Far‐field condition of vortex methods on an impulsively started two‐dimensional circular cylinder with rotation

1994 ◽  
Vol 6 (8) ◽  
pp. 2745-2756 ◽  
Author(s):  
Teruhiko Kida ◽  
Toshimi Nagata ◽  
Tomoya Nakajima
Keyword(s):  
Circular Cylinder ◽  
Field Condition ◽  
Far Field ◽  
Two Dimensional ◽  
Vortex Methods

Asymptotic Solutions and Radiation Conditions for Second-Order Diffracted Waves

1989 ◽  
Vol 111 (3) ◽  
pp. 203-207
Author(s):  
H. Huang ◽  
J. Li ◽  
X. Wang
Keyword(s):  
Finite Element ◽  
Circular Cylinder ◽  
Second Order ◽  
Asymptotic Solutions ◽  
Wave Forces ◽  
Far Field ◽  
Two Dimensional ◽  
Diffracted Waves ◽  
Artificial Boundaries ◽  
Radiation Conditions

The far-field asymptotic solutions for the second-order diffracted waves have been developed, both in three and two-dimensional problems. The radiation conditions for the second-order diffracted waves are derived by using the asymptotic solutions. The nonlinear wave forces on a half-circular cylinder on seabed are presented by using finite element methods with the radiation conditions imposed on the artificial boundaries.

Two-dimensional Brinkman flows and their relation to analogous Stokes flows

2019 ◽  
Vol 84 (5) ◽  
pp. 912-929 ◽  
Author(s):  
P A Martin
Keyword(s):  
Circular Cylinder ◽  
Stokes Flow ◽  
Fluid Velocity ◽  
Additional Term ◽  
Far Field ◽  
Two Dimensional ◽  
Logarithmic Divergence ◽  
Stokes Flows ◽  
Flow Past ◽  
Logarithmic Growth

Abstract 2D Stokes flows often exhibit the Stokes paradox: logarithmic growth of the fluid velocity in the far field. Analogous Brinkman flows are governed by the same equations apart from an additional term involving a parameter $\alpha$. Although these equations reduce to those for Stokes flow when $\alpha =0$, we show that the Brinkman solutions do not approach the corresponding Stokes solutions as $\alpha \to 0$; instead, logarithmic divergence with $\alpha$ is found. We also show that Brinkman flows do not exhibit a Stokes-like paradox. These results are given in detail for two specific problems, namely flow past a rigid circular cylinder and flow past a thin rigid strip.

scholarly journals The Computation of the Magnitude of the Far Field for an Eccentric Circular Cylinder

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Bülent Yılmaz
Keyword(s):  
Circular Cylinder ◽  
Plane Wave ◽  
Radiation Condition ◽  
Higher Order ◽  
Numerical Results ◽  
Surface Radiation ◽  
Far Field ◽  
Condition Method ◽  
Radiation Conditions

The specific case of scattering of a plane wave by a two-layered penetrable eccentric circular cylinder has been considered and it is about the validity of the on surface radiation condition method and its applications to the scattering of a plane wave by a two-layered penetrable eccentric circular cylinder. The transformation of the problem of scattering by the eccentric circular cylinder to the problem of scattering by the concentric circular cylinder by using higher order radiation conditions, is observed. Numerical results presented the magnitude of the far field.

Steady approach of unsteady low-Reynolds-number flow past two rotating circular cylinders

2013 ◽  
Vol 736 ◽  
pp. 414-443 ◽  
Author(s):  
Y. Ueda ◽  
T. Kida ◽  
M. Iguchi
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Stokes Equations ◽  
Low Reynolds Number ◽  
Vortex Method ◽  
The Self ◽  
Circular Cylinders ◽  
Far Field ◽  
Flow Past ◽  
Low Reynolds

