Presentation on theme: "Chilling and freezing of foods"— Presentation transcript:
1Chilling and freezing of foods Food Modelling Club Seminar9 November 2005Chris KennedyNutriFreeze Ltd.
2Content Objectives of the models Analytical models Numerical models Determining your inputHeat transferThermal properties of foods
3Objectives Hardest part is often finding the right inputs … Mathematical modelling of freezing or chilling processes is usually performed to meet one or both of the following objectives.1.Residence time modellingI want a throughput of "x units per hour" …How big is the freezer I need?What type of freezer should I use?What does it cost?2. Quality modellingWeight lossEfficiencyEquilibrationBug growth and safetyHardest part is often finding the right inputs …
4Simple models The elementary Plank model Most heat transfer models for foods are based on two equations, namely:Newton’s equation (for heat transfer at the surface)The Fourier equation (Internal Heat conduction)
51-D Numerical solutionThe simplest geometry to start our consideration is the infinite slab. Here we assume that all of the heat transfer out of the slab is through the top and bottom surface.The slab is symmetric so we need only consider one half.Tc is the core temperature and Ts the surface temperature of the slab.
6The Plank modelThe Plank model gives a simple way of calculating freezing timesAssumesAll heat to be removed is latent heatThermal properties are constantThe final core temperature is TFNote we have rotated our slab 90o in this diagram. The distance “a” is the half-thickness of the slab.The slab started at a uniform temperature and the graph shows the temperature profile after a certain time.
7The Plank modelThe Plank Equation is derived from a consideration of the energy balance.As the freezing front moves a distance Dx into the slab it creates a new slice of frozen product of volume “A. Dx”. The latent heat removed across that slice is equal to the heat conducted from the slice to the surface which must also be equal to the heat removed at the surface.
8The Plank modelThe equations are solved analytically to give a total freezing time.
9The Plank model More generally where P and R are shape factors having values.500 and .125 for infinite plates.250 and for infinite cylindersand and for spheres
10Plank extendedPham and others have extended this equation to consider sensible heat by addition of further terms such thatThis is Newton's Law of Cooling with the factor 1+Bij/Kj added to account for internal resistance to heat flowBij/Kj is the ratio of the internal and surface resistances.
11Numerical solutionTo gain useful estimates of temperature distributions we need to use numerical methodsTo accurately predict freezing times, equilibration temperatures and surface temperatures we need to know the temperature gradients across the product as a function of time
121-D Numerical solution Let’s return to our infinite slab. Remember the heat flows are symmetric and we consider heat flow through the top and bottom surfaces only.
131-D numerical solutionFor the numerical model we “slice” the half-slab into n layers and consider the heat flows between each layer in a series of time steps.
14At each time step we calculate: 1-D Numerical solutionAt each time step we calculate:surface T using a potential divider and the heat flow from the previous stepsurface heat flow from Newton's equationeach of the internal heat flowsthe new temperature distributionThen move to the next time step
151-D Numerical modelThis figure shows the temperature evolution of each layer as a function of time in a freezing tunnel.
161-D Numerical modelAlternatively we can look at the “Key” temperatures.This slide shows the same simulation but this time we are just looking at the core (pink) and surface (blue) temperatures. The third line is the equilibrated temperature (red) calculated from the total heat content. This is the temperature that the product would equilibrate to, if the process was stopped at that point.
171-D Numerical modelWe can extract other useful information from this model, such as the Heat Flux at the surface, as shown here.
181-D Numerical model (chickens) This slide shows a simulation of the temperature profile across a chicken breast in a novel accelerated maturation chiller developed by Air Products plc.
191-D numerical modelThe 1-D method can also be applied to cylinders and spheresPackages such as HEATSOLV (available via evitherm website) also deal with more complex shapes by addition of a shape factorEquilibration temperatures allow us to calculate accurate residence timesSurface temperatures are useful for estimation of evaporative weight lossTemperature gradients allow us to deal with large or delicate products
20Finite element model FE analysis allows modelling of 3-D heat flow The basis is still the Fourier equation and Newton's Law of Cooling, but now a matrix calculationMost packages are also designed for stress modelling so this is the proffered choice of model for thermal stress analysisA number of commercial packages are available, for example:ALGORFEATELFEN
21Finite element analysis The picture here shows the result of a Finite Element Analysis of chilling of a beef leg using the ELFEN package.
22Finite element analysis Here the output is set to show the depth of crust freezing of the leg in an accelerated chilling process. The data was taken during an EU project on The Very Fast Chilling of Beef
23Determining heat transfer coefficients Most models use a single value of HTC. But heat transfer coefficients are rarely/never constant in space and time.
24The Cryomole A device for mapping heat transfer coefficients in freezers and chillers. The device is manufactured by York Electronics Centre
25The Cryomole The sensor is a known volume or surface area of copper Copper T and Air T are measured at, for example, 1 sec intervalsHTC is then calculated assuming infinite conductivity (a good assumption)
26The CryomoleRaw data from the Cryomole showing temperatures of the air and the copper probe
27CryomoleIssuesNeed to be sure that the measuring device does not change the property measuredAir flows around the mole etcLimited time as accuracy drops as the temperatures convergeActive devices may also be possibleA bit tough to use in a fluidised bed or rotary freezer!
28Thermal properties data A good model requires good thermal data for the materials concernedThe two main parameters required are the enthalpy v. temperature and thermal conductivity v. temperature relationshipsYou can of course measure these yourself (?) or get some help from a number of software programs and online databasesThe first port of call for all of these is:
29Sources of data (COSTHERM) An easy code to predict the thermal properties of foods is COSTHERMCOSTHERM was developed under the EC’s COST90Generally looked after by Paul Nesvadba of Rubislaw ConsultingThe software is a series of algorithms based on food composition where the user enters:Water contentProtein contentFat content etcFreezing point and density
30OutputsThe plots show data for heat content and thermal conductivity of product for a range of temperatures
31Sources of data (COSTHERM) Although accurate modelling requires a knowledge of the composition, this plot demonstrates the large extent to which heat content is dependent on water content.
32Sources of data (evitherm.org) COSTHERM (program for predicting thermal diffusivity of liquid food)CINDAS (thermophysical properties, mainly solids)eFoodSolver (has a thermal property predictor tool at the foot of the page) HEATSOLV (1-D heat equation solver: slab, cylinder, sphere and "fractal shape" such as a fish -somewhere between cylinder and slab)NELFOOD (food properties data)
33Nelfood available via evitherm … NELFOOD - Physical Properties of Food Database, hosted by the National Engineering Laboratory, Scotland (NEL)The NELFOOD interactive website allows users to view, add and modify bibliographic and experimental data on the physical properties of foods. Users can search throughover bibliographic references1500 materials1600 experiment data sets About one third of the data in NELFOOD concerns thermal properties of foods. Other categories are mechanical, electrical, diffusion/sorption and optical/colourThe data sets range over 24 categories encompassing 249 subcategories and 260 physical properties. Once data is found, it can be viewed, plotted, copied, and printed out.
34SummarySimple analytical models based on Plank are often sufficient to give a good approximation of residence timeFor more accurate estimates and for information on surface temperatures and temperature distributions numerical methods will provide more information
35Summary The model can only be as good as the data There are now numerous sources of data which cover a wide range of thermal properties (in addition to the data you need)Software is available to estimate thermal propertiesBest results will always be attained from actual measurements of HTC and thermal properties