ADVANCES IN FULL-SCALE WAKE-FIELD PREDICTIONS AND THE IMPLICATIONS FOR THE PROPELLER DESIGN
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1 ADVANCES IN FULL-SCALE WAKE-FIELD PREDICTIONS AND THE IMPLICATIONS FOR THE PROPELLER DESIGN Gert-Jan Zondervan*, Bram Starke Maritime Research Institute Netherlands PO Box 28, 67 AA Wageningen, The Netherlands * : Corresponding author s g.j.d.zondervan@marin.nl ABSTRACT In the design of propellers for today s advanced ships important design trade-offs have to be made regarding propulsion efficiency, cavitation-related vibration excitation, inboard noise and blade erosion. For some types of ships the design margins are extremely small and successful propellers can only be designed when the ship s hull generates a wake distribution that is sufficiently homogeneous. Therefore, it is becoming increasingly important to have reliable, accurate information on the characteristics of the wake field. Until now it has been common practice to base the propeller design on the wake field measured on. In recent years, however, considerable progress has been made in the prediction of viscous wake fields both at model and fullscale Reynolds numbers. Due to the increased quality of the solutions and the reduced calculation times these methods have become viable tools for obtaining wake field information. In this paper the results of calculations are presented obtained from MARIN s viscous-flow solver on the wake field of a high block product tanker and a large container vessel. The numerical results are compared to the results of model experiments and sea trials. Scale effects on the wake field characteristics were determined and the implications of the wake scaling on important quantities in the propeller design such as the hull pressure fluctuations and propeller forces are assessed in a tentative manner. INTRODUCTION In today s ship design the proper integration of the propeller and the ship s afterbody becomes increasingly important. Ship operators show a keen interest in maximizing the economic potential of their vessels, which results in great challenges to be met by ship and propeller designers. Tough design requirements are imposed on the design of advanced propellers in order to achieve an optimum balance between efficiency, vibration excitation levels and danger for cavitation erosion. Frequently designers are forced to adopt values for ship and propeller design parameters that are close to the generally acknowledged limits of traditional naval architecture. An interesting case, for example, is the design of future s very large container vessels (>1 TEU), which combine extremely large power levels of up to 1 MW and a single screw propulsion solution. Accommodating such high thrust densities while preventing vibration and cavitation erosion problems poses serious challenges with regard to the design of the propeller and afterbody shape. A priori knowledge of the characteristics of the ship s wake field at is extremely helpful, if not essential, to be able to design a suitable propeller. At present the velocity distribution at the location of the propeller disk is determined from measurements of the socalled nominal wake field at. Nominal wake fields are the flow fields at the stern without working propeller. Correction methods are being used to deduce the effective wake field, which, by definition, is the total velocity field minus the propeller-induced velocity field. These correction methods use certain assumptions regarding the influence of the propeller on the axial and transverse velocity components of the wake field. The resulting effective wake field remains a model-scale wake field without accurate correction for the Reynolds number effect on the flow around the hull. Computational methods based on the Reynoldsaveraged Navier-Stokes equations provide an opportunity to obtain detailed information about the stern flow field. Particular features of the wake field are the depth of the centre-line wake peak (the area of retarded flow behind the stern resulting from the boundary layer at the hull), the circumferential gradients of the axial and transverse velocity components and their dependency on the Reynolds number. In the following sections the results are presented of a study investigating the prospects of using predictions of the fullscale wake field of ships in the design process of advanced propellers. Two different ships are considered for specific reasons. The first one is a product tanker for which wake field data are available obtained from laser-doppler measurements both at model and. This vessel is a typical high block ship (C B =.8) of which the wake field is dominated by a pronounced wake peak and the presence of strong bilge vortices. The second ship is a large container vessel that could be representative for future s ultra high capacity mega-containers. Flow fields have been calculated for these ships, both at model and full-scale Reynolds numbers and were compared to the results of measurements. Calculated Reynolds scale effects on the wake fields were analyzed and possible implications for the propeller design were investigated. For this purpose the propellers of these two vessels were analyzed using these wake fields with regard to their powering performance and cavitation characteristics. THEORETICAL ASPECTS Viscous-flow computations The viscous-flow computations have been performed with the computer code, see Hoekstra and Eça (2), which solves the Reynolds-averaged Navier-Stokes equations on a boundary-fitted, single-block mesh. The steady,
