Drying 2004 Proceedings of the 14th International Drying Symposium (IDS 2004) So Paulo, Brazil, 22-25 August 2004, vol. A, pp. 326-332

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COMPUTATIONAL FLUID DYNAMIC SIMULATION OF DROPLET DRYING IN A SPRAY DRYER

Lixin Huang1, Kurichi Kumar2 and Arun.S. Mujumdar1

1. Mechanical Engineering Department, National University of Singapore, Kent Ridge Crescent, Singapore, 119260, Email: engp2416@nus.edu.sg; mpeasm@nus.edu.sg 2. CFD Division, Institute of High Performance Computing, #01-01 the Capricorn, Singapore Science Park II, Singapore 117528, Email: kkumar@ihpc.nus.edu.sg

Keywords: Atomization; Computational fluid dynamics; numerical model; particle residence time; two phases flow

ABSTRACT

This paper results of a numerical investigation of drying in a spray chamber 2.215m in diameter with a cylindrical top section 2.005m high and a bottom cone 1.725m high. A two-dimensional axi-symmetric spray dryer fitted with a pressure nozzle is simulated using the CFD package FLUENT. The predicted results by the built-in drying model in FLUENT are compared with modified drying models. The modified drying models were developed by fitting droplets or particles evaporation rate in falling rate period as a linear or a polynomial function of moisture content. Typical results viz. particle moisture content, temperature, velocity and particle histories are presented and discussed. It is found that the evaporation and drying rate is over estimated by the built-in drying model.

INTRODUCTION

The spray drying operation is widely used in many industries, e.g. chemical, ceramic, food, pharmaceutical processing etc. [Masters, 1991; Filkova and Mujumdar, 1995; Huang and Mujumdar, 2003]. However, it is not a fully mature technology yet as spray dryers are still designed mainly on the basis of experience and pilot experiments [Mujumdar, 2002].

The computational fluid dynamic (CFD) simulation technique has developed very rapidly over the past two decades. Despite difficulties in modeling the complex transport phenomena occurring in a spray dryer, CFD model results are useful to guide design and operation of spray dryers when coupled with empirical experience. Huang et al. [2003a and 2003b] and Kieviet [1997] used commercial CFD codes, e.g., FLUENT, FLOW-3D, Phoenix etc., to simulate high-temperature and low-temperature co-current spray dryers. Varying levels of success were obtained with these approaches.

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Here the objective is to present and discuss a set of numerical results obtained using the CFD software Fluent 6.1 for a co-current flow spray dryer [Fluent, 2003]. The predicted results from the built-in drying model in FLUENT are compared with modified drying models proposed here. The modified drying models are obtained by fitting the droplet evaporation rate in the falling rate drying period as linear or polynomial functions of moisture content so that they can be easily incorporated in the FLUENT software without the need for source code.

COMPUTATIONAL METHODOLOGY The governing equations for the gas and particle phases can be found in Huang et al. [2004] and the

FLUENT manual [2003]. Since space is limited, they are not repeated here. The main focus here is on the mass transfer from the droplet to gas. In general, there are the two drying rate periods, i.e., constant drying rate period (CDRP) and falling drying rate period (FDRP) during droplet drying. First we present the FLUENT model equations followed by our own models

Drying model in FLUENT

In FLUENT, the rate of vaporization in CDRP is defined by: )( ,, = isici CCkN (1)

where the mass transfer coefficient in equation (1) is calculated from the following correlation:

3/12/1,

Re6.00.2 ScD

dkSh

mi

pc +== (2)

The second period (CDRP), called droplet boiling period in FLUENT, is applied to estimate the heat and mass transfer rates due to convective boiling of the discrete phase droplet when the temperature of the droplet has reached the boiling point as long as the mass of the droplet exceeds the non-volatile fraction of water in the particle. Here, we call it boil-model or model A. The boiling mass transfer rate equation is given by [FLUENT, 2003]:

fg

ppd

ppp

p

h

TTc

dck

dt

dd )(1ln[)Re23.01(

4)( ,

,

++=

(3)

Modified drying rate model If the particle remains spherical in shape, the FDRP governing equation can be written as a diffusion

process as follows:

rC

rrC

DtC

+

=

(4)

The boundary conditions are: crCrC =)0,( at 0=t and Rr 0 ;

)(),( gsc CCkrtRC

D =

at Rr = ;

0),0( =

r

tC at 0=r .

Unfortunately, since the FLUENT source code is not available, equation (4) cannot be inserted into FLUENT. So a simple and new drying model is developed here to avoid the problem. The plot of the normalized drying rate (N/Nc) versus normalized free moisture content [(X-X*)/(Xc-X*)] is assumed to be nearly independent of the drying conditions [Sakamon, 2000]. Such a characteristic drying rate curve is illustrated in Figure 1. Thus, if the constant rate-drying rate can be estimated and the equilibrium moisture content data are available, then the falling rate curve can be estimated using this simplified method. In Figure 1, three different falling drying rate periods are tested, i.e., linear, high-order polynomial and low-order polynomial.

