Time resolved PIV and flow visualization of 3D sheet cavitation

Date Author Address

2006

EJ. Foeth, C.WH. van Doorne, T van Terwisga, B. Wieneke Deift University of Technology

Ship Hydromechanics Laboratory

Mekeiweg 2, 26282 CD Deift

Time resolved Ply and flow visualization Of 3D sheet cavitation

by

Ei. Foeth, C.W.H. van Doorne, T. van Terwisga and B. Wienke

Report Nò. 1538-P 2006

Magazine "Experiments in Fluids", Springer-verlag 2006, DOl 10.107./s00348-0O50082-9

TU D'e Ift

Deift University of Technology

Experiments in Fluids(2006)

DO! 10. 1007/s00348-005-0082-9

Rl!SIïARC'l-1 ARTICLE

E J. 'Foeth' C. W. H. van Doorne T. van Terwisga B. Wieneke

Time resolved PIV and flow visuälization of 3D sheet cavitation

Received: 20 ApriI 2005 / Revised: 22 July 2005 / Accepted: 24 October 2005 © Springer-Verlag 2006

Abstract Time-resolved PIV was applied to study ftilly

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 adversé 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

cavi-tation. An adaptive mask was developed to find the

interface'between.thevapor andiliquid phase. The velocity at the interface of the cavitywas found to be veryclose to

thevelocitypredicted by asimple streamlinemodeL Fora

visualizatión of the global flow dynamics, the laser beam was expanded and used to illuminate the entire hydrofoil

and cavitation structure. The time-resolved

record-ings 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.

i hthoductlon

Cavitation is' the evaporation of liquid' when thepressure falls below the vapor pressure. When such a low pressure región 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. Föeth () C. W. H. van Doorne T. van Terwisga

Laboratory of Ship Hydromechanics, Deift University of Technology, Mekelweg,2, 2628 ÇD Deift, The Netherlands

E,mail e.jFoeth@wbmt.tudeIft.nl

W Wieneke

LaVision GmbH, Anna-Vandenhoek-Ring 19, 37081 Goettingen, Germany

E-mail: bwieneke@lavisionde

cavity, the flow re-attaches to the hydrofoil and a

stag-nation point is formed. The positive pressure gradient in

this region forces a thin stream ofliquid upstream into thecavity, termed the re-entrantjet. When the re-entrant jet impinges farther upstream on the fluidvapor inter-face, 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 clóud, 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). How-ever, 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 mecha

nisms of the instability of the flow; secondly, building a

data set of simple cavitating flows to be used as

bench-mark 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

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 ( I 997), 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 ¡s common practice to study

the flow on a steady (3D) hydrofoil with a cavitation topology and inflow condition closely related to pro-pellers. 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 via-bility 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 PlY images. To solve the latter problem, an adaptive mask was

devel-oped 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 cavita-tion. 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.! Cavitation tunnel

The experiments were performed in the University of Delft Cavitation Tunnel shown in Fig. 1. The

measure-ment channel is 0.60 m long, the cross section is

0.297 mx0.297 m, with optical access from all sides.

Velocities up to 10 rn/s per second can be attained and the local pressure can be reduced to 5,000 Pa. The non-dimensional cavitation number, defined as

PoPv

a

I_pv0r,2 (1)

and expresses the ratio of the pressure head to the

vaporization pressure (Pv) and the dynamic pressure (0.5 p V) 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 a of nearly 7.5% within a 95% confidence

interval for the presented measurements.

Fig. I Sketch of the cavitation tunnel. Theupperand leftleg are

rectangular, the lowerand right leg are cylindrical. The flow is counter clockwise and the air is evacuated at the dome on top of the tunnel

r,

L

Fig. 2 A close-up of the test section showing the hydrofoil, the location for the camera for Ply measurements (C) and the light sheet (L)

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

I(X)Nfor the dimensionless thickness was complemented

from x=0.35 until the trailing edge, where x=[0...1]

stands for the dimensionless chordwise coordinate, by

the following polynomial:

t(x) = t(X)N +

(maxm))C

t(l)N)

x

(x1)

H(x),

C is the chord length, t the non-dimensional thickness,

'min the non-dimensional minimum trailing edge

thick-ness, and Hthe heaviside function.

