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Energy optimization of bread baking process undergoing quality constraints
Energy xxx (2016) 1e6
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Energy optimization of bread baking process undergoing quality constraints Davide Papasidero, Sauro Pierucci, Flavio Manenti* Politecnico di Milano, Dipartimento di Chimica, Materiali e Ingegneria Chimica “Giulio Natta”, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
a r t i c l e i n f o
a b s t r a c t
Article history: Received 18 December 2015 Received in revised form 5 April 2016 Accepted 7 June 2016 Available online xxx
International home energy rating regulations are forcing to use efficient cooking equipment and processes towards energy saving and sustainability. For this reason gas ovens are replaced by the electric ones, to get the highest energy rating. Due to this fact, the study of the technologies related to the energy efficiency in cooking is increasingly developing. Indeed, big industries are working to the energy optimization of their processes since decades, while there is still a lot of room in energy optimization of single household appliances. The achievement of a higher efficiency can have a big impact on the society only if the use of modern equipment gets widespread. The combination of several energy sources (e.g. forced convection, irradiation, microwave, etc.) and their optimization is an emerging target for oven manufacturers towards optimal oven design. In this work, an energy consumption analysis and optimization is applied to the case of bread baking. Each source of energy gets the due importance and the process conditions are compared. A basic quality standard is guaranteed by taking into account some quality markers, which are relevant based on a consumer viewpoint. © 2016 Elsevier Ltd. All rights reserved.
Keywords: Energy optimization Bread baking Home appliances Dynamic optimization Food quality
1. Introduction and scopes From the energy viewpoint, food cooking can be seen as a process that often requires energy of different kinds to make the raw material subject to chemical and physical transformations, undergoing specific quality constraints. Quality can be related to different aspects of food consumption, e.g. microbiological safety, food texture, internal and surface color, nutritional value, controlled origin, authenticity, etc. [1]. Energy and exergy analyses are often useful to assess the efficiencies of the production of a certain food, with particular reference to the several steps of conversion starting from the grain cultivation [2] to the food processing [3] and the following waste valorization or disposal [4]. Integration of different technologies can be a solution to achieve energy efficiency. This is particularly effective when the layout of a process or plant can be easily modified without a major technological revision, for instance with the insertion of a new equipment after the analysis of the process streams, as in the case of a cheese production plant presented by Kapustenko, Ulyev [5]. Relevant
* Corresponding author. E-mail address: fl[email protected] (F. Manenti).
examples of strategies for the energy optimization of food plants can include the choice of the appropriate ventilation strategy for a large-scale ripening room [6] as well as the implementation of simple best practices the refrigeration rooms to minimize the process energy consumption, such as an appropriate product distribution, the regular check and maintenance of the machinery and the replacement of the old devices [7]. The integration of plants with renewable energy sources (solar thermal energy, biomass, solar photovoltaic) may be implemented to contribute to substantial energy savings on the daily basis, despite the payback periods can be long and the use of some sources can have a seasonal variability. One of such applications is that proposed by Yildirim and Genc [8], that promoted a milk pasteurization process assisted by geothermal energy to increase the pasteurization capacity and undergoing a relevant process efficiency. In general, food processes often involve heating or cooling, sometimes with phase transitions. Those processes need for a high energy demand [9]. Then, a process optimization can have a considerable impact on savings [10]. On a smaller scale, commercial electric ovens are part of the domestic equipment requiring a huge amount of energy to pursue the mentioned transformation, taking advantage of few technologies such as forced hot air convection, irradiation and, sometimes, microwaves. New technologies to increase the energy efficiency of
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ovens, for instance, pulsed electric fields (PEF) (see application on carrots [11] and apple [12] drying), ohmic heating [13], jet impingement [14] are very promising techniques, which are still under investigation at prototype level, but almost never reached the market due to relative technological issues (e.g. production cost). For this reason, while many researchers are focusing on the new technologies, some are more interested in optimizing the food processes based on the consolidated technologies, usually taking into consideration the oven design step to achieve the best thermal performances [15,16]. The optimization procedure of an existing oven towards the simple implementation of control algorithms, instead of modifying the oven layout, could involve the assessment of the energy demand of food and of the related process [17], belonging to a combination of energy sources as optimization variables. To do so, a possible approach is that of considering this assessment and the related optimization to be subject to selected quality constraints, based on a specific application, i.e. bread baking, and taking advantage of an appropriate model, validated on experimental data in a previous paper from the authors [18]. The quality parameters related to the constraints can be identified from the topic-related literature to take into account the effects of the process to the product [19]. While the study of consolidated energy sources application, as well as the choice of a single bakery product, could seem limited, the presented approach could be easily extended to the new heating technologies and to different food kinds (see for instance ~ i and Salvadori [20] for a multi-objective optithe paper from Gon mization of roast beef cooking, also modeled by the authors of this paper [21]) by assessing on one hand the related impact, on the other hand the specific quality constraints based on markers identification [22].
