Wave impacts on rectangular structures

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.There is a good deal of uncertainty and sensitivity in the results for wave impact. In a practical situation, many parameters such as the wave climate will not be known with any accuracy especially the frequency and severity of wave breaking. Even if the wave spectrum is known, this is usually recorded offshore, requiring same sort of (linear) transfer function to estimate the wave climate at the seawall. What is more, the higher spectral moments will generally be unknown. Wave breaking, according to linear wave theory, is known to depend on the wave spectrum, see Srokosz (1986) and Greenhow (1989). Not only is the wave climate unknown, but the aeration of the water will also be subject to uncertainty. This affects rather dramatically the speed of sound in the water/bubble mixture and hence the value of the acoustic pressure that acts as a maximum cutoff for pressure calculated by any incompressible model. The results are also highly sensitive to the angle of alignment of the wave front and seawall. Here we consider the worst case scenario of perfect alignment. Given the above, it seems sensible to exploit the simple pressure impulse model used in this thesis. Thus Cooker (1990) proposed using the pressure impulse P(x, y) that is the time integral of the pressure over the duration of the impact. This results in a simplified, but much more stable, model of wave impact on the coastal structures, and forms the basis of this thesis, as follows: Chapter 1 is an overview about this topic, a brief summary of the work which will follow and a summary of the contribution of this thesis. Chapter 2 gives a literature review of wave impact, theoretically and experimentally. The topics covered include total impulse, moment impulse and overtopping. A summary of the present state of the theory and Cooker’s model is also presented in Chapter 2. In Chapter 3 and Chapter 4, we extend the work of Greenhow (2006). He studied the berm and ditch problems, see Chapter 3, and the missing block problem in Chapter 4, and solved the problems by using a basis function method. I solve these problems in nondimensionlised variables by using a hybrid collocation method in Chapter 3 and by using the same method as Greenhow (2006) in Chapter 4. The works are extended by calculating the total impulse and moment impulse, and the maximum pressure arising from the wave impact for each problem. These quantities will be very helpful from a practical point of view for engineers and designers of seawalls. The mathematical equations governing the fluid motion and its boundary conditions are presented. The deck problem together with the mathematical formulation and boundary conditions for the problem is presented in Chapters 5 and 6 by using a hybrid collocation method. For this case, the basis function method fails due to hyperbolic terms in these formulations growing exponentially. The formulations also include a secular term, not present in Cooker’s formulation. For Chapter 5, the wave hits the wall in a horizontal direction and for Chapter 6, the wave hits beneath the deck in a vertical direction. These problems are important for offshore structures where providing adequate freeboard for decks contributes very significantly to the cost of the structure. Chapter 7 looks at what happens when we have a vertical baffle. The mathematical formulation and the boundary conditions for four cases of baffles which have different positions are presented in this chapter. We use a basis function method to solve the mathematical formulation, and total impulse and moment impulse are investigated for each problem. These problems are not, perhaps, very relevant to coastal structures. However, they are pertinent to wave impacts in sloshing tanks where baffles are used to detune the natural tank frequencies away from environmental driving frequencies (e.g ship roll due to wave action) and to damp the oscillations by shedding vortices. They also provide useful information for the design of oscillating water column wave energy devices. Finally, conclusions from the research and recommendations for future work are presented in Chapter 8.This work is funded by the Ministry of Higher Education Malaysia and Universiti Pendidikan Sultan Idris, Malaysia

Mathematical Formulae

Mathematical Formulae intends to provide students, scientists, engineers, and researchers with a readily available reference to the mathematical formulae needed during their studies or work situation. It is a handy book that one must have on the bookshelf. The text is divided, for ease of reference, into ten main chapters embracing algebra, trigonometry, limit, differentiation and integration, vector calculus, coordinate geometry, differential equations, numerical methods, discrete mathematics, and financial mathematics. Essential theory, formulae, definitions and laws are clearly stated in this boo

Wave impacts on structures with rectangular geometries: Part 2 decks, baffles and seawalls with impermeable or porous surfaces

