Model Kaplan Turbine Blade

Flow, Turbulence and Combustion64: 119–144, 2000.© 2000Kluwer Academic Publishers. Printed in the Netherlands.

119

Measurements of Tip Vortex Characteristics and theEffect of an Anti-Cavitation Lip on a Model KaplanTurbine Blade

KIMON ROUSSOPOULOS and PETER A. MONKEWITZDGM-IMHEF/Ecublens, Swiss Federal Institute of Technology, CH-1015 Lausanne EPFL,Switzerland

Received 7 May 1999; accepted in revised form 19 January 2000

Abstract. Motivated by the problem of cavitation erosion, the position and strength of the roll-upvortex on the suction side of a Kaplan-type turbine blade with various endings is investigated. Meas-urements are made on different models with simplified two-dimensional geometries using mainlyparticle image velocimetry. It is found that the greatest danger of cavitation erosion exists when thecasing of the turbine is of the “semi-spherical” type, so that there is a large and closing clearancegap at the leading edge of the blade. Furthermore, the anti-cavitation lip used in this study is shownto be ineffective at increasing the distance of the vortex from the blade, although it does reduce thecirculation of the vortex and presumably the danger of cavitation. Our measurements are found to bein good agreement with existing models for the position of the vortex when appropriately interpreted.

Key words: turbomachinery, blade tip clearance flow, tip vortex, anti-cavitation lip, particle imagevelocimetry.

1. Introduction

The Kaplan hydraulic turbine is widely used in hydro-electric installations becauseit can function over a wide range of operating conditions with high efficiency.Kaplan (and bulb) hydraulic turbines are generally operated for maximum effi-ciency with the lowest possible outlet pressure consistent with avoiding large-scalecavitation on the blade suction surfaces. However, the core of the roll-up vortexthat forms at the tip of the blade is a region of particularly low pressure wherecavitation often does occur. If the cavitating vortex core approaches the blade ofthe turbine, then serious erosion of the blade can occur, causing loss of efficiencyand an eventual need to shut down and dismantle the installation to replace lostblade material. It is therefore important to understand the trajectory and intensityof the tip vortex and the factors affecting it so that measures can be taken to preventerosion.

Axial turbomachinery rotor blades with a clearance gap between their bladetips and the turbine casing all have tip leakage flows. In both compressors andturbines, the tip region flow tends to include a pressure-driven, oblique leakage

120 K. ROUSSOPOULOS AND P. MONKEWITZ

Table I. Geometry of the experimental blade section compared to the real blade.

Parameter Present blade model Real installation (typ. values)

Full blade L = 1025 mm L = 2–5 m

Chord used in experiments 0.35L

(plus 0.1L termination)

Blade thickness 0.03L 0.03L

(almost constant at chord (almost constant at chord

distances of 0.15–0.35L) distances of 0.15–0.35L)

Blade length 0.2L (constant section) L (varying section)

Gap thickness 0.001–0.005L 0.0005–0.001L

(0.003L for most tests)

Reynolds number 4.5× 105 3× 107

based on chord

flow from the pressure side to the suction side of the blade, and the roll-up of atip vortex in the corner bounded by the casing and the blade on the suction side.The leakage flow causes a loss in stage efficiency due to an “unloading” of thepressure difference across the blade at the tip and the vortex blocking part of theflow in the passage. Most previous studies [1–8] investigating tip vortex loci werein the context of gas turbines or compressors and were primarily concerned withreducing the accompanying losses.

Our study concentrates on hydraulic turbomachinery and in particular theKaplan turbine. In this application, the loss of efficiency is significant but thefurther hazard of cavitation erosion of regions of the turbine blade can be critical.This paper presents results of an experimental program using PIV to study theposition and strength of the roll-up vortex on the suction side of a stationary modelturbine blade in a water channel. In our experiments, the blade’s cross-section doesnot vary along the span, the proportionate clearance gap is larger than in typicalinstallations, and the Reynolds number is about 1/50 of the real case. Also, theconsequences of relative blade/wall motion are neglected. This appears justifiedas the tip flow is generally accepted to be pressure-driven [2, 4, 5] while greatlyreducing the complexity of the experimental setup. Similarly, Coriolis effects areneglected. A comparison of the key parameters of our experimental setup withthose of a full-sized Kaplan installation are given in Table I. The choice of such asimplified setup and unrealistic operating parameters was dictated by the desire toobtain reliable and detailed flow measurements for the evaluation and calibrationof numerical models. Despite the compromises, the main conclusions of the studyare considered to remain valid also for more practical situations.

The blade form used is based on a commercial design. We have investigated theuniform gap case and the case of a varying inlet gap typical of a “semi-spherical”

MEASUREMENTS OF TIP VORTEX CHARACTERISTICS 121

Figure 1. Side view of EPFL-LMF water channel. Width of contraction and working sectionis 1.2 m, design water depth in working section 0.2 m.

installation. The effect of the addition of a “lip” on the suction side of the bladein an effort to reduce the cavitation erosion by pushing the vortex away from theblade was also investigated at the suggestion of Sulzer Hydro Ltd., the commercialsponsor of the project. Booth and coworkers [6–8] considered the tip leakage withsome “winglets” similar to our lip on the suction side, pressure side and both sidesof the blade end; however they gave no details of the effect on the tip leakagevortex. Our results are compared with the predictions of models published byprevious researchers. The conclusions are also applicable to other axial bulb- orpropeller-type hydraulic turbines.

