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We present numerical simulations of laminar and turbulent channel flow of an elastoviscoplastic fluid. The non-Newtonian flow is simulated by solving the full incompressible Navier–Stokes equations coupled with the evolution equation for the elastoviscoplastic stress tensor. The laminar simulations are carried out for a wide range of Reynolds numbers, Bingham numbers and ratios of the fluid and total viscosity, while the turbulent flow simulations are performed at a fixed bulk Reynolds number equal to 2800 and weak elasticity. We show that in the laminar flow regime the friction factor increases monotonically with the Bingham number (yield stress) and decreases with the viscosity ratio, while in the turbulent regime the friction factor is almost independent of the viscosity ratio and decreases with the Bingham number, until the flow eventually returns to a fully laminar condition for large enough yield stresses. Three main regimes are found in the turbulent case, depending on the Bingham number: for low values, the friction Reynolds number and the turbulent flow statistics only slightly differ from those of a Newtonian fluid; for intermediate values of the Bingham number, the fluctuations increase and the inertial equilibrium range is lost. Finally, for higher values the flow completely laminarizes. These different behaviours are associated with a progressive increases of the volume where the fluid is not yielded, growing from the centreline towards the walls as the Bingham number increases. The unyielded region interacts with the near-wall structures, forming preferentially above the high-speed streaks. In particular, the near-wall streaks and the associated quasi-streamwise vortices are strongly enhanced in an highly elastoviscoplastic fluid and the flow becomes more correlated in the streamwise direction.
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Structured input–output analysis of stably stratified plane Couette flow
We employ a recently introduced structured input–output analysis (SIOA) approach to analyse streamwise and spanwise wavelengths of flow structures in stably stratified plane Couette flow. In the low-Reynolds-number ( $Re$ ) low-bulk Richardson number ( $$Ri_b$$ ) spatially intermittent regime, we demonstrate that SIOA predicts high amplification associated with wavelengths corresponding to the characteristic oblique turbulent bands in this regime. SIOA also identifies quasi-horizontal flow structures resembling the turbulent–laminar layers commonly observed in the high- $Re$ high- $$Ri_b$$ intermittent regime. An SIOA across a range of $$Ri_b$$ and $Re$ values suggests that the classical Miles–Howard stability criterion ( $$Ri_b\leq 1/4$$ ) is associated with a change in the most amplified flow structures when the Prandtl number is close to one ( $$Pr\approx 1$$ ). However, for $$Pr\ll 1$$ , the most amplified flow structures are determined by the product $$PrRi_b$$ . For $$Pr\gg 1$$ , SIOA identifies another quasi-horizontal flow structure that we show is principally associated with density perturbations. We further demonstrate the dominance of this density-associated flow structure in the high $Pr$ limit by constructing analytical scaling arguments for the amplification in terms of $Re$ and $Pr$ under the assumptions of unstratified flow (with $$Ri_b=0$$ ) and streamwise invariance.
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- Award ID(s):
- 1652244
- PAR ID:
- 10396179
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 948
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2022.648
