Evaluation of drag minimum for catenary curve using approximatecatenary trajectory and equivalent build up section
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For an extended reach drilling simulation, many important techniques arerequired. Torque and drag prediction is one of them. There is an opinion that catenary trajectorycan minimize drag. However, as drag is accumulated upward, drag is affected not only by bendingrate but by hook load and inclination angle at lower end of catenary. For a temporary evaluationwhether drag of catenary is the minimum or not, two types of trajectory are compared throughsimulation study. One is an approximate catenary trajectory which composed of multiple build upsection with different bending rate, and another is equivalent build up section which has the sameinclination angle and lower end as the former. The following findings are obtained.(1) Drag of approximate catenary trajectory does not remarkably decrease comparing with thatof equivalent build up section.(2) When drag of catenary trajectory decreases comparing original build up section, the majordecrease of drag may be contributed to the connecting downward tangent section.(3) In this sense, the effect of catenary for drag decrease may be said that catenary can increaseinclination angle, since high inclination angle can decrease drag over downward tangentsection.Keywords:
Catenary
ABSTRACT The flow field around a circular bridge pier is a complex three-dimensional phenomenon. Notwithstanding the considerable effort made in the study of local scour by many researchers, an understanding of the mechanics of local scour around a bridge pier remains far from complete. The drag force exerted on the structure is related to the wake. Larger the wake, higher is the drag force and scour potential. Efforts to reduce the drag by reducing/altering the wake structure are widely reported in literature. Use of slot-collar combination is one among them. In this study, an attempt has been made to establish the drag characteristics of cylindrical pier models, with different slot-collar combinations. This experimental study is conducted using a physical hydraulic model operated under clear-water and rigid bed conditions. All the experiments are conducted in a re-circulating tilting flume. Experiments are run for different combinations of slot and collar. Drag coefficient of the pier is computed using the momentum equation. The drag studies indicate that the drag coefficient in general is found to decrease with the provision of slot/collar. The value of drag coefficient is reduced by about 33 % for a bottom slot/collar combination.
Flume
Collar
Drag equation
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Abstract Modeling flow in a coral reef requires a closure model that links the local drag force to the local mean velocity. However, the spatial flow variations make it difficult to predict the distribution of the local drag. Here we report on vertical profiles of measured drag and velocity in a laboratory reef that was made of 81 Pocillopora Meandrina colony skeletons, densely arranged along a tilted flume. Two corals were CT‐scanned, sliced horizontally, and printed using a 3‐D printer. Drag was measured as a function of height above the bottom by connecting the slices to drag sensors. Profiles of velocity were measured in‐between the coral branches and above the reef. Measured drag of whole colonies shows an excellent agreement with previous field and laboratory studies; however, these studies never showed how drag varies vertically. The vertical distribution of drag is reported as a function of flow rate and water level. When the water level is the same as the reef height, Reynolds stresses are negligible and the drag force per unit fluid mass is nearly constant. However, when the water depth is larger, Reynolds stress gradients become significant and drag increases with height. An excellent agreement was found between the drag calculated by a momentum budget and the measured drag of the individual printed slices. Finally, we propose a modified formulation of the drag coefficient that includes the normal dispersive stress term and results in reduced variations of the drag coefficient at the cost of introducing an additional coefficient.
Flume
Drag equation
Zero-lift drag coefficient
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Flume
Drag equation
Zero-lift drag coefficient
Wave drag
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Settling
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Settling time
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A body moving through a fluid experiences drag, which primarily consists of two components: form drag and viscous drag. At high velocities, the form drag predominates whereas at low velocities, the viscous drag predominates. The form drag is characterized by the drag coefficient which is determined experimentally for various configurations. Similarly, the viscous drag is characterized by the drag constant which in turn is known only for specific cases and its generic governing model is not well established yet. The current study puts forward a generalized mathematical model for determination of the drag constant for frontally streamlined small axisymmetric bodies moving slowly through a fully-enclosing fluid at zero angle of attack. It has been accomplished by establishing a governing mathematical model for viscous drag, validating it via wind tunnel experiments and then comparing it with the standard linear drag equation. Conclusively, the drag constant has been determined in terms of the fluid properties and dimensions of the moving body. This paper describes the above-mentioned mathematical model followed by the process of its experimental validation and determination of drag constant.