2. Experimental Facility and Diagnostic Methods

2.1. WATER CHANNEL

Our experiments were performed in the free-surface recirculating water channelof the EPFL’s fluid mechanics laboratory, which was designed and built for thispurpose. The main features of the channel are illustrated in Figure 1. The channelhas three main sections: a flow conditioning section with honeycomb and a 4: 1contraction, a working section, and a return section. The flow is driven by a ship’spropeller in the return pipe. The working section is 1.2 m wide, 1.5 m long and hasa design depth of 0.2 m (a maximum physical depth of 0.4 m); the side walls andfloor of the working section are of glass, as is the back wall of the tunnel so thatoptical access to the working section is possible from all directions except fromupstream. The drive is able to produce a speed of 0.6 m/s in the working sectionwith a water depth 0.2 m. An independently-mounted frame above the workingsection bore the model turbine blades and other equipment.

2.2. EXPERIMENTAL CONDITIONS

All experiments presented here were performed with a flow speed of 0.5 m/s and adepth of 0.2 m in the working section of the channel. At higher speeds, deformation


Figure 2. Blade and casing arrangement in a Kaplan turbine, showing spherical andsemi-spherical casings.

of the free surface by waves around the blade was a cause for concern, but it wasfound that at 0.5 m/s the presence or absence of the free surface made a minimaldifference to the blade tip flow. The (turbulent) boundary-layer displacement thick-ness in the working section adjacent to the blade models was estimated at 3 mm.In all cases, the blades were aligned at an actual chord angle of 4.7 degrees to thefree stream to simulate the operating conditions provided by Sulzer Hydro.

2.3. THE BLADE MODELS

Figure 2 illustrates the blade arrangement in a real Kaplan installation. The blades,of variable pitch, are mounted on a hub and their tips come very close to thecasing of the turbine, leaving a small gap (typically 0.1% of the blade chord). Theblade forms are inherently three-dimensional. The casing can be spherical or semi-spherical, as illustrated in Figure 2; the former yielding greater efficiency but thelatter allowing easier manufacture and maintenance.

The experiments reported in this paper were performed on blades with a uni-form cross-section, developed at the EPFL Fluid Mechanics Laboratory, based on aKaplan blade tip section supplied by Sulzer Hydro Ltd. The Kaplan blade tip profilewas “rolled flat” and scaled to have a chord length of 1025 mm. Of the resulting


Figure 3. Truncated blade profile used in experiments, compared to complete Kaplan blade.

Figure 4. The three blade endings used in the present study.

two-dimensional blade, only the leading 350 mm were used for the model bladesection. This truncated blade was terminated with a short trailing edge designed byCFD such as to provide essentially the same loading on the first 350 mm of themodel as on the corresponding part of the complete blade profile, while avoidingany significant separation. The blade profile and the relationship to the original fullblade profile is illustrated schematically in Figure 3.

The results reported in this paper are for three blades, denoted A, B and C, eachwith different terminations as follows:

Blade A: Uniform cross-section and uniform clearance gap.

Blade B: As Blade A, but with the addition of an “anti-cavitation lip” at the tip.


Figure 5. Arrangement of CCD cameras and optics in the LMF PIV system.

Blade C: As Blade A, except that the clearance gap closes linearly from theleading edge.

The geometry of the three blades are illustrated in Figure 4. Model A represents aplain blade, fitted into a fully spherical casing (see Figure 2). Model B representsa blade in a fully spherical casing which has been fitted with a lip on the suctionside in the hope that this will displace the roll-up of the vortex further from theblade and thus offer some protection from cavitation erosion. Model C, finally,represents the case of a plain blade in a semi-spherical casing (see Figure 2). Thelinear closure is a good approximation of the actual gap variation. Models A andC were machined in a plastic modeling compound similar to nylon, while model Bwas realized with a plastic plate screwed onto the tip of blade A, which was fittedwith pressure taps on both sides and on the base (see below). The blades’ suctionsides and the anti-cavitation lip were painted black to reduce laser reflection.

Realistic clearance gaps between the truncated blade tip and the channel floorare of the order of 1 mm on the scale of the original full-length profile andwere used for some measurements, but, unless otherwise stated, experiments wereperformed with a 3 mm gap in which it was possible to make PIV measurements.

2.4. PARTICLE IMAGE VELOCIMETRY

The main experimental measurement technique used during this study was planarParticle Image Velocimetry (PIV) which is now a well-established technique fordetermining instantaneous flow velocity fields (see, e.g., [9, 10]) from the displace-ment of seed particles in the plane of a laser sheet obtained from two consecutiveimages (superimposed or recorded separately). The limitations of this techniqueare discussed by many authors, see, e.g., [9–11], and are not repeated here. In thefollowing, only the particularities of our PIV system are briefly summarized.