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In this work, the constant drying rate is estimated from the following computation:

)( wpc

c

TTAhN

= (5)

while the convective heat transfer coefficient hc is calculated from equation (6)

3/12/1 PrRe6.00.2 +==k

dhNu pc (6)

For computation of the drying rate during the falling rate period, equation (1) is re-formulated as

ppip

ff MART

pX

RTG

kN op )(

= (7)

while the mass transfer coefficient kf is calculated using equation (8)

3/12/1Re6.00.2 ScD

dkSh

i

pf +==

(8) So, based on the assumed drying rate curve in the falling rate period, the

relationship between cf NN / and *

*

XXXX

c can be obtained. Thus, the pseudo-pressure G can be

computed from the moisture content in the droplet estimated at each computing time step. It can be directly and readily input into FLUENT using its user-define-function (UDF).

Thus, three different expressions for the drying rate models for the falling rate period are obtained. We term them as low-order polynomial model (model B), linear model (model C) and high-order polynomial model (model D).

CHAMBER GEOMETRY AND BOUNDARY CONDITIONS

The simulations were performed for a steady state operation. Grid-independence of the results was demonstrated in a previous paper [Huang et al., 2003b]. The chamber is a cylinder-on-cone vessel, 2.215m in diameter with a cylindrical top section, 2.0 m high and a bottom cone, 1.725 m high. The angle of the bottom cone is 600. The atomizer is installed at the top of the drying chamber. Air is blown into it from the top center. The feed is a 50% solids solution of skim milk. The boundary conditions at the inlet, the outlet, chamber wall and the turbulence model are summarized in Table 1.

Spray issued from a pressure nozzle: The droplet size distribution is selected to be such that 10microns is the minimum droplet diameter, and 138 microns is the maximum droplet diameter with an average droplet diameter of 70 microns; it is modeled using a Rosin-Rammler distribution with these parameters and the spread parameter equal to 2.05 [Kieviet, 1997]. The velocity at discharge from the nozzle is 50 m/s.

The standard k-epsilon turbulence model is used in this work. The UDFs for the correlations between the pseudo-pressure and moisture content in droplet for different drying curve models are given below: Model B (Low-order polynomial):

1241)0101.0(355.9017)0101.0(4.62787)0101.0(66.181672 23 ++= XXXG Model C (Linear):

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14503.14881 += XG Model (High-order polynomial):

1515)0101.0(48.44480)0101.0(655.120426)0101.0(115910 23 ++= XXXG

Table 1 Boundary conditions used for simulation Air mass flow

rate (kg/s) Air temper- ature (0C)

Air absolute Humidity (kg/kg)

Total spray rate (kg/s)

Rosin-Rammler parameter

Feed temperature (0C)

0.336 195 0.01 0.0139 2.05 27

Air radial velocity (m/s)

Air axial velocity (m/s)

Air total velocity (m/s)

Turbulence k-value (m2/s2)

Turbulence -value (m2/s3)

Pressure at outlet (Pa)

-5.25 7.50 9.15 0.027 0.37 -100.0

Chamber wall thickness (m) Wall material Wall heat transfer coeff. (W/m2.K)

Air temperature outside wall (0C)

Interaction B.C. (wall and droplet)

0.002 Steel 3.5 27 Escape a

a indicates that the particles are lost from the calculation domain at the point of impact with the wall

RESULTS AND DISCUSSION

The CFD model used here has been validated in Huang et al. [2003b]. Here drying of only one typical droplet of 65micron diameter is selected for discussion. Both stochastic and deterministic models for computing the droplet trajectories are selected for discussion. The Eulerian-Lagarangian approach is used in this two-phase simulation

Particle mass histories

The plots for droplet moisture content vs. residence time using the four drying models and two

models (deterministic and stochastic) for computing particle trajectories are shown in Figure 2. They show that different drying models give different mass reduction rate histories and residual moisture. In Figure 2b, model A predicts drying of all moisture from the droplet. The other three models predicted three different but low results. They predict results which are more reasonable than those by model A. For example, since the initial falling drying rate for model D is higher than that of the other two (B and C models), it shows that less resistance for moisture transfer occurs in the initial falling drying rate period. The moisture transfer rate from interior to outside surface is very rapid. When the resistance to moisture transfer is large, the surface vapor pressure becomes smaller and smaller until it reaches the partial pressure of vapor in the gas and drying stops. Model C gives the drying curve lying between Models B and D cases. But for model A, no matter which drying and droplet surrounding conditions are applied, the droplet is dried fully if the surrounding temperature is higher than the boiling point.

Figure 2a does not show smooth results like those in Figure 2b. It is because the stochastic effect of air turbulence on particle trajectories is included in Figure 2a using the stochastic model option in FLUENT.

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(a) Stochastic model results (b) Deterministic model results

Figure 2 Particle mass vs. residence time for four models

Particle velocity and air velocity along particle trajectories Figure 3 shows the computed air velocities using the four drying models. The velocity is affected by

particles at the initial contact between the droplets and air. It is seen that the variation of velocity is significant only in the first 0.5s. This is due to the high relative velocities in the inlet region. The stochastic model predicts variation of the velocity for four drying models even after 0.5s. However, when the deterministic model is used, velocity variations are very weak after 0.5s.