This paper considers wave impacts on baffles, on baffles or decks adjacent to a vertical wall, and on porous seawalls and/or sea beds. For seawalls and vertical baffles, impacts can occur in steep waves, whilst a deck can be struck from below by a rising wave crest either in open sea or in a tank with standing waves (sloshing). A simple analytical model for the pressure impulse, P, due to a wave of idealized geometry and dynamics is developed and applied to the following geometries with impermeable surfaces: • horizontal wave impact onto a vertical wall with a deck at the waterline, • vertical wave impact under a deck in the same configuration (equivalent to vertical water impact of a horizontal plate), • horizontal wave impact onto a surface-piercing vertical baffle in open sea, • as for 3. but with the baffle in front of a wall, • as for 4. but with a deck extending from the vertical wall to the baffle, • bottom-mounted baffle in front of a wall with impact occurring on the wall. We also consider cases that complement part 1 of this paper to include the effect on impacts on a seawall with a porous sea bed and/or sea wall with/without a berm. Finally we reconsider case 3) above but with a porous baffle. The method uses eigenfunction expansions in each of the rectangular regions that satisfy some of the impermeable or porous surface conditions, and a simplified free-surface condition. Their unknown coefficients are determined from the impact boundary condition, impermeable or porous boundary conditions and by matching the solutions, in any two neighbouring rectangles, along their common boundary. Although the fluid motion is treated rather crudely, the method yields the pressure impulse throughout the entire region. Impulses, I, and moment impulses, M, on all or parts of the structure are also presented

Mathematical Model of Free Convection Boundary Layer Flow on Solid Sphere with Viscous Dissipation and Thermal Radiation

Present study considers the mathematical modeling of free convection boundary layer flow and heat transfer on a solid sphere with viscous dissipation and thermal radiation effects. The transformed partial differential equations are solved numerically by using the Keller-box method. Numerical solutions are obtained for the reduced Nusselt number, the local skin friction coefficient, the velocity and temperature profiles. The features of the flow characteristics for various values of the Prandtl number, radiation parameter and Eckert number are discussed. It is worth mentioning that the results are obtained until x = 180 degree. This is contrary to the previous report where the separation boundary layer flow occurs after x = 120 degree. The results in this paper is important for the researchers working in the area of boundary layer flow and this can be used as reference and also as complement for comparison purposes in the future

Slip Effect on Stagnation Point Flow past a Stretching Surface with the Presence of Heat Generation/Absorption and Newtonian Heating

Present study solved numerically the velocity slip effect on stagnation point flow past a stretching surface with the presence of heat generation/absorption and Newtonian heating. The governing equations which in the form of partial differential equations are transformed to ordinary differential equations before being solved numerically using the Runge-Kutta-Fehlberg method in MAPLE. The numerical solution is obtained for the surface temperature, heat transfer coefficient, reduced skin friction coefficient as well as the temperature and velocity profiles. The flow features and the heat transfer characteristic for the pertinent parameter such as Prandtl number, stretching parameter, heat generation/absorption parameter, velocity slip parameter and conjugate parameter are analyzed and discussed

Mathematical Formulae 2.0

Mathematical Formulae intends to provide students, scientists, engineers, and researchers with a readily available reference to the mathematical formulae needed during their studies or work situation. It is a handy book that one must have on the bookshelf. The text is divided, for ease of reference, into ten main chapters embracing algebra, trigonometry, limit, differentiation and integration, vector calculus, coordinate geometry, differential equations, numerical methods, discrete mathematics, and financial mathematics. Essential theory, formulae, definitions and laws are clearly stated in this boo

ETR 300 : Creative Ceiling Enterprise / Samidah Jindang... [et al.]

Creative Ceiling Enterprise adalah sebuah perniagaan yang menghasilkan produk siling berukir.Creative Ceiling juga merupakan satu-satunya syarikat bumiputra yang menceburi perniagaan ini. Syarikat ini mengeluarkan beberapa jenis siling. Antara siling yang dikeluarkan ialah : (a) Centra Panel Creative (b) Cornices Creative (c) Ceiling board Creative. Centra panel Creative dan Cornices Creative merupakan jenis siling yang digunakan di bangunan mewah seperti hotel, kondiminium, rumah banglo, istana dan sebagainya. Ceiling board Creative banyak digunakan seperti rumah, pejabat, institusi pengajian tinggi dan sebagainya. Lokasi perniagaan ini beralamat di Kampung Titi Besi, 02600 Arau, Perlis

Talking about smoking cessation with post-natal women: Exploring midwives’ experiences

This study explored midwives’ experiences of talking to post-natal women about smoking cessation. Face-to-face semi structured interviews were held with seven midwives based in the UK. Thematic analysis identified themes which provided understanding as to factors determining discussion of smoking cessation. Six themes were identified which were Post-natal Women Factors, Midwife Factors, Providing Information, Involving Others, Priorities, and Whole Family Approach. Implications for midwives working with post-natal women are discussed, including the need to increase the involvement of other healthcare professionals in supporting post-natal women to stop smoking