Marine Propeller

The classic method of predicting cavitation in marine propellers through the Burrill diagram has been employed for almost 80 years, being considered by researchers as a highly reliable tool for the use in the development of impellers of fixed pitch. There are also methodologies that consider the influence of hydrofoil on the performance of the component, relative to cavitation. However, previous work has questioned the reliability of such techniques for detecting low percentage cavitation, such as 2.5%. It is considered that both the experimental and numerical methods that give rise to those results are inaccurate to predict exact values of cavitation in such a small region. Thus, the authors propose in this paper a new methodology, which takes into account an angular modifying factor, symbolized as fba, which focuses on the cavitation index σ07R used in the classical methods, relative to the resulting velocity in the section at 0.7R of the blades. This factor considers the dimensional characteristics of the impeller, the physical properties of the fluid where it is navigating and the pressure conditions on the component axis. It is plotted against rotational speed values, in diagrams that indicate the occurrence of cavitation directly from the reading on the graph, without the need for excessive calculations. Because of the unreliability of the various methods in detecting cavitation in a very small region of the back of the blade, the diagrams are only built for percentages from 10% onwards. The fba values can be raised numerically or experimentally in tests in cavitation tunnels. However, the values of the Burrill diagram itself were employed, since they are considered highly reliable for projects that support cavitation above 10%. The intention of the method is to advance the state of the art in the knowledge of the subject and offer a facilitating tool to the designer. The results of cavitation prediction achieved herein are compatible with those from the classic methods used in the marine rotor market.

Fishing is one of major local industry in Malaysia especially in rural area. However, the rapidly increasing price of fuel is seriously affecting the local fishing industries. At present, the use of petrol (gasoline) outboard engine in small-scale fishing boats have become a popular choice instead of inboard diesel engine due to several advantages such as high speed, low weight, ease to install and space saving. However, petrol outboard engine has higher fuel consumption compared to diesel engine. Nevertheless, installing diesel engine with conventional submerged propeller in existing small-scale fishing boat is not economic since it requires major hullform modification and extra expenditure. This is due to the fact that most inshore fishing boats are of semi-planning hullform and free from appendages such as skeg and rudder stock. In addition, conventional propellers coupled to inboard diesel engines suffer on propeller losses. This paper describes a study to reduce fuel consumption by introducing a combination of diesel engine and surface piercing propeller (SPP).

The paper offers an analytical formulation of the two errors embodied in the momentum theory. The first one originates from to the use of the differential form of the axial momentum equation and the second one from the linearisation of the tangential velocity terms. Both errors are evaluated comparing the axial velocity at the disk as predicted by the momentum theories with that one obtained thorough a semi-analytical actuator disk method based on the exact solution of the flow. Several cases characterised by different values of the thrust and advance coefficient are analysed, and the range of validity of the momentum theories is discussed in depth.

The paper presents a generalized semi-analytical actuator disk model as applied to the analysis of the flow around ducted propellers at different operating conditions.
The model strongly couples the non-linear actuator disk method of Conway (J. Fluid Mech. 1998; 365: 235-267) and the vortex element method of Martensen (Arch. Rat. Mech. 1959; 3: 235-270) and it returns the exact solution, although in an implicit formulation, for incompressible, axisymmetric and inviscid flows. The solution is made explicit through a semi-analytical procedure developed and validated by Bontempo and Manna (J. Fluid Mech. 2013;728:163-195). Moreover the method duly accounts for non-uniform load radial distribution, slipstream contraction, mutual non-linear interaction between duct and propeller, wake rotation, and ducts of general shape. Thanks to its extremely reduced computational cost it can easily be integrated into design systems based on the repeated analysis scheme of hierarchical type.
A comparison between open and ducted rotors is carried out in order to quantify the effects of the duct on the overall performance of the device. Emphasis is given to the appropriate matching between the duct geometry and the propeller load to exploit the benefits that could arise ducting the propeller.