The hydrofoil is given a 3D shape by a variation in

the angle of attack (cc) along the spanwise direction (y):

C

Fig. 3 Top, side and front view of the hydrofoil. Theblack outline

in the top view indicates the viewing area of Fig. 6 (6.1-6.20)

cc(y) =

T(l6Y_

l2y

i2+i)

_{+ fi.}

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 T= 8° (Fig. 4). The angle

fi is the rotation angle of the entire hydrofoil and is equal to the angle of attack at the wall, which was zero for our Ply 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 4 2 o 0 50 lOO ISO 200 250 300 Span [mm]

This was avoided by the application of roughness ele-ments of 120 jim 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 ti equals the minimum pressure coeffi-cient (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 wasP 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 eg. Bachert (2003) The PMMA-Rhodamine B fluorescent particles' diameters are

typi-cally 20-50 jim 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

(p= 1.19x103 kg/rn3) 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 i month of continuous running.

The camera used is a LaVision Flow-master High-SpeedStar 4 (Photron Ultima APX) with a FO bit dy-namic range, I Megapixel resolütiön 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 18x18 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 03% of the chord length for Re=:3x10,, 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 PI V-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 fre-quency (1 KHz) is half the camera frefre-quency, 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 rn/s was

obtained. The interrogation areas of 32x32 pixels large,

with 75% overlap were used, resulting in a

vector-to-vector spacing of 1.46 mm. Vectors with a deviation

larger than 1.5 times the R:MS of the neighboring

vectors were considered sptirious and were removed.

The final results are smoothed once with a 3x3 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 interro-gation 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 flúid motion at the cavity interface. To improve the accuracy

of the velocity near the cavitation interface, an adaptive

mask Was applied to the Ply images to exclude the

regions occupied by 'the cavitation, the hydrofoil and the entire región 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 región 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

interface with the.iinterface 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 intermediátesteps of the adaptive mask in more detail. Figure 5.1 shows an unprocessed PIV image The upper part of the image is

dárk 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

5x5 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

bin-ary 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 con-tiguous regions (Fig. :5.4). As the intensity of the light-sheet was not constant, the threshold was varied across

the image.

Tracer particles1 typically a few pixels large, were detected in the original image by application of a

gra-dient filter using the following convolution kernels:

The gradient was calculated as + Kr. A

thresh-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.

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 irreg-ulardue to either reflections ofbright tracer particles on the interface or the absence of tracer particles.

In Fig. 5.9 the regions detected by the large

'back-ground intensity and the absence of tracer particles were

combined to find the total región 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.l'O, and the cavitationinterface

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' toe 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, añd,

therefòre, 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

sepa-'rated cavitation cloud in Fig. 5.2. From the latter image, it

can further be seen that

the cavitation

i 0

±11 +.l

+2 ±1

Kver = 2

0 +2

, Khor = O O O

1 0 +1

1 2 1

Table I Overview of the

experimental parameters Tunnel Fluid Water

Max velocity 10 rn/s.

Min pressure 5,000 Pa

Min a '05

Test section Height 0.297 rn

Width 0.297 rn

Length ₀₆ rn

Material Perspex

Wall .thickness 40 mm

Seeding Type Spherical

Diameter 20-50 pm

Light sheet Laser type. Nd:YLF

Maximum energy 10 mi/pulse

Wave length 527 nm

Pulse dùration 180 ns

Thickness 1.5 mm

Camera Type Photron Ultima APX Photron Ultima APX

Resolution 1,024x1,024 Pixels

Discretization '10 bit

Repetition rate 2,000 Hz

Imaging Lens focal length f-number

50 2.8

mm

Viewing area 180x180 mm2

Exposure delay time .1.0 IlS

Maximum particle displacement 8 Pixels

PIV analysis Interrogation, area 32x32 Pixels

Fig. 5 Steps in the adaptive mask to locating the cavity

interface.

5.1 Original Image

5.2 Sliding Median

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

inter-face is unclear by any standard in this transitional

region. The cavity cloud was seen to strongly reflect

the light sheet thereby illuminating particles outside

5,5 Sobel edge filter. Isolated pixels removed

.Ss

5.6 Threshol and conglomeration 5.9 CombInation of the two filters

the measurement plane. Furthermore, liquid and

par-ticles are ingested into the cloud during its collapse. The mask is used to identify the entire region where

PlY interrogation will lead to unpredictable results but

makes no further attempt at differentiating between

sheet and encompassed cloud structures. 5.4 Grown threshôld 5.8 Gaussian icernel 5.11 PliaI result

