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. Anandharamakrishnananandharamakrishnan@cftri.res.inDr. C. Anandharamakrishnananandharamakrishnan@cftri.res.in