INDIRECT VALIDATION IN CFD MODELING OF ...

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spray based on a standard FLUENT code verified in many literature applications ..... for a standard Fluent code, PSD was taken from previously finished projeckt.
INDIRECT VALIDATION IN CFD MODELING OF SPRAY DRYING PROCESS

Pawel Wawrzyniak, Marek Podyma, Maciej Jaskulski, Ireneusz Zbicinski

Faculty of Process and Environmental Engineering, Lodz University of Technology, 213 Wolczanska Str, 90-924 Lodz, Poland Keywords: CFD, spray drying, drying model, drying kinetics

ABSTRACT The paper presents a cautious methodology of CFD modeling of countercurrent spray drying process when there are no available experimental data which could be used to test and verify the calculations. Six numerical CFD models of drying process with growing complexity have been developed. The simplest model with water droplets evaporation and mono-disperse spray based on a standard FLUENT code verified in many literature applications was treated as reference and confident case. In the subsequent models droplets size distribution was introduced, custom drying model was developed and verified with results of preceding models. At each consecutive stage of models development, simulation results were carefully analyzed to maintain accuracy of the calculations. Finally the most complex model describing spray drying process in industrial spray drier was developed. Results of each model were compared with selected available experimental data verifying calculation quality. In each model, timeaveraged outflow gas temperature was calculated and compared to gas measure outlet temperature in an industrial tower. Presented methodology of predictive modeling can be applied in most chemical engineering processes when experimental data needed to test and verify the calculations are limited.

INTRODUCTION Majority of spray drying applications refers to the co-current flow of air and discrete phase (Kemp, 2004; Fletcher et al. 2006; Huang et al, 2003; Oakley, 2004). However, a countercurrent process has also found many industrial applications due to reduction of energy input for evaporation and integration of several unit operations in one vessel, e.g. drying, agglomeration and segregation. Due to complex dynamics of air and dried particles, counter-

current spray drying is one of the processes for which the knowledge of the mechanism of heat, mass and momentum transport, parameters controlling drying process, quality interactions, etc. is still limited (Huang et al, 2003). There are a few works in the literature which refer to modeling (Harvie, 2001) and experimental analysis of spray dryers with counter-current flow of phases, e.g. (Bayly and Jukes, 2004; Rahse and Dicoi, 2001; Piatkowski, and Zbicinski 2007). The aim of a presented work is to test a cautious methodology of CFD modeling of counter-current spray drying process when the available experimental data which could be used to test and verify the calculations are very limited.

EXPERIMENTAL Description of the drying tower A schematic diagram of the drying tower is shown in Figure 1. The dryer total height is 25,1 m and its inner diameter is 4.5 m. At the top of the drying tower there is a sackcloth filter. From the top of sack filters to the bottom of the cone, the drying chamber is 28 m high. The dryer wall is insulated with mineral wool. Slurry is sprayed with nozzles placed on two levels; 12 nozzles at upper and 8 nozzles at lower level. Usually, during drying 6 nozzles on each level are used. CFD calculations of the drying tower (3D) The main goal of this part of the project was to perform simplified CFD calculations in the spray dryer for the continuous phase in order to predict hydrodynamics of drying air, flow paths, velocity vectors, etc. As the first step to more advanced 3D CFD calculations with heat and mass transfer model, 3D calculations in isothermal conditions were performed. Development of a 3D CFD model allowed to acquire some knowledge on the behavior of continuous phase in the tower, density of numerical grids and turbulence models Figure 1. Schematic of the spray drier which should be used in this particular case. Completion of this step created background for more complex 3D CFD calculations. To create a complete picture of the air flow pattern in the tower 3D calculations of the continuous phase was made. The position of twelve inlet orifices on the boundary of the system makes analysis of the air flow difficult. 3D calculations enable the application of a precise tower geometry and also consideration of non-uniform air delivery to the tower. Having defined accurate geometry of the tower, numerical grid was generated for 3D calculations.

