpeedSence M310 camera with a resolution of 1280×1280 pixels.The recording frequency of the PIV system was set to 5000 Hz.In this study, the main tracer particle used is a hollow glass bead with a particle diameter of 50μm.In order to get more details of the flow field, discrete bubble particles are used as auxiliary tracer particles.This method has been verified and affirmed by many researchers [14].In addition, an optical filter and fluorescent paint (FP R6G) are used to block the reflections of the light sheet from the test model.In order to exclude the errors caused by static mask from the PIV analysis, an new velocity field calculation method based on self-identification of moving boundary was developed.Base on the hydrofoil boundary detection, image transform and PIV algorithms technology, the velocity field in the original PIV images have been constructed.This principle and method also have been verified and affirmed by many researchers[15-16].Meanwhile, the moment and AOA of hydrofoil are record simultaneously.

Results and discussions
Figure 4 gives the evolution of non-dimensional moment coefficient CM(CM=M/(0.5ρU∞ 2 sc 2 ), where M is the moment) and cavity area Sc/SZ(Sc is the cavitation area on the suction side of hydrofoil, Sz is the area of the section of hydrofoil) for different cavitation number(σ=2.3,1.36) at the same test condition.It's noted that the different cavitation patterns (sub cavitation, inception cavitation, sheet cavitation and cloud cavitation) are captured and recorded.As σ decreases, the variation trend of moment coefficient and cavity area is similar.However, the cavity area and moment coefficient increase significantly.
As shown in figure 4(a), three typical cavitation patterns (sub cavitation, inception cavitation and sheet cavitation) are observed for σ=2.3.As α increases, the cavity area increases volatility.When α begins to decrease, the cavity area gradually declines.The periodic development and shedding of cavity correspond to the fluctuation of moment coefficient.From α -=8°to α + =8°, the cavity disappears and the cavity area is approximately 0. In this region, the moment coefficient changes linearly.Figure 4(b) also shows different cavitation patterns in the whole pitching period for σ=1.36.As σ decreases, cavity area is larger.And the maximum cavity area Sc/SZ is 1.9.The cloud cavitation occurs at the range of α + =12°~α -=11°.Meanwhile, due to the reduction of pressure, the corresponding time and position of other cavitation patterns also changed significantly.In figure 5, the pitching period and its related flow characteristics at σ=2.3 are discussed by selecting the representative instantaneous velocity fields of the nine typical α.It's noted that there are two typical regions (low velocity zone (LVZ) and mainstream zone (MZ)) in the PIV velocity contours.The cavity region between free stream and the hydrofoil surface shows LVZ (the green zone of figure 5).With the development and shedding of cavity, the area of LVZ changes correspondingly.Meanwhile, it can be found that the large velocity gradient in LVZ.For example, when the α reaches 15°, the cavity occurs in the separated flow region, the complex dynamic stall cavitation vortices correspond to strong velocity gradient variations.As α decrease, the velocity gradient gradually declines in LVZ.In addition, there is also a large velocity gradient in the MZ parallel to the direction of incoming flow, and the velocity increases first and then decreases gradually downstream.For σ=1.36, the representative instantaneous velocity fields of the nine typical α are presented in figure 6.With the decrease of cavitation number, the area of LVZ increases due to the development of largescale cavity.At the same time, the distribution of LVZ is uneven, which is mainly caused by oscillation motion and uneven water vapor mixing.For the MZ, the unsteady characteristics of cavitation affect the flow field, resulting in the distribution of the MZ is not uniform compared with σ=2.3.

Conclusion
Hydrodynamic and PIV measurements of a pitching Clark-y hydrofoil have been performed for two cavitation numbers (σ=2.3,1.36).We have found that there are different cavitation patterns in the whole pitching period, including sub cavitation, inception cavitation, sheet cavitation and cloud cavitation.As σ decreases, the variation trend of moment coefficient and cavity area is similar.However, the cavity area and moment coefficient increase significantly.And the corresponding time and position of cavitation patterns also changed significantly.For the PIV images, there are two typical regions (low velocity zone (LVZ) and mainstream zone (MZ)).The cavity region between free stream and the hydrofoil surface shows LVZ.With the decrease of cavitation number, the area of LVZ increases due to the development of large-scale cavity.At the same time, the distribution of LVZ is more uneven, which is mainly caused by oscillation motion and intense mixing of water vapor.For the MZ, the unsteady characteristics of cavitation affect the flow field, resulting in the distribution of the MZ is not uniform compared with σ=2.3.

Figure 1 .
Figure 1.Diagram of the cavitation tunnel.

Figure 2 .
Figure 2. Variation of the α with time in the one pitching period.

Figure 3 .
Figure 3. Schematic of the PIV measurement system.

Figure 4 .
The evolution of moment coefficient and vapor area with AOA for σ=2.3, 1.36.

Figure 5 .
Figure 5. Composite PIV images at different angle of attack for σ=2.3.Colored contour plots show velocity U.

Figure 6 .
Figure 6.Composite PIV images at different angle of attack for σ=1.36.Colored contour plots show velocity U.