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Modelling of Rotary Dryer

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<strong>Modelling</strong> <strong>of</strong> <strong>Rotary</strong> <strong>Dryer</strong><br />

Dr.ir. W.Jan Coumans, TU Eindhoven<br />

Symposium Ned. Werkgroep Drogen, Utrecht, 20 nov 2008<br />

1<br />

Why modelling <strong>of</strong> dryer<br />

• Design <strong>of</strong> new dryer<br />

• Optimise performance existing dryer<br />

• Scale-up from lab-scale via pilot plant to<br />

full-scale dryer<br />

• No accurate design possible without<br />

experimental work<br />

• <strong>Modelling</strong> may reduce considerably<br />

experimental work<br />

2<br />

1


Purpose <strong>of</strong> <strong>Dryer</strong> Models<br />

• Macro balances models<br />

– Capacity heater, blower<br />

• Scoping models<br />

– Rough size estimates using simple data<br />

• Scaling models<br />

– Overall dimensions<br />

– Performance figures<br />

– Scale-up from lab to full scale<br />

• Detailed models<br />

– As scaling models<br />

– Local drying conditions needed<br />

Increasing<br />

complexity<br />

3<br />

Scientific Approach to <strong>Dryer</strong> Design<br />

4<br />

2


<strong>Rotary</strong> <strong>Dryer</strong> (convective type)<br />

Air<br />

Heater<br />

Feed<br />

Air/Solid<br />

Separator<br />

Product<br />

5<br />

Definition <strong>of</strong> Drying Problem<br />

• Configuration<br />

• Desired specifications / process conditions<br />

• Estimated specifications / process<br />

conditions<br />

• Via macro balances<br />

– Required air rate<br />

– Required heating power<br />

6<br />

3


Phases in <strong>Modelling</strong><br />

• Physical model<br />

• Mathematical model<br />

• Numerical model<br />

• Algoritm<br />

• Programming code (e.g. Matlab)<br />

• Testing<br />

• Experimental input data for model<br />

• Application <strong>of</strong> model<br />

7<br />

Configuration<br />

• No inner drum<br />

• Co-current and Counter-current<br />

• Single pass <strong>of</strong> air and particles<br />

• Indirect heating <strong>of</strong> air (no flue gasses)<br />

• Flights several types possible<br />

(shape, dimensions, number)<br />

8<br />

4


Assumptions at scale <strong>of</strong> dryer<br />

• Stationary condition at any position in dryer<br />

all variables and fluxes are constant in time<br />

• No residence time distribution <strong>of</strong> particles and<br />

air<br />

• Losses <strong>of</strong> heat over dryer wall<br />

• No losses <strong>of</strong> air and product (no leakages)<br />

9<br />

Assumptions at scale <strong>of</strong> particles<br />

• Instationary mass/heat transfer process (by<br />

definition)<br />

• Non-shrinking<br />

• No temperature gradient inside particle<br />

T averaged = T interface<br />

• Drying kinetics Characteristic Drying Curve<br />

• Sorption-isotherm e.g. Halsey’s equation<br />

10<br />

5


Macro Model for <strong>Dryer</strong><br />

Q heater<br />

mass heat<br />

G Y 0<br />

h<br />

G Y 0 Τ g0<br />

fresh<br />

h fresh Τ g,fresh<br />

Air<br />

Q w<br />

G Y final<br />

h final Τ g,final<br />

P X 0<br />

j 0 Τ p0<br />

1 2<br />

Product<br />

P X final<br />

j final Τ P,final<br />

11 Known parameters 15 Unknown parameters<br />

Fresh inlet AIR heater T g,fresh , RH fresh<br />

G , Y fresh , h fresh<br />

Inlet AIR dryer Y 0 , T g0 , h 0<br />

Outlet AIR dryer T g,final<br />

Y final , h final , RH final<br />

FEED P , X 0 , T p0<br />

j 0<br />

PRODUCT X final , ∆X eq, ∆ Teq<br />

T p,final , j final, X eq,final<br />

Heater<br />

Heat losses via wall<br />

η heater<br />

Q heater<br />

f loss<br />

Q w<br />

11<br />

Global Design <strong>of</strong> <strong>Rotary</strong> <strong>Dryer</strong><br />

