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Materials Algorithms Project
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Program MAP_STEEL_DROPCOOL

  1. Provenance of code.
  2. Purpose of code.
  3. Specification.
  4. Description of program's operation.
  5. References.
  6. Parameter descriptions.
  7. Error indicators.
  8. Accuracy estimate.
  9. Any additional information.
  10. Example of code
  11. Auxiliary routines required.
  12. Keywords.
  13. Download source code.
  14. Links.

Provenance of Source Code

C. N. Hulme-Smith
Phase Transformations Group,
Department of Materials Science and Metallurgy,
University of Cambridge,
27 Charles Babbage Road,
Cambridge, CB3 0FS, U.K.

E-mail: C. N. Hulme-Smith

Added to MAP: July 2019.

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Purpose

This program simulates the rapid cooling of alloys from the molten state and calculates the amount of austenite and ferrite during cooling. It also calculates the temperature as a function of time, which may be used for separate solid-state transformation modelling. It is to be used with MTDATA which provides thermodynamic modelling at each step of the program, to determine whether phase changes will occur and the identities and composition of newly-forming phases.

DROPCOOL was originally written under the name TeRRaCoTtA (Temporally-resolved rapid cooling of test alloys) for the InnovateUK project Series production of Lightweight parts by Isostatic pressing of Metal powders to give Material and Energy Reduction (SLIMMER).

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Specification

Language:FORTRAN 77
Product form:Source corde and Linux-compatible executable
Platform:Linux - tested on Debian 8.0 (Jessie) and 9.0 (Stretch)

Complete program.

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Description

DROPCOOL is a simulation of rapid cooling, designed to be used with small droplets, as found in the gas atomisation of liquid metals to form powders. It uses physical laws to simulate radiative and convective heat flow from spherical particle and calculates a time-resolved temperature profile. Thermokinetic modelling is used to predict solidification and the phases that form from the melt.

At each timestep, the driving force for solidification is calculated, allowing for either austenite or ferrite to be the nucleating phase. The expected number of solid nuclei is calculated at each timestep and once this expected number exceeds one, solidification is assumed to have begun. There then follows a period of recalescence during which the temperature of the droplet increases and solidification is assumed to be rapid and of the nucleating phase only. Once the temperature reaches a peak, the Scheil-Guliver model is used to determine phase fraction and composition of any new solid. In the case of ferrite being the nucleating phase, the peritectic reaction is permitted and accounted for in terms of heat flow and solid fraction. The Scheil-Guliver model is then restarted to allow any remaining liquid to solidify. Once solidification is complete, the temperature profile is calculated down to some specified end temperature, which provides a cooling profile that can be used, for example, in modelling solid-state precipitation of secondary phases.

All physical processes are modelled using physical parameters (e.g. heat capacity, thermal conductivity, etc.), which are specified in an editable input file. These may be changed without recompiling the program. These parameters are calculated for each time step by taking a weighted average of the values for the solid and liquid phases.

The as-provided executable accepts inputs from a file called input1.txt. The script simit.sh copies any nominated input file to input1.txt and executes the program, writing results to a second designated file. This script should be called using the following syntax:

         ./simit.sh input_example.dat output_example.txt
      

Alternatively, the program may be launched directly as long as the inputs are saved to a file in the same directory as the executable and named input1.txt. In this case, the results are written to the terminal unless they are redirected to a file using the standard Unix command:

        ./DROPCOOL > [results file name]
      

Files:

input_example.dat Input data file, containing physical parameters and composition.
DIRUSRAP.FOR Definitions used by MTData, provided by the National Physical Laboratory (NPL).
standard-plus.mpi Contains the definitions of the system and lists of allowed phases and components used in MTDATA. Created using the NPL's PLUS database, version 4.02.
DROPCOOL.f FORTRAN 77 source code.
DROPCOOL Linux-compatible executable compiled using the source code DROPCOOL.f.
compile Shell script capable of compiling the source code into the executable and interfacing with MTData in Debian 8.0 (Jessie).
simit.sh Shell script that executes the program, specifies an input file from which data are read and a results file to which data are written.
output_example A results file containing the output obtained when the contents of input_example.dat is used as input data.