2 double-body flow field at zero drift angle is simulated using Menter s (1997) one-equation turbulence model, extended with the correction by Dacles-Mariani et al. (1995). For the computations on a mesh typically consists of 145 points in the main stream direction, 81 points in the wall-normal direction and 45 points in girthwise direction. For the computations on the number of points in wall-normal direction is increased to 121. Mesh points are strongly clustered towards the hull to capture the gradients of the flow field that occur in the boundary layer. The governing equations are integrated down to the wall (no wall functions are used) and the maximum distance of the grid points adjacent to the hull is below y + =.3 in all computations. The iterative solution procedure is stopped as soon as the maximum variation of the non-dimensionalized pressure between two iterations drops below 5 x 1-5. The computational domain extends from midship to 25% of the ship s length beyond the stern. The width and depth of the mesh are taken approximately equal to the breadth and twice the draught of the ship, respectively. At the outer boundary of the viscous-flow domain, boundary conditions are imposed that are derived from a potential-flow calculation. In the viscous-flow computations the propeller action is represented by axial forces only. Additional effects such as from the finite number of propeller blades and the rotation of the propeller are not taken into account. However, the thrust loading has not been taken constant over the propeller disk area but varies in radial direction proportional to: F ( r) r 1 r (1) R R Here, r is the local radial distance to the hub, and R the radius of the propeller. Propeller analysis computations The computations of the propeller characteristics have been performed with MARIN s propeller analysis program ANPRO. This program comprises a suite of analysis programs built around a lifting-surface method for the calculation of the unsteady inviscid flow about propeller blades, see van Gent (1977), (198). In the lifting-surface method a linear system of equations for unknown blade loading, defined by a series of mode functions, is solved which results from the application of the no-penetration boundary condition in a series of collocation points located on the camber surface. The total value of the velocity in these points is determined by the contributions of the circumferential velocity, the velocity components induced by the propeller wake and the onset flow, which is provided by means of a ship wake field distribution. Pressure fluctuations exerted by the propeller on the hull plating have been calculated using the CAVDYN module of ANPRO. This program is an implementation of the method of Stern and Vorus (1983) which considers the dynamics of the unsteady sheet cavity on a 2D blade section as a function of the blade angle. The cavity volume V c, its variation as a function of the angular position dv c /dt and the acceleration of the cavity volume d 2 V c /dt 2 are important quantities in the determination of the pressure fluctuation levels. The non-cavitating contribution to the total level of the pressure fluctuations of these cavity volume variations and those induced by the blade passage itself are calculated as described by van Gent (1994). A distinction is made between pressure fluctuations due to the non-cavitating blade and those from the blade cavitation. The influence of the reflection of the pressure signals on the hull plating is accounted for by applying a constant solid boundary factor. The nominal wake fields, which have been used in the propeller analysis have been made effective by means of a correction method. The applied method, NOMEFF, is based on the Euler equations and uses a propeller force field approach to calculate the propeller-wake interaction velocities from a given nominal wake and a prescribed propeller thrust. CASE 1: PRODUCT TANKER To illustrate the capabilities of the flow solver the calculated wake distribution of the product tanker Sankt Michaelis is compared to laser-doppler measurements of the wake field, available from HSVA (1983). In addition the influence of the scale effects on the propeller characteristics is analyzed. Wake field calculations Starke (21) has reported adequate agreement between the experimental and predicted wake fields both at model and at full-scale Reynolds numbers. At the computation predicts a minimum axial velocity in the top of the disk of u/v s =.19, while the experiments indicate u/v s =.24. It has been reported that this difference in the axial velocity may be related to the predicted location of the bilge vortices, which are located on a lower vertical position in the computation compared to the experiments. A higher position of these vortices will result in an increased transport of high-momentum fluid to the top of the propeller disk leading to a corresponding increase of the axial velocity. This would bring the computation in closer agreement with the experiments. At the increased Reynolds number results in a reduction of the bilge vortex strength and an increase of the axial velocity in the wake peak to about u/v s =.3. Figures 1 and 2 provide a comparison between the measured and calculated full-scale axial velocity distributions at a crosssection at.23 D in front of the propeller. The fact that the sea trials were carried out with running propeller may explain the asymmetry in the iso-velocity lines around the 12 o clock position. This asymmetry is not modelled in the numerical simulations. However, the computation shows good agreement with the experiment at the starboard side of the disk (see e.g. the.7 iso-contour line). Figure 1: Measured axial velocity field at. The dashed circle corresponds to the tip radius of the propeller (.23D in front of the propeller plane).
