Modeling of viscoelastic turbulent flow in channel and pipe

Abstract

This paper investigates turbulent flows with or without polymer additives in open channels and pipes. Equations of mean velocity, root mean square of velocity fluctuations, and energy spectrum are derived, in which the shear stress deficit model is used and the non-Newtonian properties are represented by the viscoelasticity ␣ * . The obtained results show that, with ␣ * increment, ͑1͒ the streamwise velocity fluctuations is increased, ͑2͒ the wall-normal velocity fluctuation is attenuated, ͑3͒ the Reynolds stress is reduced, and ͑4͒ there is a redistribution of energy from high frequencies to the low frequencies for the streamwise component, but dimensionless distribution over all frequencies almost remains the same as that in Newtonian fluid flows. Good agreement between the derived equations and experimental data in small drag-reduction regime is achieved, which indicates that the present model is workable for Newtonian/non-Newtonian fluid turbulent flows.

Drag reduction by polymer additives from turbulent spectra

“…If δ * → 0 but c is large, then eq. ( 71) predicts v [δ * ] ∝ δ * and then the parametric relations become f ∝ Re −1/2 , in reasonable agreement with Virk's asymptote [15,[33][34][35][36]. We see however that even for large concentrations drag reduction will be very small as long as δ * ≫ δ 0…”

Time‐series and extended Karhunen–Loève analysis of turbulent drag reduction in polymer solutions

“…Another recent approach is based on phenomenological ansatzes regarding Reynolds shear stresses and eddy viscosities . In particular, Benzi and coworkers combine these ideas with the observation that in some experiments (e.g., Ref.…”

Turbulent drag reduction with polymer additive in rough pipes

“…If −u v = 0, one can obtain the velocity u + l in laminar flow from (12), and by modelling the Reynolds shear stress in (12), Dou obtained the velocity u + in fully turbulent flow (Yang & Dou 2008 …”