2. Model assumptions and equations The bread baking process is here described considering the following assumptions: Bread volume is considered constant during the process Bread is treated as homogenized multiphase medium [23] (i.e. separate mass balances are present for liquid water and water vapor) Thermal properties are calculated based on a mixture approach taking into account food macro-composition (water, fibers, fats, carbohydrates, proteins) [24]. Evaporation can occur in the whole bread volume when the local temperature exceeds 100 C. This phenomenon is taken into account by directly coupling mass and thermal balances, meaning that a plateau phase is locally reached at 100 C until all the available water is evaporated (generally experimentally well-acquainted, e.g. Ref. [25]). Two numerical step functions are applied to activate/inactivate the evaporation term in the balances, as function of temperature and water availability. Water diffusion is only dependent on a concentration gradient by considering an effective diffusivity. The process conditions are accounted by the introduction of a convection heat exchange coefficient and of an irradiation term to be used in the boundary condition for the thermal balance. The resulting model equations are: l vCw
vt
l ¼ kT kC ð Iv Þ þ V$ Dlw VCw
v vCw v þ V$ Dvw VCw ¼ kT kC Iv vt
rcp
vT þ V$ðlVTÞ ¼ kT kC Iv Hev vt
(3)
The first and the second equations represent the liquid water and the water vapor mass balances, while the last represents the thermal balance. The parameters kC and kT are step functions to take into account the evaporation condition at temperatures higher than 100 C in presence of liquid water. The boundary conditions are:
nlw $n ¼ 0
(4)
v v Cw;ext nvw $n ¼ Km Cw
(5)
4 T4 Q $n ¼ hðT Tair Þ þ sε Tcoil
(6)
Km represent the vapor mass exchange coefficient, h the heat exchange coefficient, s is the Stefan-Boltzmann constant and ε the emissivity of the bread, supposed to be equal to 0.9. For concision, the initial conditions and the supporting equations to calculate the mixture proprieties are not shown here, but can be found on the original paper.
3. Energy assessment To define an optimization strategy it is essential to define the objective function. In case of energy evaluation and optimization, one could refer to a life cycle assessment (LCA) approach, where the potential impact related to identified energy and material inputs and environmental releases is evaluated, to have a full perspective on the process [26]. Anyway, a simpler application could be founded on the evaluation of the power needed by the product to be opportunely cooked, and a “cooking program” could then be based on the combined use of the specific energy sources, rather than on different global variables, that could require the identification of the geographical origin of the input sources. By the way, both of the approaches can exploit the same (and more) quality constraints, representing a target range that should not be overstep, to fulfill the consumer's acceptability. The authors prefer to focus on the simpler approach, mainly to address the methodology, while they recognize the relevance of the LCA analyses as a powerful tool for the attainment of the same purpose from a more comprehensive perspective [27]. Within this context, the energy input is calculated based on the time integral of the heat flux on the bread surface. Even though this evaluation should be more comprehensively based on the effective consumed energy of the oven, since the focus is more on the energy needed to process the dough to become bread, the calculations are based on the heat absorbed by the bread itself. This assumption is realized through the definition of the heat fluxes and a surface integral. The absorbed energy is then represented by the integral of the heat flux with respect to the bread surface and of the process time. This results to the following expression:
Z
Z
time
surface
Energy ¼ (1)
(2)
JH Toven ; Tsurface ; t dSdt
(7)
In case of volumetric heating terms (e.g. microwave heating), this function would also include the integral over time of that term.
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4. Quality constraints As stated in the previous sections, some quality constraints should account for the acceptability of the product. Among the possible attributes to take into account, two were selected to be representative: surface browning and crumb formation. The first is a consequence of the chemical reactions producing colored compounds from sugars (caramelization, see Ref. [28]) and from sugar and aminoacids interaction (Maillard reaction, see Ref. [29]). It was stated in literature that some compounds coming from that reactions can be referred as color markers. Otherwise, a general approach could describe the surface lightness (the “L” parameter, dimensionless and ranging from 0 to 100, from the standard CIE L*a*b color scale) to be dependent on a kinetic law itself. For this reason, we took into account the use of a first-order kinetic law from a recent paper [30] to describe the lightness dynamics avoiding, for the moment being, the formation of colored chemical compounds:
dL ¼ klight ðLÞ dt
(8)
where klight ¼ klight;0 expðA=TÞ ðmin1 Þ, with klight;0 6 6 ¼ 7:9233 10 þ 2:7397 10 =aw and A ¼ 9:13657 103 þ 49:4738=aw , being aw the water activity. The first part of the activation energy parameter (A) has been increased by 5% with respect to the original value to better take into account the differences from the present case from the literature one. The second attribute, crumb formation, was addressed to be a consequence of the state transitions of the dough in the inner part. Starch gelatinization is potentially representative of this transition. A kinetic law that permit to assess a gelatinization degree (dimensionless) is taken from literature [31]:
da ¼ kgel ðamax aÞ dt
(9)
with kgel ¼ 2:8 1018 expð139; 000=RTÞ ðs1 Þ In this case, a maximum gelatinization degree was considered based on [19], as a function of the dough composition (in term of free sugars, starch, water content and possible water-binding compounds). Obviously, the surface color has a range of acceptability, which ends with dark brown before the bread gets burned. Within this context, an average lightness value is identified and used for calculations, to represent the overall color quality of the bread. On the contrary, the internal crumb formation is given a minimum gelatinization degree condition to get to satisfactory attributes, while the upper bound is considered to be acceptable (the range for quality constraints is given in Table 1).
