Use of Thomas Algorithm for Shock Wave Analysis in Bubbly Flow

2012 ◽  
Author(s):  
Mark A. Chaiko
Keyword(s):  
Shock Wave ◽  
Diffusion Equation ◽  
Fluid Model ◽  
Bubbly Flow ◽  
Bubble Radius ◽  
Gas Bubbles ◽  
Uniform Continuity ◽  
Second Order ◽  
Two Phase ◽  
Thomas Algorithm

A numerical approach is developed for simulation of pressure wave propagation in a tube containing a dilute concentration of small gas bubbles. The two-phase fluid is considered homogeneous and spatial distribution of bubbles is assumed to be uniform. Bubble oscillations are modeled using the Keller equation which accounts for liquid compressibility. Heat transfer between liquid and gas is included in the analysis through solution of the radial conduction equation for a spherical gas bubble with moving interface. An energy balance over the bubble surface determines bubble internal pressure, which is assumed to be uniform. Continuity and momentum relations for the homogenous mixture along with the Keller equation are used to derive an alternate set of equations, which are more amenable to application of elementary numerical methods. These alternate equations include a diffusion equation, which is linear in the homogeneous mixture pressure. Two additional equations define the bubble radius and gas-liquid interface speed in terms of the local spatial variation in the homogeneous pressure field. The diffusion equation is solved easily using the second-order accurate Crank-Nicolson method in conjunction with the Thomas algorithm for the discretized tridiagonal algebraic system. The remaining equations comprising the fluid model are solved with an explicit, second-order accurate predictor-corrector scheme. The present approach avoids the need for staggered grids and iterative pressure correction methods used in previous work. Numerical calculations are carried out for a shock wave in a liquid column containing gas bubbles. Results show good agreement with experimental data available in the literature.

Predicted performance of a two-phase underwater ramjet with a Laval nozzle

2018 ◽  
Vol 233 (3) ◽  
pp. 937-948
Author(s):  
Jiarui Zhang ◽  
Zhixun Xia ◽  
Liya Huang ◽  
Likun Ma
Keyword(s):  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Laval Nozzle ◽  
Fluid Model ◽  
Bubbly Flow ◽  
Engine Performance ◽  
Orifice Diameter ◽  
Two Phase ◽  
Convergent Nozzle

To predict engine performance and further instruct the integral engine design, a more reasonable and accurate numerical model of the two-phase underwater ramjet was introduced in this article by considering the bubble formation process. Two-fluid model was used to examine the bubbly flow in the nozzle and its mathematical model was solved by a fourth-order Runge–Kutta method. Subsequently, the influences of vessel velocity, gas mass flow rate, navigational depth, and orifice diameter of the bubble injector on the performance of the engine were discussed. Results show that, compared with convergent nozzle, Laval nozzle is proved to improve the thrust of the engine, especially at relatively high velocity and gas mass flow rate. With the other conditions fixed, there is an optimum vessel velocity for the ramjet, in which maximum thrust is generated. And a smaller orifice diameter always promotes the engine performance, while this promotion is negligible when the orifice diameter is smaller than 1 mm. Besides, increasing backpressure will cause serious performance drop, which means that the the two-phase underwater ramjet is only efficient for shallow depths.

CFD Modelling of Bubbly Flow in Adiabatic Upward Pipe Using a Solver Based on OpenFOAM® With the Quadrature Method of Moments

2014 ◽  
Author(s):  
Carlos Peña-Monferrer ◽  
Alberto Passalacqua ◽  
Sergio Chiva ◽  
José L. Muñoz-Cobo
Keyword(s):  
Method Of Moments ◽  
Two Phase Flow ◽  
Fluid Model ◽  
Bubbly Flow ◽  
Phase Flow ◽  
Computational Results ◽  
Quadrature Method ◽  
Cfd Modelling ◽  
Two Phase ◽  
Quadrature Method Of Moments

An Eulerian-Eulerian approach was used to model adiabatic bubbly flow with CFD techniques. The OpenFOAM® solver twoPhaseEulerFoam was modified to predict upward bubbly flow in vertical pipes. Interfacial force and bubble induced turbulence models are studied and implemented. The population balance equation included in the two-fluid model is solved to simulate a polydisperse flow with the quadrature method of moments approximation. Two-phase flow experiments with different superficial velocities of gas and water at different temperatures are used to validate the solver. Radial distributions of void fraction, air and water velocities, Sauter mean diameter and turbulence intensity are compared with the computational results. The computational results agree well with the experiments showing the capability of the solver to predict two-phase flow characteristics.

