Low KC Numbers Research Articles

Bilge keel load and hull pressure distribution on a rolling ship section with a high-order fractional step finite volume solver

Bilge keel load and hull pressure distribution are investigated. For this purpose, harmonic excited rolls of the mid-section of a KVLCC2 fitted with one bilge keel are simulated by means of a high-order fractional step finite volume solver. Fourier analysis is employed to derive drag and inertia coefficients in Morison equation and the corresponding higher harmonic terms from bilge keel load. The calculated drag and inertia coefficients as well as positive and negative pressure coefficients are validated with some published numerical and experimental results. Influence of the roll amplitude and circular frequency, height and thickness of the bilge keel, and draught is presented. In results, drag and inertia coefficients is solely determined by KC number. Effect of draught, circular frequency and thickness of bilge keel is minuscule and negligible. Bilge keel load shows pronounced nonlinearity, which reveals the importance of the higher harmonic terms. Besides, drag coefficient and jump of the pressure coefficient satisfy the relationship assumed by Ikeda et al. (1977a). Positive pressure coefficient in front of bilge keel is KC-dependent at low KC number especially when KC < 6. The empirical method underestimates the positive pressure at low KC number and overestimates the negative pressure.

Numerical based approach for predicting the response of flexible risers under oscillatory flows at Low Re and KC numbers

La predicción de respuesta en tuberías verticales flexibles se basa en modelos semiempíricos limitados por escasez de datos experimentales para modelados particulares. Este artículo presenta un enfoque numérico para predecir la respuesta de tuberías verticales flexibles en flujos oscilatorios. Se implementa un grado de libertad en un sistema de masa-resorte amortiguado, con la masa habilitada para moverse en la dirección transversal al flujo. Las ecuaciones de Navier-Stokes son discretizadas empleando el Método de Volúmenes Finitos. Los patrones de flujo en cada régimen son analizados en períodos de oscilación extensos. Se emplea un modelo bidimensional simulado en OpenFOAM. Se analiza el comportamiento del flujo, fuerzas hidrodinámicas y frecuencias para los valores de Reynolds entre 40 y 1000 utilizando 𝑲𝑪 𝟕, 𝟗. Para Reynolds, inferiores a 300, el comportamiento del modelo está de acuerdo con la literatura. Para valores de Reynolds 300 o más, algunas discrepancias aparecen en la dinámica del sistema. Los resultados numéricos obtenidos apartir del enfoque numérico propuesto concuerdan con los datos experimentales recopilados en un modelo de tubería vertical flexible

Computation of flow features and hydrodynamic coefficients around heave plates oscillating near a seabed

For the past few years, heave plates have been used in the offshore industry due to their favorable hydrodynamic characteristics in oscillating flows, i.e., increased added mass and damping. The hydrodynamic coefficients of heave plates are strongly influenced by the proximity of solid boundaries. Assessing how this variation depends on the proximity to the seabed and on the amplitude of the oscillation is the main aim of this paper. In this process, a new model describing the work done by damping in terms of the flow enstrophy is described herein. This new approach is able to provide a direct correlation between the vortex shedding processes and the linear damping coefficient. Numerical simulations have been performed using the finite volume open source solver OpenFOAM. Simulations have been conducted on a solid circular disc oscillating axially in water at various elevations above an impermeable seabed boundary. Results for hydrodynamic coefficients are validated against previously published experimental data. At low KC numbers, a systematic increase in added mass and damping, corresponding to an increase in the seabed proximity, is observed. As seen in experiments, a critical KC where the monotonic trend of the hydrodynamic coefficients with KC is disrupted and that depends on the seabed distance exists. The physical behavior of the flow around the critical KC is explained through an analysis of the flow enstrophy.

An Experimental Study on the Characteristics of Drag Force acting on a Flat Plate under Transitional and Irregular Oscillations

In order to guarantee the safety of vessels, it is very important to understand the characteristics of roll damping and to estimate it accurately. Because it affects the occurrence of parametric rolling and its amplitude significantly. However, it is very complicated to calculate roll damping theoretically, because of significant viscous components caused by vortex shedding. It is well-known that there is a prediction method of roll damping proposed by Ikeda for conventional displacement type mono-hull vessels, barge ships and small hard chine fishing boats. It has been developed based on theoretical and experimental backgrounds for regular roll motion. Therefore, it is difficult to apply it to computer simulation of transitional or irregular roll motion (i.e. roll motion and parametric rolling in irregular waves, broaching to capsize etc).The purpose of this study is to investigate the characteristics of drag force acting on a flat plate under transitional and irregular oscillation as a basic study, and to develop an estimation method of bilge-keel roll damping in time domain. First, under transitional motion, the characteristic of drag coefficient of flat plate at low Kc number is investigated experimentally. Second,using a forced sway motion device, the characteristic of drag coefficient of flat plate under transitional regular sway motion is investigated. Finally, based on the measured results, an estimation method of drag force of flat plate in time domain is proposed.

