Session X23: Free Surface Flows: Interaction with Structures II

Quantifying Air Entrainment at the Gas-Liquid Interface in Stirred Tank Reactors

Air entrainment, or surface aeration, is a critical phenomenon in mixing processes that promote the development of a multiphase flow. It can either disturb the yield of a process by enhancing oxidation or promoting separation of low-density substances in a mixture. In this study, a standard stirred tank reactor (STR) with a Rushton-type impeller is used to analyze air entrained at the air-water interface. Both impeller speed and clearance beneath the surface play a major role in the quantity of air entrained in the system. High-speed backlit imaging is used to visualize and quantify air entrainment. It will be shown that the interplay between rotation speed and clearance depth is complex. Future characterization methods will also be discussed that will quantify air entrainment volume.   

Free surface perturbations of collapsing fluid cavities in magnetized target fusion machines

Magnetized target fusion machines achieve fusion by magnetically confining plasma in a blanket (liner) of molten alloy fluid, formed by spinning the fluid in a cylindrical rotor drum to create a vortex and central cavity. The cavity, containing the plasma, is forced to collapse by injecting fluid into the rotor through an array of bore holes in the rotor walls. As the cavity collapses, the magnetic field, and plasma which it confines, are rapidly compressed heating the plasma to fusion conditions.

For fusion to be attained, it is critical that the free surface of the cavity is kept uniform throughout the collapse. This presents a challenge as the interior wall of the rotor, which is perforated with bore holes, causes a non-uniform pressure field, which results in wave-like free surface disturbances. Presently, it is not known exactly how the amplitude and shape of the disturbances are affected by the arrangement of rotor bore holes (rotor geometry).

In the present work, the influence of the rotor geometry on the free surface is investigated experimentally and numerically using a Rankine source panel method. The results are validated using commercial CFD. The influence of the rotor geometry and initial fill volume of fluid in the rotor are discussed.   

Breaking wave impact in a boiling liquid

Light fuels, such as natural gas and hydrogen are conveniently transported overseas in cryogenic liquid form, stored in huge containers where the liquid is in thermodynamic equilibrium with its own vapor, i.e., it is a boiling liquid. During shipment, the dynamical container load is shown to be almost exclusively caused by sloshing wave impact. Therefore, to study the influence of phase change on container load, we turn to the Atmosphere facility at Marin (NL), a cylindrical autoclave in which isolated water - water vapor systems can be realized at equilibrium temperatures ranging from 20 °C to 120 °C. In a 12 meter long flume, a soliton is created by means of a wave maker, which is turned into a reproducible breaking wave by an upsloping ramp at the end of the channel. Subsequently, the wave impacts onto a vertical wall, where an array of pressure transducers measures the impact load. At low temperatures, pressures are observed to exceed those measured in water-air systems by at least one order of magnitude, which is traced back to the collapse of a vapor-filled cavity. Finally we discuss the observed differences and qualitatively explain them in terms of a vapor bubble model.   

The Free Vibration of Elastic Plates in Asymmetric Contact with Water

Slamming of thin-walled structures into liquid pools presents a complex strongly-coupled fluid-structure interaction problem, whose understanding requires knowledge of the structural response of the coupled system. For our system of interest, the free vibration of three horizontally oriented aluminum plates (.4 m wide, 1.08 m long) are studied in two cases: one with the plate surround by air and the other with the plate’s bottom surface in contact with a large pool of water. Three plate geometries and mounting schemes are studied:  i) a stepped plate with thickness varying from 12.7 mm to 6.35 mm mounted with pinned supports, ii) a uniform plate with 6.35 mm thickness also with pinned supports, and iii) a uniform plate with 4.83 mm thickness simply supported at one end and clamped at the opposite end. Digital Image Correlation (DIC) is used to track the vibrational response of the plate induced by striking it with an impact hammer. Two-degree-of-freedom displacements are collected from tracking the center target's motion. Time and frequency response plots are presented for comparison between half-wet and air cases. It is found that the added mass of the water results in lower measured natural frequencies and modified mode shapes. Preliminary center point displacement records show linear damped oscillator response with the plate in air and evidence of a nonlinear oscillator response in the half-wet case. Additional results are discussed.   

Dynamics of Open-Channel Flows Over Inclined Planar Obstacles

High-resolution PIV laboratory measurements were made of the velocity field created by open-channel flows interacting with inclined planar obstacles. Eleven different inclination angles, ranging from 25^° to 90^° , were investigated. An Eulerian control volume analysis was then conducted to understand the effect of the inclination angle (θ) on how energy is dissipated over the obstacle. Results show that as θ decreases, the relative kinetic energy dissipation rate (ϵ) decreases in a non-linear but monotonic fashion. The main energy sink is identified as a recirculation eddy that is present at higher θ, but then becomes unstable and eventually diminishes as θ decreases. The dimensions of this eddy are used to describe the structure of the flow field upstream of the obstacle. The effect of the upstream inertial condition (Re) on ϵ for a fixed θ was also investigated. It was found that ϵ decreases with increasing Re in a fixed range, but below a threshold Re of ∼ 3 × 10⁴ , ϵ increases significantly due to the growing influence of viscous effects. The practical implication of this research on the development and proper use of hydraulic structures that offer both accurate flow measurement and efficient upstream stage control is discussed.   

