Cavitation inception tests on a systematic series of twobladed

Transcription

1 26 th Symposium on Naval Hydrodynamics Rome, Italy, September 2006 Cavitation inception tests on a systematic series of twobladed propellers G.Kuiper, T.J.C. Van Terwisga, G-J. Zondervan ( MARIN, Wageningen, The Netherlands), S. D. Jessup (DTRDC, Carderock, Md, USA), E.M. Krikke (Royal Netherlands Navy, The Netherlands) ABSTRACT The paper aims at propeller design techniques which suppress inception of tip vortex cavitation. Model tests provide insight in the phenomena associated with tip vortex cavitation inception on propeller blades and the important parameters are systematically varied and investigated. The application of this work is primarily directed to improvements on naval propellers. However, lessons learned are also useful in the design of propellers for merchant ships, where there is a risk of cavitation hindrance due to vibrations or noise. A systematic series of propeller blade designs has been made, based on an existing state of the art controllable pitch Naval propeller design. Geometric parameters were varied in the tip region including thickness, planform, skew, chord distribution and rake. All these parameters were varied while maintaining a constant radial loading distribution. The results of the cavitation inception tests are presented in the form of inception diagrams for the distinct types of tip vortex cavitation that can be distinguished (trailing, local tip and leading edge vortex cavitation). Cavitation inception performance is quantified by the width of the non cavitating range of operating conditions at constant σ, referred to as the cavitation bucket. The systematic tests indicate that the blade contour is an important parameter in tip vortex inception. Using the results of the systematic tests a series of propeller models were designed in an effort to improve the results further by combinations of the parameters in the systematic tests. As yet the results have shown no significant further improvements, but indicated the pitfalls and problems which have to be avoided. A low skew planform was finally designed aiming at the delay of cavitation inception. The model test results confirmed the design guidance derived from the systematic tests. Recent full scale observations confirmed the model test results and provide an illustration of the potential of the new design technique. Panel Method analysis was used to assist in the design of the various tip variants. The possibilities and shortcomings in application of inviscid computations for the analysis of tip flow are shown. INTRODUCTION Investigations into delay of the onset of cavitation on low noise propellers have traditionally been focused on inception of sheet type cavitation. The principal design objective was the bucket width of the propeller blade sections. The so-called cavitation bucket relates the minimum pressure on the blade section to the angle of attack. This has led to sections with a wide cavitation bucket, such as the Eppler sections. (Eppler and Shen, 1979, Shen and Eppler, 1981) The replacement of the traditional NACA sections with alternate section families was followed by a design method, where sections were designed with a bucket width adapted to the variations in angle of attack which were experienced. This technique was developed in a combined research program in which the US Navy, The Royal Netherlands Navy(RNN) and Marin cooperated. ( Kuiper and Jessup, 1993). As a result of the suppression of inception of sheet cavitation, the first occurrence of tip vortex cavitation became more and more dominant (Kuiper,1994). In 1996, therefore, in a new joint research effort of the

