Archive | 2019
A Semi-Analytical Method for Calculating the Hydrodynamic Force on Perforated Plates in Oscillating Flow
Abstract
A two-dimensional numerical analysis on the hydrodynamic force of perforated plates in oscillating flow is presented, and a new semi-analytical force model is proposed. Plates with ten different perforation ratios, τ , from 0.05 to 0.50 are simulated. The Keulegan–Carpenter numbers in the simulations cover a range from 0.002 to 2.2 when made nondimensional with the width of the plates. Resulting hydrodynamic added mass and damping coefficients are presented. All perforated plates with perforation ratios greater than or equal to 10% are found to be damping dominant. The numerical results are obtained using a twodimensional Navier–Stokes solver (CFD), previously validated against dedicated 2D experiments on perforated plates. Furthermore, we present verification of the code against the analytical solid flat plate results by Graham. The presently obtained hydrodynamic coefficients are compared with the state-of-the-art semi-analytical method for force coefficient calculation of perforated plates by Molin, as well as the recommended practice for estimating hydrodynamic coefficients of perforated structures by DNV GL. Based on the CFD results, a new method for calculating the hydrodynamic force on perforated plates in oscillating flow is presented. The method is based on curve fitting the present CFD results for perforated plates, to the analytical expressions obtained for solid plates by Graham. In addition to its simplicity, a strength of the method is that coefficients for both the added mass and damping are obtained. ∗Corresponding author: [email protected] INTRODUCTION Perforated and ventilated structures are commonly found in many marine applications. Examples include heave plates, wave absorbers, damping plates, hatch covers, mudmats and various protection equipments used on complex subsea structures. Many of these structures have large widths and lengths compared to their thickness, and can, in terms of flow and resulting loads, be simplified as perforated plates. Due to the industrial relevance, there has been a great deal of analytical, numerical and experimental investigations on perforated plates. Molin [1] presented an extensive review in 2011. A brief summary of some other relevant studies performed after 2011 is given in [2]. The present study is part of a bigger project (MOVE), where the motivation is to reduce uncertainty when performing marine deployment operations, which is likely to be cost saving by reducing conservatism and delays when it comes to the time used on waiting for acceptable weather conditions. The hydrodynamic behavior and forces on perforated plates are relevant in this respect. One objective of the project involves increased knowledge on the hydrodynamic loads on typical members of subsea structures, including how to account for interaction and shielding effects between different member types. In an initial study, experimentally obtained hydrodynamic force coefficients for different configurations of perforated plates and cylinders were presented [3]. The hydrodynamic forces on perforated plates is identified as the most important contribution to the total force on a subsea module. Challenges with estimating the hydrodynamic coefficients from experiments were highlighted. The initial study 1 Copyright c © 2019 by ASME was followed up with further experimental investigations and the development of a numerical viscous flow solver which can estimate hydrodynamic coefficients of subsea structures in a twodimensional setting [2]. Special attention was given to the effect of flow separation at the ends of perforated plates, which has been pointed out by several previous studies to be of importance [1, 4–7]. In the current study, we present a numerical analysis on the hydrodynamic forces of perforated plates in oscillating flow. We compare results from our numerical viscous solver with the stateof-the-art method for calculating hydrodynamic coefficients of perforated plates, and focus on how to easily estimate hydrodynamic coefficients of perforated plates. A large range of numerical simulations are performed for perforated plates with perforation ratios, τ , from 0.05 to 0.50, for Keulegan–Carpenter (KC) numbers,