Solid liquid mixing tank homogenisation

Proceedings of Global 2015 September 20-24, 2015 - Paris (France) Paper 5204

WASTE HOMOGENISATION TANK: EXPERIMENTAL VALIDATION OF A NUMERICAL STUDY

C. Macqueron, J. William, R. Le Gall, R. Demarthon, G. Piot, A. Ragouilliaux AREVA E&P – Fuel Cycle 1 rue des hérons, 78182, Saint-Quentin-en-Yvelines Cedex – France corentin.macqueron@areva.com johann.william@areva.com ronan.le_gall@areva.com romain.demarthon@areva.com gregoire.piot@areva.com alexandre.ragouilliaux@areva.com Abstract – In the framework of final waste conditioning, legacy sludge produced by the original La Hague effluent treatment facility has to be processed by mixing, drying and compacting. The sludge mixing operation has to be performed in a tank in the most homogeneous way in order to guarantee the final quantity of radioactive material in each container. This homogenisation task is made difficult by high density particles and by the size of the tank, which is around 240 m3. As it is not economically feasible to perform experimentations on a tank of such size, a process qualification program based on a state-of-the-art methodology, including both complementary tools mock-ups at small scales and Computational Fluid Dynamics (CFD) numerical simulations has been set up (the homogenisation of the real size tank is only demonstrated by numerical simulations). Two mock-ups, respectively of 300 L and 2 m3 that are in perfect geometrical similitude, have thus been built in the HRB development facility close to the La Hague site in order to determine the suitable rotation speed of the real size tank impeller to ensure a good homogeneity, based on physical and scale-up/similitude reasoning. The mock-ups are used to validate the numerical simulations developed with the ANSYS FLUENT 15.0 software, by comparison with hydraulic power and solid volume fraction profiles measurements.

I. INTRODUCTION In the nuclear field, validation of process equipment at real size can often be obtained only once the installation is built. In order to anticipate and to limit the industrial risks, it can be useful to rely on CFD (Computational Fluid Dynamics) numerical modeling that must be qualified on the equipment operating conditions. In this way, it contributes to obtain robustness in the demonstration of the safety report or for performance checking.

The objective of the present paper is to detail the qualification methodology developed to deal with high capacity stirred tank homogenisation without performing full scale tests before building the final industrial tank. The methodology relies on a joint approach between numerical modeling and validation tests at different reduced scales.

Once the qualification of numerical methodology is

demonstrated, extrapolation to the full scale in a numerical way can be considered.

Only partial results will be presented here for confidentiality reasons.

II. STATE-OF-THE-ART AND PROBLEMATIC Solid-liquid mixing processes have already been studied by several authors to investigate the influence of hydrodynamics and mixing on solids suspension. For example, Zwietering [3] described the rotation speed at which solid particles are just suspended from the bottom of the tank, and Mersmann [4] determined the minimum rotation speed for off-bottom lifting or for settling avoidance. These approaches are generally too specific to one mixing system to be extrapolated easily and are only

focused on single-staged impellers and low suspension quality. Procedures to determine the speed to attain high homogeneity, especially with multi-staged impellers, are still lacking to our knowledge.

In the framework of final waste conditioning, the legacy sludge produced by the original La Hague effluent treatment facility has to be processed by mixing, drying and compacting. The sludge mixing process has to be performed in a tank in the most homogeneous way in order to guarantee the final quantity of radioactive material in each container. This homogenisation task is made difficult by high density particles and by the size of the tank, which is around 240 m3 in the present case. Moreover, it is interesting to get an idea of the impeller rotation speed required to reach a high homogenisation level for a given impeller design, given that electrical power of the motor must be determined early in the project.

As it is not economically feasible to perform experimentations on a tank of such size, a process qualification program based on a state-of-the-art methodology has been set up including both complementary tools: mock-ups at small scales and Computational Fluid Dynamics (CFD) numerical simulations. CFD modeling used an Eulerian-Granular multiphase approach to investigate homogenisation quality.

