Propeller Design

A design by optimization of tip-loaded propellers (CLT) is proposed and implemented. The approach include a parametric description of the propeller, an in-house developed Boundary Element Method (BEM) to evaluate the performances of the propellers and an optimization algorithm based on modeFRONTIER environment to drive the design process. Results for the parent propeller, in terms of both open water performances and unsteady cavitation, were validated via available experimental measurements and RANS calculations. The proposed optimized geometries are finally checked by means of dedicated RANS calculations to assess the reliability of the proposed design approach.

Multi-objective functions of the propeller blade optimization are always regarded as important aspects of propeller design. This paper particularly presents a computational method to estimate the hydrodynamic performances including minimum cavitation, highest efficiency, and acceptable blade strength. The included parameters are as well, the number of blades, chord length, thickness, camber, pitch, diameter and skew. We also discuss the effect of the skew on the propeller performance and extract a formulation for these propose. In the optimization process, the evolution strategy (ES) technique is linked to the computational method to obtain an optimum blade. In order to allow the large variation of blade form during optimization process, the propeller section is represented by NURBS. New propeller forms are also obtained from the well-known B-series and DTRC are taken as initial forms in the optimization process at design speed of typical ships. The benchmark results for the two test cases prove the designed optimum propeller to be acceptable.

The paper describes the assessment of two different actuator disc models as applied to the flow around open propellers. The first method is based on a semi-analytical approach returning the solution for the nonlinear differential equation governing the axisymmetric, steady, inviscid and incompressible flow around an actuator disc. Despite its low computational cost, the method does not require simplifying assumptions regarding the shape of the slipstream, e.g. the wake contraction is not disregarded or prescribed in advance. Moreover, the presence of a tangential velocity in the wake as well as the spanwise variation of the load are taken into account. The second one is a commonly used procedure based on CFD techniques in which the effects of the propeller are synthetically described through a set of body forces distributed over the disc surface. Both methods avoid the difficulties and the computational costs associated with the resolution of the propeller blades geometrical details. The comparison is based on an in-depth error analysis of the two procedures which results in a set of reference data with controlled accuracy. An excellent agreement has been documented between the two methods while the computational complexity is obviously very different. Among other things the comparison is also aimed at verifying the accuracy of the semi-analytical approach at each point of the computational domain and at quantifying the effect of the errors embodied in the two methods on the quality of the solution, both in terms of global and local performance parameters. Furthermore, the paper provides a set of reference solutions with controlled accuracy that could be used for the verification of new and existing computational methods. Finally, the computational cost of the semi-analytical model is quantified, thus providing a valuable information to designers who need to select a cost effective and reliable analysis tool.

A B S T R A C T Marine propellers design requirements are always more pressing and the application of unusual propulsive configurations, like ducted propellers with decelerating nozzles, may represent a valuable alternative to fulfill stringent design constraints. Accelerating duct configurations were realized mainly to increase the propeller efficiency in the case of highly-loaded functioning. The use of decelerating nozzles sustains the postponing of the cavitating phenomena that, in turn, reflects into a reduction of vibrations and radiated noise. The design of decelerating nozzle, unfortunately, is still challenging. The complex interaction between the propeller and the nozzle, both in terms of global flow feature and local (tip located) phenomena, is not yet fully understood. No extensive systematic series, as in the case of accelerating configurations, are available and the design still relies on few measurements and data. On the other hand, viscous flow solvers appear as reliable and accurate tools for the prediction of complex flow fields and their application for the calculation of ducted propeller performance and nozzle flow was almost successful. Hence, using CFD as a part of a design procedure based on optimization, by combining a parametric description of the geometry, a RANSE solver (OpenFOAM) and a genetic type algorithm (the modeFrontier optimization environment), is the obvious step towards an even more reliable ducted propeller design. An actuator disk model is adopted to include efficiently the influence of the propeller on the flow around the duct; this allows avoiding the weighting of the computational effort that is necessary for the calculations of the thousands of geometries needed for the indirect design by optimization. Design improvements, in model scale, are measured by comparing, by means of dedicated fully resolved RANSE calculations, the performance of the optimized geometries with those of conventional shapes available in literature. For both nozzle typologies, dedicated shapes reducing the risk of cavitation and increasing the delivered thrust are obtained, showing the opportunity of customized nozzle design out of usual systematic series. In addition, by analyzing the results of the optimization histories, appropriate design criteria are derived for both accelerating and decelerating nozzle shapes.

The paper presents the validation of a generalised semi-analytical actuator disk model as applied to the study of the flow around ducted propellers. The method, which returns the exact solution as a superposition of ring vortex, duly accounts for the rotation of the wake, the convergence of the slipstream, and the nonlinear mutual interaction between the duct and the propeller. Furthermore, it can deal with an arbitrary radial distribution of the load and ducts of general shape. In order to validate the previously mentioned actuator disk model, results obtained through it are compared with those provided by the so-called " CFD actuator disk method ". The latter is a widely diffused tool for the analysis of the flow around open and ducted propellers which models the rotor by means of radial profiles of blade forces distributed over a disk surface. In this paper, evidence has been given of the excellent agreement between the results of the two methods. Thanks to its extremely reduced computational cost the semi-analytical method is well suited to be integrated into design systems based on the repeated analysis scheme of hierarchical type.

