Journal of Food Engineering 77 (2006) 500–513
www.elsevier.com/locate/jfoodeng
Modeling, simulation and optimization of a
beer pasteurization tunnel
E. Dilay a, J.V.C. Vargas
b
a,*
, S.C. Amico a, J.C. Ordonez
b
a
Department of Mechanical Engineering, Federal University of Parana, CP 19011, 81531-990, Curitiba/PR, Brazil
Department of Mechanical Engineering and Center for Advanced Power Systems, Florida State University, Tallahassee, FL 32310-6046, USA
Received 28 June 2005
Available online 22 August 2005
Abstract
This paper introduces a general computational model for beer pasteurization tunnels, which could be applied for any pasteurization tunnel in the food industry. A simplified physical model, which combines fundamental and empirical correlations, and principles of classical thermodynamics, and heat transfer, is developed and the resulting three-dimensional differential equations are
discretized in space using a three-dimensional cell centered finite volume scheme. Therefore, the combination of the proposed simplified physical model with the adopted finite volume scheme for the numerical discretization of the differential equations is called a
volume element model, VEM [Vargas, J. V. C., Stanescu, G., Florea, R., & Campos, M. C. (2001). A numerical model to predict the
thermal and psychrometric response of electronic packages. ASME Journal of Electronic Packaging 123(3), 200–210]. The numerical
results of the model were validated by direct comparison with actual temperature experimental data, measured with a mobile temperature recorder traveling within such a tunnel at a brewery company. Next, an optimization study was conducted with the experimentally validated and adjusted mathematical model, determining the optimal geometry for minimum energy consumption by the
tunnel, identifying, as a physical constraint, the total tunnel volume (or mass of material). A parametric analysis investigated the
optimized system response to the variation of total tunnel volume, inlet water temperature, production rate, pipe diameter and insulation layer thickness, from the energetic point of view. It was shown that the optimum tunnel length found is ÔrobustÕ with respect to
the variation of total tunnel volume, combining quality of the final product with minimum energy consumption. The proposed
methodology is shown to allow a coarse converged mesh through the experimental validation of numerical results, therefore combining numerical accuracy with low computational time. As a result, the model is expected to be a useful tool for simulation, design,
and optimization of pasteurization tunnels.
Ó 2005 Elsevier Ltd. All rights reserved.
Keywords: Pasteurization; Mathematical modeling; Volume element model; Optimization
1. Introduction
Through the past decades, the economic and environmental cost of energy has been steadily increasing. Such
growth makes fuel usage and energy efficiency important
*
Corresponding author. Tel.: +55 41 361 3307; fax: +55 41 361
3129.
E-mail addresses: [email protected], [email protected]
(J.V.C. Vargas).
0260-8774/$ - see front matter Ó 2005 Elsevier Ltd. All rights reserved.
doi:10.1016/j.jfoodeng.2005.07.001
factors to be taken into account in the building of new
factories.
In a brewery company, the cost of electric energy and
fuels comprises 20–30% of production costs in the two
stages of bottled beer production, namely: (i) Grain
processing, i.e., unit operations such as clarification,
milling, fermentation and filtration and (ii) Beer packaging, which includes all operations undergone by the glass
bottle, from its receiving, washing, filling up and pasteurization to its secondary packaging and transportation. Among all the equipments, the pasteurization
E. Dilay et al. / Journal of Food Engineering 77 (2006) 500–513
501
Nomenclature
A
c
cp
cv
Dpd
E
f
g
h
h
H
K
k
L
Lb
m
m_
n
nb
nc
nve
Nu
Pb
Pr
Q_
Re
T
~
T
t
tx
u
U
Up
U_ p
v
V
V
W
area, m2
specific heat, J/(kg K)
specific heat at constant pressure, J/(kg K)
specific heat at constant volume, J/(kg K)
pipe diameter, m
energy, J
friction factor
gravity, m/s2
convection heat transfer coefficient, W/m2 °C
wall-averaged heat transfer coefficient, W/
m2 °C, Eq. (11)
tunnel height, m
curve pressure drop coefficient
thermal conductivity, W/m °C
tunnel length, m
bottle height, m
mass, kg
mass flow rate, kg/s
number of volume elements in one tunnel
zone
number of bottles in one volume element
number of curves
total number of volume elements in the
tunnel
average Nusselt number
bottle production rate, bottle/h
Prandt number, m/a
heat transfer rate, W
Reynolds number
temperature, °C
temperature vector, °C
time, s
residence time in a VE, s
horizontal velocity, m/s
global heat transfer coefficient, W/m2 °C
aggregated pasteurization unit, PU
pasteurization unit aggregation rate, PU/min
vertical velocity, m/s
total tunnel volume, m3
pipe cross section average velocity, m/s
tunnel width, m
tunnel deserves most attention since it consists of a great
number of electric pumps, with high steam consumption
in a complex heat regeneration system.
The pasteurization process was invented by the
French scientist Louis Pasteur in 1864, when he demonstrated that wine diseases are caused by micro-organisms that can be killed by heating the wine to 55 °C
for several minutes. The process therefore consists of a
subtle heating of a food product to around 60 °C and
maintenance of this temperature for a few minutes in
W_
x
X
y
power, W
horizontal coordinate, m
fitting parameter in Eq. (11)
vertical coordinate, m
Greek symbols
a
thermal diffusivity, m2/s
d
insulation layer thickness, m
dw
wall thickness, m
Dp
pressure drop, Pa
Dx
volume element length, m
e
tolerance value, Eq. (28)
m
kinematic viscosity, m2/s
q
density, kg/m3
Subscripts
1
external ambient
a
air
b
bottle
be
beer
c
consumption
f
air/water fog
g
glass
i
volume element number
in
input value
ins
insulation material
int
internal
min
minimum
out
output value
p
water pipe
r
water spray
rt
total water spray
s
tunnel cross-section
t
water inside the tank
tot
total
ve
volume element
w
wall
wa
water
wt
water tank wall
z
zone number
order to inactivate or eliminate potentially harmful
micro-organisms. The process stabilizes the product
for a certain period of time, without severe variation
of its organoleptic characteristics.
Pasteurization has been used by the beer industry
since the nineteenth century, remaining practically
unaltered, being carried out on the already bottled
product (in-package pasteurization). Since the 60Õs,
however, with the introduction of pasteurization tunnels, this activity has reached high production levels.