3
instance the paper from Ref. [33] for a review of innovative strategies of general dynamic optimization and that of [34] for a specific reference to food processes). Among these, the easiest to implement concerns the division of the time domain into discrete intervals, every of which has the possibility to turn convection or irradiation on or off by changing the air and coil temperatures in order to use convection, irradiation or both of them within a selected range of operation. Indeed, this is just a simplification, since the best solution would be achieved by selecting continuous functions instead of discrete stepwise functions, or a high number of discrete, piecewise functions. Within this context, the authors chose to apply this simplified approach to get a reasonable result without relevant calculation times, since every step of the model solution could need few minutes. Due to these considerations, the optimization strategy will consist in the following steps: 1. The time domain is divided into N intervals of the same size. 2. An initial set of temperatures, Tconv,j and Tirr,j, is selected as the starting values in the N intervals. 3. The model is solved and the objective function at the end of the process is evaluated 4. The variable related to the constraints are analyzed to evaluate the acceptability of the product 5. If the product is acceptable, the procedure is iterated from point number 2 by opportunely changing the temperatures of each interval, until the objective function reaches a minimum. The optimization problem can be then schematized as follows:
8 minE Tirr;j ; Tconv;j > > < s:t: a > 0:65 > > : Lightness2½0:4; 0:6
(10)
The boundaries for the convection and irradiation temperature are listed in Table 2. 6. Model implementation The numerical implementation has been made through the use of the software COMSOL Multiphysics 5.0 [35], enabling the solution of the PDE model with a finite element approach. The optimization is based on the optimization module from the same program and based on N ¼ 4 and 8 equal time intervals of 600 s and 300 s (the total process time is 2400 s). To get a reasonable quick solution, the finite elements mesh for the spatial discretization consists of about 700 elements, with 420 boundary elements and 92 edge elements. The considered geometry is comparable to an Italian bread kind “pagnotta”, approximately consisting of half oblate ellipsoid. The geometry and mesh is represented in Fig. 1.
5. Optimization procedure Bread baking is a batch process, like many other food processes (see for instance [32] for microbial generation of aroma and [15] also related to the bread baking process). Several strategies could be applied to get a reasonable dynamic optimization (see for
Table 2 Boundary values for the optimization variables. Variable
Marker
Lower bound
Upper bound
Units
Tconv,j Tirr,j
Convection air temperature Irradiating coil temperature
120 120
250 250
C C
Table 1 Upper and lower values for the optimization constraints. Attribute
Marker
Lower bound
Upper bound
Units
Average browning Crumb formation
Lightness, L Gelatinization Degree, a
40 0.65
60 e
(Dimensionless) (Dimensionless)
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It is worth underlining that a finer mesh would lead to a better solution in towards process understanding and detail definition. On the other hand, the calculation effort would not suit the optimization purpose. A single iteration for the optimization requires between 3 and 4 min with an Intel™ Core-i7® processor and this leads to a total optimization time of 12 h with about 150 iterations. 7. Results and discussion The base case is represented by a baking process with the same process time (2400 s) and a constant temperature of 180 C in the oven (both for irradiation and air, as shown by Fig. 2. The quality parameters evolution is reported in Fig. 3). It has been compared to the optimized cases to analyze the results. As showed from Figs. 4 and 6, the optimization procedure suggested a higher temperature both for convection and irradiation in the initial phase of the optimized case. In this phase, the dough gets heated but the surface temperature is still not too high to cause browning (as shown from Figs. 5 and 7). Gelatinization, on the other hand, starts at lower temperatures, approaching the requested values in the first half of the baking process. When the surface temperature reaches about 80 C browning phenomena get started, the reaching a considerable browning rate at approximately 120 C (first time step, 600 s). To avoid excessive lightness decrease (i.e., browning), the algorithm suggests for a decrease in temperature in the next step. The second part of the process shows a drop in the convection air temperature, indicating that the surface temperature is adequate for browning, but since the gelatinization target is already reached, no need for higher gelatinization degree. In this case, we see a temperature drop for the surface, indicating that while the heat is still penetrating due to the Fourier's law (by thermal conduction) the surface does not need for higher temperatures. In the last time period both of the temperatures lower to minimize the energy transferred to the product. It is possible to suppose that with a different approach that could include the stop of the baking process, one should predict a lower cooking time. In addition, the gelatinization degree shows a decrease in the last part due to the change in the maximum degree associated with a water activity decrease. The energy absorbed by the bread for the optimal solution is 1.40 MJ, with a 20% save with respect to the base case, which leads to an absorbed energy value of 1.75 MJ, In that case the final gelatinization degree is 0.791 and the lightness value is equal to
Fig. 2. Bread and oven temperature profiles (base case).
