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Different Modeling and Simulation Approaches for Food Processing Operations
Different Modeling and Simulation Approaches for Food Processing Operations Cornelia Rauh, Institute of Food Biotechnology and Food Process Engineering, Berlin, Germany; Institute of Fluid Mechanics, Friedrich-Alexander University of Erlangen-Nuremberg, Erlangen, Germany; and Institute of Fluid Mechanics, Friedrich-Alexander University of Erlangen-Nuremberg Campus Busan, Busan, Republic of Korea Antonio Delgado and Jinyoung Park, Institute of Fluid Mechanics, Friedrich-Alexander University of Erlangen-Nuremberg, Erlangen, Germany; and Institute of Fluid Mechanics, Friedrich-Alexander University of Erlangen-Nuremberg Campus Busan, Busan, Republic of Korea Ó 2016 Elsevier Inc. All rights reserved.
Introduction and Basic Considerations Basic Considerations on Food Processing Modeling and Simulation Approaches Balancing Approaches Balancing Approaches for Thermal Processes Considering Pure Time Dependence Balancing Approaches Including Spatiotemporal Effects Knowledge-Oriented Approaches Hybrid Approaches Conclusions and Outlook References
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Introduction and Basic Considerations The term modeling holds different meanings in the scientific literature. Model systems in experiments provide the opportunity for researchers to study the behavior of another system of interest with similar properties. In this article, modeling is defined as the action of theoretical abstraction of the behavior of cause-and-effect chains and the expression of such behavior in mathematical terminology. Since modeling and simulation are very similar in this sense, both terms are often used interchangeably in the literature. In this article, simulation summarizes all algorithms for solving the mathematical models. Data management procedures such as algorithms, data storing, and parallel processing procedures for representation of the behavior of a given system inspired by previously constructed theoretical models are mainly reviewed here. Similar misunderstandings exist regarding the difference between systems and processing. A system may consist of material and nonmaterial components, any physicochemical and biological interactions between these components, and the corresponding storage, while a process consists of transportation and transformation of mass, momentum, and energy. Therefore, modeling and simulation of food processing must include approaches that reflect the conservation of mass, momentum and energy, as well as physical, chemical, and biological reactions. Modeling and simulation have demonstrated to be powerful tools for representing a wide variety of natural and technical processes. Food processing is characterized by both structures with various specific length scales and mechanisms that require different timescales for the physicochemical interactions of the food material of interest. The length scales change from the molecular level to production level by over 10 orders of magnitude. Successful modeling and simulation of food processing first needs the knowledge that food is biomatter, a substance consisting of biotic and abiotic components with diverse levels of thermal, chemical, and biological potentials (Bahadir et al., 2000). The complexity of biomatter as a material makes acquisition of new knowledge on its behavior extremely difficult. In addition, the material components may display different states of aggregation (gaseous, liquid, or solid states) which often leads to soft-matter behavior with high sensitivity to mechanical loads. This article reviews different modeling and simulation methods connected to the complexity of food processing technology and the associated knowledge. Thus, in addition to classical numerical simulation procedures, based on finite discretization procedures, and advanced numerical methods (Lattice Boltzmann Approach) for high-performance computing, statistical, data mining, and cognitive methods (Artificial Neuronal Networks and Fuzzy Logic) are covered. Hybrid methods are also explored for overcoming restrictions of single methods. First, modeling and simulation in connection to the mechanical and thermal effects occurring during the thermal treatment of food, which is currently the most widespread processing method, is considered. Given the well-known restrictions imposed by classical thermal treatment, emerging techniques are geared toward affecting the food matter in a specific way. In most processing scenarios, these technologies should increase the biological and chemical safety of the product (Ananta et al., 2001; Margosch et al., 2004, Kilimann et al., 2006; Odriozola-Serrano, 2013), reduce the impact of the process on the food via general minimal processing, i.e., increasing the quality of the product (Durek et al., 2011), and create new food structures as well as products (Hinrichs, 2000). The most prominent examples of such techniques are the so-called nonthermal treatment
Reference Module in Food Sciences
http://dx.doi.org/10.1016/B978-0-08-100596-5.03229-7
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Different Modeling and Simulation Approaches for Food Processing Operations
methods such as ultrahigh-pressure (UHP) treatment, supercritical fluids, ultrasonic treatment, plasma, and pulsed electric fields (PEF) (Knoerzer et al., 2011). In these processes, food experiences very specific and extreme conditions. Supercritical extraction is utilized for the exceptional physicochemical properties of a solvent fluid that displays the thermodynamic properties of both the gaseous state and the liquid state. Thermodynamic transition between the gas and the liquid states results in a decrease in the solvent’s viscosity and an increase in the diffusion constant as well as material peculiarities. In this context, surface energies drop, and hardly soluble substances can be extracted, even at industrial scale (Eckert et al., 1996; Higashi et al., 2001; Jaeger et al., 2002; Sarrade et al., 2003; Eder et al., 2003; Hu et al., 2011). Processes such as UHP treatment of solid and liquid biomatter, as well as phase transitions at pressures up to several hundreds of MPa, must involve at least one substance capable of flowing. If the biomatter holds this capability, it is often directly compressed or deformed by normal stresses. In other cases, indirect compression via pressure transmitting liquid is performed. In such systems, the product is packaged and separated from the pressurizing medium. One peculiarity of modeling the UHP treatment of food is that, even in liquid components, the nonnegligible effects of compressibility result in the conversion of the mechanical energy provided by the pressure into inner energy. Thermal phenomena also occur during high-pressure processing. For food capable of flowing, these effects induce natural convection driven by temperature heterogeneities or density gradients that are practically unavoidable during food processing. In addition, the natural flow phenomena may interfere with the flow field produced by the movement of a pressurizing piston. It acts directly inside the pressure chamber or outside as part of a pressure transducer system. As a result, modeling and simulation must take thermofluiddynamical effects into consideration. This also applies for modeling and simulating food processing by PEF, another emerging processing technology for preserving liquid foods flowing through a treatment chamber by inactivating spoilage microorganisms and enzymes (Martín-Belloso et al., 2011; Elez-Martínez et al., 2012; Odriozola-Serrano et al., 2013; Krauss et al., 2011). PEF provides an alternative to thermal preservation processes since it maintains the naturalness of the food such as its sensory, nutritional, and functional properties to a higher degree than in processes using thermal energy for inactivation. Regardless of the inactivation mechanism, experiments have shown that the electric field strength and treatment time are the major process parameters. Unwanted temperature increase in the chamber due to dissipative effects induced by the present electric field also plays a crucial role (Lindgren et al., 2002). Thus, the thermofluiddynamic effects directly result from the coupled convective transport of mass, momentum, and thermal energy in the liquid food. Hence, the impact of PEF on the inactivation of food spoilage microorganisms and enzymes in the liquid food can be better understood when the PEF process is modeled and simulated to reveal the spatiotemporal distribution of electric field strength, temperature, and inactivation in the treatment chamber.
