Vortex shedding and evolution induced by a solitary wave propagating over a submerged cylindrical structure

The shedding and evolution of the vortical structures generated by a solitary wave propagating over a submerged cylindrical structure are investigated experimentally and numerically. The cylindrical structure consists of two concentric cylinders and represents a simplified model for an offshore submerged intake structure typically used in coastal power plants. Flow visualization by dye injection is used to identify the dominant vortical structures near the structure. The flow visualization results show an unexpected flow reversal that causes shedding of secondary vortical structures. The experimental results are used to check a three-dimensional volume of fluid-large eddy simulation (VOF-LES) numerical model. The VOF-LES model is then used to further study the flow structure. A total of six dominant vortical structures generated by the wave motion are identified, followed by two more generated by the flow reversal. In summary, this paper provides the vorticity evolution for a complex fluid–structure interaction problem and a three-dimensional numerical simulation tool has also been validated, which can be extended to study more complex geometries and wave conditions.     

Wave reflection by a submerged cycloidal breakwater in presence of a beach with different depth profiles

In this work, formulas for the reflection and transmission coefficients of one-dimensional linear water waves propagating over a submerged structure with a cycloidal cross section in presence of a sloping beach are determined. In the specialized literature, the previous coefficients are obtained mainly for the limit of linear water waves, considering that the water depth upstream and downstream of the structure is flat. For the analysis, we have obtained an approximate analytical solution to the dimensionless Modified Mild-Slope Equation, which models the interactions of a wide range of water waves, from short waves to long waves. The results shown that the presence of small breakwaters not always generate increments on the reflection coefficients, but on the contrary case they contribute to the reflection of the waves decreasing, which is due to the interference of energy that exists between the inclined beach and the structure. To validate the approximate analytical solution, we present a comparison against analytical solutions reported in the specialized literature, obtained with the aid of linear long wave theory, and a numerical solution, all the solutions adjust properly. Results of this study are expected to be used by coastal engineers for preliminary feasibility and desk design of submerged cycloidal breakwaters.     

Water wave radiation by a sphere submerged in water with an ice-cover

Using the multipoles method, we formulate the problems of radiation (both heave and sway) of water waves by a submerged sphere in deep as well as in uniform finite depth water with an ice-cover, with the ice-cover being modelled as an elastic plate of very small thickness. In each case this leads to an infinite system of linear equations which are solved numerically by standard techniques. The added-mass and damping coefficients for a heaving and swaying sphere are obtained and depicted graphically against the wave number for various values of the radius of the submerged sphere and flexural rigidity of the ice-cover to show the effect of the presence of ice-cover on these quantities. When the flexural rigidity is taken to be zero, the numerical results for the added-mass and damping coefficient for water with a free surface are recovered.     

Phase velocity effects of the wave interaction with exponentially sheared current

The nonlinear interaction between the unidirectional bichromatic wave-train and exponentially sheared current in water of an infinite depth is investigated. The model is based on the vorticity transport equation and the exact free surface conditions, without any assumptions for the existence of small physical parameters. Earlier works of the wave–current interaction were mainly restricted to either current acted on the monochromatic wave or irregular waves limited to irrotational current. Different from these previous works, no constraint is made in our model for amplitudes of the primary wave, and the current owns an exponential type profile along the vertical line. To ensure that the effect of vorticity on the phase velocity is consistent with earlier derivation, the case of a small amplitude wave traveling on the exponentially sheared current is examined firstly. Then the effect of nonlinearity on the phase velocity of primary waves in a bichromatic wave-train is considered. Accurate high-order approximations of the phase velocity are obtained under consideration of both the nonlinear wave self–self and mutual interactions. Finally, the combined effect of vorticity and nonlinearity on the phase velocity is investigated through the case of a bichromatic wave-train propagating on an exponentially sheared current. It is found that the characteristic current slope determines the effect of vorticity on the phase velocity caused by nonlinear wave self–self and mutual interactions, and the surface current strength may amplify/reduce this effect.     

Performance-based design and analysis of flexible composite propulsors

Advanced composite propellers, turbines, and jet engines have become increasingly popular in part because of their ability to provide improved performance over traditional metallic rotors through exploitation of the intrinsic bend–twist coupling characteristics of anisotropic composite materials. While these performance improvements can be significant from a conceptual perspective, the load-dependent deformation responses of adaptive blades make the design of these structures highly non-trivial. Hence, it is necessary to understand and predict the dependence of the deformations on the geometry, material constitution, and fluid–structure interaction responses across the entire range of expected loading conditions.The objective of this work is to develop a probabilistic performance-based design and analysis methodology for flexible composite propulsors. To demonstrate the method, it is applied for the design and analysis of two (rigid) metallic and (flexible) composite propellers for a twin-shafted naval combatant craft. The probabilistic operational space is developed by considering the variation of vessel thrust requirements as a function of the vessel speed and wave conditions along with the probabilistic speed profiles. The performance of the metallic and composite propellers are compared and discussed. The implications of load-dependent deformations of the flexible composite propeller on the operating conditions and the resulting performance with respect to propeller efficiency, power demand, and fluid cavitation are presented for both spatially uniform and varying flows. While the proposed framework is demonstrated for marine propellers, the methodology can be generally applied for any marine, aerospace, or wind energy structure that must operate in a wide range of loading conditions over its expected life.     