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Three mesh densities were tested to obtain an accurate and grid-independent solution. Two examples of mesh generated (370k, 463k) are presented in Figure 2. Finally, the mesh with 370 000 elements was used in the calculations which was a compromise between accuracy of the calculations and reasonable computing time. Convergence coefficients of initial 3D calculations performed in steady-state conditions (k- turbulence model) were not satisfactory. It has been found that due to tower diameter and construction of air inlets, despite the constant initial conditions, flow instability was too big to obtain an accurate solution. Finally, the calculations were performed in unsteady-state conditions. This approach increased significantly the computational time, but it enabled to obtain stable and reliable solutions of flow in the spray drying tower.

370 k

463k

The CFD calculations were performed at constant air temperature. 120°C. The selected temperature reflects the mean flow condition in the drying tower. Convergence coefficients were below critical values which guaranteed correctness of the solutions.

Figure 2. Numerical meshes tested for 3D CFD calculations

Figure 3. displays air velocity field contours in the tower for two subsequent calculation steps, while Figure 4. shows a picture of static pressure after 20 sec of the process time. CFD calculated axisymmetric velocity field and the lack of oscillations appeared to be the most characteristic feature of flow in the analyzed tower.

A 3D KINETIC MODEL OF ENERGY FLOW IN A COUNTER-CURRENT SPRAY DRYING TOWER FOR POLYDISPERSE SPRAY One of the main aims of the project was to develop a 3D model of counter-current spray drying kinetics for the tower. There experimental measurements which could be used to test and verify the calculations are very limited. The following concept to obtain an accurate and confident model of spray drying process. Six spray drying models were developed, starting from the simplest (water evaporation, mono-disperse spray) to the most complex one describing spray drying process in the industrial drying tower. Figure 5. shows schematically our concept how to gradually develop a confident model of spray drying process.

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Figure 1 Velocity field inside the air-distributing ring after 10s and 20s, air temperature 120°C (colored by hot air flow velocity, m/s)

Built in evaporation

Water Droplet: WD

One Diameter: 1D WD_1D_STD

PSD WD_PSD_STD

Figure 4. Static pressure distribution in the drying tower, air temperature 120°C (colored by static pressure, Pa)

CUSTOM evaporation (UDF)

Water Droplet (f=1): WD

One Diameter: 1D WD_1D_CUSTOM

Solid Patricle ( f=F(X,Xcr)): SP

One Diameter: 1D SP_1D_CUSTOM

No agglomeration: SP_PSD_CUSTOM

PSD

Agglomeration SP_PSD_CUSTOM_A

Figure 5. List of CFD models developed to obtain to a confident model of spray drying process

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CFD models symbol list: WD

– Evaporation from water droplet – constant drying rate period only

SP

– Solid Particle – Discrete evaporation with the falling drying rate period taken into account (implementation of Custom evaporation required)

1D

– All particles of the same diameter (150 microns)

PSD

– Particle Size Distribution described by Rossin-Rammler equation

STD

– Built in solver own mechanism for heat and mass exchange between discrete and continuous phase

CUSTOM – Custom (UDF) mechanism for heat and mass exchange between discrete and continuous phase – Discrete phase agglomeration process included

A

The simplest of the developed models (water evaporation, mono-disperse spray) was based on a standard FLUENT code. This model of spray drying process was verified in many literature applications so it can be treated as confident. The model became a basis for further substantial changes in the CFD code to adjust it to project requirements. PSI Cell (Particle Source In Cell) model was used in order to determine parameters of the disperse phase (particle temperature, moisture content, velocity, residence time).

DISCRETE PHASE MODEL DESCRIPTION As it was mentioned before, due to the lack of experimental data concerning air temperature profiles inside the column, a model of spray drying kinetics for the tower had to be developed. To achieve this, heat and mass transfer between the discrete and continuous phases had to be calculated on the basis of transport equations. Basic equations formulating the model are delivered below. Mass transfer: Mass transfer from the particle to drying air was described by the eq. 1: dmp dt

= f ∙ k c ∙ Ap ∙ (cp − cg ) ∙ MH2 O

(1)

where: m

kc – mass transfer coefficient [ s ] f – correction coefficient (eq. 3.2.) Ap – particle area [m2 ] cp – water vapor concentration on the particle surface [

kmol m3

]

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cg – water vapor concentration in the drying air, [

kmol m3

]

kg

MH2O – molecular weight of water: 18 [kmol] Mass transfer coefficient kc was calculated from Nusselt correlation (eq. 2): kc =

DAB d

(2 + 0.6 ∗ Re0.5 + Sc 0.33 )

(2)

where: DAB – diffusion coefficient of water vapor in the air [

m2 s

]

dp – particle diameter [m] Re – Reynolds number [-] Sc – Schmidt number [-]

Heat transfer: Particle temperature is updated according to a heat balance that relates the sensible heat change in the particle to the convective heat transfer between the droplet and the continuous phase and heat used for evaporation (eq. 3).

mp Cp

dTp dt

= α ∙ Ap (Tg − Tp ) +

dm dt

∙r

(3)

where: mp – particle mass [kg] J

Cp – particle heat capacity [kg∙K] Tp – particle temperature [K] W

α – heat transfer coefficient [m2 ∙K]

Ap – particle area [m2 ] Tg – temperature of continuous phase [K] J

r – latent heat [kg]

Heat transfer coefficient α was calculated from Ranz-Marshal correlation (eq. 4): λ

α = d (2 + 0.6 ∗ Re0.5 + Sc 0.33 )

(4)

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RESULTS CFD calculations of spray drying process for WD_1D_STD configuration The main goal of calculations at this step was to develop a confident CFD model of spray drying process based on the standard Fluent code to check correctness of all boundary and initial conditions and to compare theoretical results with available experimental data. The standard Fluent code enables determination of a full picture of continuous phase and dispersed phase flow in the dryer for evaporation of water, however introduction of a solid content to the calculation process requires the development of our own part of the code (UDF) which might always introduce a systematic or random error to the calculations. As this time there were no experimental measurements available, and the only way of model verification was to compare real and theoretical outlet gas temperature. It was important to start simulations with a relatively simple approach. This configuration of spray drying process was verified in many literature applications and can be a basis for further substantial changes in the CFD code to adjust it to project requirements. Figure 6. shows both outlet average air temperature in relation to time and averaged air temperature at the outlet. We may observe oscillations of the average outlet air temperature, however time average outflow gas temperature calculated as an arithmetic average temperature at subsequent time steps (during 25 sec) was equal to 91.0°C which matches perfectly with data from industrial dryer and confirms consistency and correctness of our model and enables its further development. Outlet average air temperature Time-averaged air temperature at the outlet 130

temperature [°C]

120 110 100 90 80 70 60 0

5

10

15

20

25

time [s] Figure 6. Average outlet air temperature and time-averaged air temperature at the outlet

Important information is provided by a comparison of velocity contours obtained in the evaporation model with profiles for isothermal gas flow Figure 3. Picture of the flow is entirely different; if there is no evaporation process the gas flow is stable, uniform, practically without oscillations (Figure 7). The picture of flow changes dramatically when the discrete phase is introduced; evaporation changes the air flow pattern to oscillating and unstable. We may expect even more instability if poly-disperse atomization, solid phase and agglomeration at further steps are taken into account.

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The next Figure 8 shows vectors of velocity magnitude at a selected time step (1.52 sec) in the whole dryer and conical section. The flow is not symmetrical, large vortex can be observed in the conical section, air velocities are the highest on the level of air inlets but quickly decrease both in the upward and downward direction of flow.

