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In the present paper an experimental and numerical analysis of an unconventional CLT propeller is carried out. Two different numerical approaches, a potential panel method and an RANSE solver, are employed. Cavitation tunnel experiments are carried out in order to measure, as usual, thrust, torque, and cavity extension for different propeller working points. Moreover, LDV measurements are performed to have a deep insight into the complex wake behind the propeller and to analyze the dynamics of generated tip vortexes. The numerical/experimental analysis and comparison of results highlight the peculiarities of this kind of propellers, the possibility to increase efficiency and reduce cavitation risk, in order to exploit the design approaches already well proven for conventional propellers also in the case of these unconventional geometries.

Energy saving is a primary objective, historically the first, and, probably still now, the most important one, in the design of marine propellers. The constant increase of oil price, the more strict regulations in terms of air pollution, and the limits for NO_{X} and SO_{X} emissions require more and more efficient designs. Modern design approaches, like fully numerical lifting line/lifting surface codes and optimization applied to potential panel methods satisfy this objective and allow to design conventional propellers with maximum efficiency for a given operating point. On the other hand, nonconventional propellers, like Contracted and Loaded Tip CLT and Kappel like geometries, represent a further opportunity to increase efficiency and reduce the risk of cavitation, without the employment of completely different propulsive solutions, like contra- and corotating propellers or by the adoption of ducts, stators or wake regularizers.

At the same time, also requirements in terms of radiated noise and vibration emissions became more strict: avoidance of negative effects on marine life and reduction of the risk of hydroacoustic signature are the primary aims of new commercial and navy constructions. CLT propellers may represent a valid answer to these demands, even if the effects of some peculiar phenomena, such as the cavitating vortices at tip, need further investigation.

The first concept of tip-loaded propellers goes back to late seventies: Tip Vortex Free propellers were the first application of the Loaded Tip concept, that quickly evolved toward the CLT solution when also contraction of the fluid vein has been taken into account for the definition of the optimal geometry (

CLT propellers are characterized by a monotonic increase of pitch from blade root to tip, a finite chord at tip, moderate values of skew, and an endplate at the outermost radial edge of the blade towards the pressure side. Full-scale installations and observations, together with model scale measures and theoretical studies, as reported by SISTEMAR (

The gain in efficiency is obtained by the displacement of the maximum load towards the tip, that is made possible, without high noise and energy losses (typical of tip loaded conventional propellers) by the presence of the endplate. In fact, the outer radial sections of the blade contribute more efficiently to the generation of thrust: velocities are higher and, geometrically, local pitch angle is lower, that is, the local lift is more “aligned” with the axial propeller direction. A way to achieve high efficiency is, thus, to produce the most part of the required propeller thrust in this region of the blade. The additional span (not in the radial direction) provided by the endplate allows to locate the maximum load near the blade tip with a gradual and smooth reduction of the loading curve. In this way, it is possible to avoid the presence of a strong tip vortex and the higher values of induced velocities on the propeller plane, whose effect on the hydrodynamic pitch is fundamental in achieving high values of efficiency.

The presence of the endplate itself, that increases the pressure difference on the tip region and allows to adopt a finite chord at tip, produces higher value of thrust per unit area and a local unload of the sections. The resulting smaller optimum diameter allows the propeller to operate in a more uniform hull wake, with wider propeller sections passing through areas where the change in local wake can be strong, achieving more stable cavity bubbles and less cavity induced vibrations (but higher fluctuations of delivered thrust).

However, several problems, connected with the peculiarities of this kind of propellers, still need to be investigated. The shape and position of the endplate poses some issues regarding local strength, the overall influence on propeller mechanical characteristics and the higher risk of “double” tip vortex cavitation. Tip vortexes are, in fact, the main sources of energy loss, propagated noise, and induced vibrations. Also, optimal unconventional propellers, of course, like conventional ones, have to deal with the interactions between incoming flow and generated vortical structures to achieve high efficiency. If the hydroacoustic noise and the fluctuating pressures on the hull have to be minimized (or, at least, monitored), as today more frequently requested directly during the preliminary propeller design, the knowledge of the tip vortexes dynamics becomes a key aspect for the noise characterization of these kind of unconventional propellers, with respect of which few literature is available for designers. The peculiarity of the propeller geometry, moreover, is expected to produce very complex wake fields: blade trailing wake is subjected to large deformations as a combination between skew distribution and interaction between tip vortexes at the endplate. Strength and position of vortex cores, that in general is a matter of interest for conventional propellers and, during the design phase, a key aspect for the accurate evaluation of load distribution (see, e.g., the wake alignment issues in [

