In the paper the paths of bubbles emitted from the brass nozzle with inner diameter equal to 1.6 mm have been analyzed. The mean frequency of bubble departure was in the range from 2 to 65.1 Hz. Bubble paths have been recorded using a high speed camera. The image analysis technique has been used to obtain the bubble paths for different mean frequencies of bubble departures. The multifractal analysis (WTMM - wavelet transform modulus maxima methodology) has been used to investigate the properties of bubble paths. It has been shown that bubble paths are the multifractals and the influence of previously departing bubbles on bubble trajectory is significant for bubble departure frequency fb > 30 Hz.
Designers of all types of equipment applied in oxygenation and aeration need to get to know the mechanism behind the gas bubble formation. This paper presents a measurement method used for determination of parameters of bubbles forming at jet attachment from which the bubles are displaced upward. The measuring system is based on an optical tomograph containing five projections. An image from the tomograph contains shapes of the forming bubbles and determine their volumes and formation rate. Additionally, this paper presents selected theoretical models known from literature. The measurement results have been compared with simple theoretical models predictions. The paper also contains a study of the potential to apply the presented method for determination of bubble structures and observation of intermediate states.
The hulls of naval ships are exposed to forces and moments coming from internal and external sources. Usually, these are interactions that can be described mathematically by harmonic and polyharmonic functions. The shock of UNDEX type (underwater explosion) works completely differently and its time waveform is difficult to describe with mathematical functions as pressure vs. time. The paper presents a simplification of physical and mathematical models of 1-D kickoff pressure whose aim is performance the simulation of the external force of the detonation wave. The proposed models were verified and tuned on naval, sea trials. The main goals of the proposed models are to perform simulation calculations of the detonation pressure for different explosion charge weights from different distances of the UNDEX epicentre for the design process of machine foundation. The effects of pressure are transformed as impulses exposed on shock absorber mounted at light shock machine.
Feasibility of a model of gas bubble break-up and coalescence in an air-lift column enabling determination of bubble size distributions in a mixer with a self-aspirating impeller has been attempted in this paper. According to velocity measurements made by the PIV method with a self-aspirating impeller and Smagorinski’s model, the spatial distribution of turbulent energy dissipation rate close to the impeller was determined. This allowed to positively verify the dependence of gas bubble velocity used in the model, in relation to turbulent energy dissipation rate. Furthermore, the range of the eddy sizes capable of breaking up the gas bubbles was determined. The verified model was found to be greatly useful, but because of the simplifying assumptions some discrepancies of experimental and model results were observed.
The paper presents a photographic analysis of the break-up of gas bubbles flowing out of the outlets of a self-aspirating disk impeller. It was found that bubbles detached from the interfacial surface most often disintegrate to form several daughter bubbles. Further in the work, the population balance model was verified for several formulas describing the bubble break-up rate. It has been found that a good fit to the experimental data is provided by the formula given by Laakkonen for 5 daughter bubbles. The possibility of using the Monte Carlo method to model the bubble break-up processwas also determined. For this method, a good agreement of results was achieved for the division into a maximum of 10 daughter bubbles. In the case of this method it was also found necessary to use the function of break-up frequency at a higher rate for smaller bubbles.
The aim of the paper is a theoretical analysis of propagation of high-intensity acoustic waves throughout a bubble layer. A simple model in the form of a layer with uniformly distributed mono-size spherical bubbles is considered. The mathematical model of the pressure wave’s propagation in a bubbly liquid layer is constructed using the linear non-dissipative wave equation and assuming that oscillations of a single bubble satisfy the Rayleigh-Plesset equation. The models of the phase sound speed, changes of resonant frequency of bubbles and damping coefficients in a bubbly liquid are compared and discussed. The relations between transmitted and reflected waves and their second harmonic amplitudes are analyzed. A numerical analysis is carried out for different environmental parameters such as layer thicknesses and values of the volume fraction as well as for different parameters of generated signals. Examples of results of the numerical modeling are presented.
Based on hydrodynamic data, Kato-Wen and Kunii-Levenspiel bubbling-bed model parameters, supplemented with assumptions characteristic for tested confined fluidised bed, were analysed. The calculated bubble diameters and the bed composition proved essential influence of inter-particle space of packed compacted component onto fluidisation character. The usability of the conducted model analysis was also confirmed. Finally, it can be concluded that Kunii-Levenspiel and Kato- Wen models with characteristic assumptions (for the tested bed) can be applied for calculation of the confined fluidised bed layer porosity. Discrepancies of ε f value, determined on the basis of the above mentioned bubbling-bed models do not exceed 8% of the error. The model parameters obtained from the matching the model relations to experimental data εf = f(u0) allow an analysis of the fluidisation character as well as gas velocity regime and the fluidised bed structural composition identification. A description of the regime of the process in which confined fluidised bed is characterised with an increase of mass and heat transfer rate is also possible using relation (17) derived in the present study.
