Hydrodynamic Solution of the Virtual Mass Coefficient of a Vortex Ring Moving in a Fluid

2008 ◽  
Vol 47 (4) ◽  
pp. 1081-1084 ◽  
Author(s):  
Abdullah Abbas Kendoush
Keyword(s):  
Vortex Ring ◽  
Virtual Mass ◽  
Hydrodynamic Solution ◽  
Mass Coefficient

Effects of the electric field on the virtual mass of a flowing fluid sphere

2009 ◽  
Vol 87 (10) ◽  
pp. 1095-1098
Author(s):  
Abdullah Abbas Kendoush
Keyword(s):  
Experimental Data ◽  
Electric Field ◽  
Liquid Medium ◽  
Fluid Sphere ◽  
Virtual Mass ◽  
Flowing Fluid ◽  
Hydrodynamic Solution ◽  
Mass Coefficient

A hydrodynamic solution was used to calculate the virtual mass coefficients of a flowing fluid sphere in a liquid medium subjected to an electric field. The values of the virtual mass coefficient of the bubble and a drop were found to be different from the classical value of half. The new result was validated by comparison with the experimental data of other investigators.

Analysis of drag and virtual mass forces in bubbly suspensions using an implicit formulation of the lattice Boltzmann method

2002 ◽  
Vol 452 ◽  
pp. 61-96 ◽  
Author(s):  
K. SANKARANARAYANAN ◽  
X. SHAN ◽  
I. G. KEVREKIDIS ◽  
S. SUNDARESAN
Keyword(s):  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Volume Fraction ◽  
Computational Cost ◽  
Computational Experiments ◽  
Mass Force ◽  
Virtual Mass ◽  
Time Step ◽  
Mass Coefficient ◽  
Boltzmann Method

We present closures for the drag and virtual mass force terms appearing in a two-fluid model for flow of a mixture consisting of uniformly sized gas bubbles dispersed in a liquid. These closures were deduced through computational experiments performed using an implicit formulation of the lattice Boltzmann method with a BGK collision model. Unlike the explicit schemes described in the literature, this implicit implementation requires iterative calculations, which, however, are local in nature. While the computational cost per time step is modestly increased, the implicit scheme dramatically expands the parameter space in multiphase flow calculations which can be simulated economically. The closure relations obtained in our study are limited to a regular array of uniformly sized bubbles and were obtained by simulating the rise behaviour of a single bubble in a periodic box. The effect of volume fraction on the rise characteristics was probed by changing the size of the box relative to that of the bubble. While spherical bubbles exhibited the expected hindered rise behaviour, highly distorted bubbles tended to rise cooperatively. The closure for the drag force, obtained in our study through computational experiments, captured both hindered and cooperative rise. A simple model for the virtual mass coefficient, applicable to both spherical and distorted bubbles, was also obtained by fitting simulation results. The virtual mass coefficient for isolated bubbles could be correlated with the aspect ratio of the bubbles.

Short surface waves due to an oscillating immersed body

1953 ◽  
Vol 220 (1140) ◽  
pp. 90-103 ◽  
Keyword(s):  
Fluid Motion ◽  
Short Wave ◽  
Virtual Mass ◽  
Wave Problem ◽  
Rigorous Solution ◽  
Period 2 ◽  
Small Constant ◽  
Present Solution ◽  
Mass Coefficient ◽  
Huygens Principle

A long circular cylinder of radius a , with its axis horizontal, is half-immersed in a fluid under gravity and is making periodic vertical oscillations of small constant amplitude and of period 2 π /σ about this position. It is required to find the resulting fluid motion when the parameter N = σ 2 a / g is large; the method of an earlier paper (Ursell 1949) is then unworkable. The present solution is made to depend on an integral equation (3∙15) which can be chosen to have a kernel tending to zero with N -1 , and which is solved by iteration. Successive terms in the iteration are of decreasing order, and the convergence of the method for sufficiently large N is proved. Expressions are given for the virtual-mass coefficient (5∙1) and for the wave amplitude at infinity (5∙7). The present work appears to be the first practical and rigorous solution of a short-wave problem when a solution in closed form is not available. It is suggested that a similar technique may be applicable to the diffraction problems of acoustics and optics, which have hitherto been treated by the approximate Kirchhoff-Huygens principle.

The drag force on a collapsing bubble

2008 ◽  
Vol 222 (7) ◽  
pp. 1225-1235
Author(s):  
A A Kendoush
Keyword(s):  
Experimental Data ◽  
Drag Coefficient ◽  
Numerical Solutions ◽  
Bubble Surface ◽  
Dimensionless Time ◽  
Virtual Mass ◽  
Controlled Processes ◽  
Diffusion Controlled ◽  
Mass Coefficient ◽  
Theoretical Results

Equations were derived for the prediction of the drag coefficient of a collapsing bubble during its flow in liquid. Expressions were obtained analytically for the drag coefficient in terms of Reynolds, Peclet, and Jakob numbers as well as a dimensionless time for the collapse of a thermally controlled bubble. Equations were derived for the drag coefficient and virtual mass coefficient for a collapsing bubble under inertia-controlled and mass-diffusion-controlled processes. The flow and thermal parameters were obtained by solving the viscous dissipation integral around the bubble surface. These new theoretical results showed agreement with previously reported numerical solutions and experimental data. Some avenues for further research were pointed out.