From a numerical point of view, a lot of interest has been dedicated to the analysis and development of new propulsion concepts [

In the present work, both the numerical approaches, a potential panel method and a RANSE code, are applied for the analysis of open water CLT propeller performances, including prediction of steady cavitation extent and propeller wake. While the former approach can be considered the best compromise between accuracy and computational time in the initial design stage (suitable to have an initial estimation of forces and cavitation extent), the latter represents a reliable tool to analyze the effects of viscosity that, especially in off-design conditions, where potential approaches generally fails, are the leading aspects. The reliability of both the approaches are investigated and their application limits for unconventional geometries highlighted through a dedicated experimental campaign carried out at the Cavitation Tunnel of the University of Genoa and comparing with previous results obtained during tests carried out at CEHIPAR towing tank. In particular, after some preliminary tests in order to evaluate mechanical characteristics to be compared with CEHIPAR results, LDV measurements in steady conditions have been conducted. Measurements include velocity/vorticity fields characterization on a series of transversal planes at different distances from the propeller disc, for a given operating condition. Results are compared with the numerical computations and the location and evolution of the tip vortexes are highlighted. Finally, cavity extension, are investigated at different load and cavitation index conditions. Also, in this case, comparison with computations provides useful information about the reliability of the numerical methodologies adopted.

The experimental facilities are described in Section

Experiments were carried out at Cavitation Tunnel facility of the Department of Naval Architecture and Electrical Engineering of the University of Genoa (DINAEL), whose layout is schematically represented in Figure

Main dimension of DINAEL cavitation tunnel.

The Cavitation Tunnel is also equipped with instrumentation for nonintrusive measurement of velocity field, that is, Laser Doppler Velocimeter (Figure

LDV system.

Measurements of the three velocity components of the flow upstream and downstream of the propeller have been performed by means of a four-beam two-color fibre optic LDV system with back-scatter collection optics (Dantec Fiber Flow). The light source is a 5 W argon ion laser operating at 514.5 nm (green), 488 nm (blue). In order to solve the zero velocity ambiguity and to reduce angle bias, a 40 MHz Bragg cell has been used. The probe consists of an optical transducer head of 60 mm diameter, with a focal length of 400 mm and a beam separation of 38 mm, connected to the emitting optics and to the photomultipliers by means of optic fibres. Typical probe volume dimensions were 190

In the present experiment, an ensemble averaging technique suitable for LDV data processing has been applied. A reference signal has been derived directly from the propeller shaft encoder, and hence can be considered in phase with the relevant periodic phenomenon. To obtain statistically accurate ensemble averages, a total of 100000 validated data for each velocity component have been sampled at each measuring position. Instantaneous velocities are sorted into 360 phase bins, each representing a particular phase of the cycle. Taking into account the direct relation between period of the cycle and propeller rotational speed, each bin represents a particular angular position among a total of 360.

A comprehensive review of errors in laser-Doppler velocimetry measurements and guidelines to evaluate them is given in Min [

A generic instantaneous quantity (i.e., velocity component) is a function of time (

The equations defining the ensemble average procedure are as follows:

instantaneous quantity:

ensemble averaged quantity:

root mean square of the random unsteady fluctuations:

In order to survey all the three velocity components using a 2D LDV it has been necessary to perform measurements in two different configurations: the first one through the upper window of the cavitation tunnel, the second one through a lateral window. Special attention has been dedicated to the selection of the most appropriate measurement configuration in order to maximize spatial measurement resolution and limit the smoothing of velocity gradient.

Measurements have been performed for ten axial stations, described in details in Table

Measurements stations.

Station | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | |

Axial position |
−0.25 | 0.2375 | 0.4875 | 0.5125 | 0.6 | 0.7 | 0.8 | 0.9 | 0.9875 | 1.0125 |

Effective measurement points.

The reference coordinate system adopted for the presentation of results and the conventions on the sign of axial, radial and tangential velocities are summarized in Figure

Coordinate reference system and velocity convention.

The numerical modeling of Contracted and Tip Loaded Propellers, from and hydrodynamic point of view is equivalent to the conventional propellers case. Once the geometry has been defined, paying special attention to the modeling of the endplate, the hydrodynamic characteristics of CLT propellers can be computed straightforward applying both potential and RANSE solvers.