In this work, the analysis of the Kriso Container Ship (KCS) test case using the OpenFOAM RANS solver is proposed. Both ship resistance in calm water, propeller open water performances, self-propulsion calculations are proposed and the numerical results are validated by a comparison with the model scale experiments shared in literature and through workshops. The analyses are carried out applying the open source tools, from pre-to post-processing, available in the OpenFOAM environment, namely snappyHexMesh for the generation of the computational mesh, simpleFoam, pimpleDyMFoam, LTSInterFoam for the solution of the various hydrodynamic problems and Paraview for the post-processing of the results. The comparison with the experimental measurements, finally, demonstrates the maturity of these solvers for a reliable and, from an engineering point of view, accurate prediction of some of the peculiar characteristics of the flow ships and propellers are subjected to.

Bu çalışmada, literatürde standart test pervanesi olarak yer alan iki farklı gemi test pervanesinin analizleri yapılmış ve performans değerleri hesaplanmıştır. Analizi yapılan pervanelerden biri, DTMB (David Taylor Model Basin) 4119 kodu ile adlandırılan, David Taylor model deney havuzunda geliştirilmiş, 5 pervaneli bir seriye ait ve doğrulama çalışmalarında sıklıkla kullanılan, 3 kanatlı bir pervanedir. Diğeri ise, PPTC (Potsdam Propeller Test Case) VP1304 olarak adlandırılan, birçok akademik çalışmada kullanılmış, 5 kanatlı ve kanat açıları kontrol edilebilir bir pervanedir. DTMB 4119 ve VP 1304 standart test pervanelerinin analizleri ANSYS kullanılarak Hesaplamalı Akışkanlar Dinamiği (HAD) yöntemiyle yapılmıştır. Analiz sonuçları ile bulunan performans değerlerindeki hata oranları hesaplanmış ve literatürdeki diğer çalışmalar ile değerlendirilmiştir. DTMB 4119 pervanesi analiz sonuçları, panel metodu ve HAD yöntemiyle elde edilen sonuçlar ile karşılaştırılmıştır. Ayrıca, VP1304 pervanesi için hesaplanan performans parametreleri açık su pervane testi sonuçları ile karşılaştırılmıştır. Bu çalışma ile pervane analizleri için oluşturulan analiz altyapısı test edilmiş olup izlenen yöntem HAD analiz altyapısının bir doğrulama yöntemi olarak gerçekleştirilmiştir. Abstract DTMB 4119 Ship Propeller, VP 1304 Propeller, Computational Fluid Dynamics (CFD), CFD Method, Modelling and Analysis, Validation In this study, two different marine propellers, cited as standard test propellers in literature, were analysed and performance values were calculated. One of the analysed propellers is a propeller called David Taylor Model Test Basin (DTMB) 4119, developed in David Taylor Model Test Basin, one of the 5-propeller series with 3 blades and frequently used in validation studies by many researchers. The other one is another marine propeller, called PPTC (Potsdam Propeller Test Case) VP1304, with a 5-blade and controllable pitch type, also used as a benchmark propeller in many academic studies. DTMB 4119 and VP 1304 propellers were analysed with ANSYS, for employing the Computational Fluid Dynamics (CFD) method. The error rates in performance values were calculated and evaluated against other studies in literature. DTMB 4119 propeller analysis results were compared against the results obtained using panel and RANS methods. Furthermore, VP1304 analysis results were examined with the results obtained in open water tests cited literature. With this study, the analysis infrastructure established for analysing the marine propellers was tested and the methodology followed herein was considered as a validation of the CFD infrastructure.

