Swelling

Letters swelling like bread

Goals of this Unit:

Heat the letters gradually from the outside.
Make density and viscosity dependent on temperature.

The fluid-mechanical problem We want the letters to behave like bread dough getting heated in an oven. To do this we need to apply heat gradually to the outside of the letters and we need the letters to swell and to change their texture during the heating process. Apply heat to the letters First of all, we want the letters to have a free surface so they can change their shape. This is achieved by setting their ACTIVE flags to ACTIVE$init_never$, which lets the boundaries of the letters participate in the initial filling of the point cloud but ignores them afterwards.

"C" = " BC0 ACTIVE$init_never$ IDENT%BND_slip% MAT$Mat1$ TOUCH%TOUCH_liquid% MOVE-1 LAYER0 CHAMBER1 SYMMETRYFACE2 " "F" = " BC0 ACTIVE$init_never$ IDENT%BND_slip% MAT$Mat1$ TOUCH%TOUCH_liquid% MOVE-1 LAYER0 CHAMBER1 SYMMETRYFACE3 " "D" = " BC0 ACTIVE$init_never$ IDENT%BND_slip% MAT$Mat1$ TOUCH%TOUCH_liquid% MOVE-1 LAYER0 CHAMBER1 SYMMETRYFACE4 "

This creates free surface particles at the boundaries "C", "F" and "D", which can now be referenced by the boundary condition "0". We force their temperature to grow linear with time. Its value starts by 0 at Y%ind_time% = 0 and scales up to a maximum of 1 at Y%ind_time% = 2.

BC_T(0) = (%BND_DIRICH%, [min( 0 + 0.5*Y%ind_time% , 1 )] )

Manipulate density and viscosity By letting the density of the particles increase with temperature, we can induce an expansion of the letters. We also want the viscosity to increase with temperature, thus simulating the hardening of the dough during the baking process. Finally, we restrain both parameters, thus modeling the end condition when the dough has fully transformed into bread. All of this can be achieved very simply via the max-function.

density($Mat1$) = [max(1-0.7*Y%ind_T% , 1-0.7)] ... eta($Mat1$) = [&eta_min& + (max(Y%ind_T%,0.001)^1.5)*30]

Here is an intermediate result of the simulation, where one can see the temperature distribution throughout the letters: Here should be a picture

Figure 1: A cross-section of the letters taken mid-simulation

Suggestions for exploring MESHFREE

Exchange the temperature boundary conditions for the letters and the plate
Tinker with the provided expressions for density and viscosity. You could for example impose smaller or higher boundaries on the density