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E. Dilay et al. / Journal of Food Engineering 77 (2006) 500–513
The continuous pasteurization of the product occurs by
means of the traveling of the bottle through the tunnel,
which consists of progressive hotter zones, holding
zones and progressively cooler zones (Engelman & Sani,
1983). The process temperature is controlled by the temperature of the water spray on the bottles inside the tunnel. The tunnel may have as many as eight heating zones
with a system of shell and tube heat exchangers, regeneration and steam water heating.
Factors such as bottle size, shape and material influence the specific processing conditions, such as residence
time within the tunnel, to achieve appropriate results. In
order to monitor the pasteurization process, i.e., to measure the lethal effect of the heat treatment on the microorganisms, the concept of Pasteurization Unit [PU] was
introduced. It was defined that 1 PU is aggregated to the
product when it is exposed to the temperature of 60 °C
for one minute. Additionally, the rate of pasteurization
units aggregated per unit of time (min), U_ p ðT Þ, was tabulated as a function of the temperature, T, the product is
exposed to, which in turn is a function of time, t, in a
pasteurization tunnel (Broderick, 1977). The total number of pasteurization units aggregated to the product in
the pasteurization process is therefore evaluated by
Broderick (1977)
Z ttot
Up ¼
U_ p ðT b Þ dt
ð1Þ
0
where ttot is the total processing time and Tb is the temperature at the center of the bottle, and U_ p ðT b Þ is obtained in this work from an exponential curve fit of
tabulated data (Broderick, 1977) for the range
45 °C 6 Tb 6 65 °C, as follows:
U_ ¼ 2.82 109 e0.32811T b
ð2Þ
p
It is a common practice to aggregate 19 PU to the
product, although 13.7 PU are known to ensure product
stability (Broderick, 1977). Due to operational difficulties related to discontinuities of other equipments in
the production line, the number of PU is considered adequate if kept in the 15–30 PU range. Further heat treatment may cause undesirable side reactions in the
product, altering beer flavor and foam formation (Zufall
& Wackerbauer, 2000).
The modeling of a pasteurization tunnel may be used
to predict the operation status of the pasteurization process, in order to suggest changes to the design, operation, or even for process optimization. The heating
process inside a beer bottle traveling through a pasteurization tunnel was modeled previously by Brandon,
Gardner, Huling, and Staack (1984) who found a considerable axial thermal gradient during the initial heating, and a uniform temperature distribution after that.
Horn, Franke, Blakemore, and Stannek (1997) described a model for the unsteady convective heat transfer inside a bottle, taking into account the influence of
the convective flow on pasteurization and staling effects
and showed that the traditional procedure for determining pasteurization units (PU) can considerably overestimate the actual effect if the reference point is not chosen
accurately regarding bottle size and shape. The author
also suggested that convective transport of micro-organisms and staling effects have to be taken into account
during the design of a tunnel pasteurization plant if
increasing demands on product quality are to be met.
Kumar and Bhattacharya (1991) simulated natural
convection heating of a canned liquid food during sterilization by solving the governing equations of mass,
momentum and energy conservation, using a finite element code. It was found that the can coldest portion
fluctuates in a region around 10–12% of the can height
from its bottom, at a radial distance approximately
half-way between the center of the can and its inner wall.
Tattiyakul, Rao, and Datta (2001), on the other hand,
found a non-uniform temperature distribution with different slowest heating points when modeling heat transfer to a canned corn starch dispersion, where a finite
element based simulation software (FIDAP) was used
to solve the governing mass, momentum and energy
transport equations.
Ghani, Farid, and Chen (2002) carried out a threedimensional analysis of a soup can being heated from
all sides up to 121 °C, where the temperature transient,
the velocity field and the slowest heating zone (SHZ)
during natural convection heating were calculated. In
this case, the partial differential equations describing
mass, momentum and energy were numerically solved
using a commercial software called Phoenics (2005),
which is based on a finite volume method of analysis.
Horizontally laid cans showed slower heating than vertically laid ones due to the enhancement of natural convection caused by the greater height of the latter.
Zheng and Amano (1999) adopted two different approaches to model the pasteurization tunnel: (i) The
Lumped Parameter Method (LPM), which was used to
model the whole pasteurization system, including pipes,
zones and heat exchangers and (ii) The Computational
Fluid Dynamics (CFD) technology to calculate the heat
transfer and fluid flow rates in the heat exchanger tank.
The temperatures of the spray water and the products in
the pasteurization process were calculated and compared reasonably well with the experimental data.
Beck and Watkins (2003) presented a heat and mass
transfer model of sprays of several fluids, including
water, which was based upon an assumed distribution
of the number of drops. With that information, the
drops size distribution was obtained from the solution
of the mass and momentum conservation equations.
Collisions and drag force were accounted for. The heat
transfer problem was solved by applying the energy
equation to the liquid and surrounding air, together
with the ideal gas model. All equations were solved
E. Dilay et al. / Journal of Food Engineering 77 (2006) 500–513
numerically by the finite volume method. The model
also captured the conic sprays behavior and evaporating
sprays.
Rosen and Dincer (2003) reported that the industry
usually conducts energetic analyses, at a macroscopic level, by pinpointing the largest energy consumer component in the plant for a more detailed analysis. For
example, in the case of breweries, the beer pasteurization
tunnel would be selected for a more detailed analysis.
Following that path, the authors developed a methodology for the exergetic and cost analysis of processes and
systems. The analysis was based on the amounts of exergy, cost, energy and mass (EXCEM) involved in the
particular process or system. The work presented a series of applications in engineering processes, such as
power and hydrogen generation, and investigated the
relations between exergy loss and capital cost, and
between exergy and environmental impact.
Sarimveis, Angelou, Retsina, Rutherford, and Bafas
(2003) investigated the utilization of mathematical programming tools to optimize the energy management of
a power generation plant for the paper industry. The
objective was to reach self-sufficiency in electrical power
and steam with the lowest possible cost. The proposed
methodology was based on the development of a detailed mathematical model of the power generation
plant, using balances of mass and energy, and a mathematical formulation from the energy demand contract,
what could be translated into a linear optimization programming problem. The results showed that the method
could be a useful tool for production cost reduction because it minimizes the fuels and electric energy costs.
