Experimental Study on Ocean Internal Wave Force on Vertical Cylinders in Different Depths

A series of experimental studies about the force of internal solitary wave and internal periodic wave on vertical cylinders have been carried out in a two-dimensional layered internal wave flume. The internal solitary waves are produced by means of gravitational collapse at the layer thickness ratio of 0.2, and the internal periodic waves are produced with rocker-flap wave maker at the layer thickness ratio of 0.93. The wave parameters are obtained through dyeing photography. The vertical cylinders of the same size are arranged in different depths. The horizontal force on each cylinder is measured and the vertical distribution rules are researched. The internal wave heights are changed to study the impact of wave heights on the force. The results show that the horizontal force of concave type internal solitary wave on vertical cylinder in the upper-layer fluid has the same direction as the wave propagating, while it has an opposite direction in the lower-layer. The horizontal force is not evenly distributed in the lower fluid. And the force at different depths increases along with wave height. Internal solitary wave can produce an impact load on the entire pile. The horizontal force of internal periodic waves on the vertical cylinders is periodically changed at the frequency of waves. The direction of the force is opposite in the upper and lower layers, and the value is close. In the upper layer except the depth close to the interface, the force is evenly distributed; but it tends to decrease with the deeper depth in the lower layer. A periodic shear load can be produced on the entire pile by internal periodic waves, and it may cause fatigue damage to structures.

Diffraction of Water Waves by A Vertically Floating Cylinder in A Two-Layer Fluid

In this paper, the diffraction of water waves by a vertically floating cylinder in a two-layer fluid of a finite depth is studied. Analytical expressions for the hydrodynamic loads on the vertically floating cylinder are obtained by use of the method of eigenfunction expansions. The hydrodynamic loads on the vertically floating cylinder in a two-layer fluid inelude not only the surge, heave and pitch exciting forces due to the incident wave of the surface-wave mode, but also those due to the incident wave of the internal-wave mode. This is different from the case of a homogenous fluid. Some given examples show that, for a two-layer fluid system with a small density difference, the hydrodynamic loads for the surface-wave mode do not differ significantly from those due to surface waves in a single-layer fluid, but the hydrodynamic loads for the internal-wave mode are important over a wide range of frequencies. Moreover, also considered are the free surface and interface elevations generated by the diffraction wave due to the incident wave of the surface-wave and interhal-wave modes, and transfer of energy between modes.

Experimental Study on 2-D Focusing Wave Run-up on A Vertical Cylinder

In this paper,the focused wave groups with different parameters and their actions on a vertical cylinder are experimentally studied. The harmonic wave characteristics of the focusing waves are analyzed by the addition and subtraction of the crest and trough focusing waves. The analyzed results show that higher order harmonics can be generated because of the interaction of component waves. Nonlinearity increases with the inputted wave amplitude and the frequency width increment. Further, the wave run-up around the vertical circular cylinder is experimentally studied. It increases with the wave steepness and the relative cylinder diameter increase. However, the variations of wave run-up around the circular cylinder are different. The researches provide a reference for further numerical studies.

Transient analysis of diffusive chemical reactive species for couple stress fluid flow over vertical cylinder

The unsteady natural convective couple stress fluid flow over a semi-infinite vertical cylinder is analyzed for the homogeneous first-order chemical reaction effect. The couple stress fluid flow model introduces the length dependent effect based on the material constant and dynamic viscosity. Also, it introduces the biharmonic operator in the Navier-Stokes equations, which is absent in the case of Newtonian fluids. The solution to the time-dependent non-linear and coupled governing equations is carried out with an unconditionally stable Crank-Nicolson type of numerical schemes. Numerical results for the transient flow variables, the average wall shear stress, the Nusselt number, and the Sherwood number are shown graphically for both generative and destructive reactions. The time to reach the temporal maximum increases as the reaction constant K increases. The average values of the wall shear stress and the heat transfer rate decrease as K increases, while increase with the increase in the Sherwood number.

Analytical Study on Wave Diffraction from a Vertical Circular Cylinder in Front of Orthogonal Vertical Walls

In this paper, the principle of mirror image is used to transform the problem of wave diffraction from a circular cylinder in front of orthogonal vertical walls into the problem of diffraction of four symmetric incident waves from four symmetrically arranged circular cylinders, and then the eigenfunction expansion of velocity potential and Grafs addition theorem are used to give the analytical solution to the wave diffraction problem. The relation of the total wave force on cylinder to the distance between the cylinder and orthogonal vertical walls and the incidence angle of wave is also studied by numerical computation.