Numerical simulation of a solitary wave interaction with submerged multi-bodies

The problems of a solitary wave passing over rectangular cylinders have been analysed. The numerical simulation is based on the full nonlinear two-dimensional Navier-Stokes equations which are solved by the finite difference method. The free surface is dealt with by the Volume of Fluid method (VOF). Results for a solitary wave passing over a single cylinder are compared with the experimental data of Seabra-Santos, Penouard and Temperville^[2] and better agreement is obtained than those obtained from the long wave equation based on the potential flow theory. Results are also given for two cylinders with different gaps. The project supported by the National Natural Science Foundation of China and the Development Foundation of Science and Technology of Shanghai Education Committee and the Royal Society.     

Vortex shedding induced by a solitary wave propagating over a submerged vertical plate

Experimental study was conducted on the vortex shedding process induced by the interaction between a solitary wave and a submerged vertical plate. Particle image velocimetry (PIV) was used for quantitative velocity measurement while a particle tracing technique was used for qualitative flow visualization. Vortices are generated at the tip of each side of the plate. The largest vortices at each side of the plate eventually grow to the size of the water depth. Although the fluid motion under the solitary wave is only translatory, vortices are shed in both the upstream and downstream directions due to the interaction of the generated vortices as well as the vortices with the plate and the bottom. The process can be divided into four phases: the formation of a separated shear layer, the generation and shedding of vortices, the formation of a vertical jet, and the impingement of the jet onto the free surface. Similarity velocity profiles were found both in the separated shear layer and in the vertical jet.     

外爆条件下冲击波与组合壳结构的相互作用

为研究冲击波与组合壳结构的相互作用,针对带防护墙的地面直立钢筋混凝土组合壳结构,考虑结构安置于地面和周边围土2种工况,开展结构爆炸实验,分析了结构外表面冲击波荷载分布及振动特性。实验结果表明:冲击波作用下,结构外表面爆炸荷载主要产生在冲击波绕射过程,确定荷载时应考虑冲击波压力在绕射传播过程中的自然衰减;整个结构中与冲击波最早接触的构件先产生振动,而后由于结构整体参与使得振动频率降低,振动幅值减小;结构周边围土可降低防护墙迎爆部分构件的振动频率,减小防护墙和组合壳的振动幅值。     

Analytical study for oblique wave interaction with a submerged horizontal perforated plate near a partially reflecting vertical wall

Meccanica - A novel iterative analytical solution is developed to study the oblique wave interaction with a horizontally submerged perforated plate near a partially reflecting vertical wall. The...     

Shock wave interaction with a cloud of particles

The present paper is devoted to experimental and theoretical investigation of the shock wave (SW) propagation in a mixture of gas and solid particles in the presence of explicit boundaries of the two-phase region (cloud of particles). The effect of the qualitative change in the supersonic flow behind the SW in a cloud of particles within the range of the volume concentration of the disperse phase 0.1-3% is experimentally shown and theoretically grounded. Received 15 April 1996 / Accepted 3 June 1996     

Generic non-linear modelling of a bi-material composite beam with partial shear interaction

Composite members composed of two materials joined by shear connection find widespread use in engineering infrastructure, in both traditional practice and innovative applications. Studies in the literature dating back nearly 60 years have elucidated the mechanics of the behaviour of these composite structural members in which the solution for the slip at the interface between the materials was determined by solving a linear differential equation. However, these solutions are based on a linear formulation of the strain-displacement relationship, and in some applications this relationship must be represented in non-linear form, so that the second order effects in the member can be quantified correctly. This paper presents such a study for a composite member with two materials, being typical of a steel-concrete composite beam in structural engineering. It quantifies the restraint of the member ends by longitudinal and rotational elastic springs, so that the axial tension developed is a function of the transverse loading, material properties, cross-sectional properties and the restraint stiffness. The problem is treated using minimisation of the total potential stored in the two members, the elastic shear connection at their interface, the restraints at the ends and the work done by the transverse forces, for which the differential equations for the deformations can be determined from routine variational calculus. The non-linear equation of equilibrium relating the external loading to the internal actions is stated in closed form by invoking the static and kinematic boundary conditions for the member. The solution is compared with closed form treatments derived elsewhere, and a representative member is analysed so that the influences of the non-linearity, end restraint stiffness and degree of partial shear interaction on its behaviour can be examined.     