In sum, the literature review showed that several
studies developed mathematical models for pasteurization processes and specific parts of the process (e.g.,
sprays) ranging from simple to complex. The literature
also shows that energy or exergy based models have
been applied to the analysis and optimization of several
industrial processes and systems. However, no optimization studies were found in the literature for pasteurization tunnels. In that context, the objective of this
study is to develop a simplified mathematical model to
obtain the energetic behavior of a pasteurization tunnel
used for bottled beer production, that is capable of performing a geometric optimization of typical pasteurization tunnels. The energetic analysis comprises the energy
supplied to the equipment via steam and electric energy.
Steam is used for water heating, whereas the pumps that
promote water circulation use electric energy.
2. Mathematical model
Although there are several detailed (and complex)
models to apply for isolated processes within a pasteurization tunnel, two or three dimensional models are usu-
503
ally not suitable for the analysis of the whole system,
because they require the solving of partial differential
equations for the flow simulation for many different flow
configurations and operating parameters. Such models
lead to high cost and computational time even for the
simulation of a few selected cases, what practically discards the possibility of an optimization study.
In an earlier work presented by Vargas, Stanescu,
Florea, and Campos (2001), a general computational
model combining principles of classical thermodynamics
and heat transfer was developed for electronic packages
and the resulting three-dimensional differential equations were discretized in space using a three-dimensional
cell centered finite volume scheme. The combination of
the proposed physical model with the finite volume
scheme was called a volume element model (VEM). This
methodology showed to be accurate enough to capture
the thermal response of the system, and at the same time
requiring low computational time. Therefore, the volume element model methodology was selected to model,
simulate, and optimize the beer pasteurization tunnel in
the present work.
Fig. 1 shows schematically the interactions (mass and
energy flow) between volume elements in a beer pasteurization tunnel. The tunnel zones are divided into n volume elements, each containing three systems: (1) air/
water fog system generated by the spray, (2) mass of
bottles system, and (3) water system, which defines the
portion of the water tank within the specific volume element (VE). System 3 is not shown in Fig. 1, but it is right
below each volume element shown in Fig. 1. For clarity,
system 3 is shown in Fig. 2, which shows how the water
recirculates in each volume element, being collected in
the bottom part of the volume element, in the water tank
and pumped up to the appropriate spray on the top of
each volume element in a predefined zone of the tunnel,
according to the distribution shown in Fig. 3. To each
system, mass and energy conservation equations are
applied, as follows:
2.1. Air/water fog system
Applying the first law of thermodynamics to the air/
water fog system, it follows:
Q_ w;i þ Q_ i þ m_ r;i cwa ðT in;wa T i Þ þ m_ i1 cp;f T i1
m_ i cp;f T i þ m_ iþ1 cp;f T iþ1 m_ i cp;f T i
dT i
ð3Þ
¼ mf cv;f
dt
where Q_ w;i and Q_ i are the heat transfer rate between system 1 and the external environment and between system
1 and the mass of bottles (system 2) within the volume
element Vi, respectively; m_ r;i ; m_ i1 and m_ iþ1 are the water
mass flow rate entering the VE through the spray, the
air/water fog mass flow rate from the preceding VE
504
E. Dilay et al. / Journal of Food Engineering 77 (2006) 500–513
Fig. 1. Schematic diagram of system 1 (air/water fog) and system 2 (mass of bottles), and mass flow rates in each volume element.
Fig. 2. Schematic diagram of system 3 (water).
Fig. 3. Schematic diagram of the water circulation in the entire pasteurization tunnel.
and from the successive one, respectively; m_ i is the air/
water fog mass flow rate exiting the VE to the next,
which is taken by the model as approximately equal to
the air/water fog mass flow rate exiting the VE to the
previous one; cwa, cp,f, and cv,f are the specific heat of
the water, of the air/water fog at constant pressure
and of the air/water fog at constant volume, respectively; mf is the mass of air/water fog in the volume element; Tin,wa is the inlet water temperature; Ti, Ti+1 and
Ti1 are the temperatures of the air/water fog inside the
E. Dilay et al. / Journal of Food Engineering 77 (2006) 500–513
VE ‘‘i’’, inside the next element, and the previous one,
respectively.
The heat transfer rate lost by the VE to the surroundings through the walls is calculated by
Q_ w;i ¼ U w;i Aw;i ðT 1 T i Þ
ð4Þ
where Uw,i is the global heat transfer coefficient between
the air/water fog system and the surroundings through
the walls and T1 is the external ambient temperature.
The calculation of Uw,i is carried out by
1
1
dw
d
1
þ þ
þ
ð5Þ
U w;i ¼
h1 k w k ins hint
where kw is the thermal conductivity of the wall material, dw is the wall thickness, kins is the thermal conductivity of the insulation material, d is the insulation
material thickness; h1 the convection heat transfer coefficient outside the tunnel walls, and hint the convection
heat transfer coefficient between the air/water fog and
the walls. Such variables are assumed as input parameters of the model.
The mass flow rates are evaluated by
m_ i1 þ m_ iþ1 ¼ 2m_ i
As
m_ i ¼ qf ui
2
ð6Þ
ð8Þ
where v represents the air/water fog velocity in the vertical direction, i.e., the direction of the height.
Since oy H and ox Dx, one may write
ui
v
Dx H
) ui vDx
H
ð9Þ
with v being calculated from m_ r;i , for v ffi m_ r;i =ðqwa DxW Þ.
In zone 1, m_ 0 ¼ qa u1 A2s represents the surrounding air
entering the tunnel (following the direction of bottle
movement entering the tunnel) calculated from u1 obtained with Eq. (9), whereas in zone 8, m_ nþ1 ¼ qa un A2s
represents the surrounding air entering the tunnel (in
the opposite direction of bottle exiting the tunnel), also
calculated from un obtained with Eq. (9).
The heat transfer rate between systems 1 and 2 is
given by
Q_ i ¼ hi Ab ðT b;i T i Þ
where Ab is the total external surface area of the mass of
bottles within a VE, and Tb,i is the internal bottle
temperature.
In Eq. (10), the convection heat transfer between the
air/water fog and the mass of bottles, hi, was estimated
as the average convection heat transfer coefficient for a
turbulent boundary layer over a plane wall, h. Therefore, hi is calculated based on a formula presented by
Bejan (1993, Chapter 5) for the calculation of the wall b
averaged Nusselt number NuLb ¼ hL
, for 5 105 6
k wa
8
ReLb 6 10 , and Pr P 0.5, as follows:
hi ¼ h ¼ X
NuLb k wa
Lb
4=5
¼X
0.037Pr1=3 ðReLb 23; 550Þk wa
Lb
ð11Þ
where Pr = 7.0 for water and ReLb ¼ vLb =mwa , with Lb
being the height of the bottle for an isothermal wall condition. As hi is directly related to the heat transfer of the
whole tunnel system and the beer bottle, a fitting X factor was included in the correlation, initially set to 1, and
calibrated in the present work, based on experimental
measurements, by a trial-and-error numerical
procedure.