The paper analyses the flow around a marine propeller ducted with a so-called decelerating nozzle both through the axial momentum theory and the nonlinear semi-analytical actuator disk model. While the well-known and widely diffused axial momentum theory can be successfully employed only to qualitatively investigate the characteristics of the flow around a ducted propeller, the nonlinear and semi-analytical method can instead evaluate the thrust exerted by the duct for different values of the overall thrust and advance coefficients. There are several advantages characterising the more advanced actuator disk method. Specifically, the wake convergence and rotation may be fully taken into account, the shape of the duct and of the radial distribution of the load can be of general type, and, finally, the mutual interaction between the duct and the propeller may be readily dealt with. The methods are employed to investigate the effects of the decelerating nozzle on the efficiency and on the cavitation condition of the propeller. In particular, the influence of some duct geometrical parameters on the device performance is thoroughly analysed providing useful insights on the operating principles of this kind of propulsive systems.

Despite its unphysical tip singularity and the violation of the angular momentum balance, the classical uniformly-loaded propeller without wake rotation still represents the benchmark model both for theoretical and practical applications. The model originates from the so-called Axial Momentum Theory which is further simplified removing the radial variability of the load. However, as well-known, some mathematical simplifications are customarily introduced in this theory when the axial momentum equation is applied in a differential form. Yet, the available literature generally seems to disregard their impact on the accuracy of the predicted flow. In this paper, the errors introduced by these simplifying assumptions are evaluated by comparing the results of the aforementioned theory with those of an actuator disk approach which models the propeller wake through a force-free ring-vortex sheet. The comparison shows that significant local errors arise in the tip region, especially for highly loaded rotors. INTRODUCTION The performance analysis of open propellers is typically carried out through several numerical approaches such as lifting line (Dorfling and Rokhsaz 2014; Wald 2006), lifting surface (Hanson 1985; Schulten 1996) and panel methods (Palmiter and Katz 2010; Valarezo 1990). Obviously, classical CFD techniques are also frequently employed in turbomachinery field (Bernardini et al. 2011; Insinna et al. 2015; Manna et al. 2005, 2012; Venters et al. 2018) to develop both blade-resolved and blade unresolved models (Jha et al. 2014; Jha and Schmitz 2018). However, thanks to its robustness and simplicity, the so-called Blade-Element Momentum Theory still represents the most popular approach. This theory stems from the coupling of the Blade-Element Theory and of the Momentum Theory (MT). Two versions of this latter theory exist: the Generalised (GMT) and the Axial (AMT) Momentum Theory (Bontempo and Manna 2017e). While the former takes into account the wake rotation, the AMT completely disregards the tangential velocity, even in the wake. The MT relies on the steady, incompressible, axisymmetric and inviscid flow assumptions. However, additional simplifying assumptions are typically introduced when the MT is used to evaluate local quantities such as the radial distribution of the axial velocity at the disk. Specifically, as shown in Bontempo and Manna (2016b, 2017b,c,d) and Glauert (1935), the AMT disregards the axial contribution of the pressure forces on the lateral surfaces of the infinitesimal streamtubes swallowed by the rotor. Due to the great relevance of this theory, the evaluation of its errors and the impact on the reliability of its results are of interest. Generally, the evaluation of these errors is carried out by comparing the MT results with those of more advanced actuator disk approaches which do not rely on the MT simplifying assumptions. For example, consider the nonlinear actuator disk of Wu (1962) further developed by Conway (1998), Bontempo et al. (2015) and Bontempo and Manna (2016a,

Highlights:  (1)  KVLCC2 propeller has been analyzed in different wake distributions in presence of waves.  (2)  Effect of wake change, ship motions, RPM variation and speed loss has been studied.  (3)  Significant increase in pressure pulses was observed due to wake change in waves.  (4)  It is found that having a wake data in waves could be beneficial for designing a propeller.

The axisymmetric flow field around a ducted rotor is thoroughly analysed by means of a nonlinear and semi-analytical model which is able to deal with some crucial aspects of shrouded systems like the interaction between the rotor and the duct, and the slipstream contraction and rotation. Not disregarding the more advanced CFD based methods, the proposed procedure is characterised by a very low computational cost that makes it very appealing as analysis tool in the preliminary steps of a design procedure of hierarchical type. The work focuses on the analysis of the effects of the camber and thickness of the duct cross section onto the performance of the device. It has been found that an augmentation of both camber and thickness of the duct leads to an increase of the propulsive ideal efficiency.

A proper orthogonal decomposition (POD)-based method is proposed to reduce the dimensions of the design space for the shape optimisation of marine propellers. The effectiveness of the proposed approach is proven in the case of the INSEAN-E779A propeller, which blade shape is modified to maximise efficiency while reducing suction side cavitation. The 23-dimensions design space defined by the conventional shape representation is reduced by the POD method to 5, 12 and 15 dimensions, retaining up to the 98% of the geometric variance of the original space. A multi-objective optimisation algorithm drives the simulation-based design optimisation (SBDO) process in the new design spaces using BEM for the hydrodynamic predictions. Finally, optimal designs are verified using RANSE to assess the correlation between the performance improvements, the dimensionality reduction and the corresponding geometric variance. The effectiveness of the proposed POD-SBDO framework is discussed with respect to a design by optimisation process relying on the conventional parametric representation of the blade geometry.

The paper presents a newly developed method for the analysis of the flow around open rotors characterised by hubs of general shape. The exact and implicit solution of the axysimmetric, inviscid and incompressible flow is represented as the superposition of infinite ring vortices properly arranged along the hub surface and the rotor wake. The solution is made explicit through a semi-analytical and iterative procedure. The proposed semi-analytical approach can deal with hubs of arbitrary shape and with quite general rotor load distributions. The method strongly couples the flow induced by the rotor and the hub. Moreover, the contraction/divergence and the rotation of the wake can be fully taken into account. The results of the semi-analytical method are also compared with those obtained with a widely diffused actuator disk model based on computational fluid dynamics (CFD) techniques. Finally, in comparison to more advanced methods, such as those relying on a CFD approach, this method is characterised by an extremely reduced computational cost. The computer code is freely available on contacting the authors.