Seediscussions,stats,andauthorprofilesforthispublicationat:http://www.researchgate.net/publication/272238750

ResidenceTimeDistributionAnalysisofaTaylorCouetteContactorbyComputationalFluidDynamicsusingOpenFoamCONFERENCEPAPERDECEMBER2013

DOWNLOADS30

VIEWS47

5AUTHORS,INCLUDING:

AbhishekSinghIndiraGandhiCentreforAtomicResearch12PUBLICATIONS0CITATIONS

SEEPROFILE

BalamuruganManavalanIndiraGandhiCentreforAtomicResearch31PUBLICATIONS4CITATIONS

SEEPROFILE

KamachiMudaliMudaliIndiraGandhiCentreforAtomicResearch397PUBLICATIONS1,694CITATIONS

SEEPROFILE

RajamaniNatarajanIndiraGandhiCentreforAtomicResearch125PUBLICATIONS259CITATIONS

SEEPROFILE

Availablefrom:ShekharKumarRetrievedon:15September2015

CHEMCON-2013, Mumbai, 27-30 Dec 2013,

1

Residence Time Distribution Analysis of a Taylor

Couette Contactor by Computational Fluid

Dynamics using OpenFoam

Abhishek Singh, M. Balamurugan, Shekhar Kumar*, U. Kamachi Mudali, R. Natarajan

Corresponding author. Email: shekhar@igcar.gov.in

1Reprocessing Group, IGCAR Kalpakkam, 603102 India.

2E-mail addresses: shekhar@igcar.gov.in

Abstract: Taylor Couette flow is the phenomenon of fluid flow between the annular gap of two coaxial cylinders, one or both

rotating along their common axis, which results into the formation of Taylor vortices above a critical Taylor number. When a

small amount of axial flow is introduced to the Taylor couette flow, it tries to carry Taylor vortices along its direction which

results into radial mixing due to the toroidal motion of fluid elements. This type of flow can be considered as similar to the

ideal plug flow reactor according to earlier studies. Authors have experimentally characterized the non-ideal flow in a Taylor-

couette extractor column by pulse response analysis. In this paper, details of experimental work and unique computational fluid

dynamics results related to the above mentioned work are discussed.

Keywords: Taylor couette phenomenon, residence time distribution, solvent extraction, computational fluid dynamics

1. Introduction:

Taylor Couette Contactor (TCC) is a single compact unit

which operates on the action of centrifugal force. The

design of the TCC is based on Taylor-Couette principle

where the inner cylinder rotates and the outer cylinder

remains stationary. In the annular region between these

two co-axial cylinders fluid is filled which forms taylor

vortices when the inner cylinder is rotated above the

critical taylor number.

2 Taylor-Couette flow and flow instability:

Taylor Couette flow is the phenomenon of fluid flow

between the annular gap of two coaxial cylinders, one or

both rotating along their common axis, which results into

the formation of Taylor vortices above a critical Taylor

number. At relatively low inner cylinder speeds, the flow

in the annular region is dominated by the viscous forces and a tangential flow is obtained. As we increase the inner

cylinder speed the centrifugal forces begin to dominate the

viscous forces resulting into centrifugal instabilities this

phenomenon is known as taylor couette flow. Earlier Couette [1] and Mallock [2] had carried out several

experiments on this centrifugal instability phenomenon

and they noted instabilities at certain rotational speeds.

Later on Taylor used the linear theory of instability to give

a solution for these centrifugal instabilities. He gave a

dimensionless number known as the Taylor number (Ta)

which is the ratio of the centrifugal force and viscous

force and can be expressed mathematically as :

(1)

Later on Chandrashekhar [3] found the critical taylor

number (Tacr) which depicted the transition from the

Couette flow (CF) to Taylor vortex flow (TVF). He also

showed that with the introduction of the axial flow in the

annular region along with the taylor-couette flow there is a

CHEMCON-2013, Mumbai, 27-30 Dec 2013,

2

delay in the onset of centrifugal instabilities which can be

represented by the Eqn.(2) where the critical taylor

number is the function of the axial reynold number shown

in Eqn.(3)

