Laurence R. McGlashan

CoMo (Computational Modelling) GroupGraduate Conference Presentation 30th March 2010

Computational Modelling of Multiphase, Turbulent, (Reactive) Flows

Contents

2

1) Theory- Computational Fluid Dynamics (CFD)- Population Balances (PBE)

2) Methods- Quadrature Method of Moments (QMoM)- Direct Quadrature Method of Moments (DQMoM)

3) Results- Coupled CFD/PBE with complex closures

3

What to take away from this talk

Multiphase processes are encountered frequently in industry (e.g. gas-liquid contacting, reactors, drying).

The aim of this research is to improve multiphase flow models by coupling population balance equations (PBEs) to computational fluid dynamics (CFD) codes.

Coupling population balances to computational fluid dynamics codes can help predict trends in behaviour of multiphase flows in real equipment.

4

Why is this research relevant?

Multiphase processes are:

• highly complex• challenging to solve numerically• computational models and methods are not general

e.g. Recent TCE article on improving the efficiency of a rotating disc contactor (RDC). They used a pilot plant.

CFD is cheap, especially when it is free (OpenFOAM†)!

† http://www.openfoam.com

What problem will I solve?

5

toluene

water

ROTATION

6

Code Design

7

How may this problem be solved?

Euler/Euler Euler/Lagrange Volume of FluidLevel Set

Increasing Scale

8

Why use a population balance?

Euler/Euler – no information on the size distribution of the dispersedphase.

Droplets with different sizes will have different effects on the drag force on the continuous phase.

Volume of Fluid Method: Air bubble rising in water.

Theory

9

Navier-Stokes equations

10

The equations governing fluid flow are conceptually simple:

1) The mass of fluid is conserved.2) Rate of change of momentum equals the sum of forces on a fluid element. Newton's 2nd Law (F = m a).

Treat the fluid as a continuum. i.e. individual molecular interactions are ignored.

ρux + (ρu

x)δx

∂∂x

ρux

δz

δx

δy

11

Reynolds Averaging

Turbulent flows are Random / Chaotic

time

So the following substitutions are applied to the Navier-Stokes equations:

12

Multiphase Flow – Euler/Euler

Non-Conservative form of the momentum equation:

Continuity:

Conservative form of the momentum equation:

13

Drag force

Important, as this is how the coupling between CFD and PBEis achieved.

Turbulence Modelling

14

Mixture Models

Continuous Models

Continuous & Dispersed Models

- Averaged flow variables

- Apply algebraic relationship to get turbulence in the dispersed phase.

- Solve separate turbulence equations for each phase and couple them.

15

Theory – Population Balances

16

The Number Size Density

f 0 [m

-3 m

-1]

Droplet diameter [mm]

17

Population Balance Equation

18

Droplet Coalescence

19

Coalescence Models

efficiency collision probability

20

Droplet Breakup

21

Numerical Methods

22

Quadrature Approximation

N = 2

23

Solving the PBE - QMoM

QMoM

• Transport moments• To evaluate the source terms, the quadrature weights and positions must be calculated from the moments.

24

Solving the PBE - DQMoM

DQMoM

• Transport quadrature weights and weighted positions directly.• Source terms and moments are calculated directly from these quantities.

25

Numerical Algorithm

Results

26

27

Rotating disc contactor

toluene

water

100 L/hour of each phase.

Initial volume fraction of 0.1for toluene.

The wall’s rotation speed ischanged to see the effecton the size distribution of thetoluene droplets.

Rotations of 150/300 rpm areused.

28

RDC – continuous phase velocity

0.12

0

Continuous PhaseVelocity (m/s)

150 rpm 300 rpm

29

RDC – CFD only

RDC – Sauter diameter

30

150 rpm 300 rpm

7

2.5

SauterDiameter(mm)

RDC – result of coupling CFD/PBE

31

No coupling Coupling

0.08

0

Continuous PhaseVelocity (m/s)

Rotation speed150 rpm

32

Summary

Two moment methods have been tested and validated to solve the population balance.

A multi-fluid CFD solver has been tested and validated on a rotating disc contactor.

The PBE and CFD solvers have been coupled. The importance of that coupling has been demonstrated.

33

Acknowledgements

Jethro AkroydTatjana ChevalierAlastair Smith

In particular: