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, dust explosions, spray drying, safety, combustion
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 has been developed. The
simplest model with water droplets evaporation and monodisperse 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 were
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 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.
Figure 1. Schematic of the spray drier
2
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,
monodisperse 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.
3
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
4
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, monodisperse 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:
(1)
where:
kc – mass transfer coefficient
f – correction coefficient (eq. 3.2.)
Ap – particle area [ ]
cp – water vapor concentration on the particle surface
cg – water vapor concentration in the drying air,
MH2O – molecular weight of water: 18
5
Mass transfer coefficient kc was calculated from Nusselt correlation (eq. 2):
(2)
where:
DAB – diffusion coefficient of water vapor in the air
dp – particle diameter [ ]
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).
(3)
where:
mp – particle mass [kg]
Cp – particle heat capacity
Tp – particle temperature [K]
– heat transfer coefficient
Ap – particle area
Tg – temperature of continuous phase [K]
r – latent heat
Heat transfer coefficient
was calculated from Ranz-Marshal correlation (eq. 4):
(4)
6
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 polydisperse atomization, solid phase and agglomeration
at further steps are taken into account.
7
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)
8
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.
9
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 polydisperse 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
140
temperature [°C]
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.
14
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, monodisperse
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.
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