Michele La Rocca

ON THE ANALYSIS OF SLOSHING OF WATER IN RECTANGULAR CONTAINERS: NUMERICAL STUDY AND EXPERIMENTAL VALIDATION

Abstract In this work the analysis of sloshing of water in rectangular open tanks has been extensively carried out. Two mathematical models are employed, respectively the Reynolds Averaged Navier Stokes Equations (RANSE) and the Shallow Water Equations (SWE). The RANSE are solved using a modified form of the well established MAC method (SIMAC) able to treat both the free surface motion and the viscous stresses over the rigid walls accurately. The Shallow Water Equations are solved by means of a simple and powerful algorithm (CE-SE) able to deal with large impacting waves over the tank walls. Successively, in order to validate the mentioned algorithms and for a better understanding of the sloshing phenomenon, experimental tests have been carried out using a 0.5 m breadth rectangular tank in periodic roll motion. It has been shown that RANSE provide more accurate solutions than SWE for small or moderate amplitudes of excitation. In particular in this paper it is proved that the shallow water approximation can be efficiently adopted within liquid depth to tank breadth ratio = 0.15, when examining the sloshing problem. By increasing the water level inside the tank, results by SWE show large qualitative and quantitative disagreement with experiments. Nevertheless, in the case of large amplitude excitation, when sprays and large breaking waves are expected, SWE provide a fairly good estimate of the sloshing induced waves. Finally a simple baffle configuration inside the tank has been considered. By the analysis of numerical results, it has been observed that the presence of a vertical baffle at the middle of the tank dramatically changes the sloshing response compared to the unbaffled configuration. It produces a jump-like effect, resulting in a weak magnification of the dynamic loads on the vertical walls out of resonance, and a strong reduction of the dynamic loads in the resonance condition.

Experimental and numerical simulation of three-dimensional gravity currents on smooth and rough bottom

The dynamics of a three-dimensional gravity current is investigated by both laboratory experiments and numerical simulations. The experiments take place in a rectangular tank, which is divided into two square reservoirs with a wall containing a sliding gate of width b. The two reservoirs are filled to the same height H, one with salt water and the other with fresh water. The gravity current starts its evolution as soon as the sliding gate is manually opened. Experiments are conducted with either smooth or rough surface on the bottom of the tank. The bottom roughness is created by gluing sediment material of different diameters to the surface. Five diameter values for the surface roughness and two salinity conditions for the fluid are investigated. The mathematical model is based on shallow-water theory together with the single-layer approximation, so that the model is strictly hyperbolic and can be put into conservative form. Consequently, a finite-volume-based numerical algorithm can be applied. The Godu...

A fully nonlinear model for sloshing in a rotating container

In this paper a theoretical and experimental analysis of sloshing in 2D and 3D free-surface configurations is performed. In particular, the case of a tank rotating around a horizontal axis has been considered. The fluid is assumed to be incompressible and inviscid. A fully nonlinear mathematical model is defined by applying the variational method to the sloshing. The damping of gravity waves has been accounted by introducing a suitable dissipation function from which generalized dissipative forces are derived. A modal decomposition is then adopted for the unknowns and a dynamical system is derived to describe the evolution of the physical system. An experimental technique has been applied to select the leading modes, whose evolution characterizes the physical process, i.e. captures the most of the kinetic energy of the process. A very good agreement between experimental and numerical results confirms the validity of the methodological approach followed.

A two-layer shallow water model for 3D gravity currents

A two-layer, shallow-water model for three-dimensional (3D) gravity currents is proposed. The formulation results from the shallow-water-equations for two layers of immiscible liquids, subjected by the rigid-lid condition, so that the upper surface of the lighter layer remains perfectly flat during the motion. The arising pressure must be determined by solving the equations of motion, which is no problem for two-dimensional and axisymmetric gravity currents because the pressure is easily eliminated. In 3D gravity currents, the pressure is determined by solving a Poisson equation, together with momentum and mass balance equations. By means of a suitable scaling and a perturbation expansion, the equations are uncoupled from each other so that the problem is considerably simplified. Numerical results are compared with 3D lock-exchange release experiments. A comparison between numerical and experimental results of the gravity current indicates a fairly good agreement, whereas the results concerning the upper layer field variables shows that the numerical results are consistent with the experiments.

Reassessing the single relaxation time Lattice Boltzmann method for the simulation of Darcy’s flows

It is shown that the single relaxation time (SRT) version of the Lattice Boltzmann (LB) equation permits to compute the permeability of Darcy’s flows in porous media within a few percent accuracy. This stands in contrast with previous claims of inaccuracy, which we relate to the lack of recognition of the physical dependence of the permeability on the Knudsen number.