Basic Considerations on Food Processing A continuum approach (Baehr and Kabelac, 2006) is postulated in this article. Dimensional variables (marked by *) influencing food processing are the scalar thermodynamic state variables: mass m*, volume V*, specific volume v*, pressure p*, temperature T*, specific internal energy u*, specific entropy s*, specific enthalpy h*, specific free energy f*, and specific free enthalpy g*. For ! a , and also second- and third-order kinematic tensors food capable of flowing, the vector variables, velocity U , and acceleration ! such as Rivlin-Ericksen and Levi-Civita tensors, are used for the calculation of deformations (Spurk, 2004). Furthermore, food capable of flowing can be treated by the basic thermofluiddynamic equations, a system of nonlinear partial differential equations (PDEs) that model both the convective and diffusive transport of matter, momentum, and energy. With these equations, the importance of the transport mechanisms can be assessed experimentally, theoretically, and numerically. Mechanical stresses represent a key quantity in food processing. They appear from forces arising during storage and transportation of food, or they can be applied to create specific structures or to disrupt undesired ones. Furthermore, mechanical stresses can be applied for the inactivation of cellular systems as seen in UHP treatments, extraction of food components, or selection of microbial ecologies (Hartmann et al., 2004). With regard to deformation, solid food and food capable of flowing differ in their magnitude. While a solid food deforms up to a limit under constant, time-independent mechanical load, food capable of flowing tends to deform to infinity. Thus, for solid food, mechanical stresses depend on a suitable measure such as the shear angle, as it depends on the deformation rate such as the shear rate for food capable of flowing. Modeling must consider material properties and their spatial distribution such as homogeneity and isotropy that are related to the structure and texture. Due to the complexity of biomatter, complete homogeneity and isotropy cannot be achieved. This inhomogeneity and anisotropy can result in problems during scale-up (Hartmann and Delgado, 2003). Kinetic models also play an important role in food processing, especially for biologically active matter in metabolic processes. The characteristic length scale is in the order of magnitude of a few micrometers for microorganisms, and the microbial population consists of billions of individuals for lab-scale reactors. Thus, classic kinetic models include no more than average statistical measures for biological reactions. Therefore, modeling of biological processes, particularly for industrial plants, does not represent homogeneity due to the large dimensions. Moreover, the inhomogeneity from mechanical and energetic processes can have a significant impact on food safety and quality. Furthermore, high complexity of transport processes in suspended (a)biotic particles, particularly for particles of larger length scales than microorganisms, exists in a wide variety of food processing, for example, in fluidized bed reactors for drying (Díez et al., 2011).
Different Modeling and Simulation Approaches for Food Processing Operations
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Modeling and Simulation Approaches In this article, three different categories of approaches are reviewed: balancing, knowledge-oriented, and hybrid methods.
Balancing Approaches Balancing approaches are preferred with sufficient process knowledge for the formulation of balance equations. For the simplest balancing approaches, food processing is described by quantities that are depending only on a single independent variable. In this case, modeling results in a single or a set of ordinary differential equations (ODEs) that can be solved analytically or numerically. Food processing also depends on spatial coordinates if material or process inhomogeneities exist. The spatial dependence results in PDEs for modeling. Therefore, an analytical solution can only be expected for very simple initial and boundary conditions. For food capable of flowing that can be considered as isotropic, homogeneous, Newtonian, electrically, and magnetically nonactive, the balance equations read in dimensionless notation as follows (Kowalczyk and Delgado, 2007; Delgado et al., 2008; Rauh et al., 2009; Rauh and Delgado, 2008). The transport of mass (v, partial derivative; V, nabla operator; r, density; t, time) can be expressed by the continuity equation as . vr þ V$ rU ¼ 0: vt
[1] .
The transport of momentum (Re, Reynolds number; Fr, Froude number; s, stress tensor; Fg , dimensionless gravitational force) can be expressed as r
. . . vU 1 1. V$s þ Fg : þ r U $V U ¼ Vp Re Fr vt
[2]
The thermal energy (cp, thermal capacity; D, substantial derivative; Ec, Eckert number; b, thermal expansion coefficient; Pr, Prandtl number; l, thermal conductivity; F, dimensionless dissipation; PT0 ¼ b0 T0 ) can be expressed as r cp
DT Dp 1 Ec ¼ PT0 EcbT þ V$ðlVTÞþ F: Dt Dt Re Pr Re
[3]
These balance equations can be derived by considering the change of the quantity in question, in terms of mass, momentum, and energy, in a given balance volume that is assumed to be constant and locally fixed. The dimensionless notation provides the opportunity to study the influence of dimensionless groups instead of numerous single parameters for similarity analysis. The similarity analysis that results in dimensionless notation used in eqns [1]–[3] requires characteristic reference parameters and adequate length L0 and velocity scales U0. A correspondent time scale t0 can be inferred for the motion of the biomatter due to forced convection, while a characteristic velocity cannot be given a priori for natural convection. The reference velocity, which results from a balance of driving and hindering forces in the natural flow field, is often used in literature (Spurk, 2004). Rauh and Delgado (2008) and Delgado et al. (2008) have published pioneering works in which they report that analog balances also apply for other scalar biological and biochemical quantities. Balance equation for the biochemical activity f is derived by these authors as follows ! vf 1 þ V fU ¼ V$ D4 Vf þ Da0 Q4 ; vt Re0 Sc0
[4]
as required for modeling of the effect of transport processes on enzymes (Sc, Schmidt number; D4, diffusion coefficient; Da, Damköhler number; Q4, source or sink due to kinetic model of biochemical reaction) (Ludikhuyze et al., 1998a,b; Rauh et al., 2009; Rauh and Delgado, 2011; Grauwet et al., 2012).
Balancing Approaches for Thermal Processes Considering Pure Time Dependence Considering pure time dependence leads to an ODE. Most prominent examples for pure time dependence represent kinetic equations that express the temporal evolution of physical, chemical, or cellular systems. The temporal evolution considers the generation or the decay of a particulate food structure, bubbles in foam, or a material component in a (bio)reaction. Pure time dependency is also considered for describing the time dynamic of processes in process control. In these cases, the mathematical abstraction associated with modeling results in an implicit, nth order ODE Fðt; y; y0 ; y00 ; .; yn Þ ¼ 0
[5]
where the prime (ʹ) represents the ordinary time derivative of the quantity considered, such as colony-forming units (CFU) and enzyme or particle concentration. Adequate solution procedures, such as finding root function by direct integration, separation of variables, Ansatz functions, and series expansions must be found.
