MIXING XVII

Mixing Time: A CFD Approach

Lanre M. Oshinowo, André Bakker, Elizabeth MarshallFluent Inc., 10 Cavendish Court, Lebanon, NH 03766 USA

17th Biennial North American Mixing Conference

Banff, Alberta

August 15-20, 1999

MIXING XVII

Overview

� Description and background of mixing time� Mixing tank modeling using CFD� Estimating the mixing time� Case studies: Experimental validation� Mixing time results

� Steady and unsteady flow fields

� Summary and Conclusions

MIXING XVII

Mixing Time

� Mixing time is the time taken to homogenize the liquid contents of the tank after a step change in composition

� The transport of a tracer helps to understand the degree of homogeneity in the agitated tank� Circulation time used to gauge the bulk motion induced

by the impeller(s)� Mixing (or blend) time can be used to evaluate the

mixing equipment design to obtain ideal mixing

MIXING XVII

Mixing Time: Complications

� Typically, correlations of mixing time data are used� Mixing time depends on a large number of

variables:� Impeller type, diameter and Reynolds number� Scale� Feed location and the location of probes� Multiple impellers� Internals� Fluid properties, etc.

� Difficulties establishing a set of correlations for the wide range of variables, most importantly, scale

� Can lead to inaccuracies in mixing time prediction

MIXING XVII

Mixing Time: CFD Approach

� Utilize CFD for the prediction of mixing time by eliminating the guesswork in tank configuration, scale, and fluid properties

� Leverage the flexibility to change tank scale, flow regimes/impeller location and number of impellers

� Evaluate a method of predicting mixing time

MIXING XVII

CFD Modeling of Mixing Tanks

� Impeller Modeling was done using:� Impeller boundary conditions applied from LDA� Multiple Reference Frame (MRF) Model, steady-state� Sliding Mesh Model, time-dependent

� Turbulence Models used were:� Standard k-ε, RNG k-ε, Reynolds Stress Model, LES

� Mixing time was predicted using:� Unsteady Particle Tracking� Transient transport of a neutrally-buoyant tracer (Scalar)

Increasing computational expense

MIXING XVII

Flow Regimes

Radial Disk turbine

� H=T= 0.202 m

� Di= 0.074 m� C/T=0.33

� N = 290 rpm

� ReD = 26,000

Pitched Blade turbine

� H=T= 0.292 m

� Di=0.102 m� C/T=0.46

� N = 60 rpm

� ReD = 10,000

Hydrofoil + Concave-Blade Turbine

� T = 2 m

� DCD-6=0.8 m; C=0.6m

� DHE-3=1.04 m; Z=1.04m� N = 84 rpm

� ReD ~ 1e6

MIXING XVII

Validating the Radial Disk Turbine Influence of Turbulence Models

+90mm

Radial coordinate, mm

w/vtip

LDA data : Z. Jaworski, K. N. Dyster and A. W. NienowUniversity of Birmingham, UK

Normalized tangential velocity profiles at the mid-baffle position

Np=4.64 (4.85)NQ=0.67 (0.7)

MIXING XVII

Validating the Pitched Blade Turbine

LDALDA PIVPIV CFDCFD

Velocity vector field in mixing tankData Source: Myers, K.J., Ward, R.W. & Bakker, A. (1997) J. Fluids Eng. v.119, p.623

MIXING XVII

LDA Radial Velocity LDA Axial VelocityPIV Radial ValocityPIV Axial VelocityCFD Radial VelocityCFD Axial Velocity

Validating the PBT, contd.

r/D0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

-0.10

-0.05

0.00

0.05

0.10

0.15Nor

mal

ized

Vel

ocity

-0.5-0.4-0.3-0.2-0.10.00.10.2

-0.15

-0.10

-0.05

0.00

0.05

0.10

0.15

y/H=0.6

y/H=0.4

y/H=0.2Data Source: Myers, K.J., Ward, R.W. & Bakker, A. (1997) J. Fluids Eng. v.119, p.623

MIXING XVII

Mixing Time Calculations

� Unsteady particle tracking� Release of a number of neutrally-buoyant particles� Turbulent dispersion of particles accounted for� Particle concentration sampled at various times

� Transport of a tracer � Small amount of liquid tracer added near liquid surface� Concentration of tracer monitored as a function of time� Similar to experimental techniques