On the Numerical Study of Bubbly Flow Created by Ventilated Cavity

2010 ◽  
Vol 29-32 ◽  
pp. 143-148
Author(s):  
Min Xiang ◽  
S.C.P. Cheung ◽  
Ji Yuan Tu ◽  
Wei Hua Zhang ◽  
Yang Fei
Keyword(s):  
Flow Field ◽  
Void Fraction ◽  
Numerical Study ◽  
Fluid Model ◽  
Bubbly Flow ◽  
Bubble Diameter ◽  
Flow Region ◽  
Valuable Insight ◽  
Two Phase ◽  
Ventilated Cavity

The aim of the study was to develop a numerical model to reproduce the bubbly flow field created by ventilated cavity which includes three different regions. The model was established based on the Eulerian-Eulerian two-fluid model coupled with a population balance approach which is solved by the Homogeneous Multiple-Size-Group (MUSIG) model to predict bubble size distribution. Base on the model, the simulation was carried out at the experimental condition of Su et al. (1995). Firstly three regions were successfully captured proved by the spatial voidage distribution and streamline shape. Then distributions of void fraction and Sauter mean bubble diameter at various sections below the cavity corresponding to three regions respectively were plotted against experimental data. A close agreement was observed in the void fraction distribution which indicates that qualitative details of the structure of the two-phase flow field below the cavity was successfully produced. The Sauter mean bubble diameter in the pipe flow region was under-predicted for about 10%. In conclusion, the proposed model was validated in predicting the multi-region flow field below the ventilated cavity which will provide a valuable insight in designing and controlling of the two phase systems with the detailed flow field information obtained.

Two-Phase Flow Pressure Drop in Right Angle Bends

2000 ◽  
Vol 122 (4) ◽  
pp. 761-768 ◽  
Author(s):  
Edward Graf ◽  
Sudhakar Neti
Keyword(s):  
Pressure Drop ◽  
Flow Boiling ◽  
Fluid Model ◽  
Bubbly Flow ◽  
Centrifugal Forces ◽  
Two Phase ◽  
Void Fractions ◽  
Aspect Ratios ◽  
Numerical Predictions ◽  
Two Fluid Model

Gas-liquid two-phase bubbly flows in right angle bends have been studied. Numerical predictions of the flow in right angle bends are made from first principles using an Eulerian-Eulerian two-fluid model. The flow geometry includes a sufficiently long inlet duct section to assure fully developed flow conditions into the bend. The strong flow stratification encountered in these flows warrant the use of Eulerian-Eulerian description of the flow, and may have implications for flow boiling in U-bends. The computational model includes the finer details associated with turbulence behavior and a robust void fraction algorithm necessary for the prediction of such a flow. The flow in the bend is strongly affected by the centrifugal forces, and results in large void fractions at the inner part of the bend. Numerical predictions of pressure drop for the flow with different bend radii and duct aspect ratios are presented, and are in general agreement with data in the literature. Measurements of pressure drop for an air-water bubbly flow in a bend with a nondimensional bend radius of 5.5 have also been performed, and these pressure drop measurements also substantiate the computations described above. In addition to the global pressure drop for the bend, the pressure variations across the cross section of the duct that give rise to the fluid migration (due to centrifugal forces), and stratification of the phases are interesting in their own right. [S0098-2202(00)01004-X]

Image Based Bubbly Flow Feature Identification Using Deep Learning

2021 ◽  
Author(s):  
Takashi Furuhashi ◽  
Takuro Sasaki ◽  
Shuichiro Miwa
Keyword(s):  
High Speed ◽  
Nuclear Reactor ◽  
Two Phase Flow ◽  
Fluid Model ◽  
Bubbly Flow ◽  
Interfacial Area ◽  
Liquid Interface ◽  
Phase Flow ◽  
Two Phase ◽  
Interfacial Area Concentration

Abstract Gas-liquid two-phase flow has high potential in heat transfer and mixing capabilities, and therefore it is utilized in various technologies such as nuclear reactor and chemical plants. There are several flow regimes since the gas-liquid interface transforms constantly. For the sake of safety and optimization in operating plants, it is crucial to understand the behavior of the gas-liquid interface. We have focused on extracting the bubble features in the bubbly flow by filming the bubbly flow with a high-speed camera and training convolutional neural network (CNN) for feature extraction. The assumption made was bubbles in the bubbly flow being ellipsoids. Since void fraction and interfacial area concentration are one of the geometric parameters in the two-phase flow models, like two-fluid model, it becomes possible to evaluate the flow field of the two-phase flow quickly and quantitively by calculating these parameters from the extracted features. We have compared two-phase flow parameters with the conventional object detection method using bounding boxes, and the new ellipse fitting method to identify the best region proposal shape. As a result, the conventional method showed higher accuracy in extracting bubble features under our flow conditions.