3 z[m] Cavitation number s [-] Cavitation bucket y[m] Lift coefficient C l [-] Figure 2: Calculated axial velocity field at. The dashed circle corresponds to the tip radius of the propeller (.23D in front of the propeller plane). Propeller analysis An analysis has been carried out to illustrate the implications of the scale effect on several relevant quantities in the propeller design. For this purpose a propeller geometry has been generated which is believed to be quite similar to the actual full-scale 5.7-m propeller of the ship. The propeller was analyzed for thrust loading C T =1.17 while rotating at 127 RPM. The computations have been performed for two wake fields, the computed effective model-scale and full-scale wake fields. Because the cavitation on well-designed propellers is typically concentrated in the tip region, a profile section at.9r has been selected for an analysis of the propeller s cavitation characteristics. The cavitation behaviour of this section for the two wake fields is shown in Fig. 3. The operational envelope curves in the diagram show the variation of the cavitation number σ defined by Eq. (2) in an arbitrary point on the blade section calculated for the two wake fields. p p v + ρgh σ = (2) ρv Here, p denotes the static pressure, p v the water vapour pressure and h the local submergence. The cavitation number varies with the pressure of the water column as the blade section makes a complete rotation. The variation of the section lift coefficient depends on the profile design and the variation of the angle of attack as the profile section passes through the wake field of the ship. Also included in the diagram is the cavitation bucket of the profile section, which shows the variation of the value of the minimum pressure coefficient (C p ) at both sides of the profile section as a function of the angle of attack. Cavitation is supposed to occur when the minimum pressure coefficient becomes equal to the value of the critical cavitation number (-C p = σ). The results clearly show that the operational envelope of the full-scale wake field extends over a smaller range of lift coefficients than the model-scale wake field. Therefore, it can be concluded that the tip sections of the propeller experience a smaller variation of the angle of attack than predicted using the model-scale wake field, which is a consequence of the reduction of the wake peak at. Figure 3: Calculated cavitation bucket in relation to model-scale and full-scale operational curves. In this case the propeller is not highly loaded and the velocity of the propeller tip is rather low. This results in moderate values of the cavitation number along the operational envelope which, in combination with the width of the cavitation bucket, does not lead to much difference in the cavitation extent for the model-scale and full-scale wake fields. It should be noted that due to numerical deficiencies in the nominal to effective correction method the axial velocity at the 6 o clock position is overestimated for the model-scale wake field. This results in an exaggeration of the underloading of the propeller blade in this position and the wide leftward sweep of the operational curve. The positive margin against the inception of pressure side cavitation, however, is clearly larger at. The variation of the cavity volume as a function of the blade position angle is shown in Fig. 4. It is clear that although percentage wise the changes are large, the total volume is very small for this propeller, making the volume increase irrelevant for the level of the pressure fluctuations on the hull. For the present condition the amplitude of the 1 st harmonic of the pressure fluctuations increases only 5 per cent. Cavity volume [m 3 ] Figure 4: Cavity volume variations as function of blade angle.
