On algebraic TVD-VOF methods for tracking material interfaces

We revisit simple algebraic VOF methods for advection of material interfaces based of the well established TVD paradigm. We show that greatly improved representation of contact discontinuities is obtained through use of a novel CFL-dependent limiter whereby the classical TVD bounds are exceeded. Perfectly crisp numerical interfaces are obtained with very limited numerical atomization (flotsam and jetsam) as compared to previous SLIC schemes. Comparison of the algorithm with accurate geometrical VOF shows larger error at given mesh resolution, but comparable efficiency when the reduced computational cost is accounted for

Energy dissipation mechanisms in spilling and in highly aerated plunging breaking events

The dissipation mechanisms characterizing wave breaking processes are analysed starting from the results of numerical simulations. The two-fluids numerical model is based on a Navier-Stokes solver for a single incompressible fluid with density and viscosity smoothly varying across the air-water interface. An interface capturing approach is employed which allows to deal with topological changes of the free surface and thus to describe the air entrainment processes that can occur in breaking processes. In the study, the evolution of periodic wave trains is considered. The initial wave profile and velocity field are assigned as those of a third order Stokes wave, and the initial steepness ε is in the range 0.2 - 0.65. The Weber number of the simulations corresponds to a fundamental wavelength of about 27 cm. With such conditions, the wave train remains regular for ε = 0.2 and 0.3. A gentle spilling breaking occurs when ε = 0.35 whereas the breaking is found to be of the plunging type for ε ≥ 0.37. The analysis is carried out in terms of velocity and vorticity fields, energy contents in both air and water, energy dissipation terms in water, bubble dynamics and spectra of the free surface elevation before and after the breaking. The validity of some important assumptions of the model on the solution are evaluated as well. For ε = 0.35, surface tension effects suppress the jet formation at the crest and the breaking occur with the growth of a bulge which resembles the shape of the whitecaps in open ocean. A shear layer develops at the toe of the bulge due to the interaction of the fluid in the bulge with the fluid underneath, which is responsible for the dissipation of the extra-energy. At least for the configuration adopted in the present study, the analysis of the local energy density shows that almost all the extra-energy of the wave, i.e. the additional energy of the wave with respect to the highest non-breaking case, is accumulated inside the bulge at the onset of the breaking. The extra-energy is progressively dissipated within three wave periods and, at the end of this stage, the resulting wave is quite similar to the highest non-breaking wave (ε = 0.30). In the plunging breaking cases, the energy amount dissipated by the breaking process is larger than the extra-energy content of the initial wave with respect to the highest non-breaking solution. For highly aerated breaking events, a significant amount of work is spent in entrapping the air cavity against the action of the buoyancy. In the next stage, the air cavity collapses and fragments into a bubble cloud immersed in a highly rotational flow with large velocity gradients. As a consequence, most of the potential energy accumulated by the entrained air cavities is dissipated by the viscous effects acting around the bubbles. It is found that this mechanism is responsible for the dissipation of as much as 50 % of the total amount of energy dissipated by the breaking process. Although some of the above results were already argued on the basis of experimental observations, the numerical results provide a much clearer picture of the phenomenon

Energy dissipation mechanisms in wave breaking processes

The mechanisms governing the energy dissipation in wave breaking processes are investigated numerically by a two-fluid numerical model. The flow is assumed two-dimensional and both air and water are considered as incompressible. Simulations are carried out for periodic wave trains with different initial amplitude. Attention is devoted to two cases in which the wave train evolves toward a spilling and a plunging breaking event. The analysis covers: velocity and vorticity field, work done against pressure forces, viscous dissipation and bubbles dynamics. It is shown that in gentle spilling case, dissipation is mostly due to the viscous effects in the shear layer generated by the interaction between the fluid in bulge and the flow underneath. This effect dissipates all the extra-energy and progressively reconducts the wave to the highest non-breaking solution. In the plunging breaking case, the rather important role played by the entrainment of the large air cavity at the breaking onset is highlighted. Results show that the work is initially spent in entraining the air cavity against the buoyancy. In the next stage the cavity fragments into a cloud of small bubbles immersed in a highly rotational flow and large velocity gradients. Most of the potential energy accumulated by the air cavity is thus dissipated in the bubble cloud by the strong viscous effects, whereas only a little amount is returned to water in the degassing phase

Hydrodynamic analysis of the water landing phase of aircraft fuselages at constant speed and fixed attitude

In this paper the hydrodynamics of fuselage models representing the main body of three different types of aircraft, moving in water at constant speed and fixed attitude is investigated using the Unsteady Reynolds-Averaged Navier-Stokes (URANS) level-set flow solver $\chi$navis. The objective of the CFD study is to give insight into the water landing phase of the aircraft emergency ditching. The pressure variations over the wetted surface and the features of the free surface are analysed in detail, showing a marked difference among the three shapes in terms of the configuration of the thin spray generated at the front. Such a difference is a consequence of the different transverse curvature of the fuselage bodies. Furthermore, it is observed that at the rear, where a change of longitudinal curvature occurs, a region of negative pressure (i.e. below the atmospheric value) develops. This generates a suction (downward) force of pure hydrodynamic origin. In order to better understand the role played by the longitudinal curvature change on the loads, a fourth fuselage shape truncated at the rear is also considered in the study. The forces acting on the fuselage models are considered as composed of three terms: the viscous, the hydrodynamic and the buoyancy contributions. For validation purposes the forces derived from the numerical simulations are compared with experimental data.Comment: 21 pages, 13 figure

