Session L22: Turbulence: Rotating Flows

Energy spectrum and interscale transfer in non-homogeneous rotating flow: the case of a mixer

Time-resolved 2D2C PIV measurements are carried out in a water tank agitated by four blades rotating at constant speed. Different blade geometries with rectangular and fractal-like shapes are tested in order to change the turbulence properties. In some runs, vertical bars (baffles) on the walls are used to break the rotation of the flow and see the impact on the results.

A classical energy spectrum slope close to -5/3 is identified in the configurations with baffles. On the other hand, a steeper slope (between -2.3 and -1.9) is found for the configurations without baffles where the flow is strongly rotating. The analysis of the second order structure functions gives similar trends with a close to r^2/3 dependence on two-point separation r for the baffle configurations and a close to r evolution for the configurations without baffles.

Estimates of average interscale transfer and interspace transport rates are also evaluated from the data. These rates, defined from the Kármán-Howarth-Monin-Hill equation (KHMH), are used to quantify the impact of the rotation and non-homogeneity on the interscale transfer. A complementary equation to the KHMH one is also analysed and provides additional information for these flows.

    

Data reconstruction of rotating turbulent flows with Gappy POD and Generative Adversarial Networks

Two methods are used to reconstruct two-dimensional instantaneous velocity module fields in a turbulent flow under rotation. The first method is Gappy POD, in which we use proper orthogonal decomposition (POD) to complete flow fields from gappy data, while the second one reconstructs the flow fields using convolutional neural networks embedded in a Generative Adversarial Network (GAN). We first show that there is always an optimal number of POD modes for Gappy POD reconstruction regarding a specific gap. In order to systematically compare the applicability of the two tools, we consider one square gap at the center with different gap sizes. Results show that compared with Gappy POD, GAN reconstruction not only has a smaller L2 error, but also better turbulent statistics of both the velocity module and the velocity module gradient. This can be attributed to the ability of nonlinearity expression of the network and the presence of adversarial loss during the GAN training. We also investigate effects of the adversarial ratio, which controls the compromising between the L2 error and the statistical properties. Finally, we access the reconstruction on random gappiness. Both methods perform well for small and medium gappiness, while GAN works better when the gappiness is large.   

Effects of boundary conditions on the dynamics of convection-driven plane layer dynamos.

Rapidly rotating convection-driven dynamos are investigated under different kinematic and magnetic boundary conditions using direct numerical simulations. At a fixed rotation rate, represented by the Ekman number, E=5×10^-7, the thermal forcing is varied from 2 to 20 times its critical value (R=Ra/Ra_c=2-20, where Ra is the Rayleigh number), keeping the fluid properties constant (Pr=Pr_m=1, where Pr and Pr_m are the thermal and magnetic Prandtl numbers. For R=3, the horizontal and vertical velocities are higher with no-slip conditions compared to free-slip conditions at the wall. The structure and strength of the magnetic field produced by the dynamos, especially near the walls, depend on both velocity and magnetic boundary conditions. Though the leading-order force balance in bulk remains geostrophic, the Lorentz force becomes comparable to the Coriolis force inside the thermal boundary layer with no-slip, electrically conducting conditions. We also find enhanced heat transfer in the rotating dynamo convection, as compared with non-magnetic rotating convection, with the peak enhancement lying in the range R=3-4. The dynamo action may significantly enhance the heat transport for free-slip conditions by suppressing large-scale vortex formation. However, the peak enhancement is found at R=3 with no-slip, electrically conducting walls, which can be attributed to a local magnetorelaxation of the rotational constraint due to enhanced Lorentz force inside the thermal boundary layer.     

Annular Geoinspired Soft Mixer

A geoinspired soft mixer with application to bladeless bioreactors is studied. It is fitted with an internal cylinder in order to shine light within the reactors, in order to grow microalgae (dinoflagellates), when the concentration of cells is large (and hence the optical penetration depth is small). This mixer is an evolution of the cylindrical soft mixer (Meunier (2020), J. Fluid Mech. 903, A15), inspired by the precession of the Earth. It consists of an annular cavity rotating around its axis and is tilted from the vertical. The base flow is forced by the free surface to a global inertial flow (Kelvin modes). When the height of fluid is equal to a multiple of a half-wavelength, there is a resonance of the base flow. At the resonance the amplitude of the base flow is saturated by Ekman pumping, with a scaling proportional to the inverse of the square root of the Ekman number. Furthermore, for sufficiently large tilt angles and small Ekman numbers, the base flow triggers a parametric triadic instability involving interaction with two additional Kelvin modes. This instability promotes an efficient mixing within the annulus, with a shear rate of the order of 50% the angular velocity. However, this shear intensity is weaker than with a standard Rushton turbine classicaly used in stirred tank (approximately 5 times smaller), making of the annulus an appropriate bladeless mixer for large-scale bioreactors.   

Effect of swirl on linear formation of streaks in jets

Streaks in turbulent jets are a recent finding, dominating kinetic energy at low frequencies. It is an experimental result that is interesting in and of itself as one of the few coherent structures observed in this setting. Similar structures are known to be present and play a critical role in wall-bounded transition to turbulence. We propose to investigate the linear dynamics of streak generation in swirling jets. We compute a turbulent baseflow from the RANS equations at high Reynolds number, then leverage resolvent and modal analysis to study linear amplification mechanisms of the turbulent jet. We study a 2D azimuthally decomposed geometry with a 3D incompressible flow, and look at the effect of swirl on the linear mechanisms that give rise to growth of streaks. We include a nozzle in the calculation and use an eddy viscosity obtained from our RANS calculation.

