Large Vertical Cylinder Research Articles

3D ISPH erosion model for flow passing a vertical cylinder

In this paper a 3D incompressible Smoothed Particle Hydrodynamics (ISPH) erosion model is proposed to simulate the scouring process around a large vertical cylinder. The erosion model is based on the turbidity water particle concept and the sediment motion is initiated when the fluid bottom shear stress exceeds the critical value. The previous 2D SPH sediment initiation model is expanded by combining the effects of both transverse and longitudinal sloping beds in a practical 3D situation. To validate the developed model, a laboratory flume experiment was carried out to study the clear water scouring around a vertical cylinder under unidirectional current, in which high-speed video cameras were used for the real-time monitoring of sediment movement. The 3D ISPH results are compared with the experimental data with good agreement in terms of the scouring patterns and scales. Besides, the computed flow velocity field suggests that both the horseshoe vortices and lee-wake flows around the cylinder have been realistically simulated.

Numerical simulation of wave interaction with vertical circular cylinders of different submergences using immersed boundary method

A three-dimensional numerical model has been developed to simulate wave-structure interaction over an uneven bottom. This model is an extension of the earlier multiple-layer σ-coordinate model (Lin, 2006) by including the direct-forcing immersed boundary method to deal with curved body surfaces. The model verification for free surface computation is firstly conducted. One case is regular wave diffraction over a large vertical circular cylinder. The computational results show good agreement with the analytical solution. The other is nonlinear wave interaction with a fixed floating vertical circular cylinder. The numerical results of free surface agree well with the experimental results and other numerical data found in literatures. The model verification of force and moment is done next. For solitary wave interaction with a vertical circular cylinder, the numerical results are compared with the experimental data and good agreements have been obtained for wave elevation and net wave force acting on the cylinder. For wave diffraction around a fixed submerged vertical cylinder in a finite water depth, the horizontal forces, vertical forces and moments on the structure agree well with the analytical solution and numerical results of a higher order boundary element method.

Reliability research on fatigue life of spots of semi-submerged drilling unit

Based on the calculated results of the simplified model of deep-water semi-submerged drilling unit, the model of deep-water semi-submerged drilling unit is built by reasonably simplifying. The large vertical cylinder (MacCamy-Fuchs) formula is modified according to this model, then the modified formula is utilized to obtain the wave load spectrum which acts on the columns of the semi-submerged drilling unit. By using ANSYS software, a spectrum analysis process is established to calculate the stochastic response spectrum of the model that is subjected to the wave load spectrum which has been calculated. Then the power spectral density of stochastic response of the key nodes can be obtained. Based on the Miner model and the first excursion failure criterion, the fatigue life reliability of the key nodes is calculated.

A perturbation DRBEM model for weakly nonlinear wave run-ups around islands

In this paper, the dual reciprocity boundary element method (DRBEM) based on the perturbation method is presented for calculating run-ups of weakly nonlinear long waves scattered by islands. Under the assumption that the incident waves are harmonic, the time-dependent nonlinear Boussinesq equations are transformed into three time-independent linear equations by using the perturbation method, where, besides nonlinearity ε , the dispersion μ 2 is also included in the perturbed expansion. The first-order solution η 0 is found by using the linear long-wave equations. Then η 0 is used in two second-order governing equations related to the dispersion and nonlinearity, respectively. Since no any omission and approximation for the seabed slope ∇ h and its derivatives is made, there are the third- and fourth-order partial derivatives of η 0 appeared in the right-hand sides of two governing equations of the second-order. By employing a transformation, those third- and fourth-order partial derivatives are removed therefore large errors in approximating these derivatives are eliminated. To validate the new model, wave diffractions around a large vertical cylinder for 13 cases are first considered. It is found that the nonlinear contributions to the new model are significant for weakly nonlinear waves with a much better comparison with experimental results obtained than for the linear diffraction theory. It is also found that the dispersive effects play an important role in improving the accuracy of the new model as numerical results obtained from the Boussinesq equations (with dispersion terms) are more accurate than those from the Airy's equations (without dispersion term). Then the combined wave diffraction and refraction by a conical island is also modelled and discussed. Our model is not only accurate as the dispersive effects have been included but also computationally efficient since the domain integrals are merely evaluated by distributing collocation points over that surface.

