A mixed approach with meta-modelling techniques and machine-learning algorithms is here applied to the minimization of the lap time of a Formula 1 race car. The fine tuning of the front wing is performed in order to optimize the car for each specific racetrack. This task is performed by a simplified model, which is trained by some high-fidelity fluid dynamic simulations and then extended to the complete design space. The resulting tool is reliable, fast and easy to use. The accuracy of the resulting speed profiles of the chosen car in comparison with available measurements is indicating the overall reliability of the procedure.

Recently, an algorithm for coupling a Finite Volume (FV) method, that discretize the Navier-Stokes equations on block structured Eulerian grids, with the weakly-compressible Lagrangian Smoothed Particle Hydrodynamics (SPH) was presented in [16]. The algorithm takes advantage of the SPH method to discretize flow regions close to free-surfaces and of the FV method to resolve the bulk flow and the wall regions. The continuity between the two solutions is guaranteed by overlapping zones. Here we extend the algorithm by adding the possibility to have: 1) net mass transfer between the SPH and FV sub-domains; 2) free-surface across the overlapping region. In this context, particle generation at common boundaries is required to prevent depletion or clustering of particles. This operation is not trivial, because consistency between the Lagrangian and Eulerian description of the flow must be retained to ensure mass conservation. We propose here a new coupling paradigm that extends the algorithm developed in [16] and renders it suitable to test cases where vorticity and free surface significantly pass from one domain to the other. On the SPH side, a novel technique for the creation/deletion of particle was developed. On the FV side, the information recovered from the SPH solver are exploited to improve free surface prediction in a fashion that resemble the Particle Level-Set algorithms. The combination of the two new features was tested and validated in a number of test cases where both vorticity and front evolution are important. Convergence and robustness of the algorithm are shown.

The understanding of the performance of a propeller in realistic operative conditions is nowadays a key issue for improving design techniques, guaranteeing safety and continuity of operation at sea, and reducing maintenance costs. In this paper, a summary of the recent research carried out at CNR-INSEAN devoted to the analysis of propeller loads in realistic operative scenarios, with particular emphasis on the in-plane loads, is presented. In particular, the experimental results carried out on a free running maneuvering model equipped with a novel force transducer are discussed and supported by CFD (Computational Fluid Dynamics) analysis and the use of a simplified propeller model, based on Blade Element Momentum Theory, with the aim of achieving a deeper understanding of the mechanisms that govern the functioning of the propeller in off-design. Moreover, the analysis includes the scaling factors that can be used to obtain a prediction from model measurements, the propeller radial force being the primary cause of failures of the shaft bearings. In particular, the analysis highlighted that cavitation at full scale can cause the increment of in-plane loads by about 20% with respect to a non-cavitating case, that that in-plane loads could be more sensitive to cavitation than thrust and torque, and that Reynolds number effect is negligible. For the analysis of cavitation, an alternative version of the BEMT solver, improved with cavitation linear theory, was developed.

Modal decomposition techniques are used to analyse the wake field past a marine propeller achieved by previous numerical simulations (Muscari et al. Comput. Fluids, vol. 73, 2013, pp. 65-79). In particular, proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) are used to identify the most energetic modes and those that play a dominant role in the inception of the destabilization mechanisms. Two different operating conditions, representative of light and high loading conditions, are considered. The analysis shows a strong dependence of temporal and spatial scales of the process on the propeller loading and correlates the spatial shape of the modes and the temporal scales with the evolution and destabilization mechanisms of the wake past the propeller. At light loading condition, due to the stable evolution of the wake, both POD and DMD describe the flow field by the non-interacting evolution of the tip and hub vortex. The flow is mainly associated with the ordered convection of the tip vortex and the corresponding dominant modes, identified by both decompositions, are characterized by spatial wavelengths and frequencies related to the blade passing frequency and its multiples, whereas the dynamic of the hub vortex has a negligible contribution. At high loading condition, POD and DMD identify a marked separation of the flow field close to the propeller and in the far field, as a consequence of wake breakdown. The tonal modes are prevalent only near to the propeller, where the flow is stable; on the contrary, in the transition region a number of spatial and temporal scales appear. In particular, the phenomenon of destabilization of the wake, originated by the coupling of consecutive tip vortices, and the mechanisms of hub-tip vortex interaction and wake meandering are identified by both POD and DMD.