� Flow field required can be steady, frozen unsteadyor unsteady

MIXING XVII

Time-varying Concentration

� Multiple locations can be sampled simultaneously to show concentration changes in many locations in the tank

� Mixing time, t99, is the time taken for the uniformity, U, to reach 0.99, where

� The t99 is determined at various locations in the tank and averaged to obtain the mixing time

( )∞

∞ −−=C

tCCU

)(1

MIXING XVII

Influence of Measurement LocationDual impeller HE-3 + CD-6

0.00

1.00

2.00

0 10 20 30 40 50

Point 1

Point 2

Point 3

Point 4

U

Time, s

t99= 20s

t99= 21.4s

t99= 27.4s

t99= 55.8s

MIXING XVII

Time, s0 5 10 15 20 25

U

0.2

0.4

0.6

0.8

1.2

0.0

1.0

FIX-RSMMRF-RSMMRF-RNGMRF-k-e

Influence of Turbulence ModelsUniformity; Radial Disk Turbine

� Predicted mixing times, t99, at the sample location� FIX, RSM = 13.6s

� MRF, k-ε = 9.6s� MRF, RNG = 22.8s� MRF, RSM = 11.6s

Sample

Location

MIXING XVII

Time, s

0 20 40 60 80 100 120

U

0.2

0.4

0.6

0.8

0.0

1.0

FIX: t99=112sMRF: t99=54s

Influence of Impeller Modeling

Time, s

0 5 10 15 20

U

0

1

2

3

4

FIX: t99=11.6sMRF: t99=10.0s

Time, s

0 5 10 15 20

U

0.0

0.5

1.0

1.5

2.0

MRF: t99=12.2sFIX: t99=21.4s

Radial Turbine

Dual Impeller (CD-6+HE-3)

PBT

� Modeling impeller with velocity data predicts greater t99

MIXING XVII

Mixing Time Correlations

� Fasano, J.B., Bakker, A. & Penney, W.R. (1994)

( )5.099

1ln

−−=

Z

T

T

DaN

Ut b

Impeller Style a b

Radial Disk6 blades

1.06 2.17

Pitched4 blades

0.641 2.19

High-efficiency3 blades

0.272 1.67

� Prochazka and Landau (1961), Moo-Young et al (1972), Sano & Usui (1985), RaghavRao and Joshi (1988)

MIXING XVII

Comparison to Correlations

t 9 9 ( C o r r . ) t 9 9 ( C F D )

R T 8 ( ± 3 0 % ) 1 0 . 5 ± 0 . 9

P B T 7 2 ( ± 3 0 % ) 6 1 . 5 ± 9 . 3

H E - 3 + C D - 6 1 5 ( ± 3 0 % ) 3 2 ± 3 4 . 7( 1 7 .6 ,1 3 . 6 ,1 2 . 8 , 8 4 )

Time in seconds

� The CFD mixing time results were the average of multiple locations in the tank

� The dual impeller systems shows the influence of locally poor mixing on the average mixing time in the tank

MIXING XVII

Mixing Time Calculations in an Unsteady Flow Field

� The sliding mesh model was used to set up the transient motions of the impeller in the tank.

� Two turbulence model approaches were evaluated:� Reynolds-Averaged Navier-Stokes turbulence model,

i.e., Standard k-ε, RNG k-ε, Reynolds Stress Model� Large Eddy Simulation or LES

MIXING XVII

Cross-correlation results

30

35

40

45

50

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

1.E+01

0 5 10 15 20

t (*0.05s)N

orm

aliz

ed C

ross

-C

orr

elat

ion

Fu

nct

ion

LES

RANS

1 impeller revolution( ) ∫ τ+=τ

∞→ttCtC

TR

Txy d)()(

1lim 21

� The time delay between the maximum values of Rxy(t) gives the average convection velocity of the tracer “front”

� Can be related to mixing efficiency

MIXING XVII

Summary

� Mixing time can predicted using CFD in a variety of tank configurations

� Unsteady tracer CFD calculations on a steady-state flow field gave good comparisons with correlations of experimental data

� Modeling the presence of the impeller is important for improving mixing time predictions

� Both RANS-based and LES turbulence modeling can be used with an unsteady sliding mesh model to calculate the transport of the tracer