Drag equation
Constant (computer programming)
Wave drag
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Drag equation
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Non-spherical particles and their interaction with the surrounding fluids are omnipresent in nature and industry. While moving through fluids, particles are subjected to drag forces which is key in understating their dynamic behaviour and is highly dependent on their shape. In this research, to investigate the drag force acting on ellipsoidal particles, numerical simulations and twelve drag models are utilised to predict the particles' drag coefficients. The results are compared in a unified framework using Zingg charts. Most models compare well with the simulation results in both drag coefficient values and trends. The maximum error of these models ranges from 40% to 150%. Some models such as Haider and Levenspiel, Ganser, and Leith are capable in estimating the ellipsoids' drag coefficient with high accuracy while others either overestimate or underestimate the values. Each drag model is suitable for particles in a specific shape category including compact, bladed, elongated, or flat.
Ellipsoid
Drag equation
Zero-lift drag coefficient
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This paper presents numerical predictions of drag parachutes using commercial software. Two models of drag chutes with different projected area were selected to examine their flow dynamics parameters such as drag coefficient, drag force and flow characteristics downstream the drag chutes. Turbulent ranges of flow speed were considered. It was seen that the improved version of drag chute gave more stability in flow dynamics compared to the conventional type of drag chute.
Zero-lift drag coefficient
Drag equation
Wave drag
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Modeling flow in a coral reef requires a closure model that links the local drag force to the local mean velocity. However, the spatial flow variations make it difficult to predict the distribution of the local drag. Here we report on vertical profiles of measured drag and velocity in a laboratory reef that was made of 81 Pocillopora Meandrina colony skeletons, densely arranged along a tilted flume. Two corals were CT-scanned, sliced horizontally, and printed using a 3-D printer. Drag was measured as a function of height above the bottom by connecting the slices to drag sensors. Profiles of velocity were measured in-between the coral branches and above the reef. Measured drag of whole colonies shows an excellent agreement with previous field and laboratory studies; however, these studies never showed how drag varies vertically. The vertical distribution of drag is reported as a function of flow rate and water level. When the water level is the same as the reef height, Reynolds stresses are negligible and the drag force per unit fluid mass is nearly constant. However, when the water depth is larger, Reynolds stress gradients become significant and drag increases with height. An excellent agreement was found between the drag calculated by a momentum budget and the measured drag of the individual printed slices. Finally, we propose a modified formulation of the drag coefficient that includes the normal dispersive stress term and results in reduced variations of the drag coefficient at the cost of introducing an additional coefficient.
Flume
Drag equation
Zero-lift drag coefficient
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This paper describes a new method and a set of equations for calculating the force-deflection characteristics of the catenary anchor leg. The traditional catenary equations reference horizontal deflection of the catenary top to the catenary generation point which is used to mathematically ?generate" the catenary curve shape. The catenary generation point is not stationary; its horizontal and vertical positions change as the catenary deflects. Thus several cumbersome calculations are required to relate deflection to its original position in the no-load case. The simplified catenary equations, discussed in this paper, directly reference the horizontal catenary top deflection to a stationary point corresponding to the no-load or undeflected position of the catenary. They avoid the complexities of calculating the scope of the catenary and the position of the catenary generation point. This greatly simplifies the analysis of catenary anchor leg moorings. The simplified catenary equations are presented for two cases. In the first case, the lowest point of the catenary, called the base point, is tangent to the ground plane, so that no uplift is applied. In the second case, the catenary applies an uplift force to an anchor on the ground plane, and the base point is below the ground plane. This paper will be of interest to the designers of catenary mooring systems, suspension bridges and other catenary structures and systems.
Catenary
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