Characteristic scales and drag reduction evaluation in turbulent channel flow of nonconstant viscosity viscoelastic fluids

Abstract

The polymer-induced drag reduction in turbulent viscoelastic channel flow is customarily investigated from first principles through direct numerical simulations. In contrast to Newtonian fluid mechanics, in viscoelastic fluid mechanics there are more parameters and those are typically referenced under standard, zero shear-rate conditions. For a nonconstant viscosity non-Newtonian fluid it is necessary to correlate the effective wall viscosity to the parameters of the model. This correlation can only be evaluated a posteriori based on the wall statistics. It is used here to relate the computational to the wall units. Furthermore, the relationship between the effective wall properties and the corresponding steady shear values is elucidated. Moreover, an accurate and robust procedure for evaluating the overall drag reduction is presented.

Turbulent drag reduction by polymer additives in parallel-shear flows

“…The approximate mean wall shear rate, estimated from shear viscosity curves, is the shear rate corresponding to τ w computed from pressure-drop measurements at time t. This procedure is possible because the rheometer provides the link between shear stress and shear rate through the measured shear viscosity. We note that the mean shear rate determined in this 827 R4-7 manner is merely an approximation for shear-thinning fluids and is exact only in the Newtonian limit (Housiadas & Beris 2004). As expected, the polymer data lie between Virk's MDR and the correlation of Blasius or Dean (1978) for Newtonian turbulent flow, f approaching the Newtonian values with increasing pumping time.…”

Karhunen–Loeve representations of turbulent channel flows using the method of snapshots

“…In the viscoelastic cases, it is evident that the mass ux increases as the Weissenberg number increases with the bulk Reynolds numbers being 3497, 3748, and 4273 for We = 25, 50, and 125, respectively. The corresponding drag reduction values are 23, 38, and 58% which were obtained using the relations derived by Housiadas and Beris [40].…”

“…For all cases a zero shear-rate friction Reynolds number of 180 has been chosen, the computational box size is 9 × 2 × 4:5 in the x, y, and z directions, respectively, and the mesh resolution is 96 × 97 × 96 in those directions. The nonlinear terms in (40) and (41) were fully dealiased in the x-z plane using a 144 × 97 × 144 grid according to the standard three-halves rule. The total integration time required to achieve a statistically steady state is 60 computational units for the Newtonian case, and 80 computational time units for the viscoelastic cases.…”

A new method preserving the positive definiteness of a second order tensor variable in flow simulations with application to viscoelastic turbulence

“…Since then, using either implicit or explicit smoothing procedures, many successful numerical simulations of viscoelastic turbulent drag reducing flows have been performed within our research group [11,[17][18][19][20]36] and others [8,28,27,34]. Upwind techniques can and have been developed that preserve the positive definiteness and simultaneously do the smoothing.…”

“…The degree of smoothness introduced to the solution using the numerical diffusion method is proportional to the numerical diffusivity parameter, D þ 0 , made dimensionless with respect to the zero-shear rate wall units [17][18][19][20]. As in the LES applications, the optimum value for this parameter depends on the mesh resolution, becoming smaller as the mesh resolution increases.…”