The Smoothed Particle Hydrodynamics (SPH)method is revisited within a Large Eddy Simulation (LES)perspective following the recent work of [1]. To this aim, LESfiltering procedure is recast in a Lagrangian framework bydefining a filter centred at the particle position that moves withthe filtered fluid velocity. The Lagrangian formulation of LES isthen used to re-interpret the SPH approximation of differentialoperators as a specific model based on the decomposition of theLES filter into a spatial and time filter.The derived equations represent a general LES-SPH schemeand contain terms that in part come from LES filtering and inpart derive from SPH kernels. The last ones lead to additionalterms (with respect to LES filtering) that contain fluctuations inspace, requiring adequate modelling. Further, since the adoptedLES filter differs from the classical Favre averaging for thedensity field, fluctuation terms also appear in the continuityequation.In the paper, a closure model for all the terms is suggested andsome simplifications with respect to the full LES-SPH model areproposed. The simplified LES model is formulated in a fashionsimilar to the diffusive SPH scheme of Molteni & Colagrossi[2] and the diffusive parameter is reinterpreted as a turbulentdiffusive coefficient, namely ? ? . In analogy with the turbulentkinetic viscosity ? T , the diffusive coefficient is modelled througha Smagorinsky-like model and both ? T and ? ? are assumed todepend on the magnitude of the local strain rate tensor D.Some examples of the simplified model are reported forboth 2D and 3D free-decaying homogeneous turbulence andcomparisons with the full LES-SPH model are provided.

The Smoothed Particle Hydrodynamics (SPH) method, often used for the modelling of the Navier- Stokes equations by a meshless Lagrangian approach, is revisited from the point of view of Large Eddy Simulation (LES). To this aim, the LES filtering procedure is recast in a Lagrangian framework by defining a filter that moves with the positions of the fluid particles at the filtered velocity. It is shown that the SPH smoothing procedure can be reinterpreted as a sort of LES Lagrangian filter- ing, and that, besides the terms coming from the LES convolution, additional contributions (never accounted for in the SPH literature) appear in the equations when formulated in a filtered fashion. Appropriate closure formulas are derived for the additional terms and a preliminary numerical test is provided to show the main features of the proposed LES-SPH model.

The interference between the hull, propeller and rudder remarkably affects the control and maneuvering capabilities of marine vehicles. In case of twin screw/twin rudder ships, the asymmetric evolution of the wake past the hull causes the asymmetric functioning of the propeller-rudder system. Systematic investigations on this aspect for twin screw ships are limited. Available experimental data carried out on simplified hull-propeller-rudder system and captive model tests do not allow to completely understand the fluid mechanism at the basis of the hydrodynamic interaction that should be taken into account in simplified maneuvering mathematical models for preliminary predictions. In this paper the hull-propeller-rudder interactions phenomena for a twin screw/twin rudder model are investigated by URANS simulations, with a particular focus on the asymmetry of the propeller-rudder system. To this aim, captive model tests consisting of pure rudder and coupled drift-yaw motions corresponding to the steady phases of turning circle maneuvers at different rudder angles (?=15°÷35°) are performed at the speed correspondent to Fr=0.265. Moreover, a free running maneuvering simulation is also performed to gain more insight on the transient phase of the maneuver. An identity rudder lift methodology is applied to synthesize the hull-propeller-rudder interactions by means of a flow straightening coefficient; the analysis highlights that these effects are weak and invariant with respect to the rudder angle on the windward shaft, whereas on the leeward side these effects are extremely sensitive to the evolution of the hull and propeller wake.

