effect of a baffle length

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Simulation of an Effect of a Baffle Length on

the Power Consumption in an Agitated Vessel

Palani Sivashanmugam and S. Prabhakaran

Abstract

Agitated vessels are often used for homogenization of the miscible liquids in chemical, bio-

chemical, and food industries. Computational fluid dynamics (CFD) is a useful tool for studying

fluid flows, including those of mixing systems. It is particularly powerful where the ability existsto corroborate model results with available data. The CFD simulation was carried out for Rushton

and Smith turbines agitators. The standard k- model has been used for turbulence modeling. The

data obtained by simulation are matching with the literature experimental value for standard baffle

with the discrepancy of less than + 4.5% for power number. The simulated results for agitated

vessel with short baffle (non-standard) are agreeing with the literature values within plus or minus

5% for Power Number.

KEYWORDS: agitated vessel, power consumption, short baffles, CFD, turbine agitators



1. INTRODUCTION

Agitators are used widely for mixing of miscible and immiscible fluid, dispersion

of gas in liquid, suspension of solids in liquid as it is done in hydrogenation of oils. Various types of agitators are used for different applications of mixing and

agitation. Among these turbine type agitator is used widely for dispersing gasinto liquid, which is very much required in fermentation and effluent treatment

application. Prior to 1970s, researchers recognized that the angle of impeller

blade, vessel geometry, baffle were plays the major role in agitated vessel and

postulated that an impeller with more baffle can perform better in terms of power consumption. Since then, impellers with angle of blades have been discarded, and

the 6-blade disk turbine impeller with 4- baffle has become the most popular

impeller.The power consumption depends on the geometrical parameters of the

agitator, baffles and vessel. The power curves for different agitators working inthe vessel equipped with standard baffles (i.e. baffle length L is equal to liquidheight H in the vessel) were reported by Joanna Karcz, Marta Major, 1998.

During recent years, the studies on power consumption for the impeller-vessel

systems of different geometry have been continued by many research workers.

Using CFD, one can understand the mechanism of mixing of fluids in mixingtanks with much easier and economical than the use of experiments. Also CFD

simulation is useful for predicting the vessel hydrodynamics in a wide range of

operational conditions or various geometries. Computational Fluid Dynamics(CFD) has already been used in many studies to predict flow patterns and local

gas volume fractions in the stirred gas-liquid vessels (Bakker and Van Den

Akker,1994; Morud and Hjertager,1996; Derksen, 2002; Van Den Akker, 2007).CFD has reached a level that gives reliable and accurate results for predicting the

flow field in stirred vessels (Sommerfeld and Decker,2003). Several methods had been successfully developed to simulate the flow in a stirred vessel, where good

agreement of the mean flow field with experimental data was achieved. Three-

dimensional steady-state predictions based on this approach were presented byVlaev, and. Staykov, 2001. Mavros and Mann extended this approach to simulate

two-phase flow in a Rushton stirred vessel.

This paper presents the simulation results of an effect of a baffle length on

the power consumption in the agitated vessel with different high-speed agitatorsand the results were compared with the experimentally reported literature value.

1

Sivashanmugam and Prabhakaran: Simulation of an Effect of a Baffle Length on the Power Consumption in an Agitated Vessel

Published by The Berkeley Electronic Press, 2008



Table 1. Geometrical parameters of the agitators

No Agitator d/D Z a/d b/d Remarks

1 Rushton

Turbine

0.33 6 0.25 0.2

2 Smith Turbine 0.33 6 0.25 0.2 R = b/2

(a) Rushton turbine

(b) Smith turbine

Figure 2. Diagram of agitators

3. CFD SIMULATION METHODS

Three main generalized approaches namely multiple reference frame (MRF),

computational snapshot, and sliding mesh approach are used to predict the flow

field in an agitated vessel. The first two approaches involve steady state

computation producing time average flow filed and the third involves transientcomputation to produce time accurate flow filed. The computational domain

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representing mixer is divided into two non-overlapping regions –one surrounding

the impeller and the other representing the rest of the vessel. In this paper MRF

approach has been tried. The brief description of this approach is as follows:

initially simulation of flow is done for inner domain surrounding the impeller in areference frame rotating with impeller. The flow field separating (interface) the

inner and outer domain serves as boundary conditions for simulation of flow fieldin the outer domain of the frame reference model. This results in the revised

boundary conditions for flow field inner domain. The procedure is repeated till

suitable numerical convergence criterion is achieved.

