Contribution to the modelling of chocolate tempering process
Special Symposium - Innovations in Food Technology (LMC Congress)
Flexible Production, PAT & Modelling (Food-3a)
Keywords: chocolat, CFD, tempering, transport phenomena
Tempering process refers to a controlled melting and cooling of chocolate in order to achieve at the end the correct crystalline structure of the constituent cocoa butter (form V of the six different polymorphic forms). Well tempered chocolate is shiny, even-coloured, crisp, and smooth tasting, while badly tempered chocolate is chalky and grainy, within the form of an unattractive, dull brown mass streaked with grey.
The trick to tempering is to control the temperature of the melted chocolate very precisely: first cooling it and then reheating slightly or adding crystallization nuclei such as solid chocolate.
In this study, a mathematical model is developed in order to get a better analysis and control of the tempering process.
The system considered here is the one used by professional pastry chefs and chocolatiers for dipping, moulding and decorating. A batch of chocolate is first molten in a bowl placed in a temperature controlled water bath. The molten batch is then cooled at ambient temperature, while gently mixed by hand. At a given temperature, the liquid chocolate is seeded with a given amount of small solid pieces (for instance crystals of solid chocolate) to ensure the crystallization under the best form (V).
The modelling work aims to predict the evolution with time of the temperature field inside the chocolate during the cooling and crystallization phase.
Firstly, the mixing of melted chocolate is studied without taking care of any heat transport. A mechanical stirrer is designed to simulate the manual mixing in a controlled manner. Even if it can be anticipated that melted chocolate exhibits non-Newtonian behaviour because of the importance of solid particles (of sugar, cocoa and milk powder) dispersed in the continuous fat melted phase, a laminar Newtonian flow is considered. A CFD simulation is performed using Fluent software, whose results display a mainly axial secondary flow.
Secondly, on the basis of this flow analysis, the transient heat transfer problem is simplified by neglecting the convective terms in the heat balance equation but using an effective thermal conductivity parameter to take into account enhancement of heat transport by the mixing process. This one is therefore modelled as a thermal diffusion process between neighbouring fluid layers.
The resulting transient axisymetric heat conduction equation complemented with adequate boundary conditions is solved using Femlab. The value of the effective conductivity is fitted against experimental results, more precisely the temperature measured in the center of the bowl. A value of 10,7 W/m K is obtained, which is one order of magnitude higher than the thermal conductivity of molten chocolate.
A very good agreement is observed for the whole temperature field. Indeed, predicted transient temperatures compare very well to experimental data obtained with thermocouples set at 6 different locations within the melted chocolate.
Thirdly, a sink term is added to the thermal balance equation to take into account the additional cooling arising from the latent heat of melting of the solid pieces used as crystallization seeds. This term is written under the form of a kinetic reaction whose parameters are identified from an adiabatic melting experiment.
The resulting model gives finally an accurate prediction of the cooling rate and the temperature field within a mass of melted chocolate let at ambiant temperature and seeded with small solid grains. On-going works focus on the development of a shrinking core model to better describe the step of seeds melting. The nucleation process will then be studied in order to complete the model. Such models should be useful to identify better criteria for good tempering conditions.
See the full pdf manuscript of the abstract.
Presented Wednesday 19, 15:50 to 16:05, in session Flexible Production, PAT & Modelling (Food-3a).