Ducted propellers are unconventional systems that are usually adopted for ship propulsion. These devices have recently been studied with medium-fidelity computational fluid dynamics code (based on the potential flow hypothesis) with promising results. However, these tools, even though they provide a good prediction of the forces and moments generated by the blades and the duct, are not able to provide insight into the flow field characteristics due to their crude flow approximations. On the contrary, modern high-fidelity viscous-based computational fluid dynamics codes could give a better description of the near and far-field flow of these particular devices. In the present paper, forces and the most significant features of the flow field around two ducted propellers are analyzed by means of both experimental and computational fluid dynamics approaches. In particular, accelerating and decelerating ducts are considered, and we demonstrate the ability of the adopted solver to accurately predict the performance and the flow field for both types. These results, in particular for the less-studied decelerating duct, designate CFD as a useful tool for reliable designs.

This paper completes the work presented in the companion paper [Bontempo et al., Appl. Ocean Res., 58 (2016) 322 - 330] by presenting the investigation of the flow around a propeller ducted with a so-called accelerating duct.
To this aim, both the axial momentum theory and a nonlinear actuator disk method are used.
The straightforward application of the first approach reveals that if the duct and rotor thrusts are concordant, then a beneficial effect on the propulsive efficiency can be readily obtained by enclosing a propeller in an accelerating duct.
When the more advanced nonliner actuator disk method is applied to verify the outcomes of the axial momentum theory additional information on the performance of the device are obtained.
Moreover, the nonlinear actuator disk method is also employed to investigate, through experimental design techniques, the effect of the key geometrical parameters of the duct onto the efficiency and robustness of this kind of propulsive system.
In particular, it has been found that a propulsive efficiency gain can be achieved through a duct thickness, camber and chord increase, and through an incidence decrease.

In this work was reported the analysis of the flow in the stern region and the hull-propeller interactions of a (semi-) planing hull using the commercial URANS code Siemens PLM Star CCM+. In the present study was conducted the resistance and self-propulsion test simulations to get self-propulsion factors (the wake and thrust deduction factors), using the Computational Fluid Dynamics (CFD) techniques. The computational results were validated by comparing with the benchmark towing tank data. The simulation of self-propulsion test is a non-trivial task for the high speed craft, in particular defining the correct trim and so the correct wake field. The reliability of the results is strictly connected to the high quality of the resistance test simulation and to the propeller-discretization method. The purpose of the current studies is to provide reliable and fast results of self-propulsion test simulation for the Fast Displacement hulls. For this reason, starting from different propeller discretization methods (i.e. the Actuator Disk method and the Fully Discretized Propeller) the results were compared in terms of accuracy and of computational effort. To take into account the motion of the hull and motion of the Fully Discretize Propeller the overset mesh technique was employed in all simulations.

The design of a propeller for a high-speed craft is addressed by using a multi-objective numerical optimization approach. By combining a fast and reliable Boundary Elements Method, a viscous flow solver based on the RANSE approximation, a parametric 3D description of the blade and a genetic algorithm, the new propeller shape is designed to improve the propulsive efficiency, reduce the cavitation extension, increase the cavitation inception speed and maximize, at the same time, the ship speed. Rather than by constraining the propeller delivered thrust, indeed, the proposed procedure works together with an engine-propeller matching algorithm that, each time a new propeller is defined, identifies the achievable maximum speed and the resulting engine functioning point that turn in additional goals for the optimization. A set of optimal propellers, obtained through the design by optimization based on potential flow calculations, are preliminary selected for additional viscous analyses in order to further validate the results of the BEM calculations and provide a deeper insight into the complex flow fields of high-speed propellers useful for choosing the optimal geometry. The improvements observed at the cavitation tunnel and the substantial increase of the maximum ship speed during sea trials on a high-speed craft provided by Azimut|Benetti prove the reliability of the design procedure.

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.