Flow Dynamics Around a Stationary Flat Plate in Proximity to a Free Surface

This work presents a comprehensive experimental investigation of the flow dynamics around a stationary, rigid flat plate positioned close to a free surface. The study employs water tunnel experiments and time-resolved particle image velocimetry (PIV) measurements to explore the interaction between the flat plate and the free surface, considering variations in angles of attack (AOA), Reynolds number (Re), and plate proximity to the free surface. For AOA≤5, when the flat plate is in the vicinity of the free surface, a regular shear layer forms on both sides of the plate, unaffected by the Re. However, for 10≤AOA≤30 and low Re numbers, the shear layer exhibits a jet-like behavior. This jet-like flow extends over the suction side of the plate, and the Coanda effect facilitates its attachment along the plate's surface at various angles of attack. As the Reynolds number increases to intermediate ranges, the shear layer separates from the plate, leading to the formation of shed vortices in the wake. Subsequently, at higher Re numbers, the free surface deformation compels the flow to reattach to the plate. Increasing the submerged height proves effective in eliminating the jet-like flow pattern for different AOAs and Re numbers.   

Vortical dynamics of supercritical flows in the vicinity of hydraulic structures

Supercritical flows in the vicinity of hydraulic structures exhibit complex vortical dynamics governed by the interaction of three relevant hydrodynamic processes: (i) boundary layer separation at the front side of the obstacle; (ii) the presence of a horseshoe vortex system due to the negative pressure gradient, and (iii) unsteady oscillations of the free surface in the form of a hydraulic jump. In this investigation, we characterise the physical phenomena involved in this interaction for different Reynolds and Froude numbers. To describe the large-scale vortical structures, we present a novel numerical solver which combines an Artificial-Compressibility 3D Navier-Stokes solver with a Level-Set method with a geometric-based reinitialisation approach that ensures accurate mass-conservation. We focus on the momentum transport processes that connect the unsteady local dynamics of the three flow features described above and their effects on wake recovery, free-surface evolution, and bottom shear distribution.   

Experimental study on the resistance of a partially submerged flat plate travelling in a field of synthetic ice floes

The resistance of a partially submerged flat plate traveling in a field of synthetic ice floes is investigated experimentally. The experiments are conducted in a towing tank, and the flat plate is installed on a carriage moving horizontally along the tank. In the experiments, the flat plate is 122 cm long, 61 cm wide, and 4.1 cm thick. The ice floes, which are made of polypropylene, are 7.6 cm in length, 7.6 cm in width, and 1.3 cm in thickness. Before each experimental run, the area coverage of the ice floes on the water surface is 90%. In a set of experimental conditions, the submergence depth (D) of the plate is varied from 4.1 cm to 24.9 cm, the pitch angle of the plate (α) is varied from 10° to 30°, and the forward speed (V) of the plate is varied from 0.9 m/s to 3.7 m/s. At a given experimental condition with a specific combination of D, α and V, resistance data is also collected without the presence of ice floes. At the same D, α and V, it is found that the resistance with the presence of ice floes is greater than that without the presence of ice floes. The difference in resistance (ΔR) between conditions with and without the presence of ice floes is found to increase with increasing V. Furthermore, the ratio of the resistance without the presence of ice floes to the resistance with the presence of ice floes increases as V, α and D increase. The scaling of resistance and its correlation with various physical parameters are further explored.    

Stability of array configurations under the action of deviatoric mean drift forces

Monochromatic waves incident on an array of structures give rise to nonlinear mean drift forces acting on the structures within the array. These drift forces are not purely in the direction of wave propagation, but have a significant component perpendicular to the wave propagation. If the structures are not rigidly connected but, say, individually moored to the bottom, these deviatoric drift forces can, in contrast to effect of the linear time-periodic exciting forces, cause a change of the spatial configuration of the array. This can lead to possible collisions between the structures, or lead to excitation or mooring forces that are significantly different than those for which the structures were designed. Using computational simulations and theoretical analysis, we study the equilibrium spatial configurations of arrays of axisymmetric bodies under the action of inter-body mean drift forces in monochromatic waves. We discuss the stability of equilibrium configurations with respect to deviations in body positions, and we address the effect of the equilibrium type on the mean drift force in the direction of wave propagation. We study this problem within the potential flow theory, employing the multiple scattering framework to obtain the non-linear, second-order mean drift force from the first-order linear potential. This study can be relevant for the design of floating wind farms, wave energy converter arrays, as well as harbor operations.   

Motion of a disk embedded in a nearly-inviscid Langmuir film

The translation of a disk in a Langmuir film bounding a liquid substrate is a classical hydrodynamic problem, dating back to Saffman (J. Fluid Mech., vol. 73, 1976, p. 593) who focused upon the singular problem of translation at large Boussinesq number. A semi-analytic solution of the dual integral equations governing the flow at arbitrary Boussinesq numbers was devised by Hughes, Pailthorpe & White (J. Fluid Mech., vol. 110, 1981, p. 349). When degenerated to the inviscid-film limit, it produces the value 8 for the dimensionless translational drag, which is 50% larger than the classical 16/3-value corresponding to a free surface. While that enhancement has been attributed to surface incompressibility, the mathematical reasoning underlying the anomaly has never been fully elucidated. Here we address the inviscid limit from the outset, revealing a singular mechanism where half of the drag is contributed by the surface pressure. We proceed beyond that limit, considering a nearly-inviscid film. A naive attempt to calculate the drag correction using the reciprocal theorem fails due to an edge-singularity of the leading-order flow. We identify the formation of a boundary layer about the edge of the disk, where the flow is primarily in the azimuthal direction with surface and substrate stresses being asymptotically comparable. Utilizing the reciprocal theorem in a fluid domain tailored to the asymptotic topology of the problem produces the requisite drag correction.   

Swirling Fluid Reduces the Bounce of Partially Filled Containers

Certain spatial distributions of water inside partially filled containers can significantly reduce the bounce of the container. In experiments with containers filled to a volume fraction ϕ, we show that rotation offers control and high efficiency in setting such distributions and, consequently, in altering bounce markedly. High-speed imaging evidences the physics of the phenomenon and reveals a rich sequence of fluid-dynamics processes, which we translate into a model that captures our overall experimental findings.