4 The distribution of the thrust density computed for the model-scale and full-scale wake fields is shown in Figs. 5 and 6. The results indicate that the thrust distribution is more homogeneous at due to the reduced strength of the bilge vortices compared to the model-scale prediction. 3.E+5 2.5E+5 2.E thrust [N] 1.5E+5 1.E E E Full scale Model scale Figure 7: Calculated blade thrust variation. 1 8 Figure 5: The thrust density distribution calculated for the model-scale wake field in kn/m Y/R (%) X/R (%) Figure 6: The thrust density distribution calculated for the fullscale wake field in kn/m 2. The influence on the blade thrust variation and the thrust eccentricity is further illustrated in Figs. 7 and 8. The results show a reduced variation of the blade thrust with the blade angle at and a slight shift of both the horizontal and vertical thrust eccentricity. These figures also give an indication of the scale effect on the lateral propeller forces and moments. 4 5 Model scale Full scale Figure 8: Variation of thrust eccentricity (% of radius). CASE 2: CONTAINER VESSEL The second case considers a 7 TEU container vessel with an installed power of 6 MW in order to illustrate the influence of wake field scale effects for a more highly loaded propeller. Wake field calculations A comparison between the experimental and predicted nominal wake fields at is given in Figs. 9 and 1. Here it is seen that the strength of the bilge vortex, present in the upper half of the propeller disk, is somewhat underestimated in the computation. Consequently, the transport of high-momentum fluid to the top of the propeller disk is underestimated as well, resulting in a predicted minimum axial velocity in the top of the propeller disk of u/v s =.39, compared to u/v s =.47 in the experiments.
5 .8.6 Propeller analysis EXPERIMENT Figure 9: Comparison between the experimental (left) and predicted (right) nominal axial wake field at. The dashed circle corresponds to the propeller tip..1 V s A similar analysis of the wake field scale effects on the propeller performance has been made for the container vessel. For this purpose an 8.8-m diameter propeller was been designed for the vessel. The propeller was analyzed for a typical design condition for a thrust loading C T =1.12 in which the propeller rotates at 1 RPM. The computations have been performed for the measured and computed wake field at as well as the computed full-scale wake field. The operational envelopes of the.9r tip section computed for the three wake fields is shown in Fig. 12 with its cavitation bucket. As in the case of the product tanker, it can be observed that the envelope computed for the full-scale wake field extends over a smaller range of lift-coefficients than in the case of the model-scale wake field. The margin against the inception of pressure side cavitation is considerably larger at full scale, implying that it is possible to minimize the cavitation at the suction side by a more accurate tuning of the camber. It is furthermore noted that the tip sections of the present propeller are more sensitive to cavitation (cf. Fig. 3) because of the higher circumferential tip velocity of the propeller blades, resulting in lower cavitation numbers (exp.) (calculated) (calculated) EXPERIMENT Cavitation number σ [-] Cavitation bucket.5 Figure 1: Comparison between the experimental (left) and predicted (right) nominal transverse wake field at. The dashed circle corresponds to the propeller tip. The predicted full-scale wake field of the container vessel is presented in Fig. 11. Compared to the model-scale wake field the iso-velocity lines have shifted towards the 12 o clock position. This indicates the presence of a thinner boundary layer (and wake) in the full-scale result, which is in agreement with the higher Reynolds number. Furthermore, the full-scale computation predicts a less developed bilge vortex in the transverse field..1 V s Lift coefficient C l [-] Figure 12: Cavitation bucket in relation to calculated operational curves. The variation of the cavity volume calculated for the model-scale and full-scale wake fields is shown in Fig. 13. The cavity volume and its variation are clearly much smaller for the full-scale wake field. A reduction of the amplitudes of the 1 st harmonic of the pressure fluctuations of about 25 per cent is calculated for the full-scale wake field Cavity volume [m 3 ] Figure 11: Predicted wake field at (left: axial distribution, right: transverse distribution). The dashed circle corresponds to the propeller tip Figure 13: Cavity volume variation as a function of the blade angle.
