Abstract
OpenFOAM was utilized for analyzing bubble behavior and deformation of free liquid surface due to bubble formation and bursting in a rectangular container. Influence of three system parameters, orifice diameter, number of orifices and spacing between orifices, on various bubble dynamics and deformation of gas-liquid interface is presented. The study also incorporates information on bubble formation, bubbling frequency, and orientation of bubbles. Considering different orifice spacing, bubbling synchronicity is also reported. Details regarding interaction of wakes during bubble coalescence for single, double and triple inlet orifices are presented. The deformation of free liquid surface due to bubble formation and bursting is quantified using a new parameter called deformation index (D *L ). The analyses indicate that the frequency of bubble detachment is augmented with increase in orifice diameter and number of orifices. However, bubble detachment frequency is reduced when orifice spacing increased. Orientation of detached bubbles keeps on changing for larger orifice spacing. Results show that variations of these geometric parameters have substantial influence on free liquid surface deformation due to bubble bursting and other bubble behavior. Using results of these studies, one can develop a bubble-generating device for optimal performance.
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Abbreviations
- Ar:
-
Archimedes number, \({\rm{Ar}} = {{{\rm{g}}{{\rm{L}}^3}{\rho _l}({\rho _b} - {\rho _l})} \over {{\mu ^2}}}[ - ]\)
- Bo:
-
Bond number, \({\rm{Bo}} = {{{\rho _l}{\rm{g}}{{\rm{L}}^2}} \over \sigma }[ - ]\)
- C:
-
courant number [-]
- D:
-
diameter of storage tank [m]
- Db :
-
equivalent bubble diameter [mm]
- Dbav :
-
average equivalent bubble diameter [mm]
- D *L :
-
deformation index, \({\rm{D}}_L^* = {{{{\rm{D}}_L}} \over {\rm{D}}}[ - ]\)
- DL :
-
length of deformed free liquid surface [m]
- Do :
-
orifice diameter [mm]
- Dt :
-
detachment time [s]
- Eo:
-
Eötvös number, \({\rm{Eo}} = {{{\rm{\Delta }}\rho {\rm{g}}{{\rm{L}}^2}} \over \sigma }[ - ]\)
- ET :
-
end time [s]
- \(\overrightarrow {\rm{F}} \) :
-
body force at the interface due to surface tension [Nm−2]
- g:
-
acceleration due to gravity [m s−2]
- L:
-
characteristics length [m]
- Mo:
-
Morton number, \({\rm{Mo}} = {{{\rho _l}\mu _l^4} \over {{\rm{\Delta }}\rho {\sigma ^3}}}[ - ]\)
- Os :
-
orifice spacing [mm]
- p_rgh :
-
pseudo or hydrostatic pressure [Pa]
- Re:
-
Reynolds number, \({\mathop{\rm Re}\nolimits} = {{{\rho _l}{\rm{VL}}} \over {{\mu _l}}}[ - ]\)
- ST :
-
start time [s]
- t/T:
-
time [s]
- u, v, w:
-
X, Y and Z component velocities [m/s]
- Vg :
-
velocity of gas [ms−1]
- We:
-
Weber number, \({\rm{We}} = {{{\rho _l}{{\rm{V}}^2}{\rm{L}}} \over \sigma }[ - ]\)
- X, Y, Z:
-
cartesian co-ordinates [m]
- Yp :
-
vertical location of the bubble from column bottom [m]
- δx, δy:
-
grid size long X and Y direction [m]
- δt:
-
time step [s]
- ρ :
-
density [kgm−3]
- σ :
-
surface tension [Nm−1]
- μ :
-
dynamic viscosity [Pa·s]
- 1, 2:
-
fluid 1, fluid 2
- av:
-
average
- b:
-
bubble/body
- g:
-
gas phase
- l :
-
liquid phase
- max:
-
maximum
- o:
-
orifice
- p:
-
position
- s:
-
spacing
- *:
-
dimensionless quantity
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Sarath, S.R., Jayakumar, J.S. Bubble dynamics and deformation of free liquid surface in aerated liquid storage tanks. Korean J. Chem. Eng. 38, 716–735 (2021). https://doi.org/10.1007/s11814-021-0747-y
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DOI: https://doi.org/10.1007/s11814-021-0747-y