Hussein Zekri - Academia.edu (original) (raw)
Papers by Hussein Zekri
European Journal of Pure and Applied Mathematics
The hydrodynamic problem of a two-dimensional symmetric wedge vertically entering the water, init... more The hydrodynamic problem of a two-dimensional symmetric wedge vertically entering the water, initially flat, with a deadrise angle of 30° is considered. This numerical study assesses turbulence, gravity, viscosity, and surface tension during the early stage of penetration. The OpenFOAM software package has been used to simulate the water entry of the wedge at a constant speed of 3 m/s. The governing equations have been numerically built in the solver called overInterDyMFoam. The method has also been used to model the turbulence effect. The effects of turbulent and laminar flow assumptions and for the laminar flow, viscosity, gravity, and surface tension influence on pressure distributions along the wedge's walls have been investigated. It is illustrated that turbulence, viscosity, and surface tension have negligible effects on the pressure distribution in the primary water entry process. However, the pressure distribution is found to be significantly influenced by gravity.
European Journal of Pure and Applied Mathematics
We numerically study gravity’s effect on sloshing in a two-dimensional tank which is highly fille... more We numerically study gravity’s effect on sloshing in a two-dimensional tank which is highly filled by water (95% water and 5% air). Both fluids are considered to be incompressible and inviscid. The surface tension and phase change are neglected. OpenFOAM software is used for the simulation. A standing wave of water impacting the lid of the tank at its center and a symmetric wetted region starts to advance along the lid. The simulation carried out (only on the right-half side of the tank due to symmetric geometry of the impact) with and without gravity to investigate the influence of gravity on this impact. The numerical results are validated by comparing to published data. The effect of gravity on the size of the wetted region, free-surface elevation and on the pressure distribution has been analyzed. It is shown that gravity is affecting the free-surface elevation and consequently the size of the wetted region. These effects growth as time goes. Pressure distribution along the wett...
Violent liquid sloshing is of concern to cargo tank designers due to the problems of safety in ex... more Violent liquid sloshing is of concern to cargo tank designers due to the problems of safety in extreme loadings. It is an interesting topic with still some disputable problems. For example Abramson, Bass, Faltinsen and Olsen [1] investigated the sloshing and resultant loads in liquid natural gas carriers for different tank geometries and liquid fill depths. Ibrahim [3] provided a comprehensive study with examples of free tank motions. Cooker [2] analysed with experiments a horizontal rectangular wave tank which swings at the lower end of a pendulum. Ten, Malenica and Korobkin [5], presented a semianalytical approach for fluid-structure interactions inside tanks in different impact situations with high and low fillings. Our work is about the sloshing of standing waves inside a closed highly filled container. Unsteady two-dimensional (2-D), irrotational flow is treated. The liquid-roof interaction is discussed with and without the effect of gravity and a comparison is made. The short-...
Advances in Science and Technology Research Journal, 2019
International Journal of Differential Equations, 2011
We study the existence and uniqueness of the solutions of mixed Volterra-Fredholm type integral e... more We study the existence and uniqueness of the solutions of mixed Volterra-Fredholm type integral equations with integral boundary condition in Banach space. Our analysis is based on an application of the Krasnosel'skii fixed-point theorem.
Fluid-structure interaction is a well-known and complicated problem. Its formulation requires sim... more Fluid-structure interaction is a well-known and complicated problem. Its formulation requires simpli�cations in modelling, and usually the presence of gravity is one aspect which is neglected, especially in violent impact. In this thesis we account for the in uence of gravity on two physically di�erent but mathematically similar two-dimensional ows. First (in Chapters 2{4), sloshing impact of a standing wave on the lid of a rigid tank, and second (in Chapter 5), impact of a rigid blunt body entering water which is initially at rest. Chapter 1 presents the motivation, literature, aim and structure of the thesis. In Chapter 2, gravity is neglected and model equations are solved analytically, in particular the linearised hydrodynamic problem with and without the lid using the Wagner approximation, time and coordinate stretching, and displacement potential. Chapter 3, introduces gravity into the formulation and the model is solved semi-analytically to determine its in uence on the width...
The numerical solution for a time-fractional diffusion equation supplemented with initial and bou... more The numerical solution for a time-fractional diffusion equation supplemented with initial and boundary conditions is considered. The scheme is based on the Galerkin finite element method. The uniform space discretization is applied to study the stability of the solution of the problem within our approach. An analytically solvable example is presented to make a comparison between the exact solution and our numerical solution. By presenting the absolute error with different step-sizes and different values for time-fractional derivative, reliability and efficiency of our proposed numerical method is manifested.
We consider the effects of gravity on the two-dimensional flow caused by a symmetric body vertica... more We consider the effects of gravity on the two-dimensional flow caused by a symmetric body vertically entering into initially calm water at constant speed. Surface tension, viscosity and the compressibility of the liquid are neglected. The flow is potential. The region of contact of the water with the body surface starts from a single point and grows monotonically in time. The effects of gravity on the size of the contact region, the hydrodynamic force on the body, the hydrodynamic pressure distribution on the wetted part of the body surface, and the free-surface elevation are analysed for the initial stage of impact, using asymptotic methods with a small-valued gravity-related parameter. It has been well accepted that the effects of gravity on water impact characteristics are small. The analysis reveals that the effects of gravity are relatively small even for impact conditions, where formally these effects should be included in the model. It is found that gravity: slows down the co...
