Phase transition models with hysteresis

Most materials in slPCMlib database have different heat capacity data for heating and cooling. These PCM show thermal hysteresis in the phase change. The following models are considered to account for thermal hysteresis:

These models are phenomenological models. They require only two fixed phase fraction-temperature curves for increasing and decreasing temperature. These are the phase fraction functions for heating and cooling in the slPCMlib database.

The models are included in the Modelica/Dymola library GitHub-slPCMlib.

Examples



Interrupted melting and solidification

The predicted phase fractions are very different for hysteresis each model. It is obvious, that that the curve track model is not able to reproduce hysteresis for interupted/ incomplete phase change processes, see below.

Curve track model

Curve switch model

Curve scale model

Rate-independence

All models are rate-independent: increased heating rates lead to faster melting but result in the same state (phase fraction) for any stopping temperature. Accordingly, also the magnitude of the hysteresis is rate-independent, compare left and right plots.

Curve track model
       

Curve switch model
       

Curve scale model
       

Heat conduction in PCM

This example considers heat conduction in PCM on a rectangular 2D (x,y) domain. A perfect temperature control is assumed at the boundaries of the domain and a sinusoidal excitation signal. For the numerical solution the heat conduction equation is discretized. For each grid point a discrete heat conduction equation and a (curve scale) hysteresis model are solved. Computed phase fractions and enthalpies are highligthed for three grid points (green, magenta, blue).

PCM on a rectangular 2D (x,y) domain

Curve scale model


References