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Process Conditions

Temperature

This section starts with the specification of the temperature boundary condition, if neither temperature coupling nor 1d_temp is chosen in section Model at the top of the input file. Three alternatives are available to describe the type of temperature trend: If the flag linear is chosen, the number of connecting points has to be defined. Then, first the initial temperature at the bottom of the simulation domain and the initial temperature gradient in z-direction are requested. Afterwards, for each connecting point, the time, the temperature at the bottom, and the temperature gradient in z-direction have to be specified. The temperature and temperature gradient will be interpolated linearly between these transition points. In this way, an arbitrarily complex temperature-time profile can be applied. If the number of connection points is set to 0, only the initial temperature at the bottom, the temperature gradient in z direction and a constant cooling rate in K/s are requested.

Example 1

Definition of linear temperature trend and connecting points

...
# Process Conditions
# ==================
#
# Temperature
# -----------
# Type of temperature trend?
# Options:   linear     linear_from_file     profiles_from_file
linear
# Number of connecting points?    (integer)
2
# Initial temperature at the bottom?  (real)  [K]
1150.0    
# Temperature gradient in z-direction?  [K/cm]
0.0    
# 1 Connecting point, time  t [sec]?
2.5
# 1 Connecting point, temperature
1125.
# 1 Connecting point, temp. gradient in z-direction [K/cm]
5.0
# 2 Connecting point, time t [sec]?
7.5
# 1 Connecting point, temperature
1000.0
# 2 Connecting point, temp. gradient in z-direction [K/cm]
25.0
...

Using the flag linear_from_file, it is also possible to read the same information from a file consisting of three columns: the time in seconds, the temperature at the bottom in Kelvin, and the gradient in Kelvin per centimetre. This allows a more compact input for extensive temperature-time input data.

While the first two options always lead to linear temperature profiles in z-direction, the option profiles_from_file allows reading time-dependent non-linear temperature profiles from a series of ASCII data files (or from different columns of a single data input file). Again, the number of connection points has to be specified, and for each of those points, the time and a file name, optionally with specification of the used columns, has to be given. The example file T021_Grain_Growth_Profiles.dri illustrates the use of this option for simulation of grain growth in the heat-affected zone of a welding (see Grain Growth Examples).

If the release of latent heat is enabled (lat_heat in section Model Specification), input of the thermal boundary condition is made via the heat flux (in [Js/cm^3]) instead of a cooling rate or temperature trend (DTA approximation). Like in the case of the temperature trend, an input of variable heat flux-time relations is possible via connection points or by reading from a file. Of course, the option profiles_from_file is not available in case of using latent heat.

Thermo-physical properties for 1D temperature solver

If the option 1d_temp has been selected at the beginning of the input file (see Thermal Conditions, a one-dimensional temperature field is applied as extended temperature boundary condition. The initial temperature field can either be read from a text file or be specified in linear approximation by input of a value for the upper and lower end of the 1d-temperature field.

In case any type of boundary condition has been chosen for the 1D temperature field, which requires further input of values or data sources (g,f,j, see section Boundary Conditions) the corresponding input has to be included here.

Then, the user has to choose whether to apply constant thermo-physical data (enthalpy, heat capacity and thermal diffusivity) for this temperature field, or to specify files where these thermophysical data shall be read from as a function of temperature. All three thermodynamic quantities are read separately for the part of the 1D-temperature field which lies above and below the micro-simulation domain. This can be important if e.g. a strongly undercooled columnar dendritic front is simulated.

In many cases, all this thermophysical information can be taken (iteratively) from the dTLat output of a prior MICRESS® simulation[1]. Alternatively, the thermo-physical data file may be created using Thermo‑Calc™.

Boundary values for phase field

If any fixed (f) or wetting (w) condition has been specified for the phase-field in section Boundary Conditions, corresponding values need to be given here.

1D far field for solute diffusion

In case of concentration coupling, a one-dimensional far field approximation for solute diffusion can be applied as modified boundary condition in z-direction using the keyword 1d_far_field. This option typically is used for simulation of directional solidification and has two effects:

1.) An additional one-dimensional concentration field is added as extension to the top of the simulation domain. This is helpful for resolving long-range diffusion fields without having to increase the calculation domain.

2.) In the upper part of the normal simulation domain, diffusion is also solved in 1D-approximation, starting from a given distance from a growth front.

If 1d_far_field is enabled, one has to specify the length (in cells) of the 1D external extension. The spatial resolution of the external 1D-concentration field is the same as for the normal simulation domain. Next, the distance from the growth front in \mu m from which diffusion shall be solved in 1D has to be specified. The position of the growth front is defined as the point with the highest z-coordinate which contains phases other than the matrix phase (the matrix phase is automatically determined as the phase which is present at the top left corner at the beginning). The advantage of this approximation is a speed-up of the simulation run.