From particle velocity histories shown in Figure 4, particle velocity is seen to decrease very rapidly from the initial high velocity to less than 10m/s. But the randomness of turbulence leads to a significant effect on the particle velocity except at the start of the droplet from the nozzle. They fluctuate very strongly during all its residence in the drying chamber. It also is due to droplet size variation from different evaporation rates obtained using different drying models. On the other hand, the velocity variation cannot be seen clearly in the deterministic model (not shown here). Only weak fluctuations can be found in the initial 0.5s and at the end of the travel.

Figure 3 Air velocities along particle path for stochastic model Figure 4 Particle velocities computed using stochastic model

Particle temperature and air temperature variation along particle trajectories

Typical droplet temperature histories for different models using the stochastic model are shown in

Figure 5. It shows that the temperature rises to and remains at boiling point according to Model A. The

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other three models do not follow this trend since the temperature can exceed the boiling point depending on the heat balance of the convective heat transfer rate from air and heat absorption due to evaporation.

Figure 5 Particle temperature histories for stochastic model Figure 6 Air temperatures along particle trajectory

Figure 6 portrays predicted air temperature variation along the particle path. From this figure, one can see that the temperature variation is significant when the stochastic model is used; this is especially in the initial contact between droplets and air. By contrast, the air temperature does not show significant variation for the deterministic model (not shown here). The temperature difference among the four drying models is only due to the different evaporation rates given by the four drying models.

Particle trajectories

The predicted particle trajectories are

shown in Figure 7. It is clearly seen that the particle will have a different fate when different drying models are used, e.g., models B and D will lead the particle to exit from the outlet and the linear and boil models will have the particle hit the conical wall. It is also due to the stochastic effect on particle trajectories. It should be noted that the particle paths can be totally different from these predicted results shown here due to the turbulence effect. By contrast, the four drying models do not lead to particle trajectories which are significantly different. Figure 7 Particle trajectories for stochastic model

CONCLUSIONS

Three new drying models for the falling rate period based on the concept of characteristic drying rate

are proposed and examined. They predict the droplet/particle drying histories in the falling rate period. The built-in drying model in FLUENT possibly over-estimates the drying rate in the falling rate period.

Also, particle histories, e.g., particle moisture content, temperature, trajectories etc., are investigated using four drying rate models and two turbulence models (stochastic and deterministic models). It is found that the stochastic effect of turbulent flow has a significant influence on the particle path in the drying flow.

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Finally, the new drying models need future testing. It is necessary to include temperature effect into the drying models. The predicted results show that the temperature of particle has a significant effect on the predicted results.

NOTATION

Ap Droplet surface area m2 Cis Moisture concentration at surface mol/m

3

iC Moisture concentration in the bulk gas mol/m3 Dm Vapor diffusion coefficient m2/s cp Droplet heat capacity J/kg.K dp Droplet diameter m h Convective heat transfer coefficient W/m2.K Kc,kf Mass transfer coefficient m/s

Mp Molecule weight kg/mol Nc,Nf Evaporation rate at CDRP and FDRP kg/s Psat(Tp) Saturated vapor pressure Pa pop Operating pressure Pa

G Pseudo-pressure Pa R Universal gas constant J/mol.K T Temperature K X Moisture fraction

Greek letters Subscripts Latent heat J/kg c critical Density kg/m3 g Gas Viscosity N.s/m2 l liquid

Non-dimensional number Nu Nusselt number Re Reynolds number Sc Schmidt number Sh Sherwood number Pr Prandtl number

LITERATURE

Filkova I. and Mujumdar A.S., Industrial Spray Drying Systems; in Mujumdar A.S. (Eds.), Handbook of

Industrial Drying (2nd Ed.), Marcel Dekker, Inc.: New York, 1995, pp.263-308 Fluent Manual 2003; chap. 10: Turbulence models and chap. 19: Discrete Phase Models; www.fluent.com Huang, L and Mujumdar, A.S., Classification & Selection of Spray Dryers, Chemical Industry Digest

(India), 7-8(2003), pp.75-84 Huang, L., Kumar, K. And Mujumdar, A.S., Use of Computational Fluid Dynamics to Evaluate

Alternative Spray Chamber Configurations, Drying Technology, 21(2003a), 3, pp.385-412 Huang, L, Kumar, K and 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, 21(2003b), 6, pp.957-978

Huang, L, Kumar, K and Mujumdar, A.S., Simulation of Spray Evaporation Using Pressure and

Ultrasonic AtomizerA Comparative Analysis, TSTU Transactions, 10(2004), 1(in press) Kieviet, F.G, Modeling Quality in Spray Drying, PhD thesis, Endinhoven University of Technology, the Netherlands, 1997 Masters, K., Spray Drying Handbook, Longman Scientific & Technical and John Wiley & Sons, Inc., New York, 1991 Mujumdar, A.S., Drying Research- Current Status and Future Trends, Developments in Chemical

Engineering and Mineral Processing, 10(2002), 3/4, pp.225-246 Sakamon Devahastin, Mujumdars practical guide to industrial drying, Exergex corporation, Canada, 2000