Session P15: General Fluid Dynamics

Relative impacts of permeability heterogeneity and viscosity contrast on solute transport and mixing in porous media

Solute transport in porous media is affected by several factors. The heterogeneous structure of the permeability field is a key factor controlling the spreading and mixing behaviors of a solute cloud. On the other hand, other factors such as the viscosity contrast between the dissolved solute and the ambient fluid can also play an important role. This work aims to explore the impact of field heterogeneity and viscosity contrast on the transport behavior of an inert solute in a two-dimensional flow field. We performed high-resolution numerical simulations based on the spectral method to solve coupled flow and transport equations for a given range of viscosity contrast and log-permeability variance. We analyze the degree and rate of mixing, contour length of the solute cloud, spatial statistics of the concentration field and arrival times at a control plane to characterize spreading and mixing in the domain. We provide a quantitative separation of the impacts of fingering and heterogeneity and we parameterize the concentration probability distribution function. We find that the interplay between viscous fingering, high-permeability channeling, and low-permeability stagnation at small scales create important features in the spreading and mixing characteristics.   

A Numerical Investigation Of Rolling and Sliding Motion of Spheres in Confinement

The motion of spheres in fluids is one of the fundamental problems in fluid mechanics. At low Reynolds numbers, the problem is simplified significantly and it is possible to obtain both analytical and numerical solutions in unbounded fluids. Sphere motion in confined environments, however, is a much more elaborate problem as additional boundary conditions are introduced to the system. This problem is particularly interesting because spheres in confined environments are observed to be rolling along the direction of motion or sliding against the direction of motion. The mechanisms for rolling or sliding phenomena have been studied in the literature with several different numerical models but they either lack a direct correlation with the resistive coefficients of motion or the coefficients are not reported completely or accurately. Here we report a more accurate set of resistive coefficients by utilizing a finite element model for spheres rotating inside a cylindrical channel, particularly for near-wall swimming conditions which are critical for the transition from rolling to sliding. The coefficients are utilized in explaining the sliding phenomenon, which is known to occur due to the pressure build-up between the fore and aft of the sphere.   

Attraction and Repulsion of a Pair of Sedimenting Ball-Chains at Low Reynolds Number

We explore the hydrodynamic interaction of a pair of sedimenting ball-chains at low Reynolds number. We focus on experiments and compare the results with theory and simulations. The ball-chains are a proxy to elastic filaments, with their bending capability being dependent on the number of beads present. The study is focused on the tendency of the ball-chains to attract or repel each other for certain classes of initial positions (in particular, 1. horizontal and parallel to each other and 2. one above the other at perpendicular orientations) as well as the effect of increasing the number of beads on the ball-chain particles. In experiments, the millimeter sized ball-chains sediment in a large glass tank filled with highly viscous silicon oil. We obtain two perpendicular views of the particles using two cameras, which enables us to track the motion of the particles. From the photographs, we quantify the relative dynamics and shape deformation of the particles. We compare these experimental results with the results from numerical simulations based on the multipole expansion of the Stokes equations, as implemented in the Hydromultipole numerical codes.   

The sedimentation of thin, rigid discs in a viscous fluid: \\ A numerical study using a novel augmented finite-element method

We study the sedimentation of thin, arbitrarily shaped, but (for now) rigid disks, sedimenting under gravity in a quiescent viscous fluid. The sharp edge of such disks creates a singularity in the fluidpressure. At low Reynolds number, this means that a significant contribution of the total drag comes from the vicinity of the disk edge; for a flat disk at zero Reynolds number, 30\% of the total drag is generated by the outermost 5\% of the disk radius. This implies that any under-resolution of the pressure field leads to critical errors in the sedimentation velocity; furthermore, the singularities have a severe impact on the convergence rate of standard finite-element (FE) discretisations under mesh refinement.