5.7 Grown, known hydrofoil locatIons 5.10 3D Gaussian filtering substructed

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

inter-face 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

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

cavi-tation 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 maxi-mum length and is crescent shaped due to the spanwise

variation of the lôading 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 toreflect on the envelope of the cavitation interface (de Lange 199 8), and

for a cavity with a 3D shape the reentrant jet will thus

have different directions. The re-entrant floW Will c011ide

in the center of the foil and at this point the cavity Willi quickly change from a smooth pocket of attached vapor

into ahighly turbulent region and detach from.the leading

edge [Fig. 6 (6.2-68)] The vapor cloud becomes

turbu-lent and is advecteddownst ream bythe main flow, as seen in Fig. 6 (6.16, 6.17). In the final images of thecollapse of

the vapor cloud, a clear vortex structure is observed

[Fig. 6 (6..l7-6.20)] In Fig. 6 (6.1 3-6. 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 number observed for 2D flows (IL/v0 =0.251 + o- = 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 pre-sented in later work.

3.2 Cavitation interface

The temporal development of the cavitation interface is shown in Fig. 7 fora period of 100 ms, corresponding

to a sequence of 100 PlY images. The shedding of the attached cavity is well visible The vapor cloud is fur-ther 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

evOlu-tion of the cavitaevOlu-tion cloud is more likely to be the

captured by Large Eddy Simulations (Qin 2003) The variatiön 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 idéntification of the cavitation interface

close to the leading edge.

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.)

approxi-mately stationary, (2) two-dimensional and (3) at a

pressureequal to the vapor pressure, asimple streamline model can be used to estimate the velocity at the cavi-tation interface, refered to as the vapor pressure ( Vv).

From Bernoulli's equation (P0 ±O.5p V Pv + O5p Vv)

in conjunction with Eq. 1 we obtain:

Vv/(1+o-)Vo.

(2)

Based on pressure measurements on both sides of the: contraction upstream of the measurement section, Po» and Vo were determined, and the vapor velocity was

estimated at Vv=9.24 m/s ±5%. For the veloòity

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 AE 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 down-stream. 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 stream-wise velocity is sometimes as low as 1 rn/s near the surface of the hydrofoil while the vertical velocity components can reach 4.5 rn/s.

The region directly upstream of the shed cavitation

cloud in Fig. 9 contains a large number of spurious véctors A ñumber of effects contribute to the poor

Fig. 6 Flow visualization at

14=7.04 rn/s ±1.16%, ß1°,

a=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

6.1 1=0.Oms

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 Ply images increases the PIV correlation noise significantly. Second, from the high-speed 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 ConcIuson 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. Neverthe-less, the cavitation structures were clearly visible in the Ply images, due to the reflection of light emitted by the fluorescent tracer particles. Refraction at the cavitation 6.5 1=10.0 ma 6.61=125 ma 6.71=15.0 ma 6.81=17.5 ma

6.91=20.0 nis 6.101=22.5 ms 6.111=25.0 ma 6.l2t=27,5ms

6.13t300ma 6.14t='32.5nis 6.l5t=35.Oms 6.161=37.5mg t.

6.17 1=40.0 ma 6.18 t=42.5 ais 6.19 t=450 ma 6101=47.5 ma

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. S 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

Hg. 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. IO

s

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 PlY 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 inter-face of the shed cavitation cloud that appeared was not well defined as both particles and vapor could often be

observed simultaneously, leading to reduced

perfor-mance 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 Ply images, leading to an increased noise level in this region.

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 Technol-ogy Foundation STW project TSF.61 70 and Royal Netherlands Navy. See http:/iwww.stw.nl for more details

References

Abbott 1H, von Doenhoff AE (1959) Theory of wing sections. Dover Publications mc, NY, ISBN 486-60586-8

Arakeri VH, Acosta AJ (1973) Viscous effects in the inception of cavitation on axisymmetric bodies. J Fluids Eng 95(4):519-527 Arndt REA (2002) Cävitation in vortical flows Annu Rev Fluid

Mech 34:143-175

Arndt REA, Ellis C, Paul S l995) Preliminary investigation of the use of air injection to mitigate cavitation erosion J Fluids Eng

117:498-592

Astolfi JA, Dorange P, Leroux JB, Billard JY (2000) An experimental

investigation of cavitation inception and development of partial

JA.'.

I____

I_I

.

______ ,

i4r4.

rï1

-b

_{- -lili.}

_______

.---.-

-='

_-

M'

-ïr1.

