Body In Viscous Fluid Research Articles

Developed Numerical Simulation of Falling and Moving Objects in Viscous Fluids under the Action of a Reynolds Lubrication Theory and Low Reynolds Numbers

The development work focuses on the numerical simulations of free body movement in viscous fluid. The aim is to make the simulation of very slow motion of the small body in viscous fluid. We developed bodies’ immersed dynamics simulations in viscous fluid by seeking numerical solutions for appropriate field variables. We developed the methods for vertically and spherically cylindrical objects’ motions, the forces on bodies close to a plane stationary wall are computed from the velocity and pressure fields using the Stokes equation through COMSOL Multiphysics finite element software. The Navier-Stokes equation is reduced to Stokes equation there is independence of time which means object will have an effect only on the motion and the slightly compressible flow assumption is made in order to obtain smooth solution numerically. The forces on an object in slightly compressible Stokes flow have been exerted on the falling objects. The resulting forces have compared with analytical results from the Reynolds Lubrication Theory, and achieved significant results from the development method in Matlab and achieved significant numerical simulations in COMSOL. In addition, an investigation has been made to an object swimming at low Reynolds number. At low Reynolds number moving is possible when object scale is small and flow pattern is slow and sticky. We have developed a system for a thin two-dimensional (2D) worm-like object wiggle that is passing a wave along its centreline and its motion has simulated by the Ordinary Differential Equations (ODE) system and by the Arbitrary Lagrangian-Eulerian (ALE) moving mesh technology. The development method result shows that it is possible for the small object to have a motion from one position to another through small amplitudes and wavelengths in viscous fluid.

The motion of the rigid body in the viscous fluid including collisions. Global solvability result

We shall consider the problem of the motion of a rigid body in an incompressible viscous fluid filling a bounded domain. This problem was studied by several authors. They mostly considered classical non-slip boundary conditions, which gave them very paradoxical result of no collisions of the body with the boundary of the domain. Only recently there are results when the Navier type of boundary is considered.In our paper we shall consider the Navier condition on the boundary of the body and the non-slip condition on the boundary of the domain. This case admits collisions of the body with the boundary of the domain. We shall prove the global existence of weak solution of the problem.

Self-propulsion of flapping bodies in viscous fluids: Recent advances and perspectives

Flapping-powered propulsion is used by many animals to locomote through air or water. Here we review recent experimental and numerical studies on self-propelled mechanical systems powered by a flapping motion. These studies improve our understanding of the mutual interaction between actively flapping bodies and surrounding fluids. The results obtained in these works provide not only new insights into biolocomotion but also useful information for the biomimetic design of artificial flyers and swimmers.

Small acoustically forced symmetric bodies in viscous fluids.

The total force exerted on a small rigid body by an acoustic field in a viscous fluid is addressed analytically in the limit where the typical size of the particle is smaller than both the viscous diffusion length scale and the acoustic wavelength. In this low-frequency limit, such a force can be calculated provided the effect of the acoustic steady streaming is negligible. Using the Eulerian linear expansion of Lagrangian hydrodynamic quantities (velocity and pressure), the force on a small solid sphere free to move in an acoustic field is first calculated in the case of progressive and standing waves, and it is compared to past results. The proposed method is then extended to the case of more complex shapes with three planes of symmetry. For a symmetric body oriented with one of its axis along the wave direction, the acoustic force exerted by a progressive wave is affected by the particle shape at leading order. In contrast, for a standing wave (with the same orientation), the force experienced by the particle at leading order is the same as the one experienced by a sphere of same volume and density.

Flow-induced nonequilibrium self-assembly in suspensions of stiff, apolar, active filaments.

Active bodies in viscous fluids interact hydrodynamically through self-generated flows. A stiff, apolar, active filament generates symmetric fluid flow around it and thus cannot self-propel. Here we study the mobility and aggregation induced by hydrodynamic flow in a suspension of stiff, apolar, active filaments. We consider two types of active filaments, with those producing extensile or contractile flows along their long axis. Lateral hydrodynamic attractions in extensile filaments lead, independent of the volume fraction, to anisotropic aggregates which translate and rotate ballistically. Lateral hydrodynamic repulsions in contractile filaments lead to microstructured states, where the degree of clustering increases with the volume fraction and the filament motion is always diffusive. Our results demonstrate that the interplay between active hydrodynamic flows and anisotropic excluded volume interactions provides a generic nonequilibrium mechanism for hierarchical self-assembly of active soft matter.

Swimming and pumping of rigid helical bodies in viscous fluids

Rotating helical bodies of arbitrary cross-sectional profile and infinite length are explored as they swim through or transport a viscous fluid. The Stokes equations are studied in a helical coordinate system, and closed form analytical expressions for the force-free swimming speed and torque are derived in the asymptotic regime of nearly cylindrical bodies. High-order accurate expressions for the velocity field and swimming speed are derived for helical bodies of finite pitch angle through a double series expansion. The analytical predictions match well with the results of full numerical simulations, and accurately predict the optimal pitch angle for a given cross-sectional profile. This work may improve the modeling and design of helical structures used in microfluidic manipulation, synthetic microswimmer engineering, and the transport and mixing of viscous fluids.

