wittaya julklang, boris golman school of chemical engineering suranaree university of technology...

Wittaya Julklang, Boris GolmanSchool of Chemical Engineering

Suranaree University of Technology

STUDY OF HEAT AND MASS TRANSFER DURING FALLING RATE PERIOD OF SPRAY DRYING OF A SLURRY DROPLET WITH NANOPARTICLES

School of Chemical Engineering

Introduction

1/20 Suranaree University of Technology

Spray drying is used in chemical, agricultural, food, polymer, pharmaceutical, ceramic and mineral processing industries.

•High energy efficiency comparing to other drying methods -atomization of feed slurry to small droplets generates large surface area for both heat and mass transfer

•Flexibility in meeting product requirements -free flowing powder

•Continuous, large-scale operation

• Design of high-quality product

Currently there is a growing interest in application of agglomerate of nanoparticles.

• Design of spray drying equipment

• Optimization of spray drying process

Studying on the drying kinetics of slurry droplet including with nanoparticle is important for


Drying mechanism of a slurry droplet

Suranaree University of Technology2/20

Fig.1 Typical drying behavior of a slurry droplet.

A

B C D

E F

Dro

ple

t Ave

rage

Tem

per

atu

re

Drying Time

A – B : Initial heating upB – C : Constant rate periodC – D – E : Falling rate periodE – F : Final heating

Fig.2 Variation of average droplet temperature with drying time.

ADroplet at initial

temperature

EEnd of drying

FParticle at final

temperature

Heating of droplet up to wet-bulb temperature

Drying with droplet

shrinkage

Drying with crust formation

Increasing thickness of crust layer

BDroplet at wet-bulb

temperature

CDroplet at final

Shrinkage

DDroplet at

crust formation

Sensible heating of dried

particle

3/20

Fig.2 Droplet drying in falling rate period.

Heat balance

Mass balance

cr cow w cr co

T Tdsk k

dt r r

(2)

wvw cr w

CsD M

t r

(3)


Wet core (0 ≤ r ≤ s )

Evaporation interface (r = s)

Suranaree University of Technology

2

2

1 2w w s s co co co

co

Cp Cp T T T

k t r rr

(1)

Temperature distribution

Mathematical model of drying in falling rate period

4/20


Concentration distribution2

2

2wv wv wv

cr

C C C

D t r rr

(5)

Dry crust (s ≤ r ≤ Rin)

Temperature distribution

(4) 2

2

1 2s s cr cr cr

cr

Cp T T T

k t r r r

Agglomerate surface

wvcr m wv gasdC

D k C Cdt

(7)

Heat balance

Mass balance

crcr cr gasdT

k h T Tdt

(6)

Fig.2 Droplet drying in falling rate period.

Mathematical model of drying in falling rate period

Validity of mathematical model



o Good agreement of model calculation results and experimental data for both weight and temperature of a droplet.

Fig.3 Comparison of model calculation results with experimental data.

o Experimental data are taken from : Nesic, J. Vodnik, Kinetics of droplet evaporation, Chemical Engineering Science 46 (1991) 527-537.

Time, [s]0 20 40 60 80

Dim

ensi

onle

ss d

ropl

et w

eigh

t, [-

]

0.0

0.2

0.4

0.6

0.8

1.0

Tem

pera

ture

, [o C

]

0

20

40

60

80

100Experimental droplet weight

Calculated droplet weight

Experimental droplet temperature

Calculated droplet temperature

Results School of Chemical Engineering


• In this work we studied heat and mass transfer both inside and outside of a agglomerated product by variation of following drying parameters:

Air temperature

Air flow rate

Porosity of agglomerated product



o The evaporation interface moves linearly and slowly to center of droplet in the constant rate period.

Drying time, [s]0 10 20 30 40 50 60 70 80

Nor

mal

ized

pos

itio

n of

eva

pora

tion

inte

rfac

e, [

-]

0.0

0.2

0.4

0.6

0.8

1.0

Constant rate period Falling rate period

Moving of evaporation interface

Fig.4 The movement of the evaporation interface with drying time

o The evaporation interface moves rapidly to center of agglomerated product and the moving is not linear.



Variation of air flow rate

Fig.5 Convective heat and mass transfer coefficients with air flow rate

Air flow rate, [m/s]

0.5 1.0 1.5 2.0 2.5 3.0

Con

vect

ive

mas

s tr

ansf

er c

oeff

icie

nt, k

m [

m/s

]

0.1

0.2

0.3

0.4

0.5

Con

vect

ive

heat

tra

nsfe

r co

effi

cien

t, k

h [

W/m

2 K]

100

150

200

250

300

350

400kmkh

o The rates of convective heat and mass transfer rise at high air flow rate

Heat supplied to surface of agglomerate product

Mass transfers from surface of agglomerate product to drying air



o The surface and wet core temperatures increase at high air flow rate

Normalized agglomerate radius, [-]0.0 0.2 0.4 0.6 0.8 1.0

Tem

pera

ture

, [o C

]