Figure 7. Contours of velocity profiles at subsequent time steps (every 2 sec), evaporation model WD_1D_STD

Figure 8. displays vectors of velocity magnitude at the same time step and in the same sections of the dryer but only the upward and downward direction of flow is shown. The flow goes mainly upward, the downward flow is observed in the conical section and near the wall of the tower. Figure 9. shows the contours of temperature at subsequent time steps (every 4 sec). The picture of temperature contours is as unstable as the picture of flow field contours (Figure 7). The temperature contours reflect well the character of the process; drying takes place just beneath the lower level of nozzles. Figure 8 Vectors of velocity magnitude at a selected time step (1.52 sec)

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Figure 9. Contours of temperature at subsequent time steps (every 2 sec), evaporation model WD_1D_STD

CFD calculations of spray drying process for WD_PSD_STD configuration CFD results of the calculations of spray drying for water evaporation, discrete phase without solid content, polydisperse spray are presented in Fig. 10. Rossin-Ramler equation was applied to describe particle size distribution (PSD) in the spray. Calculations were performed for a standard Fluent code, PSD was taken from previously finished projeckt. Description of the results for this case is limited to the analysis of average air temperature at the outlet to control the quality of calculations and temperature contours in the dryer to present a general picture of the drying process. Information on velocity profiles of gas and particles is less important for the calculations whose main aim is the development of an accurate model of drying and agglomeration of particles. At this step, time-averaged outflow gas temperature was determined and compared to temperature in industry. Figure 10. shows both outlet average air temperature in relation to time-averaged air temperature at the outlet. Oscillations of the average outlet air temperature occurred as in the previous model. Time-averaged outflow gas temperature calculated as an arithmetic average temperature at subsequent time steps (during 25 sec) was equal to 97.6°C which differs only about 7 deg from the experimental value.

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Outlet average air temperature Time-averaged air temperature at the outlet 120

temperature [°C]

115 110 105 100 95 90 85 80 0

5

10 time [s]

15

Figure 10. Average outlet air temperature and time-averaged air temperature at outlet

CFD calculations of spray drying process for WD_1D_CUSTOM configuration Figure 11 present CFD results of calculations of spray drying for evaporation of discrete phase with solid content taken into account and monodisperse spray with initial diameter equal to 150 microns and correction coefficient to adjust mass transfer to evaporation from solid which was equal to f = 1. CFD calculations were performed for a substantially changed FLUENT code, where evaporation law was fully described using our own UDF. If correction coefficient f=1 and mass transfer is not hampered by additional resistance, we are at the end of the constant drying rate period.

temperature [°C]

Outlet average temperature Time-averaged air temperature at the outlet 120 115 110 105 100 95 90 85 80 75 70 0

5

10 time [s]

15

20

Figure 11. Average outlet air temperature and time-averaged air temperature at outlet 10

Figure 11 shows outlet average air temperature in relation to time and averaged air temperature at the outlet. Oscillations of the average outlet air temperature occurred like in all the previous models. Time average outflow gas temperature calculated as an arithmetic average temperature at subsequent time steps (during 25 sec) was equal to 88.5°C which was very close to the experimental value (90 °C). This confirms consistence of the developed model and allows us to make next steps towards a description of spray drying of detergents.

CFD calculations of spray drying process for SP_1D_CUSTOM configuration CFD results of calculations of spray drying for evaporation from solid particles, in the falling drying rate period and monodisperse spray with initial diameter equal to 150 microns are shown in Figure 12. Critical moisture content was equal to Xcr=0.73 kg/kg. FLUENT code was upgraded again using our own UDF to perform calculations in the falling drying rate period. A comparison of the outlet average air temperature and averaged air temperature at the outlet showed that average gas temperature was equal to 86.0°C which was close to the experimental value (90 °C) which again confirmed accuracy of the preformed simulations and enabled further development of the model (Figure 12). Oscillations of the average outlet air temperature occurred like in all the previous models.

