Download - 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%
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‘Influence of heat transfer on drying of porous media.- Pore scale modeling’ , Surasani, Metzger, Tsotsas, GKMM Work Shop, Helmstedt
Introduction
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• 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
‘Influence of heat transfer on drying of porous media.- Pore scale modeling’ , Surasani, Metzger, Tsotsas, GKMM Work Shop, Helmstedt
Introduction
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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
‘Influence of heat transfer on drying of porous media.- Pore scale modeling’ , Surasani, Metzger, Tsotsas, GKMM Work Shop, Helmstedt
• 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
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‘Influence of heat transfer on drying of porous media.- Pore scale modeling’ , Surasani, Metzger, Tsotsas, GKMM Work Shop, Helmstedt
Pore network
Modeling
Consists of throats Connected with nodes (pores) Each pore is associated with a control volume Randomly distributed throat radius
• Geometry
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Pore
Evaporation
Control volume
Throat
• Assumptions Top surface is open
Air velocity is constant
‘Influence of heat transfer on drying of porous media.- Pore scale modeling’ , Surasani, Metzger, Tsotsas, GKMM Work Shop, Helmstedt
Modeling
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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
‘Influence of heat transfer on drying of porous media.- Pore scale modeling’ , Surasani, Metzger, Tsotsas, GKMM Work Shop, Helmstedt
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
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Heating modes
‘Influence of heat transfer on drying of porous media.- Pore scale modeling’ , Surasani, Metzger, Tsotsas, GKMM Work Shop, Helmstedt
v,P
Sol
id N
etw
ork
Bou
ndar
y La
yer
totL
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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
‘Influence of heat transfer on drying of porous media.- Pore scale modeling’ , Surasani, Metzger, Tsotsas, GKMM Work Shop, Helmstedt
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
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• 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
‘Influence of heat transfer on drying of porous media.- Pore scale modeling’ , Surasani, Metzger, Tsotsas, GKMM Work Shop, Helmstedt
• Heat transfer equations
Fourier’s law of heat conduction
Enthalpy balance over control volume i
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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
‘Influence of heat transfer on drying of porous media.- Pore scale modeling’ , Surasani, Metzger, Tsotsas, GKMM Work Shop, Helmstedt
• 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
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gP
*vP (T)
lP
Modeling
l g cP = P -P (σ(T))
‘Influence of heat transfer on drying of porous media.- Pore scale modeling’ , Surasani, Metzger, Tsotsas, GKMM Work Shop, Helmstedt
Solution Method
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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
‘Influence of heat transfer on drying of porous media.- Pore scale modeling’ , Surasani, Metzger, Tsotsas, GKMM Work Shop, Helmstedt
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
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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
‘Influence of heat transfer on drying of porous media.- Pore scale modeling’ , Surasani, Metzger, Tsotsas, GKMM Work Shop, Helmstedt
Dynamic heat transfer by explicit scheme
By assuming discrete time step
Due to small time steps it will cost lot of computation time
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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
‘Influence of heat transfer on drying of porous media.- Pore scale modeling’ , Surasani, Metzger, Tsotsas, GKMM Work Shop, Helmstedt
Drying algorithm flow sheet
,c ijP
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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
‘Influence of heat transfer on drying of porous media.- Pore scale modeling’ , Surasani, Metzger, Tsotsas, GKMM Work Shop, Helmstedt
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)
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‘Influence of heat transfer on drying of porous media.- Pore scale modeling’ , Surasani, Metzger, Tsotsas, GKMM Work Shop, Helmstedt
Results and conclusion
Comparison between non-isothermal and isothermal model