Scaling of Free Subduction on a Sphere

Desirous to understand the dynamics of gravity-driven subduction of oceanic lithosphere on Earth, we study a simple model of a thin axisymmetric shell of thickness h and viscosity η₁ sinking in a spherical body of fluid with radius R and a lower viscosity η₀. Using scaling analysis based on thin viscous shell theory, we identify a fundamental length scale, the bending length l_b, and two key dimensionless parameters that control the dynamics: the 'flexural stiffness' St = (η₁/η₀)(h/l_b)³ and the 'sphericity number' α = (l_b/R) cot(θ₀), where θ₀ is the angular radius of the subduction trench. To validate the scaling analysis, we obtain numerical solutions using the boundary-element method, based on new analytical point-force Green functions that satisfy free-slip boundary conditions on the sphere's surface. By comparing our solutions with those for the `flat-Earth' limit, we show that sphericity reduces the subduction rate by a factor (of up to ~ 4) that increases with increasing St and α. We shall close with a brief discussion of the implications for the dynamics of selected terrestrial subduction zones.   

Not Participating

The efficiency, operation range, and environmental safety of energy and refrigeration cycles are determined by the thermodynamic properties of available fluids. We here suggest combining gas, liquid and multistable elastic capsules to create an artificial fluid with a multitude of stable states. We study, theoretically and experimentally, the suspension's internal energy, equilibrium pressure-density relations and their stability for both adiabatic and isothermal processes. We show that the elastic multistability of the capsules endows the fluid with multistable thermodynamic properties, including the ability of capturing and storing energy at standard atmospheric conditions, not found in naturally available fluids.   

Oscillating flow around a circular cylindrical post confined between two parallel flat plates

The three-dimensional oscillatory motion of a viscous fluid around a circular post confined between two plates is considered as a model for the flow of cerebrospinal fluid around the spinal-canal nerve roots. Besides the post aspect ratio λ, the problem depends on two dimensionless parameters, namely, the Womersley number $M$ (based on the post radius and the oscillation frequency) and the ratio ε of the stroke length to the cylinder radius, the latter assumed to be small herein. In the asymptotic limit ε«1, the leading-order motion is determined by a linear problem involving the balance of the local acceleration with the pressure and viscous forces. Convective acceleration introduces a small correction of order ε, including a steady-streaming component, numerically determined. Consideration is also given to the Stokes drift associated with the oscillating flow, comparable to the steady-streaming component, the sum of both determining the time-averaged Lagrangian velocity. Results reveal the formation of inner and outer streaming regions when $M$ is larger than a critical value which depends on λ. Consideration is given to limiting solutions arising for extreme values of λ and ε.   

Steady Streaming in a Hele-Shaw Cell

This study addresses pulsating flow about a cylindrical object in a Hele-Shaw cell in the distinguished double limit where the characteristic viscous time is comparable to the oscillation time and the stroke length is comparable to the cell height. The ratio of the stroke length to the cylinder radius is used as a small parameter to analyze the flow by matched asymptotic expansions, with consideration given to two distinct flow regions, namely, a thin shear layer surrounding the cylinder whence axial vorticity is shed periodically, and a slender outer region scaling with the cylinder radius where streamlines are nearly parallel to the bounding walls. The incompressible Navier-Stokes equations are solved in both regions to describe the leading-order pulsating flow and the first-order corrections, the latter including a steady-streaming component. The steady outer flow field in the center-plane of the cell, whose streamlines are parameter-independent, is shown to reverse direction for a critical value of the fluid viscosity. Said flow is also shown to possess four vortices that perpetually entrap the majority of fluid surrounding the cylinder. The results of this study are of significant interest in micro-fluidic applications such as particle sorting and valveless pumping.   