temperature [°C]

Outlet average temperature Time-averaged air temperature at the outlet 110 105 100 95 90 85 80 75 70 65 60 0

5

10 time [s]

15

20

Figure 12. Average outlet air temperature and time-averaged air temperature at the outlet

CFD calculations of spray drying process for SP_PSD_CUSTOM configuration CFD results of the calculations of spray drying for evaporation from solid particles, calculations in the falling drying rate period and polydisperse spray are presented in Figure 13. Rossin-Ramler equation was applied to describe particle size distribution (PSD) in the spray. The FLUENT code was upgraded again using our own UDF to perform calculations in the falling drying rate period for poly-disperse spray. Analysis of the outlet average air 11

temperature in relation to time of the process showed that it was equal to 86.0°C which was identical as in the earlier calculations and close to the experimental value (90°C), Figure 13. Oscillations of the average outlet air temperature occurred like in all previous models Outlet average temperature Time-averaged air temperature at the outlet 130

temperature [°C]

120 110

100 90 80 70 60 0

5

10 time [s]

15

20

Figure 13. Average outlet air temperature and time-averaged air temperature at the outlet

CFD calculations of spray drying process for SP_PSD_CUSTOM_A configuration At this step of the project, final CFD calculations were performed to obtain a full picture of spray drying of detergents in the tower including an analysis of continuous and dispersed phase flow, heat, mass and momentum transfer between the phases and agglomeration of the material. Outlet average temperature Time-averaged air temperature at the outlet 150

temperature [°C]

140 130 120 110

100 90 80

70 60 0

5

10 time [s]

15

20

Figure 14. Average outlet air temperature and time-averaged air temperature at outlet

At the first step of the analysis of results, the outlet average air temperature in relation to time was determined and compared to the average gas temperature in the tower. The calculated 12

average outflow gas temperature was equal to 88.0°C which was close to the experimental value, Figure 14., thus confirming the accuracy of calculations.

lower nozzles level (12 m)

upper nozzles level (17.5 m)

Figure 15. Trajectories of particles injected to the dryer on the lower nozzle level (12 m) and upper nozzle level (17.5 m) colored by particle temperature.

Summarizing the analysis of continuous phase behavior, a comparison of velocity and temperature contours and vectors of velocity magnitude for upward and downward direction of flow at the same time step was made. At the next step the behavior of discrete phase will be analyzed. Figure 15. shows a comparison of particle trajectories colored by particle temperatures (°C) which reflects evaporation history, from the levels of two nozzles. The temperature of most particles is below 90°C (outlet gas temperature), however the temperature of some particles (small, dry) reaches even120°C. 13

Figure 16. presents the trajectories of particles colored by diameter injected on both nozzle levels. Bigger particles can be encountered in the conical section of the dryer, while smaller ones (up to 150 microns) which recirculate in the nozzle area undergo intensive agglomeration.

lower nozzles level (12 m)

upper nozzles level (17.5 m)

Figure 16. Trajectories of particles injected to the dryer on the lower nozzle level (12 m) and upper nozzle level (17.5 m) colored by particle diameter.

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150 um

200 um

250 um

Figure 17. Comprehensive picture of particle trajectories with the initial diameters 150, 200 and 250 microns injected to the dryer, 400 streams tracked.