Fig. 3. Lightness and Gelatinization degree (base case).
Fig. 4. Bread and oven temperature profiles (optimized case, 4 time steps).
66.2 (see Figs. 2 and 4). It is important to consider that this procedure can benefit for the use of many shorter periods to get a discrete profile more similar to a continuous one. For this reason, a simulation with 8 time steps of 300 s was also performed (see Figs. 6 and 7). In this case, the Fig. 1. Mesh and geometry of the bread sample.
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of this approach is that it easily provides new values for the operating conditions to get a lower value for the consumed energy. The optimal condition lead to a lightness degree value equal to the constraint. It is relevant to underline that the gelatinization degree is not in the same situation: from a process viewpoint, both of the quality parameters are driven by temperature, then being relatively correlated despite being one related to surface, the other to the volume. 8. Conclusions and perspectives
Fig. 5. Lightness and Gelatinization degree (optimized case, 4 time steps).
Fig. 6. Bread and oven temperature profiles (optimized case, 8 time steps).
Fig. 7. Lightness and Gelatinization degree (optimized case, 8 time steps).
absorbed energy is 1.395 MJ, slightly lower than the previous case. This indicates that there is still room for optimization with a reduced step size, to approach a continuous temperature profile. Indeed, the optimization could have reached just a local minimum, and further considerations on how to improve the model and the optimization could be made. For the time being, the relevance
The present work shows an approach to optimize the total energy absorbed by the food product, in this case bread, in a batch process with different energy sources. It is worth to underline that this approach does not require any intervention on the equipment mechanical parts and design, only needing a minor update at the control algorithms. This makes the process modification extremely cheap for the equipment (oven) manufacturer. Dealing with the process viewpoint, the optimization shows that the highest temperatures and the most important energy contribution is related to the initial dough heating part, while the final part is more related to achieve the targeted quality and require less energy. In addition, it is worth to mention that a 20% energy saving is a remarkable goal considering that oven cooking is a very widespread practice and that electric ovens are more and more common in the developed world kitchens. Despite large-scale industries are working towards energy efficiency from decades (to increase the profit margin from a best use of its resources) there is still a lot of room for improvement at the household scale. Indeed, the assumptions and simplifications limit the practical applicability of the procedure to real processes, but give some indications on how to proceed for the next steps of the process design. A dynamic optimization procedure that includes continuous temperature profiles rather than a discrete one and that could predict the stop of the process in case of achieved quality targets would be beneficial to get a higher energy saving. The possibility to include a LCA analysis to get a more comprehensive objective function could extend the interest of the purpose, and could be applicable to different food processes. Several other quality parameters can also be taken into account, for instance volume expansion, aroma production, porosity distribution, to quote a few. With the same aim, the color change and gelatinization degree (representing the cooking point) can be detailed with other specific relations, function of the chemical composition. For instance, color change can be related to the development of marker compounds, e.g. hydroxyl-methyl-furfural (HMF) or melanoidins (through absorbance measurements), proven to be related to the browning phenomena. The combined chemical and physical approach is definitely one of the aims of the present research and it is already under development. Nonetheless, a more complex model would lead to a higher computational effort, misleading from a process optimization perspective. Finally, the use of other energy sources can be taken into account, to achieve the main goal of energy efficiency. In any case, different energy sources have impact on the product quality (e.g. microwaves have a great impact on the texture development in matter of bread baking). For this reason, literature and studies on the process-product relationship have to be carefully taken into account or developed, always paying attention on both quality and energy efficiency. Within this context, the increase of few percent points in the energy transformation efficiency can have a huge impact on a global perspective, with effects on the local, regional and trans-regional scale. Acknowledgements The authors acknowledge Michele Corbetta and Francesco Rossi
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Energy optimization of bread baking process undergoing quality constraints Davide Papasidero, Sauro Pierucci, Flavio Manenti* Politecnico di Milano, Dipartimento di Chimica, Materiali e Ingegneria Chimica “Giulio Natta”, Piazza Leonardo da Vinci 32, 20133 Milano, Italy
a r t i c l e i n f o
a b s t r a c t
Article history: Received 18 December 2015 Received in revised form 5 April 2016 Accepted 7 June 2016 Available online xxx
International home energy rating regulations are forcing to use efficient cooking equipment and processes towards energy saving and sustainability. For this reason gas ovens are replaced by the electric ones, to get the highest energy rating. Due to this fact, the study of the technologies related to the energy efficiency in cooking is increasingly developing. Indeed, big industries are working to the energy optimization of their processes since decades, while there is still a lot of room in energy optimization of single household appliances. The achievement of a higher efficiency can have a big impact on the society only if the use of modern equipment gets widespread. The combination of several energy sources (e.g. forced convection, irradiation, microwave, etc.) and their optimization is an emerging target for oven manufacturers towards optimal oven design. In this work, an energy consumption analysis and optimization is applied to the case of bread baking. Each source of energy gets the due importance and the process conditions are compared. A basic quality standard is guaranteed by taking into account some quality markers, which are relevant based on a consumer viewpoint. © 2016 Elsevier Ltd. All rights reserved.