AbstractThe long-time viscous flow about two identical rotating circular cylinders in a side-by-side arrangement is investigated using an adaptive numerical scheme based on the vortex method. The Stokes solution of the steady flow about the two-cylinder cluster produces a uniform stream in the far field, which is the so-called Jeffery’s paradox. The present work first addresses the validation of the vortex method for a low-Reynolds-number computation. The unsteady flow past an abruptly started purely rotating circular cylinder is therefore computed and compared with an exact solution to the Navier–Stokes equations. The steady state is then found to be obtained for $t\gg 1$ with ${\mathit{Re}}_{\omega } {r}^{2} \ll t$, where the characteristic length and velocity are respectively normalized with the radius ${a}_{1} $ of the circular cylinder and the circumferential velocity ${\Omega }_{1} {a}_{1} $. Then, the influence of the Reynolds number ${\mathit{Re}}_{\omega } = { a}_{1}^{2} {\Omega }_{1} / \nu $ about the two-cylinder cluster is investigated in the range $0. 125\leqslant {\mathit{Re}}_{\omega } \leqslant 40$. The convection influence forms a pair of circulations (called self-induced closed streamlines) ahead of the cylinders to alter the symmetry of the streamline whereas the low-Reynolds-number computation (${\mathit{Re}}_{\omega } = 0. 125$) reaches the steady regime in a proper inner domain. The self-induced closed streamline is formed at far field due to the boundary condition being zero at infinity. When the two-cylinder cluster is immersed in a uniform flow, which is equivalent to Jeffery’s solution, the streamline behaves like excellent Jeffery’s flow at ${\mathit{Re}}_{\omega } = 1. 25$ (although the drag force is almost zero). On the other hand, the influence of the gap spacing between the cylinders is also investigated and it is shown that there are two kinds of flow regimes including Jeffery’s flow. At a proper distance from the cylinders, the self-induced far-field velocity, which is almost equivalent to Jeffery’s solution, is successfully observed in a two-cylinder arrangement.

The response of a turbulent boundary layer to lateral divergence

1979 ◽  
Vol 94 (2) ◽  
pp. 243-268 ◽  
Author(s):  
A. J. Smits ◽  
J. A. Eaton ◽  
P. Bradshaw
Keyword(s):  
Boundary Layer ◽  
Circular Cylinder ◽  
Turbulent Boundary Layer ◽  
Structural Parameters ◽  
Axial Flow ◽  
Turbulence Structure ◽  
Two Dimensional ◽  
Transition Section ◽  
Two Dimensional Flow ◽  
Made In

Measurements have been made in the flow over an axisymmetric cylinder-flare body, in which the boundary layer developed in axial flow over a circular cylinder before diverging over a conical flare. The lateral divergence, and the concave curvature in the transition section between the cylinder and the flare, both tend to destabilize the turbulence. Well downstream of the transition section, the changes in turbulence structure are still significant and can be attributed to lateral divergence alone. The results confirm that lateral divergence alters the structural parameters in much the same way as longitudinal curvature, and can be allowed for by similar empirical formulae. The interaction between curvature and divergence effects in the transition section leads to qualitative differences between the behaviour of the present flow, in which the turbulence intensity is increased everywhere, and the results of Smits, Young & Bradshaw (1979) for a two-dimensional flow with the same curvature but no divergence, in which an unexpected collapse of the turbulence occurred downstream of the curved region.

Grid-Free Vortex Methods for Natural Convection in Two-Dimensional Domains

2012 ◽  
Author(s):  
Issam Lakkis
Keyword(s):  
Natural Convection ◽  
Nonlinear Diffusion ◽  
Reacting Flows ◽  
Ideal Gas ◽  
Two Dimensional ◽  
Vortex Methods ◽  
Free Vortex ◽  
Low Mach Number ◽  
Buoyancy Driven Flows ◽  
Vorticity Generation

Vortex methods for simulating natural convection of an ideal gas in unbounded two-dimensional domains are presented. In particular, the redistribution method for diffusion is extended to enable simulation of nonlinear diffusion of an ideal gas in isobaric conditions encountered in unbounded low-Mach number flows. We also address the problem of handling source terms in grid-free vortex methods and propose a fast, accurate, and physically motivated method for solving the associated inverse problems. Examples include generation of baroclinic vorticity in non-reacting buoyancy driven flows, and in addition, generation of internal energy and species in buoyant reacting flows. Accuracy and speed of the proposed algorithms for nonlinear diffusion and vorticity generation are investigated separately. Simulations of natural convection of a “thermal patch” for Grashof number ranging from to 1562.5 to 25000 are presented.

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