Modelling transport phenomena in refrigerated food bulks, packages and stacks: basics and advances

Abstract Transport phenomena, comprising airflow, heat and mass transfer, are key processes in refrigerated storage. This paper gives a review of approaches to modelling transport phenomena in food bulks, packages and stacks. Darcy–Forchheimer porous media models have been successfully used. Ergun theory was found not directly applicable when foods are stored in packages, which cause flow confinement and vent hole resistance, invalidating traditional theory. Heat and mass transfer in food bulks has been modelled using single- and two-phase models. Suggested modifications were demonstrated to not be generally valid, leaving much scope for further development of models for refrigerated system design. Direct CFD approaches were shown to be successful alternatives to achieve this goal.

[1]  R. Sman.  Solving the vent hole design problem for seed potato packagings, with the Lattice Boltzmann scheme , 1999 .

[2]  Denis Flick,et al.  Two-dimensional simulation of turbulent flow and transfer through stacked spheres , 2003 .

[3]  M. Kaviany,et al.  Slip and no-slip temperature boundary conditions at interface of porous, plain media'conduction , 1991 .

[4]  H.P.A. Calis,et al.  CFD modelling and experimental validation of particle-to-fluid mass and heat transfer in a packed bed at very low channel to particle diameter ratio , 2003 .

[5]  Yongfu Xu,et al.  Improving the quality of stored potatoes using computer modelling , 2002 .

[6]  Anthony G. Dixon,et al.  CFD study of fluid flow and wall heat transfer in a fixed bed of spheres , 2004 .

[7]  Dean Burfoot,et al.  Predicting condensation in bulks of foodstuffs , 1999 .

[8]  R.G.M. van der Sman,et al.  Simple model for estimating heat and mass transfer in regular-shaped foods , 2003 .

[9]  R.G.M. van der Sman.  Prediction of airflow through a vented box by the Darcy–Forchheimer equation , 2002 .

[10]  Michel Quintard,et al.  Two-medium treatment of heat transfer in porous media: numerical results for effective properties , 1997 .

[11]  H. Brinkman.  A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles , 1949 .

[12]  Da-Wen Sun,et al.  Applications of computational fluid dynamics (cfd) in the food industry: a review , 2002 .

[13]  C. L. Tien,et al.  Boundary and inertia effects on convective mass transfer in porous media , 1982 .

[14]  Jacob Bear,et al.  Fundamentals of transport phenomena in porous media , 1984 .

[15]  Akira Nakayama,et al.  A Macroscopic Turbulence Model for Flow in a Porous Medium , 1999 .

[16]  Denis Flick,et al.  Experimental study of convective heat transfer during cooling with low air velocity in a stack of objects , 2004 .

[17]  D. Flick,et al.  Numerical and experimental study of airflow in a typical refrigerated truck configuration loaded with pallets , 2002 .

[18]  D. Joseph,et al.  Boundary conditions at a naturally permeable wall , 1967, Journal of Fluid Mechanics.

[19]  D. Flick,et al.  Analysis of heterogeneous cooling of agricultural products inside bins: Part II: thermal study , 1999 .

[20]  Pierre-Sylvain Mirade,et al.  Effect of design of blowing duct on ventilation homogeneity around cheeses in a ripening chamber , 2006 .

[21]  D. Tanner,et al.  A generalised mathematical modelling methodology for the design of horticultural food packages exposed to refrigerated conditions Part 2. Heat transfer modelling and testing , 2002 .

[22]  R. V. Edwards,et al.  A New Look at Porous Media Fluid Mechanics — Darcy to Turbulent , 1984 .

[23]  K. Schnitzlein,et al.  The influence of confining walls on the pressure drop in packed beds , 2001 .

[24]  Bart Nicolai,et al.  Analysis of the air flow in a cold store by means of computational fluid dynamics , 2000 .

[25]  Weeratunge Malalasekera,et al.  An introduction to computational fluid dynamics - the finite volume method , 2007 .

[26]  Denis Flick,et al.  Modélisation semi-empirique des écoulements et des transferts dans un milieu poreux en régime turbulent , 2003 .

[27]  J. De Baerdemaeker,et al.  Discrete element modelling for process simulation in agriculture , 2003 .

[28]  D. Vortmeyer,et al.  Equivalence of one- and two-phase models for heat transfer processes in packed beds: one dimensional theory , 1974 .

[29]  P. Verboven,et al.  A CONTINUUM MODEL FOR AIRFLOW, HEAT AND MASS TRANSFER IN BULK OF CHICORY ROOTS , 2003 .

[30]  Massoud Kaviany,et al.  Slip and no-slip velocity boundary conditions at interface of porous, plain media , 1992 .