ð7Þ
where qf is the density of the air/water fog and As is the
vertical cross-section area of the tunnel, defined by the
volume occupied by the air/water fog. For i ¼ 1;
m_ i1 ¼ m_ n (from the previous zone) and for i ¼ n;
m_ iþ1 ¼ m_ 1 (from the next zone).
The horizontal velocity of the air/water fog flow between the volume elements, ui, is estimated by a scale
analysis using the continuity equation for a two-dimensional domain, according to Fig. 1:
ou ov
þ ¼0
ox oy
505
ð10Þ
2.2. Mass of bottles system
The first law of thermodynamics states that
Q_ i ¼ mb;i cb
dT b;i
dt
ð12Þ
for
cb ¼
mg;i cg þ mbe;i cbe
mb;i
ð13Þ
where cb is the bottle specific heat as a function of the
weight average of the specific heat of the casing material
(glass), cg, and of the liquid (beer) inside the bottle, cbe,
considering their respective masses, mg,i and mbe,i, for a
certain VE, in which mb,i = mg,i + mbe,i is the total mass
of the set of bottles in the VE.
2.3. Water system
Applying the first law of thermodynamics to the
water inside the water tank in the volume element, as
shown in Fig. 2, it follows:
Q_ wt;i þ m_ r;i cwa T i m_ wa;i cwa T t;i þ m_ wa;iþ1 cwa T t;iþ1
¼ mt;i cwa
dT t;i
dt
ð14Þ
where Tt,i and Tt,i+1 are the temperatures of the water
inside the tank, in the VE and in the next one, respectively; mt,i is the mass of water inside the tank, in the
VE; m_ wa;iþ1 is the mass flow rate exiting the next VE
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E. Dilay et al. / Journal of Food Engineering 77 (2006) 500–513
and entering the VE. The mass flow rate exiting the VE,
and entering the previous VE, is defined by m_ wa;i ¼
m_ wa;iþ1 þ m_ r;i , with m_ wa;iþ1 ¼ 0 for i = n, i.e., in the last
VE of the zone.
The heat transfer rate between the water inside the
tank, within the boundaries of the VE, and the surroundings, Q_ wt;i , is given by
Q_ wt;i ¼ U wt;i Awt;i ðT 1 T t;i Þ
ð15Þ
where Awt is the wall area bathed by the water inside the
tank, in the VE, in contact with the external ambient
(which is at T1) and Uwt,i is the global heat transfer
coefficient between the water system and the surroundings through the walls, as follows:
1
1
dw
d
1
U wt;i ¼
þ þ
þ
ð16Þ
h1 k w k ins ht;int
where ht,int is the convection heat transfer coefficient between the water inside the tank and the walls. As in Eq.
(5), all variables in Eq. (16) are assumed as input parameters of the model.
For each zone of the tunnel, the mathematical model
is composed by 3n ordinary differential equations defined by Eqs. (3), (12), and (14), with the unknowns
Ti, Tb,i, and Tt,i. That system of equations models the
flow and energy interactions between the systems of a
particular zone of the tunnel. The tunnel is composed
by eight zones, which only differ by the origin of the
spray water. Zones 1, 2, and 3 use the water from the
tanks of zones 8, 7, and 6, respectively; zones 4 and 5
use the water from their own tanks; zones 6, 7, and 8
use the water from tanks 3, 2, and 1, respectively, as
shown in Fig. 3.
Inside a particular VE there is a certain number of
bottles, nb, which is transported through the tunnel by
a step-by-step mechanism, thus nb and Pb, the beer bottle production rate—an operating parameter—are related to the time the bottles remain in a particular VE,
tx, i.e., the residence time in a VE. In an actual beer pasteurization tunnel, the mass of bottles inside a particular
i-VE, after tx has passed, is transferred by means of the
transportation mechanism to the i + 1-VE, and so on,
therefore, the residence time in a VE for a desired bottle
production rate and the total bottle (or set of bottles in
the VE) traveling time in the tunnel are given by
tx ¼ nb =P b
and
P8
ttot ¼ tx nve
ð17Þ
where nve ¼ z¼1 nz is the total number of volume elements within the tunnel.
The mass of bottles enters each VE with an initial temperature Tb,in,i = Tb,i1, remaining inside the
VE for a time tx, then leaving it with a temperature
Tb,out,i = Tb,i. This way, the transient evolution of the
bottles temperature is calculated during its entire traveling time through the pasteurization tunnel.
2.4. Heat transfer rate input
Table 1 shows the controlled inlet water temperatures
for all zones and the calculation of the heat transfer rate
supplied to each zone z, Q_ in;z . The water that comes out
of the water tanks in zones 1, 6, 7 and 8 are not heated
by steam.
In Table 1, the total spray water mass flow rate for a
zone z, m_ rt;z , is also a design parameter which is given by
n
X
ðm_ r;i Þz
ð18Þ
m_ rt;z ¼
i¼1
The total heat transfer rate Q_ in;tot supplied to the tunnel is given by
Q_ in;tot ¼
5
X
½m_ rt cwa ðT in;wa T t;i¼1 Þz
z¼4
þ m_ rt;z¼2 cwa ðT in;wa;z¼2 T t;i¼1;z¼7 Þ
þ m_ rt;z¼3 cwa ðT in;wa;z¼3 T t;i¼1;z¼6 Þ
ð19Þ
The heat transfer rate to the bottles that travel
through the tunnel, Q_ out;b , is given by
ðT b;out T b;in Þ
Q_ out;b ¼ mb cb
ttot
ð20Þ
where mb is the mass of the set of bottles in one VE, Tb,in
and Tb,out are the set of bottles temperature when entering and exiting the tunnel, respectively, and ttot is the total travel time of one bottle (or set of bottles) in a
particular VE through the whole tunnel.