On experimental side, several sizes of glass particles have been selected to reproduce the terminal velocity of the real sludge particles sizes and measurements of axial and radial concentration profiles and power numbers have been obtained. At last, as it is questionable whether CFD modeling can be extrapolated to bigger scale, two mockups, respectively of 300 L and 2 m3 that are in perfect geometrical similitude, have been built in the HRB development hall close to La Hague to perform this study.

In this way, scale-up principles for homogeneity have been verified both experimentally and numerically.

300 L tank (factor 2.29) at intermediate level of flooding (see later).

In the following, this impeller will be called “Impeller Design n°1”.

Fig. 1. View of mock-ups impellers – 300 L tank on the left – 2 m3 tank on the right

In a second step, a scale-down of the real configuration impeller (called “Impeller Design n°2”) has been built in order to extend the conclusion of the present study. This impeller differs mainly from the first one by the shape of the axial propeller, the global movement of the fluid circulation being the same in both cases. Moreover, the adimensional geometrical quantities are kept constant.

Two water levels are considered for the 300 L tank: - one at high level, flooding the whole mixing system, - one at intermediate level (called “low level”) (first PBT stage and bottom turbine flooded) so as to be in perfect similitude with the 2 m3 tank.

Scheme of 300 L tank is given in Fig. 2.

N

Hw 3 Baffles (120°)

II.A. Experimental setup Dh

II.A.1. Mock-ups characteristics

Dr H

In order to investigate experimentally the homogenisation quality in a baffled stirred tank, two mockups have been built. The small one is made of Plexiglas so as to visualize the elevation of the cloud of particles as a function of impeller speed.

In a first step, the impeller is chosen to represent the full scale hydrodynamics movement, i.e. axial down pumping. It is made of 2 stages of axial propellers with 3 blades slanted at 45° (PBT: Pitch Blade Turbines) and one bottom turbine (6 vertical blades) for the 300 L tank (Fig. 1). The 2 m3 tank is made of one stage of axial propeller with 3 blades slanted at 45° and one bottom turbine (6 vertical blades) (Fig. 1) in geometrical similitude of the

C

W W

C Lt

Hr

q q

Dt T

Fig. 2. Scheme of 300 L tank

Geometrical characteristics of 300 L and 2 m3 tanks are given in Table I.

Where Re   L u d p is the particle Reynolds number. p

TABLE I

L

Mock-ups geometrical characteristics Tank H C C Dh Dt w

2 m3 0.68 T 0.208 T NA 0.5 T 0.3 T 0.1 T

300 L (high/low water level) 1.1 T / 0.68 T 0.208 T 0.512 T 0.5 T 0.3 T 0.1 T

II.A.4. Particles size distribution and concentration Each particle class has been characterized in term of size distribution. Results are presented Fig. 3.

Where T is the tank internal diameter (m) II.A.2. Liquid phase Tests have been performed with salted water (Na-Cl) at a concentration of 80 g/kg of water in order to increase the sensitivity of the conductivity probe measuring local concentration in the tank (see II.A.5 Concentration measurement system).

Fig. 3. Size distribution for each particle class

II.A.3. Solid phase – Particles characteristics Reduced scale tests have been carried out with glass particles. As glass density ( ~ 2500 kg/m3) is different from real sludge’s one, particles diameters are chosen according to terminal velocity of an isolated particle in fluid at rest. 3 particles diameters have been tested (d 1, d2, d3) so as to cover the real sludge terminal velocity. This terminal velocity can be obtained using the Archimedes number defined as following: d p g  L  p   L  3

Ar p 

L ² With: dp: particle diameter (m) g: gravity acceleration (9.81 m/s2) ρp: particle density (kg/m3) ρf: fluid density (kg/m3) µL: fluid dynamic viscosity (Pa.s)

Knowing the particle drop regime, the terminal velocity is obtained through Reynolds number using the following correlations ([7]) (Table II):

In order to cover sludge concentrations encountered in the chemical process, two concentrations C1 and C2 have been considered for each particle diameter.