Filling mode and regularity of vertical centrifugal casting process of titanium alloy in thin-walled cylinder cavity

The mold filling process of titanium alloy in a thin-walled cylinder cavity under vertical centrifugal casting process was studied by means of the hydraulic simulation experiments. Results show that the filling mode of the melt in the cylinder cavity varies with casting wall-thickness. When the casting wall-thickness is less than or equal to the thickness of the first layer during the filling process, the melts fill the cavity from the bottom to the top.When the casting wall-thickness is greater than the thickness of the first layer during the filling process, the melts first fill the largest radius parts of the cavity with a certain thickness of the first layer from the bottom to the top of the cavity, and then they fill the cavity from the larger radius part to the smaller radius part. The melt filling ability increases with the increment of the mold rotational speed and the pouring temperature. In another aspect, the melt filling ability rises with the decrement of the melt viscosity, and the melt with the better filling ability is prone to fill the cylinder cavity layer by layer.

HYDRODYNAMIC INTERACTION BETWEEN TWO VERTICALCYLINDERS IN WATER WAVES

The hydrodynamic interaction between two vertical cylinders in water waves is investigated based on the linearized potential flow theory. One of the two cylinders is fixed at the bottom while the other is articulated at the bottom and oscillates with small amplitudes in the direction of the incident wave. Both the diffracted wave and the radiation wave are studied in the present paper. A simple analytical expression for the velocity potential on the surface of each cylinder is obtained by means of Graf's addition theorem. The wave-excited forces and moments on the cylinders, the added masses and the radiation damping coefficients of the oscillating cylinder are all expressed explicitly in series form. The coefficients of the series are determined by solving algebraic equations. Several numerical examples are given to illustrate the effects of various parameters, such as the separation distance, the relative size of the cylinders, and the incident angle, on the first-order and steady second-order forces, the added masses and radiation-damping coefficients as well as the response of the oscillating cylinder.

The efect of the couple stress parameter and Prandtl number on the transient natural convection flow over a vertical cylinder

An analysis is performed to study transient free convective boundary layer flow of a couple stress fluid over a vertical cylinder, in the absence of body couples. The solution of the time-dependent non-linear and coupled governing equations is carried out with the aid of an unconditionally stable Crank-Nicolson type of numerical scheme. Numerical results for the steady-state velocity, temperature as well as the time histories of the skin-friction coefficient and Nus- selt number are presented graphically and discussed. It is seen that for all flow variables as the couple stress control parameter, Co, is amplified, the time required for reaching the temporal maximum increases but the steady-state decreases.

Numerical Investigation of Unsteady Free Convection on a Vertical Cylinder with Variable Heat and Mass Flux in the Presence of Chemically Reactive Species

A mathematical model is presented to study the effect of chemical reaction on unsteady natural convection boundary layer flow over a semi-infinite vertical cylinder. Taking into account the buoyancy force effects, for the situation in which the surface temperature and are subjected to the power-law surface heat and mass flux as and . The governing equations are solved by an implicit finite difference scheme of Crank-Nicolson method. Numerical results for the velocity, temperature and concentration profiles as well as for the skin-friction, Nusselt and Sherwood numbers are obtained and reported graphically for various parametric conditions to show interesting aspects of the solution.

Numerical Study of the High-Frequency Wave Loads and Ringing Response of A Bottom-Hinged Vertical Cylinder in Focused Waves

This paper presents a numerical study on the high-frequency wave loads and ringing response of offshore wind turbine foundations exposed to moderately steep transient water waves.Input wave groups are generated by the technique of frequency-focusing,and the numerical simulation of focused waves is based on the NewWave model and a Fourier time-stepping procedure.The proposed model is validated by comparison with the published laboratory data.In respect of both the wave elevations and the underlying water particle kinematics,the numerical results are in excellent agreement with the experimental data.Furthermore,the local evolution of power spectra and the transfer of energy into higher frequencies can be clearly identified.Then the generalized FNV theory and Rainey’s model are applied respectively to calculate the nonlinear wave loads on a bottom-hinged vertical cylinder in focused waves.Resonant ringing response excited by the nonlinear high-frequency wave loads is found in the numerical simulation when frequency ratios(natural frequency of the structure to peak frequency of wave spectra)are equal to 3–5.Dynamic amplification factor of ringing response is also investigated for different dynamic properties(natural frequency and damping ratio)of the structure.