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‘Influence of heat transfer on drying of porous media.- Pore scale modeling’ , Surasani, Metzger, Tsotsas, GKMM Work Shop, Helmstedt 17
Results and conclusion
S = 0.95
‘Influence of heat transfer on drying of porous media.- Pore scale modeling’ , Surasani, Metzger, Tsotsas, GKMM Work Shop, Helmstedt
Results and conclusion
S = 0.62
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‘Influence of heat transfer on drying of porous media.- Pore scale modeling’ , Surasani, Metzger, Tsotsas, GKMM Work Shop, Helmstedt
Results and conclusion
S = 0.478
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‘Influence of heat transfer on drying of porous media.- Pore scale modeling’ , Surasani, Metzger, Tsotsas, GKMM Work Shop, Helmstedt
Results and conclusion
S = 0.2
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‘Influence of heat transfer on drying of porous media.- Pore scale modeling’ , Surasani, Metzger, Tsotsas, GKMM Work Shop, Helmstedt
Results and conclusion
Temperature and saturation trends with time scale
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‘Influence of heat transfer on drying of porous media.- Pore scale modeling’ , Surasani, Metzger, Tsotsas, GKMM Work Shop, Helmstedt
Results and conclusion
Number of Clusters forming during drying
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‘Influence of heat transfer on drying of porous media.- Pore scale modeling’ , Surasani, Metzger, Tsotsas, GKMM Work Shop, Helmstedt 20
Results and conclusion
Influence of pore structure on drying behavior
‘Influence of heat transfer on drying of porous media.- Pore scale modeling’ , Surasani, Metzger, Tsotsas, GKMM Work Shop, Helmstedt
Results and conclusion
Isothermal convective flow Non-isothermal convective heating
Phase distribution Phase distribution Temperature field
Saturation S = 0.95
Influence of heat transfer on phase distributions
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‘Influence of heat transfer on drying of porous media.- Pore scale modeling’ , Surasani, Metzger, Tsotsas, GKMM Work Shop, Helmstedt
Results and conclusion
Isothermal convective flow Non-isothermal convective heating
Phase distribution Phase distribution Temperature field
Saturation S = 0.70
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‘Influence of heat transfer on drying of porous media.- Pore scale modeling’ , Surasani, Metzger, Tsotsas, GKMM Work Shop, Helmstedt
Results and conclusion
Isothermal convective flow Non-isothermal convective heating
Phase distribution Phase distribution Temperature field
Saturation S = 0.55
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‘Influence of heat transfer on drying of porous media.- Pore scale modeling’ , Surasani, Metzger, Tsotsas, GKMM Work Shop, Helmstedt
Combined convective and contact drying
Results and conclusion
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‘Influence of heat transfer on drying of porous media.- Pore scale modeling’ , Surasani, Metzger, Tsotsas, GKMM Work Shop, Helmstedt
Comparison of drying curves from convective and convective and contact drying.
Results and conclusion
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‘Influence of heat transfer on drying of porous media.- Pore scale modeling’ , Surasani, Metzger, Tsotsas, GKMM Work Shop, Helmstedt
Comparison of drying curves from convective and convective and contact drying.
Results and conclusion
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‘Influence of heat transfer on drying of porous media.- Pore scale modeling’ , Surasani, Metzger, Tsotsas, GKMM Work Shop, Helmstedt
Isothermal convective flow convective heating convective and contact heating
Influence of heat transfer on convective and convective and contact heating
Saturation S = 0.55
Results and conclusion
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‘Influence of heat transfer on drying of porous media.- Pore scale modeling’ , Surasani, Metzger, Tsotsas, GKMM Work Shop, Helmstedt 26
‘Influence of heat transfer on drying of porous media.- Pore scale modeling’ , Surasani, Metzger, Tsotsas, GKMM Work Shop, Helmstedt 27
‘Influence of heat transfer on drying of porous media.- Pore scale modeling’ , Surasani, Metzger, Tsotsas, GKMM Work Shop, Helmstedt
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).
Results and conclusion
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. )
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‘Influence of heat transfer on drying of porous media.- Pore scale modeling’ , Surasani, Metzger, Tsotsas, GKMM Work Shop, Helmstedt
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