Biological inspired particle separation by modified surface morphology

Water scarcity is a serious issue faced by communities across the globe, including those in foggy coastal regions, where the air is laden with an alternative source of fresh water.  As seen in nature, the Namib desert beetles such as O. unguicularis use their bodies to intercept the inertial fog droplets carried by the wind.  We hypothesize that the unique surface features of these beetles' backs are physical adaptations that manipulate flow and hydrodynamic interactions toward enhanced fog collection ability. Through experiments conducted with controlled fog delivery and sensitive measurements of impaction efficiency, complemented by numerical flow simulations, we find mechanisms that are responsible for dramatically increased collection:  While flow structure is modulated at the millimetric (morphological) scale to increase droplet slip velocity near target surface, hydrodynamic resistance to contact is decreased by features at the microscopic (roughness) scale.   

Anderson-Type Mixing Methods for the Convergence Acceleration of Partitioned Fluid-Structure Interaction (FSI) Algorithms

We present a stable second-order partitioned iterative scheme for solving low mass ratio FSI problems. This work generalizes the previously developed nonlinear interface force correction (NIFC) framework based on a dynamically stabilized Aitken's geometric extrapolation procedure. Similar to NIFC, which also employs an Arbitrary Lagrangian-Eulerian (ALE) finite element framework; in the present formulation, approximate interface force corrections are constructed through subiterations to account for the missing effects of off-diagonal Jacobian terms in the "black-box" partitioned staggered scheme. Specific to this work we progress the idea of nonlinear sequence transformations of the modified Shanks-kernel to derive a suite of Anderson-type mixing (ATM) methods for iterative coupling. The main feature of the ATM strategy is that it combines the independent interface vectorial information of the two domain "sequences" to obtain a better acceleration procedure. Using the numeric properties of these sequence transformations we additionally demonstrate the ability to derive data-driven filtering and preconditioning methodologies to further accelerate the convergence of highly non-linear and strongly coupled partitioned Multiphysics simulations. To critically evaluate the comparative success of our proposed iterative scheme against the presently popular interface quasi-newton inverse least-squares (IQN-ILS) and inverse multi-vector Jacobian (IQN-IMVJ) methods, we parametrically measure the fixed-point iterative convergence and solution stability properties of each of the methods mentioned for three industry-standard benchmark problems of increasing complexity.   

Microgravity Testing of Vapor Motion within Tapered Channels for Spaceflight Cryogenic Propellant Management

The use of cryogenic propellants in rocket fluid transfer and storage systems create safety and operational challenges for long-duration space missions. Screened-channel liquid acquisition devices (LADs) have long been used with storable propellants to deliver vapor-free liquid during spacecraft engine restart and liquid transfer processes. The use of LADs with cryogenic fluids is problematic due to low fluid temperatures, as external heat leaks will cause vapor bubbles to form that are difficult to remove in conventional LAD designs. A tapered LAD channel has been designed to reliably remove vapor bubbles within the device without costly thrusting maneuvers by the in-space vehicle or active separation systems. Microgravity testing of this tapered LAD technology was recently completed onboard the New Shepard suborbital launch vehicle with two different simulant cryogenic fluids. An analysis was performed on the image sequence taken of the fluid motion inside of the devices. The results of this analysis indicate that these new LADs can passively expel vapor bubbles within the channel without active measures.   

Experimental Investigation of Flow Past an Axially-Aligned Spinning Cylinder

Turbulent flow past axially aligned spinning cylinders are of common occurrence in projectiles, missiles, and munitions and the modeling and the prediction of these flow fields is crucial for their effective design. The objective of this study is to experimentally examine the flow over a single spinning cylinder and its wake to characterize the flow field and separation.  The proposed experimental investigation is performed in a low-intensity subsonic wind tunnel and will characterize the flow field of an axially-aligned cylinder. The experiment covers a Reynolds number range of up to 60,000 and rotation numbers of up to 2 (based on cylinder diameter). Full measurement of the wake is possible since a forward mounted sting is used. Experimental investigations performed to date indicate that the experimental setup is capable of accurately capturing the flow separation and the wake flow field. The results are compared with the available data in the literature.