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Modeling time dependence of food processing is often achieved by balance equations and approximations no higher than second order. Many examples are available for such cases for modeling, for generation or decay of the quantity N expressed by the first order, in which the linear ODE Nʹ(t) ¼ kN(t) accepts the analytical solution N(t) ¼ cekt, where k represents the activation energy of a (bio)chemical reaction or the inactivation constant of microorganisms (Ludikhuyze et al., 1998a,b; Ananta et al., 2001; De Heij et al., 2002; Hartmann et al., 2003; Margosch et al., 2004; Grauwet et al., 2012; Rauh et al., 2009; Kulisiewicz et al., 2012) and c represents an integration constant, which depends on the particular molecular or cellular quantity that corresponds to the initial number of CFU, initial enzyme concentration, or the reaction rate. Furthermore, if inhibition or saturation occurs, then modeling of the growth or decay has to consider a maximum value Nmax and the temporal change is also considered to be proportional to the real power p of the difference Nmax N(t), i.e., Nʹ(t) ¼ k[Nmax N(t)]pN(t). Other than the provided examples, many ODEs are difficult to be solved analytically. The literature suggested different numerical methods such as integral quadrature procedures (Davis and Rabinowitz, 2007; Krylov and Stroud, 2006; Butcher, 2000) and Runge–Kutta (RK) numerical approaches (Butcher, 2000). Simulations based on ODE models can be solved by finite discretization procedures; however, they are mainly applied for the simulation of spatiotemporal processes as shown in eqns [1]–[4].
Balancing Approaches Including Spatiotemporal Effects For realistic modeling and simulation of food processing, spatiotemporal effects must be included in addition to time-dependent effects. This is particularly important for food capable of flowing in connection with mass, momentum, and energy transfer. Among the balancing approaches suggested in literature (Denys et al., 2000a; Hartmann et al., 2003, 2004; Hartmann and Delgado, 2003; Hartmann et al., 2004; Kowalczyk et al., 2004, 2005; Rauh et al., 2009; Baars et al., 2007; Kilimann et al., 2006; Rauh and Delgado, 2008, 2010, 2011), two categories are the most notable concerning thermal effects. Conductive thermal transport leads to a single model equation for the temperature field such as the generalized Fourier’s equation (GFE). vT Y vp ¼ T þ V2 T T0 vt vt
[6]
This equation can be also derived from the energy eqn [3] with the time being normalized with inner thermal time scale sener ¼ L2 0 =a0 , negligible dissipation effect, material parameters that are not significantly affected by temperature, and no natural or forced convection. These assumptions are also valid for solid foods, packages, and the walls of thermal treatment devices. The GFE can be solved numerically or analytically for simple geometry (Denys et al., 2000a,b; Hartmann et al., 2003; Hartmann and Delgado, 2003; Carroll et al., 2003; Otero et al., 2007; Chen et al., 2007; Rauh and Delgado, 2010, 2011). For food processing simulations based on eqns [1]–[4], finite difference methods (FDM), finite volume methods (FVM), and finite element methods (FEM) are used, as suggested in literature (Ferziger and Peric, 2002; Chen, 2005). The governing partial PDEs are written in differential form for FDM. FDM is a simple and efficient numerical technique for structured meshes. FDM depends on structured or block-structured numerical meshes. The generation of structured meshes is limited to simple geometries, however. It is also not automatically conservative for transport quantities. On the other hand, FEM is better suited for complex geometries. Yet, as FEM uses unstructured finite elements, the computations are expensive (Ferziger and Peric, 2002; Chen, 2005). The PDE is multiplied by a weight function and then integrated. The solution is approximated inside the elements by a linear shape function for the assurance of the continuity of the solution across the element boundaries. For the simulation concerning the full spatiotemporal effects, the FVM is preferred. The governing balance equation is in integral form, and the corresponding discretization is based on the numerical mesh generation forming balancing control volumes.
Knowledge-Oriented Approaches Depending on the level of knowledge, different knowledge-oriented approaches are available. Pattern recognition or pure databased models are used with the lowest knowledge levels. Statistical models allow for the extraction of global product and process quantities. Cognitive approaches such as fuzzy logic (FL) or artificial neuronal networks (ANN) represent the level of human knowledge acquisition. For the characterization of thermofluiddynamic (a)biotic systems, the system variables are not defined ‘crisp’ (i.e., 0 or 1). Instead, ‘fuzzy’ statements are made (i.e., any real number between 0 and 1). For each variable and its elements x, fuzzy sets are defined by gradual membership functions m(x). FL includes expert knowledge in the modeling and simulation of the system behavior by formulating IF-THEN rules containing the influence factors. For the prediction procedure, FL formulates fuzzy sets for all input and output variables linked to their system characteristics. First, fuzzification occurs as input variables’ respective memberships are calculated. Subsequently, the IF parts of the statements are assessed and the THEN parts are calculated. Finally, defuzzification occurs as all IF-THEN statements are evaluated and converted into output variable values. Deffuzification often applies the center-of-gravity method (Kruse et al., 2011; Petermeier et al., 2002). ANN, on the other hand, imitates real biological information processing and learning procedures occurring in human and mammal central nervous system, in particular in the brain. ANN consists of interconnected neurons, which transfer information between each other. A weight, based on experience, is assigned for every connection, allowing ANN to be adaptive to inputs. The exchange and transformation of information are determined by network input function, which determines the weighted
Different Modeling and Simulation Approaches for Food Processing Operations
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sum of all inputs to a neuron; the activation function such as threshold, linear, or sigmoid function; and the output function. The learning phase of ANN is problem-dependent and is distinguished as forward learning or back propagation. ANN is a universal approximator (Díez et al., 2011), a powerful diagnosis and prognosis tool (Rauh et al., 2012), and an assistant tool for process control strategies (Batchuluun et al., 2011, 2012; Cubeddu et al., 2014).