Управление движением жесткого тела в вязкой жидкости

Управление движением жесткого тела в вязкой жидкости

0309 粘性流体中で振動する三次元物体の付加質量の数値解析(GS01-3 熱工学・流体工学,オーガナイズドセッション 13:「噴霧及び燃焼現象の解明とその利用技術」)

0309 粘性流体中で振動する三次元物体の付加質量の数値解析(GS01-3 熱工学・流体工学,オーガナイズドセッション 13:「噴霧及び燃焼現象の解明とその利用技術」)

Numerical Analysis for the Added Mass of Oscillating Body in Viscous Fluid

In many fluid-structure interaction problems, the virtual mass, namely, the added mass is one of important interests. In the present study, the authors investigate the validity of a numerical method previously proposed by them in order to specify the added mass coefficient of arbitrary two-dimensional solid bodies efficiently and conveniently. In this method, we consider a two-dimensional incompressible viscous fluid under the assumption of an infinitesimal oscillation amplitude of the body, and properly modify the Navier-Stokes equations into linear equations the Brinkman equations. The solving method is based on a discrete singularity method. In order to show the method's effectivity and validity, the authors compute some flows around the bodies with fundamental cross sections with/without sharp edges, which oscillate in infinite flow fields. In addition, the authors solve the full Navier-Stokes equations by a finite difference method, and compare with each other to specify the valid range of the method. Then, the authors confirm the nonliner amplitude effect and specify the valid range for the method.

Steady fall of a rigid body in viscous fluid

The article is devoted to the problem of the steady fall of a rigid body in viscous fluid which is described by the Stokes approximation. We consider the case when the body is also rotated.

The motion of a rigid body in viscous fluid bounded by a plane wall

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The motion of a rigid body in viscous fluid bounded by a plane wall

The boundary-integral method is used to calculate the hydrodynamic force and torque on an arbitrary body of revolution whose axis of symmetry is oriented at an arbitrary angle relative to a planar wall in the zero-Reynolds-number limit. The singular solution of the Stokes equations in the presence of a planar wall is used to formulate the integral equations, which are then reduced to a system of linear algebraic equations by satisfying the no-slip boundary conditions on the body surface using the boundary collocation method or weighted residual technique.Numerical tests for the special case of a sphere moving parallel or perpendicular to a planar wall show that the present theory is accurate to at least three significant figures when compared with the exact solutions for gap widths as small as only one-tenth of the particle radius. Higher accuracy can be achieved and solutions can be obtained for smaller gap widths at the expense of more computation time and larger storage requirements.The hydrodynamic force and torque on a spheroid with varying aspect ratio and orientation angle relative to the planar wall are obtained. The theory is also applied to study the motion of a toroidal particle or biconcave shaped disc adjacent to a planar wall. The coincidence of the drag and torque of a biconcave-shaped body and a torus having an aspect ratio b/a = 2 with the same surface area shows that in this case the hole of a torus has little influence on the flow field. On the other hand, for an aspect ratio b/a = 10, the effect of the hole is significant. It is also shown that when the body is not very close to the wall, an oblate spheroid can be used as a good approximation of a biconcave-shaped disc.

The motion of a rigid body in viscous fluid bounded by a plane wall

The boundary-integral method is used to calculate the hydrodynamic force and torque on an arbitrary body of revolution whose axis of symmetry is oriented at an arbitrary angle relative to a planar wall in the zero-Reynolds-number limit. The singular solution of the Stokes equations in the presence of a planar wall is used to formulate the integral equations, which are then reduced to a system of linear algebraic equations by satisfying the no-slip boundary conditions on the body surface using the boundary collocation method or weighted residual technique.Numerical tests for the special case of a sphere moving parallel or perpendicular to a planar wall show that the present theory is accurate to at least three significant figures when compared with the exact solutions for gap widths as small as only one-tenth of the particle radius. Higher accuracy can be achieved and solutions can be obtained for smaller gap widths at the expense of more computation time and larger storage requirements.The hydrodynamic force and torque on a spheroid with varying aspect ratio and orientation angle relative to the planar wall are obtained. The theory is also applied to study the motion of a toroidal particle or biconcave shaped disc adjacent to a planar wall. The coincidence of the drag and torque of a biconcave-shaped body and a torus having an aspect ratio b/a = 2 with the same surface area shows that in this case the hole of a torus has little influence on the flow field. On the other hand, for an aspect ratio b/a = 10, the effect of the hole is significant. It is also shown that when the body is not very close to the wall, an oblate spheroid can be used as a good approximation of a biconcave-shaped disc.

Forces on oscillating bodies in viscous fluid

AbstractThis paper describes a method for determining the fluid forces on oscillating bodies in viscous fluid when the corresponding flow problem has been solved using the finite element method. These forces are characterized by the concept of added mass, added damping and added force. Numerical results are obtained for several example body shapes. Comparison is made with exact analytical results and other finite element results for the limiting cases of Stoke's flow and inviscid flow, and good agreement is obtained. The results for finite values of the body amplitude parameter β show the appearance of added force from the steady streaming component of the flow for asymmetric bodies. Results are also obtained for the associated flow where the fluid remote from a fixed body is oscillating.

On the force acting on a body in viscous fluid

Extension of the Kelvin—Tait formula to the case of a body moving in a viscous fluid is presented, and the problem of the analog of the Onsager reciprocity relations for media with memory is discussed.