Experiments in Fluids (2006) DOI 10.1007/s00348-005-0082-9
R ES E AR C H A RT I C L E
E. J. Foeth Æ C. W. H. van Doorne Æ T. van Terwisga B. Wieneke
Time resolved PIV and flow visualization of 3D sheet cavitation
Received: 20 April 2005 / Revised: 22 July 2005 / Accepted: 24 October 2005 Springer-Verlag 2006
Abstract Time-resolved PIV was applied to study fully developed sheet cavitation on a hydrofoil with a spanwise varying angle of attack. The hydrofoil was designed to have a three-dimensional cavitation pattern closely related to propeller cavitation, studied for its adverse effects as vibration, noise, and erosion production. For the PIV measurements, fluorescent tracer particles were applied in combination with an optical filter, in order to remove the reflections of the laser lightsheet by the cavitation. An adaptive mask was developed to find the interface between the vapor and liquid phase. The velocity at the interface of the cavity was found to be very close to the velocity predicted by a simple streamline model. For a visualization of the global flow dynamics, the laser beam was expanded and used to illuminate the entire hydrofoil and cavitation structure. The time-resolved recordings reveal the growth of the attached cavity and the cloud shedding. Our investigation proves the viability of accurate PIV measurements around developed sheet cavitation. The presented results will further be made available as a benchmark for the validation of numerical simulations of this complicated flow.
1 Introduction Cavitation is the evaporation of liquid when the pressure falls below the vapor pressure. When such a low pressure region is formed near the leading edge of a hydrofoil, the flow detaches and a pocket of vapor is formed, named attached or sheet cavitation. Downstream of this sheet E. J. Foeth (&) Æ C. W. H. van Doorne Æ T. van Terwisga Laboratory of Ship Hydromechanics, Delft University of Technology, Mekelweg 2, 2628 CD Delft, The Netherlands E-mail:
[email protected] B. Wieneke LaVision GmbH, Anna-Vandenhoek-Ring 19, 37081 Goettingen, Germany E-mail:
[email protected]
cavity, the flow re-attaches to the hydrofoil and a stagnation point is formed. The positive pressure gradient in this region forces a thin stream of liquid upstream into the cavity, termed the re-entrant jet. When the re-entrant jet impinges farther upstream on the fluid–vapor interface, part of the sheet cavity is pinched off and will be advected downstream. The advected cloud is often both highly turbulent and bubbly in nature and may collapse violently depending on the pressure condition. After the shedding of a cloud, the attached cavity starts to grow again and the process is repeated. For an overview of cavitation, see Rood (1991, inception), Brennen (1995, bubble cavitation), Arndt (2002, vortical cavitation) and Franc (2001, sheet cavitation). Sheet cavitation is a major cause of noise, vibration, and erosion on ship propellers. As it is usually not possible to avoid, it has to be controlled. Although the final evaluation of a propeller design is based on model experiments, numerical tools for cavitation simulation are becoming increasingly more important. Potential flow solvers are currently the industrial standard (Young and Kinnas 2001), and both Euler (Choi and Kinnas 1998; Sauer and Schnerr 2000) and RANS (Kunz et al. 1999; Senocak and Shyy 2001) codes are frequently applied. More recently, LES is used to predict cavitation behavior (Wikstrom et al. 2003; Qin et al. 2003). However, up to now simulations are not able to capture the pressure radiated by cavitation or to predict erosion location and severity on propellers (ITTC 2002). In support of this rapidly expanding field of numerical simulation, this experimental research was started with a threefold goal; firstly, analyzing the physical mechanisms of the instability of the flow; secondly, building a data set of simple cavitating flows to be used as benchmark material and thirdly, extending the insights gained to guidelines for propeller design. Validation material in the form of cavity volume, shedding frequency, velocity fields, and pressure measurement is essential. Since cavitation forms one of the most important design criteria for ship propellers, there have been numerous experimental studies in the past. Research
