Body In Potential Flow Research Articles

Quantification of added-mass effects using particle image velocimetry data for a translating and rotating flat plate

Added mass characterises the additional force required to accelerate a body when immersed in an ideal fluid. It originates from an asymmetric change to the surrounding pressure field so the fluid velocity satisfies the no-through-flow condition. This is intrinsically linked with the production of boundary vorticity. A body in potential flow may be represented by an inviscid vortex sheet and added-mass forces determined using impulse methods. However, most fluids are not inviscid. It has been theorised that viscosity causes the ‘added-mass vorticity’ to form in an intensely concentrated boundary layer region, equivalent to the inviscid distribution. Experimentally this is difficult to confirm due to limited measurement resolution and the presence of additional boundary layer vorticity, some the result of induced velocities from free vorticity in the flow field. The aim of this paper is to propose a methodology to isolate the added-mass vorticity experimentally with particle image velocimetry, and confirm that it agrees with potential flow theory even in separated flows. Experiments on a flat-plate wing undergoing linear and angular acceleration show close agreement between the theoretical and measured added-mass vorticity distributions. This is demonstrated to be independent of changes to flow topology due to flow separation. Flow field impulse and net force are also consistent with theory. This paper provides missing experimental evidence coupling added mass and the production of boundary layer vorticity, as well as confirmation that inviscid unsteady flow theory describes the added-mass effect correctly even in well-developed viscous flows.

Low-order modeling of wind farm aerodynamics using leaky Rankine bodies

We develop and characterize a low-order model of the mean flow through an array of vertical-axis wind turbines (VAWTs), consisting of a uniform flow and pairs of potential sources and sinks to represent each VAWT. The source and sink in each pair are of unequal strength, thereby forming a “leaky Rankine body” (LRB). In contrast to a classical Rankine body, which forms closed streamlines around a bluff body in potential flow, the LRB streamlines have a qualitatively similar appearance to a separated bluff body wake; hence, the LRB concept is used presently to model the VAWT wake. The relative strengths of the source and sink are determined from first principles analysis of an actuator disk model of the VAWTs. The LRB model is compared with field measurements of various VAWT array configurations measured over a 3-yr campaign. It is found that the LRB model correctly predicts the ranking of array performances to within statistical certainty. Furthermore, by using the LRB model to predict the flow around two-turbine and three-turbine arrays, we show that there are two competing fluid dynamic mechanisms that contribute to the overall array performance: turbine blockage, which locally accelerates the flow; and turbine wake formation, which locally decelerates the flow as energy is extracted. A key advantage of the LRB model is that optimal turbine array configurations can be found with significantly less computational expense than higher fidelity numerical simulations of the flow and much more rapidly than in experiments.

Higher order hydrodynamic interaction between two slender bodies in potential flow

In this paper, we apply the slender body theory to study the effect of higher order hydrodynamic interactions between two slender bodies of revolution moving in close proximity, in an unbounded, inviscid, and incompressible fluid. We compare between leading and second-order approximations, as well as approximate and exact separation distances. The total solution is found to be valid for both small and large lateral separation distances. The contribution of the higher order forces is found to be relatively small for large separation distances, though significant for small separation distances. Comparisons with measurements and simulations are satisfactory.

The dynamics of a rigid body in potential flow with circulation

We consider the motion of a two-dimensional body of arbitrary shape in a planar irrotational, incompressible fluid with a given amount of circulation around the body. We derive the equations of motion for this system by performing symplectic reduction with respect to the group of volume-preserving diffeomorphisms and obtain the relevant Poisson structures after a further Poisson reduction with respect to the group of translations and rotations. In this way, we recover the equations of motion given for this system by Chaplygin and Lamb, and we give a geometric interpretation for the Kutta-Zhukowski force as a curvature-related effect. In addition, we show that the motion of a rigid body with circulation can be understood as a geodesic flow on a central extension of the special Euclidian group SE(2), and we relate the cocycle in the description of this central extension to a certain curvature tensor.

The dynamics of a rigid body in potential flow with circulation

We consider the motion of a two-dimensional body of arbitrary shape in a planar irrotational, incompressible fluid with a given amount of circulation around the body. We derive the equations of motion for this system by performing symplectic reduction with respect to the group of volume-preserving diffeomorphisms and obtain the relevant Poisson structures after a further Poisson reduction with respect to the group of translations and rotations. In this way, we recover the equations of motion given for this system by Chaplygin and Lamb, and we give a geometric interpretation for the Kutta-Zhukowski force as a curvature-related effect. In addition, we show that the motion of a rigid body with circulation can be understood as a geodesic flow on a central extension of the special Euclidian group SE(2), and we relate the cocycle in the description of this central extension to a certain curvature tensor.

Note on the induced Lagrangian drift and added-mass of a vortex

Darwin (1953) introduced a simple heuristic that relates the Lagrangian fluid drift induced by a solid body propagating in irrotational flow to its virtual- or added-mass. The force required to accelerate the solid body must also overcome this added-mass. An extension of Darwin's (1953) method to the case of vortices propagating in a real fluid is described here. Experiments are conducted to demonstrate the existence of an added-mass effect during uni-directional vortex motion, which is analogous to the effect of solid bodies in potential flow. The definition of the vortex added-mass coefficient is modified from the solid body case to account for entrainment of ambient fluid by the vortex. This modified coefficient for propagating vortices is shown to be equal in magnitude to the classical coefficient for a solid body of equivalent boundary geometry. An implication of these results is that the vortex added-mass concept can be used as a surrogate for the velocity potential, in order to facilitate calculations of the pressure contribution to forces required to set fluid into unsteady vortical motion. Application of these results to unsteady wake analyses and fluid–structure interactions such as vortex-induced vibrations is suggested.

Synthesis of two-dimensional bodies in potential flow

This paper describes the incorporation of simple potential flow theory with limited interactive graphics to produce a computer program for the potential flow analysis of a wide variety of two-dimensional bodies. The general program approach is explained and three particularly effective program techniques developed specifically for use in this program are described. These techniques allow the location of stagnation points, the closure of a streamline, and the tracing of streamline patterns for complex flow. Several possible applications of the program are cited and some examples of these applications are shown.