2 parties involved, methods for delaying tip vortex cavitation inception were investigated aiming at developing propeller design tools for this purpose. This paper is based on some of the findings of this research effort. Numerous ideas have been proposed to suppress tip vortex cavitation inception on propellers or foils. A review was given in 1979 by Platzer and Souders (1979). Most devices, however, imply sharp corners or edges in the tip region and experience has shown that possible benefits in suppression of the tip vortex are mostly overshadowed by promotion of cavitation inception on those edges. The only method applied generally to delay tip vortex inception has therefore been a reduction of the tip loading. number and a more or less empirical scaling law is generally used (McCormick,1962) in which the inception index of a vortex is taken proportional to the Reynolds number to a certain power. Depending on the facility used this power varies between 0.2 and 0.5. For the prediction or scaling of tip vortex inception a viscous calculation could provide valuable insights. Such a viscous calculation method is not yet readily available. Early efforts with RANS codes were carried out on foils (Dacles-Mariani and Zilliac, 1005), and nowadays viscous calculations on propellers in uniform conditions are being performed (e.g in the EC project Leading Edge). Unsteady tip vortex calculations are possible, but very time consuming and the convergence and grid independency remains very problematic. These calculations are still far from being used as a design tool. During the start of the TIPVOR project the only design tool available with a certain degree of accuracy and stability was the non-cavitating, fully wetted panel code for propellers. TYPES OF TIP VORTICES ON PROPELLERS The TIPVOR research project started with a detailed investigation on the physics of the tip vortex near inception of cavitation in the vortex core. Attention was given to the accuracy of the determination of inception at model scale and it was concluded that the blade geometry was a major factor in this.. Since model propellers today are manufactured with numerically controlled tools, the variation in tip geometry and thus the variation between blades has been significantly reduced. This also proves that the geometry has a major influence on the inception of cavitation. Instead of investigating the devices as in Figure 1, it was therefore decided to investigate the geometry of a faired conventional propeller tip and to develop design methods for this geometry. Fig. 1.From Platzer ans Souders, Tools for the prediction of tip vortex strength are scarce. For example the relation between the blade loading from 0.9R to the tip as a measure for the strength of the tip vortex has been used. This relation could provide a qualitative indication of a vortex strength, useful for comparing the strength of the tip vortex at various propellers or at various radial loading distributions, but it is far from a prediction of the inception conditions. From comparisons between tip vortex inception at model and full scale it has become clear that viscous effects are strong. The minimum pressure in a noncavitating vortex is strongly dependent on a Reynolds Closer examination of various inception conditions showed that three types of tip vortices could be distinguished: the trailing tip vortex, the local tip vortex and the leading edge tip vortex. (Terwisga et al, 1999) Trailing type of vortex cavitation is generally associated with a vortex, building up strength in downstream direction. The physical mechanism involved is the roll-up process of the trailing vorticity behind the blades. Cavitation inception occurs away from the blade (detached inception), but very often cavitation develops up to the blade or cavitation moves rapidly towards the blade after inception. The main parameter to affect the strength of the trailing

3 vortex is the radial loading distribution. Most attention has been given in literature to this type of tip vortex cavitation. Fig. 2 Trailing tip vortex.(attached) Leading-edge vortex cavitation is another form of vortex cavitation that can be observed on propeller blades. Similar to the development of a tip vortex on a delta wing, a cavitating vortex can be seen breaking away from a propeller blade. A Navy propeller will have a strongly unloaded tip in order to delay tip vortex cavitation. It will have a reduced loading at the blade hub to avoid hub and root cavitation, and consequently it will have it s loading concentrated in the middle of the blade. This leads to a vortex originationg at the leading edge, passing the tip at some distance. The behaviour of the leading-edge vortex can be very dynamic, depending on the blade loading and will not cavitate if not sufficiently strong. Fig. 4 Local tip vortex Fig. 5 Paint test on pressure side of parent propeller at low loading (K T =0.05) Fig. 3 Leading edge tip vortex Local tip vortex cavitation originates from separation of the flow at the very tip of the propeller blade. The pressure distribution on the tip and the geometry of the tip play an important role. At a light tip loading this type of cavitation is not related to the roll-up of the tip vortex. At moderate tip loading it may coincide with trailing vortex cavitation. Local and leading edge vortex formation can also merge. A local tip vortex occurs downstream of the blade tip, a leading edge vortex originates upstream of the tip and in the limit they coincide. Distinction between the two is useful, however, because in many cases the two types of vortices occur simultaneously. They can often be distinguished more clearly from a paint test in steady (open water) conditions (Fig.5). The inception conditions of a propeller are of course dependent on the first type of tip vortex inception which occurs. It is important to distinguish between them because the parameters influencing their inception, and therefore the ways to improve a design, are quite different. Inception of the trailing vortex can be controlled by the loading distribution of the sections at the tip. Inception of a leading edge vortex can be influenced by the leading edge contour and its loading. Inception of the local tip vortex depends both on tip loading and geometrical details of the blade tip.. POTENTIAL FLOW ANALYSIS As mentioned in the introduction, viscous codes are still insufficient for design purposes and in the TIPVOR project it was therefore investigated if and how potential flow calculations could be used for the optimisation of tip vortex inception. The employed code, PSF10, is able to calculate the potential flow about a rotating propeller in open water condition. In

