pore scale modeling

Thermal Process EngineeringOtto-von-Guericke-University Magdeburg

Germany

DFG Graduiertenkolleg 828„Micro-Macro-Interactions in Structured Media and

Particle Systems“

V. K. Surasani, T. Metzger, E. Tsotsas

INFLUENCE OF HEAT TRANSFER ON THE DRYING OF POROUS MEDIA.– PORE SCALE MODELING

DFG

GKMM-Work Shop, Helmstedt

‘Influence of heat transfer on drying of porous media.- Pore scale modeling’ , Surasani, Metzger, Tsotsas, GKMM Work Shop, Helmstedt

Drying of porous materials Examples and advantages of drying

PlasticsCoffee

Introduction

Food Wood

• To prevent Microbiological Activities.• <10-12% moisture preserve inherent quality, prevent breakage during transportation and grading.

• For quality processing of plastics.• To prevent material inconsistencies in the end-product.

• Retaining the taste, appearance, and nutritive value of fresh food. • Better than canning and freezing for preservation.

• To increase dimensional stability.• <15 % of moisture increases its strength by 50%

1


Introduction

2

• Porous media Solid material with irregularly shaped and positioned pores. Usually, structural properties are averaged over representative volume

Realization of void space

• Geometry

• Mechanism of transport

Introduction

Convection Diffusion and conduction. Adsorption . Phase change The coupling of mass and heat transfer

• Continuous models


Introduction

3

Fundamental draw backs in continuous models Transport mechanisms at micro level. Cluster formation (dry and wet patch formations) Effective parameters as functions of liquid saturation (e.g. diffusivity, permeability etc.) Accounts geometry of pore space

• Motivations

Introduction to pore network models


• Overview of presentation

2-D square network data structure (geometry).

Model of heat and mass transfer for convective drying.

Explaining solution method through transport mechanisms.

Simulation results of kinetics and phase and temperature evolutions during drying for mono-modal and bimodal networks.

Comparison between convective and convective and contact heating modes

4


Pore network

Modeling

Consists of throats Connected with nodes (pores) Each pore is associated with a control volume Randomly distributed throat radius

• Geometry

5

Pore

Evaporation

Control volume

Throat

• Assumptions Top surface is open

Air velocity is constant


Modeling

6

Sol

id N

etw

ork

totL

Boundary Layer

1 2 1 3totβLSh= =0.664×Re Sc

δ

BL

δN =

βL

totuLRe =

ν

v,P

Bou

ndar

y La

yer


Sol

id N

etw

ork

v,P

Bou

ndar

y La

yer Convective air at T

Convective air at T

Sol

id N

etw

ork

v,P

Bou

ndar

y La

yer

Contact heating TC =T

a) Convective heating

b) Convective and contact heating

Modeling

7

Heating modes


v,P

Sol

id N

etw

ork

Bou

ndar

y La

yer

totL

8

Modeling

Partially filled pore

Gas pore

Liquid pore

Partially filled throat

Gas throat

Liquid throat

Isolated throat

*

v,i i(P (T ))

v,i(P )

l,i(P )

Pore and throat conditions


Constant total pressure in gas phase. Quasi-steady diffusive vapor transport

during emptying of throat. Liquid transfer due to capillary force. Liquid viscosity is neglected in the model. Local thermal equilibrium between

different phases within control volume Heat transfer only due to conduction.

Non-isothermal model

9

• Vapor mass balance equations2

ij ijA = πr4v,iv

v,ij ijj j v,j

P-PPMδM = A ×ln =0

L RT P-P

For pore network

For boundary layer ijA = LW

Modeling

L

L

w

i j

j

j

j

cvA

ijr

4 4*

ij i j ij jj=1 j=1

g ×(lp -lp ) = g lp vlp ln(P-P ) G LP LP


• Heat transfer equations

Fourier’s law of heat conduction

Enthalpy balance over control volume i

10

Enthalpy of control volume

Thermal conductivities and heat capacities depend on throat saturations

L

L

w

i j

j

j

j

cvA

ijr

i jij cv,ij ij

(T -T )Q = A λ

L

2 2cv,ij ij cv,ij ij s ij ij lA λ =(A - πr )λ + πr S λ

4 42 2

i p i i ij p s ij ij p l1 1

L LV (ρC ) V πr (ρC ) πr S (ρC )