Hybrid Approaches Hybrid approaches make synergistic use of different approaches to offer unique possibilities. Hybrids can be divided into three different classes: 1. hybrids that include knowledge purely via classical balancing equations; 2. hybrids that combine knowledge represented by classical balancing equation with knowledge gained by statistical, data mining, and cognitive approaches; and 3. hybrids that directly utilize experimentally accessible knowledge for modeling and simulation for food processing. For the first class of hybrids, physicochemical quantities (e.g., density, viscosity, elasticity, thermal capacity, heat conductivity, pH, and reaction rate and order) are generally required for solving the balance equations. Different combinations of approaches are suggested in the literature. For example, fluid structure interactions during food processing can be evaluated by combining structural investigation of the biotic components by the FEM and thermofluiddynamic examination by the FVM (Hou et al., 2012; Münsch et al., 2012). Iqbal et al. (2012) proposed investigating the dynamics of fluidized bed reactors by simulating the fluid movement via FVM and the dynamics of the bed beads via discrete element method. Among the second class of hybrids there are hybrids that are based on data mining (Fayyad et al., 1996). These have only been used for a few cases in food processing (Gänzle et al., 2007; Kessler et al., 2006). For cognitive-balancing hybrids, prediction of the transport of mass and momentum in food applications by combination of ANN and FVM to solve the transport eqns [1] and [2] were studied by Delgado et al. (1996), Benning et al. (2002), and Rauh et al. (2012). Recent literature describes the following hybrids in regard to food processing: l l l l l l
Neuro-analytical hybrids for implementation of results of analytical solutions in ANN, Neuro-numerical hybrids for implementation of results of numerical simulations in ANN, Fuzzy-numerical hybrids for implementation of results of numerical simulations in FL systems, Numero-neuronal hybrids for implementation of results of ANN in numerical simulations, Numero-experimental hybrids for implementation of experimental data in numerical simulations, Numero-statistical hybrids for implementation of results of statistical methods in numerical simulations.
The first method mentioned in the name of the hybrids is the main method and the second is the assisting method. Two directions of information transport are considered. For example, for neuro-numerical hybrids, numerical results are used as training sets for ANNs, while numerical results are used as the knowledge base to generate fuzzy rules for fuzzy-numerical hybrids. ANNs are used to improve the solution performance of numerical simulations in numero-neuronal hybrids. Physical boundary and initial conditions for the modeling and simulation of (a)biotic thermofluiddynamic systems can be generated with an ANN trained with experimental, analytical, or numerical data (Díez, 2009; Díez et al., 2011). The third class of hybrids implements experimental knowledge on (1) the dynamics of the transport of mass, momentum, and energy, (2) characteristic features such as phase transition curves, and (3) the existence of typical phenomena and patterns such as pH and ‘dead zones’ in the food treatment process.
Conclusions and Outlook Process, structure, and function are very closely interlinked in food science. Processes influence the structure of the treated material and, in turn, this leads to changes in functionality of the material. This interaction affects a wide range of characteristic scales, especially for timescales and length scales. Modeling and simulation of process–structure–function relations has to consider different scales and connections between mechanisms at different scales. Spatiotemporal fields that influence process–structure interactions are created by thermofluiddynamic effects, which play a crucial role in processing of food capable of flowing. Selecting appropriate approaches is dependent on the available knowledge about the system of interest. The state of the art in modeling and simulation for food processing is closely linked to the availability of balancing equations on the continuum level as shown in eqns [1]–[4]. However, any mechanism or structure at molecular level is often not considered due to the required validity of continuum hypothesis (Delgado et al., 2008). Also, for the case of complex rheology, it is often simplified to pure viscous behavior. Balancing equations are only applicable for a few cases. Therefore, combining different methods, such as balancing, cognitive, and statistical approaches, appears to be the first-choice method for their synergistic effects. On the other hand, there are enormous challenges related to effective use of these hybrids, particularly for scale-bridging effects. Per se scale-bridging methods such as Lattice Boltzmann Methods, however, are becoming more accessible (Iglberger und Rüde, 2010; Feichtinger et al., 2011; Anderl
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et al., 2014a,b,c). Moreover, approaches that allow easy integration of balancing and nonbalancing methods are being established. One of the prominent examples is Petri reference nets that enable dealing of complex concurrent and recurring processes in complete industrial plants (Durek et al., 2011; Delgado et al., 2013).
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Ultrahochdruckbehandlung von Lebensmitteln mit Schwerpunkt Milch und milchprodukte-phänomene, Kinetik und Methodik. Fortschr. Ber. VDI 3 (656) (VDI-Verlag, Düsseldorf). Hou, G., Wang, J., Layton, A., 2012. Numerical methods for fluid-structure interaction - a review. Commun. Comput. Phys. 12, 337–377. Hu, M., Benning, R., Ertunc, Ö., Neukamm, J., Bielke, T., Delgado, A., Vanusch, N., Berger, A., 2011. Mass transfer of organic substances in supercritical carbon dioxide. J. Phys. Conf. Ser. 327, 012041. Iglberger, K., Rüde, U., 2010. Massively parallel granular flow simulation with non-spherical particles. Comput. Sci. Res. Dev. 25 (1–2), 105–113. Iqbal, N., Rauh, C., Delgado, A., 2012. Numerical simulation of dense fluid-particle flows using a hybrid approach of computational fluid dynamics (CFD) and discrete element method (DEM). In: Proceedings in Applied Mathematics and Mechanics. Jaeger, P.T., Eggers, R., Baumgartl, H., 2002. Interfacial properties of high viscous liquids in a supercritical carbon dioxide atmosphere. J. Supercrit. Fluids 24, 203–217.