For the present study, a custom two-camera system, developed at the EPFLFluid Mechanics Laboratory and shown schematically in Figure 5, has been used.The two light-intensified digital cameras (model “4Quick05” of Stanford ComputerOptics with a cooled CCD array of 768 by 512 pixels) are arranged in such a way


as to receive the same image, focussed onto their image intensifiers by a singleobjective lens (for the present study, two objective lenses were used, a 210 mmlens for work through the channel floor and a 450 mm lens for maximum magni-fication when working from the end wall of the facility) and split thereafter by a50% beam splitter (see also [12]). As the two image intensifiers can be operatedindependently as electronically controlled shutters, each camera records one imageof the pair needed for the determination of the seed particle displacement fieldwith an arbitrary time delay between them, such that directional ambiguity andother problems of the double-exposure technique are avoided. The cameras werecontrolled by a PC and images were transferred to the PC by two dedicated framegrabbers. Another advantage of the electronic shutters is the possibility of usinga continuous wave laser for the light sheet. One drawback of the two-camera ar-rangement is, of course, the need for careful alignment of the cameras and mirrors.With our system it was possible to achieve a sub-pixel alignment accuracy. Thisis, however, very time-consuming and the alignment procedure must be repeateddaily. In practice, it was found that a misalignment of 2–3 pixels was tolerable as itcould be compensated for by calibration with an accuracy that did not significantlydegrade the displacement measurements. The calibration consisted of recording animage with both cameras simultaneously and of computing the offset vectors acrossthe field by cross-correlation. The misalignment could then be removed from thePIV results by vector subtraction.

For the experiments reported in this study, it was necessary to operate in mostcases near the maximum gain of the cameras and with the longest possible exposuretimes (of the order of 1 ms with time delays of the same order). A continuous waveargon-ion laser, operated at a power of 3 W, was used to create the laser sheetwith a system of mirrors and lenses mounted on traverses permitting adjustmentof the orientation (vertical or horizontal) and thickness of the sheet. A difficultyarose as most of our PIV measurements were aimed at measuring secondary flowsin a plane normal to the main flow (laser sheet normal to the main flow). In thissituation, particles naturally tend to move out of the illuminated region during thetime delay between the two PIV images. Therefore, a rotating octagonal prismwas used as the final element of the optical system to move the laser sheet in themain flow direction, i.e. in the sheet-normal direction. As the prism rotated, thelaser sheet swept downstream through a distance of 10 mm and “jumped” backupstream as the next face of the prism was struck.

For seeding, commercially-available, silver-coated spherical particles (sold aspaint additive) were used. Their mean diameter was 20µm, and their density 1.3times that of water. The seeding density turned out to be a critical parameter since,in our apparatus, both the laser sheet and the line of sight of the camera passedthrough water over a large distance. This caused, at too high a particle density, lightscattered from particles in the laser sheet to illuminate other particles in the line ofsight of the camera, thus leading to an unacceptable signal to noise ratio (imagecontrast). On the other hand, a low particle density causes an unacceptably high


number of erroneous displacement vectors (false correlations) and inaccuracies ofthe valid vectors. Therefore, the present studies were performed with typically 4–5 particles in an interrogation window, which is at the lower limit of the particledensity recommended by Keane and Adrian [11] for cross-correlation analysis. Inorder to satisfy the requirement [11] of a sufficient ratio between particle imageand pixel size, the camera was deliberately defocussed, when necessary, to spreadparticle images over several pixels.

The images were analyzed using the commercial “Visiflow” software marketedby AEA Technology. Standard PIV analysis, without windowing of the initialimages, was performed using cross-correlation of corresponding interrogation win-dows, where the peak of the cross-correlations was located by a Gaussian fit. Inmost cases, interrogation windows of 64 by 64 pixels with a 50% overlap wereused, corresponding to arrays of 23 by 15 velocity vectors. In our measurements,typically 5% of the vectors were identified by the software as false vectors (visible,e.g., at the edges of Figure 8) as a result of too few particles in the interrogationwindow, particles moving out of the laser sheet despite its motion with the mainflow, inadequate illumination, etc. Visiflow permits the replacement of false vectorsby vectors corresponding to the second or third peak in the cross-correlation or bya weighted average of surrounding vectors. The option of using higher correla-tion peaks drastically reduced the number of interpolations necessary to replacefalse vectors to less than 1% in most cases. Regarding the accuracy of the validvectors, the accuracy of the displacement computation for a single interrogationwindow is estimated as being about 0.25 times the displacement corresponding toa pixel, since the key requirements for sub-pixel accuracy (see, e.g., [9–11] andthe discussion above) are met by our setup. Furthermore, all the results presentedhere are averages over several vector fields, which further reduces the statisticalerror in regions of steady flow. On this basis, the error of our PIV measurements isestimated as being about±5% of the largest velocity in the field. Finally, Visiflowwas also used to compute the vorticity field from groups of nine vectors (vectorwhere vorticity is estimated plus its eight neighbors).

2.5. PRESSURE MEASUREMENTS

The blade model A was equipped with 84 pressure taps of 0.5 mm diameter aroundthe blade and on its base. The taps were connected via fine steel tubes through theblade interior to its top, above the water surface, and further by plastic tubing toone of two 12-channel commutators of “scanivalve” type. After careful purgingof the system to avoid errors due to hydrostatic pressure differences, pressureswere measured with a single differential high-precision transducer, ELECTORRmodel GA 76 with a pressure range of±5 mBar, and a sensitivity of 1 V/mBar. Toreduce errors resulting from drift, all pressure measurements were made relative toa reference pressure tap on the pressure side, 100 mm from the leading edge and10 mm above the bottom of the blade.


