https://www.me.iastate.edu/files/2012/05/pecs_le.pdf

Lagrangian-Eulerian methods for multiphase flows

/pdf/study-of-the-added-mass-of-cylinders-and-spheres-1pvuxyh6dg.pdf

Study of the Added Mass of Cylinders and Spheres

The motion of a spherical inclusion released in a vertical solid-body rotation flow is investigated theoretically and experimentally. Solid spheres and bubbles are considered. The particle Reynolds number, the Taylor number, the Weber number and the capillary number are smaller than unity. The motion equations of the inclusion are obtained by revisiting the hydrodynamic equations. The axial (vertical) motion and the horizontal motion are uncoupled, even though they are sensitive to the rotation rate of the flow. Analytical solutions of the particle motion equation are compared to experimental results obtained by releasing a particle in a rotating tank filled with silicone oil. For solid spheres and bubbles, both the terminal velocity and the particle ejection rate (or trapping rate) predicted by the theory agree with experiments, without any empirical adjustment. In particular, the experimental device enables us to check the validity of various theories involving solid or gaseous inclusions with or without inertia or history effects. It is observed that the mobility tensor obtained by writing the fluid motion equations in the rotating frame accurately predicts the horizontal particle trajectory, like the Boussinesq-Basset equation obtained by writing the fluid motion equations in the non-rotating frame and neglecting the horizontal contribution of inertia effects.

On the effect of inertia and history forces on the slow motion of a spherical solid or gaseous inclusion in a solid-body rotation flow

The hydrodynamic loads due to the interaction of a small-amplitude internal solitary wave with a submerged circular cylinder in a two-layer system of miscible fluids were studied experimentally. The dependence of the internal-wave transmission coefficient on the position of the center of the cylinder relative to the pycnocline and on the ratio of the cylinder diameter to the fluid-layer thickness was obtained. The effects of the pycnocline thickness and the depth of the center of the cylinder on the value of the hydrodynamic loads were studied. Visualization of the flow structure was performed.

Experimental Study of the Dynamic Effect of an Internal Solitary Wave on a Submerged Circular Cylinder

The present experimental study is designed to measure the motion of a spherical particle in a noninertial reference frame when the environment oscillates horizontally at a prescribed frequency and amplitude. Measurements are compared with theoretical equations of motion, for example, Basset [A Treatise on Hydrodynamics (Deighton Hall, London, 1888), Vol. 2], over wide ranges of density ratio (ρf/ρp), inverse Stokes number (δ), and amplitude ratio (Ap/Af), the three most critical nondimensional parameters. The experimental configuration consists of a bubble or solid sphere rising or falling in a bubble column while vibration occurs in the horizontal direction. Motion is measured with a high speed video camera and contemporary image and signal processing techniques are used to evaluate the data. The setup closely resembles multiphase flow in a Coriolis flow meter, a device which measures mass flow rate and density by oscillating two tubes at resonance. Accurate predictions of the motion of the sphere may le...

Experimental study of oscillatory motion of particles and bubbles with applications to Coriolis flow meters

The present work presents an experimental study on a free-falling rigid sphere in a quiescent incompressible newtonian fluid, placed in an oscillating frame. The goal of this investigation is to examine the effect of the history force acting on the sphere at small Reynolds numbers (Re≤2.5) and finite Strouhal numbers (1≤Sl≤20). The particle trajectory is measured by using a high-speed video camera and modern techniques of image processing. The average terminal velocity, the oscillation magnitude, and the phase shift with the oscillating frame are measured and compared with those obtained from theoretical approaches. The comparison is made by solving the equation of motion of the sphere with and without the history force. In addition to the significant role that this force plays in the momentum balance, it was found that the correction of the added mass force and the history force by the empirical coefficients of Odar and Hamilton (J Fluid Mech 18:302–314, 1964; J Fluid Mech 25:591–592, 1966) are not necessary in our Re and Sl ranges. The added mass is the same as that obtained by the potential flow theory and the history force is well predicted by the Basset expression (Treatise on hydrodynamics, 1888).

Mustapha Abbad

Papers

Effects of the history force on an oscillating rigid sphere at low Reynolds number