BHAGAT.pdf Final2

8/8/2019 BHAGAT.pdf Final2

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Studies in bubble formation-IV : Bubble formation at porous discs

B. Bowonder and R. Kumar

Rajesh Kumar Bhagat


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Overview

Introduction Mathematical model

Results summary Conclusions

Indian Institute of Science 2010


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Objective and motivation

To study the bubble formation from porous disk and predict a model which can explain the physics of problem from first principle.

There was no paper to explain the effect of

surface tension and viscosity, so address that problem.



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phenomena of bubbleformation


First stage is expansion stage.

Second stage is detachment stage.

. ., - -A Ohnuki et al Development of Multidimensional

Two Fluid Model Code ACE 3D for,Evaluation of Constitutive Equations J - / -JAERI Data Code 96 033 ( ).1996
http://jolisf.tokai.jaeri.go.jp/pdf/dat/JAERI-Data-Code-96-033.pdfhttp://jolisf.tokai.jaeri.go.jp/pdf/dat/JAERI-Data-Code-96-033.pdfhttp://jolisf.tokai.jaeri.go.jp/pdf/dat/JAERI-Data-Code-96-033.pdf


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Mathematical model for the process

Force balance on bubble

Expansionstage

Detachment stage Condition for Detachment

= nertial force buoyancy force viscous force orce due to surface tension


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Assumptions for the model


Porous disc is made of large number of pores of uniformdiameter and length having same resistance. Number of operative sites is equal to number of bubblesimultaneously on the disk which is only a fraction of totalnumber of sites.

Effective pores may be made of number of pores but in thisanalysis single pore is considered and flow through a single pore is considered.Bubble arrange themselves in hexagonal close packedmanner.

Flow

rate

increase

f fe ct iv e s it es


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Mathematical model


Number of bubble by considering hexagonal close packing

Hexagonal close packing ofbubble

( )1

( )2


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Mathematical model for expansion stage

( )3



Mathematical model for detachment stage

( )IV



Verification of model

Experimental setup



Range of variable covered during investigation

variable rangeviscosity 1- 604cP

Surface tension 22.8-71.8 dyn/CmDensity 0.792-1.255 g/Cm3Flow rate of air 10-220 Cm3/secPore diameter 45-110

Superficial velocity 4.389-60.94Cm/sec



Results and discussion

,

Bubble

volume

Cm

3

,low per site Cm 3 / sec

Effect of surface tension, viscosity and pore diameter



Results and discussionEffect of surface tension,viscosity and pore diameter

,

Bubble

volume

Cm

3

,low rate per si te Cm 3 / sec




Theoretical

bubble

volume

Cm

3

ubble volume experimental Cm 3

omparison between bubble volume


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Number

o

f

sites

calc

ulated

umber of sites experimental

Comparison of number of sites


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Conclusions

With increase in pore diameter, surface tension, andviscosity, bubble volume is increasing at low flowRate, but after a certain flow rate these factors are notIncreasing the bubble volume.

With this model, there was possibility for the explanationof bubbles in fluidized bed and author was working in that area.


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Thank you


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odel for expansion stage


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odel for expansion stage


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odel for detachment stage


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odel for detachment stage


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