In this paper, we propose a Simulation-Based Design Optimization (SBDO) approach for the design of a Pre-Duct type Energy Saving Device (ESD). Pre-Ducts reduce the wake losses, contribute to a better interactions between the propeller and the hull and generate, in the end, generate an additional thrust. An integrated design approach, based on a parametric description of the duct geometry and on RANSE calculations together managed by an optimization algorithm, is developed to this aim, i.e. to maximize the thrust delivered by a Wake Equalizing Duct (WED). The Japan Bulk Carrier test case, for which experimental data regarding the effectiveness of WED is available in the literature , is considered as a reference. Results from the design activity show sensible improvements of the overall propul-sive efficiency when the Pre-Duct design is tailored to the actual hull wake shape thanks to the flexibility provided by the fully automated design approach proposed in this paper.

Accurate and reliable propeller performances predictions are a fundamental aspect for any analysis and design of a modern propeller. Prediction of cavitation and cavity extension is another important task, being cavitation one of the crucial aspects that influences efficiency in addition to propagated noise and blade vibration and erosion. Accurate prediction of induced velocity field downward the propeller plane is, moreover, mandatory for the proper design of appendages and rudders. The Potsdam Propeller Test Case within the SMP Workshop on Cavitation and Propeller Performances represents an excellent chance to test and to validate the capabilities of the University of Genova, together with its numerical tools, in predicting propeller open water performances and cavitation.

In this paper, a new design approach for propulsion shafting system is presented. The aim is to improve the dynamic response of the shafting system concerning torsional vibrations. The approach result in raising the permissible stress limits set by the Rules of the Classification Societies, and reduces the shafting response due to engine excitation without any barred speed range. A computer program to calculate the vibration response of torsional stresses (VIBRTS) using the proposed method has been developed. A numerical example of a 2-stroke, 6 cylinder marine diesel engine is investigated and the results are compared with those obtained from the basic design approaches based on the flexible shafting system, and the rigid shafting system.

The paper deals with self-propulsion problem, i.e. the solution of the flow around a hull that advances at uniform speed due to the action of the propeller. Two different approaches are presented and compared in the paper: an approximated approach, using the classical actuator disk theory to represent the time averaged fluid dynamic action of the propeller through body forces in the RANSE solver; a viscous-inviscid coupled solution, in which the hull viscous flow is solved through RANSE, the propeller hydrodynamics in the wake of the hull through an unsteady panel method and the two solutions are matched via unsteady body forces. Main differences between the two approaches are presented also in quantitative sense. The very good results obtained with the proposed V.I. coupled method make it an ideally fast and robust tool to be used for ship self-propulsion characteristics evaluation in ship routine design activities.

This paper addresses the problem of the numerical evaluation of the forces exerted by rudder/propeller complex; in particular, considering the common framework of RANS computations, different possible approximations of the propeller effect are taken into account, starting from the simplest uniform actuator disk and moving successively to an actuator disk with radial distributions of axial and tangential forces and then to a set of unsteady body forces, computed by a panel method, representative of the rotating pressure field of the propeller. All the results, in terms of global mean forces on the rudder and of fluctuating components and flow field, are compared to the full RANS computations and to the experimental results in model scale for the same configuration. The comparison of the results allows to identify the merits and the shortcomings of the different approaches, in order to select the best ones for the various possible applications, having in mind the necessity to keep the computational efforts to a reasonable level during the design phases.

In this paper, we present our analysis of the non-cavitating and cavitating unsteady performances of the Potsdam Propeller Test Case (PPTC) in oblique flow. For our calculations, we used the Reynolds-averaged Navier-Stokes equation (RANSE) solver from the open-source OpenFOAM libraries. We selected the homogeneous mixture approach to solve for multiphase flow with phase change, using the volume of fluid (VoF) approach to solve the multiphase flow and modeling the mass transfer between vapor and water with the Schnerr-Sauer model. Comparing the model results with the experimental measurements collected during the Second Workshop on Cavitation and Propeller Performance – SMP'15 enabled our assessment of the reliability of the open-source calculations. Comparisons with the numerical data collected during the workshop enabled further analysis of the reliability of different flow solvers from which we produced an overview of recommended guidelines (mesh arrangements and solver setups) for accurate numerical prediction even in off-design conditions. Lastly, we propose a number of calculations using the boundary element method developed at the University of Genoa for assessing the reliability of this dated but still widely adopted approach for design and optimization in the preliminary stages of very demanding test cases.