4 PSF10 a simple wake model was used with local pitch of the wake panels equal to the local pitch of the sections at the same radius. No contraction or roll-up was considered. In these calculations the focus is on the pressure distribution on the blades, but also on the pressure gradients near the tip and the leading edge, because these pressure gradients are the locations where separation may occur and where vortex formation can start. In later stages also the direction of the streamlines on the propeller surface was considered, mainly to see if the streamlines in the design condition would not cross the leading edge or the tip. Such a crossing will also cause a low pressure peak, but the direction of the streamlines may be a more clear indicator of problem areas. Since in the potential flow calculations there is no separation the minimum pressure in the tip region is taken as a criterion for cavitation inception. This is of course a major simplification of the pressure distribution in the viscous core of a vortex. A radial grid distribution was used. This leads to a singulare grid element in the tip. This, however, was not the major limitation of the panel calculations. The most important problem was singular behaviour of the pressure at the trailing edge in the tip region. Grid refinement was no solution, on the contrary (Fig. 5). The cause of this singularity may be the prescribed location of the wake, which is not necessarily force free in the prescribed position. Investigations have been made to improve this by adjusting the position of the first row of wake elements or by allowing a force acting on them. But these investigations are outside the scope of this paper. Fig 5 Calculated pressure distribution at 0.97R radius. At 0.99R the pressure distribution was very scattering due to this effect. So 0.97R is used as a reference, with neglect of the trailing edge singular behaviour. Apart from the fact that it proved to be very difficult to predict the minimum pressure in the tip region reliably, this singularity was sometimes so strong that it affected the radial loading distribution. This was especially the case with some highly skewed propellers DEVELOPMENT OF A SYSTEMATIC TWO BLADED PROPELLER SERIES In finding relevant parameters describing the propeller blade geometry, the distinction between the mentioned types of tip vortices plays an important role. The parameters chosen for optimisation are often dictated by the propeller design method. Design parameters such as camber, thickness and angle of attack of the blade thickness are parameters because they are used in the design of the propeller. In the present investigation the focus was on the pressure distribution near the tip, as calculated by the panel code. This makes it possible to use more integral variables involving also the radial distribution of the sectional characteristics. The parameters chosen were: the shape of the blade contour, the shape of the tip geometry the rake at the tip. These are more general features of a propeller blade design and are more difficult to quantify in a single geometry parameter. Therefore the following approach was chosen: a systematic variation of a parent propeller. In this way the possibilities of the panel code in treating the difficult problem of tipvortex development was investigated and design criteria could be deduced for improvement of tip vortex cavitation inception. To investigate the cavitation inception characteristics as accurately as possible by means of model experiments, the inflow conditions have to be defined and have to be repeatable. This is very difficult in non-uniform inflow, because of the interaction between the wake generating structure (a hull, a dummy model or a wake screen) and the propeller. Therefore propellers were used in open water, with a uniform, undisturbed inflow. The disadvantage of such a condition is that the vortex exists over a long time and gas diffusion can influence the inception conditions, leading to so-called gaseous cavitation where the pressure in the cavitating core has a pressure higher than the vapour pressure. This risk was minimized by using a moderate gas content in the tunnel (5 to 6 ppm) in combination with roughness (60 microns carborundum) at the leading edge and tip of the blades. The relative lack of nuclei in the inflow is compensated by the generation of nuclei on the roughness elements and the roughness acts as a local

