Drag coefficient and formation length at the onset of vortex shedding

• Published in: Physics of fluids (1994) Vol. 31; no. 1
• Main Authors: Chopra, Gaurav, Mittal, Sanjay
• Format: Journal Article
• Language: English
• Published: Melville American Institute of Physics 01.01.2019
• Subjects: Circular cylinders; Coefficient of variation; Computational fluid dynamics; Drag coefficients; Finite element method; Flow equations; Fluid dynamics; Fluid flow; Incompressible flow; Kinetic energy; Physics; Reynolds number; Steady flow; Suction; Two dimensional flow; Viscosity; Vortex shedding; Vortices
• ISSN: 1070-6631; 1089-7666
• DOI: 10.1063/1.5075610

The flow past a circular cylinder at a low Reynolds number (40 ≤ Re ≤ 180) is investigated. A stabilized finite element method is utilized to solve the incompressible flow equations in two-dimensions. The critical Re for the onset of vortex shedding (Rec) is estimated to be 46.985. The variation of time-averaged coefficient of drag (C¯D) with Re is found to be non-monotonic for Re > Rec. Unlike for the steady flow, the pressure component of C¯D increases with an increase in Re in a short range of Re for Re > Rec. This increase is due to a significant rise in the peak suction, near the shoulder of the cylinder, of the time-averaged flow, with Re. Several definitions of vortex formation length (Lf), proposed in the past, are reviewed and compared. A new definition, based on the fluctuation in the local kinetic energy of the flow, is proposed. The variation of Lf with Re is compared with Lw, the separation bubble length. Lf is found to be significantly larger than Lw for Re close to Rec. The difference between the two lengths decreases with an increase in Re. The meaning of Lf, in terms of flow physics, is explored. It is found that the vortices form in the near wake, even for Re close to Rec. They become stronger as they convect downstream and gain full strength at a location Lf downstream of the cylinder, beyond which they begin to decay.