Figure 6. Chord-wise pressure profile at mid-span of blade A (relative to the reference pointon the pressure side).

2.6. FLOW VISUALIZATION

Flow visualization experiments were carried out, notably by means of fluorescenedye leaked into the tip vortex from the leading edge corner of the blade tip andilluminated by the laser sheet. This allowed the trajectory of the tip vortex as well asits degree of unsteadiness to be captured on video. The visualization was not usedfor quantitative measurements, except to verify that the observed vortex positionwas in agreement with the PIV measurements, but rather to increase the qualitativeunderstanding of the vortex behavior.

3. Experimental Results

In presenting the results, a coordinate system is adopted wherex is oriented inthe direction away from the suction side of the blade,y indicates elevation abovethe channel floor andz indicates position along the chord line measured from theblade’s leading edge.

3.1. PRESSURE MEASUREMENTS

Figure 6 shows the mean pressure distribution around the blade midspan, whileFigure 7 shows the pressure distribution over the blade height on the pressure andsuction sides at a distance of 200 mm from the leading edge. Since all pressuremeasurements were made relative to a reference pressure tap on the pressure side(see the previous section), thecp values are close to zero on the pressure side. FromFigure 6 it appears that, away from the leading edge (in the region 100–300 mmfrom the leading edge), the blade has a nearly constantcp loading of about 1.0, astypically found on real turbine blades.


Figure 7. Span-wise pressure profile at 200 mm from leading edge of blade A (relative to thereference point on the pressure side).

Figure 7 demonstrates that there is practically no pressure unloading until thelowest 5 mm of the blade. An interesting feature of the distribution of Figure 7 arethe pressure values at the two pressure taps on the end face of the blade (in the gap)which are included in the diagram at zero height. It is noted that the gap pressureat the tap close to the pressure side is lower than that near the suction side. This isthe consequence of a separation that occurs at the corner with later reattachment; asmall recirculation region under the blade was clearly seen in a flow visualizationvideo. It therefore appears that a “vena contracta” forms at this corner with locallyhigher speed and lower pressure in the gap (see also [3]). Beyond this recirculationregion, some pressure recovery is clearly obtained along the gap. It is possible thatthis localized region of very low pressure, which was not investigated further, maybe critical for cavitation formation.

3.2. FLOW IN THE GAP

PIV measurements made in the gap between the blades and the wall are shown inFigures 8 to 11, on which the outline of the profile is shown for better orientation(note that for these figures the coordinatex is measured from the chord line ofthe profile). Figures 8 and 9 show the flow field in the region 0≤ z < 160 mm,including the leading edge, with and without the presence of the anti-cavitation lip.The continuation of Figures 8 and 9 in the profile midsection (140 mm≤ z <

300 mm) is shown in Figures 10 and 11, respectively. These measurements wereall made with a gap of 3 mm between the blade and the glass floor. A laser sheet,with a thickness of 0.3 mm, was placed in the middle of the gap. Measurementswere made with the 210 mm objective lens through the channel floor. The analysiswas performed with a 32 by 32 pixel interrogation window, resulting in a vectorfield of 49×33 vectors. Each of these figures was obtained by averaging over three


Figure 8. Flow in mid-gap plane in the leading edge region of blade A with a 3 mm gap.

Figure 9. Flow in mid-gap plane in the leading edge region of blade B with a 3 mm gap.


Figure 10. Flow in mid-gap plane in the midsection of blade A with a 3 mm gap.

Figure 11. Flow in mid-gap plane in the midsection of blade B with a 3 mm gap.


separate PIV measurements. A high incidence of error vectors can be seen at theleft and right-hand sides of the figures. These regions coincide with the edges of thelaser sheet and, since illumination is insufficient there, no attempt has been madeto replace these error vectors. Since the flow was essentially steady, apart fromsome variability in the location of the separation line beyond the suction side ofthe blade, a good accuracy of thevalid vectors in the central portion of the figures,estimated at±0.02 m/s, was obtained.

The incipient flow (from left to right) is clearly identified far from the blade. Inthe plane of measurement, the flow turns under the blade very close to the pressureside of the blade (on the figures, the lower profile contour). The turn angle is foundto be essentially uniform over the gap, equal to 45–50 degrees, and surprisinglyalso independent of the presence of the anti-cavitation lip. Looking more closely atthe magnitude of the velocity vectors, the flow appears to be accelerated under theblade, from about 0.3 m/s away from the blade on the pressure side to a velocityof 0.5 m/s under the blade. The lower flow speed on the pressure side is due tothe laser sheet being in the channel-floor boundary layer. In the center-plane ofthe gap and in the jet emerging from it, on the other hand, the total flow velocity isfound to be within 5% of the free stream velocity (0.5 m/s). This would be expectedfrom inviscid theory as the gap jet and the external flow on the suction side (witha velocity near the free stream velocity for the present lightly loaded blade, exceptin the immediate neighborhood of the leading edge) come from the same reservoir(along different streamlines) and are at the same pressure. This suggests, that themaximum velocity in the gap and at its exit is little affected by viscous effects. Incomparing Figures 8 and 9, we observe that the flows are remarkably similar. Wadia[8] computed a 10% reduction in leakage flow with a similar lip at comparableconditions; we found no measurable (consistent) change in fluid velocity in thegap center-plane with and without the lip but, since sufficiently accurate velocityprofiles across the gap could not be obtained with the PIV technique, we cannotdraw any definitive conclusion regarding the total leakage flow.

