Modeling Microwave Heating During Batch Processing of Liquid Sample in
a Single Mode CavityS. Curet1, F. Bellincanta Begnini, O. Rouaud1, L. Boillereaux1
1L’UNAM Université, ONIRIS, CNRS, GEPEA, UMR6144, Nantes, F-44322, France
Model Design
Microwave heating
Simulationresults
Experimentsvs. model
Conclusion/ Perspectives
2
Pin = 50 W
t = 160 s
Model Design
Microwave heating
Simulationresults
Experimentsvs. model
Conclusion/ Perspectives
3
Mesh generation in COMSOL®
• 811 988 tetrahedral elements (440 581 elements for the water sample).
water
Model Design
Microwave heating
Simulationresults
Experimentsvs. model
Conclusion/ Perspectives
4
Governing equations
• Heat transfer equation (HT module)
absp QTkdivt
TC
).(
Thermophysical propertiesof pure water*
Microwave absorbed power (W.m-3)
Resolution of the Maxwell’s equations
* From the COMSOL® material library
Model Design
Microwave heating
Simulationresults
Experimentsvs. model
Conclusion/ Perspectives
5
Governing equations
• Electric field propagation (RF module)
Maxwell’s equations for a TE10 rectangular waveguide (sinusoidal time-varying fields with w = 2p f)
Qabs : volumetric heating rate (W.m-3)
s : Electrical conductivity (S/m)
f : frequency of microwaves (2.45×109 Hz)
e0 : permittivity of free space (F.m-1)
er’’ : relative dielectric loss factor
Elocal: local electric field strength (V.m-1)
000
0
'2
0
1 0 ewwe
se
kwithE
jkE rr
²'.'..2
10 localrabs EQ eew
Model Design
Microwave heating
Simulationresults
Experimentsvs. model
Conclusion/ Perspectives
6
Governing equations
• Fluid flow modeling (CFD module)
Incompressible Navier-Stokes equations
)(
)(0
momentumUPgdt
Ud
continuityz
w
y
v
x
u
UUt
U
dt
Udwith
u, v, w : velocity field components following x, y and z directions
: density of water (kg.m-3)
P: static pressure (Pa)
: dynamic viscosity of water (Pa.s)
Model Design
Microwave heating
Simulationresults
Experimentsvs. model
Conclusion/ Perspectives
7
Governing equations
• Initial & boundary conditions
z
by
y
ax
x
atnEnEnj
xLzLzatn
xzatab
PZEwith
a
xEE
zyxtatE
r
r
sampleair
inTEin
,0
0
0./
,2/,2/0
,4cos
,00
0
0
00
H
HH
wsee
p
wallsboundaryexternalatTThTk
zyxtatTT ,00
interfaces container-liquid0
220,00 00
theatU
mmLwithzyxtatgLPandU
HT
RF
CFD
Model Design
Microwave heating
Simulationresults
Experimentsvs. model
Conclusion/ Perspectives
8
Material properties = f (q °C)
• Dielectric properties of pure water* (2.45 GHz)
* Zhang, Q., T. H. Jackson and A. Ungan. Numerical modeling of microwave induced natural convection. International Journal of Heat and Mass Transfer 43: 2141-2154 (2000).
Model Design
Microwave heating
Simulationresults
Experimentsvs. model
Conclusion/ Perspectives
9
Temperature distribution at t =160 s
q (°C)
At the end of microwave processing, the surface of the water is close to 70 °C while the external temperatures of the walls range from 55 to 60 °C (PTFE is only heated by conduction)
Model Design
Microwave heating
Simulationresults
Experimentsvs. model
Conclusion/ Perspectives
10
v (m/s) q (°C)
waves, Pin = 50W , f=2.45GHz
water
PTFE® support plate
Velocity fields and temperature variations = f (t)
x
z
Model Design
Microwave heating
Simulationresults
Experimentsvs. model
Conclusion/ Perspectives
11
v (m/s)
Cross sections areas of velocity fields
Model Design
Microwave heating
Simulationresults
Experimentsvs. model
Conclusion/ Perspectives
12
Cross sections areas of velocity fieldsat t = 160 s
At the end of processing, the gravitationally driven flow of water leads to max velocity gradients around ≈ 6 mm/s
v (m/s)
Model Design
Microwave heating
Simulationresults
Experimentsvs. model
Conclusion/ Perspectives
13
Cross sections areas of temperature and electric field shape at t = 80 s
q (°C)
E/ E0
The hot spots are depicted at the near bottom zone of the liquid-container interface
Model Design
Microwave heating
Simulationresults
Experimentsvs. model
Conclusion/ Perspectives
14
Experimental validation of numerical results
fairly good agreement between exp. vs. numerical modelAs Gr* ↗, microwave induced natural convection ↗ as a function
of processing time
k
QLgGr abs
2
52*
T1, T2 and T3:2 mm, 5 mm and 10 mm below the upper water surface
- 2 mm- 5 mm- 10 mm
Model Design
Microwave heating
Simulationresults
Experimentsvs. model
Conclusion/ Perspectives
15
Highlights
• « Modeling microwave heating of a liquid sample in a static configuration »:
Non uniform inner temperature distribution within a small liquid sample (8.5 mL)
Modeling enables to locate precisely the hot spots.
The Navier-Stokes equations must be coupled to the heat transfer and the Maxwell’s equations in order to give realistic results.
High computational resources are needed for a strong coupling between the differential equations.
Model Design
Microwave heating
Simulationresults
Experimentsvs. model
Conclusion/ Perspectives
16
Future prospects
• Extension of this preliminary study to investigate the development of microwave applicators dedicated to liquid phase processing under continuous flows.
Thank you for your attention,
