High cooling rate and high resolution simulations

dendritic solidification, eutectics, peritectics,....
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Yongliang Ou
Posts: 4
Joined: Fri Dec 11, 2020 1:16 pm
anti_bot: 333

High cooling rate and high resolution simulations

Post by Yongliang Ou » Sat Dec 12, 2020 3:14 pm

Dear all,

Hi! Recently I try to simulate the dendrite formation process with high cooling rates (106 K/s) and high temperature gradients (105 K/cm). In the beginning, I used grid spacing 0.07 \text{\mu m} and found the driving force of the dendrite tip fluctuates a lot during the continuous dendrite growing process. I think theoretically the driving force of the dendrite tip should remain relatively stable during the continuous growth process, due to similar phase-field around the tip. So I try to change the grid spacing to 0.01 \text{\mu m} and do the high-resolution simulation. Other parameters I used are listed below.

Code: Select all

# Phase interaction data
# ======================
#
# Data for phase interaction 0 / 1:
# ---------------------------------
# Simulation of interaction between phases 0 and 1?
# Options: phase_interaction  no_phase_interaction
#  [standard|particle_pinning[_temperature]|solute_drag]
#   | [redistribution_control]
phase_interaction redistribution_control
# 'DeltaG' options:  default
# avg ...[] max ...[J/cm^3] smooth ...[Deg] noise ...[J/cm^3] offset ...[J/cm^3]
avg 0.90 max 200.00 noise 1.00
# I.e.:  avg +0.90  smooth  +0.0  max +2.00000E+02
# Type of interfacial energy definition between phases 0 and 1?
# Options:  constant  temp_dependent
constant
# Interfacial energy between phases 0 and 1? [J/cm**2]
#     [max. value for num. interface stabilisation [J/cm**2]]
1.62E-6 1.62E-5
# Type of mobility definition between phases 0 and 1?
# Options: constant temp_dependent dg_dependent [fixed_minimum]
constant
# Kinetic coefficient mu between phases 0 and 1  [ min. value ] [cm**4/(Js)] ?
1
# Is interaction isotropic?
# Options: isotropic
#          anisotropic [junction_force] [harmonic_expansion]
anisotropic
# Anisotropy of interfacial stiffness? (cubic)
# 1 - delta * cos(4*phi), (delta =delta_stiffness =15*delta_energy)
# Coefficient delta (<1.) ?
0.28800
# Anisotropy of interfacial mobility? (cubic)
# 1 + delta * cos(4*phi)
# Coefficient delta (<1.) ?
0.28800
As @janin said before, in the 'DeltaG' option, I use an average factor of 0.9 because I think it belongs to highly numerically unstable, i.e. poorly resolved computations. The results are still bad and shown as follows.
Screenshot from 2020-12-12 13-02-09.png
Screenshot from 2020-12-12 13-02-09.png (234.49 KiB) Viewed 270 times
Screenshot from 2020-12-12 13-02-30.png
Screenshot from 2020-12-12 13-02-30.png (826.22 KiB) Viewed 270 times
Screenshot from 2020-11-15 19-26-10.jpg
Screenshot from 2020-11-15 19-26-10.jpg (269.36 KiB) Viewed 270 times
My question is:
  • How to do simulations with high cooling rates and high temperature gradients?
  • How to do high-resolution i.e. small grid spacing simulations?

Thanks in advance and best regards,
Yongliang Ou

Bernd
Posts: 1179
Joined: Mon Jun 23, 2008 9:29 pm

Re: High cooling rate and high resolution simulations

Post by Bernd » Sat Dec 12, 2020 7:09 pm

Dear Yongliang Ou,

Technically, it is very easy to increase resolution: you only need to decrease the grid spacing and increase the number of cells in x- and z-direction accordingly. However, your simulation domain is already huge, so I think it makes sense to have some basic considerations before.

