Flow past a cylinder: shear layer instability and drag crisis

Abstract

Flow past a circular cylinder for Re = 100 to 10 7 is studied numerically by solving the unsteady incompressible two-dimensional Navier-Stokes equations via a stabilized finite element formulation. It is well known that beyond Re ∼ 200 the flow develops significant three dimensional features. Therefore, two dimensional computations are expected to fall well short of predicting the flow accurately at high Re. It is fairly well accepted that the shear layer instability is primarily a two dimensional phenomenon. The frequency of the shear layer vortices, from the present computations, agree quite well with the Re 0.67 variation observed by other researchers from experimental measurements. The main objective of this paper is to investigate a possible relationship between the drag crisis (sudden loss of drag at Re ∼ 2 × 10 5 ) and the instability of the separated shear layer. As Re is increased the transition point of shear layer, beyond which it is unstable, moves upstream. At the critical Reynolds number the transition point is located very close to the point of flow separation. As a result, the shear layer eddies cause mixing of the flow in the boundary layer. This energizes the boundary layer and leads to its reattachment. The delay in flow separation is associated with narrowing of wake, increase in Reynolds shear stress near the shoulder of the cylinder and a significant reduction in the drag and base suction coefficients. The spatial and temporal power spectra for the kinetic energy of the Re = 10 6 flow are computed. As in two dimensional isotropic turbulence, E(k) varies as k −5/3 for wavenumbers higher than energy injection scale and as k −3 for lower wavenumbers. The present computations suggest that the shear layer vortices play a major role in the transition of boundary layer from laminar to turbulent state.1

Desenvolvimento da modelagem de turbulência e interação fluido-estrutura para as vibrações induzidas por vórtices de cilindro rígido.

“…Firstly, the overall trends of all parameters were well captured, in-cluding the qualitative behavior seen near the critical Reynolds numbers, which suggests that the drag crisis is mainly two-dimensional, as observed by Singh & Mittal (2005). Also, the qualitative aspects of the flow field and aspects such as the bifurcation of the Navier-Stokes equations leading to vortex-shedding, or also the secondary vortices associated with instabilities of the shear layer next to the separation.…”

“…However, in LES, the treatment of turbulence close to the objects is usually modeled (simplified, using sub-grid scale models or even wall functions) and not simulated such as in DNS, with serious consequences for wall-bounded flows. That has been seen in Singh & Mittal (2005), who have done two-dimensional LES calculations for a wide range of Reynolds numbers, up to Re = 10 7 . It is clear that the simplifications introduced by subgrid models, two-dimensional computations and insufficient grid and time step discretization cause drag coefficients to be up to 50% larger than experimental results.…”

“…Firstly, as stressed by Mittal & Balachandar (1995), Singh & Mittal (2005), beyond Re > 200 the flow undergoes three-dimensional transitional instabilities, hence the two-dimensional computations tend to poorly represent the phenomena. The two-dimensional computations overestimate the drag and base suction due to a higher level of Reynolds stresses, which result in a shorter formation length behind the bluff body.…”

“…6.1.5 Shear-Layer Transition Regime -1, 000 < Re < 200, 000 Williamson (1996), Singh & Mittal (2005) have identified the range 1, 000 < Re < 200, 000 as the Shear-Layer Transition Regime. In this regime, the base suction increases and the formation length of the mean recirculation region decreases.…”

“…That was also explored by Vaz et al (2007), Pengan (2010), Klaij (2008) with SST, showing the limitations of the three-dimensional modeling with traditional modeling and identifying the need of better assessment of the three-dimensional turbulent behavior within URANS. In the last years, different models have been developed with that objective, such as the Partially-Average Navier Stokes (PANS) equations (GIRIMAJI, 2006), Detached Eddy Simulations (DES) (TRAVIN et al, 1999), Delayed Detached Eddy Simulations (DDES) (SPALART et al, 2006) among others. present a comparison of RANS, SAS, DES and PANS models for the backward facing step case, shedding light on some of their differences and capabilities.…”