Modeling Melting and Solidification

Flow Resistance Due to Solidification

The Melting and Solidification model simulates only the effect of phase change on the energy equation; it does not modify the momentum equations. A further model is required to account for the change in material properties from the liquid state to the solid state.

Depending on the value of the relative solid fraction (specifying to which extent the liquid has solidified), there are three optional models available:

• Slurry Viscosity Model

  For low values of solid fraction the mixture is considered as a slurry, where solid grains are suspended in the melt nearly without interacting with each other. Their effect on the flow is often modeled as a relative solid fraction-dependent viscosity.

  The Metzner method is implemented to increase the viscosity (slurry viscosity) up to the critical solid fraction (approximately 0.3) (see Eqn. (2713)), which models the solidified grains flowing with the fluid without much interaction. However, using a range of viscosity larger than about two orders of magnitude can be unstable.

• Mushy Zone Permeability Model

  When the solid volume fraction increases, equiaxed grains grow and start to agglomerate and to form dendritic regions. Dendrites also grow from cooled solid surfaces or the solidification front into the melt. A partially solidified stationary region permeated with dendrites is called a “mushy zone”. The flow resistance in a mushy zone can be modeled similar to an isotropic porous medium, using the Carman-Kozeny Mushy Zone Permeability method (see Eqn. (2717)). This model is used for relative solid volume fractions above the specified critical solid fraction (approximately 0.3).

• Flow Stop Functionality

  To stop the flow on solidification completely, you can use the flow stop functionality. The Melting-Solidification Flow Stop model is activated above the specified flow stop solid fraction (approximately from 0.4 through 1). The resistance that the Slurry Viscosity and Mushy Zone Permeability models add to moving fluids depends on the flow velocity. When the velocity is zero, the effect of both models is also zero. In the presence of pressure gradients, or body forces such as gravity, a creeping flow develops independently of the magnitude of slurry viscosity or mushy zone permeability.

Applicability of the Flow Resistance Models

The Slurry Viscosity model and the Mushy Zone Permeability model affect the flow properties of a partially solidified liquid only. You need these models only when you are simulating impure substances such as alloys. You do not need them, for example, when you simulate ice melting in a stationary container.

If you simulate the melting and solidification process of a pure substance, use the Melting and Solidification model only. Partial solidification is not possible for pure substances. To prevent creeping flows, you can additionally activate the flow stop functionality.

When simulating melting and solidification of impure substances, use the following table to determine which flow resistance models to apply.