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Kessler, B., Benning, R., Wenning, M., Schmitt, J., Scherer, S., Delgado, A., 2006. Entwicklung eines Hybriden Identifizierungstools von Mikroorganismen mittels FTIR-Spektren. Chem. Ing. Tech. 78, 1234–1239. Kilimann, K., Kitsubun, P., Delgado, A., Gänzle, M., Chapleau, N., Le Bail, A., Hartmann, C., 2006. Experimental and numerical study of heterogeneous pressure-temperatureinduced lethal and sublethal injury of Lactococcus lactis in a medium scale high-pressure autoclave. Biotechnol. Bioeng. 94, 655–666. Knoerzer, K., Juliano, P., Roupas, P., Versteeg, C., 2011. Innovative Food Processing Technologies: Advances in Multiphysics Simulation. John Wiley & Sons, Chichester. Kowalczyk, W., Delgado, A., 2007. Dimensional analysis of thermo-fluid-dynamics of high hydrostatic pressure processes with phase transition. Int. J. Heat Mass Transf. 50, 3007–3018. Kowalczyk, W., Hartmann, C., Delgado, A., 2004. Modelling and numerical simulation of convection driven high pressure induced phase changes. Int. J. Heat Mass Transf. 47, 1079–1089. Kowalczyk, W., Hartmann, C., Luscher, C., Pohl, M., Delgado, A., Knorr, D., 2005. Determination of thermophysical properties of foods under high hydrostatic pressure in combined experimental and theoretical approach. Innov. Food Sci. Emerg. Technol. 6, 318–326. Kruse, R., Borgelt, C., Klawonn, F., Moewes, C., Ruß, G., Steinbrecher, M., 2011. Computational Intelligence. Vieweg þ Teubner, Wiesbaden. Krylov, V.I., Stroud, A.H., 2006. Approximate Calculation of Integrals. Dover Publications, New York. Kulisiewicz, L., Wierschem, A., Rauh, C., Delgado, A., 2012. Inactivation of enzymes by pressure. In: Eggers, R. (Ed.), Industrial High Pressure Applications. Wiley VCH, Weinheim. Lindgren, M., Aronsson, K., Galt, S., Ohlsson, T., 2002. Simulation of the temperature increase in pulsed electric field (PEF) continuous flow treatment chambers. Innov. Food Sci. Emerg. Technol. 3, 233–245. Ludikhuyze, L., Indrawati, I., Van den Broeck, I., Weemaes, C., Hendrickx, M., 1998a. Effect of combined pressure and temperature on soybean lipoxygenase. 1. Influence of extrinsic and intrinsic factors on isobaric-isothermal inactivation kinetics. J. Agric. Food Chem. 46, 4074–4080. Ludikhuyze, L., Indrawati, I., Van den Broeck, I., Weemaes, C., Hendrickx, M., 1998b. Effect of combined pressure and temperature on soybean lipoxygenase. 2. Modeling inactivation kinetics under static and dynamic conditions. J. Agric. Food Chem. 46, 4081–4086. Margosch, D., Gänzle, M.G., Ehrmann, M.A., Vogel, R.F., 2004. Pressure inactivation of Bacillus endospores. Appl. Environ. Microbiol. 70, 7321–7328. Martín-Belloso, O., Sobrino-López, A., Elez-Martínez, P., 2011. Pulsed electric field processing. In: Sun, D.W. (Ed.), Handbook of Food Safety Engineering. Wiley-Blackwell, Oxford, pp. 603–626. Münsch, M., Delgado, A., Breuer, M., 2012. Fluid-structure interaction in turbulent flows and the influence of les subgrid-scale models. In: Proceedings of ECCOMAS 2012, pp. 3944–3963. Odriozola-Serrano, I., Aguiló-Aguayo, I., Soliva-Fortuny, R., Martín-Belloso, O., 2013. Pulsed electric fields processing effects on quality and health-related constituents of plantbased foods. Trends Food Sci. Technol. 29, 98–107. Otero, L., Ramos, A.M., de Elvira, C., Sanz, P.D., 2007. A model to design high-pressure processes towards an uniform temperature distribution. J. Food Eng. 78, 1463e1470. Petermeier, H., Benning, R., Delgado, A., Kulozik, U., Hinrichs, J., Becker, T., 2002. Hybrid model of the fouling process in tubular heat exchangers for the dairy industry. J. Food Eng. 55, 9–17. Rauh, C., Delgado, A., 2008. Thermofluiddynamics in liquid media during biotechnological processes under high pressure. Proc. Appl. Math. Mech. 8, 10663–10664. Rauh, C., Delgado, A., 2010. Analytical considerations and dimensionless analysis for a description of particle interactions in high pressure processes. High Press. Res. 30, 567–573. Rauh, C., Delgado, A., 2011. Computational fluid dynamics applied in high-pressure processing scale-up. In: Knoerzer, K., Juliano, P., Roupas, P., Versteeg, C. (Eds.), Innovative Food Processing Technologies: Advances in Multiphysics Simulation. John Wiley & Sons, Chichester, pp. 57–74. Rauh, C., Baars, A., Delgado, A., 2009. Uniformity of enzyme inactivation in a short-time high-pressure process. J. Food Eng. 91, 154–163. Rauh, C., Singh, J.P., Nagel, M., Delgado, A., 2012. Objective analysis and prediction of texture perception of yoghurt by hybrid neuro-numerical methods. Int. Dairy J. 26, 2–14. Sarrade, S., Guizard, C., Rios, G.M., 2003. New applications of supercritical fluids and supercritical fluids processes in separation. Sep. Purif. Technol. 32, 57–63. Spurk, J.H., 2004. Strömungslehre. Einführung in die Theorie der Strömungen. Springer, Berlin.
Introduction and Basic Considerations Basic Considerations on Food Processing Modeling and Simulation Approaches Balancing Approaches Balancing Approaches for Thermal Processes Considering Pure Time Dependence Balancing Approaches Including Spatiotemporal Effects Knowledge-Oriented Approaches Hybrid Approaches Conclusions and Outlook References
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Introduction and Basic Considerations The term modeling holds different meanings in the scientific literature. Model systems in experiments provide the opportunity for researchers to study the behavior of another system of interest with similar properties. In this article, modeling is defined as the action of theoretical abstraction of the behavior of cause-and-effect chains and the expression of such behavior in mathematical terminology. Since modeling and simulation are very similar in this sense, both terms are often used interchangeably in the literature. In this article, simulation summarizes all algorithms for solving the mathematical models. Data management procedures such as algorithms, data storing, and parallel processing procedures for representation of the behavior of a given system inspired by previously constructed theoretical models are mainly reviewed here. Similar misunderstandings exist regarding the difference between systems and processing. A system may consist of material and nonmaterial components, any physicochemical and biological interactions between these components, and the corresponding storage, while a process consists of transportation and transformation of mass, momentum, and energy. Therefore, modeling and simulation of food processing must include approaches that reflect the conservation of mass, momentum and energy, as well as physical, chemical, and biological reactions. Modeling and simulation have demonstrated to be powerful tools for representing a wide variety of natural and technical processes. Food processing is characterized by both structures with various specific length scales and mechanisms that require different timescales for the physicochemical interactions of the food material of interest. The length scales change from the molecular level to production level by over 10 orders of magnitude. Successful modeling and simulation of food processing first needs the knowledge that food is biomatter, a substance consisting of biotic and abiotic components with diverse levels of thermal, chemical, and biological potentials (Bahadir et al., 2000). The complexity of biomatter as a material makes acquisition of new knowledge on its behavior extremely difficult. In addition, the material components may display different states of aggregation (gaseous, liquid, or solid states) which often leads to soft-matter behavior with high sensitivity to mechanical loads. This article reviews different modeling and simulation methods connected to the complexity of food processing technology and the associated knowledge. Thus, in addition to classical numerical simulation procedures, based on finite discretization procedures, and advanced numerical methods (Lattice Boltzmann Approach) for high-performance computing, statistical, data mining, and cognitive methods (Artificial Neuronal Networks and Fuzzy Logic) are covered. Hybrid methods are also explored for overcoming restrictions of single methods. First, modeling and simulation in connection to the mechanical and thermal effects occurring during the thermal treatment of food, which is currently the most widespread processing method, is considered. Given the well-known restrictions imposed by classical thermal treatment, emerging techniques are geared toward affecting the food matter in a specific way. In most processing scenarios, these technologies should increase the biological and chemical safety of the product (Ananta et al., 2001; Margosch et al., 2004, Kilimann et al., 2006; Odriozola-Serrano, 2013), reduce the impact of the process on the food via general minimal processing, i.e., increasing the quality of the product (Durek et al., 2011), and create new food structures as well as products (Hinrichs, 2000). The most prominent examples of such techniques are the so-called nonthermal treatment
