Simulations of three-dimensional viscoelastic flows past a circular cylinder at moderate Reynolds numbers

Abstract

The results from a numerical investigation of inertial viscoelastic flow past a circular cylinder are presented which illustrate the significant effect that dilute concentrations of polymer additives have on complex flows. In particular, effects of polymer extensibility are studied as well as the role of viscoelasticity during three-dimensional cylinder wake transition. Simulations at two distinct Reynolds numbers (Re = 100 and Re = 300) revealed dramatic differences based on the choice of the polymer extensibility (L2 in the FENE-P model), as well as a stabilizing tendency of viscoelasticity. For the Re = 100 case, attention was focused on the effects of increasing polymer extensibility, which included a lengthening of the recirculation region immediately behind the cylinder and a sharp increase in average drag when compared to both the low extensibility and Newtonian cases. For Re = 300, a suppression of the three-dimensional Newtonian mode B instability was observed. This effect is more pronounced for higher polymer extensibilities where all three-dimensional structure is eliminated, and mechanisms for this stabilization are described in the context of roll-up instability inhibition in a viscoelastic shear layer.

Viscoelastic flow simulations in model porous media

“…Though direct numerical simulations on the pore scale can predict exact flow features of a viscoelastic fluid through a representative porous medium, they are limited due to the high computational costs and convergence issues in a three-dimensional framework. Previously, many researchers have investigated numerically the flow of viscoelastic fluids through simple porous media using both finite-element and finite-volume methods [12][13][14][15]. The viscoelastic fluid flow through a periodic array of cylinders and the effects of permeability were studied by Alcocer and Singh [16].…”

Dynamics of a single buoyant plume in a FENE-P fluid

“…More recently, numerical simulations [10][11][12][13][14][15][16][17][18][19][20][21] have added to our understanding of the physical mechanisms responsible for this phenomenon. The major practical effect of polymer addition has been found, in every case without exception, to be a drag reduction by as much as 80%.…”

“…The polymer conformation evolves according to (4) where α p , the polymer diffusivity in the solution, is introduced to insure numerically stable solutions. 21 This system of equations, along with the incompressibility constraint ∂ i V i = 0, was solved using a pseudo-spectral code 26 in a channel geometry in which all field variables are expanded in Fourier modes in the horizontal (x-z) plane and Chebyshev modes in the vertical (y) direction. The resolution was 64 × 65 × 16 in the x, y, and z directions, and the corresponding domain lengths were L x = πh, L y = 2h, and L z = πh.…”

“…No flux conditions (∂C ji /∂y = 0) were applied to the conformation at the top and bottom walls. 21 Since the gravitational body force acts in the negative y direction in these simulations, a nominally twodimensional single laminar buoyant plume was produced by imposing a Gaussian temperature profile θ = θ max e −f (x) at the bottom wall, where f(x) = (x − L x /2) 2 /(2σ 2 ), θ max is the maximum temperature at the wall, σ = L x /10, and x varies from 0 to L x . The temperature at the top wall was kept fixed (θ = 0).…”

Flow past a cylinder in diluted polymer solutions

“…In fact, both drag enhancement and drag reduction of the cylinder were reported at present (James & Acosta, 1970;Verhelst & Nieuwstadt, 2004;François et al, 2008;Oliveira & Miranda, 2005;Richter et al, 2010). The drag behavior of a cylinder in polymer solutions was not clear until a recent numerical work by Xiong et al (2010).…”