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Proceedings ArticleDOI

Flow Past Rotating Low Axis Ratio Elliptic Cylinder

About: The article was published on 2016-06-13. It has received None citations till now. The article focuses on the topics: Flow (mathematics).
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Journal ArticleDOI
TL;DR: The term immersed boundary (IB) method is used to encompass all such methods that simulate viscous flows with immersed (or embedded) boundaries on grids that do not conform to the shape of these boundaries.
Abstract: The term “immersed boundary method” was first used in reference to a method developed by Peskin (1972) to simulate cardiac mechanics and associated blood flow. The distinguishing feature of this method was that the entire simulation was carried out on a Cartesian grid, which did not conform to the geometry of the heart, and a novel procedure was formulated for imposing the effect of the immersed boundary (IB) on the flow. Since Peskin introduced this method, numerous modifications and refinements have been proposed and a number of variants of this approach now exist. In addition, there is another class of methods, usually referred to as “Cartesian grid methods,” which were originally developed for simulating inviscid flows with complex embedded solid boundaries on Cartesian grids (Berger & Aftosmis 1998, Clarke et al. 1986, Zeeuw & Powell 1991). These methods have been extended to simulate unsteady viscous flows (Udaykumar et al. 1996, Ye et al. 1999) and thus have capabilities similar to those of IB methods. In this review, we use the term immersed boundary (IB) method to encompass all such methods that simulate viscous flows with immersed (or embedded) boundaries on grids that do not conform to the shape of these boundaries. Furthermore, this review focuses mainly on IB methods for flows with immersed solid boundaries. Application of these and related methods to problems with liquid-liquid and liquid-gas boundaries was covered in previous reviews by Anderson et al. (1998) and Scardovelli & Zaleski (1999). Consider the simulation of flow past a solid body shown in Figure 1a. The conventional approach to this would employ structured or unstructured grids that conform to the body. Generating these grids proceeds in two sequential steps. First, a surface grid covering the boundaries b is generated. This is then used as a boundary condition to generate a grid in the volume f occupied by the fluid. If a finite-difference method is employed on a structured grid, then the differential form of the governing equations is transformed to a curvilinear coordinate system aligned with the grid lines (Ferziger & Peric 1996). Because the grid conforms to the surface of the body, the transformed equations can then be discretized in the

3,184 citations

Journal ArticleDOI
TL;DR: In this paper, the Navier-Stokes equations on a rectangular domain are applied to the simulation of flow around the natural mitral valve of a human heart valve, where the boundary forces are of order h − 1, and because they are sensitive to small changes in boundary configuration, they tend to produce numerical instability.

2,517 citations

Journal ArticleDOI
TL;DR: In this paper, the onset of periodic behavior in two-dimensional laminar flow past bodies of various shapes is examined by means of finite-element simulations, and the transition from steady to periodic flow is marked by a Hopf bifurcation, which is located by solving an appropriate extended set of steady-state equations.
Abstract: The onset of periodic behaviour in two-dimensional laminar flow past bodies of various shapes is examined by means of finite-element simulations. The transition from steady to periodic flow is marked by a Hopf bifurcation, which we locate by solving an appropriate extended set of steady-state equations. The bodies considered are a circular cylinder, triangular prisms of various shapes, and flat plates and elliptical cylinders aligned over a range of angles to the direction of flow. Our results for the circular cylinder are in good agreement with experimental observations and with the results of time-dependent calculations.

500 citations

Journal ArticleDOI
TL;DR: In this article, the stability analysis of flow past a spinning circular cylinder placed in a uniform stream is investigated via two-dimensional computations, and a stabilized finite element method is utilized to solve the incompressible Navier-Stokes equations in the primitive variables formulation.
Abstract: Flow past a spinning circular cylinder placed in a uniform stream is investigated via two-dimensional computations. A stabilized finite element method is utilized to solve the incompressible Navier–Stokes equations in the primitive variables formulation. The Reynolds number based on the cylinder diameter and free-stream speed of the flow is 200. The non-dimensional rotation rate, α (ratio of the surface speed and freestream speed), is varied between 0 and 5. The time integration of the flow equations is carried out for very large dimensionless time. Vortex shedding is observed for α < 1.91. For higher rotation rates the flow achieves a steady state except for 4.34 < α < 4:70 where the flow is unstable again. In the second region of instability, only one-sided vortex shedding takes place. To ascertain the instability of flow as a function of α a stabilized finite element formulation is proposed to carry out a global, non-parallel stability analysis of the two-dimensional steady-state flow for small disturbances. The formulation and its implementation are validated by predicting the Hopf bifurcation for flow past a non-rotating cylinder. The results from the stability analysis for the rotating cylinder are in very good agreement with those from direct numerical simulations. For large rotation rates, very large lift coefficients can be obtained via the Magnus effect. However, the power requirement for rotating the cylinder increases rapidly with rotation rate.

431 citations

Journal ArticleDOI
TL;DR: In this paper, the authors numerically investigated two-dimensional laminar flow past a circular cylinder rotating with a constant angular velocity, for the purpose of controlling vortex shedding and understanding the underlying flow mechanism.
Abstract: The present study numerically investigates two-dimensional laminar flow past a circular cylinder rotating with a constant angular velocity, for the purpose of controlling vortex shedding and understanding the underlying flow mechanism. Numerical simulations are performed for flows with Re=60, 100, and 160 in the range of 0⩽α⩽2.5, where α is the circumferential speed at the cylinder surface normalized by the free-stream velocity. Results show that the rotation of a cylinder can suppress vortex shedding effectively. Vortex shedding exists at low rotational speeds and completely disappears at α>αL, where αL is the critical rotational speed which shows a logarithmic dependence on Re. The Strouhal number remains nearly constant regardless of α while vortex shedding exists. With increasing α, the mean lift increases linearly and the mean drag decreases, which differ significantly from those predicted by the potential flow theory. On the other hand, the amplitude of lift fluctuation stays nearly constant with in...

279 citations