Short crested wave–current forces around a large vertical circular cylinder

An analytical solution for the diffraction of short crested incident wave along positive x-axis direction on a large circular cylinder with uniform current is derived. The important influences of currents on wave frequency, water run-up, wave force, inertia and drag coefficients on the cylinder profiles are investigated for short-crested incident wave. Based on the numerical results, we find wave frequency of short crested wave system is affected by incident angle and the strength of the currents. The wave frequency increases or decreases with increasing current speed following or opposing wave propagating direction. It shows that the effects of current speeds, current directions on water run-up on the circular cylinder with different radius for different wave numbers are very conspicuous when the incident wave changes from long crested plane waves to short-crested waves. With the increase of current speed, the water run-up on the cylinder becomes more and more high, and will exceed that of long crested plane wave and short crested wave case without currents even though the current speed is small. The total wave loads, inertia coefficient and drag coefficient exerted on a cylinder with currents would be larger compared to the wave loads exerted pure short-crested waves. Therefore, ocean engineers should consider the short crested wave–current load on marine constructs carefully.

Experimental investigation of pressure distribution on a cylinder due to the wave diffraction in a finite water depth

The experimental investigations on the pressure distribution around a large vertical cylinder fixed on a wave channel, piercing the free surface and subjected to regular waves have been carried out. Recently, considerable advances have been made in the development of analytical techniques for studying non-linear wave loading phenomena on large structures. However, there is a lack of high quality experimental data that may be used for validating the analytical and numerical solutions obtained. This paper describes the design and execution of an experiment conducted at the Hydraulics Laboratory in the Civil Engineering Department of the Istanbul Technical University. Experimental measurements of pressures at different locations are presented including comparisons with the computational results. This study showed that the experimental and computational results generally exhibited better correlation, however, the measured pressure values diverged from the computational results while approaching the free surface.

Wave Scour around a Large Vertical Circular Cylinder

This paper presents the results of an experimental study on the steady-streaming flow and the resulting scour process around a large vertical circular cylinder exposed to a progressive wave. The flow is in the unseparated flow regime [the Keulegan-Carpenter number at the bed being KC < O(1)]. The diffraction effect is existent. Two kinds of experiments were made: (1) rigid bed; and (2) actual scour. Detailed velocity measurements were made near the bed in the vicinity of a cylinder (1 m in diameter) in the rigid-bed experiments. These measurements show a strong presence of a 3D steady streaming induced by the waves. No such streaming exists in the absence of the cylinder. The rigid-bed experiments together with the actual scour tests indicate that the waves stir up the sediment and bring it in suspension, and the steady streaming carries the sediment away from the cylinder, leading to scour. The scour is found to depend mainly on KC and the diffraction parameter, the cylinder-diameter-to-the-wave length r...

A note on second-order wave forces on a circular cylinder in finite water depth

This paper presents the second-order diffraction problem for a large vertical cylinder. Expressions have been obtained for three second-order forces, namely waterline force, dynamic force, and quadratic force. The first-order potentials contribute to waterline and dynamic forces, whereas the second-order potentials contribute to the quadratic force. This quadratic force is obtained with the knowledge of the linear diffraction potential only using the Green's function method; an explicit form of the quadratic potential is not needed. The theory in this paper emphasizes on the contribution of the second-order forces to the total force.

Natural-Convection Film- Boiling Heat Transfer. (Experiments of Subcooled Film Boiling with Long Vapor Film).

Heat transfer in natural-convection film boiling with a long vapor film was investigated experimentally. Experiments of film boiling on horizontal cylinders of large diameter and long vertical cylinders were conducted to investigate the effect of liquid subcooling on the film-boiling heat transfer. The test liquid was R-113 at atmospheric pressure, and the following results were obtained in the experiments. For cylinders of both types, local heat-transfer coefficients of saturated and subcooled film boiling were much higher than the respective predictions from the two-phase boundary layer theory. In the case of vertical cylinders, the local heat-transfer coefficient did not depend on the distance from the leading edge even if the liquid was subcooled. In the case of horizontal cylinders of large diameter, the local value did not strongly depend on the distance from the stagnation point for saturated film boiling, but it depended on the distance and reached a maximum at a distance from the stagnation point with increasing liquid subcooling. As for the averaged heat-transfer coefficient of horizontal cylinders of large diameter, it increased with increasing liquid subcooling but did not depend on the diameter even under subcooled conditions.

