The Force Distribution Exerted by Surface Waves on Piles

Abstract

t Experimental data for the foroe distribution on three model oylindrioal piles for three nave conditions.are presented. These results are compared to the previously published theory.**' Introduetiom The purpoao of this report is to present experimental data on the foroe distribution exerted by surfaoe waves on piles* From these data the ooeffioients of drag and mass that appear in the equation**' for the foroe were obtained* The experimental results were compared to the calculated foroe distribution* In order to simplify the presentation, the foroe (lbs) was divided by the projected area ( Figure 1)* The displacement of the pile segment was converted to a foroe by means of a oonversion faotor obtained by calibration. In order to obtain a flow pattern similar to a continuous pile and to reduce the tare on the pendulum rod, a cylindrical shroud representing a pile was plaoed between the one-inoh segment and the pivot (whioh was always above the wave surfaoe)* By the use of a frame, a dummy pile seotion was held below the one-inoh segment to represent the lower portion of a oontinuous pile* The tare of the system without the segment was a very small peroentage of the foroe on the segment* The natural frequency of the system was relatively near the frequency of the uniform, periodio wave trains* This oaused considerable, unavoidable trouble whioh the one-inoh segment was near the surfaoe of the waves; ©specially when the waves were very steep and when the waves were in relatively shallow water* "lumbers in ( ) are reference numbers.

Performance Characteristics of a Suspended‐Catalyst Oscillatory Membrane Photocatalytic Reactor

“…in which ε is the power dissipation per unit mass of the fluid (W kg −1 ), which for a channel spacing S ch may be determined from the fluid force F f acting on the promoters using the Morison equation . For an oscillatory surface with N promoters, this force is given as …”

Offshore turbines with bottom-fixed or floating substructures

“…In recent simulation studies for FOWTs, Morison's equation has always been considered as an alternative option to the panel code method with Cummins' equation (as described in more detail later). Originally, Morison's equation was developed to model the ocean wave forces on slender piles fixed at the seabed, see [63]. It models the horizontal force ∆ f f f in the normal directions k of the body surface on a discrete "strip" i, which is a cylindrical section with diameter D and length ∆l.…”

Iterative Frequency-Domain Response of Floating Offshore Wind Turbines with Parametric Drag

“…In the time-domain, the frequency-dependence results in a convolution integral, representing fluid memory effects (see Cummins' equation [20]). Viscous effects are usually accounted for through the inclusion of the quadratic drag term of Morison's equation [21]. This drag results on the one side in an excitation force, due to the wave particle motion, next to the Froude-Krylov and diffraction pressures from the panel code computation.…”

“…Morison's original formulation [21] was extended for the present work to account, firstly, for the relative fluid velocity due to the body motion and secondly, for heave plates with force components in vertical direction (in the body-fixed frame). The substructure is discretized through nodes as shown in Figure 2.…”