A 3D investigation of the dynamic loads over an array of in-line cylinders at low KC and Re numbers

The oscillating flow around an infinite array of circular cylinders at low Keulegan-Carpenter numbers and Reynolds numbers is investigated numerically using a 3D mathematical model. Three different regimes of the Tatsuno and Bearman (1990) map are investigated; the first one is a 2D symmetric regime, whereas the second and the third are asymmetric and 3D. In each regime, the gap between two neighboring cylinders has been varied in a very wide range, from the case of practically isolated cylinder to the case of very strong interference. As regards the isolated cylinder, the mean value of the inertia coefficient is much more affected by the 3D effects than that of the drag coefficient. Conversely, the variation along the axial direction of the sectional drag coefficient is much stronger than that found for the sectional inertia coefficient. In all cases investigated, the reduction of the gap between cylinders has two main effects: first, it causes the reduction of the Morison coefficients; second, in the 3D regimes, the gap enhances 3D motion in the range of moderate values due to the interaction between vortex structures released by two neighboring cylinders, whereas a further reduction of the gap in the range of small values tends to reduce the three-dimensionality of flow field up to a complete suppression occurring for very small values of the gap. Finally, we propose a very simple parameterization that gives the Morison coefficients as a function of the gap once the values for the case of isolated cylinder are known.

Forces on partly buried, tandem twin cylinders in waves at low Keulegan-Carpenter numbers

This study deals with the forces on the circular cylinder, laid on, or partly buried in the bed with a parallel twin dummy cylinder nearby and without it. They were determined by measuring the pressure distribution on the cylinder in the case of wave at low KC numbers. The forces on the cylinder were calculated by the integration of the measured pressures determined by pressure transducers on the surface of the cylinder. Force coefficients were obtained for the low KC numbers (KC<5), for the burial-depth-to-the diameter ratio = 0–0.7. The distance between axis of the measurement and dummy cylinders to diameter ratio (x/D) was 2, 1.5 and 1. The dummy cylinder was replaced downstream and upstream of the measurement cylinder.

Hydrodynamic forces on a partly buried cylinder exposed to combined waves and current

The present study extends the investigations of the hydrodynamic forces on a cylinder, laid on, or partly buried in the bed. They were determined by measuring the pressure distribution on the cylinder surface in the case of steady current, waves and coexisting flow. The pressure distribution around the cylinder was measured by using pressure transducers, which were replaced in the cylinder. Force coefficients were obtained for the ranges of Re=0.8×10 4–1.5×10 4, for steady current, low KC numbers (KC<5) for wave alone case and, for current-to-wave velocity ratio=0, 3, 6 and infinity (current) for coexisting flow. The forces were also determined for the various burial-depth-to-diameter ratios between 0 and 0.7 values of the cylinder.

Flow Characteristics of a Rectangular Cylinder with a Cross-Section of Various Width/Height Ratios Submerged in Oscillatory Flow.

The forces acting on and the flow patterns around a rectangular cylinder with a cross-section of width/height ratio of 0.2-3.0 submerged in oscillatory flow were studied by using a U-tube water tank. Measurements of both in-line and transverse forces on a rectangular cylinder were made in a wide range of Keulegan-Carpenter number (KC) from 1 to 160. The force signals were analyzed spectrally to obtain major frequencies. Flow visualization was also employed to confirm the relationship between flow patterns and force coefficients. In this paper we discussed the influence of the width/height ratio of the rectangular cylinder on the flow patterns and the fluid dynamic characteristics of the cylinder in oscillatory flow. It was found that the drag force coefficient CD of the cylinder with d/h=0.6 ratios becomes the biggest beyond KC〓120, compared to that with other d/h in oscillatory flow. The good correlation between CD and wake width has been successfully obtained. The variations of CD values in low KC number region were classified into three groups, flat-plate-type, square-cylinder-type and circular-cylinder-type by the d/h ratio. In the cases of d/h=0.4 and 0.6, a phenomenon was found that the flat-plate-type can be shifted to square-cylinder-type by changing KC number. Based on the analysis of the major frequency components of the fluctuating transverse forces, it revealed that the value of Strouhal number reduced by the maximum velocity is similar with the result in the case of a uniform flow.

