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.

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.

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.

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.

Prediction of Unsteady Rotor-Surface Pressure and Heat Transfer From Wake Passings

1992 ◽  
Vol 114 (4) ◽  
pp. 807-817 ◽  
Author(s):  
L. T. Tran ◽  
D. B. Taulbee
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Boundary Layer ◽  
Heat Flux ◽  
Unsteady Flow ◽  
Rotor Blade ◽  
Numerical Solutions ◽  
Inviscid Flow ◽  
Blade Surface ◽  
Blade Passage

The research described in this paper is a numerical investigation of the effects of unsteady flow on gas turbine heat transfer, particularly on a rotor blade surface. The unsteady flow in a rotor blade passage and the unsteady heat transfer on the blade surface as a result of wake/blade interaction are modeled by the inviscid flow/boundary layer approach. The Euler equations that govern the inviscid flow are solved using a time-accurate marching scheme. The unsteady flow in the blade passage is induced by periodically moving a wake model across the passage inlet. Unsteady flow solutions in the passage provide pressure gradients and boundary conditions for the boundary-layer equations that govern the viscous flow adjacent to the blade surface. Numerical solutions of the unsteady turbulent boundary layer yield surface heat flux values that can then be compared to experimental data. Comparisons with experimental data show that unsteady heat flux on the blade suction surface is well predicted, but the predictions of unsteady heat flux on the blade pressure surface do not agree.

scholarly journals Computational simulation of a single Taylor bubble rising in a vertical column with stagnant liquid

2021 ◽  
Vol 9 (2B) ◽  
Author(s):  
Francisco Rogerio Teixeira Nascimento
Keyword(s):  
Open Source Software ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Computational Simulation ◽  
Navier Stokes ◽  
Vertical Column ◽  
Navier Stokes Equations ◽  
Taylor Bubble ◽  
Two Fluids ◽  
Bubble Rising

This work presents a computational simulation of a single Taylor bubble rising in a vertical column of stagnant liquid. The computational simulation was based on the Navier-Stokes equations for isothermal, incompressible, and laminar flow, solved by using the open source software OpenFOAM. The two fluids were assumed immiscible. The governing equations were discretized by the volume-of-fluid (VOF) method and solved using the Gauss iteration method. Parametric mesh was used in order to improve the modeling of curvilinear geometry. Numerical solutions were obtained for the rise velocities and shapes of the bubbles which are in excellent agreement with experimental data and correlations from literature.

Prediction of Unsteady Rotor-Surface Pressure and Heat Transfer From Wake Passings

1991 ◽  
Author(s):  
Le T. Tran ◽  
Dale B. Taulbee
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Boundary Layer ◽  
Heat Flux ◽  
Unsteady Flow ◽  
Rotor Blade ◽  
Numerical Solutions ◽  
Inviscid Flow ◽  
Blade Surface ◽  
Blade Passage

The research described in this paper is a numerical investigation of the effects of unsteady flow on gas turbine heat transfer, particularly on a rotor blade surface. The unsteady flow in a rotor blade passage and the unsteady heat transfer on the blade surface as a result of wake/blade interaction are modeled by the inviscid flow/boundary layer approach. The Euler equations which govern the inviscid flow are solved using a time accurate marching scheme. The unsteady flow in the blade passage is induced by periodically moving a wake model across the passage inlet. Unsteady flow solutions in the passage provide pressure gradients and boundary conditions for the boundary-layer equations which govern the viscous flow adjacent to the blade surface. Numerical solutions of the unsteady turbulent boundary layer yield surface heat flux values which can then be compared to experimental data. Comparisons with experimental data show that unsteady heat flux on the blade suction surface is well predicted, but the predictions of unsteady heat flux on the blade pressure surface do not agree.

A Viscous-Inviscid Interaction Procedure—Part 1: Method for Computing Two-Dimensional Incompressible Separated Channel Flows

1986 ◽  
Vol 108 (1) ◽  
pp. 64-70 ◽  
Author(s):  
O. K. Kwon ◽  
R. H. Pletcher
Keyword(s):  
Experimental Data ◽  
Finite Difference ◽  
Turbulent Flows ◽  
Inviscid Flow ◽  
Companion Paper ◽  
Separated Flows ◽  
Two Dimensional ◽  
Boundary Layer Equations ◽  
Interaction Scheme ◽  
Laminar And Turbulent Flows

A viscous-inviscid interaction scheme has been developed for computing steady incompressible laminar and turbulent flows in two-dimensional duct expansions. The viscous flow solutions are obtained by solving the boundary-layer equations inversely in a coupled manner by a finite-difference scheme; the inviscid flow is computed by numerically solving the Laplace equation for streamfunction using an ADI finite-difference procedure. The viscous and inviscid solutions are matched iteratively along displacement surfaces. Details of the procedure are presented in the present paper (Part 1), along with example applications to separated flows. The results compare favorably with experimental data. Applications to turbulent flows over a rearward-facing step are described in a companion paper (Part 2).