(2)

(3)

3. Experimental

3.1 Equipment

The experimental setup consisted of a Taylor couette

contactor and one feed pump along with the product and

feed tanks. The mixing section consists of a vertical co-

axial cylindrical annulus with inner rotating cylinder (OD

22 mm) and an outer fixed cylinder (ID 25 mm), the

annular gap width thus being 1.5 mm. The total height of

the working annular space i.e. the mixing section is 250

mm yielding an aspect ratio (L/d) of 83.34 and a working

volume of 27.69 cm3. The top and bottom settling sections

are made up of glass of 200 mm length each with a combination of a frustum(50 mm height , and inner

diameters of 88mm and 22mm respectively) and a

cylinder (height 150 mm and inner diameter 88 mm).Each

settling zone has two openings which are 90 mm apart and

diametrically opposite. The inner rotating cylinder is made up of stainless steel and is pivoted at its base and the

arrangement is made to reduce vibrations and any introduction of eccentricity is completely prohibited. The

test fluid is pumped inside the top opening of the

equipment a precision metering pumps (ISMATEC MFP

Process drives (ISM-909) + FMI Q series Pumpheads).

The continuous phase from the feed tank was fed to the

top inlet through soft-tubes. The settler was provided with

an overflow tube and a drain tube for continuous operation

of the Taylor coquette equipment. The continuous phase

outlet was connected to a laboratory pH meter (Metrohm

model 827 pH meter) for the continuous monitoring of the

pH. The view of the experimental setup in operation is

shown in Fig.1.

3.2 Experimental procedure

Demineralised water was used as a testing fluid and a

standard 4 N nitric acid as the tracer respectively. Initially

the bottom settling zone was filled with CCl4 so that there

was no introduction of the testing fluid in that part. Then

the mixing zone was filled with the testing fluid at a

constant flow rate till a steady state was achieved. It was

checked that the pH measured at the outlet should match the pH of the testing fluid. Then the first series of

experiments were conducted for 0 rpm inner cylinder

rotation rate and the axial flow rate was varied from 10 and 20 ml/min respectively. Once the flow became stable and the value in the pH meter becomes steady, 2ml of 4N

HNO3 pulse was injected from the inlet and a stop watch

was started. The readings in the pH meter were noted down

at an interval of 30 sec. The experiment was stopped when

the pH meter reading becomes steady again and reaches

approximately the initial pH of the testing fluid. Keeping

all the parameters same a set of experiments was conducted

for 100, 200, 400, 600, 800 rpm and the pH readings were

noted down for the 10 and 20 ml/min inlet flow rates

respectively. The resultant data was converted to

concentration scale and then the numerical analysis for

RTD was performed.

1. Water tank 4. Regulator 7. pH meter 10. Tracer injector

2. Peristaltic

pump

5. Electric

motor

8.Constant

head

11. Bottom

section filled

with CCl4

3. Pump

Controller

6. TCC 9. Outlet tank

Figure 1 : Schematic of the setup for the residence time distribution analysis of

the Taylor Couette Contactor

3.3 Data analysis

Inorder to characterize flow, it is necessary to know the

residence-time distribution, earliness of mixing, and state

of aggregation of the fluid [1]. If the latter two factors can

be ignored, the mean residence time can be determined as follows:-

(Mean residence time of the Cpulse):

(4)

(Variance of the curve):

CHEMCON-2013, Mumbai, 27-30 Dec 2013,

3

(5)

(To find the Ecurve):

(6)

Total number of tanks in series can be calculated by the

following relation:

(7)

4. Computational fluid dynamics methodology

Numerical simulations for the above Residence time

distribution analysis has been done using the OpenFoam

(version 2.0.1) at various rotational speeds and flow rates.