The energy balance for the entire tunnel states that
Q_ in;tot ¼ Q_ out;b þ Q_ 1 ¼ Q_ out;tot
ð21Þ
and by combining Eqs. (4) and (15), Q_ 1 (total heat
transfer rate lost by the tunnel to the external ambient)
is given by
Q_ 1 ¼
8 X
n
X
ðQ_ w;i þ Q_ wt;i Þz
z¼1
ð22Þ
i¼1
Table 1
Modeling parameters of the energetic interactions between tunnel
zones
Zone
Tin,wa (input water
temperature)
Q_ in;z (input heat transfer
rate in zone z)
1
2
Tin,wa,z=1 = Tt,i=1,z=8
Input parameter
Tin,wa,z=2 = 45 °C
Input parameter
Tin,wa,z=3 = 55 °C
Input parameter
Tin,wa,z=4 = 60 °C
Input parameter
Tin,wa,z=5 = 62 °C
Tin,wa,z=6 = Tt,i=1,z=3
Tin,wa,z=7 = Tt,i=1,z=2
Tin,wa,z=8 = Tt,i=1,z=1
Q_ in;1 ¼ 0
Q_ in;2 ¼ m_ rt;z¼2 cwa
ðT in;wa;z¼2 T t;i¼1;z¼7 Þ
Q_ in;3 ¼ m_ rt;z¼3 cwa
ðT in;wa;z¼3 T t;i¼1;z¼6 Þ
Q_ in;4 ¼ m_ rt;z¼4 cwa
ðT in;wa;z¼4 T t;i¼1;z¼4 Þ
Q_ in;5 ¼ m_ rt;z¼5 cwa
ðT in;wa;z¼5 T t;i¼1;z¼5 Þ
Q_ in;6 ¼ 0
Q_ in;7 ¼ 0
Q_ in;8 ¼ 0
3
4
5
6
7
8
E. Dilay et al. / Journal of Food Engineering 77 (2006) 500–513
2.5. Water pumps power
The computation of the power necessary for the eight
circulation pumps is calculated based on the pressure
drop within the set of pipes. The pressure drop within
the water spray feeding pipes was calculated for each
tunnel zone by the pressure drop formula (e.g., Bejan,
1995)
2Lp nc K
2
Dpz ¼ f
þ
ð23Þ
qwa V
2
Dp
where f is the friction factor within the pipes, Dp the pipe
diameter, Lp the total pipe length, nc the number of
curves, K the pressure drop coefficient of each curve,
qwa is the water density, V ¼ m_ rt;z =ðqwa Ap Þ is the water
average velocity in the pipes cross section, and Ap is
the cross section area of the pipes.
The friction factor f is calculated from the Reynolds
number, ReDp , for turbulent flow through smooth ducts,
as follows (e.g., Bejan, 1995):
f ¼
0.0791
1=4
ReDp
ReDp ¼
for 2 103 < ReDp < 2 104
Dp V
mwa
ð24Þ
ð25Þ
where mwa is the water kinematic viscosity.
The necessary power to pump all spray water for a
particular zone, W_ z , and the total pumping power required by the tunnel to operate, W_ tot , are calculated by
(e.g., Fox & McDonald, 1992)
Dp
W_ z ¼ m_ rt;z z
qwa
8
X
W_ tot ¼
W_ z
ð26Þ
ð27Þ
z¼1
3. Numerical method
In order to solve the system of ordinary differential
equations comprising Eqs. (3), (12), and (14), a classical
4th/5th order adaptive time step vectorial Runge–Kutta
method (Kincaid & Cheney, 1991, Chapter 8) was
implemented computationally in Fortran language.
The temperatures Ti, Tb,i, and Tt,i, and the quantities
Up, Tb,max, Q_ in , Q_ out , and W_ tot were the program outputs.
The initial objective of the study was to validate the
numerical results with the tunnel operating at steady
state, and sequentially to use the experimentally validated model to optimize the tunnel configuration. The
numerically computed temperatures Ti, Tb,i, and Tt,i
on steady state were then used to compute Q_ in and
Q_ out through Eqs. (18)–(22). The adopted criterion to
verify that steady state operation was reached, was de-
507
fined by comparing the three systems temperatures (Ti,
Tb,i, and Tt,i) in all volume elements at times t + Dt
and t, where Dt is an appropriate simulation time interval (e.g., Dt = tx). In the model, each system temperature forms a vector with nve positions, to account for
the temperatures of the three systems in a total of nve
volume elements. To accomplish that task, the Euclidean norm of each nve-dimensional temperature vector
was utilized as follows:
k~
T ðt þ DtÞ ~
T ðtÞk=k~
T ðtÞk < e
ð28Þ
where ~
T represents any of the three systems temperature
vector and e is a tolerance value, which was set to 0.001
in the present work.
4. Results and discussion
4.1. Model experimental validation
The first part of the results consisted of the experimental validation of the numerical results obtained with
the model for an existing beer pasteurization tunnel. The
real-time experimental temperature data were obtained
with a mobile temperature recorder in a Ziemann Liess
pasteurization tunnel (model PII 45/330).
The traveling thermograph is a portable equipment
used to evaluate the temperature profile within the bottles. The temperature sensor, a PT100 thermoresistor, is
installed inside an actual beer bottle, which then travels
through the tunnel as a common bottle, recording temperature variation data, later acquired, by a computer.
The geometric characteristics of the modeled pasteurization tunnel where bottle transportation occurs are:
H = 2 m, W = 4 m and L = 33 m. The bottle natural
honeycomb arrangement in the transport belt in each
VE follows the geometry shown in Fig. 4, and the number of bottles in each VE is calculated by
W
1
Db
4L
nb ¼
ð29Þ
cos p6 Db nve
where Db is the bottle diameter.
The pipe parameters used in Eqs. (23)–(27) were obtained from the characteristics of the pasteurization tunnel as given by the supplier. The air/water fog properties
were evaluated for humid air, considering a relative
humidity of 100%. Physical properties of interest of
the fluids and the materials (e.g., glass, steel), and other
input data for the program, were obtained from the literature (Atkins, 1998; Bird, Stewart, & Lightfoot, 2002;
Bejan, 1995; Burmeister, 1993).