Computation of hydrodynamic forces on vibrating multiple large vertical cylinders of arbitrary section

Some offshore structures consist of several uniform vertical cylinders of arbitrary section, which are in close proximity to each other. The interaction between their vibration and fluid motion is of importance in many design cases. A type of local disturbance source has been recently introduced by the present authors, which, being distributed on the sectional contour of the cylinder together with the well-known wave source, is used to estimate the three-dimensional hydrodynamic forces on a single cylinder of arbitrary section oscillating or vibrating in still waters (the so-called radiation problem). In the present paper, the solution method is extended to investigate the hydrodynamic forces on multiple large vertical cylinders of arbitrary section and the dynamic interference between them, which are fundamentally significant for further studies of the fluid-structure interaction problem.

Natural-Convection Film-Boiling Heat Transfer. 4th Report. Experiments of Subcooled Film Boiling with Long Vapor Film.

Heat transfer in natural-convection film boiling with long vapor film is investigated experimentally. Experiments of film boiling on horizontal cylinders of large diameter and long vertical cylinders are conducted to investigate the effect of liquid subcooling on film-boiling heat transfer. The test liquid is R-113 at atmospheric pressure. For cylinders of both types, local heat transfer coefficients of saturated and subcooled film boiling are much higher than the predictions from two-phase boundary layer theory. In the case of vertical cylinders, local heat transfer coefficients do not depend on the distance from the stagnation point even if the liquid is subcooled. In the case of horizontal cylinders of large diameter, the local value of saturated film boiling dose not strongly depend on the distance from the stagnation point, but it comes to depend on the distance with increasing subcooling. In particular, the local value reaches a maximum at a distance from the stagnation point. As for averaged heat transfer coefficients of horizontal cylinders of large diameter, they increase with increasing subcooling but do not depend on the diameter even under subcooled conditions.

Hydrodynamic Coefficients of Vertical Cylinders of Arbitrary Section

The calculation of added masses and damping coefficients of a large surface-piercing vertical cylinder of arbitrary section extending to the seabed and undergoing harmonic oscillations is described. The linear radiation problem in three dimensions is reduced to a series of two-dimensional problems in the horizontal plane by the use of appropriate eigenfunctions that represent the variation of the velocity potential in the vertical direction. Each of these is solved by a numerical approach based on the method of integral equations. Comparisons are made with an analytic solution available for the case of a circular cylinder. Results are also provided for square cylinders, and the application to typical offshore structures subject to base motions is discussed.

Dynamic pressures on a large vertical cylinder due to random waves

The hydrodynamic pressures due to random waves on a large vertical cylinder, resting on a flume bed and piercing above the free surface has been investigated experimentally in constant water depth. The test cylinder was fixed with diaphragm-type pressure transducers at nine different pressure ports with one of them at the still water level (S.W.L.) itself. The cylinder was rotated about its own axis to study the pressure distribution around its circumference. The time histories of the water surface elevation and the corresponding dynamic pressures exerted on the cylinder have been analysed in the frequency domain. The experimental results are compared with the theoretical results based on the linear diffraction theory of MacCamy and Fuchs and the agreement is satisfactory. Finally, the hydrodynamic pressure coefficients obtained from random wave tests are compared with those from regular wave tests.

Diffracted wave field and dynamic pressures around a vertical cylinder

Investigations on the hydrodynamic pressures due to regular and random waves exerted on a large vertical cylinder in a constant water depth are reported in this paper. In the experimental investigation, the test cylinder embedded with diaphragm-type pressure transducers at nine different elevations was rotated about its axis to measure the dynamic pressure around its circumference. The wave field in the neighbourhood of the cylinder was measured at six different locations. The results of the experiments are compared with the linear diffraction theory of MacCamy, R. C. and Fuchs, R. A. [(1954) Wave forces on piles: a diffraction theory. U.S. Army Beach Erosion Board, Technical Memorandum No. 69]. In general, the agreement between the theoretical and experimental results is found to be satisfactory. A comparison between the regular and random wave test results is also presented and discussed.

