Znak katedry

Department of process engineering U218

Research project: Waffle baking

Preface and links:

Project "Hydrophobierung and biologische Abbaubarkeit von Materialien aus nachwachsenden Rohstoffen" , was initiated in 1996 at TU Dresden, Institute fur Lebensmittel und Bioverfahrenstechnician by Prof.Lothar Linke. This project is a good example of cooperation between Germans (TU Dresden /supervisor/, Ingenieurburo dur Nahrungsgutertechnician IBN GmbH Dresden) and Czechs ( ICT Prague, and CTU in Prague). The project is supported by Deutsche Bundesstiftung Umwelt . Our contribution is oriented on the mathematical modelling of the process of waffle baking:
  1. Process description
  2. Mathematical models
  3. Parametric identification
  4. Results
  5. Technological impacts and open questions

Abstract:

Physical models describing baking of the starch based biologically degradable products (dishes, packages, etc.) are suggested and verified by experiment. Suggested pressure baking technology is similar to the contact heating of waffles in a toaster: raw material - water suspension of starch and additives (e.g. cellulose) - is placed into a closed planar mould and heated by contact with walls having a constant temperature.



The time courses of temperature, measured at the centre of the narrow gap between the walls (the gap thickness is only 4 mm) exhibit a local maximum - suspension temperature increases to cca 120-1400 C, then decreases and only after some time monotonic rises to the wall temperature 1800 C! Also the pressure, measured at the centre of the heated sample is characterised by one or two distinct peaks of about 2-3 bars. Crust and core models try to explain these non-usual phenomena assuming that the boiling temperature of free water - and thus the temperature of suspension- is controlled by the pressure of the evaporated steam. Three phases of thermal processing are analysed separately:
Waffle baking (animated)
  1. The first phase is heating of a more or less homogenous layer of water suspension up to the onset of boiling.
  2. The second phase is characterised by evaporation of free water and by formation of a growing solid crust. At the same time the liquid core expands, driven by pressure of steam, which leaves the crust-core interface and flows through the porous crust and along the walls of the mould. The friction loses in the crust and in the interstitial spaces at the wall determine pressure at the crust-core interface, and are manifested as the first peak of recorded pressure.
  3. When the crust is fully developed and the expansion stops, the last phase of heating, accompanied by the evaporation of the remaining bound water, begins. The sample temperature no longer depends on the boiling temperature and steadily approaches the temperature of wall.
The second peak of pressure that was sometime observed can be ascribed to the non uniform distribution of pressure along the surface of sample.

The lowest pressure (approximately atmospheric pressure) must be at the periphery, but a low pressure means a low temperature of boiling, therefore a large difference between the temperature of wall and the temperature of the crust-core interface. Thus the temperature gradient and the crust growth rate is greatest at the periphery of the baked sample and just there the solid crust is soonest developed. This firm peripheral crust closes the remaining liquid suspension inside the sample and prevents its further expansion, which causes the pressure increase.

Mathematical models

Simplest mathematical models are crust-core integral models, describing the whole sample in terms of mean temperature, mean pressure, volume of sample and mean thickness of crust as functions of time. This integral model forms a basis for the shell element, which can be used in a finite element program,

More details, concerning transversal temperature, pressure and moisture profiles, are obtained by two dimensional models using finite difference methods. Some results (temperature and crust thickness as functions of time) are shown in Fig.



Technological impacts and open questions

Even if the theoretical analysis and numerical simulation of baking process has not been fully completed and a match with experimentally measured data is not excellent, some conclusions can be drawn:
This project is far from being finished, and the research, coordinated by TU Dresden continues.

Experiments (photogallery of samples)




@TEC: 3. 3.2003 Change language to English DEFAULT BACKpeoples U218 FS-CVUT Interesting links mailto: Zitny