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Open accessJournal ArticleDOI: 10.1063/5.0037971

Falling balls in a viscous fluid with contact: Comparing numerical simulations with experimental data

02 Mar 2021-Physics of Fluids (AIP Publishing LLC AIP Publishing)-Vol. 33, Iss: 3, pp 033304
Abstract: We evaluate a number of different finite-element approaches for fluid–structure (contact) interaction problems against data from physical experiments. This consists of trajectories of single particles falling through a highly viscous fluid and rebounding off the bottom fluid tank wall. The resulting flow is in the transitional regime between creeping and turbulent flows. This type of configuration is particularly challenging for numerical methods due to the large change in the fluid domain and the contact between the wall and the particle. In the finite-element simulations, we consider both rigid body and linear elasticity models for the falling particles. In the first case, we compare the results obtained with the well-established Arbitrary Lagrangian–Eulerian (ALE) approach and an unfitted moving domain method together with a simple and common approach for contact avoidance. For the full fluid–structure interaction (FSI) problem with contact, we use a fully Eulerian approach in combination with a unified FSI-contact treatment using Nitsche's method. For higher computational efficiency, we use the geometrical symmetry of the experimental setup to reformulate the FSI system into two spatial dimensions. Finally, we show full three-dimensional ALE computations to study the effects of small perturbations in the initial state of the particle to investigate deviations from a perfectly vertical fall observed in the experiment. The methods are implemented in open-source finite element libraries, and the results are made freely available to aid reproducibility.

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7 results found


Journal ArticleDOI: 10.1140/EPJP/S13360-021-01428-6
Abstract: An analytical and numerical study for the creeping flow caused by a solid spherical particle with a slip-flow surface is considered in the presence of a fluid–fluid plane interface. The particle rotating about or translating along an axis perpendicular to the interface. The motion is investigated in the limit of low capillary number where in this situation the interface is of negligible deformation. Using a bipolar coordinate system, the stream functions are constructed for both fluid phases as Reynolds number tends to zero. The novelty of this work is allowing the slip on the surface of the particle. The matching boundary conditions at the plane interface and the slip boundary condition on the particle’s surface are applied to the truncated solutions to specify the unknown coefficients. A comparison is made between the results of the analytical solution and the results obtained from a boundary collocation method. The torque and drag force exerted on the particle are calculated using both techniques, which are found in perfect agreement. In addition to compression with collocation techniques, we also studied the predicted changes in the drag force and torque due to the presence of the plane interface and the slippage at the surface of the particle. Our results of the drag force and torque are compared with the available data in the literature for the special cases. The work is motivated by its possible application as an analytical tool in the study of locomotion of microswimmers near an interface such as synthetic swimmers and microorganisms.

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Topics: Drag (59%), Slip (materials science) (57%), Boundary value problem (55%) ... show more

3 Citations


Open accessJournal ArticleDOI: 10.1016/J.IJMULTIPHASEFLOW.2021.103589
Abstract: The settling process and wall impact of large spherical particles in a stagnant, highly viscous fluid has been observed by means of high-speed shadow imaging. The particles included in this study vary in size and material properties: steel, polytetrafluorethylen (PTFE), polyoxymethylen (POM), or rubber. The corresponding terminal Reynolds numbers range from 333 to 4012, covering in principle the transitional and Newton regime for drag forces. However, most particles do not reach the terminal velocity before colliding with the impact object. Therefore, the main focus of this study is set on particle settling and collision in the transitional regime. For collision studies, the Stokes number just before impact is also relevant, and lies in the range 50 St 2250 . The settling curves obtained experimentally (characterized by vertical position and vertical velocity component) are compared with numerical and analytical solutions. The latter has been derived on the basis of nominal terminal velocity and relaxation time for the Stokes and Newton regimes. The numerical model takes into account the side walls and the corresponding correction of the drag coefficient. A deviation between experimental results and analytical solution was observed in all cases where the terminal Reynolds number is larger than 300 and smaller than 1100. It appears that, in this flow regime, the settling process of the spheres is already affected at a long distance from the impact object, leading to an early but significant deceleration. Moreover, a reduced settling velocity was observed along the whole trajectory for the PTFE particles with the lowest terminal Reynolds number. All these effects are captured in the numerical model and the corresponding results agree fairly well with the experiments. There is one exception, induced by particle rotation, which is not considered in the current model. In that case, it is not possible to correctly predict the settling process. All processed datasets are available via the Mendeley Data repository Hagemeier (2020). Two additional effects have been observed during this study. First, a bright region was detected around all PTFE spheres. It finally was found to be due to total light reflection around the sphere, but, to the best of our knowledge, this peculiarity has never been reported before. Being purely optical, this does not effect the settling behavior for PTFE. On the other hand, partial absorption of liquid at the particle surface was observed for rubber, leading to a reduced sedimentation velocity. This property, already documented for homogeneous porous particles, is found here for a rubber particle with almost impermeable core.