Generally, the length scale for microstructure formation - and thus the required grid resolution - not only depends on time-scale/cooling rate, but also on the energy scale (interface energy) and kinetics (diffusion coefficients). While I do not know which diffusion coefficients you apply (we typically use ~1x10-5 cm2/s for liquid metals if we do not have other data available), I think your interface energy is untypically low, at least for metallic systems. Increasing it to a value of 1-2x10-5 J/cm2 perhaps could already solve your problems without increasing resolution...

If you nevertheless need to increase grid resolution, you should do it step-wise. Keep in mind that changing grid spacing by a factor of ζ while keeping the domain size constant, will increase calculation time for the diffusion solver alone by a factor of 1/ζ4 in 2D-simulations. For the simulation time required for list-operations or phase-field solver, it would be 'only' 1/ζ2. If you have a look at the .TabP output for your current simulation run, you can roughly estimate the expected simulation times. In any case, I would recommend to use the smallest domain size which is absolutely necessary while trying out numerical parameters.

Bernd

Yongliang Ou
Posts: 4
Joined: Fri Dec 11, 2020 1:16 pm
anti_bot: 333

Re: High cooling rate and high resolution simulations

Post by Yongliang Ou » Mon Dec 21, 2020 1:54 pm

Dear Bernd,

Thank you so much for the suggestion! We increased the spacing to be 0.07 \mum and the interface energy to be 1.62E-5 J/cm2, as shown below.

Code: Select all

 
 # Phase interaction data
 # ======================
 #
 # Data for phase interaction 0 / 1:
 # ---------------------------------
 # Simulation of interaction between phases 0 and 1?
 # Options: phase_interaction  no_phase_interaction
 #  [standard|particle_pinning[_temperature]|solute_drag]
 #   | [redistribution_control]
 phase_interaction redistribution_control
 # 'DeltaG' options:  default
 # avg ...[] max ...[J/cm^3] smooth ...[Deg] noise ...[J/cm^3] offset ...[J/cm^3]
 avg 0.90 max 200.00 noise 0.10
 # I.e.:  avg +0.90  smooth  +0.0  max +2.00000E+02
 # Type of interfacial energy definition between phases 0 and 1?
 # Options:  constant  temp_dependent
 constant
 # Interfacial energy between phases 0 and 1? [J/cm**2]
 #     [max. value for num. interface stabilisation [J/cm**2]]
 1.62E-5
 # Type of mobility definition between phases 0 and 1?
 # Options: constant temp_dependent dg_dependent [fixed_minimum]
 constant
 # Kinetic coefficient mu between phases 0 and 1  [ min. value ] [cm**4/(Js)] ?
 0.1
 # Is interaction isotropic?
 # Options: isotropic
 #          anisotropic [junction_force] [harmonic_expansion]
 anisotropic
 # Anisotropy of interfacial stiffness? (cubic)
 # 1 - delta * cos(4*phi), (delta =delta_stiffness =15*delta_energy)
 # Coefficient delta (<1.) ?
  0.28800    
 # Anisotropy of interfacial mobility? (cubic)
 # 1 + delta * cos(4*phi)
 # Coefficient delta (<1.) ?
  0.28800    
 #
 # Data for phase interaction 1 / 1:
 # ---------------------------------
 # Simulation of interaction between phases 1 and 1?
 # Options: phase_interaction  no_phase_interaction  identical phases nb
 #  [standard|particle_pinning[_temperature]|solute_drag]
 #   | [redistribution_control]
 no_phase_interaction
 
Under the diffusion data, we chose the diagonal methods, as shown below.