4.1 (a) Model Formulation

For the CFD analysis a 3D geometry has been prepared

using the blockMesh functionality in the OpenFoam

(version 2.0.1) .In the present case simpleFoam solver was

used. The following continuity and momentum equations

were solved using the above solver:

Continuity equation:

(8)

Momentum equation:

(9)

The velocity ui can be written as a sum of mean velocity

and fluctuating velocity:

(10)

Putting the above combination of mean and averaged

velocity in Eqs. (7) and (8) and Reynolds averaging we

get:

(11)

This can be written as the following continuity equation

(12)

(13)

This can be further written as the following momentum

equation

(14)

Standard k- Model

In the present work, the standard k- model has been

adopted to carry out the steady three dimensional CFD

simulations in the annular and bottom region of the TCC (

Taylor couette contactor) The conservation equation for

the turbulent kinetic energy (k) and dissipation () can be

expressed as (Launder and Spalding (1974)) ,

k equation

(19)

equation

(20)

The turbulent eddy viscosity, t can be computed from the

following correlation,

(21)

For the k- model

(22)

In the above Eqns. (14) and (15), C1, C2, C are turbulent

model constant, k, are the turbulent Prantl number.

The standard values selected for turbulent parameters such

as C, C1, C2, k, are 0.09, 1.44, 1.92, 1.0 and 1.3

respectively.

4.1 (b) Model formulation for species transport

After the flow in the present geometry was converged the

simulation of passive tracer was done. A pulse of the

tracer was given at the inlet with unit mass fraction. After

CHEMCON-2013, Mumbai, 27-30 Dec 2013,

4

two iterations the mass fraction of the tracer was again set

to zero. The following transport equations were solved for

the above case:

(23)

In Eqn. (18), Tk is the local mass fraction of the tracer and

Deff is the effective diffusion coefficient:

(24)

Where Dt is the eddy diffusion coefficient and Dm is the

molecular diffusion coefficient. Dt and Dm can be

estimated by the equations given below:

(25)

(26)

4.2 Numerical Framework

The geometry of the annular and the bottom region of the

Taylor Couette Contactor (TCC) is shown in Figure 3.

The model geometry is meshed using unstructured

tetrahedral grids. The minimum and maximum grid

volume sizes are 1.405174e-002 and 4.950891e-002 cubic

meter respectively. The unstructured grid is chosen for

discretization .

4.3 Boundary Conditions

The computational domain is confined to the annular

mixing section and the conical bottom region till the

outlet. Velocity inlet condition is specified for the fluid

inlet. Inner cylinder is described as the rotating wall. No

slip boundary condition was imposed for all the walls.

Pressure outlet condition was provided at the fluid outlet.

The ambient pressure has been considered to be

atmospheric pressure.

4.4 Solution Strategies

We have used simpleFoam solver for the present problem.

In this problem we encounter swirl flow in the mixing

section and the bottom region. Hence PISO ((Pressure

Implicit with Splitting of Operators) scheme was used for

pressure velocity coupling and solving momentum

equation by segregated implicit method. The discretization

of the momentum equation was done by Gauss upwind

scheme. The preconditioned conjugate gradient solver

(PCG) and preconditioned bi-conjugate gradient solver

(PBiCG) were used for pressure and velocity respectively.

After the flow gets fully developed in the given geometry

a pulse of tracer was injected. scalarTransportFoam solver

was used to calculate the concentration of the tracer at the

outlet keeping the simulation in unsteady state. During the

unsteady state simulation only the scalar concentration

changed with time.

5. Results and Discussion

The flow is carried from the upper mixing annular section

to the bottom section from where it goes to the outlet. In

this study we aim to investigate the flow behavior in the

annular zone as well as the bottom section. The residence

time distribution analysis of the mixing as well as the

bottom section has also been performed. All the

simulations are carried out using the OPENFOAM vs 2.0.1 and ParaView vs 3.10.1. The results are shown in the

table(1) and table(2) below:

5 Validation of CFD Model

The model has been validated by comparing the residence

time distributions and the exit age distribution curves. It is

observed that our CFD predictions agree fairly well with

the experimental data generated during the residence time

6 Conclusion

(1) An experimental residence time distribution technique

has been developed which is capable of analyzing pulse

Sr

no

RPM Mean

residence time

Variance Total number of

tanks in series

Exp

(min)

CFD

(min)

Exp

(min2)

