Numerical Simulation of Three-Dimensional Flow Past a Cylinder Oscillating at the Strouhal Frequency

2014 ◽  
Vol 137 (1) ◽  
Author(s):  
S. Peppa ◽  
L. Kaiktsis ◽  
G. S. Triantafyllou
Keyword(s):  
Numerical Simulation ◽  
Stokes Equations ◽  
Oscillation Amplitude ◽  
Three Dimensional ◽  
Spectral Element ◽  
Transverse Oscillation ◽  
3D Flow ◽  
Flow Past ◽  
Flow Past A Cylinder ◽  
Uniform Stream

The paper presents computational results of 3D flow past a cylinder forced to oscillate: (a) transversely with respect to a uniform stream and (b) both transversely and in-line with respect to a uniform stream, following a figure-eight trajectory. For a flow from left to right the figure-eight is traversed counterclockwise in the upper half-plane. Direct numerical simulation (DNS) of the Navier–Stokes equations for 3D flow is performed using a spectral element code. Computations are carried out for a Reynolds number equal to 400, at a transverse oscillation frequency equal to the natural frequency of the Kármán vortex street. For both oscillation modes, the transverse oscillation amplitude is varied from 0 to 0.60 cylinder diameters. The forces on the cylinder are calculated and related to flow structure in the wake. The results indicate that, in general, the presence of in-line oscillation increases the magnitude of forces acting on the cylinder, as well as the power transfer from the flow to the structure. Flow visualizations indicate that, for the figure-eight mode, low-amplitude forcing tends to reduce the wake three-dimensionality. However, at high oscillation amplitudes, the wake structure is found to become more complex at increasing amplitude.

Numerical Simulation of Three-Dimensional Flow Past an Oscillating Cylinder

2013 ◽  
Author(s):  
Sofia Peppa ◽  
Lambros Kaiktsis ◽  
George Triantafyllou
Keyword(s):  
Stokes Equations ◽  
Oscillation Amplitude ◽  
Three Dimensional ◽  
Spectral Element ◽  
Transverse Oscillation ◽  
Navier Stokes ◽  
Three Dimensional Flow ◽  
Dimensional Flow ◽  
Flow Past ◽  
Uniform Stream

The paper presents computational results of three-dimensional flow past a cylinder forced to oscillate: (a) transversely with respect to a uniform stream, and (b) both transversely and in-line with respect to a uniform stream, following a figure-eight trajectory. For a flow from left to right the figure-eight is traversed counter-clockwise in the upper half-plane. DNS of the Navier-Stokes equations for three–dimensional flow is performed using a spectral element code. Computations are carried out for a Reynolds number equal to 400, at a transverse oscillation frequency equal to the natural frequency of the Kármán vortex street. For both oscillation modes, the transverse oscillation amplitude is varied from zero to 0.60 cylinder diameters. The forces on the cylinder are calculated and related to flow structure in the wake. The results indicate that, in general, the presence of in-line oscillation increases the magnitude of forces acting on the cylinder, as well as the power transfer from the flow to the structure. Flow visualizations indicate that, for the figure-eight mode, low-amplitude forcing tends to reduce the wake three-dimensionality. However, at high oscillation amplitudes, the wake structure is found to become more complex at increasing amplitude.

A Comparison of Forces in Two- and Three-Dimensional Flow Past an Oscillating Cylinder

2015 ◽  
Author(s):  
Sofia Peppa ◽  
Lambros Kaiktsis ◽  
Christos Frouzakis ◽  
George Triantafyllou
Keyword(s):  
Stokes Equations ◽  
Oscillation Amplitude ◽  
Three Dimensional ◽  
Oscillation Mode ◽  
Transverse Oscillation ◽  
Two Dimensional ◽  
Three Dimensional Flow ◽  
Dimensional Flow ◽  
Flow Past ◽  
Two Dimensional Flow