5 nuclei generator. This reduces the risk of accumulation of large amounts of gas in the tip vortex. The risk of gaseous cavitation was further reduced by using the experimental procedure of calling inception first, while determining desinence of the vortex cavitation immediately after that. In case of strong hysteresis the desinent inception conditions were used in combination with a short duration of the cavitation. The inception conditions were determined in the Large Cavitation Tunnel of Marin and in some cases also in the 36 tunnel of the David Taylor Model Basin in Carderock, USA. A hub was manufactured in which two blades could be inserted. The diameter of the two bladed propeller was 40 cm, large enough to ensure geometric accuracy when the blades were manufactured with a numerically controlled milling machine. The selection of a two bladed propeller simplified the calculations because of a reduction of the blade to blade interference. THE PARENT PROPELLER DESIGN A 2 bladed parent propeller was designed to have the same blade sections and radial loading distribution as a typical high quality navy propeller. The inception characteristics measured for the various tip vortex types are presented in the inception diagram in Fig. 5. right hand side represent the inception conditions of suction side cavitation, the curves on the left hand side are the inception conditions of pressure side cavitation. Only the curves of tip vortex cavitation are given here. A propeller with optimum inception conditions has all types of cavitation incepting at the same time. A propeller that is optimum from a cavitation inception point of view has a bottom of the bucket as low as possible while the operational curve crosses through the lowest point of the bucket. Such an optimisation criterion can lead, however, to a very narrow bucket, which in practice is useless because the propeller is never operating exactly along its operational curve (e.g. due to added resistance due to wind and waves or pitch variations in case of controllable pitch propellers). Therefore the width of the bucket near the bottom is even more important. In the present investigation the width of the bucket at a cavitation index of 2 has been used as a criterion. This width is indicated in Fig. 5 and is expressed in the range of the thrust coefficient K t. The bucket width of the parent propeller was and trailing vortex inception was the critical type, very close to local vortex inception. The purpose of the present investigation is to increase this bucket width. VARIATION OF THE TIP LOADING Fig. 5. Inception diagram of the parent propeller This diagram shows the so-called cavitation bucket, inspired by the shape of a bucket. The curves on the To achieve the highest possible cavitation inception speed the operating curve of the propeller has to intersect the lowest point of the cavitation bucket. The pitch of the propeller, and especially the pitch of the tip, plays an important role here. It is not possible to simply adjust the pitch of the parent propeller, because in that case also the radial loading distribution varies strongly. To verify that the tip loading can adjust the cavitation bucket to bring it in line with the operating curve a separate two bladed propeller was designed with a more unloaded tip. The loading from 0.8R towards the tip was decreased, the loading around 0.6R was increased, to maintain the same power vs. rpm relationship as the parent propeller. From panel code calculations it was found that such a change would result in an increased suction peak at the leading edge near the tip, so the camber of the tip sections was adjusted. After a number of iterations the pressure peak near the leading-edge at 0.97R was designed in such a way that it matched the minimum pressure at the pressure side (Fig.6). The tip loading was significantly reduced with only a positive loading in the forward part of the section.

6 Fig.6 Pressure distributions at 0.97 R on parent and unloaded tip variant In this way the pressure gradient perpendicular to the leading edge was minimized. The resulting unloaded tip propeller had the same open water performance as the parent propeller. The thrust coefficient and the efficiency in the inception region (around Kt=0.1) were less than 1% different from the parent propeller. This is to illustrate that even a change in loading of the tip requires a complete redesign of the propeller. All the subsequent variations in this project were the result of a series of calculations in which a variant was optimized. The resulting cavitation bucket of the unloaded variant is shown in Fig. 7. There is a difference between local and leading edge inception at the pressure side, indicating that the shape of the tip can probably be further improved. The bucket width of the unloaded tip propeller was 0.085, slightly, but not significantly less than the parent propeller. But the shift of the bucket is considerable and illustrates that with a proper choice of the tip loading the bucket can be adjusted to the operating curve without significant loss of bucket width. Fig.7. Cavitation bucket of unloaded tip variant. (dotted lines are from the parent propeller) VARIATION OF TIP THICKNESS The flow around the propeller tip is highly threedimensional and sectional considerations are losing their hydrodynamic significance very close to the tip. The idea is that a thicker tip causes a lower pressure gradient along the contour, thus suppressing boundary layer separation and subsequent vortex formation.. The maximum thickness in the tip region was varied using several variants in the design stage, as shown in Fig. 8. The gray area indicates the final increase in tip thickness which was applied for the model propeller with a thicker tip. Fig.8 Variations of the radial distribution of the maximum thickness.

7 As can be seen the parent propeller already had an increased thickness at the tip. The chordwise position of the maximum thickness was varied in order to decrease the pressure gradient perpendicular to the blade contour in the tip region while delaying as much as possible the formation of low pressure peaks at σ n = 2. In all cases the radial loading distribution at the tip was maintained. The influence of the applied thickness variations on the pressure distribution was most pronounced at higher blade loadings, but remained very small Although a reduction of the pressure gradient at the leading edge, upstream of the tip, could be obtained, the effect on the bucket width was small. The type of inception found on the thicker tip was local tip vortex cavitation, both at the pressure and the suction side. The thicker leading-edge suppresses leading edge vortex formation, and the increased surface area at the tip apparently also decreases the strength of the trailing vortex, but at the expense of local vortex formation. The bucket width of this variant was 0.08 and no improvement over the parent could be obtained. Fig. 8 VARIATION OF THE CHORDLENGTH AT THE TIP A traditional way to reduce tip vortex cavitation is to increase the chord length of the tip. The idea is to reduce the pressure gradient perpendicular to the tip contour while maintaining the loading. Since also the skew at the leading edge was used as a parameter, the increase of the chord length was obtained using the same leading edge contour, thus creating a strong tail at the tip. The length of the sections above 0.7 R was increased up to 50%. Here the panel code gave severe complications, because of numerical errors that occured at the trailing edge of the outer sections. The pressure peaks were so strong that the sectional lift and thus the propeller thrust could not be calculated reliably. The loading at the trailing edge was subsequently reduced by adapting the camber. The non-dimensional pressure coefficients are given in Fig.8 for the parent and in Fig.9 for the chord variant. Fig. 9 Figs.8 and 9. Pressure distributions on parent propeller and on the increased chord length variant at Kt=0.15 The pressure gradient near the tip could be reduced significantly, which leads to the expectation that tip vortex inception would be significantly reduced. The result of the inception test was more complex, however. Inception of the the leading edge tip vortex was delayed, resulting in a move to the right in the inception diagram. But the local tip vortex at the suction side remained unchanged. The net result was a considerable narrowing of the width of the cavitation bucket from to This might still be improved by also shifting the local inception curve, e.g by altering the camber distribution of the sections, but this would still lead to a bucket width which is comparable to the parent propeller and not to any significant improvement. Based on these results any positive effect on the inception of the tip-vortex of an elongation of the chord length coult not be confirmed.