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Topics: Settling (64%), Terminal velocity (57%), Stokes number (56%) ... show more

3 Citations


Open accessJournal ArticleDOI: 10.1007/S10013-021-00477-9
Abstract: An accurate prediction of the translational and rotational motion of particles suspended in a fluid is only possible if a complete set of correlations for the force coefficients of fluid-particle interaction is known. The present study is thus devoted to the derivation and validation of a new framework to determine the drag, lift, rotational and pitching torque coefficients for different non-spherical particles in a fluid flow. The motivation for the study arises from medical applications, where particles may have an arbitrary and complex shape. Here, it is usually not possible to derive accurate analytical models for predicting the different hydrodynamic forces. The presented model is designed to be applicable to a broad range of shapes. Another important feature of the suspensions occurring in medical and biological applications is the high number of particles. The modelling approach we propose can be efficiently used for simulations of solid-liquid suspensions with numerous particles. Based on resolved numerical simulations of prototypical particles we generate data to train a neural network which allows us to quickly estimate the hydrodynamic forces experienced by a specific particle immersed in a fluid.

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Topics: Particle (55%), Drag (54%), Lift (force) (53%) ... show more

2 Citations


Open accessJournal ArticleDOI: 10.1016/J.SIMPA.2021.100070
Stefan Frei1, Thomas Richter, Thomas Wick2Institutions (2)
01 May 2021-
Abstract: We describe the Software package LocModFE, which is an implementation of a locally modified finite element method for an accurate solution of interface problems. The code was originally developed in the finite element library Gascoigne 3d and has now been rewritten in the widerspread library deal.II. This makes the concept of locally modified finite elements accessible to many users all over the world. Applications range from simple Poisson interface problems over multi-phase flows to complex multi-physics problems, such as fluid–structure interactions. Being based on deal.II, it provides plenty of possibilities for future extensions, e.g., parallel computing, multigrid solvers or mesh adaptivity.

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1 Citations


Open accessJournal ArticleDOI: 10.1063/5.0062688
20 Aug 2021-Physics of Fluids
Abstract: Geometric confinements play an important role in many physical and biological processes and significantly affect the rheology and behavior of colloidal suspensions at low Reynolds numbers. On the basis of the linear Stokes equations, we investigate theoretically and computationally the viscous azimuthal flow induced by the slow rotation of a small spherical particle located in the vicinity of a rigid no-slip disk or inside a gap between two coaxially positioned rigid no-slip disks of the same radius. We formulate the solution of the hydrodynamic problem as a mixed-boundary-value problem in the whole fluid domain, which we subsequently transform into a system of dual integral equations. Near a stationary disk, we show that the resulting integral equation can be reduced into an elementary Abel integral equation that admits a unique analytical solution. Between two coaxially positioned stationary disks, we demonstrate that the flow problem can be transformed into a system of two Fredholm integral equations of the first kind. The latter are solved by means of numerical approaches. Using our solution, we further investigate the effect of the disks on the slow rotational motion of a colloidal particle and provide expressions of the hydrodynamic mobility as a function of the system geometry. We compare our results with corresponding finite-element simulations and observe very good agreement.

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Topics: Integral equation (58%), Rotation around a fixed axis (53%), Reynolds number (52%) ... show more

1 Citations


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69 results found


Journal ArticleDOI: 10.1016/0009-2509(61)80035-3
Howard Brenner1Institutions (1)
Abstract: Bipolar co-ordinates are employed to obtain “exact” solutions of the equations of slow, viscous flow for the steady motion of a solid sphere towards or away from a plane surface of infinite extent. Two cases are considered: (i) the plane surface is rigid and fluid adheres to its surface; (ii) the plane is a free surface on which the tangential stresses vanish. Deformation of the surface in the latter case is neglected. Numerical results are provided for the corrections to Stokes' law necessitated by the presence of the plane boundary at a finite distance from the particle. Application of the results to end-effect correlations in the falling-ball viscometer are discussed.

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Topics: Plane (geometry) (60%), Free surface (58%), Surface (mathematics) (57%) ... show more

1,419 Citations


Journal ArticleDOI: 10.1016/0045-7825(81)90049-9
Abstract: A transient, finite element formulation is given for incompressible viscous flows in an arbitrarily mixed Lagrangian-Eulerian description. The procedures developed are appropriate for modeling the fluid subdomain of many fluid-solid interaction, and free-surface problems.

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1,383 Citations



Journal ArticleDOI: 10.1016/0045-7825(82)90128-1
Abstract: Finite element models are presented for the prediction of the non-linear response of fluid-structure systems exposed to transient dynamic loading. An arbitrary Lagrangian-Eulerian kinematical description of the fluid domain is adopted in which the grid points can be displaced independently of the fluid motion. This formulation leads to an easy and accurate treatment of fluid-structure interfaces and permits significant fluid sloshing and swirling to occur without producing excessive distorsions of the computational mesh. Several applications are presented to illustrate the potential of the proposed modelling procedures.

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Topics: Material point method (61%), Mixed finite element method (58%), Finite element method (56%) ... show more

1,276 Citations


Open accessJournal ArticleDOI: 10.1007/S007910050004
Joachim Schöberl1Institutions (1)
Abstract: In this paper, the algorithms of the automatic mesh generator NETGEN are described. The domain is provided by a Constructive Solid Geometry (CSG). The whole task of 3D mesh generation splits into four subproblems of special point calculation, edge following, surface meshing and finally volume mesh generation. Surface and volume mesh generation are based on the advancing front method. Emphasis is given to the abstract structure of the element generation rules. Several techniques of mesh optimization are tested and quality plots are presented.

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Topics: Mesh generation (63%), Volume mesh (57%), Constructive solid geometry (54%) ... show more

998 Citations


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20217