Follow the steps listed below to use the module:

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References

  1. D. Bergmann, U. Fritsching & K. Bauckhage, A mathematical model for cooling and rapid solidification of molten metal droplets, International Journal of Thermal Science, 39 (2000) 53-62.

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Parameters

Input parameters

file input_example.dat
DIAMETER - REAL
Diameter of the droplet in micrometres (μm).

STARTING_TEMP — DOUBLE PRECISION
Temperature at which the simulation starts in °C.

END_TEMP — DOUBLE PRECISION
Temperature at which the simulation is terminated in °C.

GAS_TEMP — DOUBLE PRECISION
Temperature of the quenching fluid in °C.

WALL_TEMP — DOUBLE PRECISION
Temperature of the wall of the quenching chamber in °C.

DROP_SPEC_HEAT — DOUBLE PRECISION
Specific heat capacity of the starting liquid in J mol-1 K-1.

LIQ_SPEC_HEAT — DOUBLE PRECISION
Specific heat capacity of the enriched liquid during solidification in J mol-1 K-1.

SOL_SPEC_HEAT — DOUBLE PRECISION
Specific heat capacity of the solid mass in J mol-1 K-1.

TIME_STEP — DOUBLE PRECISION
The number of seconds by which the time increments after each iteration of cooling.

HEAT_TRANS_COEFF — DOUBLE PRECISION
The heat transfer coefficient between the droplet and the quenching medium in W m-2 K-1.

EMISSIVITY — DOUBLE PRECISION
The emissivity (efficiency with which thermal energy is radiated) of the droplet; dimensionless.

TOT_COMP(11) — DOUBLE PRECISION
Overall composition of the droplet in the order: C, Mn, Ni, Cr, Al, Si, Mo, Co, W and V. The final element of the array is unused. The composition is specified in wt%. This order and/or number of coefficient may be changed by making a new multiphase input (.mpi) file in MTData and updating the source code to match the size of the array ot the number of alloying elements.

MPIFILE — CHARACTER (20 CHARACTERS)
The multiphase input (.mpi) file used by MTData that defines the elements and phases that may be used in calculations. The name may be changed, or a new file may be created from within MTData, using normal MTData commands.

MPRFILE — CHARACTER (20 CHARACTERS)
The multiphase results (.mpr) file used by MTData that contains results of thermodynamic calculations. The name may be specified as “''” (i.e. two single quotation marks, which is interpreted as blank by the program. This results in the .mpr file taking the same name as the .mpi file. An alternative filename may be given, but is restricted to 20 characters. This limit can be changed by altering the variable declaration in the source code and recompiling the program.

Output parameters

File output_example.dat

THE_TIME — DOUBLE PRECISION
The time (s) after each iteration of the cooling calculations.

THE_TEMP — DOUBLE PRECISION
The temperature (°C) after each timestep.

SOLIDFRAC —- DOUBLE PRECISION
The molar fraction of solid that has formed up to and including the latest timestep (total time given by the variable THE_TIME). This variable will only be printed once solidification begins.

SOLIDPHASE — CHARACTER
Gives the MTData name for the solid phase that formed in the most recent timestep. Only one phase may form in any one step. Austenite is called FCC_A1 and ferrite is BCC_A2. This variable will only be printed once solidification begins.

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Error Indicators

The program will print out descriptive error indicators should the program execute abnormally. Each error message is unique and will provide a quick way to find the affected part of the source code.

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Accuracy

No information supplied, although some data may be available in MTData technical manuals and documentation associated with the NPL PLUS database, version 4.02.

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Further Comments

None.

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Example

1. Program text

Complete program.