Finally, a comprehensive picture of particle trajectories with the initial diameters 150, 200 and 250 microns injected to the dryer, presented in Figure 17, shows a complex pattern of particle flow and agglomeration in the counter-current industrial tower. 15

CONCLUSIONS Results of CFD calculations of static pressure distribution in the inlet air ring showed almost symmetrical flow around the vertical plane defined by the axis of air inlet tube. Air flow rates at the consecutive inlet orifices did not differ more than 20%. 3D CFD calculations of isothermal air flow in the dryer showed axisymmetric velocity field, high stability and lack of flow oscillations in the tower which was a result of symmetrical flow around the inlet air ring. Only at the bottom of the conical section of the tower small air swirls could be observed. A concept to obtain an accurate and confident CFD model of spray drying process for the situation when there are no experimental measurements which could be used to test and verify the calculations was proposed. Six CFD spray drying models starting from the simplest one which was verified in numerous literature applications (water evaporation, mono-disperse spray) to the most complex one describing spray drying process in the tower were developed. At each consecutive stage of models development, simulation results were carefully analyzed to maintain accuracy of the calculations. In each model, time-averaged outflow gas temperature was determined and compared to gas outlet temperature in the tower, the difference was in the range from 2 to 5°C which matched perfectly the data from the industrial tower. CFD calculations show that the picture of flow in the tower changes entirely in comparison to isothermal flow if heat and mass between the phases discrete phase is considered; evaporation changes the air flow pattern to oscillating and unstable. Additionally, we observed that the more complex was the model, the more instable was the flow. Final CFD calculations enabled us to obtain a full picture of spray drying of detergents in the tower including the analysis of continuous and disperse phase flow, heat, mass and momentum transfer between the phases and agglomeration of the material. In all calculations it was found that outlet gas temperature exceeded temporarily 120°C . The evaporation history of particles injected on two nozzle levels showed that the temperature of most particles was below 90°C (outlet gas temperature), however the temperature of some particles (small, dry) might reach even120°C. Analysis of the trajectories of particles with the initial diameters: 150, 200 and 250 microns injected on the lower and upper nozzle level showed that 8% of particles with the initial diameter 150 microns, 22% of particles with the initial diameter 200 microns and 99% of particles with the diameter 250 microns would escape from the drying chamber, the rest of particles would stay in the chamber, recirculate and agglomerate.

REFERENCES Barton J. (2002), Guide to dust explosion prevention and protection, Parts 1-3, ISBN 08295 293 7/8/9, Institution of Chemical Engineers. Bayly, A.E.; Jukes, P.; Groombridge, M.; McNally, C. Airflow patterns in a counter-current spray drying tower simulation and measurement. In Proceedings of the 14th International Drying Symposium, Sao Paulo, Brazil, August 22-25, 2004; vol. B 775-778.

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Fletcher, D.F.; Guo, B.; Harvie, D.J.E.; Langrish, T.A.G.; Nijdam, J.J.; Williams, J. What is important in the simulation of spray dryer performance and how do current CFD models perform? Applied Mathematical Modelling 2006, 30 (11), 1281-1292. Harvie, D.J.E.; Langrish, T.A.G.; Fletcher, D.F. Numerical simulations of gas flow patterns within a tall-form spray dryer. Transactions of the Institution of Chemical Engineers 2001, 79(A), 235-248. Huang, L.; Kumar, K.; Mujumdar, A.S. A parametric study of the gas flow patterns and drying performance of co-current spray dryer: results of a computational fluid dynamics study, Drying Technology 2003, 21 (6), 957-978. Kemp, I.C. Drying in the context of the overall process, Drying Technology 2004, 22 (1-2), 377-394. Oakley, D.E. Spray dryer modeling in theory and practice, Drying Technology 2004, 22 (6), 1371-1402. Piatkowski, M.; Zbicinski, I. Analysis of the mechanism of counter-current spray drying. Transp. Porous Med. 2007, 66 (1-2), 89-101. Podyma M., Zbiciński I., Wawrzyniak P., Bartczak Z., Rabaeva J. (2010), Modeling of air flow in an industrial counter current spray drying tower, Proceedings of 17th International Drying Symposium (IDS 2010) Magdeburg, Germany, Vol. B, pp.1209-1214. Rahse, W.; Dicoi, O. Spray Drying in Detergent Industry, In Proceedings of Spray Drying’01 Conference, Dortmund, Germany, October 8-10, 2001; 83-87.

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