The vortex-body interaction problem, that characterizes the flow field of a rudder placed downstream of a single-blade marine rotor, is investigated by numerical simulations. The particular topology of the propeller wake, consisting of a helicoidal vortex detached from the blade tips (tip vortex) and a longitudinal, streamwise oriented vortex originating at the hub (hub vortex), embraces two representative mechanisms of vortex-body collisions: the tip vortices impact almost orthogonally to the mean plane, whereas the hub vortex travels in the mean plane of the wing (rudder), perpendicularly to its leading edge. The two vortices evolve independently only during the approaching and collision phases. The passage along the body is instead characterized by strong interaction with the boundary layer on the rudder and is followed by reconnection and merging in the middle and far wake. The features of the wake were investigated by the l2-criterion and typical flow variables (pressure, velocity and vorticity) of the instantaneous flow field; wall pressure spectra were analysed and related to the tip and hub vortices evolution, revealing a non-obvious behaviour of the loading on the rudder, that can be related to undesired unsteady loads.

Marine propellers in behind-hull conditions develop, in addition to thrust and torque, in-plane loads that are strictly related to fatigue stress of the propulsive shaft bearings, hull-induced vibrations and the dynamic response of the ship while maneuvering or experiencing wave induced motions. An in-depth understanding of their nature as well as their quantification in typical design and off-design operative scenario is fundamental for improving ship design criteria. This issue is tackled in the present work by means of URANS simulations and simplified propeller theories to assess the correlation between inflow conditions and propeller loads. In particular, the analysis is carried out for the same twin screw model recently considered in free running maneuvering model tests (Ortolani et al., 2015a, 2015b) and further aims to provide a complementary and deeper insight to the outcome of these experiments. The first part of the study is focused on the straight ahead motion and the steady turning maneuvers with rudder deflections of 15°, 25° and 35° and Froude number equal to 0.26.

Recently, an algorithm for coupling a Finite Volume (FV) method, that discretize the Navier-Stokes equations on block structured Eulerian grids, with the weakly-compressible SPH was presented. The algorithm takes advantage of the SPH method to discretize flow regions close to free-surfaces and of Finite Volume method to resolve the bulk flow and the wall regions. The continuity between the two solution is guaranteed by overlapping zones. Here we extend the algorithm in by adding two new features: 1) creation/deletion of particles at the boundary of the SPH sub-domain; 2) crossing of the free-surface on the coupling region. In this context, particle generation is particularly complex because of the Lagrangian character of SPH, which has to be consistent with the Eulerian description of the flow in the Finite Volume method. We propose here a new technique based on a shifting technique specifically conceived for the coupling procedure. The creation/deletion technique was validated on different test cases with particular attention to mass conservation. On the Finite Volume side, a new technique for free surface capturing, inspired by the Particle Level-Set algorithms, was developed and implemented. The combination the two new features was tested and validated in the case of vortex/free surface interaction. A final application of the new coupled solver is given for a violent sloshing flow in a tank.

The present investigation focuses on the effects of the stern appendages and the propulsion system on the hydro-loads generated by the propeller during off-design conditions, with particular emphasis on the in-plane components. Recent experimental investigations carried out by free running model tests [7,8] and CFD analysis [5] for a modern twin screw model, highlighted that maneuvers at small drift angles and yaw rates might be as critical as the tighter ones due to complex propeller-wake interactions. Therefore, design criteria should take into account also these operative conditions, in order to reduce the effects of propeller-wake interaction phenomena that degrade the overall propulsive efficiency, induce shaft/hull structural vibration and increase noise emission. In the present study we analyze the effects of geometric and propulsive modifications with respect to the twin screw configuration studied in [5]. In particular, the effect of the centreline skeg, propeller direction of rotation and control strategies of the propulsion plant on the propeller bearing loads have been investigated from the analysis of the nominal wake in maneuvring conditions, computed by unsteady RANSE simulations coupled with a propeller model based on Blade Element Theory. The considered test cases were turning circle maneuvers with different rudder angles at FN = 0.265.