Keywords: Energy optimization Bread baking Home appliances Dynamic optimization Food quality
1. Introduction and scopes From the energy viewpoint, food cooking can be seen as a process that often requires energy of different kinds to make the raw material subject to chemical and physical transformations, undergoing specific quality constraints. Quality can be related to different aspects of food consumption, e.g. microbiological safety, food texture, internal and surface color, nutritional value, controlled origin, authenticity, etc. [1]. Energy and exergy analyses are often useful to assess the efficiencies of the production of a certain food, with particular reference to the several steps of conversion starting from the grain cultivation [2] to the food processing [3] and the following waste valorization or disposal [4]. Integration of different technologies can be a solution to achieve energy efficiency. This is particularly effective when the layout of a process or plant can be easily modified without a major technological revision, for instance with the insertion of a new equipment after the analysis of the process streams, as in the case of a cheese production plant presented by Kapustenko, Ulyev [5]. Relevant
* Corresponding author. E-mail address: fl[email protected] (F. Manenti).
examples of strategies for the energy optimization of food plants can include the choice of the appropriate ventilation strategy for a large-scale ripening room [6] as well as the implementation of simple best practices the refrigeration rooms to minimize the process energy consumption, such as an appropriate product distribution, the regular check and maintenance of the machinery and the replacement of the old devices [7]. The integration of plants with renewable energy sources (solar thermal energy, biomass, solar photovoltaic) may be implemented to contribute to substantial energy savings on the daily basis, despite the payback periods can be long and the use of some sources can have a seasonal variability. One of such applications is that proposed by Yildirim and Genc [8], that promoted a milk pasteurization process assisted by geothermal energy to increase the pasteurization capacity and undergoing a relevant process efficiency. In general, food processes often involve heating or cooling, sometimes with phase transitions. Those processes need for a high energy demand [9]. Then, a process optimization can have a considerable impact on savings [10]. On a smaller scale, commercial electric ovens are part of the domestic equipment requiring a huge amount of energy to pursue the mentioned transformation, taking advantage of few technologies such as forced hot air convection, irradiation and, sometimes, microwaves. New technologies to increase the energy efficiency of
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ovens, for instance, pulsed electric fields (PEF) (see application on carrots [11] and apple [12] drying), ohmic heating [13], jet impingement [14] are very promising techniques, which are still under investigation at prototype level, but almost never reached the market due to relative technological issues (e.g. production cost). For this reason, while many researchers are focusing on the new technologies, some are more interested in optimizing the food processes based on the consolidated technologies, usually taking into consideration the oven design step to achieve the best thermal performances [15,16]. The optimization procedure of an existing oven towards the simple implementation of control algorithms, instead of modifying the oven layout, could involve the assessment of the energy demand of food and of the related process [17], belonging to a combination of energy sources as optimization variables. To do so, a possible approach is that of considering this assessment and the related optimization to be subject to selected quality constraints, based on a specific application, i.e. bread baking, and taking advantage of an appropriate model, validated on experimental data in a previous paper from the authors [18]. The quality parameters related to the constraints can be identified from the topic-related literature to take into account the effects of the process to the product [19]. While the study of consolidated energy sources application, as well as the choice of a single bakery product, could seem limited, the presented approach could be easily extended to the new heating technologies and to different food kinds (see for instance ~ i and Salvadori [20] for a multi-objective optithe paper from Gon mization of roast beef cooking, also modeled by the authors of this paper [21]) by assessing on one hand the related impact, on the other hand the specific quality constraints based on markers identification [22].
