Numerical simulation of flow around an orbiting cylinder at different ellipticity values

Abstract

This paper deals with the numerical simulation of low Reynolds number flow (Re ¼ 120-180) past a circular cylinder in orbital motion. The Navier-Stokes equations, pressure Poisson equations and continuity are written in primitive variables in a noninertial system fixed to the orbiting cylinder and solved by the finite difference method. Ellipticity values between 0 and 1.2 (from pure in-line oscillation through a full circle and beyond) were investigated. Sudden changes in state (jumps) are found when time-mean or root-mean-square values of force coefficients or energy transfer are plotted against ellipticity. Pre-and post-jump analysis was carried out by investigating limit cycles, time-histories, phase angles and flow patterns. These investigations revealed that ellipticity can have a large effect on the energy transfer between the incompressible fluid and a circular cylinder forced to follow an orbital path, and that small changes in the amplitude of transverse motion can have a dramatic effect. The phase angle was altered by about 1801 at the jumps. Also investigated were the direction of orbit, which affects the state curves belonging to the time-mean values of lift only, and the effect of initial conditions, which alters the location of jumps without changing the state curves. r

Sudden and Gradual Alteration of Amplitude During the Computation for Flow Around a Cylinder Oscillating in Transverse or In-Line Direction

“…The TM of C L and t q shows two envelope curves, or state curves, which are almost parallel with each other, and between which the solution jumps. State curves for the TM of C D and C pb and for all rms curves, on the other hand, intersect each other at A y =0 [15]. For an orbiting cylinder jumps between the two state curves occur in all TM and rms curves.…”

“…The Navier-Stokes equations are integrated explicitly and continuity is satisfied at every time step. For further details see [14] and [15].…”

“…The 2D code developed by the author has been extensively tested against experimental and computational results for a stationary cylinder ( [16], [17], see [14], [15]) and computational results for cylinders oscillating in transverse or in in-line directions or following a circular path, including [6], [10] and [18], with good agreement being found, [15]. For this study the dimensionless time step was 0.0005 and the number of grid points 361x236.…”

“…This selection of f ensures synchronization or lock-in at moderate amplitude values of A x or A y . In this study the flow was considered to be locked-in for both in-line and transverse cylinder oscillation when the vortex shedding frequency f v is equal to the frequency of cylinder oscillation f. For in-line oscillation, lock-in was found earlier in the vicinity of the natural vortex shedding frequency f v0 , as well as the double of this frequency [15,18]. Here the first, narrower lock-in domain has been chosen.…”

“…The cylinder was started at different positions, characterized by polar angle Θ, since earlier investigations showed that this initial condition may have an effect on the solution, [15]. If not otherwise stated Θ=0º, meaning that the cylinder is started from its farthest downstream position (Θ increases in the clockwise direction).…”