The numerical study presented in Part I (Dubbioso et al., 2017) on the bearing loads developed by the propellers of a twin screw model during quasi-steady conditions is extended to transient maneuvers. In the previous study, numerical simulations highlighted that the hydrodynamic loads might experience significant peak at moderate turning rates due to complex interaction of the propeller with the wake. In the present paper, the complete turning circle maneuver at ? 1/4 35 ? at Fr 1/4 0:265 is numerically simulated in order to analyze the character of the blade loads during the transient phases after the actuation of the rudder (start and pull-out). The analysis shows that the overall degradation of the propeller performance may occur also at kinematic conditions weaker than those usually considered as the most critical ones (in general, tight maneuvers); therefore, these conditions should be accounted for also in the early design phases.

The study of energetic free-surface flows is challenging because of the large range of interface scales involved due to multiple fragmentations and reconnections of the air-water interface with the formation of drops and bubbles. Because of their complexity the investigation of such phenomena through numerical simulation largely increased during recent years. Actually, in the last decades different numerical models have been developed to study these flows, especially in the context of particle methods. In the latter a single-phase approximation is usually adopted to reduce the computational costs and the model complexity. While it is well known that the role of air largely affects the local flow evolution, it is still not clear whether this single-phase approximation is able to predict global flow features like the evolution of the global mechanical energy dissipation. The present work is dedicated to this topic through the study of a selected problem simulated with both single-phase and two-phase models. It is shown that, interestingly, even though flow evolutions are different, energy evolutions can be similar when including or not the presence of air. This is remarkable since, in the problem considered, with the two-phase model about half of the energy is lost in the air phase while in the one-phase model the energy is mainly dissipated by cavity collapses.

An algorithm for coupling a classical Finite Volume (FV) approach, that discretize the Navier-Stokes equations on a block structured Eulerian grid, with the weakly-compressible SPH is presented. The coupling procedure aims at applying each solver in the region where its intrinsic characteristics can beexploited in the most efficient and accurate way: the FV solver is used to resolve the bulk flow and the wall regions, whereas the SPH solver is implemented in the free surface region to capture details of the front evolution. In order to avoid the difficulties connected with inhomogeneous domain decomposition, in both SPH and FV regions a weakly compressible flow model was firstly tested. However, the coupling procedure has beenimplemented in order to allow the adoption of different time steps between the two solvers. Thanks to this feature, it will be shown that the proposed technique is also able to reproduce an inhomogeneous coupling. Indeed, the FV solver, because of the space discretization adopted and the implicit time integration, naturally tends to an incompressible discrete solver, wherever the time step is much larger of what required to capture compressibility effects. The different coupling strategies as well as convergence studies have been carried out in the 2D framework.The reported results clearly prove that the combined use of the two solvers is convenient from the point of view of both accuracy and computing time.

The starting transient of highly under-expanded supersonic jets is studied by means of very high resolution weighted essentially non oscillatory finite volume schemes, coupled with a positivity-preserving scheme in order to ensure positivity of pressure and density for high compression/expansion ratio. Numerical behaviour of the schemes is investigated in terms of grid resolution, formal accuracy and different approximated Riemann solvers. The transient flow field is also discussed.

In the present paper, the analysis of the turning capability of the naval supply vessel presented in Part I (Broglia et al., 2015) is continued with different stern appendages, namely twin rudder and centreline skeg. The main purpose of the analysis is to assess the capability of an in-house CFD tool in capturing the different manoeuvring characteristics of the ship hulls; the test case is challenging, as the difference be- tween the two configurations lies in the complex flow structure related to rudder-propeller interactions. Moreover, although the twin rudder solution slightly improves the poor course keeping ability of the original vessel, the course stability remains poor and, consequently, large lateral motions and drift angle have to be expected during the manoeuvre. The manoeuvring capabilities of the new configuration are discussed and compared with the single rudder configuration, focusing on the nature of the hydrodynamic forces and moments acting on the main hull and appendages during the transient and stabilized phases of the manoeuvre. Emphasis will be also given to the different contributions of the propulsion system in the twin rudder configuration, that results from the different rudder-propeller interaction