CFD simulation can be carried out by solution of continuity equation andtime averaged Navier-stroke equations;

{ } 0ρdiv =U (1)

{ } { } { } { } .u'u'ρdivµdiv pρdivρt

FUUUU +−+∇+−∇=+∂∂

(2)

Several turbulence models such as k-epsilon, k-omega, etc are availablefor carrying out simulation. Among these models k-epsilon is very widely used

because of its reasonable accuracy for a wide range of turbulent condition in an

agitated vessel. The following two equations have to be solved along with the

above equation for k-ε turbulence model.

{ } { } ρε2µk σk"

µdivk ρdivρk

tij1

1−+

∇=+

∂∂

EU (3)

{ } { }k

ερC-2µ

k

εCε

σε

µdivερdivρε

t

2

2εijij11ε1

EEU ×+

∇=+

∂∂ (4)

Where

∂∂

+∂∂

=i

j

j

ii

xx2

1 jE

UU(5)

Solution of Eqs (3) and (4) give spatial variation of k and ε which in turn

can be used to find out spatial variation of turbulent viscosity or eddy viscosity µ t using the Prandtl-Kolmogorov relation

ε

k ρCµ

2

µt = (6)

Once µ t is known, expression of turbulent stresses appearing in Eq.(2)can be given as

ijijt ji ρk δ3

22µu'u'ρ −=− E (7)

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International Journal of Food Engineering, Vol. 4 [2008], Iss. 2, Art. 3

http://www.bepress.com/ijfe/vol4/iss2/art3



The standard values of different constants appearing in Eqs (3),(4) and (6)

are C µ = 0.09, σk =1.00, σε = 1.3, C 1ε =1.44 and C 2ε =1.92Commercial CFD software FLUENT was used to perform simulation. To

start with several exploratory simulations were carried out using MRF approach

to finalize the geometry and to conduct grid independent test and the result isshown in Figure 3. From this figure it is observed that accuracy of the result

increases with increase in mesh (cell) volume and became constant at 176550

cells. Final CFD simulations were done at this cell number. Figure 4 presents thetypical appearance of the vessel with meshed condition.

Mesh volume Vs Power Number

0

2

4

6

0 200000 400000 600000 800000 1E+06 1E+06

Mesh Volume

P o w e r N u m b e r

Figure 3. Effect of mesh volume number on simulated power number

Figure 4. Diagram of the meshed agitated vessel

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Figure 5. Simulated and Experimental power

Number for Rushton Turbine p/H=0

0

1

2

3

4

5

6

7

10000 100000 1000000

Reynolds Number


Simulation value

literature Value


number for smith turbine p/H= 0

0

1

2

3

4

5

6

10000 100000 1000000

Reynolds Number

P o w

e r N u m b e r

Simulation Value

:iterature Value

7






numberfor Rushton Turbine p/H = 0.17

0

2

4

6

8

10000 100000 1000000

Reynolds Number


Simulation Value

Literature value


number for Smith Turbine p/H = 0.17

0

2

4

6

8

10000 100000 1000000

Reynolds Number


Simulation Value

Literature Value

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Figure 9. Simulated and Experimental power number for Rushton Turbine p/H = 0.33

0

2

4

6

8

10000 100000 1000000

Reynolds Number


Simulation Value

Literature Value



0

2

4

6

8

10000 100000 1000000

Reynolds Number


Simulation Value

Literature value

9






number for Rushton Turbine p/H = 0.5

0

2

4

6

8

10000 100000 1000000

Reynolds Number

P o w e r N u b e r

Simulation Value

Literature value


nmuber for Smith Turbine p/H = 0.5

0

2

4

6

8

10000 100000 1000000

Reynolds Number

P o

w e r N u m b e r

Simulation value

Literature value

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Figure13. Simulated and Experimental power number for Rushton Turbine p/H = 0.67