Modification of the Classical Theory of the Virtual Mass of an Accelerating Spherical Particle

2006 ◽  
Author(s):  
Abdullah Abbas Kendoush
Keyword(s):  
Boundary Layer ◽  
Spherical Particle ◽  
High Speed ◽  
Boundary Layer Separation ◽  
Solid Sphere ◽  
Virtual Mass ◽  
Original Solution ◽  
Rotating Sphere ◽  
A Value ◽  
Mass Coefficient

A semi-analytical solution to the virtual mass of a spherical particle accelerating at high speed is obtained. Boundary layer separation coupled with potential flow was assumed around the solid sphere. The new solution of the virtual mass coefficient CV converges to the original solution of 0.5 upon removing the separation. The author showed earlier (Kendoush, J. Appl. Mech. 72(801)2005) that the virtual mass coefficient could reach a value of five for a rotating sphere in fluids.

The Virtual Mass Theory of a Taylor Bubble Rising in Vertical Pipes

2018 ◽  
Vol 140 (5) ◽  
Author(s):  
Abdullah Abbas Kendoush
Keyword(s):  
Experimental Data ◽  
Numerical Solutions ◽  
Inviscid Flow ◽  
Virtual Mass ◽  
Transient Conditions ◽  
Taylor Bubble ◽  
Low Viscosity ◽  
Present Solution ◽  
Mass Coefficient ◽  
Bubble Rising

Analytical solutions were obtained for the virtual mass of a Taylor bubble rising in a liquid confined by a circular pipe under transient conditions. The solution of the virtual mass coefficient was based on potential inviscid flow. The present solution is applicable to low viscosity liquids and to Capillary number (Ca)<0.005. The virtual mass solution showed dependence on bubble geometry. The present solution was validated by comparison with the available numerical solutions and experimental data of other investigators.

Note on the long-wave limit of the virtual-mass coefficient for a half-immersed circular cylinder heaving on water of finite depth

1976 ◽  
Vol 76 (1) ◽  
pp. 29-34 ◽  
Author(s):  
P. F. Rhodes-Robinson
Keyword(s):  
Circular Cylinder ◽  
Preliminary Analysis ◽  
Preceding Paper ◽  
Finite Depth ◽  
Virtual Mass ◽  
Long Wave ◽  
Mass Coefficient ◽  
Wave Limit

This note provides numerical values for the long-wave limit of the virtual-mass coefficient relating to the heaving motion of a half-immersed circular cylinder on water of finite depth, found analytically by Ursell in the preceding paper; some preliminary analysis is needed, however.

The Inertia of the Anterior Leaflet of the Heart’s Mitral Valve

2010 ◽  
Author(s):  
Abdullah A. Kendoush ◽  
Muralidhar Padala ◽  
David Icenogle ◽  
Ajit P. Yoganathan
Keyword(s):  
Mitral Valve ◽  
Computational Models ◽  
Virtual Mass ◽  
Complete Model ◽  
Fluid Medium ◽  
Mitral Valves ◽  
Mass Effects ◽  
Mechanical Valves ◽  
Mass Coefficient ◽  
Bileaflet Mechanical Valves

Virtual mass effects generate forces that act on any object accelerating in a fluid medium. While there have been computational models of bileaflet mechanical valves that include virtual mass effects [1], current computational models of fluid structure interaction of native mitral valves do not consider virtual mass effects, resulting in an incomplete measure of the forces acting on the valve. As far as the authors aware no closed-form relationship for the virtual mass coefficient, Cm, of the native mitral valve has been determined. Integrating the effects of virtual mass into computational models of the mitral valve would result in a more complete model, and could yield more accurate and relevant results from computational models of the mitral valve.

Experimental Determination of the Virtual Mass Coefficient for Two Spheres Accelerating in a Power Law Fluid

2010 ◽  
Vol 132 (12) ◽  
Author(s):  
Abbas H. Sulaymon ◽  
Catherine A. M. E. Wilson ◽  
Abeer I. Alwared
Keyword(s):  
Reynolds Number ◽  
Power Law ◽  
Reynolds Numbers ◽  
Separation Distance ◽  
Virtual Mass ◽  
Power Law Fluid ◽  
Mass Coefficient ◽  
Single Sphere ◽  
Power Law Index

The virtual mass coefficient is determined experimentally for the motion of two spheres side by side and in line in a power law fluid. The velocities of the two accelerating spheres and their separation distance was measured as they accelerated under the action of driving weights through a cylindrical column filled with different concentrations of polyacryamaide solution (0.01%, 0.03%, 0.05%, and 0.07% by weight). For comparison purposes, the experiments were repeated with water. Various densities of spheres and separation distances were examined. Within the range of power law indices (0.61–0.834) and Reynolds numbers (1.1–75) examined, the virtual mass coefficient was found to decrease with an increasing Reynolds number for the two spheres moving side by side, and found to be greater than 0.5 when the spheres were touching each other. As the distance between the spheres increased, the virtual mass coefficient was found to decrease and approached the single sphere value of 0.5 when the distance between the spheres was more than ten radii. When the spheres were in line and touching each other, the virtual mass coefficient was found to be less than 0.5, however, when the distance between the spheres increased, the virtual mass coefficient increased and approached the value of 0.5. The virtual mass coefficient was found to be consistent with the shear thinning behavior; for a given Reynolds number, it increased with an increasing power law index.

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