The numerical results were obtained for a bottle
external diameter Db = 0.082 m. The tunnel was divided
in volume elements distributed along the 8 zones. Zones
1, 2, 3, 6, and 8 were divided in 8 VE each, zones 4, 5,
508
E. Dilay et al. / Journal of Food Engineering 77 (2006) 500–513
t [min]
0
20
40
60
95
80
70
Tt ≡ T
60
50
T
40
Tb
[o C]
30
Zone 8
Zone 7
Zone 6
Zone 5
Zone 4
Zone 3
10
Zone 2
Zone 1
20
0
0
Fig. 4. Upper view of the geometric distribution of the bottles inside a
volume element.
and 7 were divided in 14, 21, and 7 VE, respectively. A
larger number of volume elements was allocated in the
mesh where the input heat transfer rate is larger. Therefore, the mesh had a total of 82 VE, i.e., nve = 82. Once
the geometry of the tunnel is established (L, W), and a
desired bottle production rate Pb is selected, nb is determined through Eq. (29) and tx, ttot through Eq. (17).
Fig. 5 shows the numerical results obtained with the
computer simulation for the temperatures of the three
systems, i.e., mass of bottles, Tb, air/water fog, T, and
water inside the tank, Tt, as functions of the x position
from the entrance of the pasteurization tunnel. The T
and Tt curves, which are practically coincident, show
the existence of temperature plateaus in each tunnel
zone. On the other hand, the Tb curve, shows that the
bottles temperature increase monotonically up to zone
5, and decrease from zones 6–8, i.e., the model qualitatively captures the actual tunnel behavior.
The integration of Eq. (1), using the temperature
numerical simulation results to obtain the U_ p value from
Eq. (2), produced Up = 45.0 which was not representative of the actual value calculated with the experimentally measured temperatures in the tunnel. Therefore,
the model was adjusted by calibrating the value of the
fitting parameter X in Eq. (11), by a trial-and-error procedure, bringing the numerically obtained Up closer to
the experimental value (Up = 23.5). The result of the
procedure was X = 0.2, such that the numerically computed value of the total number of pasteurization units
aggregated in the beer pasteurization process was
Up = 23.8.
Fig. 6 shows the mass of bottles temperature data obtained with the traveling thermograph, Tb, as a function
of the x position from the entrance of the pasteurization
tunnel. In the same figure it is also shown the mass of
5
10
15
20
x [m]
25
30
35
Fig. 5. Numerical results for the temperatures of the three systems of a
volume element, T, Tt (coincident with T) and Tb, in time and along
the pasteurization tunnel.
x [m]
0
4
8
12
16
20
24
28
32
70
Experimental
Model (X = 1)
Adjusted Model (X = 0.2)
65
60
Tb
[ o C]
55
50
45
40
35
30
0
20
40
60
80
90
t [min]
Fig. 6. Variation of bottle temperature throughout the tunnel as
measured in an actual experiment and as predicted by the model before
and after parameter adjustment.
bottles temperature data obtained with the numerical
simulation before and after model adjustment. It is seen
that the adjusted curve shows an excellent agreement
with the experimental one. In fact, the largest observed
difference between the experimental and calibrated
model curves is of about 4 °C in the 30–40 °C temperature range, being even lower (2 °C) in the range of
most interest to the pasteurization process, 50–60 °C.
Therefore, from this point on, all numerical results are
obtained from the mesh with nve = 82, which is a coarse
converged mesh, mainly considering the size of a pasteurization tunnel.
E. Dilay et al. / Journal of Food Engineering 77 (2006) 500–513
4.2. Optimization
320
An optimization study was carried out to seek the
tunnel optimal configuration for minimum energy consumption. The tunnel total consumed power is evaluated
by the sum of water pumping power, W_ tot , and total heat
transfer rate consumed for water heating, Q_ in;tot
315
E_ c ¼ Q_ in;tot þ W_ tot
W ¼
V
LH
V = 264 m3
310
Ec
[kW]
305
Pb = 71500 bottle / h
300
ð30Þ
65000
295
The design constraint used in the optimization procedure was a fixed mass of material (or fixed volume—V)
for tunnel construction. The tunnel dimensions L and W
in the optimization were varied, whereas, H was kept
constant since it is related to the bottle height. As the total volume, V, and height, H, of the tunnel are fixed,
tunnel dimensions, W and L have a one-to-one relationship given by
509
58500
290
285
0
5
10
15
20
25
L [m]
Fig. 7. Length optimization for a fixed volume of V = 264 m3, for
three different production rates Pb.
ð31Þ
From the point of view of heat transfer, the larger the
tunnel external surface, the larger the heat loss to the
external ambient, i.e., Q_ 1 is proportional to surface
area. The total water pumping power is proportional
to the pressure drop in the water pipes, which is proportional to L and W, i.e., DP = f(L, W). As there is water
circulation between the zones, the longer the distance
between the zones (larger L), the higher the pressure
drop. Following Eq. (31) the increase in L also implies
a decrease in W. On the other hand, for a larger W, a
smaller L will result. So, there must be an optimal set
of tunnel geometric parameters (L,W)opt, such that the
tunnel total consumed power, E_ c , is minimum.
The pasteurization tunnel total volume is V = 264
m3, with water mass flow rates of m_ rt;z ¼ 83.3 kg/s, for
zones z = 1, 2, 3, 6, 7 and 8, m_ rt;z ¼ 288.9 kg/s for zone
z = 4, and m_ rt;z ¼ 233.3 kg/s for zone z = 5, all being
the actual existing tunnel process parameters. The optimum (L, W) pair for minimum E_ c is shown in Fig. 7,
where the tunnel total consumed power is noted for
Lopt 12 m, which corresponds to Wopt 11 m, i.e., a
geometric configuration slightly rectangular is expected
to result in minimum power consumption. For the optimization procedure, in which the total tunnel length was
varied, the zone length versus total tunnel length ratios
were kept as the same as the existing tunnel tested in this
study.
It is also seen in Fig. 7 that the shape of the curves are
not parabolic. Although the pipe distribution within the
tunnel leads to a symmetrical W_ tot curve, the heat loss
through the walls increases with external surface, proportional to L. The combination of these two trends
leads to a slight deformation of curve shape to the right
for all numerically tested production rates, namely,
71,500, 65,000, and 58,500 bottles/h, which is the actual
existing tunnel bottle production rate. Although it is not
shown in Fig. 7, the total power consumption of the
existing tunnel tested in this study (L = 33 m,
W = 4 m) was evaluated with Eq. (30) and the result
was E_ c ¼ 328.6 kW. An inspection of Fig. 7 shows for
the optimized configuration (L,W)opt = (12 m, 11 m)
that E_ c;min ¼ 287.6 kW. Therefore, the optimized tunnel
operating with a bottle production rate of 58,500 bottles/h is expected to consume 12% less power than
the existing tunnel tested in this study.
