Potential Flow Theory and Numerical Analysis of Forces on Cylinders Induced by Oscillating Disturbances

2012 ◽  
Vol 134 (3) ◽  
Author(s):  
Daniel T. Valentine ◽  
Farshad Madhi
Keyword(s):  
Unsteady Flow ◽  
Vortex Shedding ◽  
Potential Flow ◽  
Model Problem ◽  
Complete Solution ◽  
Boundary Integral ◽  
Circular Cylinders ◽  
Method Of Images ◽  
Surface Distribution ◽  
Flow Problems

The complete solution of several two-dimensional potential flow problems are reported that deal with the unsteady flow around circular cylinders. Three of the flows considered are induced by an oscillating disturbance near the cylinder. The three elemental disturbances examined are (1) a pulsating source, (2) a pulsating doublet, and (3) a pulsating vortex. The formulas for the force acting on the cylinder due to each of the elemental disturbances were derived by applying the method of images. These results were checked by deriving the equivalent surface distribution of sources to model the cylinder by applying Green’s second identity. The theory helped direct the development of a boundary-integral numerical model described and applied in this paper to solve the unsteady flow around a circular cylinder due to an arbitrarily specified oscillatory disturbance near the cylinder. The numerical method is validated by comparing predictions of the force with the exact solutions. We applied the theory to examine a model problem related to the vortex-shedding force that causes vortex-induced vibration.

Unsteady Potential Flow Theory and Numerical Analysis of Forces on Cylinders Induced by Nearby Oscillating Disturbances

2009 ◽  
Author(s):  
Daniel T. Valentine ◽  
Farshad Madhi
Keyword(s):  
Numerical Model ◽  
Unsteady Flow ◽  
Potential Flow ◽  
Complete Solution ◽  
Boundary Integral ◽  
Circular Cylinders ◽  
Two Dimensional ◽  
Method Of Images ◽  
Surface Distribution ◽  
Flow Problems

The complete solution of several two-dimensional potential flow problems are reported that deal with the unsteady flow around circular cylinders. Three of the flows considered are induced by an oscillating disturbance near the cylinder. The three elemental disturbances examined are (1) a pulsating source, (2) a pulsating doublet and (3) a pulsating vortex. The formulas for the force acting on the cylinder due to each of the elemental disturbances were derived by applying the method of images and checked by deriving the equivalent surface distribution of sources to model the cylinder starting with Green’s second identity. The theory helped direct the development of a boundary-integral numerical model described and applied in this paper to solve the unsteady flow around a circular cylinder due to an arbitrarily specified oscillatory disturbance near the cylinder. The numerical method is validated by comparing predictions of the force with the exact solutions.

Potential Flow Past a Group of Circular Cylinders

1971 ◽  
Vol 93 (4) ◽  
pp. 636-642 ◽  
Author(s):  
C. Dalton ◽  
R. A. Helfinstine
Keyword(s):  
Potential Flow ◽  
Lift Coefficient ◽  
Controlling Factors ◽  
Circular Cylinders ◽  
Method Of Images ◽  
Single Cylinder ◽  
Flow Past ◽  
Inertial Coefficient

The problem of an accelerating potential flow past a group of stationary circular cylinders is considered using the method of images. The problem is formulated so that the number and location of the cylinders is arbitrary so long as there is no overlap between adjacent cylinders. Inertial and lift coefficients are determined for several different cylinder arrangements. The inertial coefficient for a cylinder can vary in either direction from its single-cylinder value of 2.0. The controlling factors on this variation are the relative geometric position of the cylinder within the group and its distance from its neighbors. These same factors determine, as is expected, the lift coefficient values. In two example configurations, there is even a drag-type force generated on an individual cylinder in the potential flow.

Appraisal of Universal Wake Numbers From Data for Roughened Circular Cylinders

1983 ◽  
Vol 105 (4) ◽  
pp. 464-468 ◽  
Author(s):  
G. Buresti
Keyword(s):  
Surface Roughness ◽  
Reynolds Number ◽  
Drag Coefficient ◽  
Vortex Shedding ◽  
Physical Interpretation ◽  
Potential Flow ◽  
Bluff Body ◽  
Cross Flow ◽  
Sufficient Accuracy ◽  
Circular Cylinders

An analysis was carried out to check whether certain existing universal wake numbers can characterize the cross-flow around roughened circular cylinders in transitional regimes. The results confirmed the soundness of the idea of the existence of a link between the drag coefficient of a bluff body, its pressure distribution, and the frequency of the shedding of vortices in its wake. In particular, Bearman’s number and Griffin’s number were shown to be able to describe this link with sufficient accuracy and to be a function of the Reynolds number based on the typical dimension of the surface roughness. A physical interpretation of Griffin’s number was also given which permits to link the drag force with the velocity of the potential flow at separation and the frequency of vortex shedding.

A Numerical Study of Vortex Shedding From One and Two Circular Cylinders

1981 ◽  
Vol 32 (1) ◽  
pp. 48-71 ◽  
Author(s):  
P.K. Stansby
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Vortex Shedding ◽  
Potential Flow ◽  
Numerical Study ◽  
Circular Cylinders ◽  
Discrete Vortex ◽  
Formation Region ◽  
Flow Features ◽  
The Mean

SummaryA discrete-vortex representation of the wake of a circular cylinder, in which vortices are convected in a potential-flow calculation and maintain their identities unless they approach one another or a surface closely, predicts many of the unsteady flow features and is computationally more efficient than other schemes. The mean rate of shedding of vorticity is adjusted to be compatible with experiments at a high subcritical Reynolds number of 3 × 104 and the model gives reasonable predictions of separation, drag, lift, Strouhal number and vorticity loss in the formation region. The method is extended to accommodate a second cylinder and many of the surprising features which have been observed experimentally with two cylinders in a side-by-side arrangement are reproduced.

scholarly journals Hydromechanics of low-Reynolds-number flow. Part 2. Singularity method for Stokes flows

1975 ◽  
Vol 67 (4) ◽  
pp. 787-815 ◽  
Author(s):  
Allen T. Chwang ◽  
T. Yao-Tsu Wu
Keyword(s):  
Exact Solutions ◽  
Stokes Flow ◽  
Fundamental Solutions ◽  
The Body ◽  
Circular Cylinders ◽  
Geometrical Parameters ◽  
Flow Problems ◽  
Singularity Method ◽  
Wide Range ◽  
Body Shapes

The present study further explores the fundamental singular solutions for Stokes flow that can be useful for constructing solutions over a wide range of free-stream profiles and body shapes. The primary singularity is the Stokeslet, which is associated with a singular point force embedded in a Stokes flow. From its derivatives other fundamental singularities can be obtained, including rotlets, stresslets, potential doublets and higher-order poles derived from them. For treating interior Stokes-flow problems new fundamental solutions are introduced; they include the Stokeson and its derivatives, called the roton and stresson.These fundamental singularities are employed here to construct exact solutions to a number of exterior and interior Stokes-flow problems for several specific body shapes translating and rotating in a viscous fluid which may itself be providing a primary flow. The different primary flows considered here include the uniform stream, shear flows, parabolic profiles and extensional flows (hyper-bolic profiles), while the body shapes cover prolate spheroids, spheres and circular cylinders. The salient features of these exact solutions (all obtained in closed form) regarding the types of singularities required for the construction of a solution in each specific case, their distribution densities and the range of validity of the solution, which may depend on the characteristic Reynolds numbers and governing geometrical parameters, are discussed.

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