• Macro model Heater capacity and Air rate<br />

• Air rate + v g,superficial Diameter D<br />

• Ratio L/D Length <strong>of</strong> dryer<br />

• L and D Volume <strong>of</strong> dryer<br />

Other scenarios possible<br />

• Drying kinetics estimated drying time τ<br />

• τ + product rate + volume Holdup<br />

• Drying kinetics = f(material, process conditions )<br />

• Hold-up = f(flights, slope, diam, rpm, friction coeff, .. )<br />

12<br />

6


h 0<br />

Symbols & Units<br />

Q w<br />

h final<br />

Y 0<br />

G<br />

T g<br />

v g<br />

Y<br />

heat<br />

mass<br />

Y final<br />

P<br />

X 0<br />

j 0<br />

v p<br />

0<br />

z<br />

L<br />

• Flows<br />

P = product flow<br />

kg dry solid/s<br />

G = air flow<br />

kg dry air/s<br />

• Moisture content:<br />

X = moisture in product kg w/kg dry solid<br />

Y = moisture in air<br />

kg w/kg dry air<br />

• Enthalpy content:<br />

j = enthalpy content product kJ/kg dry solid<br />

h = enthalpy content air kJ/kg dry air<br />

X<br />

X final<br />

j final<br />

T p<br />

14<br />

13<br />

Equations in Control Volume ∆z<br />

h 0<br />

∆Q w<br />

h final<br />

Y 0<br />

G<br />

T g<br />

v g<br />

q<br />

Y<br />

j w<br />

Y final<br />

P<br />

X 0<br />

T p<br />

v p<br />

0<br />

z z+∆z<br />

L<br />

X<br />

X final<br />

j final<br />

j 0<br />

• Conservation laws<br />

– Dry solid & dry air<br />

– Moisture<br />

– Enthalpy<br />

• Heat & mass transfer<br />

– q is heat flux in kJ/m 2 s<br />

– j w<br />

is mass flux in kg/m 2 s<br />

– coupling q and j w<br />

• Material transport<br />

– Model Friedman & Marshall<br />

– Model Matchett & Baker<br />

• Material properties<br />

– Characteristic drying curve<br />

– Sorption-isotherm<br />

• Psychrometric equations<br />

• Physical properties<br />

7


1. Moisture Balance (stationary)<br />

h 0<br />

∆Q w<br />

h final<br />

Y 0<br />

G<br />

T g<br />

v g<br />

q<br />

Y<br />

j w<br />

Y final<br />

P<br />

X 0<br />

v p<br />

0<br />

z z+∆z<br />

L<br />

X<br />

X final<br />

j final<br />

T p<br />

16<br />

j 0<br />

∆X<br />

∆Y<br />

P ⋅ + G ⋅ =<br />

∆z<br />

∆z<br />

0<br />

15<br />

2. Enthalpy Balance (stationary)<br />

h 0<br />

∆Q w<br />

h final<br />

Y 0<br />

G<br />

T g<br />

v g<br />

q<br />

Y<br />

j w<br />

Y final<br />

P<br />

X 0<br />

j 0<br />

v p<br />

T p X<br />

∆j<br />

∆h<br />

∆Q P ⋅ + G ⋅ + w<br />

= 0<br />

∆z ∆z ∆z<br />

j = cpsTp + X ⋅ cpsTp<br />

∆Q<br />

w<br />

h = cpaTg + Y ( ∆ hv0 + cpdTg<br />

)<br />

0<br />

z z+∆z<br />

L<br />

∆z<br />

( g Tambient<br />

)<br />

= U T −<br />

X final<br />

j final<br />

8


¾. Mass & Heat Transfer Rates<br />

3<br />

dX<br />

− = f ⋅ k<br />

dt<br />

ρ ( Y − Y)<br />

⋅ a<br />

p<br />

f = Φ<br />

m f i s<br />

m 2 /kg ds<br />

DRYING KINETICS<br />

Characteristic Drying Curve (CDC)<br />

X − Xeq<br />

Φ =<br />

Xcr<br />

− Xeq<br />

4<br />

q = α T − T<br />

( )<br />

p h g p<br />

17<br />

X eq and Sorption Isotherm<br />

• Equilibrium Moisture Content X eq at a<br />

given temperature T p and relative humidity<br />

<strong>of</strong> air<br />

• Generally a w =a w (X eq ,T p )<br />