On the suction side, the flow clearly continues past the edge of the blade to a sep-aration line, beyond which we find again the unperturbed channel-floor boundarylayer. At the separation line fluid that has flowed under the blade is turned upwards,out of the horizontal measuring plane, eventually to roll up into the tip clearancevortex. The separation line starts at the leading edge of the blade, and moves awayfrom the blade with increasing downstream distance. As for the flow velocity in thegap, the presence of the anti-cavitation lip appears to have remarkably little effecton the position of the separation line.

3.3. MEASUREMENTS OF THE SECONDARY TIP CLEARANCE VORTEX FLOW

Measurements were made of the tip vortex with the three blade configurations, “A”,“B” and “C” at distances of 78, 128, 180 and 250 mm from the leading edge, withadditional measurements at 320 mm in the configuration “C”. The laser optics was


arranged to give a vertical sheet of 3 mm thickness normal to the main flow in thechannel. The speed of the rotating prism was adjusted to traverse the laser sheet inthez-direction at a speed slightly slower than the main flow velocity in accordancewith the slower axial flow in the vortex. The camera was positioned to record theparticle image through the glass window at the end of the water channel with theobjective lens of 450 mm focal length. At the typical observing distance equivalentto 3.8 m through air (taking refraction at the air-glass-water interface into account),the field of vision was approximately 72 mm by 48 mm. The field of view was closeto the floor of the channel and the edge of the blade without imaging directly thelaser reflections from these surfaces. A target grid was used both to compute thescale factors for the analysis and to determine the exact measurement position withrespect to the blade and the channel floor. To obtain a sufficient depth of focusand sharpness, a diaphragm of 65 mm diameter was placed on the main lens. Thecamera axis was aligned within 2 degrees to the local mean flow direction withinthe field of view such as to minimize the contribution to the particle displacementsfrom misalignment. Note that thex-axis for these secondary flow measurements isdefined differently than for Figures 8 to 11: it is roughly perpendicular to the localblade surface and its origin is conveniently chosen on the suction surface of theblade, as in a “body-fitted” coordinate system.

The exposure time and the delay between the two cameras were 2 ms (except forthe measurements of profile C where the secondary flow is of greater magnitudeand exposures and delays of 1 ms were used). PIV analysis was performed withsquare interrogation windows of 64 by 64 pixels and 50% overlap, resulting in23× 15 velocity vectors. The instantaneous velocity vectors are estimated to beaccurate to within 0.004 m/s (0.008 m/s for profile C). Furthermore, at least 10vector fields were acquired in each position and the results averaged in order toprovide a comparison with mean velocity fields obtained from Reynolds-averagednumerical models.

The primary results of the measurements of the clearance vortex are a series ofmean secondary velocity and vorticity fields. Examples at 180 mm from the leadingedge are shown in Figure 12 for the three blades tested, all with a 3 mm gap. Inthese plots the clearance vortex is well in evidence and the vorticity maximum isseen to correspond well to the apparent center of the vortex motion on the velocityplots.

3.4. TRAJECTORY OF THE VORTEX CENTER

The trajectory of the vortex center, defined as the center of the concentric vorticitycontours, can now be estimated from its measured position at differentz-stations,shown in Figure 13. The reader is reminded here that the coordinate origin is thevertical projection of the bladesuctionside (not including the anti-cavitation lip!),at the particularz-position, onto the channel floor as in Figure 12. The accuracyof the measured vortex-center position is approximately±2 mm. The data for


Figure 12. Examples of PIV measurements of secondary flow and derived vorticity at 180 mmfrom the leading edge of blades A (top), B (center) and C (bottom), all with a 3 mm gap.


Figure 13. Mean position of vortex centers at different distances from the leading edge, forblades A, B and C with a 3 mm gap.

the blade with and without the anti-cavitation lip (blades A and B) is again notsignificantly different. However, for the substantially different blade C, the muchstronger vortex (see Figure 12) is always closer to the blade than for blades A andB.

3.5. UNSTEADINESS OF THE VORTEX POSITION

It is important to note that the results presented above are for the mean vortexposition. The vortex is seen to move significantly about this mean position, both inthe individual PIV measurements and during flow visualization. Figure 14 showsthe instantaneous centers of the vortex at 20 different times (from 20 randomly-timed PIV images; some centers coincide), measured at 180 mm from the leadingedge of blade A. The variability is significant as the vortex center moves approx-imately 15 mm horizontally and 8 mm vertically. The mean of these centers is seento coincide very closely with the center of the vortex in the mean image, whichindicates that the number of vector fields (≥ 10) we chose to determine the meanvelocity field is sufficient. Figure 14 reveals that the mean flow (as in Figure 12)


Figure 14. Twenty instantaneous vortex center positions and their geometric mean at 180 mmfrom the leading edge of blade A with a 3 mm gap.

is not necessarily representative of the actual flow that occurs. The instantaneousvortex is generally smaller and more intense than the mean vortex: in this dataseries the mean of the peak vorticities of the individual realizations is three timesthe peak vorticity of the mean vortex (the variability of the peak vorticity betweenrealizations is±30%).

