The unsteady forces acting on a body depend strongly on the local flow structures such as vortices. A quantitative understanding of the contribution of these structures to the instantaneous overall force is of fundamental significance. In the present study, a three-dimensional (3-D) vortex force map (VFM) method, extended from a two-dimensional (2-D) one, is used to provide better insight into the complex 3-D flow dynamics. The VFM vectors are obtained from solutions of potential equations and used to build the 3-D VFMs where the critical regions and directions associated with significant positive or negative contributions to the forces are identified. Using the existing velocity/vorticity field near the body, these VFMs can be used to obtain the body forces. A decomposed form of the force formula is also derived to separate the correction term contributed from the uncaptured vortices (close to or far away from the body). The present method is applied to the starting flow of a delta wing at high angle of attack, where LEVs are enhanced and stabilized by an axial flow effect. The analogy between the normal force of a slender delta wing and that of a 2-D flat plate with a steadily growing span is demonstrated via the VFM analysis. We find, for this application, that the force evolution exhibits some similar behaviour to a 2-D airfoil starting flow and, surprisingly, the force contribution mainly comes from the conical vortex sheet rather than the central core. Moreover, a quantitative understanding of the influence of LEVs in different evolution regimes on the body force is demonstrated.

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Vortex force maps for three-dimensional unsteady flows with application to a delta wing

In this paper, a dynamic model of an offshore drilling riser is developed based on the Hamilton principle. The developed dynamic model is transformed into a finite element model by introducing an approximate solution which chooses the Hermite cubic interpolation function of bending beam element as the shape function. Thereafter, the standard Newmark integration is applied to numerically simulate the dynamic responses of offshore drilling risers with varied system parameters, including the length of riser, top tension ratio, and buoyant factor. Based on the results of numerical simulation, under the influences of sea wind, sea current, and the periodic excitation of sea wave, the offshore drilling riser experiences a fast lateral deflection phase in the beginning, a reciprocating deflection phase in the following long duration, and then, a periodic oscillation when it reaches the dynamic stable condition, respectively. The riser system working in deeper water with a higher top tension ratio and a lower buoyant factor shows more controllable vibration and less lateral deflection.

/pdf/mathematical-modelling-and-dynamic-analysis-of-an-offshore-2qg2la06u4.pdf

Mathematical Modelling and Dynamic Analysis of an Offshore Drilling Riser

Dynamic responses of a flexible pipe conveying variable-density fluid and experiencing cross-flow and in-line coupled vortex-induced vibrations

An experimental investigation on interfering VIVs of double and triple unequal-diameter flexible cylinders in tandem

Influence of the internal varying density flow on the vibrations and fatigue damage of a top-tensioned riser undergoing vortex-induced vibrations

Drag and added mass coefficients of a flexible pipe undergoing vortex-induced vibration in an oscillatory flow

Magnification of hydrodynamic coefficients on a flexible pipe fitted with helical strakes in oscillatory flows

The formation and evolution of wingtip vortex system generated from three wing configurations are simulated with the improved delayed detached eddy simulation (IDDES) method. Numerical results show that each layout produces an interacting wingtip vortex system. These three corresponding vortical interactions are, respectively, the interaction between wingtip vortex and its counter-rotating vortex, winglet-tip vortex, and winglet four-vortex system. The fluid entrainment of ambient fluid and vortical impulse transport resulted from inductive effect have been founded generally existing in its formation and evolution. These two dominated mechanisms account for induced drag generation. On one hand, the winglet with toed-out angle is considered capable of changing the flow field around the winglet, and decomposing the winglet-tip vortex into four small vortices. Due to quite few fluid entrainment effects, this typical four-vortex system that cannot merge and only dissipate in the near wake scarcely contributes to the induced drag. On the other hand, a potential drag reduction method is also indicated that a lower induced drag can be obtained when the merger of wingtip and winglet-tip vortex is controlled and eliminated. This investigation will offer a novel perspective to guide the design of wingtip device and method of crusing resistance reduction for aircrafts.

Yifan Wang

Papers

Drag and added mass coefficients of a flexible pipe undergoing vortex-induced vibration in an oscillatory flow

Magnification of hydrodynamic coefficients on a flexible pipe fitted with helical strakes in oscillatory flows

Generation Mechanism and Reduction Method of Induced Drag Produced by Interacting Wingtip Vortex System