II.A.5. Concentration measurement system The concentration measurement principle retained in this study is based on electrical conductivity measurement of the mixture. Indeed, salted water is a better electrical conductor (around 100 mS/cm) than water from the network (conductivity around 300 µS/cm). On the other side, the conductivity of a solid/liquid mixture decreases as the solid volume fraction increases (glass particles are electrical insulators). The ratio of both conductivities (mixture / fluid without glass particles) is directly related to the local solid volume fraction. This measurement principle is applied to an annular conductivity probe (Mettler-Toledo InPro 7250 called “probe 1” in the following). The induced current between two inductive coils (one generator and one receptor) is generated by the conductive fluid movement in the annular space (Fig. 4).

First results were obtained with this probe positioned vertically at different radii/heights in the tank.

TABLE II Particle drop regime and relationship between Archimedes and Reynolds numbers Drop regime

Stokes

Validity domain Arp< 27,6

Re p 

Correlation Ar 0, 687 1  0,15 Re p 18

Van Allen

27.6 < Arp< 4.4 105

Re p 

Ar 0, 687 1  0,15 Re p 18

Newton

4.4 105< Arp< 1.1 1011

Generator









Re p  3 Ar 

0, 5

1

1

Receptor

Toroidal coil

Inducted current

Fig. 4. Conductivity annular probe (Mettler-Toledo InPro 7250) and working principle – probe 1

Due to its geometrical shape, measurements were sometimes disturbed with particles settling in the measurement control volume in particular in cases where flow velocities were weak (low impeller speed). To avoid this phenomenon, a second conductivity probe (MettlerToledo InPro 7100, called “probe 2” in the following) has been tested (Fig. 5). The working principle is similar to the previous one, based on electrical conductivity measurement between 4 electrodes (2 generators and 2 receivers).

TABLE III Radial positions of local concentration measurements – 300 L tank – distance from tank axis r/T

P5

P1

P3

P6

P2

P4

0.284

0.305

0.336

0.377

0.436

0.461

TABLE IV Axial positions of local concentration measurements – 300 L tank – distance from tank bottom h/T

H1

H2

H3

H4

H5

H6

H7

H8

0.169

0.225

0.350

0.475

0.600

0.725

0.850

0.975

From these measurements, the Relative Standard Deviation (RSD) can be evaluated to characterize the level of homogeneity for a given rotation speed.

RSD* 

To compensate for the effect of temperature variation of the fluid on conductivity measurement, probes are equipped with an integrated thermocouple with a control system allowing an automatic correction before data acquisition.

II.A.6. Axial and radial concentration measurement Radial and axial concentration profiles have been obtained from local measurements. The different positions are shown on Fig. 6 and in Tables III and IV. cuve 300L (T = 690 mm) 1,2

P5 P3

P6

P2



II.A.7. Impeller power number measurement The power number (Np) is a quantity important in a stirred system, since it is linked to hydraulics power dissipated inside the tank through the following relation for a turbulent and newtonian fluid [8]: P   L N P N 3 D5

With: P: dissipated power (W) L: fluid density (kg/m3) N: rotation speed (round per second) D: impeller diameter (m) The dissipated power in a tank filled with water is obtained from fluid temperature elevation as a function of time for a given rotation speed (assuming that thermal échauffement au niveau bas (153,4 L) losses are negligible during the test) (Fig. 7).

P4

0,8

0,6

1,2 H1&100rpm H1&150rpm

1,0

0,4

H1&175rpm H1&200rpm

0,8

(T-T0) = f(t) [°C]

adimensionalheight hauteur réduite h/T [-]

P1



With: n: number of measurement positions Cij: local concentration measurement at radial position i and axial position j CV* : theoretical (mean) volume fraction (C 1 or C2)

Fig. 5. Conductivity probe (Mettler-Toledo InPro 7100) – probe 2

1

12

2 1  1 n   Cij  CV*  CV*  n 1 i 1

0,2

0 0

0,1

0,2

0,3

0,4

adimensional radius rayon réduit r/T [-]

Fig. 6. Positions of axial and radial measurements – 300 L tank

0,5

H1&225rpm

0,6

0,4

0,2

0,0

-0,2 0

1000

2000

3000 temps [s]

4000

5000

6000

Fig. 7. Fluid temperature elevation as function of time – 300 L tank – high water level

The power number is obtained using the following relation: NP 

L

 V Cp dT dt V Cp P  L  3 5 dT dt 3 5 N D  L N 3 D5 N D

during the experimentations that, thanks to the baffles, the free surface remains effectively almost flat.