On the effect of the intrinsic viscosity in a two-layer shallow water lattice Boltzmann model of axisymmetric density currents

In this work, a numerical assessment of the suitability of a Single Relaxation Time (SRT) Lattice Boltzmann Method (LBM) model to simulate axisymmetric gravity currents is carried out. The model results are compared with both experimental data and other numerical models. The particular SRT formulation employed is known to converge, in the limit of low Knudsen number, to the two-layer 2D Shallow Water Equations (SWEs) set with a viscosity term featuring a closed theoretical formulation. Even with the lowest viscosity achievable by the method, its effect is shown to become important in most of the cases analysed, thus posing some serious constraints on possible application of the single relaxation time LBM method to simulate the lock-release generated-type gravity currents analysed here. The comparison with classical numerical models shows that the the viscous effects in the LBM model can be well reproduced employing coefficients derived from the above-mentioned theoretical formulation.

Regularized lattice BGK versus highly accurate spectral methods for cavity flow simulations

The regularized lattice BGK (RLBGK) is validated against high-accuracy spectral Chebyshev methods for lid-driven cavity flows. RLBGK is shown to provide a viable alternative to standard lattice BGK schemes, with significant enhancement of numerical stability at a very moderate computational extra-cost.

Unconfined lock-exchange gravity currents with variable lock width: laboratory experiments and shallow-water simulations

ABSTRACT The dynamics of unconfined gravity currents generated by a lock-exchange with different lock widths is considered. The gravity currents were generated by density differences caused by a salinity gradient and were realized both numerically and experimentally. Several runs were carried out in order to study the role played by the lock width in the current dynamics. Numerical simulations were performed with a new single-layer, 2D, shallow-water model, which accounts for the dilution of the gravity current due to the entrained ambient fluid. By the comparison between experimental and numerical results, the relevant role played by the entrainment in the propagation velocity of the front emerges, mainly for the cases with a narrow lock. The effect of the lock width on the current dynamics is also highlighted: the lock chocks the flow causing a localized loss of mechanical energy and a consequent deceleration of the flow. Results show that the smaller is the lock, the larger is the loss of energy.

A gas-kinetic model for 2D transcritical shallow water flows propagating over dry bed

Abstract The solution of fluid dynamics problems has recently witnessed a remarkable increase in the formulation of Boltzmann-based approaches, mainly triggered by the numerous advantages stemming from the concrete possibility of employing a low number of allowed velocities, which is the basis of the Lattice-Boltzmann (LB) methods. The field of Shallow Water (SW) modeling also took advantage of these techniques, but there are still open problems related to the practical impossibility to simulate transcritical flows while retaining the intrinsic simplicity of the LB approaches. This problem is even more crucial if one considers that transcritical flows always develop whenever a transition over dry bed occurs. Since such vertically integrated models are currently the mostly employed ones for simulating technically interesting flows, and since these flows often require the flooding of an initially dry bed, the application of LB methods seems to be facing its limits. The Gas Kinetic Method (GKM) overcomes this issue, integrating the Boltzmann equations in continuous velocity space. In this work, we formulate and extensively test a GKM-based model for solving the SW equations, which is able to manage the propagation over uneven dry bed. The benchmarking, carried out against analytical, experimental and previously proposed numerical reference solutions, shows promising results of the proposed approach.

Understanding the Behaviour of Gravity Currents in Tideless Estuaries and Considering the Impact of Sea Level Rise within the Nile Estuary

ABSTRACT Mahgoub, M.; Hinkelmann, R., and La Rocca, M., 2015. Understanding the behaviour of gravity currents in tideless estuaries and considering the impact of sea level rise within the Nile Estuary. Gravity currents are complex phenomena that occur in estuaries, and the complexity of these phenomena is even higher for tideless estuaries. To improve the process of understanding such phenomena, the three-dimensional TELEMAC3D modelling system was used to model the Nile estuary as an example of tideless estuaries. The nonhydrostatic simulation and the use of a complex turbulence model were necessary. The current mean flow conditions were modelled first; the results were then compared with three scenarios of sea level rise to study its impact. According to the model results, the salt wedge was not stagnant but fluctuated in cycle-like variations; the fluctuations were higher at the surface and smaller near the bottom, and at the end of the salt wedge, no fluctuations were noticed. The salt concentration and hence the density differs significantly throughout the salt wedge in the longitudinal direction as well as in the vertical direction. Changes in density in the lateral direction were also noticed; greater concentrations were at greater water depths for the same transverse section. The sea level rise caused greater saltwater intrusion inside the Nile and the greater the sea level rise, the more the intrusion increased. To maintain the current saltwater intrusion length without any increase, discharging additional water from the Edfina Barrage (the last barrage on Rosetta branch) could be used as a direct mitigation option; however, doing so, could have negative consequences on the water budget of the country.