55

60

65

70

75

80

85

90

1.00 1.73 2.00

Air flow rate, (m/s)

Dry crust thickness 0.0005 m



o The temperature difference between surface and wet core increases as thickness of dry crust increase

Fig.6 Temperature profile inside the agglomerate at different air flow rate




Fig.7 Concentration of water vapor inside the agglomerate at different air flow rates

Normalized agglomerate radius, [-]

0.0 0.2 0.4 0.6 0.8 1.0

Con

cent

rati

on o

f wat

er v

apor

, [km

ol/m

3 ]

0.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

0.016

1.00 1.73 2.00

Air flow rate, (m/s)Dry crust thickness0.0005 m


o At the same thickness of dry crust the concentration of water vapor inside the dry crust slightly increase at high air flow rate.

o As the thickness of dry crust increases, the accumulation of water vapor inside dry crust rises



Normalized agglomerate radius, [-]

0.0 0.2 0.4 0.6 0.8 1.0

Con

cent

rati

on o

f wat

er v

apor

, [km

ol/m

3 ]

0.000

0.002

0.004

0.006

0.008

0.010

0.012

0.014

0.016

1.00 1.73 2.00

Air flow rate, (m/s)Dry crust thickness0.0005 m



o No difference in water vapor concentration is observed at the agglomerate surface.

Fig.7 Concentration of water vapor inside the agglomerate at different air flow rates



o The agglomerated product is dried more quickly at high air flow rate.

Drying time, [s]

0 10 20 30 40 50

Dim

ensi

onle

ss a

gglo

mer

ate

wei

ght ,

[-]

0.70

0.75

0.80

0.85

0.90

0.95

1.00

1.00 1.73 2.00

Air flow rate, (m/s)


Fig.8 Dimensionless weight of the agglomerate dried at various air flow rates.



Variation of air temperature

Fig.9 Convective heat and mass transfer coefficients with drying air temperature.

o The rates of convective heat and mass transfer rise at high air temperature





o The drying rate of agglomerated product in the falling rate period rise at high air temperature.

Drying time, [s]

0 10 20 30 40

Dim

ensi

onle

ss a

gglo

mer

ated

wei

gh, [

-]

0.70

0.75

0.80

0.85

0.90

0.95

1.00

101150200

Temperature, [oC]

Variation of air temperature

Fig.10 Dimensionless weight of the agglomerate dried at various air flow temperature.



Diameter of agglomerated product, [m]

0.0010 0.0012 0.0014 0.0016 0.0018 0.0020Con

vect

ive

mas

s tr

ansf

er c

oeff

icie

nt, k

m [

m/s

]

0.10

0.11

0.12

0.13

0.14

0.15

0.16

0.17

0.18

Con

vect

ive

heat

tra

nsfe

r co

effi

cien

t, k

h [

W/m

2 K]

100

110

120

130

140

150

160

170

180kmkh

Variation of porosity of agglomerated product

Fig.11 Convective heat and mass transfer coefficients with agglomerated product size.

o The rates of convective heat and mass transfer declines at large size of agglomerated product





o As the porosity of agglomerated product rises, the mass transfer inside the dry crust increases but the heat transfer decreases.

Fig.12 The effective diffusivity and thermal conductivity of dry crust with porosity of agglomerated product


Porosity of agglomerated product, [-]0.0 0.1 0.2 0.3 0.4 0.5 0.6

Eff

ecti

vive

dif

fusi

vity

of

dry

crus

t, D

cr [

m2 /s

]

0.0

5.0e-6

1.0e-5

1.5e-5

2.0e-5

2.5e-5

The

rmal

con

duct

ivit

y of

dry

cru

st, k

cr [

W/m

K]

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

Dcrkcr



o The drying time of low porosity agglomerate is shorter in comparison with loose agglomerate

Drying time, [s]

0 10 20 30 40 50 60

Dim

ensi

onle

ss a

gglo

mer

ate

wei

ght,

[-]

0.6

0.7

0.8

0.9

1.0

0.30.40.5

Porosity

Fig.13 Dimensionless weight of the agglomerate dried at various porosity of agglomerated product.


ConclusionsSchool of Chemical Engineering


Dry crust and wet core temperatures increased with drying time during the falling rate period due to the accumulation of heat in the dry crust

The difference in temperature between the agglomerate surface and the wet core raised with time as a result of heat transfer resistance of the growing crust layer

The accumulation of water vapor in the crust also increased with drying time owing to the enlarging mass transfer resistance

ConclusionsSchool of Chemical Engineering


The rate of mass transfer enhanced at the same position in the crust layer at higher crust temperature.

The drying rate in the falling rate period is governed by the heat and mass transfer resistances both inside and outside the agglomerate

wittaya julklang, boris golman school of chemical engineering suranaree university of technology...

Documents

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rate period of spray

droplet shrinkage

rate period slide

wetbulb temperature

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drying methods atomization

typical drying behavior