Stability Analysis of One-Dimensional Steady Cavitating Nozzle Flows With Bubble Size Distribution

1999 ◽  
Vol 122 (2) ◽  
pp. 425-430 ◽  
Author(s):  
Yi-Chun Wang
Keyword(s):  
Stability Analysis ◽  
Size Distribution ◽  
Bubble Size ◽  
Bubble Dynamics ◽  
Bubble Size Distribution ◽  
Strong Interactions ◽  
One Dimensional ◽  
Bubble Sizes ◽  
Flow Variables ◽  
Nozzle Flows

A continuum bubbly mixture model coupled to the Rayleigh-Plesset equation for the bubble dynamics is employed to study one-dimensional steady bubbly cavitating flows through a converging-diverging nozzle. A distribution of nuclei sizes is specified upstream of the nozzle, and the upstream cavitation number and nozzle contraction are chosen so that cavitation occurs in the flow. The computational results show very strong interactions between cavitating bubbles and the flow. The bubble size distribution may have significant effects on the flow; it is shown that it reduces the level of fluctuations and therefore reduces the “cavitation loss” compared to a monodisperse distribution. Another interesting interaction effect is that flashing instability occurs as the flow reaches a critical state downstream of the nozzle. A stability analysis is proposed to predict the critical flow variables. Excellent agreement is obtained between the analytical and numerical results for flows of both equal bubble size and multiple bubble sizes. [S0098-2202(00)00702-1]

A Numerical Study of Dispersed Air Bubbles in a Hydrotransport Pipeline Flow

2002 ◽  
Author(s):  
C. D. Wang ◽  
D. Eskin ◽  
Y. Leonenko ◽  
S. Lezhnin ◽  
O. Vinogradov
Keyword(s):  
Pressure Drop ◽  
Dissolution Rate ◽  
Size Distribution ◽  
Bubble Size ◽  
Numerical Study ◽  
Bubble Size Distribution ◽  
Turbulent Pipe Flow ◽  
Pure Liquid ◽  
Size Change ◽  
Bubble Sizes

Different flow pattern maps and theoretical models were employed to determine the flow velocity needed to provide the dispersed-bubble flow in a hydrotransport pipeline. Comparison and analysis of the results has been carried out. The maximum and minimum bubble sizes were determined by semi-experimental methods. A log-normal function was employed to describe the bubble size distribution. A model for the bubble size change in the turbulent pipe flow was applied to study the evolution of the overall bubble size distribution. This model takes into account the competing factors influencing the bubble size: 1) dissolution (turbulent diffusion) of air in the liquid, causing bubble shrinkage; 2) pressure drop along the pipeline, causing bubble growth. Numerical analysis shows that the bubble dissolution rate strongly depends on the initial air hold-up and initial bubble size. An increase of air hold-up leads to a fast decrease of the dissolution rate. At sufficient high air hold-ups, the dissolution effect becomes negligible and air bubble sizes are dominantly controlled by the pressure drop. Smaller bubbles have higher dissolution rates than larger ones. Compared with a pure liquid flow under the same flow conditions, the effect of air hold-up is stronger in the slurry flow because of the smaller volume occupied by the liquid.

scholarly journals A Review of Bubble Dynamics in Liquid Metals

Metals ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 664
Author(s):  
Tim Haas ◽  
Christian Schubert ◽  
Moritz Eickhoff ◽  
Herbert Pfeifer
Keyword(s):  
Size Distribution ◽  
Bubble Size ◽  
Bubble Dynamics ◽  
Liquid Metals ◽  
Bubble Formation ◽  
Bubble Size Distribution ◽  
The State ◽  
Open Questions ◽  
Casting Ladle ◽  
Metallurgical Processes

Gas bubbles are of major importance in most metallurgical processes. They promote chemical reactions, homogenize the melt, or float inclusions. Thus, their dynamics are of crucial interest for the optimization of metallurgical processes. In this work, the state of knowledge of bubble dynamics at the bubble scale in liquid metals is reviewed. Measurement methods, with emphasis on liquid metals, are presented, and difficulties and shortcomings are analyzed. The bubble formation mechanism at nozzles and purging plugs is discussed. The uncertainty regarding the prediction of the bubble size distribution in real processes is demonstrated using the example of the steel casting ladle. Finally, the state of knowledge on bubble deformation and interfacial forces is summarized and the scalability of existing correlations to liquid metals is critically discussed. It is shown that the dynamics of bubbles, especially in liquid metals, are far from understood. While the drag force can be predicted reasonably well, there are large uncertainties regarding the bubble size distribution, deformation, and lift force. In particular, the influence of contaminants, which cannot yet be quantified in real processes, complicates the discussion and the comparability of experimental measurements. Further open questions are discussed and possible solutions are proposed.

scholarly journals Numerical investigation on the performance of coalescence and break-up kernels in subcooled boiling flows in vertical channels