In Figs. 8 and 9, in which the water mass flow rates
distribution, m_ rt;z , is kept constant and the tunnel volume is, respectively, 10% and 20% lower than the actual
tunnel, a similar trend to Fig. 7 is observed, with a minimum near L 12 m. As the total tunnel volume was
reduced, two other bottle production rates were tested,
namely, 52,000 and 45,500 bottles/h. From the engineering point of view, the most important conclusion of the
analysis of Figs. 7–9 is that the optimum tunnel length
Lopt 12 m is shown to be ÔrobustÕ with respect to
changes in total tunnel volume and bottle production
rate, for 211 m3 6 V 6 264 m3 and 45,500 bottles/
h 6 Pb 6 72,000 bottles/h.
Fig. 10 compiles the results presented in Figs. 7–9, for
a production rate of 58,500 bottles/h, showing the
resulting minimum tunnel total energy consumption,
the pumping power, the supplied heat transfer rate,
and the number of pasteurization unities aggregated to
the product, therefore allowing tunnel optimization
analysis regarding pasteurization unities aggregated to
the product in the bottles. It can be seen that for higher
V values, E_ c;min increases since Q_ in;tot and W_ tot also increase. Most importantly, Fig. 10 also shows that to obtain a value of 22.5 PU, as it is expected from the beer
pasteurization process (Broderick, 1977), a tunnel volume of only 224 m3 is necessary, instead of the current
264 m3 of the existing tunnel analyzed in this study.
Thus, the optimized tunnel could still pasteurize the beer
510
E. Dilay et al. / Journal of Food Engineering 77 (2006) 500–513
consumption reduction of 12%, compared to the existing tunnel tested in this study.
310
V = 237 m3
305
4.3. Parametric analysis
300
Ec
295
[kW]
Pb = 65000 bottle / h
290
58500
285
52000
280
275
0
5
10
15
20
25
L [m]
Fig. 8. Length optimization for a fixed volume of V = 237 m3, for
three different production rates Pb.
300
V = 211 m3
295
290
Ec
285
[kW]
Pb = 58500 bottle / h
280
52000
275
45500
270
265
0
5
10
15
20
25
L [m]
Fig. 9. Length optimization for a fixed volume of V = 211 m3, for
three different production rates Pb.
300
35
E c, min
250
Wtot
30
Wtot
Up
Qin , tot 200
E c, min
[kw]
The parametric analysis described in this section was
carried out using the optimum pair (L,W)opt = (12 m,
11 m) found for V = 264 m3, a fixed spray water mass
flow rates distribution, m_ rt;z , and water pipe diameter
Dp = 150 mm, the latter two taken as the same as in
the actual existing tunnel. The selected parameters were
water pipe diameter, insulation thickness, bottle production rate and inlet spray water temperature of zone 2;
the former two are design parameters whereas the latter
two are operating parameters.
The bottle production rate, Pb, has a direct influence
on the necessary heat transfer rate to produce the desired thermal treatment. Fig. 11 shows the variation of
Up and E_ c;min with respect to Pb. The increase on transport velocity for higher bottle production rates does not
imply extra pumping power, however it causes an increase in the heat absorbed by the tunnel and a decrease
of bottles heat exposure time within the tunnel, leading
to lower values of Up. From Fig. 11, it is noticed that to
achieve, for instance, 20 PU (within the range from 15 to
30 PU) aggregated to the product, the bottle production
rate could be elevated to 72,000 bottles/h, far higher
than 58,500 bottles/h in use by the brewery company
with the existing tunnel tested in this work. However,
such an increase in bottle production rate may not be
achievable due to constraints imposed by other equipments down the production line. Anyway, it is an important finding of this work that the studied pasteurization
tunnel is over-designed for the specified bottle production rate.
The pumping power W_ tot is a function of the water
flow rate m_ rt;z , the pipe diameter and the total pipe
length (considering pipes and valves), which is related
to L and W. For a certain water flow rate, a decrease
25
L opt ≈ 12 m
150
310
[PU]
D p = 150 mm
20
100
E c, min
Q in , tot
50
15
210
220
230
240
250
260
270
V[ m 3 ]
Fig. 10. Variation of minimum power consumption, E_ c;min , and
aggregated pasteurization units, Up with respect to total tunnel
volume, V, for a bottle production rate of Pb = 58500 bottle/h.
[kW]
30
Up
300
295
290
34
(L, W)opt = (12m,11m) 32
305
Pb = 58500 bottle/h
Up
V = 264 m 3
28
Up
26
[PU]
24
E c , min
22
285
58000 60000
20
62000 64000 66000 68000 70000 72000
Pb [ bottle / h ]
according to the recommended value of 22.5 PU, with a
15% smaller volume configuration and a total power
Fig. 11. Variation of Ec,min and the corresponding Up with respect to
bottle production rate, Pg, for Dp = 150 mm.
E. Dilay et al. / Journal of Food Engineering 77 (2006) 500–513
in pipe diameter is responsible for an increase in mean
velocity and ReDp value; this in turn results in an increase
in pressure drop and pumping power. It is possible to
observe from Fig. 12 that Q_ in;tot is practically unaltered
with the variation of Dp, since E_ c;min ðE_ c;min ¼ W_ tot þ
Q_ in;tot Þ and the W_ tot curves remained almost equally
spaced for 120 mm 6 Dp 6 220 mm. The pipe diameter
is also directly related to the pressure drop and the necessary pumping power for tunnel operation. With
Dp = 150 mm, E_ c;min ¼ 292 kW is found from Fig. 12,
whereas for Dp = 200 mm, E_ c;min ¼ 150 kW, a value
50% smaller than the former. Here, a thermoeconomics study is recommended to evaluate if power savings
would compensate the investment on larger diameter
pipes, because there may be space constraints within
the equipment that may discard the use of larger diameter pipes.
Since the tunnel operates in a temperature higher
than the room temperature, there is a heat transfer leak
rate through the exterior walls of the tunnel, which may
be reduced with insulation. Therefore, the parameter
wall insulation was studied by the introduction of an
insulation material (mineral wool) of a certain thickness,
d. Fig. 13 shows that an increase in thickness causes an
expected reduction of heat loss to the external ambient,
Q_ 1 , and consequently, for the same inlet spray water
temperatures, a reduction of heat absorbed by the tunnel Q_ in;tot .