interests have varied from the influence of the boundary layer on the cavitation on axis-symmetric headforms (Arakeri and Acosta 1973), to the cavitation patterns observed on two-dimensional (2D) hydrofoils (Astolfi et al. 2000). Callenaere et al. (2001) used a 2D backward facing step to create a sheet cavity behind the step. Despite the 2D geometry of the setup, the cavity was often found to shed vapor clouds intermittently and at random locations, leading to a completely 3D and complex flow field. Laberteaux and Ceccio (2001) showed that the sweep (or skew) of the applied hydrofoil had a significant effect on the topology of the cavity and on the direction of the re-entrant jet. For this 3D geometry, the cavity was found to be far more stable. The importance of the re-entrant jet was further demonstrated by Kawanami (1997), who blocked the re-entrant jet and subsequently altered the cavitation behavior. From these and other experiments, it has become clear that the form and stability of the cavitation is very sensitive to the 3D geometry of the hydrofoil. Cavitation on ship propellers is distinctly 3D due to the 3D geometry of the propeller, the radially increasing velocity, the finite span of the blade and the periodic change of inflow conditions due to the wake behind a ship. As studying cavitation on a rotating object is inherently more difficult, it is common practice to study the flow on a steady (3D) hydrofoil with a cavitation topology and inflow condition closely related to propellers. A 3D hydrofoil with its shedding mechanism depending on its spanwise loading and reduced wall influence has a more structured and repeatable sheet than a 2D hydrofoil at a constant angle of attack. This allows for observations of the influence of controlled 3D effects. Ultimately, we hope to be able to adjust the propeller design in such a way that the cavitation pattern is stabilized and the vapor shedding will be minimized. The main purpose of this paper is to show the viability of time resolved PIV measurements (Raffel et al. 1998) for the study of sheet cavitation. In Sect. 2, we first present the experimental setup and the applied methods including a description of the cavitation, the applied 3D hydrofoil and the PIV setup. A common problem in the application of optical techniques to two-phase flows is the risk of strong reflections in the direction of the camera and the obstruction of the optical path (Tassin 1995). The first problem was avoided by the use of fluorescent tracer particles in combination with an optical filter in front of the camera lens blocking all laser light (Gopalan and Katz 2000; Bachert 2003). Particle images of good quality were obtained in the liquid phase, whereas the regions occupied by the vapor in the cavity appeared as blurred region in the PIV images. To solve the latter problem, an adaptive mask was developed to find the interface between the vapor and the liquid phase, as is discussed in Sect. 2.4. In Sect. 3 the results are presented. When the vapor regions were excluded from the PIV analysis, the velocity of the liquid phase could be evaluated within about 1 mm from the cavity interface. Visualization is another indispensable
tool for the study of the global dynamics of the cavitation. When the laser beam was expanded to illuminate the entire hydrofoil and cavitation structure, it was possible to obtain clear movies of the sheet cavity and vapor shedding. Finally, we summarize the work and draw some conclusions in Sect. 4.
2 Experimental setup and methods 2.1 Cavitation tunnel The experiments were performed in the University of Delft Cavitation Tunnel shown in Fig. 1. The measurement channel is 0.60 m long, the cross section is 0.297 m·0.297 m, with optical access from all sides. Velocities up to 10 m/s per second can be attained and the local pressure can be reduced to 5,000 Pa. The nondimensional cavitation number, defined as r¼
P0 PV ; 1 2 2 qV0
ð1Þ
and expresses the ratio of the pressure head to the vaporization pressure (PV) and the dynamic pressure (0.5 q V20) at the entrance of the test section. The pressure was measured with ten Keller PAA-15 pressure transducers at each wall of both the inlet and the outlet of the test section, and on two locations before the contraction upstream of the test section (Fig. 2). These sensors were calibrated in situ to within 1% error with a Keller PAA-33 pressure transmitter located in the test section. The velocity at the entrance of the test section (V0) was estimated from the pressure drop over the contraction and the known contraction ratio. Uncertainty analysis and error propagation indicated an uncertainty in r of nearly 7.5% within a 95% confidence interval for the presented measurements.