[31]  Bart Nicolai,et al.  Combined discrete elements and CFD modelling of air flow through randomly filled boxes with spherical food products , 2004 .

[32]  Marcelo J. S. de Lemos.  Turbulent kinetic energy distribution across the interface between a porous medium and a clear region , 2005 .

[33]  S. Amara.  Ecoulements et transferts thermiques en convection naturelle dans les milieux macro-poreux alimentaires application aux refrigerateurs menagers , 2005 .

[34]  Dean Burfoot,et al.  Simulating the bulk storage of foodstuffs , 1999 .

[35]  C. McGreavy,et al.  Fluid flow and heat transfer past two spheres in a cylindrical tube , 1986 .

[36]  Nicholas John Smale.  Mathematical modelling of airflow in shipping systems : model development and testing : a thesis presented in partial fulfilment of the requirements for the degree of Doctor of Philosophy in Food Technology at Massey University, Palmerston North, New Zealand , 2004 .

[37]  K. J. Beukema,et al.  Heat and mass transfer during cooling and storage of agricultural products as influenced by natural convection , 1980 .

[38]  Anthony G. Dixon,et al.  Comparison of CFD simulations to experiment for convective heat transfer in a gas-solid fixed bed , 2001 .

[39]  Lynn F. Gladden,et al.  Simulation of packed bed reactors using lattice Boltzmann methods , 2005 .

[40]  Anthony G. Dixon,et al.  Computational fluid dynamics simulations of fluid flow and heat transfer at the wall-particle contact points in a fixed-bed reactor , 1999 .

[41]  Eduard Egusquiza,et al.  Influence of the turbulence model in CFD modeling of wall-to-fluid heat transfer in packed beds , 2005 .

[42]  Stephen Whitaker,et al.  Momentum transfer at the boundary between a porous medium and a homogeneous fluid-I. Theoretical development , 1995 .

[43]  Stephen Whitaker,et al.  Heat and Mass Transfer in Porous Media , 1984 .

[44]  Florian Huber,et al.  Numerical simulations of single phase reacting flows in randomly packed fixed-bed reactors and experimental validation , 2003 .

[45]  Jacob Bear,et al.  Transport Phenomena in Porous Media , 1998 .

[46]  D. Nield.  Modelling Fluid Flow in Saturated Porous Media and at Interfaces , 2002 .

[47]  Jacques Comiti,et al.  A new model for determining mean structure parameters of fixed beds from pressure drop measurements: application to beds packed with parallelepipedal particles , 1989 .

[48]  Savvas A. Tassou,et al.  Modelling the environment within a wet air-cooled vegetable store , 1998 .

[49]  Lattice Boltzmann schemes for convection-diffusion phenomena : application to packages of agricultural products , 1999 .

[50]  Tadhg Brosnan,et al.  Precooling techniques and applications for horticultural products — a review , 2001 .

[51]  Marcelo J.S. de Lemos,et al.  Macroscopic turbulence modeling for incompressible flow through undeformable porous media , 2001 .

[52]  Pierre-Sylvain Mirade,et al.  Three-dimensional CFD calculations for designing large food chillers , 2002 .

[53]  Digvir S. Jayas,et al.  Resistance to airflow through clean and soiled potatoes , 1993 .

[54]  Martine Baelmans,et al.  Airflow through Beds of Apples and Chicory Roots , 2004 .

[55]  A. C Cleland,et al.  A generalised mathematical modelling methodology for design of horticultural food packages exposed to refrigerated conditions: part 1, formulation , 2002 .

[56]  Martine Baelmans,et al.  Sensitivity of temperature and weight loss in the bulk of chicory roots with respect to process and product parameters , 2004 .

[57]  Martine Baelmans,et al.  CFD model of the airflow, heat and mass transfer in cool stores , 2005 .

[58]  Robert F. Boehm,et al.  Flow and heat transfer around a linear array of spheres , 1994 .

[59]  I. F. Macdonald,et al.  Flow through Porous Media-the Ergun Equation Revisited , 1979 .

[60]  J. L. Lage,et al.  A general two-equation macroscopic turbulence model for incompressible flow in porous media , 1997 .

[61]  N. Wakao,et al.  Dispersion-Concentric Model for packed bed heat transfer , 1977 .

[62]  C. D. Baird,et al.  Resistance to Air Flow of Oranges in Bulk and in Cartons , 1985 .

[63]  G. Alvarez,et al.  Analysis of heterogeneous cooling of agricultural products inside bins Part I: aerodynamic study , 1999 .

[64]  S. Ergun.  Fluid flow through packed columns , 1952 .