The document describes a 3D CFD model of a stirred tank with gas-liquid two-phase flow. Simulations were conducted for various impeller speeds and gas inlet flow rates. Key findings include: 1) Gas holdup, liquid velocity, and bubble size distributions were simulated and compared to experimental data. 2) Increasing inlet gas flow rate or impeller speed led to higher gas holdup but smaller average bubble sizes. 3) Gas accumulated between the impellers and tank walls, while smaller bubbles were more dispersed throughout the tank.

2. Introduction
 Stirred tanks with gas liquid two-phase flow are very widely
used in chemical and biochemical engineering process
 Stirred tanks are commonly used in reactors of
 Detergent plants
 Paint mixing units
 Food processing plants
 Many researchers carried out numerical simulations on this
gas –liquid flow in a stirred tank, with many assumptions and
predictions
 Ranade and Khopkar, Pinelli
 Zhang

3. Introduction (Contd.)
 3D CFD model of a gas-liquid two
phase stirred tank with 2 six blade
turbines and 4 baffles were
developed
 Impeller rotation speeds and inlet
gas flow rates are varied
 Simulation, Analysis and Model
predictions about gas holdup and
liquid velocity distributions are
carried out generally

4. Hydrodynamic Characteristics
 Gas holdup
 A dimensionless key parameter for design purposes that
characterizes transport phenomena of bubble columns
 Liquid velocity
 Bubble size fractions
 Transient bubble diameter distributions
 Inlet air flow rate
 Impeller rotation speed

5. Computational Fluid Dynamics
 Branch of fluid dynamics,
used to solve nonlinear
differential equations
involving fluid flow using
numerical methods and
algorithms
 Extensive applications
 Aerospace
 Turbo machinery
 Nuclear thermal hydraulics
 Automotive etc Numerical
Analysis
Fluid
Dynamics
Compute
r
Science

6. Why CFD ????
 Less time consuming & less expensive compared to
experiments
 Powerful visualization capabilities
 Predicts performance before modifying or installing actual
systems or a prototype
 Predict which design changes are most crucial to enhance
performance

7. Model
 Eulerian approach is adopted
 Stationary frame of reference
 Unstructured grid
 Two phases
 Dispersed and continuous phases
 Satisfies compatibility condition
   1 g l
 Continuity balance equation for each phase
 
 u  0 g    
  

g g
g g
t
 
 u  0 l    
  

l l
l l
t

8. Model (Contd.)
 The momentum balance equation for each phase
 Drag force exerted by dispersed phase on continuous phase
 Lift force acting perpendicular to the direction of relative
motion of two phases

9. Numerical Modeling
 Finite Element Method with a multi-grid solver was
adopted (CFX 10.0)
 Computational domain of the stirred tank divided into
 Rotating impeller domain
 Stationary tank domain
 Solver run over 70 s of computed time
 Unstructured grids with a number of 1944 for impellers and
97104 for the tank were implemented

10. Mesh partitions

11. Test Setup
 5L distilled water is filled into the tank (fig shows the case
when static water height was 20 cm while height of tank as
30 cm)
 Operating conditions:
 Rotation speed : 200, 400, 600 rev/min
 Inlet air flow rate : 4, 6, 8L/min
 Each measurement repeated 3 times
 Overall gas holdups measured from height fluctuations of
the water after gas injection for specified operating
conditions

12. Test Setup (Contd.)
Physical dimensions of the stirred tank reactor, side view and top view (unit: mm)

13. Results and discussions
 Simulations of the stirred tank were carried out for five
different operating conditions
 Gas flow number and Froude number are dimensionless
 Rotation speed is fixed (Rs = 400 rev/min) an inlet air flow rate
is varied and vice versa (Qg = 6L/min)
 Summary of operating conditions in this study
Case No. 1 2 3 4 5
Impeller speed (rpm) 400 400 400 200 600
Gas flow rate (L/min) 4 6 8 6 6
Gas flow number 0.060 0.090 0.120 0.180 .060
Froude number 0.249 0.249 0.249 0.062 0561

14. Gas holdup
 The volume fraction of dispersed gas phase is referred to as
the gas hold-up
 Volume averaged overall gas holdup along time
 Time averaged local gas holdups along transversal courses
 Transient gas holdup distributions at horizontal and
vertical positions were simulated and analyzed

16. Volume averaged overall gas holdups
Along time courses under different operating conditions
A: Qg = 6 L/min, Rs = 200, 400, 600 rev/min
B: Rs = 400 rev/min, Qg = 4, 6, 8 L/min.

17. Model simulated time-averaged local gas
holdups along transversal course
(X = 0 mm, Y = 15–75 mm) at different vertical positions (Z = 5,30,65,100,125,160 mm)
under different operating conditions(Qg = 6 L/min, Rs = 200, 400, 600 rev/min).

18. Model simulated time-averaged local gas
holdups along transversal course
(X = 0 mm, Y = 15–75 mm) at different vertical positions (Z = 5, 30,65,100,125,160 mm)
under different operating conditions (Rs = 400 rev/min, Qg = 4,6,8 L/min).

19. Model predictions of transient gas holdup
distributions at the vertical sections
(X = 0 mm) and under different operating
conditions (Rs = 400 rev/min, Qg = 4, 6, 8
L/min) with t = 10, 40, 70 s.
(X = 0 mm) and under different operating
conditions (Qg = 6 L/min, Rs = 200, 400, 600
rev/min) with t = 10, 40, 70 s.