The existing tested tunnel in this study does not use
any insulation (d = 0 mm), but if a 200-mm thick insulation layer is used, Q_ in;tot may be reduced from 55.5 to
50.1 kW. However, such power saving is not so high
compared to total tunnel power consumption E_ c;min ¼
294.5 kW and, again, a thermoeconomics study may
conclude that investment on insulation material may
not be justified by the power saving of about 2% only.
800
(L, W)opt = (12m,11m)
600
Pb = 65000 bottle / h
500
E c, min
400
56
55
( L, W) opt = (12m,11m)
295
54
Pb = 71500 bottle / h
290
53
Qin , tot
[kW]
285
E c , min
52
280
51
275
E c, min
[kW]
270
50
Qin , tot
265
49
260
1000
48
0
200
400
600
800
[ mm ]
Fig. 13. Variation of E_ c;min and Q_ in;tot , with respect to thermal
insulation thickness, d, for a bottle production rate of Pb = 71,500
bottle/h.
The inlet spray water temperatures of zones 2, 3, 4,
and 5 are controlled by independent PID (proportional–integral–derivative) type meshes, and each temperature is set by a digital controller. The behavior of
zones 2 and 3 shows similar characteristics and regenerate heat from zones 7 and 6, respectively. For this reason, it is sufficient to analyze the behavior of one of
those zones with respect to the variation of inlet spray
water temperature. The variation of Q_ in;tot with the inlet
spray water temperature is shown in Fig. 14. Heat regeneration with zone 7 leads to a stabilization effect on
Q_ in;tot since the water of tank 7 returns with an increasingly higher temperature, therefore stabilizing the
Tin,wa,z=2 Tt,i=1,z=7 term that defines Q_ in;tot , as it
was shown previously in Table 1. The Up value increases
exponentially with the spray water temperature, as a result of Eqs. (1) and (2), and depicted in Fig. 14. It is also
important to notice that E_ c;min is equal to the heat transfer rate entering the tunnel plus the pumping power, the
latter being considered not affected by the temperature
(neglecting density and viscosity variations in the
300
E c, min
Q in , tot
E c, min
300
[kW]
200
Wtot
200
150
(L, W)opt = (12m,11m)
32
Pb = 65000 bottle / h
30
Up
28
[PU]
Up
26
100
24
100
Qin , tot
50
140
34
V = 264 m3
E c , min
250
[kW ]
0
120
300
V = 264 m 3
V = 264 m 3
700
Wtot
511
160
180
200
220
D p [mm]
Fig. 12. Total water pumps required power, W_ tot [kW], as a function
of the water pipes diameter, Dp [mm], for a bottle production rate of
Pb = 65,000 bottle/h.
22
20
0
20
30
40
50
60
70
80
Tin ,wa ,z= 2 [ o C]
Fig. 14. Variation Up and Q_ in;tot with respect to the inlet water
temperature of zone 2, Tin,wa,z=2.
512
E. Dilay et al. / Journal of Food Engineering 77 (2006) 500–513
temperature range herein analyzed). Thus, E_ c;min shows a
behavior similar to Q_ in;tot with respect to the variation of
Tin,wa,z = 2.
That analysis shows that spray water temperatures of
zones 2 and 3 have a small influence on the total power
consumption of the tunnel. However they strongly affect
pasteurization unities aggregated to the product. Therefore, the inlet spray water temperatures of zones 2 and 3
are shown to be important operating parameters to control the pasteurization units aggregated to the product.
5. Conclusions
A mathematical model was introduced in this study
to simulate computationally the energetic behavior of
a pasteurization tunnel used in a beer production
process. The numerically calculated bottle temperature curves were compared to actually measured temperatures. The numerical simulation results were then
calibrated by a model adjustment procedure. The experimentally validated model was then utilized to optimize
the geometric configuration of the tunnel and to perform a parametric analysis to investigate the behavior
of the optima found, with respect to several design
and operating parameters.
The total tunnel volume was fixed in the optimization
procedure. This constraint accounts for the finiteness of
available space (or material) to build any pasteurization
tunnel. It was shown that a slightly rectangular tunnel is
the optimum geometric configuration considering total
power consumption, i.e., the sum of heat transfer rate
supplied to the tunnel and water pumping power. It
was also shown that the optimum tunnel length found
is ÔrobustÕ with respect to the variation of total tunnel
volume, combining quality of the final product with
minimum energy consumption.
A parametric analysis demonstrated that water
pumping power may be reduced in 50% (150 kW)
if pipe diameter is increased from 150 to 200 mm and
heat transfer rate supplied to the tunnel may be reduced
in 9.73% (5.4 kW) with the use of a mineral wool insulation layer 200-mm thick. However, a thermoeconomics
study is necessary to check the technical and economical
viability of introducing these design modifications on
the tunnel.
It was also found that the temperature of the zones 2
and 3 have little influence on total power consumption.
However they have a decisive role on beer pasteurization, i.e., the number of aggregated pasteurization unities (PU) to the product.
In fact, it was shown in Fig. 10 that the optimized tunnel which is 15% smaller in volume than the existing
tested tunnel may deliver approximately the same
amount of PU to the product. Additionally, the optimized tunnel built with the same volume (or amount of
material), V = 264 m3, as the existing tested tunnel is
able to reach a bottle production rate of 72,000 bottles/
h, 23% higher than the bottle production rate currently
obtained with the existing tested tunnel in this study, still
aggregating 20.5 PU to the product (Fig. 11).
The pasteurization tunnel numerical simulation and
optimization results provided several design improvement directions to be pursued. In all, if modifications
such as thermal insulation of the tunnel, increase in pipe
diameter and optimization of the tunnel construction
geometry are carried out, a very significant reduction
in the expected total power (electricity and steam) consumption may be achieved with respect to the existing
tunnel tested configuration of this study.
The model can be easily adapted for the analysis of
pasteurization tunnels with distinct characteristics, e.g.,
geometrical configuration. The proposed methodology
is shown to allow a coarse converged mesh through
the experimental validation of numerical results, therefore combining numerical accuracy with low computational time. As a result, the model is expected to be a
useful tool for simulation, design, and optimization of
pasteurization tunnels. Furthermore, the results obtained in this study for a beer pasteurization tunnel
are a good indication that the volume element methodology could be applied efficiently to the simulation, design and optimization of similar macro physical
systems and industrial processes where diverse phenomena, several phases and different equipments are present.
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