Fig. 1 Sketch of the cavitation tunnel. The upper and left leg are rectangular, the lower and right leg are cylindrical. The flow is counter clockwise and the air is evacuated at the dome on top of the tunnel
Fig. 3 Top, side and front view of the hydrofoil. The black outline in the top view indicates the viewing area of Fig. 6 (6.1–6.20)
For the measurements, a stationary and spatially uniform inflow was applied. The unsteady behavior of the cavity will, therefore, not be driven by an external pressure field but by its intrinsic dynamics. In the future, we also plan to apply periodic inflow conditions by means of an upstream mounted flow oscillator. 2.2 Three-dimensional hydrofoil The applied 3D hydrofoil was used before in a study by Dang (2000), see Fig. 3. It spans the entire test section of 294 mm, and it has a chord length of 150 mm. The cross section of the hydrofoil is defined by the NACA0009 thickness distribution (Abbott and von Doenhoff 1959). In order to avoid damage during the manufacturing of the hydrofoil, the profile’s trailing edge was thickened to a minimum of 0.4 mm. For this, the NACA polynomial t(x)N for the dimensionless thickness was complemented from xP=0.35 until the trailing edge, where x=[0...1] stands for the dimensionless chordwise coordinate, by the following polynomial: ! tmin tð1ÞN tðxÞ ¼ tðxÞN þ max tðxÞN C x xp 2 H xp ; 1 xp C is the chord length, t the non-dimensional thickness, tmin the non-dimensional minimum trailing edge thickness, and H the heaviside function. The hydrofoil is given a 3D shape by a variation in the angle of attack (a) along the spanwise direction (y):
aðyÞ ¼ aT
3 2 ! 1 1 16 y 12 y þ1 þ b: 2 2
The hydrofoil was manufactured with a span of 300 mm trimmed to size to fit the test section. The center of rotation of the hydrofoil is located halfway down the chord. The angle of attack increases smoothly toward the center of the hydrofoil by aT=8 (Fig. 4). The angle b is the rotation angle of the entire hydrofoil and is equal to the angle of attack at the wall, which was zero for our PIV experiment. This geometry results in a low-pressure region in the center of the hydrofoil, and the cavitation will develop here first. This immediately results in a 3D shape of the sheet cavity without interference from the walls. In laminar flow, at low Reynolds number for smooth objects, cavitation forms in the regions of laminar flow separation. Therefore, a natural transition to turbulence can temporarily suppress the leading edge detachment and the cavitation inception (Franc and Michel 1985). Geometric angle of attack 8 7 6
Angle [deg]
Fig. 2 A close-up of the test section showing the hydrofoil, the location for the camera for PIV measurements (C) and the light sheet (L)
5 4 3 2 1 0 0
50
100
150
200
Span [mm]
Fig. 4 Chordwise distribution of the angle of attack
250
300
This was avoided by the application of roughness elements of 120 lm at the leading edge (4% of the chord length) as a turbulence tripping mechanism. Prior to the experiments, the tunnel was left to run for a few days under minimum pressure conditions to ensure a minimal gas content. The gas content was not measured, but the roughness will supply the degassed flow with ample nuclei for sheet cavitation to develop (Kuiper 1982). Incipient cavitation on roughness elements is typically observed when r equals the minimum pressure coefficient (Caron et al. 2000) and the nuclei content of the flow is no longer critical. 2.3 PIV setup The PIV experiment was performed with a New Wave Pegasus dual-head, diode pumped Nd:YLF laser, with a 180 ns pulse duration and an energy of 10 mJ/pulse at a repetition rate of 1,000 Hz. The light sheet was formed with a compact system of cylindrical lenses, and the lightsheet thickness was estimated at 2 mm. The energy density in the lightsheet was sufficiently low to avoid damage to the perspex windows of the test section. An optical filter and fluorescent tracer particles were applied to block reflections of the lightsheet from the cavity interface. This principle was successfully applied in cavitating flows by e.g. Bachert (2003). The PMMARhodamine B fluorescent particles’ diameters are typically 20–50 lm and emit light in the orange band (around 590 nm). Fourteen grams of tracer particles were used on the tunnel volume estimated at 7.5 m3. Although the particles are not neutrally buoyant (q=1.19·103 kg/m3) and will settle between experiments (estimated settling velocity is less than 0.3 mm/s for the largest particles), they were quickly dispersed at start-up. No appreciable decrease in the particle density was