The main topic of this study is the mathematical modelling of bubble size distributions in an aerated stirred tank using the population balance method. The air-water system consisted of a fully baffled vessel with a diameter of 0.29 m, which was equipped with a six-bladed Rushton turbine. The secondary phase was introduced through a ring sparger situated under the impeller. Calculations were performed with the CFD software CFX 14.5. The turbulent quantities were predicted using the standard k-ε turbulence model. Coalescence and breakup of bubbles were modelled using the MUSIG method with 24 bubble size groups. For the bubble size distribution modelling, the breakup model by Luo and Svendsen (1996) typically has been used in the past. However, this breakup model was thoroughly reviewed and its practical applicability was questioned. Therefore, three different breakup models by Martínez-Bazán et al. (1999a, b), Lehr et al. (2002) and Alopaeus et al. (2002) were implemented in the CFD solver and applied to the system. The resulting Sauter mean diameters and local bubble size distributions were compared with experimental data.
An optical tomograph in which a tested object is illuminated from five directions has been presented in the paper. The measurements of luminous intensity after changing into discrete signals (0 or 1) in the detectors equipped with 64 optical sensors were subjected to reconstruction by means of the matrix algorithm. Detailed description of the measuring sensor, as well as the principles of operation of the electronic system, has been given in the paper. Optical phenomena occurring at the phase boundary while transmitted through the sensor wall and phenomena inside the measuring space have also been taken into account. The method of the sensor calibration has been analysed and a way of technical solution of the problem under consideration has been discussed. The elaborated method has been tested using objects of the known shape and dimensions. It was found that reconstruction of the shapes of moving bubbles and determination of their main parameters is also possible with a reasonable accuracy.
The main topic of this study is the experimental measurement and mathematical modelling of global gas hold-up and bubble size distribution in an aerated stirred vessel using the population balance method. The air-water system consisted of a mixing tank of diameter T = 0.29 m, which was equipped with a six-bladed Rushton turbine. Calculations were performed with CFD software CFX 14.5. Turbulent quantities were predicted using the standard k-ε turbulence model. Coalescence and breakup of bubbles were modelled using the homogeneous MUSIG method with 24 bubble size groups. To achieve a better prediction of the turbulent quantities, simulations were performed with much finer meshes than those that have been adopted so far for bubble size distribution modelling. Several different drag coefficient correlations were implemented in the solver, and their influence on the results was studied. Turbulent drag correction to reduce the bubble slip velocity proved to be essential to achieve agreement of the simulated gas distribution with experiments. To model the disintegration of bubbles, the widely adopted breakup model by Luo & Svendsen was used. However, its applicability was questioned.
Electroflotation is used in the water treatment industry for the recovery of suspended particles. In this study the bubble formation and release of hydrogen bubbles generated electrolytically from a platinum cathode was investigated. Previously, it was found that both the growth rate and detachment diameter increased with increasing wire diameter. Conversely, current density had little effect on the released bubble size. It was also found that the detached bubbles rapidly increased in volume as they rose through the liquid as a result of decreasing hydrostatic pressure and high levels of dissolved hydrogen gas in the surrounding liquid. The experimental system was computationally modelled using a Lagrangian-Eulerian Discrete Particle approach. It was revealed that desorption of gaseous solutes from the electrolyte solution, other than hydrogen, may have a significant impact on the diameter variation of the formed bubbles. The simulation confirmed that liquid circulation, either forced or induced by the rising bubble plume, influences both the hydrogen supersaturation (concentration) in the neighbourhood of the electrode and the size of the resulting bubbles.
In the present research, an experimental investigation was conducted to assess the heat transfer coefficient of aqueous citric acid mixtures. The experimental facility provides conditions to assess the influence of various operating conditions such as the heat flux (0–190 kW/m2), mass flux (353–1059 kg/m2s) and the concentration of citric acid in water (10%– 50% by volume) with a view to measure the subcooled flow boiling heat transfer coefficient of the mixture. The results showed that two main heat transfer mechanisms can be identified including the forced convective and nucleate boiling heat transfer. The onset point of nucleate boiling was also identified, which separates the forced convective heat transfer domain from the nucleate boiling region. The heat transfer coefficient was found to be higher in the nucleate boiling regime due to the presence of bubbles and their interaction. Also, the influence of heat flux on the heat transfer coefficient was more pronounced in the nucleate boiling heat transfer domain, which was also attributed to the increase in bubble size and rate of bubble formation. The obtained results were also compared with those theoretically obtained using the Chen type model and with some experimental data reported in the literature. Results were within a fair agreement of 22% against the Chen model and within 15% against the experimental data.
The flow structure around rising single air bubbles in water and their characteristics, such as equivalent diameter, rising velocity and shape, was investigated using Particle Image Velocimetry (PIV) and Shadowgraphy in a transparent apparatus with a volume of 120 mL. The effect of different volumetric gas flow rates, ranging from 4 μL/min to 2 mL/min on the liquid velocity was studied. Ellipsoidal bubbleswere observedwith a rising velocity of 0.25–0.29m/s. It was found that a Kármán vortex street existed behind the rising bubbles. Furthermore, the wake region expanded with increasing volumetric gas flow rate as well as the number and size of the vortices.
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