© 2011 ANSYS, Inc. April 17, 20231

Presented by

Raj Kumar Saini

Department of Energy Science and Engineering

Indian Institute of Technology Bombay

Powai MH(India)-400076

Numerical simulation of pulsatile flow in a disc and doughnut column

© 2011 ANSYS, Inc. April 17, 20232

o What is disc and doughnut pulsed column (DDPC)?

Introduction

o Applications Solvent extraction for biotechnology, waste water

treatment, heat sensitive materials purification, product recovery

o AdvantagesHigh (reasonable) capacity : 20-30 m3/m2-hrLow cost investmentHigh residence timeSmaller footprintNumber of theoretical stages of pulsed column is required one-third of extraction column

o DisadvantagesLimited stages due to back mixingMass transfer efficiency of commercial DDPC is low

© 2011 ANSYS, Inc. April 17, 20233

Challenges

To increase the interfacial area in pulsating flow through a disc and doughnut pulsed column

Maximization of the mass transfer efficiency of disc and doughnut pulsed column

Objective and Challenges

Objective: Investigation of pulsating flow in

disc-doughnut pulsed column for single phase flow

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Disc and doughnut pulsed column

© 2011 ANSYS, Inc. April 17, 20235

o Governing equation (in cylindrical coordinates) in non-dimensional form:

Continuity equation:

The radial components of the momentum conservation equation:

The axial components of the momentum conservation equation:

Mathematical modeling

The velocity for pulsatile flow is combination of mean and fluctuating velocity:

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o Non dimensional numbers :

μ - Viscosity

ρ - Density,

x0 - Amplitude of pulse

R - Radius

ω– Angular frequency

Mathematical modeling contd…

o Boundary conditions

Inlet - mass flow rate

Outlet -OUTFLOW

where, mass flow rate (kg/s), t time (s) and ω angular frequency (rad/s)

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o Finite volume method

o Pressure-based solver used (ANSYS FLUENT 13.0)

o Unsteady simulation

o Second order wind scheme used for discretization method (momentum)

o Structured grid (Mesh)

o The absolute convergence criteria 1×10−9 (unit of field variable)

Numerical method used for simulation

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o Velocity profile , through annulus for fully developed profile steady state is given as:

Where is a constant and value is 0.02

o Reynolds number (Re=49.26)

(Bird .et al 2006)*

Validation: case-1: Flow in annulus

© 2011 ANSYS, Inc. April 17, 20239

o The pulsatile velocity

o ω=0.01 rad/s, St = 0.16 and Re= 0.99

o Streamline flow pattern is plotted in DDPC at a) t=T/20 , b) t=9T/20

Validation: case-2: Flow reversibility for Re<<1

a) t=T/20,

b) t=9T/20 For Re<1 and St<0.2 the flow is reversible

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o Different zones for Reattachment length, l

Measuring zones o Mass flow rate

Parameter SymbolColumn diameter D (mm)Thickness of disc and doughnut δ(mm)Disc and doughnut space H (mm)Diameter of disc d (mm)Diameter of aperture(doughnut) D0(mm)

Table. Parameters of DDPC

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o Effect of angular frequency on Normalized reattachment length

at time 3T/8

Results and discussions

As angular frequency increases, reattachment length decreases

Zone-1 Zone-2 Zone-3

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o Effect of amplitude on Normalized reattachment length

at time 3T/8

Results and discussions contd…

Zone-1 Zone-2 Zone-3

As Strouhal number increases reattachment length also increases

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o Single phase flow in DDPC by CFD, at low St and Re has been simulated

o The flow is reversible for low Reynolds and Strouhal numbers as expected (Re<1. & St <0.2)

o Simulation results agree well with the analytical solutions in the low Re and St regime

o At lower frequency the effect of St on reattachment length is not significant

o At higher frequencies, the reattachment length increases with increase in St

Conclusions

© 2011 ANSYS, Inc. April 17, 202314

1. Bird R. B, Stewart W.E, L. E. N., 2006. Transport Phenomena. Second Edition. Wiley India Pvt. Ltd.

2. Bujalski, J., Yang, W., Nikolov, J., Solnordal, C., Schwarz, M., 2006. Measurement and CFD simulation of single-phase flow in solvent extraction pulsed column. Chemical Engineering Science 61 (9), 2930-2938.

3. Hungle Le, P. M., Kim, J., 1997. Direct numerical simulation of turbulent flow over a backward-facing step. Journal of Fluid Mechanics 330, 349-374.

4. Jian, H., Ni, X., 2005. A numerical study on the scale-up behavior in oscillatory baffled columns. Chemical Engineering Research and Design 83 (10), 1163 -170.

5. Mackley, M., Ni, X., 1991. Mixing and dispersion in a baffled tube for steady laminar and pulsatile flow. Chemical Engineering Science 46 (12), 3139 -3151.

6. Ni, X., Jian, H., Fitch, A. W., 2002a. Computational fluid dynamic modeling of flow patterns in an

7. oscillatory baffled column. Chemical Engineering Science 57 (14), 2849-2862.

8. Ni, X., Mignard, D., Saye, B., Johnstone, J. C., Pereira, N., 2002b. On the evaluation of droplet breakage and coalescence rates in an oscillatory baffled reactor. Chemical Engineering Science 57 (11), 2101-2114.

9. Z. Mehrez, M. Bouterra, A. E. C. A. B., Quere, P. L., 2010. Simulation of the periodically perturbed separated and reattaching ow over a backward-facing step. Journal of Applied Fluid Mechanics 3 (2), 1-8.

References