On coherent vortical structures in wave breaking

The flow generated by the breaking of free-surface waves in a periodic domain is simulated numerically with a gas–liquid Navier–Stokes solver. The solver relies on the volume-of-fluid method to account for different phases, and the interface tracking is carried out by using novel schemes based on a tailored total-variation-diminishing limiter. The numerical solver is proved to be characterized by a low numerical dissipation, thanks to the use of a scheme that guarantees energy conservation in the discrete form. Both two- and three-dimensional simulations have been performed, and the analysis is presented in terms of energy dissipation, air entrainment, bubble fragmentation, statistics and distribution. Particular attention is paid to the analysis of the mechanisms of viscous dissipation. To this purpose, coherent vortical structures, such as vortex tubes and vortex sheets, are identified, and the different behaviours of the vortex sheets and tubes at various Reynolds numbers are highlighted. The correlation between vortical structures and energy dissipation demonstrates clearly their close link both in the mixing zone and in the pure water domain, where the coherent structures propagate as a consequence of the downward transport. Notably, it is found that the dissipation is identified primarily by the vortex sheets, whereas the vortex tubes govern mainly the intermittency

VISIR-I: Small vessels - Least-time nautical routes using wave forecasts

A new numerical model for the on-demand computation of optimal ship routes based on sea-state forecasts has been developed. The model, named VISIR (discoVerIng Safe and effIcient Routes) is designed to support decision-makers when planning a marine voyage. The first version of the system, VISIR-I, considers medium and small motor vessels with lengths of up to a few tens of metres and a displacement hull. The model is comprised of three components: a route optimization algorithm, a mechanical model of the ship, and a processor of the environmental fields. The optimization algorithm is based on a graph-search method with time-dependent edge weights. The algorithm is also able to compute a voluntary ship speed reduction. The ship model accounts for calm water and added wave resistance by making use of just the principal particulars of the vessel as input parameters. It also checks the optimal route for parametric roll, pure loss of stability, and surfriding/broaching-to hazard conditions. The processor of the environmental fields employs significant wave height, wave spectrum peak period, and wave direction forecast fields as input. The topological issues of coastal navigation (islands, peninsulas, narrow passages) are addressed. Examples of VISIR-I routes in the Mediterranean Sea are provided. The optimal route may be longer in terms of miles sailed and yet it is faster and safer than the geodetic route between the same departure and arrival locations. Time savings up to 2.7% and route lengthening up to 3.2% are found for the case studies analysed. However, there is no upper bound for the magnitude of the changes of such route metrics, which especially in case of extreme sea states can be much greater. Route diversions result from the safety constraints and the fact that the algorithm takes into account the full temporal evolution and spatial variability of the environmental fields

Parametric study on the water impacting of a free-falling symmetric wedge based on the extended von Karman's momentum theory

The present study is concerned with the peak acceleration azmax occurring during the water impact of a symmetric wedge. This aspect can be important for design considerations of safe marine vehicles. The water-entry problem is firstly studied numerically using the finite-volume discretization of the incompressible Navier-Stokes equations and the volume-of-fluid method to capture the air-water interface. The choice of the mesh size and time-step is validated by comparison with experimental data of a free fall water-entry of a wedge. The key original contribution of the article concerns the derivation of a relationship for azmax (as well as the correlated parameters when azmax occurs), the initial velocity, the deadrise angle and the mass of the wedge based on the transformation of von Karman momentum theory which is extended with the inclusion of the pile-up effect. The pile-up coefficient, which has been proven dependent on the deadrise angle in the case of water-entry with a constant velocity, is then investigated for the free fall motion and the dependence law derived from Dobrovol'skaya is still valid for varying deadrise angle. Reasonable good theoretical estimates of the kinematic parameters are provided for a relatively wide range of initial velocity, deadrise angle and mass using the extended von Karman momentum theory which is the combination of the original von Karman method and Dobrovol'skaya's solution and this theoretical approach can be extended to predict the kinematic parameters during the whole impacting phase.Comment: arXiv admin note: text overlap with arXiv:2207.1041

Floating body impact : asymptotic and numerical solutions

This thesis is concerned with the estimate of hydrodynamic loads generated during the water entry of bodies, originally floating on a still liquid surface. The analysis assumes the fluid to be ideal and the flow potential. The liquid is treated as incompressible, but the effects of weak compressibility are carefully estimated. A theoretical estimate of the loads in the early stage after the sudden start of the vertical downward motion of the body is derived. The solution is achieved through the method of matched asymptotic expansions, by using the non-dimensional body displacement as a small parameter. A uniformly valid solution is obtained by formulating an inner problem under suitable set of stretched variables and by matching its asymptotic behaviour with the inner limit of the outer solution. The boundary value problem governing the inner solution is strongly nonlinear, with nonlinear boundary conditions imposed on unknown free surface position. The solution is obtained through suitably developed numerical iterative procedures.EThOS - Electronic Theses Online ServiceGBUnited Kingdo