    

On the inertial Landau-Levich-Deryaguin problem over a rotating disc

The so-called Landau-Levich-Deryaguin (LLD) problem treats thin viscous liquid film flows entrained by a moving solid surface. Here, we use a partially-immersed rotating disc in a liquid tank to study the role of inertia in the LLD problem. At first, we point out a rich phenomenology in the presence of strong inertia : formation of multiple liquid sheets on disc's front side, atomization of the liquid flux entrained over the disc's rim. Then, we focus on a single liquid sheet and the related average liquid flow rate entrained over a thin disc for various depth-to-radius ratio (h/R < 1). We illustrate that the liquid sheet is created through a ballistic mechanism as liquid is lifted out of the pool by the rotating disc. Also, by varying liquid viscosity, the entrained flow rate is shown to be given by the classical LLD lubrication flow approach based on both viscous and surface tension effects only, despite the large Reynolds numbers that result in 3D, non-uniform and unsteady entrained film flows. However, when the related Weber number becomes significant, strong inertial effects influence the entrained liquid flux over the disc at large radius-to-immersion-depth ratio via 3D flow stuctures wherein, a modified-LLD scaling based on ballistic fluid particle trajectory is proposed.   

Not Participating

The plane-Couette flow and the Taylor-Couette flow are two classical fluid dynamical systems that have been studied in great detail. However, the mechanism of how these two canonical flows may interact remains unexplored. Here we use a numerical method to simulate a flow geometry formed between sliding conveyor belts, which combines a linear, plane-Couette region and a curved, Taylor-Couette region. The geometry is mainly defined by the parameters L / r_i and (r_o-r_i) / r_i, where r_o, r_i are the outer and inner radius of Taylor-Couette region, and L is the length of linear plane-Couette region. When L << r_i, this system reaches the limit of the Taylor-Couette flow, while in the limit L >> r_i the plane-Couette geometry is dominant. We explore the situation where the outer belt is fixed and only the inner one is moving, and quantify the torque and drag for varying L / r_i. We draw insights about how the flow transitions from one limit to the other, with changing L / r_i, and within the merging zone.   

Centrifugal assembly of helical fibers during microfluidic twisting

Centrifugal microfluidics has been widely used to integrate different processes such as separating, mixing, and detecting molecules at the nanoscale. Aside from these unit operations, an unrecognized use of the centrifugal effect is introduced during Microfluidic Twisting (MT).

 

We investigate the assembly of helical soft matter fibers in a rotating microcapillary. During assembly, the fibers undergo phase separation, generating particle stabilized bicontinuous emulsion gels (bijels) [1]. This process is accompanied by a transition of the fiber density over time. As a result, the direction of the centrifugal force in the rotating microcapillary changes, pulling fibers of lower density towards the rotation axis, resulting in a helically woven micro rope. We use high-speed video microscopy and computer simulations to thoroughly investigate this effect. The resulting understanding enables control of the helical fiber assembly through manipulation of the densities of the fluids involved. [2, 3].

 

We envision MT to enable the fabrication of new composite materials with applications in flexible electronics, micro robotics, actuators, additive manufacturing, catalysis and tissue engineering. With these potentials, we believe that MT can become a new unit operation to advance high-throughput screening, lab-on-a-chip diagnostics, biochemical assays and material synthesis in microfluidics.

    

Flows over a spinning disc at incidence

Flows normal to the surface of stationary finite discs exhibit distinct periodic motions in their wakes marked by regular shedding of loop-like vortical structures. Most studies focus on the flows in the wake region; however, the present study focuses on the flows upstream and near the surface of spinning discs at incidence.  Flows are studied over a range of angles of incidence, 0 ≤ α ≤ 36^◦, spinning at angular velocities, Ω = 0 & ± 6.2 rev/s, in a freestream velocity of U_∞ = 2 m/s. The Reynolds number based on the diameter of the disc is 2.7 × 10⁴. A smoke-wire technique is used for smoke visualization and a planar particle image velocimetry technique is used to make velocity measurements near the upstream surface.

The formation and shedding of coherent vortical structures are observed near the upstream surface of the disc over the full range of angle of incidence. Two vortex shedding modes are observed, though signatures of both modes are present over the full range of angle of incidence. The primary mode is more prevalent at low angles of incidence and the secondary at high angles. The flows over spinning discs generally mimic flows over nonspinning discs, but resulting centrifugal forces affect vortex formation and decay. Time averaged velocity measurements provide axial and radial velocity profiles that are compared to existing analytic solutions.   

Criteria for the asymptotic turbulence in rapidly rotating convection

Turbulent rotating convection is the primary source of heat and momentum transfers in planetary and stellar flows. Key control parameters–the viscosity and the thermal diffusivity–in the flows are extremely small. As a result, theories often assume the existence of an asymptotic diffusivity-free heat scaling in the rapidly rotating convection, where the heat flux is independent of viscosity and thermal diffusivity. It is believed that when this heat scaling is achieved, the whole system becomes asymptotic or fully turbulent. Here, by performing extensive direct numerical simulations, we show that despite that the heat scaling behaves asymptotic, the kinetic energy dissipation rate can still be viscosity dependent, indicating the whole system is not fully asymptotic yet. A straightforward revision that bridges such a gap is presented based on the exact relations that link the dissipation rates with the heat transfer. Besides the heat scaling, an asymptotic Reynolds number scaling and a convective length scaling can be derived as well. The extrapolation of the results to more extreme parameters is only possible when all the three scalings are satisfied and when the flow is fully turbulent. Most importantly, realizing the asymptotic heat scaling itself does not necessarily signal the onset of the asymptotic or fully turbulent state in rapidly rotating convection.