SET_CONDITION

Variable

Legal variables are pressure (P), temperature (T) or heat extracted (Q) as a function of time (TIME), TIME_TEMPERATURE_PAIRS (T-T-P) that specifies temperature at a specific time and lets the program calculate the cooling or heating rate, or LOOKUP_TABLE_TEMPERATU that reads a file with time-temperature pairs. For Q the amount of extracted heat per time unit is normalized and the size of the system is normalized to 1 mole of atoms.

For example, if you enter T-T-P at the Variable prompt then at the next prompt:

TIME,TEMPERATURE

Specify temperature and time pairwise such as e.g.:

0 1400

60 1200

* 1200

Where entering an asterisk(*)" is required in order to indicate the end time of a simulation.

For LOOKUP_TABLE_TEMPERATU the file should look similar except for the end time:

0 1473

60 1273

1000 1173

For the lookup table some optimization is done. Redundant pairs are removed when reading the data.

Tips to Determine the Temperature as a Function of Time

The two methods to determine the temperature as a function of time, TIME_TEMPERATURE_PAIRS and LOOKUP_TABLE_TEMPERATU, are used in different ways based on the type of simulation.

• TIME_TEMPERATURE is a shortcut to the ordinary temperature condition and is translated into a series of different temperature conditions. For example, they appear as a series of conditions if the conditions are listed. This sets some limits on the time-step that is used, occasionally overriding the limit set in the SET_SIMULATION_TIME command. The time-step is also adjusted to always coincide with the time giving in the time-temperature pair. Therefore it is recommended that this option is only used for a limited number of pairs, e.g. a linear approximation of a heat-treatment cycle. For the input to be valid, the last time in the set of pairs must be given as a wildcard ^*.

• LOOKUP_TABLE stores the time and temperature pairs and interpolates within the table in order to obtain the correct temperature for a certain time. The time-step is limited by how much the temperature is allowed to change over the time-step besides the maximum limit provided by the SET_SIMULATION_TIME command. This allows for the use of a very large dataset containing several hundred values, e.g. a measured temperature from a solidification. Should the simulation exceed the last time given in the table, an error message is shown but the simulation will continue using the last temperature in the list.

Condition type

Defines the type of boundary condition to be specified. The options may in most cases be functions of both TIME, T (temperature) and P (pressure). The default is CLOSED_SYSTEM which is equivalent to setting the fluxes of all components to zero at the boundary.

Options are:

• FIX_FLUX_VALUE: Enter functions that yield the flux times the molar volume for the independent components. May be a function of time, temperature and pressure.
• STATE_VARIABLE_VALUE: A legal expression in POLY-3 syntax that reduces the degrees of freedom. This type of boundary condition should be used with the uttermost care as no checks are done if it is a legal expression in advance.

• ACTIVITY_FLUX_FUNCTION or POTENTIAL_FLUX_FUNCTION: These types of boundary conditions are used to take into account the finite rate of a surface reaction. The flux for the independent components must be given in the format:

  

  or

  

  where f and g may be functions of time (TIME), temperature (T), and pressure (P), and N is an integer.

The activities are those with user defined reference states. The function is the mass transfer coefficient, is the activity of the corresponding species in the gas and N is a stoichiometric coefficient.

For more details see L. Sproge and J. Ågren, “Experimental and theoretical studies of gas consumption in the gas carburizing process” J. Heat Treat. 6, 9–19 (1988).

• ITERATIVE_ACTIVITY_FLUX_FUNCTION: Same as activity flux function above. However, an iterative scheme is used to determine the flux. This method may be used instead of activity flux function when the latter has problems.
• CLOSED_SYSTEM: Corresponds to a fix flux value, which is set to zero at all times.
• MIXED_ZERO_FLUX_AND_ACTIVITY: The flux of selected components is set to zero and the activity of others may be set to a prescribed value.
• GAS: The flux of selected components is set to zero and the activity of others may be set to a prescribed value. This option is used for treating an expanding system, e.g. the growth of an external oxide scale.

High time limit

The upper time limit to be used when entering a time dependent function. An asterisk * indicates the high limit as infinity.