DNS results are presented for three-dimensional flow past a circular cylinder forced to oscillate both in the transverse and in-line direction with respect to a uniform stream, at Reynolds number equal to 400, and are compared against simulation results for two-dimensional flow. The cylinder follows a figure-eight motion, traversed either counter-clockwise or clockwise in the upper half-plane for a flow stream from left to right. The transverse oscillation frequency is equal to the natural frequency of the Kármán vortex street. The Navier-Stokes equations are solved using a spectral element code, and the forces acting on the cylinder are computed for both three- and two-dimensional flow. The results demonstrate that the effect of cylinder oscillation on the flow structure and forces differs substantially between the counter-clockwise and the clockwise oscillation mode. For the counter-clockwise mode, forcing at low amplitude decreases the flow three-dimensionality, with the wake becoming increasingly three-dimensional for transverse oscillation amplitudes higher than 0.25–0.30 cylinder diameters, with corresponding discrepancies in forces with respect to two-dimensional flow. For the case of clockwise mode, a strong stabilizing effect is found: the wake becomes two-dimensional for a transverse oscillation amplitude of 0.20 cylinder diameters, and remains so at higher amplitudes, resulting in nearly equal values of the force coefficients for three- and two-dimensional flow.

scholarly journals Computational Algorithms for Solving Spectral/$hp$ Stabilized Incompressible Flow Problems

2016 ◽  
Vol 8 (4) ◽  
pp. 21 ◽  
Author(s):  
Rakesh Ranjan ◽  
Anthony Theodore Chronopoulos ◽  
Yusheng Feng
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Higher Order ◽  
Navier Stokes ◽  
Krylov Methods ◽  
Higher Order Methods ◽  
The Past ◽  
Flow Past ◽  
Flow Past A Cylinder ◽  
Computationally Intensive

In this paper we implement the element-by-element preconditioner and inexact Newton-Krylov methods (developed in the past) for solving stabilized computational fluid dynamics (CFD) problems with spectral methods. Two different approaches are implemented for speeding up the process of solving both steady and unsteady incompressible Navier-Stokes equations. The first approach concerns the application of a scalable preconditioner namely the element by element LU preconditioner, while the second concerns the application of Newton-Krylov (NK) methods for solving non-linear problems. We obtain good agreement with benchmark results on standard CFD problems for various Reynolds numbers. We solve the Kovasznay flow and flow past a cylinder at Re-$100$ with this approach. We also utilize the Newton-Krylov algorithm to solve (in parallel) important model problems such as flow past a circular obstacle in a Newtonian flow field, three dimensional driven cavity, flow past a three dimensional cylinder with different immersion lengths. We explore the scalability and robustness of the formulations for both approaches and obtain very good speedup. Effective implementations of these procedures demonstrate for relatively coarse macro-meshes<br />the power of higher order methods in obtaining highly accurate results in CFD. While the procedures adopted in the paper have been explored in the past the novelty lies with applications with higher order methods which have been known to be computationally intensive.

scholarly journals Computational Study of Three-Dimensional Flow Past an Oscillating Cylinder Following a Figure Eight Trajectory

Fluids ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 107
Author(s):  
Sofia Peppa ◽  
Lambros Kaiktsis ◽  
Christos E. Frouzakis ◽  
George S. Triantafyllou
Keyword(s):  
Computational Study ◽  
Oscillation Amplitude ◽  
Three Dimensional ◽  
Oscillation Mode ◽  
Transverse Oscillation ◽  
Cylinder Surface ◽  
Power Transfer ◽  
Three Dimensional Flow ◽  
Dimensional Flow ◽  
Flow Past

The paper presents a computational study of three-dimensional flow past a cylinder forced to oscillate in a uniform stream, following a figure-eight trajectory. Flow simulations were performed for Re = 400, for different cases, defined in terms of the oscillation mode (‘counter-clockwise’ or ‘clockwise’), for values of the ratio, F, of the transverse oscillation frequency to the Strouhal frequency close to 1.0. The results demonstrate that, for F ≤ 1.0, counter-clockwise cylinder motion is associated with positive power transfer from the flow to the cylinder, corresponding to excitation; for the clockwise motion, power transfer is negative at intermediate to high amplitudes, corresponding to damping. For the clockwise mode, in the range F = 0.9–1.1, a transition to two-dimensional vortex street is identified for transverse oscillation amplitude exceeding a critical value. This results from the induced suction of vortices, which moves vortex formation and shedding closer to the cylinder surface, thus resulting in a narrower wake, characterized by an effective lower Reynolds number. Both oscillation modes are characterized by higher harmonics in the lift force spectrum, with the third harmonic being very pronounced, while even harmonics are present for the case of clockwise mode, resulting from a wake transition to a “S + P” mode.