Code: Select all

 # Diffusion Data
 # --------------
 # ["Terse Mode": Each line starts with component number and phase number]
 # Options:   diagonal [x]   multi [y(1..k)]   multi_plus [y(1..k)]
 #  x: one of the characters "n", "d", "g", "l", "z", "i", "I", or "f"
 #  y: chain of "n", "d", "g", "l", "z", or "f" (for each component)
 #  default: "g"  resp. "gggg..."
 #  Rem: "n":no diffusion, "d": input, "f": T-dep. from file
 #       "i":infinite, "I": infinite in each grain
 #       from database: "g": global, "l": local, "z" global z-segmented
 # Extra line option: [+b] for grain-boundary diffusion
 # Extra line option (prefactor on time step): cushion <0-1>
 # Extra line option: infinite_limit [cm**2/s]
 # Extra line option: maxfactor_local [real > 1.0] (default: 10.0)
 # Extra line option: factor [real > 0.]
 # Finish input of diffusion data with 'end_diffusion_data'.
 #
 # How shall diffusion of component 1  in phase 0  be solved?
 diagonal l
 # How shall diffusion of component 1  in phase 1  be solved?
 diagonal g
 # How shall diffusion of component 2  in phase 0  be solved?
 diagonal l
 # How shall diffusion of component 2  in phase 1  be solved?
 diagonal g
 #
 # How shall the interval for updating diffusion coefficients
 # data be set?
 # Options:   constant   from_file
 constant
 # Interval for updating diffusion coefficients data? [s]
  0.10000    
 #
We checked the exact diffusion coefficient in the output file "TabD.txt", as listed below. The diffusion coefficient of components 1 and 2 in phase 0 is ~10E-5 cm2/s, but another two are not. We are not sure if it can be a problem.

