Modeling of the Bread Baking Process Using Moving Boundary and Arbitrary-Lagrangian-Eulerian (ALE) ApproachesApproaches
C. Anandharamakrishnan, N. Chhanwal, P. Karthik,
D Indrani KSMS Ragha araoD. Indrani, KSMS. Raghavarao
Central Food Technological Research Institute, Mysore
Presented at the COMSOL Conference 2010 India
Bread Baking - OverviewBread Baking Overview
Flour, yeast, salt and water
Mixing Molding BakingProoving
Cooling
(i) Evaporation of water
(ii) Volume expansion
(iii) G l ti i ti f t h
B d
(iii) Gelatinization of starch
(iv) Denaturation of protein
(v) Crust formation
2
Bread(v) Crust formation
Experimental Measurement of TemperatureExperimental Measurement of Temperature
90
100
110)
60
70
80
pera
ture
(°C
)
30
40
50
Tem
p
Right side
Center
Pilot-Scale electric heating oven
200 300 600 900 1200 1500
Time (s)
Moving Boundary Problem (MBP) Formulation for Bread BakingMoving Boundary Problem (MBP) Formulation for Bread Baking
Bread can be modelled as a system containing three different regions:
1. Crumb: Wet inner zone, where temperature does not exceed 100°C and dehydration does not occur
regions:
and dehydration does not occur.
2. Crust: Dry outer zone, where temperature increases abovetemperature increases above100°C and dehydration takes place.
3. Evaporation front: Between the Bread
pcrumb and crust, where temperature is 100°C and water evaporates.
Model FramesModel Frames
Control volume is homogeneousControl volume is homogeneous. Energy from oven ambient to bread surface is transferred by
conduction, convection and radiation. The Arbitrary-Lagrangian-Eulerian (ALE) method was applied
to describe movement of mesh during volume expansion. Only liquid diffusion in the crumb and only vapour diffusionOnly liquid diffusion in the crumb and only vapour diffusion
in the crust are assumed to occur. Water evaporates at 100°C. A smoothed Heaviside function replaces the delta function for
defining equivalent thermophysical properties in the Moving Boundary Problem formulation.y
5
Bread Geometry and MeshingBread Geometry and Meshing
13.2 cm
19 cm
Geometry of bread before baking Geometry of bread after baking
Model Development: Step 1- Governing EquationsModel Development: Step 1 Governing Equations
T
Heat Balance Equation:
TktTCp
Boundary conditions:
The heat arriving to the bread surface by convection and radiation is b l d b d ti i id th b dbalanced by conduction inside the bread
Hence,
44)( TTTThTk ss
7
Step 1- Governing EquationsStep 1 Governing Equations
Mass Balance Equation:W WDt
W
Boundary conditions:The water migrating towards the bread surface is balanced by convective flux
)()(( TPTPkWD ssg
y
where,)( ssatws TPaP
)( TPRHP sat
,
8
)( sat
MBP Formulation: Specific HeatMBP Formulation: Specific Heat
)dTTT()]X)(T(X)TT[(C f 113905417921700130 2 )dTTT()]X)(T(X)T.T.[(C ,fwwp 113905417921700130
1.0E+06
1.0E+05/kg.
°C)
1.0E+04cific
Hea
t (J/
1.0E+03
Spec
9
30 50 70 90 110 130 150Temperature (°C)
MBP Formulation: Thermal conductivityMBP Formulation: Thermal conductivity
0.9If T ≤ 100 C
If T > 100 C0.2k(T)
0.2+353.16))-exp(-0.1(T+1
0.9=(T) k
1
1.2
W/m
.K)
0 4
0.6
0.8
Con
duct
ivity
(W
0
0.2
0.4
Ther
mal
C
10
0 20 40 60 80 100 120Temperature (°C)
MBP Formulation: Density and DiffusivityMBP Formulation: Density and Diffusivity
Assuming the dough porosity equal to 75%, an apparent density is
defined as follows (Hamdami et al., 2004):
TTTif.)T( f 61180
TTTif f 31.321
Mass DiffusivityMass Diffusivity
dTTTIfdTTTIf
)T(D V8
10
1046101
11
dTTTIf. V1046
Step 2: MBP Formulation – Water activityStep 2: MBP Formulation Water activity
Change in water activity with respect to temperature and moisture
11
content:
38.01
1)5.50056.0exp(
100),(
T
WWTaw
In the present work, we use the Oswin model (Lind and Rask, 1991)
12
Setup for the volume expansion of bread
Arbitrary Lagrangian-Eulerian (ALE) is a formulation for defining a moving mesh wheredependent variables represent the mesh displacement or mesh velocity.