Flow Past a Forced Oscillating Cylinder: A Three-Dimensional Numerical Study

2019 ◽  
Author(s):  
Huan Ping ◽  
Yan Bao ◽  
Dai Zhou ◽  
Zhaolong Han
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Flow Dynamics ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Flow Past ◽  
Flow Past A Cylinder ◽  
Two Dimensional Flow

Abstract In this paper, we conducted a three-dimensional investigation of flow past a cylinder undergoing forced oscillation. The flow configuration is similar to the work of Blackburn & Henderson (1999) [1], in which Reynolds number equals to 500 and a fixed motion amplitude of A/D = 0.25. The oscillation frequencies are varied in the range near to the natural shedding frequency of a stationary cylinder. The flow dynamics are governed by Navier-Stokes equations and the solutions are obtained by employing high-order spectral/hp element method. It is found that the flow dynamics are significantly distinguished from the study of two-dimensional flow by Blackburn & Henderson (1999) [1]. The values of hydrodynamic forces are smaller compared to that in the two-dimensional study. However, lock-in boundary we identified is broader. In addition, a different type of hysteresis loop of energy transfer coefficient is obtained.

scholarly journals Numerical simulation of flow past a heated/cooled sphere

2012 ◽  
Vol 692 ◽  
pp. 332-346 ◽  
Author(s):  
Ryoichi Kurose ◽  
Mamiko Anami ◽  
Akitoshi Fujita ◽  
Satoru Komori
Keyword(s):  
Numerical Simulation ◽  
Temperature Dependence ◽  
Temperature Difference ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Boussinesq Approximation ◽  
Nusselt Numbers ◽  
Flow Past ◽  
Fluid Properties ◽  
Adiabatic Case

AbstractThe characteristics of flow past a heated/cooled sphere are investigated for particle Reynolds numbers $50\leq {\mathit{Re}}_{p} \leq 500$ in conditions with and without buoyancy by means of three-dimensional numerical simulation in which temperature dependence of fluid properties such as density and viscosity is exactly taken into account. The results show that in the absence of buoyancy, drag coefficients of the heated and cooled spheres are larger and smaller than those of the adiabatic case, respectively, and their Nusselt numbers are smaller and larger than the values estimated by a widely used empirical expression for predicting Nusselt numbers, respectively. In addition, the temperature difference between the sphere and ambient fluid strongly affects the flow separation points, size of vortex ring behind the sphere and Strouhal number for vortex shedding. These changes are attributed to the temperature dependence of fluid properties in the vicinity of the sphere. Even in the presence of buoyancy, the temperature dependence of fluid properties strongly affects the drag coefficient and Nusselt number and therefore the Boussinesq approximation becomes inapplicable as the temperature difference increases, regardless of the magnitude of the Richardson number.

Fekete-Gauss Spectral Elements for Incompressible Navier-Stokes Flows: The Two-Dimensional Case

2013 ◽  
Vol 13 (5) ◽  
pp. 1309-1329 ◽  
Author(s):  
Laura Lazar ◽  
Richard Pasquetti ◽  
Francesca Rapetti
Keyword(s):  
Degrees Of Freedom ◽  
Stokes Equations ◽  
Schur Complement ◽  
Spectral Element ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Driven Cavity ◽  
Flow Past A Cylinder ◽  
Accuracy Study

AbstractSpectral element methods on simplicial meshes, say TSEM, show both the advantages of spectral and finite element methods, i.e., spectral accuracy and geometrical flexibility. We present aTSEM solver of the two-dimensional (2D) incompressible Navier-Stokes equations, with possible extension to the 3D case. It uses a projection method in time and piecewise polynomial basis functions of arbitrary degree in space. The so-called Fekete-Gauss TSEM is employed,i.e., Fekete (resp. Gauss) points of the triangle are used as interpolation (resp. quadrature) points. For the sake of consistency, isoparametric elements are used to approximate curved geometries. The resolution algorithm is based on an efficient Schur complement method, so that one only solves for the element boundary nodes. Moreover, the algebraic system is never assembled, therefore the number of degrees of freedom is not limiting. An accuracy study is carried out and results are provided for classical benchmarks: the driven cavity flow, the flow between eccentric cylinders and the flow past a cylinder.

Sign in / Sign up

Export Citation Format

Share Document