0

2

4

6

8

10000 100000 1000000

Reynolds Number


Simulation Result

Literature Value



0

2

4

6

8

10000 100000 1000000

Reynolds Number


Simulation value

Literature Value

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Figure 15. Simulated and Experimental

power number for Rushton Turbine p/H = 1

0

2

4

6

8

10000 100000 1000000

Reynolds Number

P o w e r N u b e r

Simulation Result

Literature value

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a)

b)

Figure 16 . Radial velocity for Rushton turbine (a) p/H = 0, and

Turbulent Kinetic energy for Rushton Turbine (b) p/H = 0

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c)

d)

Figure 16 . Radial velocity for Rushton turbine (c) p/H = 0.5, and

Turbulent Kinetic energy for Rushton Turbine, (d) p/H = 0.5

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5. CONCLUSION

CFD simulation for the power consumption in agitator vessel with varying bafflelength p/H = 1; 0.67; 0.5; 0.33; 0.17 and 0 in turbulent flow conditions has been

explained in this paper using Fluent version 6.2.16. The data obtained bysimulation are matching with the literature experimental value for standard baffle

with the discrepancy of less than ±4.5% for power number. The simulated resultsfor agitated vessel with short baffle (non-standard) are agreeing with the literature

values within plus or minus 5% for power number. The reason for reduced power

consumption in nonstandard baffle has been evidenced from more uniformdistribution of turbulent kinetic energy both in radial and axial direction as

observed from turbulent kinetic energy distribution profile around the turbine

agitator.

NOMENCLATURE

a length of the agitator blade, m B width of the baffles, m

b width of the agitator blade, m

D inner diameter of the agitated vessel, m

d diameter of the agitator, m

H liquid height in the vessel, m

h distance between agitator and bottom of the vessel, m

J number of baffles

k specific turbulent kinetic energy, m2/s L length of the baffle, m

n agitator speed, s-1

P power consumption, W

Power number = P / n3 d

5 ρ

Reynolds number = n d 2ρ/ µ

p distance between lower edge of the baffle and bottom of the vessel, m R radius of the agitator blade, m

Z number of agitator bladeGreek letter

ε specific turbulent energy dissipation rate, m2/s

µ dynamic viscosity of the liquid, kg/ms

µ t turbulent viscosity or eddy viscosity , kg/msρ liquid density, kg

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REFERENCES

1. Joanna Karcz *, Marta Major ”An Effect of a Baffle Length on the Power

Consumption in an Agitated Vessel” Chemical Engineering and Processing,1998, 37 249–256.

2. Bakker, A., Van Den Akker., H.E.A., “A computational model for the gas-

liquid flow in stirred reactors”, Trans. IchemE , 1994, A72, 594-606.

3. Morud, K.E., Hjertager, B.H., LDA, “Measurements and CFD modeling of gas-

liquid flow in a stirred vessel”, Chem. Eng. Sci, 1996, 51(2), 233-249.

4. Derksen, J.J., Venneker, B.C.H., Van Den Akker, H.E.A., “Population balance

modeling of aerated stirred vessels based on CFD”,2002, AIChE J , 48(4), 673-

685.

5. Van Den Akker., H.E.A.,“ The details of turbulent mixing process and their

simulation”, Advances in Chemical Engineering,2006, 31,151-229.

6. Sommerfeld, M., Decker, S. “State of the art trends in CFD simulation of

stirred vessels”, Proceedings of the 11th European Conference on Mixing ,

Bamberg , 2003.p. 1

7. Vlaev, S.D., P. Staykov, R. Mann, H. Hristov and P. Mavros, “Experimental

and CFD Characterization of a New Energy-saving Mixing Impeller for the

Process Industries”, Paper presented at 18th North American Mixing Conference, Pocono Manor , PA, 2001,June 24-29.

8. Mavros, P., R. Mann, S.D. Vlaev and J. Bertrand, “Experimental Visualization

and CFD Simulation of Flow Patterns Induced by a Novel Energy-Saving

Dual-Configuration Impeller in Stirred Vessels”, Trans. I. Chem. E ,2001,79A, 857–866.

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