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Dynamics Near the Subcritical Transition of the 3D Couette Flow I: Below Threshold Case
The authors study small disturbances to the periodic, plane Couette flow in the 3D incompressible Navier-Stokes equations at high Reynolds number Re. They prove that for sufficiently regular initial data of size $\\epsilon \\leq c_0\\mathbf {Re}^-1$ for some universal $c_0 > 0$, the solution is global, remains within $O(c_0)$ of the Couette flow in $L^2$, and returns to the Couette flow as $t \\rightarrow \\infty $. For times $t \\gtrsim \\mathbf {Re}^1/3$, the streamwise dependence is damped by a mixing-enhanced dissipation effect and the solution is rapidly attracted to the class of \"2.5 dimensional\" streamwise-independent solutions referred to as streaks.
eBook
Nonlinear hydrodynamic instability and turbulence in pulsatile flow
Pulsating flows through tubular geometries are laminar provided that velocities are moderate. This in particular is also believed to apply to cardiovascular flows where inertial forces are typically too low to sustain turbulence. On the other hand, flow instabilities and fluctuating shear stresses are held responsible for a variety of cardiovascular diseases. Here we report a nonlinear instability mechanism for pulsating pipe flow that gives rise to bursts of turbulence at low flow rates. Geometrical distortions of small, yet finite, amplitude are found to excite a state consisting of helical vortices during flow deceleration. The resulting flow pattern grows rapidly in magnitude, breaks down into turbulence, and eventually returns to laminar when the flow accelerates. This scenario causes shear stress fluctuations and flow reversal during each pulsation cycle. Such unsteady conditions can adversely affect blood vessels and have been shown to promote inflammation and dysfunction of the shear stress-sensitive endothelial cell layer.
Journal Article
Numerical study on the internal flow characteristics of an axial-flow pump under stall conditions
When an axial-flow pump works in low flow rate conditions, rotating stall phenomena will probably occur, and the pump will enter hydraulic unsteady conditions. The rotating stall can lead to violent vibration, noise, turbulent flow, and a sharp drop in efficiency. This affects the safety and stability of the pump unit. To study the rotating stall flow characteristics of an axial-flow pump, the steady and unsteady internal flow field in a large vertical axial-flow pump was investigated using 3D computational fluid dynamic (CFD) technology. Numerical calculations were carried out using the Reynolds-averaged Navier–Stokes (RANS) solver and Menter's shear stress transport (SST) k-ω turbulence model. Steady flow characteristics including streamline, velocity vector, pressure and turbulent kinetic energy are presented and analyzed. Unsteady flow characteristics are described using post-processing signals for pressure monitoring points in the time and frequency domains. Using Q-criterion, the locations and evolution rules of the core region of the vortex structure in guide vanes under deep stall conditions were investigated. The reliability of the numerical simulation results was verified using the experimental prototype pressure fluctuation test. In this way, typical flow structure and pressure fluctuation characteristics in an axial-flow pump were analyzed, with contrastive analysis in design condition and stall conditions. Finally, the mechanism of low-frequency pressure fluctuation in a pump unit under the stall condition was revealed.
Journal Article
Droplets in homogeneous shear turbulence
We simulate the flow of two immiscible and incompressible fluids separated by an interface in a homogeneous turbulent shear flow at a shear Reynolds number equal to 15 200. The viscosity and density of the two fluids are equal, and various surface tensions and initial droplet diameters are considered in the present study. We show that the two-phase flow reaches a statistically stationary turbulent state sustained by a non-zero mean turbulent production rate due to the presence of the mean shear. Compared to single-phase flow, we find that the resulting steady-state conditions exhibit reduced Taylor-microscale Reynolds numbers owing to the presence of the dispersed phase, which acts as a sink of turbulent kinetic energy for the carrier fluid. At steady state, the mean power of surface tension is zero and the turbulent production rate is in balance with the turbulent dissipation rate, with their values being larger than in the reference single-phase case. The interface modifies the energy spectrum by introducing energy at small scales, with the difference from the single-phase case reducing as the Weber number increases. This is caused by both the number of droplets in the domain and the total surface area increasing monotonically with the Weber number. This reflects also in the droplet size distribution, which changes with the Weber number, with the peak of the distribution moving to smaller sizes as the Weber number increases. We show that the Hinze estimate for the maximum droplet size, obtained considering break-up in homogeneous isotropic turbulence, provides an excellent estimate notwithstanding the action of significant coalescence and the presence of a mean shear.
Journal Article
The centre-mode instability of viscoelastic plane Poiseuille flow
A modal stability analysis shows that plane Poiseuille flow of an Oldroyd-B fluid becomes unstable to a ‘centre mode’ with phase speed close to the maximum base-flow velocity, $U_{max}$. The governing dimensionless groups are the Reynolds number $Re = \\rho U_{max} H/\\eta$, the elasticity number $E = \\lambda \\eta /(H^2 \\rho )$ and the ratio of solvent to solution viscosity $\\beta = \\eta _s/\\eta$; here, $\\lambda$ is the polymer relaxation time, $H$ is the channel half-width and $\\rho$ is the fluid density. For experimentally relevant values (e.g. $E \\sim 0.1$ and $\\beta \\sim 0.9$), the critical Reynolds number, $Re_c$, is around $200$, with the associated eigenmodes being spread out across the channel. For $E(1-\\beta ) \\ll 1$, with $E$ fixed, corresponding to strongly elastic dilute polymer solutions, $Re_c \\propto (E(1-\\beta ))^{-3/2}$ and the critical wavenumber $k_c \\propto (E(1-\\beta ))^{-1/2}$. The unstable eigenmode in this limit is confined in a thin layer near the channel centreline. These features are largely analogous to the centre-mode instability in viscoelastic pipe flow (Garg et al., Phys. Rev. Lett., vol. 121, 2018, 024502), and suggest a universal linear mechanism underlying the onset of turbulence in both channel and pipe flows of sufficiently elastic dilute polymer solutions. Although the centre-mode instability continues down to $\\beta \\sim 10^{-2}$ for pipe flow, it ceases to exist for $\\beta < 0.5$ in channels. Whereas inertia, elasticity and solvent viscous effects are simultaneously required for this instability, a higher viscous threshold is required for channel flow. Further, in the opposite limit of $\\beta \\rightarrow 1$, the centre-mode instability in channel flow continues to exist at $Re \\approx 5$, again in contrast to pipe flow where the instability ceases to exist below $Re \\approx 63$, regardless of $E$ or $\\beta$. Our predictions are in reasonable agreement with experimental observations for the onset of turbulence in the flow of polymer solutions through microchannels.
Journal Article