heat and mass transfer in convective drying...
TRANSCRIPT
*Technical University of Civil Engineering Bucharesthttp://www.utcb.ro
Heat and Mass Transfer in Heat and Mass Transfer in Convective Drying Convective Drying
ProcessesProcesses
Camelia GAVRILA* Adrian Gabriel GHIAUS*
Ion GRUIA**
**University of Bucharesthttp://www.unibuc.ro
Presented at the COMSOL Conference 2008 Hannover
• Introduction
• Mathematical modelling of drying processes
• Modelling Results
• Conclusions
CONTENTCONTENT
Transport Phenomena5.11. 2008 2 / 18
• AIM: describe the modelling and simulation of the dehydration
of fruits and vegetables (grapes) in a complex drying system
processes, using COMSOL Multiphysics Program
– simulation of unsteady convective drying of grapes in static bed
conditions
• USE of a dynamic mathematical model, based on
– physical and transport properties
– mass and energy balances.
INTRODUCTIONINTRODUCTION
Transport Phenomena5.11. 2008 3 / 18
The simulation of various product drying systems involves
solving a set of heat and mass transfer equations which
describe:
• heat and moisture exchange between product and air,
• adsorption and desorption rates of heat and moisture
transfer,
• equilibrium relations between product and air,
• psychometrics properties of moist air.
Mathematical modellingMathematical modellingEquation typesEquation types
Transport Phenomena5.11. 2008 4 / 18
• The most rigorous methods of describing the drying process are derived from the concepts of irreversible thermodynamics in which the various fluxes are taken to be directly proportional to the appropriate “potential”, (Ghiaus, 1997).
Mathematical modellingMathematical modellingGeneral Ideas General Ideas -- 11
Transport Phenomena5.11. 2008 6 / 18
Mathematical modellingMathematical modellingGeneral Ideas General Ideas -- 22
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• For most engineering heat transfer calculations performed in
commercial food dehydration, accuracy greater than 2-5 % is
seldom needed.
• This is because errors due to varying or inaccurately
measured boundary conditions such as air temperature and
velocity, would overshadow errors caused by inaccurate
thermal properties.
Mathematical modellingMathematical modellingGeneral Ideas General Ideas -- 33
Transport Phenomena5.11. 2008 9 / 18
• Most thermal property models are empirical rather than
theoretical
- they are based on statistical curve fitting rather than
theoretical derivations involving heat transfer analysis
• The water is treated as a single, uniform component of the
food product. It could be argued that the thermal properties of
water in the food depend on how it is configured or “bound”
within the product.
Where
XX - grape moisture content;
T T - the air temperature;
ρρb b - bulk bed density;
c c - specific heat capacity;
λλ - thermal conductivity;
DDeffeff - effective mass diffusivity.
Mathematical modellingMathematical modellingEquationsEquations
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The mass balance inside the product can be written as:
and the heat-energy balance can be set down as
( )∂ ρ∂
ρ∂∂
bb eff
Xt
div DXz
⋅= ⋅ ⋅⎛
⎝⎜⎞⎠⎟
ρ∂∂
λ∂∂b c
Tt
divTz
⋅ ⋅ = ⋅⎛⎝⎜
⎞⎠⎟
Mathematical modellingMathematical modellingParameters for Corinthian grapesParameters for Corinthian grapes
Transport Phenomena5.11. 2008 10 / 18
691Bulk bed density, ρb [kg/m3]
3.6·10-9Effective diffusion, Deff, [m2/s]
3600Specific heat, c, [J/kg K]
0.5721Thermal conductivity, λ, [W/m K]
75Water content, W, [%]
ValueItem
Results and DiscussionResults and Discussion
Transport Phenomena5.11. 2008 11 / 18
• COMSOL Mutiphysics program is used to simulate the
dehydration of grapes in a complex drying system
processes which correspond to the numerical solution of
these model equations.
• The above system of non-linear Partial Differential
Equations, together with the already described set of initial
and boundary conditions, has been solved by Finite
Elements Method implemented by Comsol Multiphysics 3.4.
Results and DiscussionResults and Discussion
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• Steps:
- Build the geometry of the
model,
-Fix the boundary settings,
the mesh parameters
-Fix the Parameters for
Corinthian grapes
- Compute the final solution.Results from the compute solution in COMSOL Multiphysics
Results and DiscussionResults and DiscussionTemperatureTemperature
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• Evolution of grape temperature during the drying process, at the surface and bottom of the bed and as an average. • Differences of temperature between the base and surface of the bed appear only during the first period of drying, approx. the first 5 hours. After this the bed temperature remains uniform Evolution of grape temperature during
the drying process.
0 5 10 15 20 25 30 35
25
30
35
40
surface of grape bed average bottom of grape bed
Tem
pera
ture
, oC
Time, h
Results and DiscussionResults and DiscussionMoistureMoisture
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• Evolution of grape moisture content at the surface and bottom of the bed and as an average value.
• During the whole process the moisture content of the grapes is uniform within the bed thickness. This is due also to the small thickness of the grape bed.Evolution of grape moisture content
during the drying process.
0 5 10 15 20 25 30 35
0.5
1.0
1.5
2.0
2.5
3.0 surface of grape bed average bottom of grape bed
Moi
sture
con
tent
, kg/
kg-d
b
Time, h
Results and DiscussionResults and DiscussionDrying RateDrying Rate
Transport Phenomena5.11. 2008 15 / 18
• Parameter: drying rate- Represents the rate of evaporated water from one square meter of drying product.
• At the beginning of the process it increases from 0.06 g/s m2 to 0.12 g/s m2 and then has a very small decreasing slope.
• At the end of the process it decreases rapidly.
Drying rate vs. drying time for grape dehydration.
0 5 10 15 20 25 30 35
0.06
0.07
0.08
0.09
0.10
0.11
0.12
0.13
0.14
Dry
ing
rate
, g/s
m2
Time, h
Results and DiscussionResults and DiscussionDDryingrying AAirir TTemperatureemperature
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Drying air temperature at different locations vs. drying time.
0 5 10 15 20 25 30 35
25
30
35
40
45
50
55
60
65
70
preheated exhaust ambient
inlet drying room outlet drying room inlet heat exchanger
Tem
pera
ture
, oC
Time, h
Results and DiscussionResults and DiscussionRRelative elative HHumidityumidity
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Relative humidity of drying air at different locations vs. drying time.
0 5 10 15 20 25 30 3510
20
30
40
50
60
70
inlet heat exchanger preheated inlet drying room
exhaust ambient outlet drying room
Rela
tive
hum
idity
, %
Time, h
CONCLUSIONSCONCLUSIONS
Transport Phenomena5.11. 2008 17 / 18
• We have demonstrated the versatility of COMSOL
Multiphysics with regard to the modelling and simulation of
the dehydration of grapes in a complex drying system
processes.
•The model was applied to the full scale experimental data
with good results.
*Technical University of Civil Engineering Bucharesthttp://www.utcb.ro
Camelia GAVRILA* [email protected] Gabriel GHIAUS* [email protected] GRUIA** [email protected]
**University of Bucharesthttp://www.unibuc.ro
Thank You!