8 VARIATION OF THE TIP RAKE In a previous project (AFDEASR) it was found that rake towards the pressure side was effective in widening the cavitation bucket (Kuiper,1994). Tip rake has also been applied to increase the efficiency (Anderson and Anderson, 1986). This is applied in the so-called Kappel :propeller (Anderson et al, 2002), but in that case the rake is towards the suction side and the blade tip is loaded! Here the effect of tip rake towards the pressure side in combination with the loading distribution of the parent propeller (which has an unloaded tip) is investigated, with the goal of widening the cavitation bucket. The rake which was investigated is given in Fig.10. The applied tip rake to the pressure side is rather extreme and approaches the geometry of a tip plate. reduction. This confirms that strong curvatures in the tip region should be avoided. Rake with a smoother curvature, as used in Kuiper (1994) may therefore increase the bucket width, especially the width of the bucket of local and leading edge vortex cavitation. Fig.11 Pressure distribution and direction of wall velocity of rake variant at Kt=0.15 VARIATION OF THE LEADING EDGE SKEW Fig.10 Rake variant. The design of such a blade requires accurate prediction of the flow directions, because at the tip strong curvatures are created and the flow should be aligned properly so that the flow is not be forced to separation over these curved surfaces. Therefore the flow direction was also shown in panel code results, as shown in Fig.11. Such calculations were carried out for a range of blade loadings. A criterion for the severity of the cross flow is difficult to determine, however.. The inception measurements showed a trailing vortex coming of the corner of the raked tip. Apparently there was still too much cross-flow over the strong curvature, leading to separation and vortex formation. Local and leading edge vortex inception were delayed and without the vortex on the corner of the raked tip the bucket width was increased from of the parent to , a moderate but significant increase. The premature occurrence of the trailing vortex on the raked tip reduced this width to 0.085, a moderate Skew is generally defined in terms of the midchord position of the blade sections. Since leading edge vortex formation takes place on the leading edge, the skew of the leading edge was drastically changed. Instead of a highly skewed leading edge the leading edge was made nearly straight. This leads to a strong curvature between leading edge and tip and this corner requires attention. In the calculations skew turned out to have significant effect on the radial loading distribution. It required drastic changes in camber and pitch at the tip to arrive at the same radial loading distribution as the parent propeller. In many cases which were investigated numerically, the numerical problems at the very tip prevented an accurate determination of the loading and the pressure distribution at the tip. The skew variant that was chosen, with a nearly straight leading edge, still had a slightly lower tip loading than the parent propeller. Again, this is a completely new design. Using the panel code the minimum pressure peaks in the inception region have been maximized and as a secondary criterion the pressure gradient perpendicular to the contour has been minimized. In the final skew variant the minimum pressure on the blade was closer to the leading edge compared to the

