Intermittency in the transition to turbulence

It is commonly known that the intermittent transition from laminar to turbulent flow in pipes occurs because, at intermediate values of a prescribed pressure drop, a purely laminar flow offers too little resistance, but a fully turbulent one offers too much. We propose a phenomenological model of the flow, which is able to explain this in a quantitative way through a hysteretic transition between laminar and turbulent states, characterized by a disturbance amplitude variable that satisfies a natural type of evolution equation. The form of this equation is motivated by physical observations and derived by an averaging procedure, and we show that it naturally predicts disturbances having the characteristics of slugs and puffs. The model predicts oscillations similar to those which occur in intermittency in pipe flow, but it also predicts that stationary biphasic states can occur in sufficiently short pipes

Transition to turbulence in a heated non-Newtonian pipe flow

A simplified mono-dimensional model for investigating the transition to turbulence in nonisothermal and non-Newtonian pipe flows is proposed. The flow stability is analyzed within the framework of such a model, showing that uniformly heating the pipe wall leads to an earlier transition to turbulence, while differentially heating the pipe wall produces a stabilizing effect. For power-law fluids, we also demonstrate that an increase in the power-law index, i.e., passing from shear-thinning to shear-thickening fluids, leads to a stabilization of the system

Influence of shear-thinning blood rheology on the laminar-turbulent transition over a backward facing step

Cardiovascular diseases are the leading cause of death globally and there is an unmet need for effective, safer blood-contacting devices, including valves, stents and artificial hearts. In these, recirculation regions promote thrombosis, triggering mechanical failure, neurological dysfunction and infarctions. Transitional flow over a backward facing step is an idealised model of these flow conditions; the aim was to understand the impact of non-Newtonian blood rheology on modelling this flow. Flow simulations of shear-thinning and Newtonian fluids were compared for Reynolds numbers ( R e ) covering the comprehensive range of laminar, transitional and turbulent flow for the first time. Both unsteady Reynolds Averaged Navier–Stokes ( k − ω SST) and Smagorinsky Large Eddy Simulations (LES) were assessed; only LES correctly predicted trends in the recirculation zone length for all R e . Turbulent-transition was assessed by several criteria, revealing a complex picture. Instantaneous turbulent parameters, such as velocity, indicated delayed transition: R e = 1600 versus R e = 2000, for Newtonian and shear-thinning transitions, respectively. Conversely, when using a Re defined on spatially averaged viscosity, the shear-thinning model transitioned below the Newtonian. However, recirculation zone length, a mean flow parameter, did not indicate any difference in the transitional Re between the two. This work shows a shear-thinning rheology can explain the delayed transition for whole blood seen in published experimental data, but this delay is not the full story. The results show that, to accurately model transitional blood flow, and so enable the design of advanced cardiovascular devices, it is essential to incorporate the shear-thinning rheology, and to explicitly model the turbulent eddies

Influence of shear-thinning blood rheology on the laminar-turbulent transition over a backward facing step

Cardiovascular diseases are the leading cause of death globally and there is an unmet need for effective, safer blood-contacting devices, including valves, stents and artificial hearts. In these, recirculation regions promote thrombosis, triggering mechanical failure, neurological dysfunction and infarctions. Transitional flow over a backward facing step is an idealised model of these flow conditions; the aim was to understand the impact of non-Newtonian blood rheology on modelling this flow. Flow simulations of shear-thinning and Newtonian fluids were compared for Reynolds numbers (Re) covering the comprehensive range of laminar, transitional and turbulent flow for the first time. Both unsteady Reynolds Averaged Navier-Stokes (k 􀀀 w SST) and Smagorinsky Large Eddy Simulations (LES) were assessed; only LES correctly predicted trends in the recirculation zone length for all Re. Turbulent-transition was assessed by several criteria, revealing a complex picture. Instantaneous turbulent parameters, such as velocity, indicated delayed transition: Re = 1600 versus Re = 2000, for Newtonian and shear-thinning transitions respectively. Conversely, when using a Re defined on spatially averaged viscosity, the shear-thinning model transitioned below the Newtonian. However, recirculation zone length, a mean flow parameter, did not indicate any difference in the transitional Re between the two. This work shows a shear-thinning rheology can explain the delayed transition for whole blood seen in published experimental data, but this delay is not the full story. The results show that to accurately model transitional blood flow, and so enable the design of advanced cardiovascular devices, it is essential to incorporate the shear-thinning rheology, and to explicitly model the turbulent eddies

Stability of generalized Kolmogorov flow in a channel

The Kolmogorov flow is a paradigmatic model flow used to investigate the transition from laminar to turbulent regimes in confined and, especially, in unbounded domains. It represents a solution of the forced Navier–Stokes equation, where the forcing term is sinusoidal. The resulting velocity profile is also sinusoidal with the same wavenumber of the forcing term. In this study, we generalize the Kolmogorov flow making use of a generic forcing term defined by a Fourier series that bridges the classical Kolmogorov flow to an arbitrary even-degree power-law profile. Thereafter, we perform a linear stability analysis on the power-law profiles for exponents, α=2, 4, 6, 8, and 10, and the corresponding generalized Kolmogorov flows, varying the truncation index K of the Fourier series. Several neutral stability curves are computed numerically for wall-bounded flows and the relevant critical conditions are compared in terms of critical Reynolds number, critical wavelength, and eigenspectrum at criticality. The most dangerous perturbations are thoroughly characterized, and we identify three qualitatively different most dangerous modes, depending on α, K, the Reynolds number, and the perturbation wavelength

Propagation and rupture of elastoviscoplastic liquid plugs in airway reopening model

The propagation and rupture of mucus plugs in human lungs is investigated experimentally by injecting synthetic mucus in a pre-wetted capillary tube. The rheology of our test liquid is thoroughly characterized, and four samples of synthetic mucus are considered in order to reproduce elastoviscoplastic regimes of physiological interest for airway reopening. Our experiments demonstrate the significant impact of the viscoplasticity and viscoelasticity of mucus. In support to our experiments, we propose a one-dimensional reduced-order model that takes into account capillarity, and elastoviscoplasticity. Our model manages to capture the cross-section averaged dynamics of the liquid plug and is used to elucidate and interpret the experimental evidence. Relying on it, we show that the liquid film thickening due to non-Newtonian effects favors plug rupture, whereas the increase of the effective viscosity due to higher yield stresses hinders plug rupture. As a result of such two effects, increasing the polymeric concentration in the mucus phase leads to a net increase of the rupture time and traveling length. Hence, non-Newtonian effects hinder airway reopening