CFD

(min2) Exp CFD

1 0 25.7 29.20 192.9 280.2 3.44 3.05

2 100 36.8 36.33 403.9 399.1 3.35 3.31

3 200 30.3 29.60 359.2 357.8 2.57 2.45

4 400 32.5 31.96 377.4 389.7 2.80 2.62

5 600 32.5 32.22 388.0 411.2 2.71 2.52

6 800 29.6 30.53 327.3 430.6 2.68 2.16

Table 1 : Experimental results at 10 ml per min inlet flow rate

Sr

no

RPM Mean residence

time

Variance Total number of

tanks in series

Exp

(min)

CFD

(min)

Exp

(min2)

CFD

(min2)

Exp CFD

1 0 13.4 14.29 61.62 111.8 2.93 1.83

2 100 16.0 16.98 72.95 113.7 3.53 2.54

3 200 13.0 13.96 63.01 108.0 2.71 1.80

4 400 15.7 16.40 83.62 129.7 2.95 2.1

5 600 14.1 16.88 58.41 154.5 3.44 3.43

6 800 13.3 14.37 63.66 115.4 2.77 1.90

Table 2 : Experimental results at 20 ml per min inlet flow rate

CHEMCON-2013, Mumbai, 27-30 Dec 2013,

5

response in an apparatus such as Taylor Couette Contactor

(TCC). RTD for the annular as well as the bottom section

of TCC has been studied experimentally as well as

computationally.

(2) The CFD results show more dispersion as compared to

the experimental results. Hence it could be assumed that

bypassing and dead zones are present in the studied

region.

(3) The results obtained experimentally as well as

computationally are in agreement with each other.

7. Nomenclature

CA = Exit concentration to an impulse input

L = Length of the Couette flow device (cm)

N = Total number of tanks in series

= Axial Reynolds number,

di = Inner cylinders outer diameter (cm) do = Outer cylinders inner diameter (cm)

= Mean residence time (cm)

Ta = Taylor number

Tac = Critical Taylor number

Greek symbols

= Kinematic viscosity (m2/s) t = Turbulent kinematic viscosity (m

2/s)

= Radius ratio, do/di = Dynamic viscosity = Density i = Inner cylinder rotational speed v = Viscous energy dissipation rate t = Turbulent energy dissipation rate , = Turbulent parameters = Reynold stress Subscripts

i, j, k = Indices in co-ordinate direction

r = Radial direction

z = Axial direction

= Azimuthal direction

8 Literature cited

[1] M. Couette, Etudes sur le frottement des liquides,

Annales de Chimie et de Physique 6, vol. 21, pp. 433

510, 1890.

[2] A. Mallock, Experiments on uid viscosity,

Philosophical Transactions of the Royal Society A, vol.

187, pp. 4156, 1896.

[3] S. Chandrasekhar, The stability of spiral ow between

rotating cylinders, Proceedings of the Royal Society A,

vol. 265, no. 1321, pp. 188197, 1962.

[4] G. I. Taylor, Stability of a viscous liquid contained

between two rotating cylinders, Philosophical

Transactions of the Royal Society A, vol. 223, no. 605

615, pp. 289343, 1923.

[5] K. E. Wardle, Open-source CFD simulations of liquid

liquid ow in the annular centrifugal contactor,

Separation Science and Technology, vol. 46, no. 15, pp.

24092417, 2011

[6] G. Baier and M. D. Graham, Two-uid Taylor-Couette

ow : experiments and linear theory for immiscible

liquids between corotating cylinders, Physics of Fluids,

vol. 10, no. 12, pp. 30453055, 1998.

[7] G. Baier, Liquid-liquid extraction based on a new ow

pattern: two-uid Taylor-Couette ow [Ph.D. thesis],

University of Wisconsin-Madison, Madison, Wis, USA,

2000.

[8] S. S. Deshmukh, M. J. Sathe, and J. B. Joshi, Residence

time distribution and ow patterns in the single-phase

annular region of annular centrifugal extractor,

Industrial & Engineering Chemistry Research, vol. 48,

no. 1, pp. 3746, 2009.