noticed after 1 month of continuous running. The camera used is a LaVision Flow-master HighSpeedStar 4 (Photron Ultima APX) with a 10 bit dynamic range, 1 Megapixel resolution at a repetition rate of 2 kHz, and with 2.6 GB memory. A Nikon AF Nikkor 50 mm lens was used, with an f-stop of 2.8. The field of view was 18·18 cm2, centered around the hydrofoil in the lower part of the image. Small details such as the exact location of the flow detachment at the leading edge of the foil shown by Farhat and Avellan (2001) to occur within a region as small as 0.3% of the chord length for Re=3·106, corresponding to less than 2.5 pixels for the current magnification) are invariably lost. However, the main focus of this research is to study the large scale phenomena as the shedding sequence of the attached cavity and the flow around the cavitation structures, and these were well resolved with the current setup. Cavitation clouds that occur between the camera and the lightsheet can block the view of the camera on the lightsheet. In order to (partly) avoid this problem, the camera was tilted (8.2) to view the cavitation structure
from above (Fig. 2). This inclined viewing induces a small error in the vertical velocity component of about 1.4%. Viewing under large angles results in optical aberrations and necessitates a larger depth of view but for the applied angle neither effect was noticed. 2.4 PIV analysis The evaluation of the vector fields from the PIV-images is performed with the commercial PIV-software DaVis 7.0 from LaVision, and an overview of the parameters is presented in Table 1. The effective measurement frequency (1 KHz) is half the camera frequency, as single exposure double frame PIV images were recorded. With a laser pulse delay of 250 ms a typical particle displacement of 8 pixels at a flow rate of 7 m/s was obtained. The interrogation areas of 32·32 pixels large, with 75% overlap were used, resulting in a vectorto-vector spacing of 1.46 mm. Vectors with a deviation larger than 1.5 times the RMS of the neighboring vectors were considered spurious and were removed. The final results are smoothed once with a 3·3 Gaussian kernel. The refraction at the cavitation interface makes it impossible to have a clear view of the interior of the attached cavity, and therefore no tracer particles can be distinguished inside the sheet (Fig. 5.1), but particles can be seen in the cloud. Although the optical filter in front of the camera filters out the strong reflections of the laser lightsheet, the cavity appears clearly in the PIV images, as the entire test section is illuminated by the emitted light from the fluorescent tracer particles. For interrogation areas that partly overlap the cloud, the blurred and relatively high intensity level in this region can lead to large errors in the estimated velocities of the fluid motion at the cavity interface. To improve the accuracy of the velocity near the cavitation interface, an adaptive mask was applied to the PIV images to exclude the regions occupied by the cavitation, the hydrofoil and the entire region below the hydrofoil, from the vector evaluation. 2.5 Adaptive mask In order to exclude the regions occupied by vapor from the PIV analysis, an adaptive mask was developed to find the interface between the liquid and gaseous flow regions. The region within the mask was set to zero during PIV interrogation. The mask identified the vapor region as the region where the minimal intensity (the background) level surpassed a certain threshold, due to the bright reflections on the cavity interface, combined with the regions where the intensity of gradients was small, indicating the absence of tracer particles. It is stressed that the parameters of the mask, such as threshold levels and filter lengths, were determined empirically in order to match the calculated cavitation
Table 1 Overview of the experimental parameters
Tunnel
Test section
Seeding Light sheet
Camera
Imaging
PIV analysis
Fluid Max velocity Min pressure Min r Height Width Length Material Wall thickness Type Diameter Laser type Maximum energy Wave length Pulse duration Thickness Type Resolution Discretization Repetition rate Lens focal length f-number Viewing area Exposure delay time Maximum particle displacement Interrogation area Overlap IA