2. Program data

input_example.dat

      150.0E-06     ! diameter in micrometres
      1.60E+03      ! starting temperature in Celsius
      3.0E+02       ! final temperature in Celsius
      3.0E+02       ! temperature of the atomising gas in Celsius
      4.0E+01       ! temperture of the atomiser wall in Celsius
      8.0E+02       ! specific heat capacity of the molten droplet in J/(kg K)
      8.0E+02       ! specific heat capacity of the enriched liquid in J/(kg K)
      3.0E+02       ! specific heat capacity of the solid steel in J/(kg K)
      1.0E-03       ! time step in seconds
      7.0E+00       ! interfacial heat transfer coefficient between the droplet and the gas in W/(sq.m K)
      2.0E-01       ! black-body emissivity of the droplet (dimensionless)
      0.0147        ! wt% C
      2.00          ! wt% Mn
      10.78         ! wt% Ni
      17.14         ! wt% Cr
      0.00          ! wt% Al
      0.75          ! wt% Si
      2.50          ! wt% Mo
      0.00          ! wt% Co
      0.00          ! wt% W
      0.00          ! wt% V
      0.00          ! wt% not used
      standard-plus ! name of MPI (MultiPhase Input) file for MTData calculations
      standard-plus ! name of MPR (MultiPhase Results) file for MTData calculations

    

3. Program results

RESULTS

The first four lines of the output (beginning with the inverted question mark, ¿) are due to the launch of MTData and may be ignored.

      
      ¿[37;44;0m
  
  
  
      Time / s,Temperature / C,Atomic fraction of solid,Last solid phase to form
        0.1000000E-02,1599.066
        0.2000000E-02,1598.133
        0.3000000E-02,1597.202
        0.4000000E-02,1596.273
        0.5000000E-02,1595.346
        0.6000001E-02,1594.420
        0.7000001E-02,1593.496
        0.8000000E-02,1592.574
        0.9000001E-02,1591.654
        0.1000000E-01,1590.735
        0.1100000E-01,1589.819
        0.1200000E-01,1588.903
        0.1300000E-01,1587.990
        0.1400000E-01,1587.079
        0.1500000E-01,1586.169
        0.1600000E-01,1585.260
        0.1700000E-01,1584.354
        0.1800000E-01,1583.449
        0.1900000E-01,1582.546
        0.2000000E-01,1581.645
        0.2100000E-01,1580.745
        0.2200000E-01,1579.847
        0.2300000E-01,1578.950
        0.2400000E-01,1578.056
        0.2500000E-01,1577.163
        0.2600000E-01,1576.271
        ⋮ 
        0.2570002E+00,1405.815
        0.2580002E+00,1405.200
        0.2590002E+00,1404.586
        0.2600002E+00,1403.973
        0.2610002E+00,1403.361
        0.2620002E+00,1402.750
        0.2630002E+00,1402.139
        0.2640001E+00,1401.530
        0.2650001E+00,1400.921
        0.2660001E+00,1400.313
        0.2660001E+00,1400.313,  0.1098E-07,BCC_A2    
        0.2660002E+00,1400.313,  0.1000E+01,FCC_A1    
        0.2660002E+00,1400.313,  0.1000E+01,FCC_A1    
        0.2670002E+00,1399.659
        0.2680002E+00,1399.007
        0.2690002E+00,1398.355
        0.2700002E+00,1397.704
        0.2710001E+00,1397.054
        0.2720001E+00,1396.405
        0.2730001E+00,1395.757
        0.2740001E+00,1395.110
        0.2750001E+00,1394.464
        ⋮ 
        0.1976277E+02, 300.130
        0.1976377E+02, 300.123
        0.1976477E+02, 300.115
        0.1976577E+02, 300.108
        0.1976677E+02, 300.101
        0.1976777E+02, 300.094
        0.1976876E+02, 300.087
        0.1976976E+02, 300.080
        0.1977076E+02, 300.073
        0.1977176E+02, 300.066
        0.1977276E+02, 300.059
        0.1977376E+02, 300.051
        0.1977476E+02, 300.044
        0.1977576E+02, 300.037
        0.1977676E+02, 300.030
        0.1977776E+02, 300.023
        0.1977876E+02, 300.016
        0.1977976E+02, 300.009
        0.1978076E+02, 300.002
        0.1978176E+02, 299.995
        COOLING COMPLETE.  PROGRAM ENDS SUCCESSFULLY.
    

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Auxiliary Routines

None.

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Keywords

rapid solidification, undercooling, nucleation, powder metallurgy, net-shape manufacturing, atomisation, additive manufacturing, 3D-printing

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Download

Download source code

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MAP originated from a joint project of the National Physical Laboratory and the University of Cambridge.

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