Reference Module in Food Sciences
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methods such as ultrahigh-pressure (UHP) treatment, supercritical fluids, ultrasonic treatment, plasma, and pulsed electric fields (PEF) (Knoerzer et al., 2011). In these processes, food experiences very specific and extreme conditions. Supercritical extraction is utilized for the exceptional physicochemical properties of a solvent fluid that displays the thermodynamic properties of both the gaseous state and the liquid state. Thermodynamic transition between the gas and the liquid states results in a decrease in the solvent’s viscosity and an increase in the diffusion constant as well as material peculiarities. In this context, surface energies drop, and hardly soluble substances can be extracted, even at industrial scale (Eckert et al., 1996; Higashi et al., 2001; Jaeger et al., 2002; Sarrade et al., 2003; Eder et al., 2003; Hu et al., 2011). Processes such as UHP treatment of solid and liquid biomatter, as well as phase transitions at pressures up to several hundreds of MPa, must involve at least one substance capable of flowing. If the biomatter holds this capability, it is often directly compressed or deformed by normal stresses. In other cases, indirect compression via pressure transmitting liquid is performed. In such systems, the product is packaged and separated from the pressurizing medium. One peculiarity of modeling the UHP treatment of food is that, even in liquid components, the nonnegligible effects of compressibility result in the conversion of the mechanical energy provided by the pressure into inner energy. Thermal phenomena also occur during high-pressure processing. For food capable of flowing, these effects induce natural convection driven by temperature heterogeneities or density gradients that are practically unavoidable during food processing. In addition, the natural flow phenomena may interfere with the flow field produced by the movement of a pressurizing piston. It acts directly inside the pressure chamber or outside as part of a pressure transducer system. As a result, modeling and simulation must take thermofluiddynamical effects into consideration. This also applies for modeling and simulating food processing by PEF, another emerging processing technology for preserving liquid foods flowing through a treatment chamber by inactivating spoilage microorganisms and enzymes (Martín-Belloso et al., 2011; Elez-Martínez et al., 2012; Odriozola-Serrano et al., 2013; Krauss et al., 2011). PEF provides an alternative to thermal preservation processes since it maintains the naturalness of the food such as its sensory, nutritional, and functional properties to a higher degree than in processes using thermal energy for inactivation. Regardless of the inactivation mechanism, experiments have shown that the electric field strength and treatment time are the major process parameters. Unwanted temperature increase in the chamber due to dissipative effects induced by the present electric field also plays a crucial role (Lindgren et al., 2002). Thus, the thermofluiddynamic effects directly result from the coupled convective transport of mass, momentum, and thermal energy in the liquid food. Hence, the impact of PEF on the inactivation of food spoilage microorganisms and enzymes in the liquid food can be better understood when the PEF process is modeled and simulated to reveal the spatiotemporal distribution of electric field strength, temperature, and inactivation in the treatment chamber.
Basic Considerations on Food Processing A continuum approach (Baehr and Kabelac, 2006) is postulated in this article. Dimensional variables (marked by *) influencing food processing are the scalar thermodynamic state variables: mass m*, volume V*, specific volume v*, pressure p*, temperature T*, specific internal energy u*, specific entropy s*, specific enthalpy h*, specific free energy f*, and specific free enthalpy g*. For ! a , and also second- and third-order kinematic tensors food capable of flowing, the vector variables, velocity U , and acceleration ! such as Rivlin-Ericksen and Levi-Civita tensors, are used for the calculation of deformations (Spurk, 2004). Furthermore, food capable of flowing can be treated by the basic thermofluiddynamic equations, a system of nonlinear partial differential equations (PDEs) that model both the convective and diffusive transport of matter, momentum, and energy. With these equations, the importance of the transport mechanisms can be assessed experimentally, theoretically, and numerically. Mechanical stresses represent a key quantity in food processing. They appear from forces arising during storage and transportation of food, or they can be applied to create specific structures or to disrupt undesired ones. Furthermore, mechanical stresses can be applied for the inactivation of cellular systems as seen in UHP treatments, extraction of food components, or selection of microbial ecologies (Hartmann et al., 2004). With regard to deformation, solid food and food capable of flowing differ in their magnitude. While a solid food deforms up to a limit under constant, time-independent mechanical load, food capable of flowing tends to deform to infinity. Thus, for solid food, mechanical stresses depend on a suitable measure such as the shear angle, as it depends on the deformation rate such as the shear rate for food capable of flowing. Modeling must consider material properties and their spatial distribution such as homogeneity and isotropy that are related to the structure and texture. Due to the complexity of biomatter, complete homogeneity and isotropy cannot be achieved. This inhomogeneity and anisotropy can result in problems during scale-up (Hartmann and Delgado, 2003). Kinetic models also play an important role in food processing, especially for biologically active matter in metabolic processes. The characteristic length scale is in the order of magnitude of a few micrometers for microorganisms, and the microbial population consists of billions of individuals for lab-scale reactors. Thus, classic kinetic models include no more than average statistical measures for biological reactions. Therefore, modeling of biological processes, particularly for industrial plants, does not represent homogeneity due to the large dimensions. Moreover, the inhomogeneity from mechanical and energetic processes can have a significant impact on food safety and quality. Furthermore, high complexity of transport processes in suspended (a)biotic particles, particularly for particles of larger length scales than microorganisms, exists in a wide variety of food processing, for example, in fluidized bed reactors for drying (Díez et al., 2011).
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Modeling and Simulation Approaches In this article, three different categories of approaches are reviewed: balancing, knowledge-oriented, and hybrid methods.
Balancing Approaches Balancing approaches are preferred with sufficient process knowledge for the formulation of balance equations. For the simplest balancing approaches, food processing is described by quantities that are depending only on a single independent variable. In this case, modeling results in a single or a set of ordinary differential equations (ODEs) that can be solved analytically or numerically. Food processing also depends on spatial coordinates if material or process inhomogeneities exist. The spatial dependence results in PDEs for modeling. Therefore, an analytical solution can only be expected for very simple initial and boundary conditions. For food capable of flowing that can be considered as isotropic, homogeneous, Newtonian, electrically, and magnetically nonactive, the balance equations read in dimensionless notation as follows (Kowalczyk and Delgado, 2007; Delgado et al., 2008; Rauh et al., 2009; Rauh and Delgado, 2008). The transport of mass (v, partial derivative; V, nabla operator; r, density; t, time) can be expressed by the continuity equation as . vr þ V$ rU ¼ 0: vt
[1] .
