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The influence of shear-dependent rheology on turbulent pipe flow

Published online by Cambridge University Press:  08 June 2017

J. Singh Open the ORCID record for J. Singh [Opens in a new window] ,
M. Rudman  and
H. M. Blackburn
J. Singh
Affiliation:
Department of Mechanical and Aerospace Engineering, Monash University, VIC 3800, Australia
M. Rudman*
Affiliation:
Department of Mechanical and Aerospace Engineering, Monash University, VIC 3800, Australia
H. M. Blackburn
Affiliation:
Department of Mechanical and Aerospace Engineering, Monash University, VIC 3800, Australia
*
†Email address for correspondence: [email protected]
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Abstract

Direct numerical simulations of turbulent pipe flow of power-law fluids at $Re_{\unicode[STIX]{x1D70F}}=323$ are analysed in order to understand the way in which shear thinning or thickening affects first- and second-order flow statistics including turbulent kinetic energy production, transport and dissipation in such flows. The results show that with shear thinning, near-wall streaks become weaker and the axial and azimuthal correlation lengths of axial velocity fluctuations increase. Viscosity fluctuations give rise to an additional shear stress term in the mean momentum equation which is negative for shear-thinning fluids and which increases in magnitude as the fluid becomes more shear thinning: for an equal mean wall shear stress, this term increases the mean velocity gradient in shear-thinning fluids when compared to a Newtonian fluid. Consequently, the mean velocity profile in power-law fluids deviates from the law of the wall $U_{z}^{+}=y^{+}$ in the viscous sublayer when traditional near-wall scaling is used. Consideration is briefly given to an alternative scaling that allows the law of wall to be recovered but which results in loss of a common mean stress profile. With shear thinning, the mean viscosity increases slightly at the wall and its profile appears to be approximately logarithmic in the velocity log layer. Through analysis of the turbulent kinetic energy budget, undertaken here for the first time for generalised Newtonian fluids, it is shown that shear thinning decreases the overall turbulent kinetic energy production but widens the wall-normal region where it is generated. Additional dissipation terms in the mean flow and turbulent kinetic energy budget equations arise from viscosity fluctuations; with shear thinning, these result in a net decrease in the total viscous dissipation. The overall effect of shear thinning on the turbulent kinetic energy budget is found to be largely confined to the inner layers, $y^{+}\lesssim 60$.

JFM classification

Non-Newtonian Flows: Non-Newtonian Flows Boundary Layers: Pipe flow boundary layer Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 822 , 10 July 2017 , pp. 848 - 879
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© 2017 Cambridge University Press 

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