Experimental study on the added mass and damping of a disk submerged in a partially fluid-filled tank with small radial confinement

The dynamic response of submerged and confined disk-like structures is of interest in engineering applications, such as in hydraulic turbine runners. This response is difficult to be estimated with accuracy due to the strong influence of the boundary conditions. Small radial gaps as well as short axial distances to rigid surfaces greatly modify the dynamic response because of the added mass and damping effects.In this paper, the influence of the axial nearby rigid distance on the dynamic response of a submerged disk is evaluated when the radial gap is very small. Moreover, the effects of the fluid depth and fluid viscosity on the natural frequencies and damping ratio of the submerged disk are studied. The study has been performed experimentally and numerically using structural–acoustic simulations.For the experimental investigation a test rig has been developed. It consists of a disk attached to a shaft and confined with a small radial gap inside a cylindrical container full of water. The disk can be moved up and down along the shaft to vary the axial distance to the nearby rigid surface. Piezoelectric patches are used to excite the disk and the response is measured with submersible accelerometers. Several excitation patterns can be used due to the disposition of these piezoelectric patches. For each configuration tested, the dynamic response of the structure is studied analyzing the natural frequencies and damping ratio of the disk attached to the shaft. The numerical results have been compared with the experimental results.     

Elastic field of a composite cylinder with a spatially varying dynamic eigenstrain

The analytical solutions of displacements and stresses for an eigenstrain problem in a composite bi-layered coaxial cylinder are presented in this article. The inner cylinder is assumed to undergo a dynamic, spatially varying eigenstrain. The spatial distribution of the eigenstrian is taken to be a quadratic polynomial with arbitrary coefficients along the radial direction. Furthermore, the eigenstrain is assumed to be harmonically time-dependent. Elasticity equations are constructed to directly solve the problem. The effect of spatial distribution, as well as the angular frequency of the eigenstrain on the elastic response of the composite cylinder has been illustrated graphically.     

Numerical study of formation of solitary strain waves in a nonlinear elastic layered composite material

Propagation of nonlinear strain waves through a layered composite material is considered. The governing macroscopic wave equation for the long-wave case was obtained earlier by the higher-order asymptotic homogenization method (Andrianov et al., 2013). Non-stationary dynamic processes are investigated by a pseudo-spectral numerical procedure. The time integration is performed by the Runge–Kutta method; the approximation with respect to the spatial co-ordinate is provided by the Fourier series expansion. The convergence of the Fourier series is substantially improved and the Gibbs–Wilbraham phenomenon is reduced with the help of Padé approximants. As result, we explore how fast and under what conditions the solitary strain waves can be generated from an initial excitation. The numerical and analytical solutions (when the latter can be obtained) are in good agreement.     

A study of shock wave interaction with a rotating cylinder

Shock wave reflection over a rotating circular cylinder is numerically and experimentally investigated. It is shown that the transition from the regular reflection to the Mach reflection is promoted on the cylinder surface which rotates in the same direction of the incident shock motion, whereas it is retarded on the surface that rotates to the reverse direction. Numerical calculations solving the Navier-Stokes equations using extremely fine grids also reveal that the reflected shock transition from RR MR is either advanced or retarded depending on whether or not the surface motion favors the incident shock wave. The interpretation of viscous effects on the reflected shock transition is given by the dimensional analysis and from the viewpoint of signal propagation.Received: 24 April 2002, Accepted: 16 August 2002, Published online: 25 March 2003     

Numerical study on the performance of a twin-raft wave energy dissipator in a stilling basin

In this paper, a raft-typed wave energy dissipator is proposed, and a mathematical model for the hydrodynamics of such a dissipator is presented, based on Reynolds-averaged Navier–Stokes equations. The model is validated by a comparison of the numerical results with the results of other investigators. The validated model is then utilized to examine the effect of wave height, wave frequency, damping coefficient, flow velocity on wave energy dissipation ratio and wave transmission coefficient for a hinged twin-raft wave energy dissipator. Our results reveal that the differences in behaviour exhibited by an inviscid fluid and a viscous fluid can be large and vary considerably, depending on the flow velocity.     

Study of water waves with submerged obstacles using a vortex method with Helmholtz decomposition

The present study develops a 2‐D numerical scheme that combines the vortex method and the boundary integral method by a Helmholtz decomposition to investigate the interaction of water waves with submerged obstacles. Viscous effects and generation of vorticity on the free surface are neglected. The second kind of Fredholm integral equations that govern the strengths of vortex sheets along boundaries are solved iteratively. Vorticity is convected and diffused in the fluid via a Lagrangian vortex (blob) method with varying cores, using the particle strength exchange method for diffusion, with particle redistribution. A grid‐convergence study of the numerical method is reported. The inviscid part of the method and the simulation of the free‐surface motion are tested using two calculations: solitary wave propagation in a uniform channel and a moving line vortex in the fluid. Finally, the full model is verified by simulating periodic waves travelling over a submerged rectangular obstacle using nonuniform vortex blobs with a mapping of the redistribution lattice. Overall, the numerical model predicts the vortices' evolution and the free‐surface motion reasonably well. Copyright © 2008 John Wiley & Sons, Ltd.