Code: Select all

 #  Simulation   Temperature   Diff. C.   Diff. C.   Diff. C.   Diff. C.
 #   time [s]        [K]       P 0 C 1    P 0 C 2    P 1 C 1    P 1 C 2
  0.000000         920.000     0.00E+00   0.00E+00   0.00E+00   0.00E+00
 2.0000000E-04     917.097     8.30E-05   2.99E-05   2.47E-08   2.71E-08
 4.0000000E-04     914.194     8.18E-05   2.98E-05   2.35E-08   2.58E-08
 6.0000000E-04     911.291     8.05E-05   2.96E-05   2.23E-08   2.46E-08
 8.0000000E-04     908.388     7.93E-05   2.95E-05   2.12E-08   2.34E-08
 1.0000000E-03     905.485     7.81E-05   2.93E-05   2.01E-08   2.23E-08
 1.2000000E-03     902.582     7.69E-05   2.91E-05   1.91E-08   2.12E-08
 1.4000000E-03     899.679     7.57E-05   2.90E-05   1.81E-08   2.01E-08
 1.6000000E-03     896.776     7.45E-05   2.90E-05   1.72E-08   1.91E-08
 1.8000000E-03     893.873     7.32E-05   2.91E-05   1.63E-08   1.82E-08
 2.0000000E-03     890.970     7.19E-05   2.93E-05   1.55E-08   1.72E-08
 2.2000000E-03     888.067     7.06E-05   2.96E-05   1.47E-08   1.64E-08
 2.4000000E-03     885.164     6.91E-05   3.01E-05   1.39E-08   1.55E-08
 2.6000000E-03     882.261     6.75E-05   3.10E-05   1.32E-08   1.47E-08
 2.8000000E-03     879.358     6.56E-05   3.29E-05   1.25E-08   1.40E-08
 3.0000000E-03     876.455     6.22E-05   3.79E-05   1.18E-08   1.33E-08
 3.2000000E-03     873.552     5.66E-05   4.88E-05   1.12E-08   1.26E-08
 3.4000000E-03     870.649     5.51E-05   4.99E-05   1.06E-08   1.19E-08
 3.6000000E-03     867.746     5.37E-05   5.08E-05   9.98E-09   1.13E-08
 3.8000000E-03     864.843     5.23E-05   5.18E-05   9.44E-09   1.07E-08
 4.0000000E-03     861.940     5.10E-05   5.27E-05   8.91E-09   1.01E-08
 4.2000000E-03     859.037     4.98E-05   5.31E-05   8.42E-09   9.55E-09
 4.4000000E-03     856.134     4.86E-05   5.39E-05   7.95E-09   9.03E-09
 4.6000000E-03     853.231     4.73E-05   5.48E-05   7.50E-09   8.54E-09
 4.8000000E-03     850.328     4.61E-05   5.55E-05   7.07E-09   8.07E-09
 5.0000000E-03     847.425     4.49E-05   5.63E-05   6.67E-09   7.62E-09
 5.2000000E-03     844.522     4.38E-05   5.68E-05   6.29E-09   7.19E-09
 5.4000000E-03     841.619     4.26E-05   5.75E-05   5.92E-09   6.79E-09
 5.6000000E-03     838.716     4.15E-05   5.82E-05   5.58E-09   6.41E-09
 5.8000000E-03     835.813     4.04E-05   5.88E-05   5.25E-09   6.04E-09
 6.0000000E-03     832.910     3.93E-05   5.95E-05   4.94E-09   5.69E-09
 6.2000000E-03     830.007     3.84E-05   5.99E-05   4.65E-09   5.37E-09
 6.4000000E-03     827.104     3.73E-05   6.05E-05   4.37E-09   5.05E-09
 6.6000000E-03     824.201     3.63E-05   6.10E-05   4.11E-09   4.76E-09
 6.8000000E-03     821.298     3.53E-05   6.16E-05   3.86E-09   4.48E-09
 7.0000000E-03     818.395     3.44E-05   6.22E-05   3.62E-09   4.21E-09
 7.2000000E-03     815.492     3.35E-05   6.25E-05   3.40E-09   3.96E-09
 7.4000000E-03     812.589     3.26E-05   6.30E-05   3.19E-09   3.72E-09
 7.6000000E-03     809.686     3.17E-05   6.34E-05   2.99E-09   3.50E-09
 7.8000000E-03     806.783     3.08E-05   6.39E-05   2.80E-09   3.28E-09
 8.0000000E-03     803.880     2.99E-05   6.44E-05   2.62E-09   3.08E-09
 8.2000000E-03     800.977     2.91E-05   6.46E-05   2.46E-09   2.89E-09
 8.4000000E-03     798.074     2.83E-05   6.50E-05   2.30E-09   2.71E-09
 8.6000000E-03     795.171     2.75E-05   6.54E-05   2.15E-09   2.54E-09
 8.8000000E-03     792.268     2.67E-05   6.58E-05   2.01E-09   2.38E-09
 9.0000000E-03     789.365     2.60E-05   6.62E-05   1.88E-09   2.23E-09
 9.2000000E-03     786.462     2.52E-05   6.63E-05   1.76E-09   2.09E-09
 9.4000000E-03     783.559     2.45E-05   6.67E-05   1.64E-09   1.95E-09
 9.6000000E-03     780.656     2.38E-05   6.70E-05   1.53E-09   1.82E-09
 9.8000000E-03     777.753     2.31E-05   6.73E-05   1.43E-09   1.70E-09
 1.0000000E-02     774.850     2.24E-05   6.76E-05   1.33E-09   1.59E-09
 1.0200000E-02     771.947     2.18E-05   6.77E-05   1.24E-09   1.49E-09
 1.0400000E-02     769.044     2.11E-05   6.80E-05   1.15E-09   1.39E-09
 1.0600000E-02     766.141     2.05E-05   6.82E-05   1.07E-09   1.29E-09
 1.0800000E-02     763.238     1.98E-05   6.84E-05   9.98E-10   1.21E-09
 1.1000000E-02     760.335     1.92E-05   6.87E-05   9.28E-10   1.12E-09
 1.1200000E-02     757.432     1.87E-05   6.87E-05   8.62E-10   1.05E-09
 1.1400000E-02     754.529     1.81E-05   6.89E-05   8.01E-10   9.73E-10
 1.1600000E-02     751.626     1.75E-05   6.91E-05   7.43E-10   9.05E-10
 1.1800000E-02     748.723     1.70E-05   6.93E-05   6.89E-10   8.41E-10
 1.2000000E-02     745.820     1.64E-05   6.94E-05   6.39E-10   7.82E-10
 1.2200000E-02     742.917     1.59E-05   6.95E-05   5.92E-10   7.26E-10
 1.2400000E-02     740.014     1.54E-05   6.96E-05   5.48E-10   6.73E-10
 1.2600000E-02     737.111     1.49E-05   6.98E-05   5.07E-10   6.25E-10
 1.2800000E-02     734.208     1.44E-05   6.99E-05   4.69E-10   5.79E-10
 1.3000000E-02     731.305     1.39E-05   7.00E-05   4.33E-10   5.36E-10
 1.3200000E-02     728.402     1.34E-05   7.00E-05   4.00E-10   4.96E-10
 1.3400000E-02     725.499     1.30E-05   7.01E-05   3.69E-10   4.59E-10
 1.3600000E-02     722.596     1.25E-05   7.02E-05   3.41E-10   4.25E-10
 1.3800000E-02     719.693     1.21E-05   7.03E-05   3.14E-10   3.92E-10
 1.4000000E-02     716.790     1.17E-05   7.03E-05   2.89E-10   3.62E-10
 1.4200000E-02     713.887     1.13E-05   7.03E-05   2.66E-10   3.34E-10
 1.4400000E-02     710.984     1.09E-05   7.04E-05   2.45E-10   3.08E-10
 1.4600000E-02     708.081     1.05E-05   7.04E-05   2.25E-10   2.84E-10
 1.4800000E-02     705.178     1.01E-05   7.05E-05   2.07E-10   2.62E-10
 1.5000000E-02     702.275     9.71E-06   7.05E-05   1.90E-10   2.41E-10
After the simulation, We found the results still need to be improved because:
  • The driving force of the dendrite tip varies a lot during the dendrite growth process. But I think it should stay relatively constant during the dendrite growing process.
  • The small circular liquid phase formed between dendrites should not appear after solidification.
So my questions are,
  • Is our analysis correct?
  • How should we improve it?
Screenshot from 2020-12-21 13-33-44.png
Screenshot from 2020-12-21 13-33-44.png (238.35 KiB) Viewed 235 times