The transport of momentum (Re, Reynolds number; Fr, Froude number; s, stress tensor; Fg , dimensionless gravitational force) can be expressed as r
. . . vU 1 1. V$s þ Fg : þ r U $V U ¼ Vp Re Fr vt
[2]
The thermal energy (cp, thermal capacity; D, substantial derivative; Ec, Eckert number; b, thermal expansion coefficient; Pr, Prandtl number; l, thermal conductivity; F, dimensionless dissipation; PT0 ¼ b0 T0 ) can be expressed as r cp
DT Dp 1 Ec ¼ PT0 EcbT þ V$ðlVTÞþ F: Dt Dt Re Pr Re
[3]
These balance equations can be derived by considering the change of the quantity in question, in terms of mass, momentum, and energy, in a given balance volume that is assumed to be constant and locally fixed. The dimensionless notation provides the opportunity to study the influence of dimensionless groups instead of numerous single parameters for similarity analysis. The similarity analysis that results in dimensionless notation used in eqns [1]–[3] requires characteristic reference parameters and adequate length L0 and velocity scales U0. A correspondent time scale t0 can be inferred for the motion of the biomatter due to forced convection, while a characteristic velocity cannot be given a priori for natural convection. The reference velocity, which results from a balance of driving and hindering forces in the natural flow field, is often used in literature (Spurk, 2004). Rauh and Delgado (2008) and Delgado et al. (2008) have published pioneering works in which they report that analog balances also apply for other scalar biological and biochemical quantities. Balance equation for the biochemical activity f is derived by these authors as follows ! vf 1 þ V fU ¼ V$ D4 Vf þ Da0 Q4 ; vt Re0 Sc0
[4]
as required for modeling of the effect of transport processes on enzymes (Sc, Schmidt number; D4, diffusion coefficient; Da, Damköhler number; Q4, source or sink due to kinetic model of biochemical reaction) (Ludikhuyze et al., 1998a,b; Rauh et al., 2009; Rauh and Delgado, 2011; Grauwet et al., 2012).
Balancing Approaches for Thermal Processes Considering Pure Time Dependence Considering pure time dependence leads to an ODE. Most prominent examples for pure time dependence represent kinetic equations that express the temporal evolution of physical, chemical, or cellular systems. The temporal evolution considers the generation or the decay of a particulate food structure, bubbles in foam, or a material component in a (bio)reaction. Pure time dependency is also considered for describing the time dynamic of processes in process control. In these cases, the mathematical abstraction associated with modeling results in an implicit, nth order ODE Fðt; y; y0 ; y00 ; .; yn Þ ¼ 0
[5]
where the prime (ʹ) represents the ordinary time derivative of the quantity considered, such as colony-forming units (CFU) and enzyme or particle concentration. Adequate solution procedures, such as finding root function by direct integration, separation of variables, Ansatz functions, and series expansions must be found.
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Modeling time dependence of food processing is often achieved by balance equations and approximations no higher than second order. Many examples are available for such cases for modeling, for generation or decay of the quantity N expressed by the first order, in which the linear ODE Nʹ(t) ¼ kN(t) accepts the analytical solution N(t) ¼ cekt, where k represents the activation energy of a (bio)chemical reaction or the inactivation constant of microorganisms (Ludikhuyze et al., 1998a,b; Ananta et al., 2001; De Heij et al., 2002; Hartmann et al., 2003; Margosch et al., 2004; Grauwet et al., 2012; Rauh et al., 2009; Kulisiewicz et al., 2012) and c represents an integration constant, which depends on the particular molecular or cellular quantity that corresponds to the initial number of CFU, initial enzyme concentration, or the reaction rate. Furthermore, if inhibition or saturation occurs, then modeling of the growth or decay has to consider a maximum value Nmax and the temporal change is also considered to be proportional to the real power p of the difference Nmax N(t), i.e., Nʹ(t) ¼ k[Nmax N(t)]pN(t). Other than the provided examples, many ODEs are difficult to be solved analytically. The literature suggested different numerical methods such as integral quadrature procedures (Davis and Rabinowitz, 2007; Krylov and Stroud, 2006; Butcher, 2000) and Runge–Kutta (RK) numerical approaches (Butcher, 2000). Simulations based on ODE models can be solved by finite discretization procedures; however, they are mainly applied for the simulation of spatiotemporal processes as shown in eqns [1]–[4].
Balancing Approaches Including Spatiotemporal Effects For realistic modeling and simulation of food processing, spatiotemporal effects must be included in addition to time-dependent effects. This is particularly important for food capable of flowing in connection with mass, momentum, and energy transfer. Among the balancing approaches suggested in literature (Denys et al., 2000a; Hartmann et al., 2003, 2004; Hartmann and Delgado, 2003; Hartmann et al., 2004; Kowalczyk et al., 2004, 2005; Rauh et al., 2009; Baars et al., 2007; Kilimann et al., 2006; Rauh and Delgado, 2008, 2010, 2011), two categories are the most notable concerning thermal effects. Conductive thermal transport leads to a single model equation for the temperature field such as the generalized Fourier’s equation (GFE). vT Y vp ¼ T þ V2 T T0 vt vt
[6]
This equation can be also derived from the energy eqn [3] with the time being normalized with inner thermal time scale sener ¼ L2 0 =a0 , negligible dissipation effect, material parameters that are not significantly affected by temperature, and no natural or forced convection. These assumptions are also valid for solid foods, packages, and the walls of thermal treatment devices. The GFE can be solved numerically or analytically for simple geometry (Denys et al., 2000a,b; Hartmann et al., 2003; Hartmann and Delgado, 2003; Carroll et al., 2003; Otero et al., 2007; Chen et al., 2007; Rauh and Delgado, 2010, 2011). For food processing simulations based on eqns [1]–[4], finite difference methods (FDM), finite volume methods (FVM), and finite element methods (FEM) are used, as suggested in literature (Ferziger and Peric, 2002; Chen, 2005). The governing partial PDEs are written in differential form for FDM. FDM is a simple and efficient numerical technique for structured meshes. FDM depends on structured or block-structured numerical meshes. The generation of structured meshes is limited to simple geometries, however. It is also not automatically conservative for transport quantities. On the other hand, FEM is better suited for complex geometries. Yet, as FEM uses unstructured finite elements, the computations are expensive (Ferziger and Peric, 2002; Chen, 2005). The PDE is multiplied by a weight function and then integrated. The solution is approximated inside the elements by a linear shape function for the assurance of the continuity of the solution across the element boundaries. For the simulation concerning the full spatiotemporal effects, the FVM is preferred. The governing balance equation is in integral form, and the corresponding discretization is based on the numerical mesh generation forming balancing control volumes.
