Turbulent channel flow of generalized Newtonian fluids at a low Reynolds number

Abstract

Abstract

Effects of shear-thinning rheology on near-wall turbulent structures

“…Many experimental (Park et al 1989;Pinho & Whitelaw 1990;Pereira 1994) and numerical (Rudman & Blackburn 2003Gavrilov & Rudyak 2016) studies have reported features common to the low drag reduction (LDR) regime (Warholic, Massah & Hanratty 1999), such as enhancement of streamwise turbulence intensity and suppression of other cross-sectional intensities, decrease in Reynolds shear stress and overall reduction of turbulent production with shear-thinning fluid behaviour. More recently, and based on observations of the Reynolds stress budgets and to the overall turbulent kinetic energy, for turbulent pipe (Singh, Rudman & Blackburn 2017) and channel (Arosemena et al 2021) flows, strain-rate-dependent rheology has been found to be mainly important within the inner layer region. This remark is supported as well by the Singh, Rudman & Blackburn (2016) results where, for a fixed GN fluid rheology within the inner layer region, no significant differences are observed in the mean-flow and first-order statistics even if different apparent fluid viscosity profiles are attained outside the inner layer.…”

“…Singh, Rudman & Blackburn (2018) also reported small contributions from viscosity fluctuation terms to the mean shear stress budget, mean flow and turbulent kinetic energy budget up to moderate frictional Reynolds numbers, Re τ = 323-750. Arosemena et al (2021) further reasoned that observed drag-reducing features with shear-thinning behaviour are likely related to important changes to the near-wall turbulent structures and, in consequence, to the self-sustaining process occurring near the wall.…”

“…In contrast to studies about polymer solutions accounting for viscoelastic effects, works related to drag-reducing GN fluids have not directly addressed probable mechanisms leading to disruption of the self-sustaining process in the absence of elastic effects and, in general, less attention has been given to the phenomenological changes in the near-wall turbulence structures; for instance, observations about structures are limited to instantaneous contours of the streamwise streaks, two-point velocity correlations and integral length scales (see e.g. Rudman & Blackburn 2006, Singh et al 2017, Arosemena et al 2021 or alternatively Appendix A) whereas findings about the quasi-streamwise vortices are not often reported.…”

“…The data to be analysed are taken from channel flow simulations of GN fluids at a target Re τ = ρu τ h/μ w = 180 (Arosemena et al 2021). Here, ρ is the fluid density, u τ = (τ w /ρ) 1/2 is the frictional velocity defined in terms of the shear stress at the wall τ w , h is the channel half-width and μ w is the nominal wall viscosity (Draad, Kuiken & Nieuwstadt 1998;Ptasinski et al 2001).…”

“…Considering the previous context, this work focuses on purely viscous fluids and is an extension of the turbulent channel flow study of Arosemena, Andersson & Solsvik (2021). Our aim is to explore the changes on the near-wall turbulent structures, in particular the quasi-streamwise vortices, due to shear-thinning fluid behaviour; a non-Newtonian rheology exhibiting drag-reducing features.…”