3.6. STRENGTH OF THE VORTEX

The risk of damage to the turbine blade from cavitation is influenced by both theposition of the vortex and its intensity. The intensity of the vortex can be quantifiedby many parameters, including: the peak vorticity of the vortex, the cross-sectionalarea of the vortex, and the total circulation around the vortex. The factor that moststrongly influences cavitation is the minimum pressure in the vortex, which is nota simple function of any of these quantities. We chose to quantify the strength ofthe vortex by its total circulation, which is the only parameter considered that ispreserved in the process of averaging over a number of flow realizations. Since itis an integral parameter, it is also the least affected by random errors, and it seemsreasonable to expect that a vortex with greater circulation would carry a greaterrisk of cavitation.

A particular problem arises, however, since, in many cases, we do not havemeasurements over the whole cross-section of the vortex, because it was notpossible to make measurements close to the channel floor, the blade and theanti-cavitation lip. An approximate method was devised based on completing themissing parts of the vorticity distribution by interpolation, i.e. by making reason-able assumptions on the vortex shape and vorticity distribution or, equivalently, onthe missing arc length over which velocity needs to be integrated. Table II showsthe estimated circulation of the vortex at different distances from the leading edgefor the three blades considered in the study. Also shown is the percentage of this


Table II. Estimated circulation for the three blades with a 3 mm gap, at various distances from theleading edge.

Blade A Blade B Blade C

Distance Estimated % of Estimated % of Estimated % of

from leading circulation circulation circulation circulation circulation circulation

edge (mm) (×103 m2s−1) extrapolated (×103 m2s−1) extrapolated (×103 m2s−1) extrapolated

78 5.8 40 4.2 59 4.3 11

128 10 24 7.8 27 9.3 53

180 10 27 5.0 5 23 32

250 16 15 9.2 11 43 11

320 – – – – 39 14

circulation which has been estimated by interpolation; the higher this figure the lessreliable the circulation estimate. From this table, it is seen that the configurationsA and B have similar circulation in the leading-edge region of the profile, butfurther back, at positions where the anti-cavitation lip is present, configuration Bhas significantly lower circulation (50% lower at 180 mm, just after the lip reachesits full width, and 33% lower at 250 mm). These differences are large comparedwith the expected errors and so are considered reliable. In terms of implications forblade damage, we note that the anti-cavitation lip of section B does seem to give aworthwhile reduction in the intensity of the vortex, and so is probably effective inreducing cavitation erosion even though the vortex position is not changed.

In the case of profile C, the circulation is generally greater than for profiles Aor B, and at 180 and 250 mm from the leading edge it is 2–3 times as strong. Inview of the greater gap thickness between the leading edge and this point this is notsurprising, since the configuration near the leading edge of this blade tip is similarto that of half a delta wing which is known to produce a powerful vortex. Combinedwith the observed relative closeness of the vortex to the blade, this clearly makesconfiguration C the most prone to cavitation damage.

3.7. EFFECTS OF VARYING GAP THICKNESS

To complete the study, the effect of varying the thickness of the gap between theblade and the channel floor was investigated for selected cases. Measurementsare reported at 180 mm from the leading edge for four different gap thicknesses,with all other experimental parameters the same as above. The estimated vortexcirculations for the profiles A and B are listed in Table III, while the correspondingposition of the vortex centers are shown in Figure 15. It reveals no clear trend forthe displacement of the vortex core as the gap thickness is changed, but it shouldbe borne in mind that the position uncertainty is±2 mm so that the actual displace-ments may be close to zero. It is worth noting, however, that the anti-cavitation lip


Table III. Mean vortex circulation at 180 mm from the leadingedge for blades A and B and different gap thicknesses from 1to 4 mm.

Profile – gap Estimated circulation % of circulation

thickness (mm) (×103m2s−1) extrapolated

A-1 3 50

A-2 7 33.6

A-3 10.3 27

A-4 9.1 5.1

B-1 0.35 0

B-2 3.36 4.7

B-3 4.98 5.4

B-4 3.93 0

Figure 15. Mean vortex center positions at 180 mm from leading edges of blades A and Bversusgap thickness.

(blade B) does seem to result in a consistent outward displacement of the vortexcore by a distance of 3±1 mm as the gap is increased from 1 to 4 mm.