6 Finally, the scale effect on the blade thrust variation and the thrust eccentricity is shown in Figs. 14 and 15. In can be seen that the percentual change in the blade thrust variation is smaller than in the previous case, see Fig. 7, although of similar magnitude. However, a difference of 5 per cent is observed in the thrust eccentricity. This indicates a similar deviation in the value of the horizontal bending moment. thrust [N] 1.E+6 9.E+5 8.E+5 7.E+5 6.E+5 5.E+5 4.E+5 3.E+5 2.E+5 1.E+5.E Full scale Model scale Figure 14: Calculated blade thrust variation as a function of the blade angle. Y/R (%) X/R (%) Model scale Full scale Figure 15: Variation of thrust eccentricity (% of radius). CONCLUDING REMARKS In this paper results are presented of a study investigating the prospects of using viscous-flow computations of the full-scale wake field in the design process of propellers. For two cases, the product tanker Sankt Michaelis and a large container vessel, the influence of the Reynolds number effect on several relevant quantities in the propeller design is investigated. The results of the viscous-flow computations show a significant influence of the Reynolds number on the wake field properties. The boundary layer thickness of the hull is smaller at resulting in a narrower, less pronounced wake peak. Consequently the axial component of the velocity in the wake is larger at compared to. Also a clear scale effect is shown on the strength and position of the bilge vortices, which affects the transverse velocity field. The results of the propeller analysis for both considered cases demonstrate the sensitivity of the predictions for the details of the wake field. For the product tanker the influence of the wake-field scaling on the levels of the pressure fluctuations is limited because of the small amount of cavitation of the propeller due to its moderate loading and tip velocity. More significant, however, is the influence on the forces and moments that are acting on the propeller and the shaft. Knowledge on the details of the fullscale wake field gives the designer the opportunity to further optimize the propeller by reducing unnecessarily large design margins. This can be achieved for instance by optimizing the blade area and thickness to increase the efficiency and reduce the weight of the propeller. For the container vessel the pressure fluctuation levels are much more influenced by the scale effect of the wake field. The cavitation on the propeller is more pronounced and the variation of the cavity volume is decreased considerably. Values of 25 per cent are found for the reduction of the 1 st harmonic of the pressure fluctuations. Forces and moments on the propeller are also affected as shown by the 5 per cent shift of the vertical thrust eccentricity. In view of the obtained results it appears that wake predictions from viscous-flow methods are becoming promising new tools for the propeller designer. More accurate predictions of the full-scale wake field provide the opportunity to reduce cavitation design margins, resulting in more efficient propellers with higher blade loading and higher tip velocities. The predictions become increasingly helpful when the propeller induced pressure fluctuations are dominated by the influence of cavitation and when strict limitations to the allowed propeller excitation have been agreed. They could become indispensable in case of demanding design problems such as for future s mega-container vessels where there appears a clear need to apply the available margins more accurately. REFERENCES Dacles-Mariani et al., (1995), Numerical / experimental study of a wingtip vortex in the near field, AIAA Journal, Vol. 33, pp van Gent, W., (1977), On the use of lifting surface theory for moderately and heavily loaded ship propellers, PhD thesis Delft University of Technology. van Gent, W., (198), Derivation of propeller blade section properties from lifting surface theory, International Shipbuilding Progress, Vol. 27, No van Gent, W., (1994), Pressure field analysis of a propeller with unsteady loading and sheet cavitation, 2 th ONR Symposium, Santa Barbara, California. Hoekstra, M. and Eça, L., (2), an efficient method for ship stern flow calculations, In Third Osaka Colloquium on Advanced CFD Applications to Ship Flow and Hull Form Design, Osaka, Japan. HSVA-Bericht Nr (1983), Korrelation van Nachstromaufmessungen an Modell und Grossausfuerung. Menter, F.R., (1997), Eddy viscosity transport equations and their relation to the k-ε model, J. of Fluids Eng., Vol. 199, pp Starke, A.R. (21), A validation study of wake-field predictions at model and Reynolds numbers, In Fourth Numerical Towing Tank Symposium, Hamburg, Germany Stern, F. and Vorus, W.S., (1983), A non linear method for predicting unsteady sheet cavitation on marine propellers, Journal of ship research, Vol. 27, No. 1, pp
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