1. Ivan Fořt1, Bohuš Kysela2, Jiří Konfršt2
CFD SIMULATION OF TURBULENT VELOCITY FIELD IN THE DISCHARGE STREAM FROM A STANDARD RUSHTON TURBINE IMPELLER
Ivan Fořt1, Bohuš Kysela2, Jiří Konfršt2
1)Department of Process Engineering, Faculty of Mechanical Engineering,
CTU in Prague, Czech Republic
2)Institute of Hydrodynamics AS CR, v.v.i.
Prague, Czech Republic

2. Introduction
The flow inside the agitated vessel has a key role in the mixing process. Only the CFD modeling gives us the complex information about the whole flow field in contrary with the results of the experimental measurements. The enormous progress of the computational equipment has allowed using exacting turbulence models for the solution of the flow in the agitated vessel.
The aim of our study is the description of the turbulent velocity field in the discharge stream from the standard Rushton turbine impeller in pilot plant mixing vessel with baffles at the wall. Investigation has been carried out experimentally (LDA technique) as well as by means of CFD simulation, where the Large Eddy Simulation (LES) approach has been used with a Sliding Mesh (SM) model for the impeller movement. 2

3. Calculated instantaneous turbulent flow field in the plane between adjacent baffles (the standard Rushton turbine impeller in asymmetrical vertical (axial) position). 3

4. CFD calculations
A commercial ANSYS FLUENT v.13.0 solver of the finite volume method was employed. The turbulence was modelled by LES with SM simulation for the impeller movement. The sub-grid-scale aproach was used: Smagorinsky-Lilly model (Smagorinsky parameter C = 0.17) with Second Order Implicit scheme. The boundary conditions: water level to symmetry and others to no slip wall (shaft with impeller speed velocity). The walls of the vessel and baffles were provided by the boundary layer mesh.
Mesh in the baffles vicinity and on the impeller surface. 4

5. Sliding region – cylindrical shape (distance D/10 from the cylindrical envelope)
Solved hexahedral mesh consist of either 2.5∙106 cells (LES1) or 7.5∙106 cells (LES2). Finer mesh corresponds to the maximal cell size under 2 mm (measuring LDA volume).
Time step: 1/1000 s (must not exceed 1/60 of one impeller revolution).
Calculation time: 60 s
(20 s necessary for the flow development), results were time averaged for ensemble-averaging.
Mesh (LES1) on the vessel wall and impeller with depicted sliding region around the impeller. 5

6. Experimental
Pilot plant mixing vessel (T = 300 mm) with four baffles at its wall. Water at room temperature as the working liquid. Impeller speed
n = 300 rpm (impeller Reynolds number ReM =5.0∙104 ).
Impeller: a standard Rushton turbine.
Pilot plant mixing equipment:
(H/T = 1; D/T = 1/3; C/D = 3/4;
b/T = 1/10; four baffles).
Standard Rushton turbine:
(w/D=1/5; D1/D=3/4; C/D=3/4;
l/D = 1/4; t/D = 1/50; six blades). 6

7. Photo of pilot plant mixing equipment with a six-blade standard Rushton turbine impeller (motor 2.2 kW, impeller speed n ∈<50;1500> min-1).
Photo of laser beams LDA setup
(adjusted for two-component measurement: radial and tangential). 7

8. Photo of pilot plant glass cylindrical mixing vessel with rotating six-blade standard Rushton turbine impeller (n = 300 min-1). 8

9. Laser Doppler Anemometry (LDA)
One component measurements of the radial instantaneous velocity were performed in the impeller discharge stream: the vertical plane between two adjacent baffles. Dimensionless radial coordinates r*=2r/D: 1.2; 1.4; 1.6; 1.8; 2.0; 2.2.
One component LDA system:
Coherent INNOVA 305 Ion-Argon supply (power 5 W),
DANTEC fiberflow transmiting optics,
P80 DANTEC BSA processor,
BSA Flow software v3.0 installed on standard PC,
S-HGS (Silver coated – Hollow Glass Spheres) - mean diameter 10 mm, density 1.1 g/cm3 – trace particles.
The measurement was performed through the glass flat bottom of the vessel with back scattering mode – length of measurement: 3 min in each measuring position of the optical probe (ellipsoid with characteristic dimension approx. 2 mm). 9

10. Results and Discussion
1. Axial profiles of the dimensionless radial mean ensemble- averaged velocity component in the discharge stream from a standard Rushton turbine impeller. (w – height of impeller blade, pDn – impeller tip speed):
(𝑟 ∗ = 2𝑟 𝐷 =𝑐𝑜𝑛𝑠𝑡.)
vers.
2. Axial profiles of the ensemble-averaged dimensionless r.m.s. of the radial fluctuation velocity in the discharge stream from a standard Rushton turbine impeller:
(𝑟 ∗ = 2𝑟 𝐷 =𝑐𝑜𝑛𝑠𝑡.)
vers. 10

