The diffraction of a solitary wave by a circular cylinder

This paper contributes to the diffraction of a solitary wave by a cylinder, governed by the Boussinesq eq. The Spectrum Method is used to transform 2·D eqs.into a set of 1·D eqs., which is solved by F. D. M. The example given in the paper shows that this method is both accurate and cost effective.     

Real-time nonlinear cylinder wave force reconstruction in stochastic wave field considering second-order wave effects

This study provides a novel method for reconstructing real-time nonlinear wave forces on a large-scale circular cylinder by considering second-order wave effects. Potential theory is utilized for deriving the expression of wave forces with the measured data of wave elevation. Approximate expressions of quadratic transfer functions are built with undetermined coefficients, which are resolved by using the historical data of measured wave elevation. Two different algorithms, including fast Fourier transform (FFT) and recursive least squares (RLS), are adopted for real-time reconstruction. Hydrodynamic tests are conducted in the wave flume on a circular cylinder to examine the effectiveness of the nonlinear reconstruction method. Comparative results demonstrate that the accuracy of real-time reconstructed wave forces is significantly enhanced by the present method. The over-prediction errors at force crests and the under-prediction errors at force troughs have been reduced. Furthermore, comparative results show that the nonlinear method implemented by the FFT algorithm provides more accurate results, whereas the RLS algorithm is more time cost efficient.     

Simulation of blast wave propagation over a cylinder

A numerical study of the interaction of plane blast waves with a cylinder is presented. Computations are carried out for various blast-wave durations and comparisons are obtained with the corresponding results of planar shock-wave. Both inviscid and viscous results based on the solution of the Euler and Navier-Stokes equations are presented. The equations are solved by an adaptive-grid method and a second-order Godunov scheme. The shock wave diffraction over the cylinder is investigated by means of various contour plots, as well as, pressure and skin-friction histories. The study reveals that the blast-wave duration significantly influences the unsteady flow over the cylinder. The differences between the viscous and inviscid results are also discussed. Received 2 March 1996 / Accepted 28 February 1997     

Unsteady interaction of shock wave diffracting around a circular cylinder in air

The reflection and diffraction of a planar shock wave around a circular cylinder are a typical problem of the complex nonlinear shock wave phenomena in literature. It has long been studied experimentally, analytically as well as numerically. Takayama in 1987 obtained clear experimental pictures of isopycnics in shock tube under the condition that the impinging shock wave propagates as far as 3 diameters away from the cylinder. To know more completely the whole unsteady process, it is desirable to get experimental results in a region which is more than 10 diameters away from the cylinder. This is what has been done in this paper by using the pulsed laser holographic interferometry for several shock Mach numbers of the impinging shock. Results for several moments are shown, giving more knowledge about the whole unsteady flow field. This is useful for a reliable and complete understanding of the changing force acting on the cylinder, and provides interesting data to check the performance of many recently developed high resolution numerical methods for unsteady shock wave calculation. The project suported partially by National Natural Science Foundation of China     

A second order stationary solution of the three dimensional wave diffraction potential

A theory on the second order wave diffraction by a three dimensional body fixed in a regular sea has been developed in the present paper. By regarding the sinusoidal disturb potential as a stationary solution of an initial value problem, and using Laplace transformation method and Tauberian theorem, the boundary value problems of stationary solution of the first and second order diffraction potential have been derived in this paper. Furthermore, the explicit solution of the second order stationary diffraction potential has been obtained with the method of the double Fourier transformation. It is found that the asymptotic behaviour of the second order stationary solution at far field is dependent on two wave systems, the first is “free wave”, travelling independently of the first order wave system, the other is “phase locked waves”, which accompany the first order waves. At the same time, the radiation conditions of the second order diffraction problems are derived. We also find that one can still pursue a steady state formulation with the inclusion of Rayleigh damping. Finally, as an example, the second order wave forces upon a fixed vertical circular cylinder have been calculated, and the numerical results agree well with the experimental data.     