9 parent propeller. Also the low pressure region at the tip near the trailing edge was considerably smaller. So the pressure gradients were not reduced. The design condition was at Kt=0.12, but the development of the pressure distribution is more clearly seen at Kt=0.15 as shown in Fig. 12. There is a low pressure peak at the leading edge near the tip, which is expected to give sheet cavitation, and one at the tip near the trailing edge, which is expected to give local vortex cavitation. Fig.13 Inception diagram of skew variant. AN INTERMEDIATE EVALUATION Fig.12 Pressure distribution on the suction side of the skew variant at Kt=0.15. The big surprise came with the inception diagram of this skewed variant, as shown in Fig.13. The inception data of the parent propeller have again been inserted in the diagram. The position of the bucket reveals its lighter tip loading compared to the parent propeller. But the width is considerably larger (0.113), especially due to the shift of the pressure side local tip vortex inception. At the suction side the trailing vortex is the first to come in, indicating that a slight further reduction of the tip loading might even improve the bucket width. Local inception at the tip is second at the suction side and occurs in the same condition as on the parent propeller.. At this point the following evaluation was made. As to the panel code as a tool it was concluded that the singularity at the tip was a serious handicap to assess and optimize certain shapes. The risk of local tip vortex inception could not be predicted using the minimum pressure in the trailing edge region of the tip. These numerical errors should be investigated further. The assessment of the risk of trailing vortex inception using the loading of the tip region can be used in a comparative sense. Absolute prediction of trailing vortex inception on the basis of panel code calculations is not possible or inaccurate. The tip loading can be used to shift the inception bucket of trailing vortex cavitation, but not without redesigning the sections. The panel calculations are especially useful to avoid premature sheet cavitation and bubble cavitation. The avoidance of leading edge peaks in the pressure distribution is a necessary condition for the avoidance of sheet cavitation, but also for vortex cavitation. For the prediction of vortex cavitation the pressure gradient perpendicular to the tip has been used, but the results of this criterion are indicative at best. The investigated variants showed in the first place that the parent propeller was a very good design, which

10 was difficult to optimize further with conventional changes. Only the lengthening of the chord at the tip and application of rake showed the potential of a moderate improvement of the cavitation bucket, but this would require further (experimental) optimization cycles because the improvement was beyond the capabilities of panel code predictions. with a value of 0.16 compared to of the parent propeller! The only significant improvement was found on the skew variant. This parameter has therefore been investigated further. FORWARD SKEW VARIANT As a consequence of the previous results a variant was designed with forward skew. Again this was a variant with the same loading distribution as the parent propeller, and the blade sections in terms of pitch, camber and thickness distribution have been adjusted to minimize leading edge pressure peaks in the inception region of the thrust coefficient. The application of skew influences the boundary layer development over the propeller blades. For backward skewed propellers the combined effect of flow retardation inside the boundary layer and centrifugal forces working on the boundary layer flow particles cause a redirection of retarded vortical flow towards the tip. This results in an accumulation of vorticity in this region of the propeller and in a increase of the tipvortex strength. In the case of forward skew, the hypothesis is that due to the shape of the leading-edge the radial flow components near the leading-edge will be in the direction of the hub rather than the tip. It is supposed that forward skew helps in redirecting the vorticity away from the tip and therefore prevents the accumulation of vorticity into a tip-vortex. The forward skew variant had a trailing edge with little skew and unfortunately this resulted again in numerical problems in the panel code. The tip loading from 0.95R showed an increase of the loading relative to the parent propeller, but this was considered due to the numerical difficulties. The experimental results for the forward skewed propeller are given in Fig.14. The bucket width is determined at the suction side by trailing tip vortex inception. Even then the bucket width is 0.113, comparable with the variant with the straight leading edge. The fact that the trailing vortex cavitates first at the suction side confirms that the tip loading was indeed higher than the parent propeller. This can in principle be corrected by adjusting the pitch at the tip, but this requires a new design. When the trailing tip vortex is ignored the bucket width is indeed very large Fig. 14. Inception diagram of forward skew variant. This forward skew variant was also tested at a slightly lower pitch setting (P/D (0.7R)= 1.4 instead of 1.6). This reduces the tip loading. The result was a shift of the bucket, but the bucket width, including the position of the trailing vortex inception line, was not changed. This illustrates that the shift of the trailing vortex line requires a new radial loading distribution at the same loading, and therefore a new design. With such a new design the bucket width could be increased further. The effect of skew on the bucket width, and especially on the local pressure side inception, lead to further variations. RAISED FOREHEAD VARIANT Forward skew may be one step too far for most ship owners and therefore an alternative blade contour was tried nick-named the raised forehead contour, as shown in Fig.15. The raised forehead blade contour is thought to be a practical compromise between the straight leading-edge of the tested skew variant and that of an ordinary skewed propeller.

