Hele-Shaw flow

About: Hele-Shaw flow is a research topic. Over the lifetime, 5451 publications have been published within this topic receiving 151320 citations.

On the scaling of the slip velocity in turbulent flows over superhydrophobic surfaces

Abstract: Superhydrophobic surfaces can significantly reduce hydrodynamic skin drag by accommodating large slip velocity near the surface due to entrapment of air bubbles within their micro-scale roughness elements. While there are many Stokes flow solutions for flows near superhydrophobic surfaces that describe the relation between effective slip length and surface geometry, such relations are not fully known in the turbulent flow limit. In this work, we present a phenomenological model for the kinematics of flow near a superhydrophobic surface with periodic post-patterns at high Reynolds numbers. The model predicts an inverse square root scaling with solid fraction, and a cube root scaling of the slip length with pattern size, which is different from the reported scaling in the Stokes flow limit. A mixed model is then proposed that recovers both Stokes flow solution and the presented scaling, respectively, in the small and large texture size limits. This model is validated using direct numerical simulations of turbulent flows over superhydrophobic posts over a wide range of texture sizes from L+ ≈ 6 to 310 and solid fractions from ϕs = 1/9 to 1/64. Our report also embarks on the extension of friction laws of turbulent wall-bounded flows to superhydrophobic surfaces. To this end, we present a review of a simplified model for the mean velocity profile, which we call the shifted-turbulent boundary layer model, and address two previous shortcomings regarding the closure and accuracy of this model. Furthermore, we address the process of homogenization of the texture effect to an effective slip length by investigating correlations between slip velocity and shear over pattern-averaged data for streamwise and spanwise directions. For L+ of up to O(10), shear stress and slip velocity are perfectly correlated and well described by a homogenized slip length consistent with Stokes flow solutions. In contrast, in the limit of large L+, the pattern-averaged shear stress and slip velocity become uncorrelated and thus the homogenized boundary condition is unable to capture the bulk behavior of the patterned surface.

Influence of global rotation and Reynolds number on the large-scale features of a turbulent Taylor–Couette flow

Abstract: We experimentally study the turbulent flow between two coaxial and independently rotating cylinders. We determined the scaling of the torque with Reynolds numbers at various angular velocity ratios (Rotation numbers) and the behavior of the wall shear stress when varying the Rotation number at high Reynolds numbers. We compare the curves with particle image velocimetry analysis of the mean flow and show the peculiar role of perfect counter-rotation for the emergence of organized large scale structures in the mean part of this very turbulent flow that appear in a smooth and continuous way: the transition resembles a supercritical bifurcation of the secondary mean flow.

Measurement of the scaling of the dissipation at high Reynolds numbers

Abstract: We present experimental results from a mechanically driven turbulent flow in helium gas at low temperature. A large range of Reynolds numbers, extending over three decades (up to 5000 for ${\mathit{R}}_{\ensuremath{\lambda}}$) is investigated. We perform torque measurements and determine the dissipation locally by two methods, using the third-order structure function and the energy spectrum. Related quantities, such as the Kolmogorov and Taylor scales, are determined. Both methods give consistent measurements for ${\mathit{R}}_{\ensuremath{\lambda}}$g1000 but differences are observed at lower values. The scaling of the dissipation is determined by using a single power law to fit the whole range of Reynolds numbers; we recover the classical value (exponent equal to 3) when dissipation is calculated by using a third-order structure function, while a significantly lower value is obtained when a spectral method is used. The question of the viscosity dependence of the dissipation is thus left open. Several issues, such as the anisotropy, homogeneity of the flow, and Taylor hypothesis are discussed.

Granular gravitational collapse and chute flow

Abstract: We argue that inelastic grains in a flow under gravitation tend to collapse into states in which the relative normal velocities of two neighboring grains is zero. If the time scale for this gravitational collapse is shorter than inverse strain rates in the flow, we propose that this collapse will lead to the formation of granular eddies, large-scale condensed structures of particles moving coherently with one another. The scale of these eddies is determined by the gradient of the strain rate. Applying these concepts to chute flow of granular media (gravitationally driven flow down inclined planes), we predict the existence of a bulk flow region whose rheology is determined only by flow density. This theory yields the Pouliquen flow rule, correlating different chute flows; it also accounts for the different flow regimes observed.