11. Axial profiles of the dimensionless ensemble-averaged radial component of the mean velocity in the discharge stream from a standard Rushton turbine impeller (C/T = 1/3): Zone of Flow Establishment (ZFE) 𝑟 ∗ <1.8. 11

12. Axial profiles of the dimensionless ensemble-averaged radial component of the mean velocity in the discharge stream from a standard Rushton turbine impeller (C/T = 1/3): Zone of Established Flow (ZEF) 𝑟 ∗ ≥1.8. 12

13. 𝜎 𝑊 𝑟 ∗ = 1 𝑁 𝑖=1 𝑁 𝑊 𝑟,𝐿𝐷𝐴 ∗ −𝑊 𝑟,𝐶𝐹𝐷 ∗ 2 1/2
Mean square difference s beween the measured 𝑊 𝑟,𝐿𝐷𝐴 ∗ and calculated 𝑊 𝑟,𝐶𝐹𝐷 ∗ data of dimensionless radial component of the mean ensemble-averaged velocity (number of measurement points in one axial profile z*: N = 24)
𝜎 𝑊 𝑟 ∗ = 1 𝑁 𝑖=1 𝑁 𝑊 𝑟,𝐿𝐷𝐴 ∗ −𝑊 𝑟,𝐶𝐹𝐷 ∗ /2 r*
s LES1
sLES2
Zone
1.2
0.074
0.042
ZFE
1.4
0.090
0.051
1.6
0.075
0.049
1.8
0.065
0.057
ZEF
2.0
0.024
2.2
0.052
0.041
Note:
2.5∙106 cells
7.5 ∙106 cells 13

14. Axial profiles of the dimensionless r. m
Axial profiles of the dimensionless r.m.s of the radial fluctuation velocity in the discharge stream from a standard Rushton turbine impeller in the Zone of Flow Establishment (ZFE) with influence of periodic pseudoturbulence (frequency of impeller blades: n·NB; (n – impeller speed, NB – number of impeller blades). 14

15. Axial profiles of the dimensionless r. m
Axial profiles of the dimensionless r.m.s of the radial fluctuation velocity in the discharge stream from a standard Rushton turbine impeller in the Zone of Established Flow (ZEF) – random turbulence, only. 15

16. 16 Zone of Flow Establishment (ZFE) r* < 1.8
Zone of Established Flow (ZEF)
r* > 1.8
Power spectral density of the radial component of fluctuation velocity in the impeller discharge stream (Rushton turbine). 16

17. Power spectral density of the radial component of fluctuation velocity in the impeller discharge stream (Rushton turbine).
16b

18. Axial profiles of the dimensionless r. m
Axial profiles of the dimensionless r.m.s of the radial fluctuation velocity in the discharge stream from a standard Rushton turbine impeller in the Zone of Flow Establishment (ZFE) and in the Zone of Established Flow (ZEF). 17

19. 18 Impeller power input: 𝑷=𝟐𝝅𝒏 𝑴 𝒌
Mk – impeller torque obtained from the force balance in the impeller surface provided by the CFD calculations
n – impeller speed
r – density of agitated liquid
𝑷𝒐= 𝑷 𝝆 𝒏 𝟑 𝑫 𝟓 = 𝟓.𝟑𝟐
Impeller power number: (from CFD calculation, LES2)
Experimental correlation (Bujalski et al., Chem. Eng. Sci. 42(2), , 1987) for turbulent regime of flow of agitated liquid:
𝑷𝒐=𝟐.𝟓𝟏𝟐 𝒕 𝑫 −𝟎.𝟏𝟗𝟓 𝑻 𝑻 𝒐 𝟎.𝟎𝟔𝟑 = 𝟓.𝟎𝟎
(from correlation)
t = 2 mm (thickness of the separating disc of Rushton turbine impeller)
D = 100 mm (impeller diameter)
T = 300 mm (vessel diameter); To = 1 m 18

20. Conclusions
LES approach can be successfully used for description of the turbulent velocity field in the discharge flow from a standard Rushton turbine impeller.
Axial profiles of the radial component of the mean ensemble-averaged velocity in the discharge stream from a standard Rushton turbine impeller correspond to the idea of the impeller considered as a submerged tangentially symmetrical jet.
Discharge flow from a standard Rushton turbine impeller can be divided to the Zone of Flow Establishment adjacent to the impeller and the Zone of Established Flow where the periodic portion of turbulence from rotating impeller blades disappears.
The impeller power number derived from the impeller torque calculations of the presented LES numerical modeling is very close to the value of this quantity (Po) estimated from empirical correlation based on the results of experimental determination.
LES approach of description of the turbulent velocity field in mechanically agitated system is strongly dependent on the density of grid of the solved mesh. 19

21. ACKNOWLEDGEMENT This research has been subsidized by the research projects GA ČR P101/12/2274, RVO and
INGO LG 20