2. Model assumptions and equations The bread baking process is here described considering the following assumptions: Bread volume is considered constant during the process Bread is treated as homogenized multiphase medium [23] (i.e. separate mass balances are present for liquid water and water vapor) Thermal properties are calculated based on a mixture approach taking into account food macro-composition (water, fibers, fats, carbohydrates, proteins) [24]. Evaporation can occur in the whole bread volume when the local temperature exceeds 100 C. This phenomenon is taken into account by directly coupling mass and thermal balances, meaning that a plateau phase is locally reached at 100 C until all the available water is evaporated (generally experimentally well-acquainted, e.g. Ref. [25]). Two numerical step functions are applied to activate/inactivate the evaporation term in the balances, as function of temperature and water availability. Water diffusion is only dependent on a concentration gradient by considering an effective diffusivity. The process conditions are accounted by the introduction of a convection heat exchange coefficient and of an irradiation term to be used in the boundary condition for the thermal balance. The resulting model equations are: l vCw
vt
l ¼ kT kC ð Iv Þ þ V$ Dlw VCw
v vCw v þ V$ Dvw VCw ¼ kT kC Iv vt
rcp
vT þ V$ðlVTÞ ¼ kT kC Iv Hev vt
(3)
The first and the second equations represent the liquid water and the water vapor mass balances, while the last represents the thermal balance. The parameters kC and kT are step functions to take into account the evaporation condition at temperatures higher than 100 C in presence of liquid water. The boundary conditions are:
nlw $n ¼ 0
(4)
v v Cw;ext nvw $n ¼ Km Cw
(5)
4 T4 Q $n ¼ hðT Tair Þ þ sε Tcoil
(6)
Km represent the vapor mass exchange coefficient, h the heat exchange coefficient, s is the Stefan-Boltzmann constant and ε the emissivity of the bread, supposed to be equal to 0.9. For concision, the initial conditions and the supporting equations to calculate the mixture proprieties are not shown here, but can be found on the original paper.
3. Energy assessment To define an optimization strategy it is essential to define the objective function. In case of energy evaluation and optimization, one could refer to a life cycle assessment (LCA) approach, where the potential impact related to identified energy and material inputs and environmental releases is evaluated, to have a full perspective on the process [26]. Anyway, a simpler application could be founded on the evaluation of the power needed by the product to be opportunely cooked, and a “cooking program” could then be based on the combined use of the specific energy sources, rather than on different global variables, that could require the identification of the geographical origin of the input sources. By the way, both of the approaches can exploit the same (and more) quality constraints, representing a target range that should not be overstep, to fulfill the consumer's acceptability. The authors prefer to focus on the simpler approach, mainly to address the methodology, while they recognize the relevance of the LCA analyses as a powerful tool for the attainment of the same purpose from a more comprehensive perspective [27]. Within this context, the energy input is calculated based on the time integral of the heat flux on the bread surface. Even though this evaluation should be more comprehensively based on the effective consumed energy of the oven, since the focus is more on the energy needed to process the dough to become bread, the calculations are based on the heat absorbed by the bread itself. This assumption is realized through the definition of the heat fluxes and a surface integral. The absorbed energy is then represented by the integral of the heat flux with respect to the bread surface and of the process time. This results to the following expression:
Z
Z
time
surface
Energy ¼ (1)
(2)
JH Toven ; Tsurface ; t dSdt
(7)
In case of volumetric heating terms (e.g. microwave heating), this function would also include the integral over time of that term.
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4. Quality constraints As stated in the previous sections, some quality constraints should account for the acceptability of the product. Among the possible attributes to take into account, two were selected to be representative: surface browning and crumb formation. The first is a consequence of the chemical reactions producing colored compounds from sugars (caramelization, see Ref. [28]) and from sugar and aminoacids interaction (Maillard reaction, see Ref. [29]). It was stated in literature that some compounds coming from that reactions can be referred as color markers. Otherwise, a general approach could describe the surface lightness (the “L” parameter, dimensionless and ranging from 0 to 100, from the standard CIE L*a*b color scale) to be dependent on a kinetic law itself. For this reason, we took into account the use of a first-order kinetic law from a recent paper [30] to describe the lightness dynamics avoiding, for the moment being, the formation of colored chemical compounds:
dL ¼ klight ðLÞ dt
(8)
where klight ¼ klight;0 expðA=TÞ ðmin1 Þ, with klight;0 6 6 ¼ 7:9233 10 þ 2:7397 10 =aw and A ¼ 9:13657 103 þ 49:4738=aw , being aw the water activity. The first part of the activation energy parameter (A) has been increased by 5% with respect to the original value to better take into account the differences from the present case from the literature one. The second attribute, crumb formation, was addressed to be a consequence of the state transitions of the dough in the inner part. Starch gelatinization is potentially representative of this transition. A kinetic law that permit to assess a gelatinization degree (dimensionless) is taken from literature [31]:
da ¼ kgel ðamax aÞ dt
(9)
with kgel ¼ 2:8 1018 expð139; 000=RTÞ ðs1 Þ In this case, a maximum gelatinization degree was considered based on [19], as a function of the dough composition (in term of free sugars, starch, water content and possible water-binding compounds). Obviously, the surface color has a range of acceptability, which ends with dark brown before the bread gets burned. Within this context, an average lightness value is identified and used for calculations, to represent the overall color quality of the bread. On the contrary, the internal crumb formation is given a minimum gelatinization degree condition to get to satisfactory attributes, while the upper bound is considered to be acceptable (the range for quality constraints is given in Table 1).