The meshes are made of around 5 million hexahedral and tetrahedral cells (Fig. 8).

With: V: tank volume (m3) Cp: heat capacity of water (J/kg/K) The measured power number is the total power number (each flooded stages are taken into account), related to the PBT impeller diameter (not the bottom turbine diameter).

II.B. Computational Fluid Dynamics Modeling The models are developed with the ANSYS FLUENT 15.0 [6] software, using the Eulerian-Granular multiphase formulation. In this approach, the particles are not individually tracked but are represented as a continuous media coupled with the fluid phase [6]. This model has shown good results at high mass concentration (up to 50%) [5]. The phenomena taken into account are the following:  fluid movement due to the impeller rotation (Sliding Mesh or Multiple Reference Frame approach [6])  turbulence (k-ε realizable mixture, standard wall functions [6])  sedimentation (gravity)  two-way fluid-particle interactions : o drag coefficient (Gidaspow model [6]) o virtual mass o turbulent dispersion force (Diffusion-inVOF or Simonin model [6])  two-way particle-particle interactions [6] In steady-state, the particle mass conservation is ensured using a User-Defined Function (UDF) that rearranges the particle volume fraction after each iteration (if required), following the idea described in reference [2].

At numerical convergence, the mass correction becomes null.

All the particles are supposed to be at the median diameter of the size distribution.

The pseudo-transient [6] approach has been used for steady-state calculations.

The free surface is assumed to remain flat and is modelled as a wall with no shear stress. It is checked

Fig. 8. 300 L tank mesh

III. RESULTS & DISCUSSIONS III.1. Physical validation The physical validation of the model is checked by comparison between numerical results and measurements of power numbers and volume fractions profiles.

Table V shows that the model accuracy for power numbers is within ±15%, which is considered to be acceptable.

TABLE V Total power numbers

Fig. 9 shows an example of a typical axial volume profile for a relatively homogeneous suspension and Fig. 10 shows the corresponding volume fraction field.

Fig. 9. An example of an axial volume fraction profile (homogeneous suspension, 300 L tank, high level, C1, d3)

Fig. 11. An example of an axial volume fraction profile (heterogeneous suspension, 2 m3 tank, C2, d3)

Fig. 12. An example of a volume fraction field (heterogeneous suspension, 2 m3 tank, C2, d3) Fig. 10. An example of a volume fraction field (homogeneous suspension, 300 L tank, high level, C1, d3)

Fig. 11 shows an example of a typical axial volume profile for a heterogeneous suspension and Fig. 12 shows the corresponding volume fraction field.

These results (Fig. 9-12) show that the model is capable of reproducing the concentration measurements with reasonable accuracy in homogeneous suspensions, but this accuracy decreases in heterogeneous suspensions.

Fig. 13 shows the RSD as a function of the rotation speed for the 2 m3 tank.

Fig. 13. RSD as a function of the rotation speed (2 m3 tank, C2, d3)

It seems that the model is always overestimating the quality of the suspension (Fig. 13) by a factor of around 2 to 3, and the height of the particle ‘cloud’ (Fig. 11).

Nevertheless, the numerical model predicts the same rotation speed for which the homogenisation ‘plateau’ (Fig. 13) starts as the experiments. In consequence, ‘scanning’ the rotation speed in the full scale computation allows determining the optimum speed over which no homogeneity improvement will be obtained, even if the absolute homogenisation quality might not be obtained precisely by the modelling (and might in the present case be overestimated by a factor of around 2 to 3).

As sensitivity studies, the Sliding Mesh [6] transient method has been compared to the Multiple Reference Frame [6] steady-state method. For the turbulent dispersion force, which has been shown to be an important parameter for solid-liquid suspensions [10], the Diffusion-in-VOF [6] model has also been compared to the Simonin [6] model.

