The forced vibrations of a cylinder at low Reynolds number flow, an investigation of the non-lock-in and lock-in regions

Abstract

The present thesis is examining the forced vibrations of a circular cylinder in the low Reynolds number flow of 200. A numerical study is performed that employs an already existing algorithm developed by (Breuer 1998) and enhanced with the characteristic of the cylinder’s motion by (MadaniKermani 2014) who employed the moving frame of reference method of (L. Li, Sherwin et al. 2002). The algorithm was extensively assessed for the benchmark studies of flow around a stationary circular cylinder. A new observation was made on the effect of the aspect ratio of the computational cells in the mid region of the wake. The studies so far are emphasizing on the characteristic of a dense mesh, with a small aspect ratio, in the high divergence areas in the near region of the cylinder surface, neglecting the effect of the regions away from the surface. The present study on a stationary circular cylinder flow, proved that the aspect ratio of the distant cells has a significant effect on the St number and the force coefficients. The main study of the thesis emphasizes on the lock-in region where the wake oscillates in unison with the harmonic motion of the cylinder. The study makes a new observation on the qualitative and quantitative description of the lock-in conditions. In particular, it reveals two regions of resonance and non-resonance lock-in. Despite the fact that the lock-in is achieved, when the frequency ratio is in the first part of the region away from the unity ratio, the forces are not greatly magnified. As the ratio approaches the unity the forces experience a resonance that reaches the highest value after the unity. Furthermore, the adaptation time of the flow to the motion of the cylinder is examined and extends the results of (Anagnostopoulos 2000) to the full extent of the lock-in and the non-lock-in regions. More precisely the flow strives to reach a steady state when it is in the lock-in region rather in the non-lock in cases it reaches the steady state faster. It is postulated that the adaptation time depends on both the numerical and the physical adaptation. Moreover, the force coefficients characteristic of sinusoidal behaviour in the lock-in region is attempted to be approximated by a Newton polynomial that is built by making use of the divided differences method. The amplitude of the forces is approximated by a third degree Netwon polynomial built from the results of the present thesis simulations. The use of an approximation is providing faster results ignoring the need for a full resolution of the Navier-Stokes equation.