3
instance the paper from Ref. [33] for a review of innovative strategies of general dynamic optimization and that of [34] for a specific reference to food processes). Among these, the easiest to implement concerns the division of the time domain into discrete intervals, every of which has the possibility to turn convection or irradiation on or off by changing the air and coil temperatures in order to use convection, irradiation or both of them within a selected range of operation. Indeed, this is just a simplification, since the best solution would be achieved by selecting continuous functions instead of discrete stepwise functions, or a high number of discrete, piecewise functions. Within this context, the authors chose to apply this simplified approach to get a reasonable result without relevant calculation times, since every step of the model solution could need few minutes. Due to these considerations, the optimization strategy will consist in the following steps: 1. The time domain is divided into N intervals of the same size. 2. An initial set of temperatures, Tconv,j and Tirr,j, is selected as the starting values in the N intervals. 3. The model is solved and the objective function at the end of the process is evaluated 4. The variable related to the constraints are analyzed to evaluate the acceptability of the product 5. If the product is acceptable, the procedure is iterated from point number 2 by opportunely changing the temperatures of each interval, until the objective function reaches a minimum. The optimization problem can be then schematized as follows:
8 minE Tirr;j ; Tconv;j > > < s:t: a > 0:65 > > : Lightness2½0:4; 0:6
(10)
The boundaries for the convection and irradiation temperature are listed in Table 2. 6. Model implementation The numerical implementation has been made through the use of the software COMSOL Multiphysics 5.0 [35], enabling the solution of the PDE model with a finite element approach. The optimization is based on the optimization module from the same program and based on N ¼ 4 and 8 equal time intervals of 600 s and 300 s (the total process time is 2400 s). To get a reasonable quick solution, the finite elements mesh for the spatial discretization consists of about 700 elements, with 420 boundary elements and 92 edge elements. The considered geometry is comparable to an Italian bread kind “pagnotta”, approximately consisting of half oblate ellipsoid. The geometry and mesh is represented in Fig. 1.
5. Optimization procedure Bread baking is a batch process, like many other food processes (see for instance [32] for microbial generation of aroma and [15] also related to the bread baking process). Several strategies could be applied to get a reasonable dynamic optimization (see for
Table 2 Boundary values for the optimization variables. Variable
Marker
Lower bound
Upper bound
Units
Tconv,j Tirr,j
Convection air temperature Irradiating coil temperature
120 120
250 250
C C
Table 1 Upper and lower values for the optimization constraints. Attribute
Marker
Lower bound
Upper bound
Units
Average browning Crumb formation
Lightness, L Gelatinization Degree, a
40 0.65
60 e
(Dimensionless) (Dimensionless)
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It is worth underlining that a finer mesh would lead to a better solution in towards process understanding and detail definition. On the other hand, the calculation effort would not suit the optimization purpose. A single iteration for the optimization requires between 3 and 4 min with an Intel™ Core-i7® processor and this leads to a total optimization time of 12 h with about 150 iterations. 7. Results and discussion The base case is represented by a baking process with the same process time (2400 s) and a constant temperature of 180 C in the oven (both for irradiation and air, as shown by Fig. 2. The quality parameters evolution is reported in Fig. 3). It has been compared to the optimized cases to analyze the results. As showed from Figs. 4 and 6, the optimization procedure suggested a higher temperature both for convection and irradiation in the initial phase of the optimized case. In this phase, the dough gets heated but the surface temperature is still not too high to cause browning (as shown from Figs. 5 and 7). Gelatinization, on the other hand, starts at lower temperatures, approaching the requested values in the first half of the baking process. When the surface temperature reaches about 80 C browning phenomena get started, the reaching a considerable browning rate at approximately 120 C (first time step, 600 s). To avoid excessive lightness decrease (i.e., browning), the algorithm suggests for a decrease in temperature in the next step. The second part of the process shows a drop in the convection air temperature, indicating that the surface temperature is adequate for browning, but since the gelatinization target is already reached, no need for higher gelatinization degree. In this case, we see a temperature drop for the surface, indicating that while the heat is still penetrating due to the Fourier's law (by thermal conduction) the surface does not need for higher temperatures. In the last time period both of the temperatures lower to minimize the energy transferred to the product. It is possible to suppose that with a different approach that could include the stop of the baking process, one should predict a lower cooking time. In addition, the gelatinization degree shows a decrease in the last part due to the change in the maximum degree associated with a water activity decrease. The energy absorbed by the bread for the optimal solution is 1.40 MJ, with a 20% save with respect to the base case, which leads to an absorbed energy value of 1.75 MJ, In that case the final gelatinization degree is 0.791 and the lightness value is equal to
Fig. 2. Bread and oven temperature profiles (base case).