Panel/boundary elements methods model the flowfield around a solid body by means of a scalar function, the perturbation potential

For the more general problem of cavitating flow, Green’s third identity allows to solve the three dimensional differential problem as a simpler integral problem written for the surfaces that bound the domain. The solution is found as the intensity of a series of mathematical singularities (sources and dipoles) whose superposition models the inviscid cavitating flow on and around the body:

Neglecting the supercavitating case (computation is stopped when the cavity bubble reaches the blade trailing edge) and assuming that the cavity bubble thickness is small with respect to the profile chord, [

Kinematic boundary condition on the wetted solid boundaries:

Kutta condition at blade trailing edge (iteratively solved as a stagnation pressure condition):

Dynamic boundary condition on the cavitating surfaces:

Kinematic boundary condition on the sheet cavity surface, where

Cavity closure condition at cavity bubble trailing edge.

Arbitrary detachment line, on the back and/or on the face sides of the blade can be found, iteratively, applying a criteria equivalent, in two dimensions, to the Villat-Brillouin cavity detachment lines, as in Mueller and Kinnas [

If the cavity at that position has negative thickness, the detachment location is moved toward the trailing edge of the blade.

If the pressure at a position upstream the actual detachment line is below vapor pressure, then the detachment location is moved toward the leading edge of the blade.

The numerical solution consists in an iterative scheme delegated to solve the nonlinearities connected with the Kutta, the dynamic, and the kinematic boundary conditions on the unknown cavity surfaces until the cavity closure condition has been satisfied.

Viscous forces, neglected by the potential flow method, can be added in general with two different approaches. In the first case, as proposed by Hufford [

Viscous analysis of open water and cavitating propeller characteristics has been carried out through StarCCM+, a commercial finite volume RANSE solver [

The governing equations (continuity, momentum and an additional transport equation for the fraction

The StarCCM+ computational domain, by means of the symmetries, is represented by an angular sector of amplitude

Mesh refinements close to the blade. Finer mesh (1.6 million cells).

Before proceeding with the analysis of the computed results through the comparison with the experimental measures, a preliminary analysis of the convergence of the numerical solution for both the selected solvers has been carried out. Open water performances, propeller wake, and cavity extension, the main aspects of interest for which the numerical and experimental investigations have been performed, have been considered for the evaluation of the convergence behavior of the numerical solutions. In open water and in cavitating condition, both the approaches have been investigated. Instead, convergence of the propeller wake has been verified only for the RANSE solver (the panel method, in fact, has not been employed for these kind of computations).

Figure

Convergence of open water thrust and torque coefficient with the number of panels and the number of cells for the potential and the RANSE solution.

An overall good convergence has been achieved for both the solvers, but with opposite tendencies. Predicted thrust and torque by panel method, in fact, tends to increase with the number of panels (extrapolated values are 0.1859 and 0.3768 resp., for the thrust and the torque coefficient) while RANSE computations have a decreasing behavior, with extrapolated values of 0.1764, and 0.3551 respectively.

The computations of open water performances, as reported in next section, have been finally performed with the medium grid (

The convergence of the numerical solution, also for this kind of computation, has been verified on three different meshes, obtained by refining the tip region where the higher gradients are expected. Figure

Mesh arrangements for propeller wake analysis. (a) Base mesh. (b) Medium mesh. (c) Finer mesh.

Convergence of radial and tangential nondimensional velocity distribution at

Convergence of radial and tangential nondimensional velocity distribution at

Qualitatively the convergence of the solution is achieved directly from the comparison of the velocity field aft the propeller. If with the coarse mesh, it is almost impossible to identify the details of the double tip vortex structure experimentally observed (as in Figure

As better noted from Figure

The dependency of the solution on the discretization level, finally, has been verified in cavitating condition. Also, in this case, three different meshes, for the potential solver and for the viscous solution, have been investigated. As usual for the potential solution, the parameters under investigation (from which the whole discretization depends) are the number of radial sections (between 15 and 25) and the number of points along the chord (between 30 and 50), as evidenced in Figure

Discretization parameters for RANSE meshes—cavitating case.

Coarse mesh | Medium mesh | Fine mesh | |
---|---|---|---|

Base size | 1.8 times prop. diam. | 1.8 times prop. diam. | 1.8 times prop. diam. |

Prism layer thickness | 2 mm | 2 mm | 2 mm |

Number of prism Layers | 8 | 10 | 15 |

Minimum mesh surface size | 0.04% of base size | 0.02% of base size | 0.02% of base size |

Target mesh surface size | 5% of base size | 2.5% of base size | 2.5% of base size |

Total number of cells/blade | ~500 k | ~1 M | ~1.5 M |

Convergence of cavity extension with the number of panels. Open water thrust coefficient equal to 0.213 at cavitation index of 1.625.

Results, computed for a cavitation index equal to 1.625 and for an advance coefficient for which the corresponding open water thrust coefficient is equal to 0.213, are compared, in terms of cavity extension, in Figure

Convergence of cavity extension (fraction of vapor equal to 0.5) with the number of cells. Open water thrust coefficient equal to 0.213 at cavitation index of 1.625.

