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Taylor-Couette Flow Modeling (Rev.1)

The Taylor-Couette Flow is a form of viscous flow in which fluid flows between two cylindrical walls with a prescribed rotation. A diagram is shown on the right (Figure 1) where Ω is the rotational velocity, H is the distance between the two cylinders, R is the radius the outer cylinder, r is the radius of the inner cylinder and L is the length of the cylinders. When the rotating inner cylinder reaches a critical velocity, the flow of the liquid becomes unstable and creates vortices in between the layers. In this experiment, the Taylor-Couette cylinders were modeled so that the vortices would be created after reaching a critical velocity. After the initial experiment, the velocity of the inner cylinder was decreased and increased to look at how the results changed.

42 ENGINEERING

Observation of Nonaxisymmetric Standard Magnetorotational Instability Induced by a Free-Shear Layer

The standard magnetorotational instability (SMRI) with a magnetic field component parallel to the rotation axis is widely believed to be responsible for the fast accretion in astronomical disks. In conventional base flows with a Keplerian profile or an ideal Couette profile, most studies focus on axisymmetric SMRI, since excitation of nonaxisymmetric SMRI in such flows requires a magnetic Reynolds number (Rm) more than an order of magnitude larger. Here, we report that, in a magnetized Taylor-Couette flow, nonaxisymmetric SMRI with an azimuthal mode number m = 1 can be triggered by a free-shear layer in the base flow at Rm ≳1, the same threshold as for axisymmetric SMRI. Global linear analysis reveals that the free-shear layer reduces the required Rm, possibly by introducing an extremum in the vorticity of the base flow. Nonlinear simulations validate the results from linear analysis and confirm that a novel instability recently discovered experimentally [Wang et al., Nat. Commun. 13, 4679 (2022)] is the nonaxisymmetric m =1 SMRI. Further, our finding has astronomical implications as free-shear layers are ubiquitous in celestial systems, such as the disk-star boundary layer, the solar tachocline, and the edge of planet-opened gaps in protoplanetary disks.

79 ASTRONOMY AND ASTROPHYSICS

Incorporating the molecular-scale into a hydrodynamic description of confined aqueous systems

Hydrodynamics provides a continuum-level description of fluid motion, but its applicability at the nanoscale becomes uncertain due to the emerging importance of molecular-level effects such as spatial heterogeneity. Hydrodynamic boundary conditions that incorporate molecular details allow us to partition the system into a near-wall region and a bulk fluid region. We identify a hydrodynamic wall located inside the fluid that determines where slip begins. By extending the hydrodynamic wall with the slip length, the position of the extrapolated wall is established. This offers a unified description of both slip and stagnant flow behaviors, with wall hydrophobicity characterized by the relative location of the extrapolated wall with respect to the physical wall. Employing this concept in analyses of equilibrium molecular dynamics (MD) and non-equilibrium MD simulations of Couette and Poiseuille flows, our results demonstrate consistency between equilibrium and non-equilibrium approaches across different flow types and confinement levels. This demonstrates the robust nature of linear response theory. We then explore the effects of fluid-wall and bulk fluid interactions on the hydrodynamic properties. These findings enhance the effectiveness of molecular-based simulations for investigating complex confined systems in nanofluidics, biology, and colloidal science, offering a complementary molecular-scale perspective to traditional continuum approaches.

flow simulations

Magneto-Stokes flow in a shallow free-surface annulus

In this study, we analyse ‘magneto-Stokes’ flow, a fundamental magnetohydrodynamic (MHD) flow that shares the cylindrical-annular geometry of the Taylor–Couette cell but uses applied electromagnetic forces to circulate a free-surface layer of electrolyte at low Reynolds numbers. The first complete, analytical solution for time-dependent magneto-Stokes flow is presented and validated with coupled laboratory and numerical experiments. Three regimes are distinguished (shallow-layer, transitional and deep-layer flow regimes), and their influence on the efficiency of microscale mixing is clarified. The solution in the shallow-layer limit belongs to a newly identified class of MHD potential flows, and thus induces mixing without the aid of axial vorticity. We show that these shallow-layer magneto-Stokes flows can still augment mixing in distinct Taylor dispersion and advection-dominated mixing regimes. The existence of enhanced mixing across all three distinguished flow regimes is predicted by asymptotic scaling laws and supported by three-dimensional numerical simulations. Mixing enhancement is initiated with the least electromagnetic forcing in channels with order-unity depth-to-gap-width ratios. If the strength of the electromagnetic forcing is not a constraint, then shallow-layer flows can still yield the shortest mixing times in the advection-dominated limit. Our robust description of momentum evolution and mixing of passive tracers makes the annular magneto-Stokes system fit for use as an MHD reference flow.

58 GEOSCIENCES

Pseudo-viscous modeling of transport in dense granular flows for thermal energy storage applications

Dense, granular flows were examined to effectively capture and model bulk viscous properties in thin packed beds. A modified Couette cell with particle image velocimetry was used to experimentally determine pseudo-viscosity properties of four particulate media with varying morphologies: (1) iron oxide-coated SiO 2 particles, (2) CARBOBEAD CP30-60 particles, (3) CARBOBEAD CP40-100 particles, and (4) Al 2 O 3 beads. The pseudo-viscosity functions were fitted using a power law to correlate the measured shear stress as a function of measured shear rate. The pseudo-viscous functions were used as inputs to computation fluid dynamics models for a single-phase viscous fluid to predict granular flow profiles. Steady-state free surface velocity profiles at angular velocities <7 rad/s predicted by the model were in good agreement with the experimental particle image velocimetry measurements, resulting in Pearson correlation coefficients of 0.97 for iron-oxide coated SiO 2 particles and 0.95 for CP30-60 particles. As a result, this alternative approach to measuring pseudo-viscous properties under shearing and modeling bulk transport behavior of granular flow using computation fluid dynamics model offered significant reduction in computational load compared to discrete element methods.

14 SOLAR ENERGY