An assessment of turbulence models for the prediction of flow past a circular cylinder with momentum injection

Abstract

Reynolds averaged Navier–Stokes equations (RANS) are solved to simulate the flow past a circular cylinder. Momentum injection through Moving Surface Boundary-layer Control (MSBC) with zero net mass injection is implemented to achieve wake control. Popular eddy viscosity based closure models are assessed for their predictive capability of turbulent wake characteristics. For the present simulation, sub-critical Reynolds number ( Re) of 3900 is chosen, where extensive validations are available. A stabilization approach is proposed to model, predict and control vortex shedding behind a circular cylinder. Along with the mass, momentum conservation, turbulent kinetic energy (TKE) and its rate of dissipation equations are solved with the objective of achieving the annihilation of wake structures. To enable momentum injection, two simple rotary type control cylinders are located at 120°, behind the main cylinder. The ratio of the main cylinder, control cylinder and gap between them are fixed at D: 0.1D: 0.01D, respectively. These control cylinders, which are like externally controllable actuators, are assessed for their ability to influence momentum injection and hence wake patterns. The popular finite volume based Semi Implicit Pressure Linked Equations (SIMPLE) scheme is employed for the numerical calculations. Detailed assessment of different eddy viscosity based turbulence models viz., standard k – ε , Renormalization Group (RNG) k – ε , realizable k – ε and k – ε version of Kato–Launder (KL) is carried out. As a precursor, validation of turbulence statistics such as, mean streamwise velocity along the wake centerline, mean pressure coefficient on the cylinder surface and time averaged Reynolds stresses etc. is carried out against known experimental and numerical computations. The role of externally controllable actuators on the fluid flow patterns past a circular configuration is assessed with the help of streaklines, streamlines, vorticity, Reynolds stress contours etc. Complete suppression of vortex shedding is observed for an injection parameter (defined as the ratio of control cylinder velocity ( U c ) to that of the freestream ( U ∞ )) ξ = 6.0 . The results clearly demonstrate the effectiveness of a rather simple momentum injection strategy in suppressing turbulent vortex structures.