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.

The paper presents an extension to ducted rotors of the nonlinear actuator disk theory of Conway (J. Fluid Mech., vol. 365, 1998, pp. 235–267) and it is exact for incompressible, axisymmetric and inviscid flows. The solution for the velocities and the Stokes stream function results from the superposition of ring vortices properly arranged along the duct surface and the wake region. Using a general analytical procedure the flow fields are given as a combination of one-dimensional integrals of expressions involving complete as well as incomplete elliptic integrals. The solution being exact, the proper shape of the slipstream whether converging or diverging is naturally accounted for, even for heavy loads. A semi-analytical method has been developed that enables the flow induced by an actuator disk housed in a contoured duct to be solved duly accounting for the nonlinear mutual interaction between the duct and the rotor. Non-uniform load distributions, rotor wake rotation and ducts of general shapes and thickness distribution can be dealt with. Thanks to its reduced numerical cost, the method is well suited for the design and/or analysis of ducted rotors for marine, wind and aeronautical applications.

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 flow around a marine propeller is one of the most challenging hydrodynamics problems. Computational fluid dynamics (CFD) has emerged as a potential tool in recent years and has promising applications. The goal of this paper is to provide complete guidelines for geometry creation, boundary conditions setup, and solution parameters of the flow around rotating propeller. These guidelines are addressed to handle propeller simulation problems in order to achieve quick, more accurate solution with less computational cost. In this paper CFD results for flow around a marine propeller are presented. Computations were performed for various advance ratios following experimental conditions. Reynolds-Averaged Navier-Stokes (RANS) method combined with an extensive validation of two different turbulence models k-and k-was applied for the flow simulation. The computations enable direct comparison of the reliable CFD results with the experimental data.

Propeller optimisation is always the focus of the propeller design process, as such process is aimed at finding the best compromise between often conflicting objectives accounting for many design constraints. The use of optimization algorithms combined with blade shape modification techniques has been proposed by a number of research groups in the past few years and has proved to have a potential for practical applications, but integration in the everyday propeller design process is still beyond to be so consolidated. In the past one and a half year, CETENA, University of Genoa and the Fincantieri's Naval Vessels Business unit have teamed to set up a propeller optimization software environment to be used by Fincantieri's propeller designers in their everyday design work. A specification of the optimisation environment was worked out based on an analysis of the current design process, in order for the new procedures and tools to allow continuity of current practices while offering new possibilities in the comparative investigation of design variants and the identification of the very best design solution. The resulting optimisation environment integrates different software tools and consists of three main components linked by JAVA script architecture: a software tool for blade shape modification and definition (1), a BEM code for the evaluation of the propeller performance (2) and the open-source software DAKOTA to guide the optimisation (3). The software suite has been setup such as to be compatible with both Windows and Linux operating systems, in order to take advantage of all available computational resources, from single Windows workstations to the company's cluster, which operates under Linux. An ad-hoc '2D modeler' has been developed by the University of Genoa to model and modify the propeller design table, while a 3D modeller has been developed by CETENA to generate the 3D propeller description suitable for CFD RANS computations, starting from the 2D 296 propeller design curves. The propeller performance is evaluated using CRS BEM code PROCAL and the CRS Empirical Tip Vortex model. Measures of merit usually include: the propeller efficiency, pressure coefficients at specific locations on the blade back and face sides and, for an hydro-acoustic optimization, also the tip vortex induced pressure. The paper will provide details of the setup of the optimization environment focusing on an industrial application to design by optimization a naval propeller. The specific needs of the final users of the optimization suite will be highlighted and the expected benefits will be discussed, related to the time frame of the design process and the possibility of performing thorough investigations of design variants.