Forces on surface-piercing vertical circular cylinder groups on flooding staircase

Flooding into underground spaces has become a common threat and caused significant damages and casualties in the past decades. To improve the understanding of people walking through the flooding staircase, a 1:2-scale physical model of a staircase with rest platform was assembled. An instrument was developed to measure the hydrodynamic forces acting on individual vertical circular cylinders, as well as cylinder groups arranged side-by-side, in tandem and staggered cylinder arrays on the flooding staircase. The results show that the horizontal hydrodynamic force on a cylinder increases rapidly with the increasing of the inundated depth on the entrance of the staircase. With a side-by-side tight cylinder array, the force on the central cylinder is always larger than an isolated one. The force on the downstream cylinder in tandem cylinder array is always smaller. However, the drag coefficients of both cases are much larger than the corresponding ones in a horizontal bed channel. For the case of staggered cylinder array, the force on the downstream cylinder varies with the change of the transverse spacing and the longitudinal distance between cylinders.     

A new approximate analytical solution of the ideal potential flow around a circular cylinder between two parallel flat plates

In ref. [1], Lin obtained an approximate analytical solution of the ideal potential flow around a circular cylinder between two parallel flat flates.In this paper, the author shows that one may obtain the result coinciding with that obtained in ref. [1] by making use of the Shvez's method^[2]. Morever, we can obtain a more accurate result than that obtained in ref. [1], if we make use of the improved Shvez's method^[2]. Some calculating examples are presented.     

Second-order interaction of irregular waves with a truncated column

A complete semi-analytical solution is obtained for second-order diffraction of plane bichromatic waves by a fixed truncated circular column. The fluid domain is divided into interior and exterior regions. In the exterior region, the second-order velocity potential is expressed in terms of ‘locked-wave’ and ‘free-wave’ components, both are solved using Fourier and eigenfunction expansions. The resulting ‘locked wave’ potential is expressed by one-dimensional Green's integrals with oscillating integrands. In order to increase computational efficiency, the far-field part of the integrals are carried out analytically. Solutions in both regions are matched on the interface by the potential and its normal derivative continuity conditions. Based on the present approach, the sum-and difference-frequency potentials are efficiently evaluated and are used to generate the quadratic transfer functions which correlates sum-frequency QTFs for a TLP column are present, which are compared for some frequency pairs with those from a fully numerical procedure. Satisfactory agreement has been obtained. QTF spectra for a case study TLP column, generated using the semi-analytical solution are presented. Also given are the results for nonlinear wave field around the column.     

Vortex shedding around a near-wall circular cylinder induced by a solitary wave

This study developed a two-dimensional generalized vortex method to analyze the shedding of vortices and the hydrodynamic forces resulting from a solitary wave passing over a submerged circular cylinder placed near a flat seabed. Numerical results for validation are compared with other numerical and experimental results, and satisfactory agreement is found. A series of simulations were performed to study the effects of gap-to-diameter ratio and incident wave height on vorticity pattern as well as the forces exerted on the cylinder. The range of the heights of incident waves is from 0.3h to 0.7h, where h is the still water depth. The range of the gap-to-diameter ratios is from 0.1 to 0.8. The results indicate that the flow pattern and the pressure distribution change significantly because of the close proximity of the seabed where the vorticity flux on the seabed-side surface of the cylinder is suppressed. Placing the cylinder nearer the seabed increases the drag and the positive lift on the cylinder. When the gap-to-diameter ratio increases, the pattern of vortices changes because of the interaction between the main recirculation zone and the shear layers separated from the gap. The maxima of drag, lift and total force increase linearly with the height of the incident wave.     

An analytical soluion of wave forces on large square cylinder

Wave forces on large square cylinder are determined by using the conformal transformation method. It is found that only for square cylinder, the governing equation is still the Helmholtz equation after the conformal transformation. An analytical solution of wave forces on square cylinder is presented by using the solution of wave forces on a circular cylinder.