Fig. 14 shows that the model is reasonably not sensitive to these parameters.

Fig. 14. Sensitivity studies (300 L tank, high level, C 1, d3)

Based upon the previous results, the model is considered validated for engineering purposes.

III.2. Power density as a scale-up criterion for quality suspension Fig. 15 shows the RSD as a function of the power density for 300 L, 2 m3 and 240 m3 tanks (numerical results only, and with the 240 m3 tank being here a hypothetical numerical scale-up of the 300 L and 2 m3 tanks). The curves are qualitatively the same with a plateau that starts at the same power density value for each tank.

This behaviour comforts the relevance of the power density as a scale-up criterion for quality suspension, as extensively proposed in the literature (see reference [1] for instance). The conservative aspect of this criterion, stated in reference [3], is here confirmed and quantified on Fig. 16.

These results should however not be considered general. Further studies with more impeller designs should be performed (for instance for different adimensional geometric ratios, different angles of incidence, different positions from the bottom tank, etc.).

At this stage, it is hence important to keep in mind that the same global fluid movement is achieved for both designs and that the impellers shapes are close and that the adimensional characteristics quantities are kept constant (C, Dh in Table I).

Fig. 15. Scale-up (C2, d3, design n°1)

The ratios of the RSD at 2 m3 and at 240 m3 over the RSD at 300 L show little variation with power density. The ratio values (averaged over the whole power density range) are shown as a function of the linear scale factor on Fig. 16 (the 300 L tank being here the reference scale).

Fig. 17. Designs comparison – Numerical results (C2, d3)

The numerical results from Fig. 17 have to be compared to the experimental results from Fig. 18. Both figures lead to the same conclusion.

Fig. 16. RSD ratio as a function of the linear scale factor (C2, d3, design n°1)

The RSD decreases with the linear scale factor. More calculations and experimentations should be performed before making any general conclusion, but this result remains interesting and further studies might lead to the construction of a new and less conservative scale-up criterion.

III.3. Influence of impeller designs and power density Fig. 17 shows the RSD as a function of the power density for 2 m3 tanks with impeller designs n°1 and 2 (numerical results only). It appears that the curves are almost identical, comforting the idea that the power density is indeed a major contributing factor in quality suspension.

Here, the low power number of impeller design n°2 is simply overcome by a greater rotation speed in order to attain the same suspension quality as with impeller design n°1.

Fig. 18. Design comparison – experiments (here, HRB is impeller design n°1 and GPM is impeller design n°2) (C2, d3)

III.4. Power numbers – Influence between impeller stages For a multi-staged impeller, power numbers of each single impeller are often added in order to determine the total power number of the multi-staged impeller.

Table VI shows that this approach can overestimate the total power number (numerical results on 2 m3 tank).

Interactions between stages can be non-negligible and while the addition of power numbers leads to conservative results as for the mechanical stress on the stirrer, it can lead to non-conservative results as for the power density in the fluid and hence as for the suspension quality. This result is all the more true since the fluid phase (water in the present case) is newtonian and weakly viscous, leading to stronger coupling between stages than with non-newtonian viscous fluids where the flows from the impeller stages can be somewhat independent [12].

TABLE VI Power numbers (stage 1: impeller design n°2, stage 2: bottom turbine)

IV. CONCLUSIONS A methodology for qualification of the homogeneity in stirred baffled tank at huge industrial scale has been developed, based on a state-of-the-art approach including both complementary tools: mock-ups at small scales and Computational Fluid Dynamics (CFD) numerical simulations. Experimental tests at two reduced scales in similitude have been performed to determine the mixing power as well as to obtain radial and axial volume concentration profiles. The associated simulations using an Eulerian-Granular model allow to validate and to qualify the methodology.

