Nonlinear spacing and frequency effects of an oscillating cylinder in the wake of a stationary cylinder

This is the published version. Copyright 2010 American Institute of PhysicsNonlinear responses to a transversely oscillating cylinder in the wake of a stationary upstream cylinder are studied theoretically by using an immersed-boundary method at Re=100. Response states are investigated in the three flow regimes for a tandem-cylinder system: the “vortex suppression” regime, the critical spacing regime, and the “vortex formation” regime. When the downstream cylinder is forced to oscillate at a fixed frequency and amplitude, the response state of flow around the two cylinders varies with different spacing between the two cylinders, while in the same flow regime, the response state can change with the oscillating frequency and amplitude of the downstream cylinder. Based on velocity phase portraits, each of the nonlinear response states can be categorized into one of the three states in the order of increasing chaotic levels: lock-in, transitional, or quasiperiodic. These states can also be correlated with velocity spectral behaviors. The discussions are conducted using near-wake velocity phase portraits, spectral analyses, and related vorticity fields. A general trend in the bifurcation diagrams of frequency spacing shows the smaller the spacing, frequency, or amplitude, the less chaotic the response state of the system and more likely the downstream and upstream wakes are in the same response state. The system is not locked-in in any case when the spacing between the cylinders is larger than the critical spacing. The near-wake velocity spectral behaviors correspond to the nonlinear response states, with narrow-banded peaks shown at the oscillation frequency and its harmonics in the lock-in cases. High frequency harmonic peaks, caused by interactions between the upstream wake and the downstream oscillating cylinder, are reduced in the near-wake velocity spectra of the upstream cylinder when the spacing increases

Four-vortex motion around a circular cylinder

The motion of two pairs of counter-rotating point vortices placed in a uniform flow past a circular cylinder is studied analytically and numerically. When the dynamics is restricted to the symmetric subspace---a case that can be realized experimentally by placing a splitter plate in the center plane---, it is found that there is a family of linearly stable equilibria for same-signed vortex pairs. The nonlinear dynamics in the symmetric subspace is investigated and several types of orbits are presented. The analysis reported here provides new insights and reveals novel features of this four-vortex system, such as the fact that there is no equilibrium for two pairs of vortices of opposite signs on the opposite sides of the cylinder. (It is argued that such equilibria might exist for vortex flows past a cylinder confined in a channel.) In addition, a new family of opposite-signed equilibria on the normal line is reported. The stability analysis for antisymmetric perturbations is also carried out and it shows that all equilibria are unstable in this case.Comment: 27 pages, 13 figures, to be published in Physics of Fluid

Aerodynamic and Aeroacoustic Numerical Investigation of Turbofan Engines using Lattice Boltzmann Methods

International audienceIn recent years, lattice Boltzmann methods showed promising advantages over standard Navier-Stokes equation-based solvers. In this work, the capacity to predict both self noise and interaction noise is evaluated. First, a rod-airfoil interaction case is investigated, where the turbulence wake of the rod impinges the leading edge of the airfoil. Thereafter, a semi-infinite ducted axial fan is studied, where the turbulent boundary layers on each blades generate self noise which propagates into the duct, and radiates to the far-field. Subsequently, a ducted grid simulation is performed to verify the properties of the grid-generated turbulence. Finally, the grid and the axial-fan are combined within the same configuration, which comprises both self-noise and interaction noise. For each configuration, the agreements with experiments are satisfactory, however, acoustic propagation issues have been encounters from the duct intake to the free field. Nevertheless, the implemented wall model at the solid boundaries seems to correctly predict the acoustic sources on the blades

Position of static cylinder effect on base flows

This paper presents the effect of the cylinder as a passive controller on the recirculation zone behind high-speed objects. The low-pressure recirculation zone was measured for base and wall region with a portable data acquisition system using sixteen solo sensors between reattachment and separation points at angles 0°, 30°, 60°, 90°. Pressure measurements were done by the transducer of National Instruments 9205 Screw Term and Data Acquisition cDAQ-1974. The measurement was done using DAQ connected to 16 solo sensors of 0-150 psi range. In a second it is capable of scanning 250 samples, followed by computing the overall average and store it on the disk. The NI LabVIEW Academic Software using DAQ through pressure sensors acquires data from all the sixteen channels and displays it on the computer screen. The experiments were carried out for overexpanded and perfectly expanded supersonic jets at Mach 2 through the C-D nozzle for area ratio 9. It is found that the control has marginally influenced the base and wall flow field when the control was placed at different positions along the imaginary line from separation to reattachment angled at 30° to the horizontal base and the flow field in the base area along the separation line is mostly independent of its locations except near the exit of the enlarged duct where the flow field is mostly influenced by the back pressure. The control seems to be strongly effective when flow expanded is ideal

On the development of a nonlinear time-domain numerical method for describing vortex-induced vibration and wake interference of two cylinders using experimental results

A nonlinear mathematical model is developed in the time domain to simulate the behaviour of two identical flexibly mounted cylinders in tandem while undergoing vortex-induced vibration (VIV). Subsequently, the model is validated and modified against experimental results. Placing an array of bluff bodies in proximity frequently happens in different engineering fields. Chimney stacks, power transmission lines and oil production risers are few engineering structures that may be impacted by VIV. The coinciding of the vibration frequency with the structure natural frequency could have destructive consequences. The main objective of this study is to provide a symplectic and reliable model capable of capturing the wake interference phenomenon. This study shows the influence of the leading cylinder on the trailing body and attempts to capture the change in added mass and damping coefficients due to the upstream wake. The model is using two coupled equations to simulate the structural response and hydrodynamic force in each of cross-flow and stream-wise directions. Thus, four equations describe the fluid-structure interaction of each cylinder. A Duffing equation describes the structural motion, and the van der Pol wake oscillator defines the hydrodynamic force. The system of equations is solved analytically. Two modification terms are added to the excitation side of the Duffing equation to adjust the hydrodynamic force and incorporate the effect of upstream wake on the trailing cylinder. Both terms are functions of upstream shedding frequency (Strouhal number). Additionally, the added mass modification coefficient is a function of structural acceleration and the damping modification coefficient is a function of velocity. The modification coefficients values are determined by curve fitting to the difference between upstream and downstream wake forces, obtained from experiments. The damping modification coefficient is determined by optimizing the model against the same set of experiments. Values of the coefficients at seven different spacings are used to define a universal function of spacing for each modification coefficient so that they can be obtained for any given distance between two cylinders. The model is capable of capturing lock-in range and maximum amplitude