Multifractal properties of large bubble paths in a single bubble column

Mosdorf, Romuald; Wyszkowski, T.; Dąbrowski, Kamil

doi:10.2478/v10173-011-0001-9

Cited by 4 publications

(2 citation statements)

References 25 publications

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“…In the papers [15,16] the paths of bubbles emitted from the brass nozzle have been analysed. It has been shown that bubble paths have multifractal character and its properties are changed when bubble departure frequency is greater than 30 Hz.…”

Section: Introductionmentioning

confidence: 99%

Chaotic air pressure fluctuations during departure of air bubbles from two neighbouring nozzles

Mosdorf¹,

Wyszkowski²

2012

Archives of Thermodynamics

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In the experiment, bubbles were generated from two brass nozzles with inner diameters of 1.1 mm. They were submerged in the glass tank filled with distilled water. There have been measured the air pressure fluctuations and the signal from the laser-phototransistor sensor. For analysis of the pressure signal the correlation (the normalized cross -correlation exponent) and non-linear analyses have been used. It has been shown that hydrodynamic interactions between bubbles can lead to bubble departure synchronization. In this case the bubble departures become periodic. The results of calculation of correlation dimension and the largest Lyapunov exponent confirm that hydrodynamic bubble interactions observed for 4 mm spacing between nozzels cause the periodic bubble departures from two neighbouring nozzles.

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Section: Introductionmentioning

confidence: 99%

Chaotic air pressure fluctuations during departure of air bubbles from two neighbouring nozzles

Mosdorf¹,

Wyszkowski²

2012

Archives of Thermodynamics

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“…The MBR hydrodynamics are similar to bubble columns operation, with the difference that a membrane is placed inside the bubble column to extract the clean water. The placement of the membrane inside the column affects behaviour of the bubbles [2][3][4]. The main drawback of MBR systems is the fouling of the membrane, which results in frequent cleaning and replacement, making this system less appealing for full-scale applications [1].…”

Section: Introductionmentioning

confidence: 99%

Energy consumption in terms of shear stress for two types of membrane bioreactors used for municipal wastewater treatment processes

Ratkovich¹,

Bentzen²,

Rasmussen³

2012

Archives of Thermodynamics

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Two types of submerged membrane bioreactors (MBR): hollow fiber (HF) and hollow sheet (HS), have been studied and compared in terms of energy consumption and average shear stress over the membrane wall. The analysis of energy consumption was made using the correlation to determine the blower power and the blower power demand per unit of permeate volume. Results showed that for the system geometries considered, in terms the of the blower power, the HF MBR requires less power compared to HS MBR. However, in terms of blower power per unit of permeate volume, the HS MBR requires less energy. The analysis of shear stress over the membrane surface was made using computational fluid dynamics (CFD) modelling. Experimental measurements for the HF MBR were compared with the CFD model and an error less that 8% was obtained. For the HS MBR, experimental measurements of velocity profiles were made and an error of 11% was found. This work uses an empirical relationship to determine the shear stress based on the ratio of aeration blower power to tank volume. This relationship is used in bubble column reactors and it is extrapolate to determine shear stress on MBR systems. This relationship proved to be overestimated by 28% compared to experimental measurements and CFD results. Therefore, a corrective factor is included in the relationship in order to account for the membrane placed inside the bioreactor. Nomenclature A -membrane area, m 2 Ax -open cross-sectional area, m 2 C0 -bulk concentration of ferricyanide, = 3 mol/m 3 D -diffusion coefficient of ferricyanide, 6.6 × 10 −10 m 2 /s d -external doameter of the fiber for HF, m de -diameter of the probe, m e -blower efficiency, ∼0.56 EA -blower power consumption, kW F -Faraday constant, = 96500 C/mol G -amplifier gain, = 1000 g -gravity acceleration, = 9.81 m 2 /s) h -height of water above the air diffuser, m J -permeate flux, m/h L -length of the membrane module, m patm -atmospheric pressure, = 101 325 Pa QA -air flow rate, m 3 /h Qp -permeate flow, m 3 /h R -resistance, = 100 Ω SADm -specific aeration demand imparted to the membrane, m/h SADp -specific aeration demand imparted to the permeate volume T -inlet temperature, K U -module upflow aeration velocity, m/h V -volume of fluid, m 3 V0 -voltage signal, V Wm -blower power per unit membrane area, kW/m 2 Wp -blower power demand per unit of permeate volume, kWh/m 3Greek symbols δ -channel space separation for HS, m ϕ -packing density for HF, m 2 /m 3 γ -shear rate, s −1 λ -ratio of specific heat capacity at constant pressure to specific heat capacity at constant volume, = 1.4 for air µ -viscosity, Pas νe -number of electrons involved in the reaction, = 1 ρw -density of water, 998.28 kg/m 3 at 20 o C τ -shear stress, Pa

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Experimental measurement and theoretical analysis on bubble dynamic behaviors in a gas-liquid bubble column

Zhou

Kang

Huang

et al. 2020

Chemical Engineering Science

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Multifractal properties of large bubble paths in a single bubble column

Cited by 4 publications

References 25 publications

Chaotic air pressure fluctuations during departure of air bubbles from two neighbouring nozzles

Chaotic air pressure fluctuations during departure of air bubbles from two neighbouring nozzles

Energy consumption in terms of shear stress for two types of membrane bioreactors used for municipal wastewater treatment processes

Experimental measurement and theoretical analysis on bubble dynamic behaviors in a gas-liquid bubble column

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