This study revealed that:  

 III.5. Power numbers – Influence of the scale It is usually implicitly stated in the literature that the power number of an impeller is not a function of its size (reference [9] gives for instance power numbers only as a function of the design of the impeller and of linear ratios but not of the absolute size). Some authors nonetheless describe power numbers variations with the size (for instance Tsz-Chung Mak [11] reports power numbers increases up to 15% for a linear scale-up ratio of 3).

In the present study, an increase of ~15% was observed between the 2 m3 and the 300 L tanks (linear scale-up ratio of ~2.3) in the experiments and of ~4% in the calculations for impeller design n°1. It has also been observed a decrease of the power number of ~17% between the 240 m3 and the 2 m3 tanks (linear scale-up ratio of ~4.1) for impeller design n°2. The fact that the power number increases or decreases during the scale-up depending on the design is not explained and should be further studied.

The variation of the power number with the scale is rarely discussed in the literature but can have a significant impact on the dissipated power and the suspension quality.









CFD can predict the power number of an impeller within ± 15%, CFD is capable of reproducing the concentration profiles with reasonable accuracy in homogeneous suspensions, but this accuracy decreases in heterogeneous suspension (the modelling seems to overestimate the height of the particle cloud), CFD seems to be overestimating the suspension quality by underestimating the RSD by a factor of around 2 to 3 in the present study, CFD is nevertheless capable of detecting the rotation speed for which the homogeneity ‘plateau’ starts and hence the optimum rotation speed over which no homogeneity improvement will be obtained, The power density at small scale, for which a good suspension quality is obtained, is a good conservative parameter to be kept at industrial scale (with geometrical similitude and identical solid phase characteristics), Hydrodynamics interactions between impellers of a multi-staged impeller can decrease significantly the total power number.

The ‘classical’ additive ‘law’ of power numbers leads to conservative results for the mechanical stress on the stirrer, but can lead to non-conservative results for the suspension quality, The power numbers might not be independent of the scale as often implicitly indicated in the literature, and this can have a significant impact on the dissipated power and the suspension quality.

ACKNOWLEDGMENTS The authors would like to thank Richard Marcer and his team from Principia, Thierry Conte from CFDNumerics and Didier Bessette from ANSYS for their helpful contribution and advice.

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E. L. PAUL et al., Handbook of Industrial Mixing, p. 376, Wiley-Interscience (2004).

2.

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3.

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4.

A. MERSMANN et al., “Theoretical prediction of the minimum stirrer speed in mechanically agitated suspensions,” Chemical Engineering and Processing, vol. 37, p. 503-510 (1998).

5.

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6.

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7.

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8.

M. ROUSTAN et al., Techniques de l’Ingénieur, J3800, Agitation-Mélange – Concepts théoriques de base.

9.

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NOMENCLATURE CFD: Computational Fluid Dynamics PBT: Pitch Blade Turbine H: tank height (m) C: first impeller height (m) ΔC: height between first and second impeller (m) Dh: impeller diameter (m) Dt: bottom turbine diameter (m) w: baffle width (m) T: tank diameter (m) ρ: density (kg/m3) μ: dynamic viscosity (Pa.s) Cp: heat capacity (J/kg/K) Ar: Archimedes number (-) Re: Reynolds number (-) d1, d2, d3: particle diameters (m) C1, C2: concentrations (g/L) g: gravity (m/s2) r: radial position (m) h: height position (m) P1-P5, H1-H8: probe positions n: number of measurement positions Cij: local concentration (g/L) Cv*: mean concentration (g/L) Np: power number (-) N: rotation speed (RPS) P: power (W) k: turbulence kinetic energy (m2/s2) ε: turbulence dissipation rate (m2/s3) RSD: Relative Standard Deviation

10. S. GOHEL et al., “CFD Modeling of Solid Suspension in a Stirred Tank: Effect of Drag Models and Turbulent Dispersion on Cloud Height,” International Journal of Chemical Engineering, vol. 2012 (2012).

11. A. TSZ-CHUNG MAK, “Solid-liquid mixing in mechanically agitated vessels,” thesis, University of London (1992).

12. J. Kukura et al., “Understanding Pharmaceutical Flows,” Pharmaceutical Technology, vol. 26, p.48-72 (2002).