Visualization of Double-Diffusive Convection and Unsteady Solidification on a Vertical Circular Cylinder

This paper describes experimental results on the solidification process over the vertically positioned circular cylinder, placed in an aqueous solution of sodium nitrate, where the aqueous solution in the vessel is heated from the bottom. After the initiation of solidification by cooling the cylinder below the liquidus temperature, the pure ice formation on the cylinder causes the rejection of solute into the surrounding aqueous solution. The solute enriched vertical fluid layer over the ice then falls on the bottom of the vessel due to its higher density, and accumulates there. This process results in the formation of solute rich and hot horizontal layer (heavy layer), underlying the relatively cold but less concentrated fluid layer (light layer). As this process advances, however, because of the continuing influx of solute rich fluid, the lower heavy layer occupies more space, and the interface of the two layers rises slowly. The pH indicator method has been successfully employed in order to visualize the flows during this process. In this report, we document the evolution of both temperature and flow fields in the aqueous solution quantitatively, as the solidification progresses and the density discontinuity of the two layers rises.

Transient analysis of Casson fluid thermo-convection from a vertical cylinder embedded in a porous medium: Entropy generation and thermal energy transfer visualization

Thermal transport in porous media has stimulated substantial interest in engineering sciences due to increasing applications in filtration systems,porous bearings,porous layer insulation,biomechanics,geomechanics etc.Motivated by such applications,in this article,a numerical study of entropy generation impacts on the heat and momentum transfer in time-dependent laminar incompressible boundary layer flow of a Casson viscoplastic fluid over a uniformly heated vertical cylinder embedded in a porous medium is presented.Darcy’s law is used to simulate bulk drag effects at low Reynolds number for an isotropic,homogenous porous medium.Heat line visualization is also included.The mathematical model is derived and normalized using appropriate transformation variables.The resulting non-linear time-dependent coupled governing equations with associated boundary conditions are solved via an implicit finite difference method which is efficient and unconditionally stable.The outcomes show that entropy generation and Bejan number are both elevated with increasing values of Darcy number,Casson fluid parameter,group parameter and Grashof number.To analyze the heat transfer process in a two-dimensional domain,plotting heat lines provides an excellent approach in addition to streamlines and isotherms.It is remarked that as the Darcy number increases,the deviations of heat lines from the hot wall are reduced.

Conceptual Analysis of a Time-Dependent Double-Diffusive Flow over a Semi-Infinite Vertical Plate

This study is devoted to the analysis of a one-dimensional time-dependent double-diffusive flow over a semi-infinite vertical plate, under a convective surface boundary condition. Using similarity variable, the governing nonlinear partial differential equations have been transformed into a set of coupled nonlinear ordinary differential equations, which are solved numerically by using shooting method alongside with Runge-Kutta integration scheme as embedded in Maple software programme. The numerical results of the skin-friction coefficient, the Nusselt and Sherwood numbers are discussed and depicted graphically.

Numerical Investigation of Run-ups on Cylinder in Steep Regular Wave

The run-up on offshore structures induced by the steep regular wave is a highly nonlinear flow with a free surface. This article focuses on the investigation of the steep regular wave run-up on a single vertical cylinder by solving the Navier-Stokes equations. A numerical wave tank is established based on the open-source package to simulate the wave scattering induced by a vertical cylinder. The VOF method is applied to capture the large deformation and breaking of the free surface. The numerical model is validated by experimental results. The relative wave run-ups on the front face and the back face along the centerline of a cylinder are analyzed. The changes of the relative run-ups with the wave steepness, the relative diameter and the relative depth are studied. It is found that the relative run-ups on the front face and the back face of the cylinder depend mainly on the wave steepness and the relative diameter, while the dependence on the relative depth is weak. The empirical formulae are proposed to calculate the relative run-ups in terms of the wave steepness of incident regular waves and the relative diameter of a cylinder.

Thermal Diffusion Effect on MHD Heat and Mass Transfer Flow past a Semi Infinite Moving Vertical Porous Plate with Heat Generation and Chemical Reaction

The objective of present work is to study the thermo diffusion effect on an unsteady simultaneous convective heat and mass transfer flow of an incompressible, electrically conducting, heat generating/absorbing fluid along a semi-infinite moving porous plate embedded in a porous medium with the presence of pressure gradient, thermal radiation field and chemical reaction. It is assumed that the permeable plate is embedded in a uniform porous medium and moves with a constant velocity in the flow direction in the presence of a transverse magnetic field. It is also assumed that the free stream consists of a mean velocity, temperature and concentration over which are super imposed an exponentially varying with time. The equations of continuity, momentum, energy and diffusion, which govern the flow field, are solved by using a regular perturbation method. The behavior of the velocity, temperature, concentration, Skin-friction, rate of heat transfer and rate of mass transfer has been discussed for variations in the physical parameters. An increase in both Pr and R results a decrease in thermal boundary layer thickness. However, concentration decreases as Kr, Sc increase but it increases with an increase in both So and δ.