Pressure pulses evaluation is a current issue in high-performance propeller design. Usually, it has been addressed experimentally and numerically but in most cases the analysis has been limited to the verification of a given geometry identified at the end of a traditional design loop. A more direct inclusion of pressure pulses evaluation in the design procedure, for instance by very attractive multi-objective optimization approaches, could be beneficial, especially if higher fidelity codes may be exploited. Among the others, BEM represent an acceptable compromise between computational costs and accuracy, allowing to better considering propeller geometry. However, the direct computation of pressure pulses by means of BEM may be not always reliable, especially in correspondence to heavy cavitation. Hence, further validations are needed, in particular when the influence of geometrical characteristics rarely taken into account, such as rake distribution, are considered. Cavitation tunnel test, BEM and RANS calculations (monitoring cavitation extent and pressure pulses) have been consequently carried out for two propellers, designed for the same functioning conditions with different rake distributions. This allows analyzing capabilities and limitations of these numerical approaches in the light of their possible application in a design by optimization procedure.

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.

To convert the kinetic energy of marine current into electricity, the most sensible generator is a horizontal axis turbine. The know-how and the tools used for marine propulsion devices find a new range of applications in this field. An academic panel method code developed for the design of bare and ducted marine propellers was applied to design a marine current turbine. The turbine dimension and the tidal current velocity have been taken to fit the conditions in the Race of Alderney. The wing section theory and the optimum rotor theory based on the blade element momentum were used to obtain the design condition and a first geometry approaching the Betz limit for a bare rotor. The panel method was then used to verify the power coefficient obtained in the presence of the 3D effects and if the cavitation constraints are respected. Subsequently, the same panel code was used to verify if the addition of a duct could improve the power output per unit surface.

District heating networks are commonly addressed in the literature as one of the most effective solutions for decreasing the greenhouse gas emissions from the building sector. These systems require high investments which are returned through the heat sales. Due to the changed climate conditions and building renovation policies, heat demand in the future could decrease, prolonging the investment return period. The main scope of this paper is to assess the feasibility of using the heat demand-outdoor temperature function for heat demand forecast. The district of Alvalade, located in Lisbon (Portugal), was used as a case study. The district is consisted of 665 buildings that vary in both construction period and typology. Three weather scenarios (low, medium, high) and three district renovation scenarios were developed (shallow, intermediate, deep). To estimate the error, obtained heat demand values were compared with results from a dynamic heat demand model, previously developed and validated by the authors. The results showed that when only weather change is considered, the margin of error could be acceptable for some applications (the error in annual demand was lower than 20% for all weather scenarios considered). However, after introducing renovation scenarios, the error value increased up to 59.5% (depending on the weather and renovation scenarios combination considered). The value of slope coefficient increased on average within the range of 3.8% up to 8% per decade, that corresponds to the decrease in the number of heating hours of 22-139h during the heating season (depending on the combination of weather and renovation scenarios considered). On the other hand, function intercept increased for 7.8-12.7% per decade (depending on the coupled scenarios). The values suggested could be used to modify the function parameters for the scenarios considered, and improve the accuracy of heat demand estimations. Abstract The paper investigates the flow through a uniformly-loaded propeller by means of a free-wake ring-vortex actuator disk without wake rotation. In particular, the model represents the near wake by the superposition of N ring vortices, while the far wake is modelled by a semi-infinite vortex cylinder with uniform radius. This second part presents the iterative solution procedure of the method illustrated in the companion paper as well as the implementation of the wake boundary conditions. Then, the power coefficient, the ideal propulsive efficiency and the wake contraction ratio are presented as a function of the propeller thrust coefficient, thus revealing the relevance of the wake convergence effects. Finally, the method is used to investigate the main characteristics of the local flow field induced by such an actuator disk.

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,