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Register a new userViscoelastic pipe flow is linearly unstable
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Newtonian pipe flow is known to be linearly stable at all Reynolds numbers. We report, for the first time, a linear instability of pressure driven pipe flow of a viscoelastic fluid, obeying the Oldroyd-B constitutive equation commonly used to model dilute polymer solutions. The instability is shown to exist at Reynolds numbers significantly lower than those at which transition to turbulence is typically observed for Newtonian pipe flow. Our results qualitatively explain experimental observations of transition to turbulence in pipe flow of dilute polymer solutions at flow rates where Newtonian turbulence is absent. The instability discussed here should form the first stage in a hitherto unexplored dynamical pathway to turbulence in polymer solutions. An analogous instability exists for plane Poiseuille flow.
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Turbulence is the major cause of friction losses in transport processes and it is responsible for a drastic drag increase in flows over bounding surfaces. While much effort is invested into developing ways to control and reduce turbulence intensities, so far no methods exist to altogether eliminate turbulence if velocities are sufficiently large. We demonstrate for pipe flow that appropriate distortions to the velocity profile lead to a complete collapse of turbulence and subsequently friction losses are reduced by as much as 95%. Counterintuitively, the return to laminar motion is accomplished by initially increasing turbulence intensities or by transiently amplifying wall shear. The usual measures of turbulence levels, such as the Reynolds number (Re) or shear stresses, do not account for the subsequent relaminarization. Instead an amplification mechanism measuring the interaction between eddies and the mean shear is found to set a threshold below which turbulence is suppressed beyond recovery.
The impact of wall roughness on fully developed laminar pipe flow is investigated numerically. The roughness is comprised of square bars of varying size and pitch. Results show that the inverse relation between the friction factor and the Reynolds number in smooth pipes still persists in rough pipes, regardless of the rib height and pitch. At a given Reynolds number, the friction factor varies quadratically with roughness height and linearly with roughness pitch. We propose a single correlation for the friction factor that successfully collapses the data.
Considered here is the derivation of partial differential equations arising in pulsatile flow in pipes with viscoelastic walls. The equations are asymptotic models describing the propagation of long-crested pulses in pipes with cylindrical symmetry. Additional effects due to viscous stresses in bio-fluids are also taken into account. The effects of viscoelasticity of the vessels on the propagation of solitary and periodic waves in a vessel of constant radius are being explored numerically.
For wall-bounded turbulent flows, Townsends attached eddy hypothesis proposes that the logarithmic layer is populated by a set of energetic and geometrically self-similar eddies. These eddies scale with a single length scale, their distance to the wall, while their velocity scale remains constant across their size range. To investigate the existence of such structures in fully developed turbulent pipe flow, stereoscopic particle image velocimetry measurements were performed in two parallel cross-sectional planes, spaced apart by a varying distance from 0 to 9.97$R$, for $Re_tau = 1310$, 2430 and 3810. The instantaneous turbulence structures are sorted by width using an azimuthal Fourier decomposition, allowing us to create a set of average eddy velocity profiles by performing an azimuthal alignment process. The resulting eddy profiles exhibit geometric self-similar behavior in the $(r,theta)$-plane for eddies with spanwise length scales ($lambda_theta/R$) spanning from 1.03 to 0.175. The streamwise similarity is further investigated using two-point correlations between the two planes, where the structures exhibit a self-similar behaviour with length scales ($lambda_theta/R$) ranging from approximately $0.88$ to $0.203$. The candidate structures thereby establish full three-dimensional geometrically self-similarity for structures with a volumetric ratio of $1:80$. Beside the geometric similarity, the velocity magnitude also exhibit self-similarity within these ranges. However, the velocity scale depends on eddy size, and follow the trends based on the scaling arguments proposed by cite{Perry1986}.
Local dissipation scales are a manifestation of the intermittent small-scale nature of turbulence. We report the first experimental evaluation of the distribution of local dissipation scales in turbulent pipe flows for a range of Reynolds numbers, 2.4x10^4<=Re_D<=7.0x10^4. Our measurements at the nearly isotropic pipe centerline and within the anisotropic logarithmic layer show excellent agreement with distributions that were previously calculated from numerical simulations of homogeneous isotropic box turbulence and with those predicted by theory. The reported results suggest a universality of the smallest-scale fluctuations around the classical Kolmogorov dissipation length.
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