Axisymmetry Breaking to Travelling Waves in the Cylinder with Partially Heated Sidewall

The transition from an axisymmetric stationary flow to three-dimensional time-dependent flows is carefully studied in a vertical cylinder partially heated from the side, with the aspect ratio A = 2 and Prandtl number Pτ=0.021. The flow develops from the steady toroidal pattern beyond the first instability threshold, breaks the axisymmetric state at a Rayleigh number near 2000, and transits to standing or travelling azimuthal waves. A new result is observed that a slightly unstable flow pattern of standing waves exists and will transit to stable travelling waves after a long time evolution. The onset of oscillations is associated with a supercritical Hopf bifurcation in a system with O（2） symmetry.

Oscillations of elastically mounted cylinders in regular waves

Under the assumption of potential flow and linear wave theory, a semi-analytic method based on eigenfunciton expansion is proposed to predict the hydrody-namic forces on an array of three bottom-mounted, surface-piercing circular cylinders. The responses of the cylinders induced by wave excitation are determined by the equa-tions of motion coupled with the solutions of the wave radiation and diffraction problems. Experiments for three-cylinder cases are then designed and performed in a wave flume to determine the accuracy of this method for regular waves.

RULE OF TRANSIENT PHREATIC FLOW SUBJECTED TO VERTICAL AND HORIZONTAL SEEPAGE

In a semi-infinite aquifer bounded by a channel, a transient flow model is constructed for phreatic water subjected to vertical and horizontal seepage. Based on the first linearized Boussinesq equation, the analytical solution of the model is obtained by Laplace transform. Having proven the transformation between the analytical solution and some relevant classic formulas, suitable condition for each of these formulas is demonstrated. On the base of the solution, the variation of transient flow process caused by the variables, such as vertical infiltration intensity, fluctuation range of river stage, aquifer parameters such as transmissivity and specific yield, and the distance from calculating point to channel boundary, are analyzed quantitatively one by one. Lagging effect will happen to the time, when phreatic water gets its maximum fluctuation velocity, response to the varying of the variables stated above. The condition for some variables to form equivalent lagging effect is demonstrated. Corresponding to the mathematical charac teristics of the analytical solution, the physical implication and the fluctuation rule of groundwater level are discussed.

Development and Flow Modes of Vertical Taylor-Couette System with Free Surface

We have numerically and experimentally investigated the flow modes of Taylor-Couette system consisting of coaxial two cylinders with vertical axes. The inner cylinder rotates and the outer cylinder and the bottom end of the cylinders remain stationary. The upper top boundary is the free surface of the working liquid between the inner and outer cylinders and it contacts with the air. While this flow appears in fluid machinery and chemical reactors and includes industrial interests, it also contains problems of fluid mechanics, which is about the behavior of the free surface in the rotating field. In this paper, we concretely show the developments of the one cell mode flow and the three cell mode flow at a small aspect ratio. We also represent the bifurcation diagram of the flow at the moderate aspect ratio about 5.5. In the numerical simulation, the flow is rest in the initial state, and the inner cylinder is linearly or suddenly accelerated to attain a flow with a prescribed Reynolds number. When the acceleration of the inner cylinder is high, an imperfect bifurcation occurs and the flows of the secondary modes emerge. At high Reynolds numbers, the flow first has many vortices and then some of the vortices collapse and the final stable flow arises. The loci of the normal five cell mode, the anomalous six cell mode and the secondary seven cell mode are determined.

A numerical investigation of interactions between extreme waves and a vertical cylinder

In this paper,the interactions between extreme waves and a vertical cylinder are investigated through a 3-D two-phase flow model.The numerical model is verified and validated by experimental data.Then,two factors are considered,the global wave steepness and the frequency bandwidth of the wave groups,in the studies of the in-line wave forces and the wave run-up around a cylinder.It is found that both the in-line wave forces and the wave run-up are remarkably increased with the increase of the global wave steepness,whereas the effect of the frequency bandwidth on the in-line wave forces is relatively weak in comparison with its effect on the wave run-up.The minimum and maximum wave run-ups are located in the directions of 22.5°and 180°with respect to the direction of the incident waves,respectively.Additionally,a new empirical formula is proposed for predicting the in-line wave forces by using only the free surface elevations around the cylinder.The results of the formula agree well with the simulation results.