Reynolds Stress Modeling for Drag Reducing Viscoelastic Flows

Abstract

A Reynolds-stress transport equation model for turbulent drag-reducing viscoelastic flows, such as that which occurs for dilute polymer solutions, is presented. The approach relies on an extended set of Reynolds-Averaged Navier-Stokes equations which incorporate additional polymer stresses. The polymer stresses are specified in terms of the mean polymer conformation tensor using the FENE-P dumbbell model. The mean conformation tensor equation is solved in a coupled manner along with the Navier-Stokes equations. The presence of the polymer stresses in the equations of motion results in additional explicit polymer terms in the Reynolds-stress transport equations, as well as implicit polymer effects in the pressure-strain redistribution term. Models for both the explicit and implicit effects have been developed and implemented in a code suitable for boundary layer, rectangular channel and pipe-flow geometries. Calibration and validation is has been carried out using results from recent direct numerical simulation of viscoelastic turbulent flow.

Reynolds-averaged modeling of polymer drag reduction in turbulent flows

“…(13)) is comparable to the other contributions [20,5,15]. This is also in agreement with the approximations introduced in Leighton et al [14].…”

“…(17) in Newtonian fluids as an extension to classical pressure-strain models [12] by including an elliptic operator that represents non-local effects, typically referred to as elliptic relaxation [7]. Leighton et al [14], on the other hand, ignored non-locality, but introduced an explicit modification to the pressure-strain correlation to account for the polymer-induced turbulence energy redistribution; the extra term was modeled by mimicking the slow pressure-strain model [21], e.g. the first term at the right hand side of Eq.…”

“…In the following section the expressions for these terms are presented. Leighton et al [14] first proposed a turbulence model for polymer flows based on the FENE-P dumbbell rheological model. In their approach, transport equations for the Reynolds and the polymer stresses are added to the mean flow equation; closures for the unknown correlations are also introduced and encouraging results are presented for the flow in channel.…”

“…In their approach, transport equations for the Reynolds and the polymer stresses are added to the mean flow equation; closures for the unknown correlations are also introduced and encouraging results are presented for the flow in channel. One important contribution of [14] is the identification of the implicit effect of the polymers on the turbulence energy redistribution process and the introduction of a modification to the pressure-strain model. Unfortunately, only very limited results were presented for a flow demonstrating only modest levels of drag reduction.…”

A Wall Boundary Condition for the Simulation of a Turbulent Non-Newtonian Domestic Slurry in Pipes

“…Known closures include those proposed by Pinho et al [21] and Leighton et al [22]; the latter was based on a priori direct numerical simulation. However, the validation of such closures is restricted to very low Reynolds numbers, as direct numerical simulation is computationally intensive [23].…”