Lift and drag evaluation in translating and rotating non-inertial systems

In this paper relationships have been derived for lift and drag coefficients for cylindrical bodies for two cases. The relative motion between the body and the fluid is assumed to be two-dimensional and to take place in a plane perpendicular to the axis of the body. Three-dimensional effects are ignored, thus limiting the validity of the formulae to low Reynolds number flows. The fluid is assumed to be an incompressible constant- property Newtonian fluid. In the first case, an inertial system is fixed to a stationary cylindrical body. The motion of the fluid in which the body is placed is an arbitrary function of time not identically zero, e.g. the fluid can have linear and angular acceleration, such as translation, oscillation or rotation. The velocity of the fluid at a single instant is either uniform in space or, in the case of rotation, a linear function of distance from the origin of the system. In the second case, a noninertial system is fixed to an accelerating cylindrical body. The relative flow between fluid and body is kinematically the same as in the first case, but the forces acting upon the bodies differ in the two systems. This is due to the inertial forces that occur in a noninertial system. General formulae are derived for a cylindrical body of arbitrary cross-section and give the relationships between the two systems for each set of coefficients, i.e. the relationship between the lift coefficients for each case, and the same for the drag coefficient. As an example, the relationships are applied to two common cases, a circular and a rectangular cross-section cylinder

A numerical study of an inline oscillating cylinder in a free stream

Simulations of a cylinder undergoing externally controlled sinusoidal oscillations in the free stream direction have been performed. The frequency of oscillation was kept equal to the vortex shedding frequency from a fixed cylinder, while the amplitude of oscillation was varied, and the response of the flow measured. With varying amplitude, a rich series of dynamic responses was recorded. With increasing amplitude, these states included wakes similar to the Kármán vortex street, quasiperiodic oscillations interleaved with regions of synchronized periodicity (periodic on multiple oscillation cycles), a period-doubled state and chaotic oscillations. It is hypothesized that, for low to moderate amplitudes, the wake dynamics are controlled by vortex shedding at a global frequency, modified by the oscillation. This vortex shedding is frequency modulated by the driven oscillation and amplitude modulated by vortex interaction. Data are presented to support this hypothesis

Effect of oscillation amplitude on force coefficients of a cylinder oscillated in transverse or in-line directions

A finite difference solution is presented for 2D low Reynolds number flow (Re=140 and 160) past a circular cylinder placed in a uniform flow. The cylinder is oscillated mechanically either in-line or transversely under lock-in conditions. Abrupt jumps between two state curves were found for a cylinder oscillated in in-line direction in the time-mean (TM) values of lift and torque coefficients when plotted against amplitude of oscillation. Pre- and post-jump analysis carried out included the investigation of phase angle differences, limit cycles and flow patterns confirming the existence of switches in the vortex structure at certain oscillation amplitude values. The TM of drag and base pressure coefficient and the rms values of all force coefficients were continuous functions of oscillation amplitude. When the cylinder was oscillated transversely to the main stream, however, no jumps were found in the corresponding curves. Here the TM of lift and torque were found to be zero (true also for a stationary cylinder) at all amplitude values. Even though the transverse oscillation breaks the symmetry of the flow, there appears to be symmetry over a period

Sudden and gradual alteration of amplitude during the computation for flow around a cylinder oscillating in transverse or in-line direction

This study investigates the effect of altering oscillation amplitude on time-mean and root-mean-square values of force coefficients when plotted against amplitude of oscillation. The cylinder is placed in a uniform flow and is oscillated mechanically in transverse or in-line direction. The two dimensional numerical computations are carried out at Re=140 and 160, at 90% of the natural vortex shedding frequency. For in-line oscillation, jumps were found in the time-mean values of lift and torque. Both abrupt and gradual alteration of amplitude in the course of a computation had the effect of keeping the solution in one state curve, i.e., of conserving state, or inhibiting changes in vortex structure. Transverse oscillation displayed no jumps, and alteration of amplitude had no effect on the solution. Keywords: circular cylinder, in-line oscillation, lift, low Reynolds number flow, transverse oscillation

Streamwise forced oscillations of circular and square cylinders

The modification of a cylinder wake by streamwise oscillation of the cylinder at the vortex shedding frequency of the unperturbed cylinder is reported. Recent numerical simulations [J. S. Leontini, D. Lo Jacono, and M. C. Thompson, “A numerical study of an inline oscillating cylinder in a free stream,” J. Fluid Mech. 688, 551–568 (2011)] showed that this forcing results in the primary frequency decreasing proportionally to the square of the forcing amplitude, before locking to a subharmonic at higher amplitudes. The experimental results presented here show that this behavior continues at higher Reynolds numbers, although the flow is three-dimensional. In addition, it is shown that this behavior persists when the body is a square cross section, and when the frequency of forcing is detuned from the unperturbed cylinder shedding frequency. The similarity of the results across Reynolds number, geometry, and frequency suggests that the physical mechanism is applicable to periodic forcing of the classic von Ka ́rma ́n vortex street, regardless of the details of the body which forms the street

Numerical Simulations of Flows over a Forced Oscillating Cylinder

A numerical study of incompressible laminar flow past a circular cylinder forced to oscillate longitudinally, transversely and at an angle to the uniform freestream is performed using the dynamic mesh method. The simulations are conducted at a fixed Reynolds number of 80 with amplitude ratios varying between 0.14 to 0.50 and excitation frequency ratios of 0.05 to 3.0. Good agreement to previous experimental and numerical investigations is achieved in the prediction of the lock-on range, force amplifications and vortex shedding modes for longitudinal and transverse oscillations. For excitations at an angle of 60 degrees relative to the oncoming flow, previously identified modes of AI and, AII were successfully predicted. In addition, at higher amplitude ratios the entire synchronised von Karman wake street displayed a deviating effect from the centreline. Analysis of the wake response via phase plane diagrams and the transverse force coefficients revealed two lock-on regions. The extents of these lock-on regions, and the variation of the forces and near wake vortex shedding modes are presented and discussed herein