Fig. 3. Lightness and Gelatinization degree (base case).
Fig. 4. Bread and oven temperature profiles (optimized case, 4 time steps).
66.2 (see Figs. 2 and 4). It is important to consider that this procedure can benefit for the use of many shorter periods to get a discrete profile more similar to a continuous one. For this reason, a simulation with 8 time steps of 300 s was also performed (see Figs. 6 and 7). In this case, the Fig. 1. Mesh and geometry of the bread sample.
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of this approach is that it easily provides new values for the operating conditions to get a lower value for the consumed energy. The optimal condition lead to a lightness degree value equal to the constraint. It is relevant to underline that the gelatinization degree is not in the same situation: from a process viewpoint, both of the quality parameters are driven by temperature, then being relatively correlated despite being one related to surface, the other to the volume. 8. Conclusions and perspectives
Fig. 5. Lightness and Gelatinization degree (optimized case, 4 time steps).
Fig. 6. Bread and oven temperature profiles (optimized case, 8 time steps).
Fig. 7. Lightness and Gelatinization degree (optimized case, 8 time steps).
absorbed energy is 1.395 MJ, slightly lower than the previous case. This indicates that there is still room for optimization with a reduced step size, to approach a continuous temperature profile. Indeed, the optimization could have reached just a local minimum, and further considerations on how to improve the model and the optimization could be made. For the time being, the relevance
The present work shows an approach to optimize the total energy absorbed by the food product, in this case bread, in a batch process with different energy sources. It is worth to underline that this approach does not require any intervention on the equipment mechanical parts and design, only needing a minor update at the control algorithms. This makes the process modification extremely cheap for the equipment (oven) manufacturer. Dealing with the process viewpoint, the optimization shows that the highest temperatures and the most important energy contribution is related to the initial dough heating part, while the final part is more related to achieve the targeted quality and require less energy. In addition, it is worth to mention that a 20% energy saving is a remarkable goal considering that oven cooking is a very widespread practice and that electric ovens are more and more common in the developed world kitchens. Despite large-scale industries are working towards energy efficiency from decades (to increase the profit margin from a best use of its resources) there is still a lot of room for improvement at the household scale. Indeed, the assumptions and simplifications limit the practical applicability of the procedure to real processes, but give some indications on how to proceed for the next steps of the process design. A dynamic optimization procedure that includes continuous temperature profiles rather than a discrete one and that could predict the stop of the process in case of achieved quality targets would be beneficial to get a higher energy saving. The possibility to include a LCA analysis to get a more comprehensive objective function could extend the interest of the purpose, and could be applicable to different food processes. Several other quality parameters can also be taken into account, for instance volume expansion, aroma production, porosity distribution, to quote a few. With the same aim, the color change and gelatinization degree (representing the cooking point) can be detailed with other specific relations, function of the chemical composition. For instance, color change can be related to the development of marker compounds, e.g. hydroxyl-methyl-furfural (HMF) or melanoidins (through absorbance measurements), proven to be related to the browning phenomena. The combined chemical and physical approach is definitely one of the aims of the present research and it is already under development. Nonetheless, a more complex model would lead to a higher computational effort, misleading from a process optimization perspective. Finally, the use of other energy sources can be taken into account, to achieve the main goal of energy efficiency. In any case, different energy sources have impact on the product quality (e.g. microwaves have a great impact on the texture development in matter of bread baking). For this reason, literature and studies on the process-product relationship have to be carefully taken into account or developed, always paying attention on both quality and energy efficiency. Within this context, the increase of few percent points in the energy transformation efficiency can have a huge impact on a global perspective, with effects on the local, regional and trans-regional scale. Acknowledgements The authors acknowledge Michele Corbetta and Francesco Rossi
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