11 The experimental result is shown in Fig.17. The critical type of inception was local tip vortex inception. Fig. 15. Contours of parent propeller and raised forehead variant. In this variant the skew of the leading edge was reduced only over the outer 10 percent of the radius to reduce the flow in radial direction, which seems to be contributing to the development of the tip-vortex. This gives a sharp curve of the contour near the tip, which requires further attention. The contour as in Fig.15 has the same chordlength distribution as the parent propeller. A variant with a shorter chord length at the tip was also designed and investigated, but with disastrous results. The bucket width nearly disappeared! This shows that skew reduction is not a panacea that can be applied without care, but should be closely integrated into the design while giving attention to the occurrence of local pressure peaks that trigger cavitation. In order to ensure a smooth flow at the leading edge of the raised forehead an increased thickness was applied, forming a bulbous shape. The thickness distribution is given in Fig. 16. Fig. 17 Local tip vortex inception on raised forehead The result is not spectacular, because the bucket width is slightly smaller than that of the parent propeller. The suction side inception has slightly improved, but the expected improvement at the pressure side has disappeared. Given these results a further analysis was made using computed pressure distributions and streamline plots in an effort to gain more insight in the flow. Figure 18 shows the pressure distribution and the streamlines computed for the loading condition near inception at the suction side of the blade. It is shown that the streamlines follow the tip contour. Fig. 16. Thickness distribution of raised forehead variant. The raised forehead variant of Fig.15 was designed again with the same radial loading distribution as the parent propeller and without low pressure peaks at the suction side at inception loading.

12 Fig. 18 Example of correct flow lines at the suction side. The direction of the flow lines near the trailing edge indicate that no local tip vortex is developing here giving rise to inception of cavitation. The cavitation pattern in Fig 19 illustrates that vorticity developing at the trailing edge may leave the blade at 0.9R instead of at the tip. The local tip vortex inception at the tip is determined by the local flow near the raised forehead. A sheet is formed at the raised forehead, but vortex cavitation is delayed on the suction side, as shown in Fig. 19. Fig.20 Local tip vortex inception at the pressure side of the raised forehead variant. Figure 20 shows that the local tip vortex on the pressure side develops directly at the leading-edge, so at the very end of the raised forehead contour. For this condition (at a lower loading) computations were also made. The pressure distribution and streamline traces for the pressure side inception condition are shown in Figure 21. Fig. 19 Cavitation pattern on the suction side of the raised forehead variant.(σ n =2.0) The local tip vortex at the pressure side, however, was observed to develop much earlier than expected. An observation of this vortex is given in Fig.20. Fig. 21. Streamlines at raised forehead at low loading. Clearly visible is the strong cross flow in this loading condition occurring in the tip region. This cross flow is likely related to the development of a local pressure side tip vortex and could point at premature inception of this vortex. Further calculations showed that this cross flow remained strong indeed when the

13 loading was increased, resulting in a small bucket width. On the resulting propeller full scale observations were made. Fig.23 shows the maximum extent of the cavitation when the propeller operates at nearly full power! Fig.22. Streamlines at higher loading (suction side inception) In the condition of inception at the suction side (similar as in Fig.18) such a cross flow was not present, as shown in Fig.22. The described results illustrate the complexity of the design for delayed inception of the tip vortex. The major influence of the skew of the leading edge has been identified. However, a straightforward application of the raised-forehead blade contour is no guarantee for success. Not only the pressure peaks and the gradient of the pressure distribution, but also the direction of the cross-flow has to be carefully considered and controlled. FULL SCALE VALIDATION In the TIPVOR project there was no time available any more to make a raised forehead variant with a wide bucket. A full scale design was then made for a supply vessel of the Royal Netherlands Navy. Although significant gains were obtained, this vessel had many restrictions on the operating conditions, complicating a straightforward validation of the raised forehead concept. Fig 23. Cavitation observation near full power on a frigate propeller There is sheet cavitation at the raised forehead, just as in Fig.19, but the blade sections at the inner radii, that have been optimised for optimum tolerance for inception of cavitation, are such that sheet cavitation is absent at inner radii.. The important aspect is that the sheet cavitation at the raised forehead does not lead to a local tip vortex, even not in this condition of maximum power. There is a vortex coming off the tip corner, as shown in detail in Fig.24, which is very weak and dissipates quickly. Still this vortex may be the cause of local tip vortex inception at the suction side. The design method and criteria developed from the systematic design study so far were put to practice in the design of a frigate propeller for the Royal Netherlands Navy. The design of propellers for openshaft arrangements usually concerns the adaptation to a wake field dominated by the wake of the struts and the influence of the inclined shaft.