Nonlinear wave interaction with a vertical circular cylinder. Part I: Diffraction theory

A closed-form solution is developed for the velocity potential resulting from the interaction of second-order Stokes waves with a large vertical circular cylinder. At first-order, the solution is the usual linear diffraction theory. At second-order, the solution consists of forced wave motions, due to nonlinear wave-wave interactions in the free surface boundary condition, plus scattered free wave motions, due to the interaction of the forced waves with the fixed cylinder. The velocity potentials are then used to determine the theoretical free surface elevations around the cylinder consistent to second-order. Second-order terms are found to significantly alter wave envelopes around the cylinder as a result of nonlinear diffraction. For example, the maximum wave crest run-up on the cylinder from the nonlinear theory is found to exceed that predicted by the linear diffraction theory by up to 50%. A brief comparison of the nonlinear theory with the measured run-up data is found to largely confirm the theoretical solution.

Wave induced dynamic pressures on a vertical cylinder in the diffraction regime

The dynamic pressures around a large diameter vertical cylinder resting on the flume bed and piercing the free surface are measured under regular wave conditions and compared with the results of MacCamy and Fuchs' linear diffraction theory. The linear diffraction theory has been modified to account for the nonlinear effects. The results mostly pertain to deep water conditions with drag effects being negligible and are presented in nondimensional form. The agreement between the theory and experiments are in general found to be good.

Dynamic pressure distribution on a cylinder due to wave diffraction

The experimental investigations on the dynamic pressure distribution around a large vertical cylinder resting on a flume bed and piercing the free surface subjected to regular waves have been carried out in a 4-m wide wave flume in a constant water depth of 2.5 m at Ocean Engineering Centre, Indian Institute of Technology, Madras, India. The cylinder of diameter 400 mm was fixed with diaphragm type pressure transducers at eight different locations below the still water level along with one at the still water level. In addition to this, to study the effect of nonlinearity, one pressure transducer was located above the still water level. The experimental results pertaining to mostly deep water conditions are compared with MacCamy and Fuchs theory and the agreement is found to be good. In order to account for the effects of nonlinearities the above said theory has been modified the results of which are found to be in better agreement.

NONLINEAR DIFFRACTION BY A VERTICAL CYLINDER

A theoretical solution is developed for the interaction of second-order Stokes waves with a large vertical circular cylinder in water of finite depth. The solution is obtained in terms of the velocity potential such that any kinematic or dynamic quantity of interest may be derived, consistent to the second perturbation order. In this study, the second-order wave field around the cylinder is determined, showing the modification of the incident Stokes waves by wave-wave and wave-structure interactions, both in the reflection-dominated up-wave region and in the diffraction-dominated down-wave region. The theory is then compared to experimental data for wave runup and rundown amplitudes on the cylinder as well as for wave crest and trough envelopes in the up-wave and down-wave regions.

Wave loads on large vertical cylinders: A design method

The finite element method based on linear diffraction theory proposed by Zienkiewicz and Bettess (1977) has been used to compute wave loads and moments about the bed of surface piercing cylinders of circular, square, rectangular and elliptical sections for different angles of wave incidence. On the basis of the results obtained, a design method is presented in the form of simple design charts for estimating wave forces and moments on large cylinders of arbitrary sections. The numerical solutions obtained have been checked for their validity by comparing with other theoretical solutions and experimental data. Further the application of the design method to a case study shows good correlation with experimental and other theoretical solutions.

Non-linear wave loads on large circular cylinders: a perturbation technique

The forces and overturning moments exerted by second order waves on large vertical circular cylinders are analysed. The mathematical equations governing the physical system are the three-dimensional Laplace's equation satisfied by the velocity potential ϕ( x, y, z, t) and the boundary conditions, namely the dynamic boundary condition which is obtained from the Bernoulli's equation, kinematic boundary condition, radiation condition, bottom boundary condition and the zero radial velocity condition on the surface of the cylinder. The non-linearity of the mathematical problem is evidenced in the free surface boundary conditions viz. dynamic and kinematic boundary conditions. Analytical solutions are obtained using the perturbation technique. These solutions are compared with various experimental data. The comparison shows favourable agreement between the theory and the experimental results.