20. Model predictions of transient gas holdup
distributions at the horizontal sections
( Z = 5,30,65,100,125,160 mm)
under different operating conditions
(Rs = 00 rev/min, Qg = 4,6,8 L/min) with t = 40 s.
(Z = 5, 30,65,100,125,160 mm)
and under different operating conditions
(Qg = 6 L/min, Rs = 200, 400, 600 rev/min) with t = 40 s.

21. Liquid velocity
 Axial liquid velocity is selected and simulated and
experimentally measured to characterize liquid flow
fluctuations
 Volume averaged overall liquid velocity along time
 Time averaged liquid velocity along transversal courses
 Transient liquid velocity distributions along horizontal and
vertical positions

22. Volume averaged axial liquid velocities
Along time course under different operating conditions
A: Qg = 6 L/min, Rs = 200,400,600 rev/min
B : Rs = 400 rev/min, Qg = 4,6,8 L/min

23. Model simulated and experimental measured Time
averaged axial liquid velocities along transversal course
(X = 0 mm, Y = 15–75 mm) at different vertical positions (Z = 5, 30,65,100,125,160 mm) and under
different operating conditions (Qg = 6 L/min, Rs = 200,400,600 rev/min)

24. Model simulated and experimental measured Time
averaged axial liquid velocities along transversal course
(X = 0 mm, Y = 15–75 mm) at different vertical positions (Z = 5,30, 65,100,125,160 mm) and under
different operating conditions (Rs = 400 rev/min, Qg = 4,6,8 L/min)

25. Model predictions of transient liquid velocity
distributions at the vertical sections
(X = 0 mm)and under different operating
conditions (Rs = 400 rev/min, Qg = 4,6,8
L/min) with t = 10,40,70 s.
X = 0 mm)and under different operating
conditions(Qg = 6 L/min, Rs = 200,400,600
rev/min)with t = 10, 40,70s

26. Model predictions of transient liquid velocity
distributions at the horizontal sections
(Z = 5,30,65,100,125,160 mm) and under
different operating conditions (Rs = 400
rev/min, Qg = 4,6,8 L/min) with t = 40 s.
(Z = 5,30,65,100,125,160 mm) and under
different operating conditions (Qg = 6 L/min,
Rs = 200,400,600 rev/min) with t = 40 s.

27. Bubble size distribution
 The behavior of bubbles in gas–liquid stirred tanks are very
important especially in supplying oxygen from gas phase
into liquid phase
 The CFD model developed in the current work was coupled
by the MUSIG model
 This model considered several bubble group diameters
which can be represented with Sauter mean diameter
 Bubbles are divided into twenty groups and then predicted
the bubble Sauter mean diameter.
 Diameters of 20 bubble group ranged from 0.375 to
14.625mm

28. Volume averaged bubble size fractions
 Stirred tank was mainly occupied by small bubble groups
(dia less than 4 mm)
 Advantageous for fermentation process
 Improved mass and heat transfer
 Increase in specific area with small bubble diameter

29. Volume averaged bubble diameters
 Bubble Sauter mean diameter ranged from 1 to 2.5 mm
 Increase in rotation speed obviously made a decrease in
bubble diameter
 Change in inlet air flow rate under investigated range had
little effect on bubble diameter

30. Model predictions of transient bubble diameter
distributions at the vertical sections
(X = 0 mm) and under different operating
conditions(Rs = 400 rev/min, Qg = 4,6,8
L/min)with t = 10, 40,70 s.
(X = 0 mm) and under different operating
conditions (Qg = 6 L/min, Rs =
200,400,600rev/min) with t = 10,40,70 s.

31. Model predictions of transient bubble diameter
distributions at the horizontal sections
(Z = 5,30, 65,100,125,160 mm) and under
different operating conditions (Rs = 400
rev/min, Qg = 4,6,8 L/min) with t = 40 s.
(Z = 5,30, 65,100,125,160 mm) and under
different operating conditions (Qg = 6 L/min,
Rs = 200, 400,600 rev/min) with t = 40 s.

32. Conclusion
 A full-flow field, 3D transient CFD model based on
Eulerian approach was developed for a gas-liquid two phase
stirred tank with 2 six-blade turbines and 4 baffles
 MUSIG model for bubble size distribution considering coalescence
and breakup
 Increase in inlet air flow rate and rotation speed
 increase in overall gas holdup
 Increase in inlet air flow rate or decrease in rotation speed
 increase in volume-averaged axial liquid velocity
 Gas accumulated mainly in regions between the two
impellers, as well as between the upper impeller and the
top surface when inlet air flow rate was large

33. Conclusion (Contd.)
 Increase in rotation speed made a more dispersed gas
distribution all over the whole tank
 Vortices were also generated in regions of bottom of the
tank
 The tank was mainly occupied by small bubbles with
diameters smaller than 4 mm
 Larger bubbles accumulated in regions
 near the lower impeller
 between the two impellers
 between the upper impeller and the top surface
 Smaller bubbles accumulated in regions near wall
 Increase in rotation speed made a decrease in bubble
diameter

34. References
 Wang, H., Jia, X., Wang, X., Zhou, Z., Wen, J., Zhang, J.,
CFD modeling of hydrodynamic characteristics of a gas–
liquid two-phase stirred tank, 2014, J. Appl. Math. Mod.,
Vol. 38, No. 1, pp. 63-92
 Kantarci, N., Borak, F., Ulgen, K.O., Bubble column
reactors, 2005, J. Process Chemistry, Vol. 40, No. 7, pp.
2263-2283
 André Bakker, Modeling Flow Fields in Stirred Tanks,
Reacting Flows - Lecture 7, http://www.bakker.org

35. Questions