Population balance modeling of polydispersed bubbly flow in continuous casting using average bubble number density approach

2017 ◽  
Vol 319 ◽  
pp. 139-147 ◽  
Author(s):  
Zhongqiu Liu ◽  
Baokuan Li ◽  
Fengsheng Qi ◽  
Sherman C.P. Cheung
Keyword(s):  
Continuous Casting ◽  
Bubbly Flow ◽  
Population Balance ◽  
Number Density ◽  
Population Balance Modeling ◽  
Bubble Number ◽  
Bubble Number Density

Population Balance Modeling of Polydispersed Bubbly Flow in Continuous-Casting Using Multiple-Size-Group Approach

2014 ◽  
Vol 46 (1) ◽  
pp. 406-420 ◽  
Author(s):  
Zhongqiu Liu ◽  
Linmin Li ◽  
Fengsheng Qi ◽  
Baokuan Li ◽  
Maofa Jiang ◽  
...  
Keyword(s):  
Continuous Casting ◽  
Bubbly Flow ◽  
Population Balance ◽  
Size Group ◽  
Group Approach ◽  
Population Balance Modeling

scholarly journals Development of Bubble Size Correlation for Adiabatic Forced Convective Bubbly Flow in Low Pressure Condition Using CFD Code

2020 ◽  
Vol 10 (16) ◽  
pp. 5443
Author(s):  
Jinyeong Bak ◽  
Huiyung Kim ◽  
Jae Jun Jeong ◽  
Dongjin Euh ◽  
Byongjo Yun
Keyword(s):  
Bubble Size ◽  
Bubbly Flow ◽  
Flow Analysis ◽  
Low Pressure ◽  
Good Prediction ◽  
Two Phase ◽  
Local Bubble ◽  
Computational Fluid Dynamics Cfd ◽  
Bubble Number ◽  
Bubble Number Density

In a multidimensional two-phase flow analysis, bubble size significantly affects interfacial transfer terms such as mass, momentum, and energy. With regard to bubbly flow, the application of a simple correlation-type bubble size model presents certain advantages, including short calculation times and ease of usage. In this study, we propose a semi-theoretical correlation developed from a steady state bubble number density transport equation for predicting the distribution of local bubble size using a computational fluid dynamics (CFD) code. The coefficients of the new correlation were determined using the local bubble parameters obtained on the basis of three existing vertical air-water experiments. Finally, these were implemented in commercial CFD code and evaluated against experimental data, which showed that the proposed correlation exhibits good prediction capability for forced convective air-water bubbly flows under low pressure conditions.

Velocity Profile Measurements of Two-Phase Flow in Rectangular Channel Using Ultrasonic Time-Domain Correlation Method

2007 ◽  
Author(s):  
Takuya Hayashida ◽  
Hideki Murakawa ◽  
Hiroshige Kikura ◽  
Masanori Aritomi ◽  
Michitsugu Mori
Keyword(s):  
Flow Measurement ◽  
Two Phase Flow ◽  
Rectangular Channel ◽  
Correlation Method ◽  
Phase Flow ◽  
Number Density ◽  
Two Phase ◽  
Bubble Number ◽  
Bubble Number Density ◽  
Time Domain Correlation

Velocity measurement using ultrasound has attracted much attention in engineering fields and medical science field. Especially, Ultrasonic velocity profile monitor (UVP) has been in the spotlight in engineering fields, because of its many diagnostic advantages. The major advantage is that UVP can obtain instantaneous velocity distributions on beam line by measuring Doppler shift frequencies of echo signals. And UVP is applicable to existing pipes, because it is non-contact measurement technique. In recent years, various studies about UVP have been done, and UVP has already been put to practical use in engineering plants. The authors especially focused on two-phase flow measurement using ultrasound. Previously, we developed a way to measure bubbly flow using UVP. By this method, we are able to separate liquid information from bubbles information to some degrees. However, when the bubble number density is low, a problem occurs. Because the effect of liquid information is strong under that condition. From this fact, we applied the ultrasound time domain correlation method (UTDC) to two-phase flow measurement. This method is our original technique to measure the velocity distribution. It is based on the cross-correlation between two consecutive echoes of ultrasonic pulses. With this method, we can separate liquid information from bubble information even when the bubble number density is low, because reflected signals depend on the size of reflectors and frequency of ultrasound. In this study, the authors applied the UTDC to two-phase flow measurements in rectangular channel using a multi-wave ultrasonic transducer (TDX). The multi-wave TDX has two kinds of basic frequencies. One is 2MHz for the velocity of rising bubbles and the other is 8MHz for the liquid velocity. So it enables us to measure the velocity of the liquid and that of bubbles at the same point and time. The 2MHz ultrasonic element of TDX has 10mm diameter and the 8MHz ultrasonic element has 3mm diameter.