For the effective operation of sonar systems mounted inside the bulb of fast ships, it is important to reduce all the possible noise and vibration sources that radiate noise and interfere with sonar sensor response. In particular, pressure fluctuations induced by turbulent boundary layers on the sonar dome surface represent the major source of self-noise for on-board sensors. Reliable calculations of structural vibrations and noise radiated inside the dome require valid statistical descriptions of wall pressure fluctuations beneath the turbulent boundary layer. Previous research about wall pressure fluctuations deals with equilibrium turbulent boundary layers on flat plates in zero pressure gradient flow, for which scaling laws for power spectral densities and empirical models for the cross spectral densities are well established. On the contrary, turbulent boundary layers on bulbous bow exhibit the combined effects of three-dimensionality, streamline and spanwise curvatures and pressure gradients. In order to collect information about realistic configurations, wall pressure fluctuations were measured in an experimental campaign performed in a towing tank; data were collected at two different locations along a large scale model of a ship bulb and their spectral characteristics were investigated in terms of auto and cross spectral densities. Mean flow parameters of the boundary layer, required in the analysis, were obtained by a finite volume code that solves the Reynolds Averaged Navier Stokes Equations. The applicability of classical scaling laws for pressure spectra on zero pressure gradient flat plate was investigated, together with the spatial characterization of the wall pressure fluctuations in the space-frequency domain; parameters of some semi-empirical models available in the scientific literature were tuned to fit the measured pressure field.

A new algorithm for the solution of free surface flows with large front deformation and fragmentation is presented. The algorithm is obtained by coupling a classical Finite Volume (FV) approach, that discretizes the Navier-Stokes equations on a block structured Eulerian grid, with an approach based on the Smoothed Particle Hydrodynamics (SPH) method, implemented in a Lagrangian framework. The coupling procedure is formulated in such a way that each solver is applied in the region where its intrinsic characteristics can be exploited in the most efficient and accurate way: the FV solver is used to resolve the bulk flow and the wall regions, whereas the SPH solver is implemented in the free surface region to capture details of the front evolution. The reported results clearly prove that the combined use of the two solvers is convenient from the point of view of both accuracy and computing time.

Abstract The hydrodynamic characterization of control appendages for ship hulls is of paramount importance for the assessment of maneuverability characteristics. However, the accurate numerical simulation of turbulent flow around a fully appended maneuvering vessel is a challenging task, because of the geometrical complexity of the appendages and of the complications connected to their movement during the computation. In addition, the accurate description of the flow within the boundary layer is important in order to estimate correctly the forces acting on each portion of the hull. To this aim, the use of overlapping multi-block body fitted grids can be very useful to obtain both a proper description of each particular region in the computational domain and an accurate prediction of the boundary layer, retaining, at the same time, a good mesh quality. Moreover, block-structured grids with partial overlapping can be fruitfully exploited to control grid spacing close to solid walls, without propagation of undesired clustering of grid cells in the interior of the domain. This approach proved to be also very useful in reducing grid generation time. In the present paper, some details of the flow simulation around a fully appended submarine is reported, with emphasis on the issues related to the complexities of the geometry to be used in the simulations and to the need to move the appendages in order to change the configuration of the various appendages.

In the present work the simulation of water impacts is discussed. The investigation is mainly focused on the energy dissipation involved in liquid impacts in both the frameworks of the weakly compressible and incompressible models. A detailed analysis is performed using a weakly compressible Smoothed Particle Hydrodynamics (SPH) solver and the results are compared with the solutions computed by an incompressible mesh-based Level-Set Finite Volume Method (LS-FVM). Impacts are numerically studied using single-phase models through prototypical problems in 1D and 2D frameworks. These problems were selected for the conclusions to be of interest for, e.g., the numerical computation of the flow around plunging breaking waves. The conclusions drawn are useful not only to SPH or LS-FVM users but also for other numerical models, for which accurate results on benchmark test-cases are provided.