2 2j j

4 lmi

ij v,i ev,ijj=1 j=1

dH= - Q - Δh M

dt

i i p i i refH = V (ρC ) (T -T )

Modeling


• Heat transfer coefficient from analogy between heat and mass transfer

Coupling of heat and mass transfer• Equilibrium vapour pressure at menisci for vapor transfer

• Capillary pressure the menisci

Heat transfer in boundary layer

• From boundary layer theory

surf surfQ = A α (T -T )

*vP (T)

c

2σ(T)P =

r

1

3bλ Pr

α = βδ Sc

11

gP

*vP (T)

lP

Modeling

l g cP = P -P (σ(T))


Solution Method

12

Throat with highest liquid pressure pumps liquid to all remaining

evaporating throats in the same cluster

• Assumptions Quasi-steady empting of throats Capillary forces dominate over viscous forces

Liquid transport

w ij,cm,c mt

ev,ij,c1

ρ VΔt =

M

c,ijP is lowest

Liquid flow

Evaporation

Volume evaporated in time t


m,1Δt

m,3Δt

m,2Δt

m, min m,1 m,2 m,3Δt = min(Δt ,Δt ,Δt )

Cluster labeling and minimum mass transfer time step

13

To know the connectivity of liquid phase, to find menisci for which liquid pressure must be compared for the minimum mass transfer time step tm, min.

Solution Method


Dynamic heat transfer by explicit scheme

By assuming discrete time step

Due to small time steps it will cost lot of computation time

14

4 4i ji

ij ij v,i v,ijj=1 j=1

(T -T )dH= - A λ - Δh M

dt L

4i j' t

i i ij ij v,i ev,ijj=1i p i

(T -T )ΔtT = T + -A λ -Δh M

V (ρc ) L

2p i

tij

j

(ρC ) L Δt <

λmin m,min tΔt = min(Δt ,Δt )

Criteria:

Solution Method


Drying algorithm flow sheet

,c ijP

15

Data Structures, Initial and Boundary Conditions

Solve linear system for vapor transport and compute minimum mass transfer time step t m, min

Cluster Labeling

Calculate temperatures of the network by dynamic explicit method using discrete thermal time step tt.

And choose minimum time step t min

Update phase distribution and temperature field

S>0

stop

yes

no


Operating Conditions and pore networks

Results and conclusion

Initial temperature Tin = 20oC, Convective air Temperature T = 80oCContact heating temperature Tc=80oCThermal conductivity of glass s = 1 W/m/KDensity and heat capacity (Cp)s = 1.7 106 J/m3/K Pore networks

a) Mono-modal Radius distribution 40 2 µm Square lattice (51×51)

b) Bimodal Radius distribution -1 40 2 µm Radius distribution -2 100 5 µm Square lattice (51×51)

16



Comparison between non-isothermal and isothermal model

17

‘Influence of heat transfer on drying of porous media.- Pore scale modeling’ , Surasani, Metzger, Tsotsas, GKMM Work Shop, Helmstedt 17


S = 0.95



S = 0.62

17



S = 0.478

17



S = 0.2

17



Temperature and saturation trends with time scale

18



Number of Clusters forming during drying

19



Influence of pore structure on drying behavior



Isothermal convective flow Non-isothermal convective heating

Phase distribution Phase distribution Temperature field

Saturation S = 0.95

Influence of heat transfer on phase distributions

21





Saturation S = 0.70

21





Saturation S = 0.55

21


Combined convective and contact drying


22


Comparison of drying curves from convective and convective and contact drying.


23


Comparison of drying curves from convective and convective and contact drying.


24


Isothermal convective flow convective heating convective and contact heating

Influence of heat transfer on convective and convective and contact heating

Saturation S = 0.55


25


1. Pore network model including heat transfer is presented

2. The explicit method for dynamic heat transfer and quasi- steady vapor transfer is applied in solving the system.

3. Heat transfer is only due to conduction, heat sinks taken into account.

4. The effect of condensation due to temperature gradients is accounted for partially (heat pipe effect).


Conclusion

Hot cluster

Cold cluster

Future work

1.To include condensation effect completely.

2. Implementing model for different co-ordination number.

3. Application to different types of drying (contact, radiation etc. )

19


THANK YOU

pore scale modeling

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