On high-speed impingement of cylindrical droplets upon solid wall considering cavitation effects

2018 ◽  
Vol 857 ◽  
pp. 851-877 ◽  
Author(s):  
Wangxia Wu ◽  
Gaoming Xiang ◽  
Bing Wang
Keyword(s):  
Phase Transition ◽  
Shock Wave ◽  
High Speed ◽  
Solid Wall ◽  
Fluid Model ◽  
Droplet Diameter ◽  
Droplet Surface ◽  
Rarefaction Waves ◽  
Two Phase ◽  
The Impact

The high-speed impingement of droplets on a wall occurs widely in nature and industry. However, there is limited research available on the physical mechanism of the complicated flow phenomena during impact. In this study, a simplified multi-component compressible two-phase fluid model, coupled with the phase-transition procedure, is employed to solve the two-phase hydrodynamics system for high-speed cylindrical droplet impaction on a solid wall. The threshold conditions of the thermodynamic parameters of the fluid are established to numerically model the initiation of phase transition. The inception of cavitation inside the high-speed cylindrical droplets impacting on the solid wall can thus be captured. The morphology and dynamic characteristics of the high-speed droplet impingement process are analysed qualitatively and quantitatively, after the mathematical models and numerical procedures are carefully verified and validated. It was found that a confined curved shock wave is generated when the high-speed cylindrical droplet impacts the wall and this shock wave is reflected by the curved droplet surface. A series of rarefaction waves focus at a position at a distance of one third of the droplet diameter away from the top pole due to the curved surface reflection. This focusing zone is identified as the cavity because the local liquid state satisfies the condition for the inception of cavitation. Moreover, the subsequent evolution of the cavitation zone is demonstrated and the effects of the impact speed, ranging from $50$ to $200~\text{m}~\text{s}^{-1}$ , on the deformation of the cylindrical droplet and the further evolution of the cavitation were studied. The focusing position, where the cavitation core is located, is independent of the initial impaction speed. However, the cavity zone is enlarged and the stronger collapsing wave is induced as the impaction speed increases.

Complete Convective Condensation Inside Small Diameter Horizontal Tubes

2003 ◽  
Author(s):  
Be´atrice Mederic ◽  
Marc Miscevic ◽  
Vincent Platel ◽  
Pascal Lavieille ◽  
Jean-Louis Joly
Keyword(s):  
Experimental Study ◽  
Bubbly Flow ◽  
Bubble Radius ◽  
Small Diameter ◽  
Bubble Collapse ◽  
Two Phase ◽  
Narrow Channels ◽  
Horizontal Tubes ◽  
Significant Difference ◽  
Convective Condensation

An experimental study of complete convective condensation inside narrow channels is presented in this paper. Two-phase flows patterns and their transition (annular, annular-wavy, slug and bubbly flow) are visualized for the two tube diameters under study. A significant difference is observed for the two sizes of tube. Experimental results of the bubble radius decrease are then determined and compared to a model of bubble collapse in a subcooled and infinite liquid.

Numerical Simulation of Acoustic Streaming in Gas-Liquid Two-Phase Flow

2005 ◽  
Author(s):  
Bo Lu ◽  
Arthur E. Ruggles
Keyword(s):  
Numerical Solutions ◽  
Two Phase Flow ◽  
Bubble Radius ◽  
Acoustic Streaming ◽  
Gas Bubbles ◽  
Homogeneous Distribution ◽  
Phase Flow ◽  
Sinusoidal Vibration ◽  
Two Phase ◽  
Left Wall

Acoustic streaming phenomena pertaining to liquid-gas two-phase flow in a one-dimensional rigid duct is investigated numerically. The oscillatory bubbly flow is generated due to the sinusoidal vibration of the vertical left wall of the enclosure. Time-averaged streaming flow patterns exist in the duct as a consequence of interaction between gas bubbles and liquid which are similar to the Rayleigh-type acoustic streaming phenomena extensively investigated in single-phase flow. The liquid is treated as incompressible with a homogeneous distribution of non-condensable gas bubbles. The system is modeled with coupled nonlinear and flux-conservative partial differential equations combined with the Rayleigh-Plesset equation governing the bubble radius. The viscous interaction between bubbles and the surrounding incompressible liquid phase is the main mechanism for attenuation of the wave energy considered in this analysis. The numerical solutions are obtained by a control-volume based finite-volume Lagrangian method.

The Radial Migration of Bubbles in Two-Phase Bubbly Flow in Vertical Pipes

2006 ◽  
Author(s):  
Mohamed E. Shawkat ◽  
Chan Y. Ching ◽  
Mamdouh Shoukri
Keyword(s):  
Void Fraction ◽  
Fluid Model ◽  
Bubbly Flow ◽  
Optical Probe ◽  
Superficial Velocity ◽  
Turbulent Dispersion ◽  
Two Phase ◽  
Two Fluid Model ◽  
Hot Film ◽  
Two Fluid

The radial distribution of bubbles in air-water bubbly flow was experimentally investigated using a dual optical probe and hot-film anemometry. The experiments were performed in a 200mm diameter vertical pipe at liquid superficial velocity in the range of 0.2 to 0.68m/s and gas superficial velocity from 0.005 to 0.18m/s. At low void fraction flows, the radial void fraction profiles show a wall peak. As the void fraction increases the profiles tend to peak at the pipe centreline. The distribution of the net radial interfacial forces for both core and wall peak void distributions was obtained using the two-fluid model. The radial direction of the bubble migration in the pipe core was related to the ratio between the turbulent dispersion and the lift forces. The effect of the pipe diameter on this ratio was investigated.

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