Jet-to-Plate Distance Effect on Heat Transfer From a Flat Plate to an Impinging Jet at Various Reynolds Numbers

2012 ◽  
Author(s):  
Patricia Streufert ◽  
Terry X. Yan ◽  
Mahdi G. Baygloo
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Reynolds Number ◽  
Flat Plate ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Local Heat Transfer ◽  
Reynolds Numbers ◽  
Air Jet ◽  
Plate Distance

Local turbulent convective heat transfer from a flat plate to a circular impinging air jet is numerically investigated. The jet-to-plate distance (L/D) effect on local heat transfer is the main focus of this study. The eddy viscosity V2F turbulence model is used with a nonuniform structured mesh. Reynolds-Averaged Navier-Stokes equations (RANS) and the energy equation are solved for axisymmetric, three-dimensional flow. The numerical solutions obtained are compared with published experimental data. Four jet-to-plate distances, (L/D = 2, 4, 6 and 10) and seven Reynolds numbers (Re = 7,000, 15,000, 23,000, 50,000, 70,000, 100,000 and 120,000) were parametrically studied. Local and average heat transfer results are analyzed and correlated with Reynolds number and the jet-to-plate distance. Results show that the numerical solutions matched experimental data best at low jet-to-plate distances and lower Reynolds numbers, decreasing in ability to accurately predict the heat transfer as jet-to-plate distance and Reynolds number was increased.

Analytic solution of angle-ply laminated plates under extension, bending, and torsion

2019 ◽  
Vol 54 (8) ◽  
pp. 1093-1106
Author(s):  
Shen-Haw Ju ◽  
Wen-Yu Liang ◽  
Hsin-Hsiang Hsu ◽  
Jiann-Quo Tarn
Keyword(s):  
Numerical Solutions ◽  
Anisotropic Elasticity ◽  
Laminated Plates ◽  
Rectangular Section ◽  
State Space Approach ◽  
Present Solution ◽  
End Conditions ◽  
Combined Action ◽  
Space Approach

This paper develops a Hamiltonian state space approach for analytic determination of deformation and stress fields in multilayered monoclinic angle-ply laminates under the combined action of extension, bending, and torsion. The present solution satisfies the equations of anisotropic elasticity, the end conditions, the traction-free boundary conditions on the four edge surfaces of the rectangular section, and the interfacial continuity conditions in multilayered laminates. The proposed method only requires the solutions of matrix and eigen equations, regardless of the number or lamination of the layers. The finite element analyses are used to validate the accuracy of the analysis. The analytical solution and the numerical solutions are in excellent agreement.

Phase transitions on partially contaminated surface under the influence of thermocapillary flow

2019 ◽  
Vol 877 ◽  
pp. 495-533 ◽  
Author(s):  
A. V. Shmyrov ◽  
A. I. Mizev ◽  
V. A. Demin ◽  
M. I. Petukhov ◽  
D. A. Bratsun
Keyword(s):  
Experimental Data ◽  
Numerical Solutions ◽  
Thermocapillary Flow ◽  
Creeping Flow ◽  
Stagnant Zone ◽  
Surface Velocity ◽  
Condensed State ◽  
Flow Forming ◽  
Perfect Agreement ◽  
Linear Temperature

We study, both experimentally and theoretically, the fluid flow driven by a thermocapillary effect applied to a partially contaminated interface in a two-dimensional slot of finite extent. The contamination is due to the presence of an insoluble surfactant which is convected by the flow forming a stagnant zone by the colder edge of the interface. The thermocapillary surface stress is produced by a special optocapillary system, which makes it possible, first, to get an almost linear temperature profile along the interface and, second, to apply a surface pressure large enough to force the surfactant to experience a phase transition to a more condensed state. This enabled us for the first time since the release of the paper by Carpenter & Homsy (J. Fluid Mech., vol. 155, 1985, pp. 429–439) to test experimentally their theoretical predictions and obtain new results for the case when the contamination exists simultaneously in two phase states within the interface. We show that one part of the surface is free of surfactant and subject to vigorous thermocapillary flow, while another part is stagnant and subject to creeping flow with a surface velocity which is approximately two orders of magnitude smaller. We found that the extent of the stagnant zone theoretically predicted earlier does not coincide with the newly obtained experimental data. In this paper, we suggest analytical and numerical solutions for the position of the edge of the stagnation zone, which are in perfect agreement with the experimental data.

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