Calculating the Wave Force on Partially Immersed Large-Scale Horizontal Cylinders

Large-scale interceptors constitute the main structure of offshore self-driven floating marine litter collection devices,and the structural stability of such interceptors under the action of waves directly influences the overall safety of the device.When the ratio of the diameter of a horizontal cylinder in such interceptors to the incident wavelength is larger than 0.25,the wave force can be calculated by using the diffraction theory,by considering the problem as that of the interaction between the waves and a partially immersed large-scale horizontal cylinder.In this study,an analytical approach to calculate the wave force on a partially immersed large-scale horizontal cylinder was formulated by using the stepwise approximation method.Physical model tests were conducted to investigate the effects of different factors(wave height,period,and immersion depth)on the wave force on a large-scale horizontal cylinder under conditions involving short-period waves.The results show that both horizontal and vertical wave forces on the cylinder increase as the wave height(immersion depth)increases in most cases.The vertical wave force decreases with the decrease of the period.For the horizontal wave force,it increases with the decrease of the period when the wavelength is larger than the diameter of the cylinder and decreases with the decrease of the period when the wavelength is smaller than the diameter of the cylinder.

Comparison of Potential Theory and Morison Equation for Deformable Horizontal Cylinders

This study investigates the hydro-elastic behaviors of fully submerged horizontal cylinders in different regular waves.Two methods were proposed and compared in this study.The first method was based on potential theory in frequency domain and the discrete-module-beam(DMB)method,which discretizes a floating elastic structure into a sufficient number of rigid bodies while simultaneously representing the elastic behavior from beam elements with Euler-Bernoulli beam and Saint-Venant torsion.Moreover,the Morison method in time domain was employed;this method estimates wave forces from the semi-empirical Morison equation,and the elastic behavior is embodied by massless axial,bending,and torsional springs.Various parametric studies on cylinder diameter,submergence depth,and wave direction were conducted.Wave forces,dry/wet mode shapes/natural frequencies,and dynamic motions are presented and analyzed.

SECOND ORDER DIFFRACTION FORCES ON HORIZONTAL CYLINDERS

The second order diffraction forces on a floating semicircular cylinder and a submerged circular cylinder are calculated using the method of Lighthill(ref.3). The first order potential is obtained by the multipole expansion and numerical results are provided.

Viscous Effects on Wave Forces on A Submerged Horizontal Circular Cylinder

Numerical simulations are carried out for wave action on a submerged horizontal circular cylinder by means of a viscous fluid model, and it is focused on the examination of the discrepancies between the viscous fluid results and the potential flow solutions. It is found that the lift force resulted from rotational flow on the circular cylinder is always in anti-phase with the inertia force and induces the discrepancies between the results. The influence factors on the magnitude of the lift force, especially the correlation between the stagnation-point position and the wave amplitude, and the effect of the vortex shedding are investigated by further examination on the flow fields around the cylinder. The viscous numerical calculations at different wave frequencies showed that the wave frequency has also significant influence on the wave forces. Under higher frequency and larger amplitude wave action, vortex shedding from the circular cylinder will appear and influence the wave forces on the cylinder substantially.

Wave-current force on horizontal cylinder

For the calculation of wave-current force on horizontal cylinder a modified Morison's equation is used. A redefined Keulegan- Carpenter number KC2 is determined for the horizontal cylinder in wave-current co-existing field. The force coefficients are well related to the redefined KC2 number. As to the comparison with the force on vertical cylinder, the characteristics of force on horizontal cylinder are quite similar to those on vertical cylinder, but the force coefficients for horizontal cylinder are larger than those for vertical cylinder. It is proved by the authors' calculation that the results of monochromatic wave can be used directly for the determination of irregular wave-current force on horizontal cylinder in time domain.

HYDRODYNAMIC FORCE ON SMOOTH HORIZONTAL CYLINDER IN UNIFORM OSCILLATORY FLOW

The hydrodynamic forces on a smooth horizontal circular cylinder exposed to oscillating flow have been experimentally investigated at Reynolds numbers (Re) in the range 20, 000 - 260, 000 (subcritical and transcritical regimes) and Keulegan- Carpenter numbers (Kc) in the interval from 5 to 40. In the tests, the Re number and Kc number were varied inertia systematically. The drag force coefficnent CD and inertia force coefficient CM in Morison equation have been determined through the use of Least Square Method. Both total in-line force coefficient CF and transverse force (lift) coefficient CL have been analysed in terms of their maximum and root mean square values. All the in-line and lift force coefficinets were given as a function of Re and Kc number, and also their deviations with the average value have been shown. The principal results are as follows: for the Re ≥80, 000, all the hydrodynamic force coefficients, including CD, CM, CP and CL,are at best very weak functions of Reynolds number, and each of them tends towards a certain constant with increasing Kc number; for the Re< 80, 000, the drag force coefficient CD decreases with increasing Re number, and inertia force coefficient CM increases with increasing Re number.The tendencies of drag and inertia coefficients versus Kc number for the Re ≥10￣5 are very similar to the others, which are very close to the Rodenbusch and Cutierrez's (1983) but are somewhat larger than the Sarpkaya's (1976 and 1986) and Bearman et al.' s(1985).

WAVE FORCES ON INCLINED CYLINDER IN REGULAR WAVES

Through a series of model tests,the wave forces on horizontal and inclined circular cylinders are measured and analyzed.Based on Morison Equation and Stokes second order wave theory,the relationship between the hydrodynamic force coefficients with KC number and sub- merged water depth as well for horizontal cylinders are analyzed,also the relationship between the hydrodynamic force coefficients with KC number,inclined angle and the effect of water free surface as well for the inclined cylinders are investigated.