ABSTRACT
Parameter Models ....................................................................................... 319 12.3 Equations Governing the Main Thermal Processes ................................... 323
12.3.1 Navier-Stokes Equations ............................................................... 323 12.3.1.1 Relationship between Shear Stress and Shear Rate ....... 323
12.3.2 Heat Transfer Equation .................................................................. 324 12.3.2.1 Equation of State ........................................................... 325
12.3.3 Turbulence Models ........................................................................ 325 12.3.3.1 Eddy Viscosity Models .................................................. 326 12.3.3.2 Near-Wall Treatment...................................................... 328 12.3.3.3 Reynolds Stress Model .................................................. 328 12.3.3.4 Large Eddy Simulation and Direct Eddy Simulation .... 328
12.3.4 Equation for Mass Transfer ........................................................... 329 12.3.5 Radiation Models ........................................................................... 330
12.4 Solving the Transport Phenomena: State of the Art in CFD Solutions ...... 331 12.4.1 Numerical Discretization ............................................................... 331 12.4.2 Generic Equation and Its Numerical Approximation .................... 332 12.4.3 Meshing the Problem ..................................................................... 333 12.4.4 Obtaining a Solution ...................................................................... 333
12.4.4.1 Algebraic Equation System............................................ 333 12.4.4.2 Inner Iteration Loop ....................................................... 334 12.4.4.3 Outer Iteration Loop ...................................................... 335
12.5 Optimizing Conventional Thermal Processes with CFD ........................... 336 12.5.1 Sterilization and Pasteurization ..................................................... 336
12.5.1.1 Canned Foods ................................................................ 336 12.5.1.2 Foods in Pouches ........................................................... 336 12.5.1.3 Intact Eggs ..................................................................... 337
12.5.2 Aseptic Processing ......................................................................... 337
12.5.2.1 Plate Heat Exchangers for Milk Processing .................. 337 12.5.2.2 Plate Heat Exchangers for Yoghurt Processing ............. 339
12.5.3 Dehydration ...................................................................................340 12.5.3.1 Fluidized Bed Drying ....................................................340 12.5.3.2 Spray Drying ................................................................. 341 12.5.3.3 Forced-Convection Drying ............................................ 343
12.5.4 Cooking ......................................................................................... 343 12.5.4.1 Natural Convection Ovens ............................................. 343 12.5.4.2 Forced Convection Ovens .............................................. 345 12.5.4.3 Baking Ovens ................................................................346 12.5.4.4 Microwave Ovens .......................................................... 350
12.6 Modeling Emerging Thermal Technologies with CFD .............................. 351 12.6.1 High-Pressure Thermal Processing ............................................... 351 12.6.2 Ohmic Heating............................................................................... 352
12.7 Challenges Face the Use of CFD in Thermal Process Modeling ............... 352 12.7.1 Improving the Effi ciency of the Solution Process ......................... 352 12.7.2 CFD and Controlling Thermal Processing .................................... 353 12.7.3 Turbulence ..................................................................................... 354 12.7.4 Boundary Conditions ..................................................................... 354
12.8 Conclusions ................................................................................................. 355 Nomenclature ......................................................................................................... 355 References .............................................................................................................. 356
The application of the principles of fl uid motion and heat transfer to design problems in the food industry has undergone remarkable development since the early 1990s. Problems involving heat and mass transfer, phase change, chemical reactions, and complex geometry, which once required either highly expensive or oversimplifi ed computations, can now be effi ciently completed with a high level of spatial and temporal accuracy on personal computers. This remarkable progression is owing to the development of a design and analysis tool, known as computational fl uid dynamics (CFD), which can be used to tackle complex problems in fl uid mechanics and heat transfer, and many other physical processes. CFD is based on numerical methods that solve for the governing transport mechanisms over a multidimensional domain of interest. Its physical basis is rooted in classical fl uid mechanics. Since its fi rst computer implementation in the 1950s, the technical formulation of CFD has been evolving contemporaneously with the digital computer (Norton and Sun, 2007). In its present-day form, CFD can be used to effi ciently quantify many complex dynamic phenomena and as a result has developed into a multifaceted industry, generating billions of Euros worldwide within a vast range of specializations (Abbott and Basco, 1989; Xia and Sun, 2002).