• Numerous equations in literature<br />

• Example: Halsey’s equation<br />

a<br />

w<br />

⎛<br />

= exp⎜<br />

− ⎜<br />

⎝<br />

c<br />

( Xeq<br />

)<br />

m<br />

⎞<br />

⎟<br />

⎟<br />

⎠<br />

c and m are fitting parameters,<br />

and may depend on temperature<br />

18<br />

9


5. Coupling <strong>of</strong> Mass & Heat<br />

Transfer<br />

• Enthalpy-balance over particles in ∆z<br />

• Control ‘volume’ ~ 1 kg dry solids<br />

• Instationairy wet-bulb equation<br />

dX<br />

q ⋅ a = − ⋅ ∆ h +<br />

dj<br />

p s v,T i<br />

14243 1dt<br />

42443 14243 dt<br />

heat enthalpy enthalpy<br />

to for accumulation<br />

particles evaporation in particles<br />

a s = m 2 /kg ds, X = kg w/kg ds, j = kJ/kg ds<br />

19<br />

6. Velocity v p <strong>of</strong> Particles<br />

Model Friedman & Marshall<br />

1<br />

v<br />

p<br />

=<br />

S<br />

d<br />

a<br />

N<br />

0.9<br />

0.6083 G<br />

± ⋅<br />

D d P<br />

p<br />

n f<br />

⎛ ⎞<br />

a = 0.2657 + 0.2322⎜ ⎟<br />

⎝ 12 ⎠<br />

2.304<br />

plus<br />

counter-current<br />

minus co-current<br />

dz<br />

v p =<br />

dt<br />

v<br />

ps<br />

= ps<br />

π<br />

holdup =<br />

2<br />

D ρ<br />

v<br />

bulk<br />

p<br />

4<br />

P<br />

ATTENTION: this model is not consistent with CDC !!!<br />

v<br />

20<br />

10


6. Velocity v p <strong>of</strong> Particles<br />

Model Matchett & Baker-1<br />

21<br />

6. Velocity v p <strong>of</strong> Particles<br />

Model Matchett & Baker-2<br />

v<br />

p<br />

=<br />

Nta<br />

v 1 + v 2<br />

φ<br />

Nt<br />

φ<br />

a<br />

+ 1<br />

This model is consistent with CDC<br />

t<br />

a<br />

1<br />

φ = +<br />

n<br />

h0<br />

∫ θ ⋅ dh<br />

0<br />

( α)<br />

πh<br />

f 0<br />

h 0<br />

∫<br />

2De 0<br />

= ⋅<br />

gcos<br />

sin<br />

h<br />

( )<br />

θ ⋅ dh<br />

0<br />

h is holdup in a single ‘flight’ ……<br />

…which will be a function <strong>of</strong> the rotation angle θ <strong>of</strong> the drum<br />

22<br />

11


Flight Design<br />

segmented<br />

flight<br />

23<br />

Flight holdup (h)<br />

h=F(flight geometry, rotation angle, friction factor)<br />

rectangular<br />

flight<br />

friction factor<br />

tan(φ)<br />

φ θ horizontal<br />

rotation<br />

angle θ<br />

24<br />

12


6. Velocities <strong>of</strong> Particles<br />

Gas Phase and ‘Dense’ Phase<br />

Model Matchett & Baker-3<br />

0 d<br />

1 = 1 + 1<br />

v v v<br />

v<br />

g ⋅ sin( α)<br />

2<br />

0<br />

1 = ⋅ ta<br />

gasfase<br />

d − 4 2.2<br />

µ vgta<br />

1 = ⋅ ⋅ ⋅<br />

ρ<br />

2<br />

pdp<br />

v 7.45 10 Re<br />

Under loaded<br />

Design loaded<br />

v2 = fa<br />

⋅ a ⋅N ⋅D ⋅ tan( α)<br />

f a<br />

corrects for ‘overloaded’ drum<br />

‘dense’ phase<br />

Over loaded<br />

25<br />

numerical and graphical results<br />

Matlab programs and functions<br />

26<br />

13


27<br />

28<br />

14


Air<br />

temperature<br />

Product<br />

temperature<br />

29<br />

Conclusions<br />

Would I recommend you to start<br />

building dryer models<br />

I am curious myself to know which<br />

conclusions I am going to draw!<br />

14 november 2008<br />

30<br />

15

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