¡u

9.5 9.0 8.5

p

8.0 7.5 7.0 -..- A

B

- C - D

o E

i--- F

N G

sheet cavities on two-dimensional hydrofoils. In: 23rd ONR symposium on naval hydrodynamics, Val de Reuil, France Bachert R, Stoffel B (2003) Messung instationärer,

dreidimensio-naler Effekte kavitierender Strömungen an einem Einzelprofil

mit Hilfe der PIV/LIF Messtechnik, GALA-Fachtagung "Lasermethoden in der Strömúngsmesstechnik", Braunschw-eich, Germany

Brennen CE (1995) Cavitation and bubble dynamics, Oxford Engineering Science Series 44

Callènaere M, Franc JP, Michel iM (2001) The cavitation insta-bility indúced by the development of a re-entrant jet. J Fluid

Mech 444:223-265

Cäron iF, Farhat M, Avellan F (2000) Physical investigation of the cavitation phenomenon In: Sixth international symposium on fluid control, measurement and visualization (Flucome 2000), August 13-17, 2000, Sherbrooke, Canada

Chol JK, Kinnas S (l998)A 3-D Eulersolverandiits application on theanalysis ofcavitating propel!ers. ln:Twenty fifth American towing tank conference, Iowa City, IA, USA

Dang J (2000) Numerical simulation of unsteady partial cavity flows. PhD Thesis, Technical University of Delft, Dell'I Farhat M, Avellan F (200l) On the detachment of a leading edge

cavitation. In: Fourth international symposium on cavitation, Pasadena, CA, USA

Franc iF (2001') Partial cavity instabilities and re-entrant jet. In: Fourth international symposium on cavitation, Pasadena, CA, USA

Franc W, Michel JM (1985) Attachedcavitation and the boundary numerical treatment. J Fluid Mech 154:63-90

Gopalan S, Katz J (2000) Flow structure and modeling issues in the cIosureregion of attached cavitation. Phys Fluids l2(4)895-9l 1 ITTC (2002) Final report and recommendations to the 23rd ITTC by The Specialist Còmmittee on cavitation induced pressure& In: Proceedings of 23rd international towing tank conference, Venice, Italy, vol 2 pp 417-458

Kawanami Y, Kato H, Yamaguchi H, Tagaya Y, Tanimura M (1997) Mechanism and control of cloud cavitation. J Flùids Eng

1 l9(4):788-795

Kuiper 0(1982) Some expenments with specific types of cavitation on ship propellers. J Fluid Eng 1:105-114

Kunz RF, Boger DA, StinebringDR, ChyczewskiTS, Gibeling HJ (1999) A preconditioned NavierStokes method for two-phase

35 30 25 20 15 lO 5 0 -5 -lo -15 -20 -25 -30 -35 -40 -45 -50

Position ImmI

Fig. 10 Velocity profilesalong the linesdrawn in Fig. 9. The velocity profiles A E all converge toward the estimated vapor velocity of 9.24 rn/s

flows with application tocavitation prediction. American Insti-tute of Aeronautics and Astronautics, Baltimore, pp 99-3329 Laberteaux KR,Ceccio SL (2001) Partial cavity flows Pt 2 Cavities

forming on test objects with spanwise variation. J Fluid Mech

431:43-63

de Lange DF, de Bruin Gi (1998) Sheet cavitation and cloud cavitation, re-entrant jet and three-dimensionality. AppI Sci: Res

58:91-114

Qin Q, Song.CCS, Arndt REA (2003) Numerical studyofunsteady

turbulent wake behind a cavitating hydrofoil. In: Fifth inter-national symposium on cavitation, Osaka, Japan

Raffel M, Wilier C, Kompenhans J (1998) Particle imaging veloc-imetry; a practical guide, ISBN 3-540-63683-8. Springer, Berlin Heidelberg New York

Rood EP ('1991) Reviewmechanisms of cavitation inception. J Fluids Eng 113:163-1.75

Sauer J, Schnerr GH (2000) Unsteady cavitating flowa new

cavitation model based on a modified front capturing method and bubble dynamics. ASME Fluids Eng. SummerConference, FEDSM2000/l1095-2000, June Il-15, 2000, Boston, USA Senocak I, Shyy W (2001) Numerical simulation ofturbulent flows

with sheet cavitation. In: Fourth international symposium on cavitation, Pasadena, CA, USA

Tassin AL, Li CY, Ceccio SL, Bernal LP (1995) Velocity field measurementsofcavitating flows Exp Fluids 20:125-130 Wikatrom N, Bark G, Fureby C (2003) Large Eddy Simùlation of

cavitation submerged objects. In: Eighth international confer-ence on numerical ship hydrodynarnics Busan, Korea

Young YL, Kinnas SA (2001) A BEM for the prediction of

unsteady midchord Face, and/or back propeller cavitation. J Fluids Eng l23(2):31 1-3 19