Knowledge-Oriented Approaches Depending on the level of knowledge, different knowledge-oriented approaches are available. Pattern recognition or pure databased models are used with the lowest knowledge levels. Statistical models allow for the extraction of global product and process quantities. Cognitive approaches such as fuzzy logic (FL) or artificial neuronal networks (ANN) represent the level of human knowledge acquisition. For the characterization of thermofluiddynamic (a)biotic systems, the system variables are not defined ‘crisp’ (i.e., 0 or 1). Instead, ‘fuzzy’ statements are made (i.e., any real number between 0 and 1). For each variable and its elements x, fuzzy sets are defined by gradual membership functions m(x). FL includes expert knowledge in the modeling and simulation of the system behavior by formulating IF-THEN rules containing the influence factors. For the prediction procedure, FL formulates fuzzy sets for all input and output variables linked to their system characteristics. First, fuzzification occurs as input variables’ respective memberships are calculated. Subsequently, the IF parts of the statements are assessed and the THEN parts are calculated. Finally, defuzzification occurs as all IF-THEN statements are evaluated and converted into output variable values. Deffuzification often applies the center-of-gravity method (Kruse et al., 2011; Petermeier et al., 2002). ANN, on the other hand, imitates real biological information processing and learning procedures occurring in human and mammal central nervous system, in particular in the brain. ANN consists of interconnected neurons, which transfer information between each other. A weight, based on experience, is assigned for every connection, allowing ANN to be adaptive to inputs. The exchange and transformation of information are determined by network input function, which determines the weighted
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sum of all inputs to a neuron; the activation function such as threshold, linear, or sigmoid function; and the output function. The learning phase of ANN is problem-dependent and is distinguished as forward learning or back propagation. ANN is a universal approximator (Díez et al., 2011), a powerful diagnosis and prognosis tool (Rauh et al., 2012), and an assistant tool for process control strategies (Batchuluun et al., 2011, 2012; Cubeddu et al., 2014).
Hybrid Approaches Hybrid approaches make synergistic use of different approaches to offer unique possibilities. Hybrids can be divided into three different classes: 1. hybrids that include knowledge purely via classical balancing equations; 2. hybrids that combine knowledge represented by classical balancing equation with knowledge gained by statistical, data mining, and cognitive approaches; and 3. hybrids that directly utilize experimentally accessible knowledge for modeling and simulation for food processing. For the first class of hybrids, physicochemical quantities (e.g., density, viscosity, elasticity, thermal capacity, heat conductivity, pH, and reaction rate and order) are generally required for solving the balance equations. Different combinations of approaches are suggested in the literature. For example, fluid structure interactions during food processing can be evaluated by combining structural investigation of the biotic components by the FEM and thermofluiddynamic examination by the FVM (Hou et al., 2012; Münsch et al., 2012). Iqbal et al. (2012) proposed investigating the dynamics of fluidized bed reactors by simulating the fluid movement via FVM and the dynamics of the bed beads via discrete element method. Among the second class of hybrids there are hybrids that are based on data mining (Fayyad et al., 1996). These have only been used for a few cases in food processing (Gänzle et al., 2007; Kessler et al., 2006). For cognitive-balancing hybrids, prediction of the transport of mass and momentum in food applications by combination of ANN and FVM to solve the transport eqns [1] and [2] were studied by Delgado et al. (1996), Benning et al. (2002), and Rauh et al. (2012). Recent literature describes the following hybrids in regard to food processing: l l l l l l
Neuro-analytical hybrids for implementation of results of analytical solutions in ANN, Neuro-numerical hybrids for implementation of results of numerical simulations in ANN, Fuzzy-numerical hybrids for implementation of results of numerical simulations in FL systems, Numero-neuronal hybrids for implementation of results of ANN in numerical simulations, Numero-experimental hybrids for implementation of experimental data in numerical simulations, Numero-statistical hybrids for implementation of results of statistical methods in numerical simulations.
The first method mentioned in the name of the hybrids is the main method and the second is the assisting method. Two directions of information transport are considered. For example, for neuro-numerical hybrids, numerical results are used as training sets for ANNs, while numerical results are used as the knowledge base to generate fuzzy rules for fuzzy-numerical hybrids. ANNs are used to improve the solution performance of numerical simulations in numero-neuronal hybrids. Physical boundary and initial conditions for the modeling and simulation of (a)biotic thermofluiddynamic systems can be generated with an ANN trained with experimental, analytical, or numerical data (Díez, 2009; Díez et al., 2011). The third class of hybrids implements experimental knowledge on (1) the dynamics of the transport of mass, momentum, and energy, (2) characteristic features such as phase transition curves, and (3) the existence of typical phenomena and patterns such as pH and ‘dead zones’ in the food treatment process.
Conclusions and Outlook Process, structure, and function are very closely interlinked in food science. Processes influence the structure of the treated material and, in turn, this leads to changes in functionality of the material. This interaction affects a wide range of characteristic scales, especially for timescales and length scales. Modeling and simulation of process–structure–function relations has to consider different scales and connections between mechanisms at different scales. Spatiotemporal fields that influence process–structure interactions are created by thermofluiddynamic effects, which play a crucial role in processing of food capable of flowing. Selecting appropriate approaches is dependent on the available knowledge about the system of interest. The state of the art in modeling and simulation for food processing is closely linked to the availability of balancing equations on the continuum level as shown in eqns [1]–[4]. However, any mechanism or structure at molecular level is often not considered due to the required validity of continuum hypothesis (Delgado et al., 2008). Also, for the case of complex rheology, it is often simplified to pure viscous behavior. Balancing equations are only applicable for a few cases. Therefore, combining different methods, such as balancing, cognitive, and statistical approaches, appears to be the first-choice method for their synergistic effects. On the other hand, there are enormous challenges related to effective use of these hybrids, particularly for scale-bridging effects. Per se scale-bridging methods such as Lattice Boltzmann Methods, however, are becoming more accessible (Iglberger und Rüde, 2010; Feichtinger et al., 2011; Anderl
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et al., 2014a,b,c). Moreover, approaches that allow easy integration of balancing and nonbalancing methods are being established. One of the prominent examples is Petri reference nets that enable dealing of complex concurrent and recurring processes in complete industrial plants (Durek et al., 2011; Delgado et al., 2013).
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