14 The design criteria used in this numerical exercise were: Avoid low pressure peaks at the blade sections in the estimated inception conditions Minimize the pressure gradient of the pressure perpendicular to the tip Ensure that the calculated flow lines do no cross the contour Application of these criteria is by no means straightforward. In the design process, first the inception conditions, governed by operational conditions, have to be set and then a blade design meeting these requirements has to be made. Application of the criteria is far from clear in some cases and gains that are made regarding one criterion often deteriorates the other. Propeller design still is an art with many constraints. Fig.24. Detail of tip cavitation on raised forehead of a frigate propeller. In comparison with the performance of similar propeller designs it can be concluded that this was the propeller with a very small amount of cavitation in full power condition. A very clear indication of the success of the applied approach is the fact that a tip vortex could not be observed, even at the highest ship speeds. The experiences with this propeller show that a raised forehead can lead to a wide cavitation bucket, but that the calculations of the inception conditions have to be carried out very carefully. Experimental validation at model scale still is absolutely required. CONCLUDING REMARKS In the numerical and experimental study described in this paper progress has been made in understanding the tip vortex cavitation phenomenon and criteria have been devised and tested to delay the onset of this type of cavitation. A significant problem that was encountered during the numerical design evaluations has been the singular behaviour of the employed panel code near the trailing edge at the tip. Efforts to solve this problem, e.g. to neglect the Kutta condition at the trailing edge near the tip, will result in a lower resolution in that region. A solution to this problem has to be found or at least the effect of this singular behaviour on the radial loading distribution has to be avoided. A result of this study is the experience that the distinction between the origin of the tip vortex at inception is very useful. The trailing tip vortex can be optimized rather independently from the others. Local tip vortex inception can be minimized using the panel code results. Leading edge vortex cavitation cannot be estimated by the panel code. All types have to be determined experimentally, where the distinction between them is not always easy. The main result of the exercises has been the increased bucket width which can be obtained when, using the mentioned design techniques, the blade contour is adjusted. The forward skewed propeller remains an interesting option, which has to be investigated further. The raised forehead is an intermediate solution, which has shown to be effective, but which was found to require very careful design calculations. ACKNOWLEDGEMENTS. The three year TIPVOR project was supported by the Office of Naval Research, the US Navy and the Royal Netherlands Navy. The full scale validation was done on ships of the Royal Netherlands Navy. Model tests were carried out at DTRDC in Carderock, Md, USA and at Marin, Wageningen, The Netherlands

15 REFERENCES. ANDERSON, S.V., ANDERSON, P., Hydrodynamic Design of Propellers with Unconventional Geometry. Trans. RINA, ANDERSON, P., FRIESCH, J., KAPPEL, J. Development and full scale evaluation of a new marine propeller type, 97th Hauptversammlung der STG, Hamburg, 2002 DACLES-MARIANI, J., ZILLIAC,G.G., Numerical/Experimental Study of a Wingtip Vortex in the Near Field, AIAA Journal, Vol.33 NO.9, 1995, pp EPPLER,R.,SHEN,Y.T. Wing Section for Hydrofoils-Part 1:Symmetrical Profiles, J. Ship Research, Vol. 23,1979, pp KUIPER, G., JESSUP, S.D., A Propeller Design Method for Unsteady Conditions, Trans. SNAME, KUIPER, G. Effects of Skew and Rake on Cavitation Inception for Propellers with Thick Blade Sections, 20th Symposium on Naval Hydrodynamics, Santa Barbara, USA, 1994 MCCORMICK, J., On Cavitation Produced by a Vortex Trailing from a Lifting Surface, ASME J. Basic Eng., 1062, PP PLATZER, G.P., SOUDERS, W.G., Tip Vortex Cavitation Delay with Application to Marine Lifting Surfaces, DTNSRDC REP. 79/051, SHEN,Y.T.,EPPLER,R., Wing Section for Hydrofoils -Part 2 : Nonsymmetrical Profiles-, J. Ship Research, VOL 25, 1981,PP39-45 TERWISGA, T. VAN, KUIPER, G., RIJSBERGEN, M.X.VAN, On Experimental Techniques for the Determination of Tip Vortex Cavitation on Ship Propellers, ASME/JSME Fluids Engineering Summer Meeting, San Francisco,