As already discussed, CLT propellers are claimed to be unconventional propellers able to grant some advantages with respect to conventional solutions. In particular, especially at full scale, main advantages are higher efficiency, reduced cavitation, and tip vortex strengthand, in general, smaller propeller optimum diameter due to the high delivered thrust. The numerical analyses and the experimental measures, consequently, have been carried out having in mind these primary aspects: prediction/measure of propeller performances in open water, including the analysis of the propeller wake, and the prediction/measure of the steady cavity extension in design and off-design conditions. From the experimental point of view, the attention has been primarily focused on the characterization of the peculiar wake field downstream the propeller and of the steady cavity behavior as a function of load and cavitation index. Objectives of the analyses are the validation of the numerical codes both in non cavitating and in cavitating conditions and the evaluation of the capabilities of the panel method in predicting performances and the main features of the cavity bubble also for unconventional propellers.

Model scale open water computations, compared with measures carried out at CEHIPAR towing tank [

Open water propeller characteristics. RANSE and panel method in model scale compared with experimental towing tank/cavitation tunnel measures.

The complex flow structures generated by the endplate at the tip of the CLT propeller have been investigated by means of Laser Doppler Velocimetry, and measures have been compared with RANSE computations carried with the 8 million cells per blade mesh (to minimize numerical damping, as in Figure

All the used representations of velocity distributions will be organized in the way to show the experimental results in the left column and the computational ones in the right one, in order to allow a constant comparison between measures and CFD results. The incoming flow in section

Tangential nondimensional velocity distribution at

Axial, tangential, and radial nondimensional velocity distributions at

Axial, tangential, and radial vorticity distributions at

Similar considerations arise when tangential and radial velocities are considered. In this case, however, mean values of both velocities are correctly captured, with mean tangential velocity equal to about 0.2 V and a negative radial velocity indicating flow contraction. Local variations due to blade passage and to vortices are also captured, even if differences due to numerical smoothing are visible in the blade wake, which appears larger in space and slightly less pronounced in terms of absolute values (see also Figure

Axial, tangential, and radial vorticity distributions at

From all figures, it is evident that leading edge vortex has a higher strength, while blade tip vortex is weaker. Same consideration arises also when propeller cavitating behavior is analyzed (Figure

In Figure

Axial, tangential, and radial vorticity distributions at

Axial, tangential, and radial nondimensional velocity distributions at

Axial, tangential, and radial nondimensional velocity distributions at

Vortical structures at the propeller tip. Q-factor visualization.

Cavity extension for open water KT equal to 0.213, at cavitation index of 1.625. Comparison with panel and RANSE numerical computations.

In Figure

The prediction of cavity extension is another key aspect for CLT unconventional propellers. The higher load near the tip, if cavitation cannot be avoided, could stabilize cavitation itself, especially when the propeller operates in a spatial non uniform wake behind the hull. On the contrary, the longer chord at the propeller tip could locally reduce the load per unit area, reducing the risk of cavitation and the bubble extension. Moreover, the influence on the pressure field of the endplate, that, with respect to a conventional geometry, increases the overpressure on the pressure side and reduces the pressure drop on the suction side, helps to reduce the back cavity extension. Anyhow, the presence of the endplate increases the risk of cavity inception (at its root and tip), and this potential problem should be taken into account for a better propeller design.

Prediction of cavity extension is, therefore, a necessary step in understanding the flow dynamics around CLT propellers. A steady analysis performed with the panel method, that has already proven to be a reliable and sufficiently accurate approach to compute steady and unsteady cavitating flow on conventional geometries [

Five different operating points have been considered for the analysis of the cavitating performances of the CLT propeller. As for the evaluation of propeller wake, all the computations have been carried out with the thrust identity. The first analyzed point (Figure

Cavity extension for open water KT equal to 0.213, at cavitation index of 1.5 (a) and 3.3 (b). Comparison with panel and RANSE numerical computations.

Cavity extension for open water KT equal to 0.173 (a) and 0.253 (b), at cavitation index of 1.625. Comparison with panel and RANSE numerical computations.

From the experimental point of view it is possible to identify, first of all, the complexity of the vortical structures generated by the endplate. Both vortices cavitate, letting their visualization more immediate than the analysis of the velocity field downstream the propeller. The two vortexes, as previously highlighted, have different pitches, with the blade tip vortex having the higher one, causing a relative rotation of one vortex with respect to the other.