Flow structure analysis around an oscillating circular cylinder at low KC number: A numerical study

Flow fields around an oscillating circular cylinder are studied by solving the incompressible Navier-Stokes equations in primitive variable formulation. A finite volume method with a pressure predictor-corrector scheme is used and the solution procedure is accelerated by a local time stepping technique. Numerical tests are carried out at the Keulegan-Carpenter number KC < 20 and Reynolds number Re < 4000. For the symmetrical flow (at either very low KC or low Re), the vorticity decaying effect is dominant in the flow field. At higher Re, the vorticity convection becomes stronger, eventually leading to the inception of the asymmetrical flow pattern. It was found that within this critical regime the artificial disturbances imposed to the flow field play an important role in determining the flow patterns: if the flow falls into the symmetrical category, it remains symmetrical even with the artificial disturbances; while if the flow falls into the unsymmetrical category, the artificial disturbances are necessary for the correct predictions. An inception boundary of the asymmetrical flow in the KC — Re plane can thus be defined through a systematic study of the response of the flow field to the small disturbances. For the asymmetrical flow (at higher KC and/or Re), several distinguished flow patterns are identified in the numerical simulations, including quasi-symmetrical flow, diagonal vortex pair shedding, transverse street and double vortex pairs shedding. Agreement between the present results and the flow visualization (particle tracing) is generally good. The forces acting on the cylinder are also predicted for both the symmetrical and the asymmetrical flows. The conventional drag and inertia coefficients are deduced and compared with other numerical and experimental results, also showing good agreement.

Investigations of wake flows of a flat plate in steady, oscillatory and combined flows

Numerical study on near wake flows of a flat plate in three kinds of oncoming flows is made by using the discrete vortex model and improved vorticity creation method. For steady oncoming flow, both gross and detailed features of the wake flow are calculated and discussed. Then, in harmonic oscillatory oncoming flow two different wake flow patterns withK c=2,4 and 10 are obtained respectively. Our results present a new wake flow pattern for lowKc numbers (Kc<5) describing vortex shedding, pairing and moving in a period of the oscillatory flow starting from rest. The calculated drag and inertia force coefficients are closer to experimental data from the U-tube than the previous results of vortex simulation. For in-line combined oncoming flow the vortex lock-in and dynamic characteristics are simulated. The results are shown to be in good agreement with experiments.

Pressure and force measurements on a cylinder oscillated sinusoidally at low and intermediate Keulegan-Carpenter numbers

This paper describes a series of tests in which a vertical, surface piercing, circular cylinder was oscillated sinusoidally in a direction normal to its axis in otherwise still water. Results are presented in the form of pressure profiles, in-line and transverse forces and associated coefficients. Free-surface influences on the fluid loading are assessed for Reynolds numbers between 50,000 and 300,000 and Keulegan-Carpenter numbers (KC) between 0·8 and 12·1. At very low KC numbers and sub-critical Reynolds numbers viscous forces cause the drag coefficient to increase. In all cases the inertia coefficient rises just above its inviscid flow value of 2 at the lowest values of KC. At Keulegan-Carpenter numbers near 3 or 4 the flow begins to separate and the drag coefficient is a minimum. For KC>5 vortex shedding occurs and the drag and lift coefficients increase. The circumferential pressure distributions are dominated by first harmonic inertia-induced or second harmonic drag-induced components at times in the cycle when the acceleration or velocity respectively are maximum.

Wave Forces Acting on Horizontally Submerged Cylinders in Irregular Waves at low Kc number

Wave Forces Acting on Horizontally Submerged Cylinders in Irregular Waves at low Kc number

Wave Forces Acting on Horizontally Submerged Cylinders in Regular Waves at Low Kc Number

Wave forces acting on circular, square and diamond cylinders and a flat plate horizontally submerged with their axises parallel to the regular wave crests are experimentally investigated.A rapid reduction of the wave forces acting on the cylinders at low Kc number region is found to be caused by a circulating flow round the cylinder which is created by viscous wake. Flow visualization demonstrates that much larger separated vortices than those in plane oscillatory flow are created in regular waves. It is found that the vortex shedding patterns in regular wave is similar to those in plane oscillatory flow at the corresponding Kc number if a new Kc, number in terms of the circumference of the orbital motion of a fluid particle in waves instead of the diameter is defined.