interface with the interface observed by eye in the PIV images. The image was mirrored at its sides to avoid errors when a filter window exceeded the borders of the image. In Fig. 5 (5.1–5.12) we show the intermediate steps of the adaptive mask in more detail. Figure 5.1 shows an unprocessed PIV image. The upper part of the image is dark as the frame of the test section blocked the view on this region of the flow. In the first step, a sliding median filter was applied to remove the particles from the image, where the fifth minimal intensity level in a window of 5·5 pixels provided a convenient measure for the background level, displayed in Fig. 5.2. A threshold was applied to convert the background intensity into a binary image (Fig. 5.3), and pixels within a radial distance of 6 pixels of the active regions were added to the filter to consolidate groups of neighboring pixels into contiguous regions (Fig. 5.4). As the intensity of the lightsheet was not constant, the threshold was varied across the image. Tracer particles, typically a few pixels large, were detected in the original image by application of a gradient filter using the following convolution kernels: 2
3 þ1 þ2 þ1 Kver Khor ¼ 4 0 0 0 5: 1 2 1 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 þ K 2 : A threshThe gradient was calculated as Khor ver old was applied to the gradient level to obtain the binary image shown in Fig. 5.5. Groups of isolated pixels were identified and removed. The regions where no particles occured within a radial distance of 7 pixels were assigned to the masked region, as shown in Fig. 5.6. 1 ¼ 4 2 1
0 0 0
3 þ1 þ2 5; þ1
2
Water 10 5,000 0.5 0.297 0.297 0.6 Perspex 40 Spherical 20–50 Nd:YLF 10 527 180 1.5 Photron Ultima APX 1,024·1,024 10 2,000 50 2.8 180·180 1.0 8 32·32 75%
m/s Pa m m m mm lm mJ/pulse nm ns mm Photron Ultima APX Pixels bit Hz mm mm2 ls Pixels Pixels
For the detection of the cavity interface, the region occupied by the hydrofoil and the flow region below the hydrofoil were subtracted from the vapor region and the vapor region was grown by another 6 pixels to smooth the surface (Fig. 5.7). The interface was still very irregular due to either reflections of bright tracer particles on the interface or the absence of tracer particles. In Fig. 5.9 the regions detected by the large background intensity and the absence of tracer particles were combined to find the total region occupied by vapor. Small and isolated regions corresponding to the wetted flow region were removed from the filter. For the final smoothing of the cavitation interface, the temporal sequence of 2D masks was stagged into a 3D array and smoothed three times by a 3D Gaussian kernel. The final result is shown in Fig. 5.10, and the cavitation interface is shown together with the original PIV image in Fig. 5.11. The interface of the cavitation as determined by the adaptive mask corresponds reasonably well to the interface observed by eye in the PIV images. However, the absence of particle images in several regions of the flow, particularly near the leading edge where the intensity of the lightsheet was weak, resulted in masking errors. For future measurements, the light sheet will be made more homogenous for an easier identification of the sheet interface. The light sheet was aimed at the closure of the attached cavity, and, therefore, this region was well illuminated. This is illustrated by the magnified view of the cavitation interface in the neighborhood of the closure region of the attached cavity in Fig. 5.1, and around the separated cavitation cloud in Fig. 5.2. From the latter image, it can further be seen that the cavitation
Fig. 5 Steps in the adaptive mask to locating the cavity interface.
interface around the vapor cloud is not well-defined, as both particles and large reflections from the vapor cloud are observed in this region, but an exact interface is unclear by any standard in this transitional region. The cavity cloud was seen to strongly reflect the light sheet thereby illuminating particles outside
the measurement plane. Furthermore, liquid and particles are ingested into the cloud during its collapse. The mask is used to identify the entire region where PIV interrogation will lead to unpredictable results but makes no further attempt at differentiating between sheet and encompassed cloud structures.
Another problem is that vapor structures in front of the light sheet will block the view of the camera. It is, therefore, uncertain to what extent the cavitation interface detected by the mask corresponds to the actual interface in the cross section of the light sheet. However, since we performed our measurements in the symmetry plane of the 3D hydrofoil where the cavitation structures are the largest, as follows from the results of the flow visualization, we assume that the mask provides a fairly accurate estimation of the cavitation interface in the plane of the light sheet.