2016 ◽  
Vol 9 (2) ◽  
pp. 71-85 ◽  
Author(s):  
Sara Vahaji ◽  
Sherman CP Cheung ◽  
Lilunnahar Deju ◽  
Guan Yeoh ◽  
Jiyuan Tu
Keyword(s):  
Size Distribution ◽  
Bubble Size ◽  
Bubble Dynamics ◽  
Interfacial Area ◽  
Bubble Size Distribution ◽  
Heated Wall ◽  
Bubble Coalescence ◽  
Two Phase ◽  
Interfacial Area Concentration ◽  
Break Up

In order to accurately predict the thermal hydraulic of two-phase gas–liquid flows with heat and mass transfer, special numerical considerations are required to capture the underlying physics: characteristics of the heat transfer and bubble dynamics taking place near the heated wall and the evolution of the bubble size distribution caused by the coalescence, break-up, and condensation processes in the bulk subcooled liquid. The evolution of the bubble size distribution is largely driven by the bubble coalescence and break-up mechanisms. In this paper, a numerical assessment on the performance of six different bubble coalescence and break-up kernels is carried out to investigate the bubble size distribution and its impact on local hydrodynamics. The resultant bubble size distributions are compared to achieve a better insight of the prediction mechanisms. Also, the void fraction, bubble Sauter mean diameter, and interfacial area concentration profiles are compared against the experimental data to ensure the validity of the models applied.

Numerical Simulation of Heterogeneous Bubbly Flow in a Bubble Column

2006 ◽  
Author(s):  
Munenori Maekawa ◽  
Naoki Shimada ◽  
Kouji Kinoshita ◽  
Akira Sou ◽  
Akio Tomiyama
Keyword(s):  
Size Distribution ◽  
Bubble Size ◽  
Bubble Column ◽  
Fluid Model ◽  
Bubbly Flow ◽  
Bubble Size Distribution ◽  
Bubbly Flows ◽  
Bubble Coalescence ◽  
Size Distributions ◽  
Bubble Sizes

Numerical methods for predicting heterogeneous bubbly flows are indispensable for the design of a Fisher-Tropsh reactor for GTL (Gas To Liquid). It is necessary to take into account bubble size distribution determined by bubble coalescence and breakup for the accurate prediction of heterogeneous bubbly flows. Hence we implemented several bubble coalescence and breakup models into the (N+2) field model, which is a hybrid combination of an interface tracking method and a multi-fluid model. Void and bubble size distributions in an open rectangular bubble column were measured and compared with predicted ones. As a result, the following conclusions were obtained: (1) Void and bubble size distributions were not affected by inlet bubble sizes because the bubble size distribution reaches an equilibrium state at which the birth rate is equal to the death rate, and (2) the combination of Luo’s bubble breakup model and a coalescence model consisting of Prince & Blanch’s model and Wang’s wake entrainment model gave good predictions.

Hybrid Eulerian Eulerian Discrete Phase Model of Turbulent Bubbly Flow

2017 ◽  
Author(s):  
Hyunjin Yang ◽  
Surya P. Vanka ◽  
Brian G. Thomas
Keyword(s):  
Size Distribution ◽  
Bubble Size ◽  
Bubbly Flow ◽  
Bubble Size Distribution ◽  
Turbulent Dispersion ◽  
Phase Model ◽  
Discrete Phase Model ◽  
Local Bubble ◽  
Discrete Phase ◽  
Bubble Sizes

The Eulerian-Eulerian two-fluid model [1] (EE) is the most general model in multiphase flow computations. One limitation of the EE model is that it has no ability to estimate the local bubble sizes by itself. Thus, it must be complemented either by measurements of bubble size distribution or by additional models such as population balance theory or interfacial area concentration to get the local bubble size information. In this work, we have combined the Discrete Phase model (DPM) [2,8] to estimate the evolution of bubble sizes with the Eulerian-Eulerian model. The bubbles are tracked individually as point masses, and the change of bubble size distribution is estimated by additional coalescence and breakup modeling of the bubbles. The time varying bubble distribution is used to compute the local interface area between gas and liquid phase, which is used to estimate the momentum interactions such as drag, lift, wall lubrication and turbulent dispersion forces. This model is applied to compute an upward flowing bubbly flow in a vertical pipe and the results are compared with previous experimental work of Hibiki et al. [3]. The newly developed hybrid model (EEDPM) is able to reasonably predict the locally different bubble sizes and the velocity and void fraction fields. On the other hand, the standard EE model without the DPM shows good comparison with measurements only when the prescribed constant initial bubble size is accurate and does not change much.

