Study on a Flow Field around a Rotating Circular Cylinder : Wake Pattern Changes with Velocity Ratio

2004 ◽  
Vol 2004.2 (0) ◽  
pp. 295-296
Author(s):  
Yoshihiro INOUE ◽  
Akira ITO ◽  
Shintaro YAMASHITA ◽  
Hiroshi NAGATA
2013 ◽  
Vol 730 ◽  
pp. 145-161 ◽  
Author(s):  
Qiqi Wang ◽  
Jun-Hui Gao

AbstractThis paper analyses the adjoint solution of the Navier–Stokes equation. We focus on flow across a circular cylinder at three Reynolds numbers, ${\mathit{Re}}_{D} = 20, 100$ and $500$. The quantity of interest in the adjoint formulation is the drag on the cylinder. We use classical fluid mechanics approaches to analyse the adjoint solution, which is a vector field similar to a flow field. Production and dissipation of kinetic energy of the adjoint field is discussed. We also derive the evolution of circulation of the adjoint field along a closed material contour. These analytical results are used to explain three numerical solutions of the adjoint equations presented in this paper. The adjoint solution at ${\mathit{Re}}_{D} = 20$, a viscous steady state flow, exhibits a downstream suction and an upstream jet, the opposite of the expected behaviour of a flow field. The adjoint solution at ${\mathit{Re}}_{D} = 100$, a periodic two-dimensional unsteady flow, exhibits periodic, bean-shaped circulation in the near-wake region. The adjoint solution at ${\mathit{Re}}_{D} = 500$, a turbulent three-dimensional unsteady flow, has complex dynamics created by the shear layer in the near wake. The magnitude of the adjoint solution increases exponentially at the rate of the first Lyapunov exponent. These numerical results correlate well with the theoretical analysis presented in this paper.


1989 ◽  
Vol 9 (34) ◽  
pp. 273-276
Author(s):  
Takeyoshi Kimura ◽  
Michihisa Tsutahara ◽  
Zhong-yi Wang ◽  
Hiroshi Ishii

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