3 Results
to a sequence of 100 PIV images. The shedding of the attached cavity is well visible. The vapor cloud is further seen to increase quickly in height as it is advected downstream. This sudden expansion of the cavitation cloud above the hydrofoil has not been captured by 2D calculation with Euler codes (Sauer 2000). This evolution of the cavitation cloud is more likely to be the captured by Large Eddy Simulations (Qin 2003) The variation in location of the flow separation at the leading edge of the hydrofoil is not physical. It shows that the mask was less accurate near the leading edge, due to the poor illumination of this region. In future, a more homogenous light sheet will applied to improve the identification of the cavitation interface close to the leading edge.
3.1 Flow visualization For the flow visualization shown in Fig. 6 (6.1–6.20) the laser beam was expanded to illuminate the entire cavitation structure. The images were recorded with the PIV camera, repositioned to view the suction side of the hydrofoil at a straight angle. In Fig. 6.1 the attached cavity has reached its maximum length and is crescent shaped due to the spanwise variation of the loading of the hydrofoil. The strong adverse pressure gradient in the stagnation region at the downstream end of the cavity forces a re-entrant jet into the vapor structure. The velocity is known to reflect on the envelope of the cavitation interface (de Lange 1998), and for a cavity with a 3D shape the reentrant jet will thus have different directions. The re-entrant flow will collide in the center of the foil and at this point the cavity will quickly change from a smooth pocket of attached vapor into a highly turbulent region and detach from the leading edge [Fig. 6 (6.2–6.8)]. The vapor cloud becomes turbulent and is advected downstream by the main flow, as seen in Fig. 6 (6.16, 6.17). In the final images of the collapse of the vapor cloud, a clear vortex structure is observed [Fig. 6 (6.17–6.20)]. In Fig. 6 (6.13–6.18; indicated by the letter A in Fig. 6.17) also two smaller vortices are seen to form at the downstream end of the attached cavity, considered a small secondary shedding. The entire shedding cycle was very periodic and a full period took approximately 47.5 ms, corresponding to a Strouhal number of St=0.19, based on cavity chord length and mean stream velocity V0. This is significantly lower than the the Strouhal observed for 2D pffiffiffiffiffiffiffiffiffiffiffi number flows fL=V0 ¼ 0:25 1 þ r ¼ 0:33 by Arndt (1995). From this, we conclude that the behavior of the 3D cavity is significantly different from that in a 2D cavity, and a more detailed study on the 3D effect of the cavity on the re-entrant jet and global dynamics will be presented in later work. 3.2 Cavitation interface The temporal development of the cavitation interface is shown in Fig. 7 for a period of 100 ms, corresponding
3.3 PIV results Figures 8.1, 8.2 and 9 show different examples of the evaluated vector fields and the contours of the cavity interface. The velocity appears to be parallel to the interface when the cavity is attached (Figs. 8.1, 9). Assuming the flow along the cavity to be (1) approximately stationary, (2) two-dimensional and (3) at a pressure equal to the vapor pressure, a simple streamline model can be used to estimate the velocity at the cavitation interface, refered to as the vapor pressure (VV). From Bernoulli’s equation (P0+0.5q V20=PV+0.5q V2V) in conjunction with Eq. 1 we obtain: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi VV ¼ ð1 þ rÞV0 : ð2Þ Based on pressure measurements on both sides of the contraction upstream of the measurement section, P0 and V0 were determined, and the vapor velocity was estimated at VV=9.24 m/s ±5%. For the velocity field shown in Fig. 9, we have plotted the vertical velocity profiles along the indicated lines in Fig. 10. Although some fluctuations due to the mean stream turbulence can be observed, the (instantaneous) velocity of the profiles A–E are seen to converge toward the vapor velocity at the cavitation interface. For the profile F, a distinct velocity deficit is observed. This may be due to instationary effects near the end of the cavity, as the cavitation closure is moving downstream. Profile F shows that just downstream from the sheet cavity, the streamwise velocity component is 20–30% smaller than the undisturbed inflow velocity (V0). Behind the cavitation cloud, a very strong downwash is measured probably induced by the roll up of the cavitation cloud into a vortex. The streamwise velocity is sometimes as low as 1 m/s near the surface of the hydrofoil while the vertical velocity components can reach 4.5 m/s. The region directly upstream of the shed cavitation cloud in Fig. 9 contains a large number of spurious vectors. A number of effects contribute to the poor correlation in this region. As previously discussed, the
Fig. 6 Flow visualization at V0=7.04 m/s ±1.16%, b=1, r=0.77±7.4%, recorded at f=2.000 Hz showing every fifth frame. Viewing area as outlined in Fig. 3, flow from top to bottom, white lines indicate leading and trailing edge location
cavitation interface around the vapor cloud is not well defined, as both particles and large reflections from the vapor cloud are observed in this region. The large background noise in the PIV images increases the PIV correlation noise significantly. Second, from the highspeed flow visualizations, it is seen that the cavitation cloud is highly turbulent. Gopalan and Katz measured a Reynolds shear stress 25–40% of normal stress in the closure region. The loss of particle pairs due to strong out-of-plane motions is therefore high, increasing the correlation noise further.