Setup for the volume expansion of bread
The ALE is an intermediate method between the Lagrangian and the EulerianCombines the best features of both and allow moving boundaries without the need forthe mesh movement to follow the material.
0tx
Ytx
X 2
2
2
2
We propose a following model, where expansion rate is proportional to the temperature of bread
Vn = K*T
where, Vn represents the mesh velocity, K = coefficient of proportionality = 3.5x10-7 m3/K s.
Experimental Validation: Bread TemperatureExperimental Validation: Bread Temperature
6 cm from centre to right side of the bread
Centre of the breadthe bread
100
110
90
100
110
60
70
80
90
erat
ure
(°C
)
60
70
80
90
pera
ture
(°C
)
20
30
40
50
Tem
pe
Experiment-side
Simulation-side
20
30
40
50
Tem
p
Experiment-Center
Simulation-Center
200 300 600 900 1200 1500
Time (s)
200 300 600 900 1200 1500
Time (s)
Volume Expansion with Temperature changesVolume Expansion with Temperature changes
Volume Expansion of Bread During Baking Process With Temperature Profilep g g p
Process time-0 sec
9.8 cmBread height -9.8 cm
60 sec60 sec
10.8 cm10.5 cm
120 sec11 4 cm
11.8 cm
11.4 cm
Volume Expansion of Bread During Baking Process With Temperature Profilep g g p
180 sec
12.4 cm12.36 cm
240 sec
12.8 cm13.15 cm
300 sec
13.1 cm13.15 cm
Experimental Validation of Volume Expansionp p
14
12
13
cm)
11
12
ad H
eigh
t (c
Experimental
9
10
Bre
a
Simulation
80 60 120 180 240 300
Time (s)
Temperature Profile of Bread during Baking Processp g g
100.0
120.0
60 0
80.0
pera
ture
(°C
)
Center
40.0
60.0
Tem
p side point-4cmside point-8cmBottom-2.5cm
20.00 500 1000 1500Time (s)
19
Moisture Content of Bread During Baking Processg g
60 s900 s
300 s1200 s
600 s1500 s
Experimental Validation : Moisture ContentExperimental Validation : Moisture Content
0.4
0.35
g/kg
)
0.3
onte
nt (k
g
0.25
Moi
stur
e c
Experiment-Moisture contentSimulation-Moisture content
0.20 300 600 900 1200 1500
M
Time (s)
Moisture Profile of Bread during Baking Processg g
0.50
g)
0.30
0.40
nten
t (kg
/kg
0.10
0.20M
oist
ure
con
0.000 300 600 900 1200 1500
M
Time (s)
22
Simulation of Starch GelatinizationSimulation of Starch Gelatinization
The Starch gelatinization mechanism during bread baking follows first order kinetics (Zanoni et. al., 1995) ( , )
kt exp1
α - degree of gelatinization, k - reaction rate constant, t – time (s)
RTEkk a
o exp
k can be calculated using Arrhenius equation. k0 - 2.8 x 1018 s-1k0 2.8 x 10 s 1 Ea - 138 kJ/mol (based on DSC experiments)
23
Starch Gelatinization Counters During Bread Baking ProcessStarch Gelatinization Counters During Bread Baking Process
60 s 600 s
300 s 900 s
SummarySummaryA two dimensional model was developed for the bread baking process taking into account of heat and mass transfer processes as well as volume
iexpansion.
Phase change and evaporation-condensation mechanism were incorporated by defining thermo-physical properties of bread as a function of temperature y g p y p p pand moisture content.
Simulation results were validated with experimental measurements of bread temperature and moisture contenttemperature and moisture content.
Occurrence of evaporation-condensation and high value of latent heat of phase change keeps crumb temperature below 100°C.
Linear increase in volume was observed for the first four minutes and volume remains constant for remaining entire baking process. Baking process was completed in 25 minutescompleted in 25 minutes.
AcknowledgmentsAcknowledgments
Council of Scientific and Industrial Research (CSIR) for financial support through Network project for COMSOL software licensing
Department of Science and Technology (DST),Government of India for funding of this work
26
Thank You..Central Food Technological Research Institute, Mysore
Contact:Contact:
27
Dr. C. [email protected]. C. [email protected]
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