Effects of Nuclei Size Distribution on the Dynamics of a Spherical Cloud of Cavitation Bubbles

1999 ◽  
Vol 121 (4) ◽  
pp. 881-886 ◽  
Author(s):  
Yi-Chun Wang
Keyword(s):  
Nonlinear Dynamics ◽  
Size Distribution ◽  
Bubble Size ◽  
Bubble Size Distribution ◽  
Bubble Collapse ◽  
Bubble Cloud ◽  
Cloud Dynamics ◽  
Spherical Cloud ◽  
Bubble Sizes ◽  
Nonlinear Continuum

The nonlinear dynamics of a spherical bubble cloud with nuclei size distribution are studied numerically. The spectrum of nuclei is assumed uniform initially. The simulations employ a nonlinear continuum bubbly mixture model with consideration of the presence of bubbles of different sizes. This model is then coupled with the Rayleigh-Plesset equation for the dynamics of bubbles. A numerical method based on the integral representation of the mixture continuity and momentum equations in the Lagrangian coordinates is developed to solve this set of integro-differential equations. Computational results show that the nuclei size distribution has significant effects on the cloud dynamics in comparison to the results for a single bubble size. One important effect is that the bubble collapse is always initiated near the surface of the cloud, even if the cloud has a very small initial void fraction. This effect has an important consequence, namely that the geometric focusing of the bubbly shock wave is always a part of the nonlinear dynamics associated with the collapse of a spherical cloud with nuclei size distribution. The strength of the shock and the oscillation structure behind the shock front are suppressed due to the effects of multiple bubble sizes. Far-field acoustic pressures radiated by two bubble clouds, one of equal-size bubbles and the other with bubble size distribution, are also compared. It is found that the cloud containing bubbles of different sizes emits a larger noise than the cloud of identical bubbles. Explanations for this effect are also presented.

Physiochemical properties and reproducibility of air-based sodium tetradecyl sulphate foam using the Tessari method

2016 ◽  
Vol 32 (6) ◽  
pp. 390-396 ◽  
Author(s):  
Mike R Watkins ◽  
Richard J Oliver
Keyword(s):  
Size Distribution ◽  
Bubble Size ◽  
Bubble Size Distribution ◽  
Foam Density ◽  
Physiochemical Properties ◽  
Significant Difference ◽  
Experienced Operator ◽  
Sodium Tetradecyl Sulphate ◽  
Foam Production ◽  
Made In

Objectives The objectives were to examine the density, bubble size distribution and durability of sodium tetradecyl sulphate foam and the consistency of production of foam by a number of different operators using the Tessari method. Methods 1% and 3% sodium tetradecyl sulphate sclerosant foam was produced by an experienced operator and a group of inexperienced operators using either a 1:3 or 1:4 liquid:air ratio and the Tessari method. The foam density, bubble size distribution and foam durability were measured on freshly prepared foam from each operator. Results The foam density measurements were similar for each of the 1:3 preparations and for each of the 1:4 preparations but not affected by the sclerosant concentration. The bubble size for all preparations were very small immediately after preparation but progressively coalesced to become a micro-foam (<250 µm) after the first 30 s up until 2 min. Both the 1% and 3% solution foams developed liquid more rapidly when made in a 1:3 ratio (37 s) than in a 1:4 ratio (45 s) but all combinations took similar times to reach 0.4 ml liquid formation. For all the experiments, there was no statistical significant difference between operators. Conclusions The Tessari method of foam production for sodium tetradecyl sulphate sclerosant is consistent and reproducible even when made by inexperienced operators. The best quality foam with micro bubbles should be used within the first minute after production.

scholarly journals Development of Bubble Characteristics on Chute Spillway Bottom

Water ◽  
2018 ◽  
Vol 10 (9) ◽  
pp. 1129
Author(s):  
Ruidi Bai ◽  
Chang Liu ◽  
Bingyang Feng ◽  
Shanjun Liu ◽  
Faxing Zhang
Keyword(s):  
Size Distribution ◽  
Bubble Size ◽  
Dissipation Rate ◽  
Bubble Diameter ◽  
Bubble Size Distribution ◽  
Impact Zone ◽  
Air Bubble ◽  
Air Supply ◽  
Bubble Characteristics ◽  
The Impact

Chute aerators introduce a large air discharge through air supply ducts to prevent cavitation erosion on spillways. There is not much information on the microcosmic air bubble characteristics near the chute bottom. This study was focused on examining the bottom air-water flow properties by performing a series of model tests that eliminated the upper aeration and illustrated the potential for bubble variation processes on the chute bottom. In comparison with the strong air detrainment in the impact zone, the bottom air bubble frequency decreased slightly. Observations showed that range of probability of the bubble chord length tended to decrease sharply in the impact zone and by a lesser extent in the equilibrium zone. A distinct mechanism to control the bubble size distribution, depending on bubble diameter, was proposed. For bubbles larger than about 1–2 mm, the bubble size distribution followed a—5/3 power-law scaling with diameter. Using the relationship between the local dissipation rate and bubble size, the bottom dissipation rate was found to increase along the chute bottom, and the corresponding Hinze scale showed a good agreement with the observations.

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