From a numerical point of view, the main features of the sheet cavity, identified at the cavitation tunnel, are captured quite well by the two solvers. In addition to the sheet cavitation on the suction side of the blade, the numerical computations predict the development of a sheet cavity bubble (from the leading edge) on the external side of the endplate, which results in a good qualitative agreement with the experimental evidence. Prediction of tip cavitating vortexes is beyond the capabilities of the developed panel method, that is, limited to the analysis of supercavitating sections. However, the thicker sheet cavity bubble at the blade trailing edge can be considered as a symptom of probable tip vortex cavitation. Especially at the lower advance coefficient (higher open water equivalent thrust) the prediction of sheet cavitation up to the trailing edge agrees well with the observed cavitating vortexes. RANSE computation could, in principle, take into account these phenomena. However, the numerical damping and dissipation, due mainly to an inadequate mesh for the computation of this kind of phenomena, drastically reduce the resolution at blade tip and only a thick sheet cavity is predicted at the endplate root, together with the sheet cavity at the endplate leading edge, well in agreement with the experimental observations.

The numerical predictions, anyway, can be considered satisfactory for assessing the cavitation properties of the propeller. Both the approaches well predict the influence of the cavitation index and of the advance/thrust coefficient. For almost all the considered conditions, the panel method, seems to overestimate the suction side cavity bubble extension, with respect to the RANSE solver, in chordwise directions, especially at the tip, while sheet cavity lengths predicted by RANSE are more extended in the radial direction. On the endplate predicted panel method sheet cavity bubble is longer, especially at the endplate root, and overlap all the outer endplate surface for higher thrust coefficients/lower cavitation indexes, while RANSE computations are, in general, more conservative (and more similar to observations). Altogether, panel method and RANSE are very close each other.

With respect to the observed cavity extensions, and except the cavitating vortexes, both the numerical predictions are a bit overestimated, mainly along the radial direction. This difference is probably due to the observed streak cavitation [

An extensive campaign at cavitation tunnel has been carried to measure equivalent open water performances, propeller wake characteristics, and cavitation of a nonconventional CLT propeller. At the same time, two numerical approaches, a potential panel method and a RANSE solver, have been successfully applied for the correspondent numerical analysis. Numerical computations of open water model scale characteristics at the design advance coefficient are in good agreement with experimental results, with negligible differences (thrust underestimated by 1.45% in the case of the panel method, 4.3% in the case of RANSE while torque coefficient is underestimated by 1.4% and overestimated by 1.5% in case of RANSE solver and panel method resp.). In off-design conditions, an overall good agreement has been achieved, with panel method results very close to towing tank measurements in the case of thrust (with a mean difference of −1% in the considered range) and presenting a slight overestimation (about 1.3% as a mean) in the case of torque. Similarly, RANSE computations are satisfactory, with only weak underestimation of both coefficients (about 4% and 1.6% for thrust and torque coefficients resp.) for all the advance coefficients under investigation.

The LDV analysis highlighted the particular vortical wake structures associated with the endplate. The interaction between two vortical structures has been emphasized: the leading edge vortex and the blade tip vortex propagate downstream with different pitches. Also, in this case, the comparison with measures reveals that numerical computations are in good agreement for what regard the location, pitch, and, in general, the strength of the propeller wake. The sharp flow features are captured with sufficient reliability only with the finer mesh. Additional refinements seem to be necessary in the whole wake region (not only at the tip) to further minimize artificial smoothing (especially far from the propeller) and better identify flow features.

Finally, preliminary, steady, computations of the cavitating flow demonstrate that both panel method and RANSE solver can be employed, in a preliminary phase, and with sufficient accuracy, for the analysis of the cavitating behavior of these unconventional Tip Loaded Propellers. The main pattern of sheet cavitation (of sheet type at the endplate leading edge, cavitating vortexes at its edges) are predicted qualitatively and quantitatively quite well. A fine resolution of the RANSE discrete volume mesh is required for a good resolution at the tip and root of the endplate, in order to avoid smoothed solutions and to let the cavity bubble evolve also downstream into the fluid. These results allow to conclude, in any way, that the application of the potential panel method (which computational time is a fraction of that required by a viscous RANSE solver for the same flow conditions), in conjunction with a parametric geometry description and optimization algorithms may be used in an inverse design approach already demonstrated with success in case of conventional propellers [

This work was developed in the frame of the collaborative project SILENV-Ships oriented Innovative soLutions to rEduce Noise & Vibrations, funded by the European Union. within the Call FP7-SST-2008-RTD-1 Grant Agreement SCP8-GA-2009-234182. The authors also would like to thank SISTEMAR and SINM and Dr. Enrique Haimov from CEHIPAR for their support and suggestions in carrying out these analyses.