Finally, the initial concentration of the 1D extension has to be specified. Each component can be defined as constant or from_file. In the latter case, the initial concentration profile of the 1D extension is interpolated from an ASCII file containing one-dimensional information of distances (in \mu m) and corresponding concentration values. If the keyword from_file is chosen, the name and path of the file need to be specified. The file e.g. could have been written from earlier MICRESS® results in ASCII format using DP_MICRESS. Extra output files showing the concentration profiles outside the domain will be generated (1D_Ext files).

Example 2

1D far field for concentration

...
# 1D far field for solute diffusion
# ---------------------------------
# Enable one dimensional far field approximation for solute diffusion?
# Options:     1d_far_field   1d_far_field_EW  no_1d_far_field
1d_far_field
# Number of cells for the 1D external field?
500
# 1D far-field diffusion approximation was set.
# From which distance from the front should the diffusion be
# solved as 1D?  [micrometers]
200.00
# This distance is equivalent to 200 cells.
# How shall concentration of 1D extension for component 1 be set?
# Options: constant from_file
constant
# How shall concentration of 1D extension for component 2 be set?
# Options: constant from_file
constant
...

Note: If a 1D far field is used, the definition of the top boundary condition for the concentration field is applied to the top of the 1D extension!

Fix boundary conditions settings

If fix boundary conditions for concentration were chosen in the section Model, explicit values have to specified here for each component and direction.

Example 3

Fix values for concentration boundary settings

...
# Boundary concentration
# ----------------------
# Fixed value for concentration field for component 1 in Top-direction
1.0000
# Fixed value for concentration field for component 2 in Top-direction
1.0000
#
...

Moving Frame

As next, the moving frame options have to be set. This feature is very useful for simulations related to directional solidification, as it allows the reduction to a smaller simulation domain which follows the movement of the solidification front. This is shown schematically in Figure 1 and in the example for directional solidification of a conventional Ni-base superalloy in Figure 2.

Figure 1

The moving frame: the current area with the whole simulation area

This option is not available for use with latent heat (lat_heat) because it is not compatible with the assumptions of the DTA approximation. If the flag moving frame is selected, the user has to chose a criterion which controls the movement of the simulation domain. Available criteria are temperature and distance. In case of temperature, a critical temperature is requested. If the temperature at the bottom falls below this value, the domain is moved in z-direction until the bottom temperature reaches the critical value. In case of a constant cooling rate, this option leads to a constant moving velocity like in a typical Bridgman furnace experiment.

Figure 2

2D simulation with moving frame: directional solidification of IN706

If distance is selected, the distance of the solidification front (more exactly the highest position of any object with phase number >matrix phase) from the top of the simulation domain is used as criterion for movement of the simulation domain. Thus, for example, a constant distance of a dendrite tip from the top can be achieved. The matrix phase is automatically selected as the phase which is present at to top left corner at the beginning of the simulation, but also can be explicitly selected by the user as additional optional parameter in the same line with distance. A negative sign means that all phases but the one selected are considered as matrix phase. In both cases (temperature and distance), the corresponding value has to be given in the next line after the keyword.

If the out_moving_frame flag is set, a Gesamt (global) data file is additionally created for all selected graphical outputs. The corresponding files have a G appended to their root name (e.g.: SimulationG.phas under Linux). They consist of the simulation domain for the latest output (the coloured part in Figure 1, to which all the information of the grid cells that have moved out from the domain during simulation is appended (the grey part). Consequently, they can be much larger than the normal outputs and have their own geometry file (SimulationG.geoF).

Note: using the moving frame option is very reasonable in combination with the 1D far field option. This combination allows the simulation of stationary processes with long-range diffusion profiles. In most cases it is reasonable to use identical distances for the moving frame (with option distance) and for the 1D far-field diffusion approximation.

Example 4

Definition of a moving frame with the distance criterion and no data storage

...
# Moving frame
# ------------
# Moving-frame system in z-direction?
# Options:      moving_frame      no_moving_frame
moving_frame
# Should the distance or the bottom temperature be
# used as criterion for moving frame?
# Options:  distance [matrix phase (negative: special phase)] temperature
distance
# At which distance from the upper boundary should the frame
# be moved?  (real)  [micrometers]
200.0000
#
# Store data shifted out of moving-frame system?
# Options:      out_moving_frame     no_out_moving_frame
no_out_moving_frame
...


  1. B. Böttger, J. Eiken, and M. Apel. Phase-field simulation of microstructure formation in technical castings - a self-consistent homoenthalpic approach to the micro-macro problem. Journal of Computational Physics, 22818:6784–6795, oct 2009. doi:10.1016/j.jcp.2009.06.028