Mixing Time: A CFD Approach - bakker.org

Mixing Time: A CFD
Approach

Lanre M. Oshinowo, André Bakker, Elizabeth Marshall

Fluent 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

Increasing computational expense

Mixing time was predicted using:

Unsteady Particle Tracking
Transient transport of a neutrally-buoyant tracer (Scalar)

MIXING XVII

Flow Regimes

Radial Disk turbine Pitched Blade turbine Hydrofoil + Concave-Blade
H=T= 0.202 m H=T= 0.292 m Turbine
Di= 0.074 m Di=0.102 m
C/T=0.33 C/T=0.46 T=2m
N = 290 rpm N = 60 rpm
ReD = 26,000 ReD = 10,000 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

Normalized tangential velocity profiles at the mid-baffle position

w/vtip

+90mm

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

Radial coordinate, mm

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

MIXING XVII

Validating the Pitched Blade Turbine

LDA PIV CFD

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

MIXING XVII

Validating the PBT, contd.

y/H=0.6 Normalized Velocity 0.15 LDA Radial Velocity
y/H=0.4 LDA Axial Velocity
y/H=0.2 0.10 PIV Radial Valocity
PIV Axial Velocity
0.05 CFD Radial Velocity
CFD Axial Velocity
0.00
Data Source: Myers,
-0.05 K.J., Ward, R.W. &
Bakker, A. (1997) J.
-0.10 Fluids Eng. v.119, p.623

-0.15 MIXING XVII
0.2
0.1
0.0
-0.1
-0.2
-0.3
-0.4
-0.5

0.15

0.10

0.05

0.00

-0.05

-0.10
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
r/D

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 unsteady
or 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

U = 1 − (C∞ − C(t))

C∞

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

MIXING XVII

Influence of Measurement Location

Dual impeller HE-3 + CD-6

t99= 20s

2.00 Point 1
Point 2
U Point 3
Point 4
1.00
t99= 21.4s
0.00
0 t99= 27.4s
t99= 55.8s

10 20 30 40 50

Time, s

MIXING XVII

Influence of Turbulence Models

Uniformity; Radial Disk Turbine

1.2 Sample Predicted mixing
1.0 Location times, t99, at the
0.8 sample location
FIX-RSM
U 0.6 MRF-RSM FIX, RSM = 13.6s
MRF-RNG MRF, k-ε = 9.6s
0.4 MRF-k-e MRF, RNG = 22.8s
0.2 MRF, RSM = 11.6s
0.0 5 10 15 20
25
0 Time, s
MIXING XVII

Influence of Impeller Modeling

4 FIX: t99=11.6s 1.0 FIX: t99=112s
MRF: t99=10.0s MRF: t99=54s
3 0.8
Radial Turbine
U2 0.6

1 U

0 0.4
2.00
1.5 0.2 PBT

U 1.0 0.0

0.5 5 10 15 20 0 20 40 60 80 100 120

0.0 Time, s MRF: t99=12.2s Time, s
0
FIX: t99=21.4s Modeling impeller

Dual Impeller with velocity data
(CD-6+HE-3) predicts greater t99

5 10 15 20

Time, s

MIXING XVII

Mixing Time Correlations

Fasano, J.B., Bakker, A. & Impeller Style ab
Penney, W.R. (1994)
Radial Disk
6 blades 1.06 2.17

t99 = − ln(1 −U ) Pitched
4 blades
 D  b  T 0.5 0.641 2.19
 T   Z 
aN

High-efficiency 0.272 1.67
3 blades

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

MIXING XVII

Comparison to Correlations

RT t99(C o rr.) t99(C F D )
PBT 8 (± 3 0 % )
H E -3 + C D -6 7 2 (± 3 0 % ) 1 0 .5 ± 0 .9
1 5 (± 3 0 % )
Time in seconds 6 1 .5 ± 9 .3
3 2 ± 3 4 .7

(1 7 .6 ,1 3 .6 ,1 2 .8 , 8 4 )

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

= lim 1
T →∞ T
( ) ∫Rxyτ C1(t)C2 (t + τ)dt 1 impeller revolution
1.E+01

Normalized Cross- 1.E+00 LES
Correlation Function1.E-01 RANS

1.E-02

1.E-03

1.E-04

50

The time delay between the 1.E-405 5
40 0 5 10 15 20

maximum values of Rxy(t) gives 35 t (*0.05s)
30

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

MIXING XVII