Guided by the model of Song and Martinez-Sanchez [2], briefly discussed be-low, two mechanisms could be responsible for a displacement of the vortex asthe gap thickness is varied. As the gap increases, the flow rate through the gap isexpected to increase. The position of the separation line dividing the fluid emergingfrom the gap from the free flow, on the other hand, is likely to be little affected bythe gap thickness (analogous to the small effect of the anti-cavitation lip, i.e. the gapwidth). As the separation line roughly fixes the position of the outer extremity of thevortex and the increased quantity of fluid rolled up into the vortex should increaseits size (see, e.g., the model of [2]), the center would be expected to move towardsthe blade. On the other hand, viscous forces tend to reduce the flow velocity in thegap as it diminishes, which is expected to shift the separation line towards the bladeand, again, the vortex center towards the blade. Similar arguments can be made for


Figure 16. Measured non-dimensional mean vortex distancex∗ from blade pressure side,suction side and camber line,versusdistance from leading edgez∗, compared with models ofChen et al. [1] and Song and Martinez-Sanchez [2]. Blade A with a 3 mm gap.

the height of the vortex above the floor. The lack of a clear trend in Figure 15suggests that both mechanisms may be active under our experimental conditions,with the distance of the vortex core from the blade appearing to reach a maximumfor a gap thickness of around 3 mm.

Regarding the evolution of vortex circulation with gap thickness, one would apriori expect it to increase monotonically with gap thickness up to the point wherethe gap becomes so large that the vortex asymptotes to a wing-tip vortex. Thisis, however, too simplistic, as the proportion of vorticity (which may be stronglydependent on geometry)not rolled into the vortex is not considered. In this study,an increase of circulation has only been observed up to a gap of 3 mm, beyondwhich the circulation saturates or even shows a slight decrease. The effect of gapwidth (normal to the camber line) on mean circulation is evidenced by the com-parison between blades A and B in Table II for a fixed gap thickness of 3 mmand in Table III for a varying gap. In all cases, the mean circulation in case B issignificantly lower (typically half) than for blade A. Since the gap width did nothave a significant effect on the maximum velocity in the gap (see Figures 8–11), nodefinitive reason for this strong effect can be offered. It is, however, curious to notethat when compared on the basis of equal gapaspect ratio(gap width to thickness,the circulations measured for blades A and B become rather similar (compare, e.g.,case B-3 of Table III with “A-1.5”, the average between A-1 and A-2).

3.8. COMPARISON WITH EXISTING MODELS

A number of studies have been concerned with the locus of tip clearance vorticesin turbomachinery. The following comparison with our experimental results will,however, be focussed on the recent work by Chen et al. [1] and by Song andMartinez-Sanchez [2]. Chen et al. performed a numerical computation, based ona simple model of the flow, but comparisons will be made with their empirical


Figure 17. Measured non-dimensional mean vortex distance from pressure side of blades Aand B with gaps of 1–4 mm, compared with relation of Chen et al. [1] (solid line).

model for the distance of the vortex from the blade, which is in good agreementwith data from earlier publications. Song and Martinez-Sanchez offer an analyticalmodel for the position of the tip clearance vortex, based on the assumptions that theflow is inviscid and that the flow under the blade is a pressure-driven “sheet jet”.Their model gives useful insight into the mechanisms behind the vortex formation(and what might affect it) although their analytical predictions of circulation are,at first sight, in poor quantitative agreement with our results (see Section 4). Forcomparison, our data are made non-dimensional according to Chen et al.:

x∗ = x

δ, z∗ = z

δ

√1cp

2,

wherex is the distance from the blade,z is the distance along the blade from theleading edge,δ is the clearance gap thickness, and1cp the mean non-dimensionalpressure loading of the blade. Using mainly empirical arguments, Chen et al.found that the distancex of the vortex from the blade is given by the simpleproportionality

x∗ = 0.46z∗.

The model of Song and Martinez-Sanchez, on the other hand, is complex and onlysome of its features will be briefly discussed in Section 4. In both models theassumption of lightly-loaded thin blades is made. Our blade is moderately loaded(1cp ≈ 1.0) but is not thin; the distance of the vortex from the blade is in fact ofthe same order as the thickness of the blade. For this reason, the definition of thevortex distance from the blade poses a problem. The three obvious possibilities aredistance from the suction side, distance from the camber line (blade mid-plane),and distance from the pressure side. In Figure 16 the vortex trajectories predictedby Chen et al. and Song and Martinez-Sanchez, and our measurements of vortexlocation for blade A with a 3 mm clearance gap are plotted at four streamwise


Figure 18. Comparison of measured mean vortex circulation for blade A with modelprediction of Song and Martinez-Sanchez [2].

positions. It is clearly seen from this figure that the best agreement is obtainedwhen the coordinatex in the models is measured from the pressure side. This ap-pears reasonable since in both models the position of the suction side is irrelevant,save for its role in determining the blade loading. Figure 17 then shows all ourvortex trajectories for profiles A and B, including those measured at different gapthicknesses, in comparison with the fit of Chen et al. [1], with the vortex distancemeasured from the pressure side. The agreement appears quite good and, remark-ably, equally good for the blades with and without anti-cavitation lip. In fact, ourdata fall well within the scatter of previous measurements compiled in figure 5 ofChen et al. [1].

The model of Song and Martinez-Sanchez [2] also yields the circulation of thevortex (based on their assumption on the vorticity distribution) which is comparedin Figure 18 with the present mean circulation measurements for blade A at differ-ent streamwise positions. The increase of circulation with downstream distance isseen to be similar for the model and the measurements, but the latter fall belowthe model prediction by a factor 3–4. No conclusive explanation for this largediscrepancy can be offered, except for the speculation that viscous effects mayplay an important role. For instance, only a fraction of the streamwise vorticity,generated on the blade end-face within the gap, may end up in the concentratedtip vortex, while a large fraction may interact “destructively” with the streamwisevorticity of opposite sign in the casing boundary layer, i.e. the boundary layer onthe bottom wall of the water channel in the present experiment.