European Journal of Pure and Applied Mathematics
The hydrodynamic problem of a two-dimensional symmetric wedge vertically entering the water, init... more The hydrodynamic problem of a two-dimensional symmetric wedge vertically entering the water, initially flat, with a deadrise angle of 30° is considered. This numerical study assesses turbulence, gravity, viscosity, and surface tension during the early stage of penetration. The OpenFOAM software package has been used to simulate the water entry of the wedge at a constant speed of 3 m/s. The governing equations have been numerically built in the solver called overInterDyMFoam. The method has also been used to model the turbulence effect. The effects of turbulent and laminar flow assumptions and for the laminar flow, viscosity, gravity, and surface tension influence on pressure distributions along the wedge's walls have been investigated. It is illustrated that turbulence, viscosity, and surface tension have negligible effects on the pressure distribution in the primary water entry process. However, the pressure distribution is found to be significantly influenced by gravity.
European Journal of Pure and Applied Mathematics
We numerically study gravity’s effect on sloshing in a two-dimensional tank which is highly fille... more We numerically study gravity’s effect on sloshing in a two-dimensional tank which is highly filled by water (95% water and 5% air). Both fluids are considered to be incompressible and inviscid. The surface tension and phase change are neglected. OpenFOAM software is used for the simulation. A standing wave of water impacting the lid of the tank at its center and a symmetric wetted region starts to advance along the lid. The simulation carried out (only on the right-half side of the tank due to symmetric geometry of the impact) with and without gravity to investigate the influence of gravity on this impact. The numerical results are validated by comparing to published data. The effect of gravity on the size of the wetted region, free-surface elevation and on the pressure distribution has been analyzed. It is shown that gravity is affecting the free-surface elevation and consequently the size of the wetted region. These effects growth as time goes. Pressure distribution along the wett...
Violent liquid sloshing is of concern to cargo tank designers due to the problems of safety in ex... more Violent liquid sloshing is of concern to cargo tank designers due to the problems of safety in extreme loadings. It is an interesting topic with still some disputable problems. For example Abramson, Bass, Faltinsen and Olsen [1] investigated the sloshing and resultant loads in liquid natural gas carriers for different tank geometries and liquid fill depths. Ibrahim [3] provided a comprehensive study with examples of free tank motions. Cooker [2] analysed with experiments a horizontal rectangular wave tank which swings at the lower end of a pendulum. Ten, Malenica and Korobkin [5], presented a semianalytical approach for fluid-structure interactions inside tanks in different impact situations with high and low fillings. Our work is about the sloshing of standing waves inside a closed highly filled container. Unsteady two-dimensional (2-D), irrotational flow is treated. The liquid-roof interaction is discussed with and without the effect of gravity and a comparison is made. The short-...
Advances in Science and Technology Research Journal, 2019
International Journal of Differential Equations, 2011
We study the existence and uniqueness of the solutions of mixed Volterra-Fredholm type integral e... more We study the existence and uniqueness of the solutions of mixed Volterra-Fredholm type integral equations with integral boundary condition in Banach space. Our analysis is based on an application of the Krasnosel'skii fixed-point theorem.
Fluid-structure interaction is a well-known and complicated problem. Its formulation requires sim... more Fluid-structure interaction is a well-known and complicated problem. Its formulation requires simpli�cations in modelling, and usually the presence of gravity is one aspect which is neglected, especially in violent impact. In this thesis we account for the in uence of gravity on two physically di�erent but mathematically similar two-dimensional ows. First (in Chapters 2{4), sloshing impact of a standing wave on the lid of a rigid tank, and second (in Chapter 5), impact of a rigid blunt body entering water which is initially at rest. Chapter 1 presents the motivation, literature, aim and structure of the thesis. In Chapter 2, gravity is neglected and model equations are solved analytically, in particular the linearised hydrodynamic problem with and without the lid using the Wagner approximation, time and coordinate stretching, and displacement potential. Chapter 3, introduces gravity into the formulation and the model is solved semi-analytically to determine its in uence on the width...
The numerical solution for a time-fractional diffusion equation supplemented with initial and bou... more The numerical solution for a time-fractional diffusion equation supplemented with initial and boundary conditions is considered. The scheme is based on the Galerkin finite element method. The uniform space discretization is applied to study the stability of the solution of the problem within our approach. An analytically solvable example is presented to make a comparison between the exact solution and our numerical solution. By presenting the absolute error with different step-sizes and different values for time-fractional derivative, reliability and efficiency of our proposed numerical method is manifested.
We consider the effects of gravity on the two-dimensional flow caused by a symmetric body vertica... more We consider the effects of gravity on the two-dimensional flow caused by a symmetric body vertically entering into initially calm water at constant speed. Surface tension, viscosity and the compressibility of the liquid are neglected. The flow is potential. The region of contact of the water with the body surface starts from a single point and grows monotonically in time. The effects of gravity on the size of the contact region, the hydrodynamic force on the body, the hydrodynamic pressure distribution on the wetted part of the body surface, and the free-surface elevation are analysed for the initial stage of impact, using asymptotic methods with a small-valued gravity-related parameter. It has been well accepted that the effects of gravity on water impact characteristics are small. The analysis reveals that the effects of gravity are relatively small even for impact conditions, where formally these effects should be included in the model. It is found that gravity: slows down the co...