4 Conclusion and discussion Time-resolved PIV was applied to study sheet cavitation on a hydrofoil with a spanwise varying angle of attack. In order to block strong reflections of the laser lightsheet by the cavitation, fluorescent tracer particles were applied in combination with an optical filter. Nevertheless, the cavitation structures were clearly visible in the PIV images, due to the reflection of light emitted by the fluorescent tracer particles. Refraction at the cavitation
Fig. 7 Development of the cavity interface at the center plane of the foil as determined by the adaptive mask for a period of 100 ms
Fig. 8 Details of a PIV frame a at the closure region of the attached cavity; b upstream of a collapsing vapor cloud. For the attached cavity, the velocity vectors are parallel to the interface. The obstruction of the view on the light sheet close to the stagnation point at the downstream end of the cavity (indicated by the letter A) makes it impossible to observe the re-entrant jet with the current setup Fig. 9 A vector field near the end of growth cycle before post processing. Only 50% of the vectors are shown in the horizontal direction for clarity. The velocity profiles along the indicated lines are shown in Fig. 10
interface makes it impossible to see into the cavity to perform PIV in the vapor region and the re-entrant jet could not be observed from the PIV images. In order to improve the velocity estimation close to the cavitation interface, an adaptive mask was developed to exclude the vapor region from the PIV analysis. The velocity at the interface of the attached cavity was found to be parallel to the interface and very close to the vapor velocity estimated with Bernoulli’s equation. The interface of the shed cavitation cloud that appeared was not well defined as both particles and vapor could often be observed simultaneously, leading to reduced performance of the mask and PIV analysis close to the cloud. Due to strong turbulence levels around the collapsing cloud, there was a considerable loss of particle pairs in the PIV images, leading to an increased noise level in this region.
9.5
9.0
8.5
8.0
Velocity [m/s]
A B C D E F G 7.5
7.0 35
30
25
20
15
10
5
0
-5
-10
-15
-20
-25
-30
-35
-40
-45
-50
Position [mm]
Fig. 10 Velocity profiles along the lines drawn in Fig. 9. The velocity profiles A– E all converge toward the estimated vapor velocity of 9.24 m/s
For a visualization of the global flow dynamics, the laser beam was expanded and used to illuminate the entire hydrofoil and cavitation structure. The time resolved visualizations reveal the growth of the attached cavity and the cloud shedding that follows it in every detail. The vapor cloud is seen to increase remarkably in height as it is advected downstream. The vapor shedding cycle on the applied 3D hydrofoil was further found to be highly periodic with a Strouhal number 30% smaller than observed for 2D sheet cavitation. This confirms the important influence of the 3D geometry of the hydrofoil on the flow dynamics and stability of the cavitation pattern. In the near future, the current work will be extended to the study of the cavitation and flow dynamics under instationary inflow conditions, and a more profound investigation of the effect of the 3D geometry of the hydrofoil on the cavitation patterns will be performed. Acknowledgements This research is funded by the Dutch Technology Foundation STW project TSF.6170 and Royal Netherlands Navy. See http://www.stw.nl for more details.
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