scholarly journals Approximate Moment Methods for Population Balance Equations in Particulate and Bioengineering Processes

Processes ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 414
Author(s):  
Robert Dürr ◽  
Andreas Bück
Keyword(s):  
Differential Equations ◽  
Density Distribution ◽  
Population Balance ◽  
Specific Class ◽  
Number Density ◽  
Balance Equations ◽  
Population Balance Modeling ◽  
Closed Set ◽  
Population Balance Equations ◽  
Moment Methods

Population balance modeling is an established framework to describe the dynamics of particle populations in disperse phase systems found in a broad field of industrial, civil, and medical applications. The resulting population balance equations account for the dynamics of the number density distribution functions and represent (systems of) partial differential equations which require sophisticated numerical solution techniques due to the general lack of analytical solutions. A specific class of solution algorithms, so-called moment methods, is based on the reduction of complex models to a set of ordinary differential equations characterizing dynamics of integral quantities of the number density distribution function. However, in general, a closed set of moment equations is not found and one has to rely on approximate closure methods. In this contribution, a concise overview of the most prominent approximate moment methods is given.

scholarly journals Late-Holocene climate evolution at the WAIS Divide site, West Antarctica: bubble number-density estimates

2011 ◽  
Vol 57 (204) ◽  
pp. 629-638 ◽  
Author(s):  
J.M. Fegyveresi ◽  
R.B. Alley ◽  
M.K. Spencer ◽  
J.J. Fitzpatrick ◽  
E.J. Steig ◽  
...  
Keyword(s):  
Late Holocene ◽  
Accumulation Rate ◽  
Ice Core ◽  
Temperature History ◽  
Flow Density ◽  
Number Density ◽  
West Antarctica ◽  
Surface Cooling ◽  
Bubble Number ◽  
Bubble Number Density

AbstractA surface cooling of ∼1.7°C occurred over the ∼two millennia prior to ∼1700 CE at the West Antarctic ice sheet (WAIS) Divide site, based on trends in observed bubble number-density of samples from the WDC06A ice core, and on an independently constructed accumulation-rate history using annual-layer dating corrected for density variations and thinning from ice flow. Density increase and grain growth in polar firn are both controlled by temperature and accumulation rate, and the integrated effects are recorded in the number-density of bubbles as the firn changes to ice. Number-density is conserved in bubbly ice following pore close-off, allowing reconstruction of either paleotemperature or paleo-accumulation rate if the other is known. A quantitative late-Holocene paleoclimate reconstruction is presented for West Antarctica using data obtained from the WAIS Divide WDC06A ice core and a steady-state bubble number-density model. The resultant temperature history agrees closely with independent reconstructions based on stable-isotopic ratios of ice. The ∼1.7°C cooling trend observed is consistent with a decrease in Antarctic summer duration from changing orbital obliquity, although it remains possible that elevation change at the site contributed part of the signal. Accumulation rate and temperature dropped together, broadly consistent with control by saturation vapor pressure.

Progress in Modeling Injector Cavitating Flows With a Multi-Fluid Method

2006 ◽  
Author(s):  
De Ming Wang ◽  
David Greif
Keyword(s):  
Bubble Dynamics ◽  
Measurement Data ◽  
Interfacial Area ◽  
Number Density ◽  
Cavitating Flows ◽  
Set Up ◽  
Single Bubble Dynamics ◽  
Bubble Number ◽  
Bubble Number Density ◽  
Constricted Channel

A finite volume, pressure based semi-implicit algorithm is developed for solving a multi-fluid system of any number of phases with strong coupling between the phases in mass, momentum and energy transfer. The mass transfer from liquid to vapor due to cavitation is modeled based on a single bubble dynamics (Rayleigh-Plesset equation). In order to model the vapor phase of variable size distribution, or polydispersion, the transport equations of bubble number density and interfacial area are derived from taking the moments of the PDF equation in phase space. The modeling of the result equations are effected through consideration of breakup and coalescence. The k-zeta-f turbulence model is adopted which is found to be particularly effective for predicting near wall effects on the turbulence level. Validation efforts are presented in which comparison with available measurement data are made for a number of cases including constricted channel flow with sharp inlet (I-channel), with smooth inlet (Y-channel), a flash-boiling cavitation set-up, and an actual injector set-up.

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