4. Discussion and Conclusions

The tip clearance vortex and other aspects of the flow in the tip region of a sim-plified hydraulic turbine blade model have been experimentally investigated in awater channel. Measurements have been made of the position and strength of thevortex at a number of conditions, and the effect of an anti-cavitation “lip” has


Figure 19. Mean vortex position with and without anti-cavitation lip (plan view, blade contourshown as straight line).

been investigated. It is reiterated here that the present experimental conditions,at which no cavitation occurred, are relatively far from any real case. As alreadymentioned in the introduction and summarized in Table I, the Reynolds numberin our experiment was two orders of magnitude lower than in real turbines. Inaddition, relative motion between the blade and the casing, wall curvature andflow rotation effects, as well as span-wise variations in blade profile and loading,have been neglected. Also, the tip clearance in most experiments was three timesthe 1 mm required for geometric similarity with a real Kaplan turbine. Finally,the boundary layer on the channel floor may not correspond to a real case, butvirtually no data are available on real casing boundary layers. The most importantof these deviations from a full-size installation are the Reynolds number mismatchand the lack of relative motion between the blade and casing. Regarding the modelReynolds number, one may argue that it was sufficiently high for the flow aroundthe blade and the vortex to be fully turbulent and that a further increase in Reynoldsnumber usually results in little overall change of vortex flow patterns. This view issupported by the fair agreement of the measurements with inviscid models. Theneglect of the relative motion between the blade and the casing, on the other hand,is a standard assumption in tip flow modeling, as a simple estimate of the contribu-tions of pressure difference and relative wall motion to the gap flow indicates thatthe latter is negligible in most cases.

Besides providing a useful data base of tip vortex flows, the main conclusionof this study is that the anti-cavitation lip tested did not have the expected effectof significantly displacing the tip clearance vortex away from the blade, althoughit did usefully reduce the strength of the vortex. It had been anticipated that thelip would move the vortex outwards by an amount comparable to the width ofthe lip (25 mm for our model), but the measurements revealed a barely significantaverage vortex displacement of about 3 mm. In PIV measurements and in flowvisualizations, it was seen that, at the lip leading edge, the vortex actually “climbs”onto the top of the lip and, for some distance, remains clearly centered above thelip, at a distance from the blade which is slightly smaller than the mean distance


Figure 20. Sketch of vortex roll-up model due to Song and Sanchez-Martinez [2].

for the same blade profile without lip. Only further downstream, the distance of themean vortex center from the blade suction side becomes larger than the lip widthand the vortex trajectory approaches the no-lip trajectory, as shown in Figure 19.

A possible explanation for this behavior can be given on the basis of the modelby Song and Martinez-Sanchez [2], which predicts the vortex position relative tothe pressure side of the blade, without any consideration of the suction-side geo-metry. This is consistent with the hypothesis that the velocity magnitude under theblade is that of the free stream (inviscid flow) and that the velocity in the directionnormal to the blade, i.e. the flow angle, is determined by the pressure differenceacross the blade. The fluid emerging from the gap in the form of a “sheet jet” theninteracts at a separation line with the free stream. Hence, the velocity componentsin a plane normal to this separation line, and parallel to the casing wall (waterchannel floor) must be equal and, since the velocity magnitudes on both sides arealso equal, the separation line must bisect the directions of the “sheet jet” and thefree stream. At the separation line, the “sheet jet” is turned away from the wall andis rolled up into the tip vortex centered one vortex radius from the separation linetowards the blade, as illustrated in Figure 20. This model concept is fully consistentwith our measurements shown in Figures 8–11: that is, since the anti-cavitation lipof blade B does not extend to the separation line originating from the blade leadingedge, the jet emerging from under the blade remains largely unaffected by the pres-ence of the lip. The implication of the model [2] is that the anti-cavitation lip canonly be successful in moving the vortex further away from the blade if it extendsbeyond the separation line on the suction side of the casing wall, as suggested inFigure 21. Only in this case could one expect a new separation line and a new vortex


Figure 21. Sketch of vortex roll-up with large anti-cavitation lip (plan view).

to start at the lip leading edge. The two vortices originating from the blade and thelip leading edges, respectively, may still interact and eventually coalesce, but theirfinal trajectory would be expected to be determined by the new separation line,resulting in a greatly lowered risk of cavitation in the case of a “spherical” casing.For a “semi-spherical” casing, on the other hand, the experiments have shown thatthe greatest danger of cavitation occurs in the region of the closing gap such thatthe benefits of a wider lip, starting at the point where the gap becomes constant,appear questionable.

Acknowledgements

The financial support by Sulzer Hydro Ltd. and the Swiss Federal Commission forTechnology and Innovation (CTI) under grant 2905.1 is gratefully acknowledged.The authors also thank Drs. H. Keck, A. Sebestyen, P. Drtina, M. Casey and othersat Sulzer for their constant encouragement. Many of the results reported in thispaper were obtained during the semester and diploma projects carried out by Mr.Bruno Granier and other students: without their help and the expertise of the LMFtechnician team, this study would not have been possible.

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