In case you may want to know other parameters, I post below all other parameters:

Code: Select all

# Flags and settings
# ==================
#
# Geometry
# --------
# Grid size?
# (for 2D calculations: CellsY=1, for 1D calculations: CellsX=1, CellsY=1)
# Cells in X-direction (CellsX):
285
# Cells in Y-direction (CellsY):
1
# Cells in Z-direction (CellsZ):
1000
# Cell dimension (grid spacing in micrometers):
# (optionally followed by rescaling factor for the output in the form of '3/4')
0.0700
#
# Flags
# -----
# Type of coupling?
# Options:  phase  concentration [volume_change] temperature  temp_cyl_coord
#    [stress] [stress_coupled] [flow] [flow_coarse] [dislocation]
concentration
# Type of potential?
# Options:  double_obstacle  multi_obstacle   [fd_correction]
double_obstacle fd_correction
# Enable one dimensional far field approximation for diffusion?
# Options:     1d_far_field   1d_far_field_EW  no_1d_far_field
1d_far_field
# Number of cells for the 1D external field?
100
# Shall an additional 1D field be defined in z direction
# for temperature coupling?
# Options:  no_1d_temp  1d_temp  1d_temp_cylinder  1d_temp_polar [kin. Coeff]
# kin. Coeff: Kinetics of latent heat release (default is 0.01)
no_1d_temp
#
# Phase field data structure
# --------------------------
# Coefficient for initial dimension of field iFace
#  [minimum usage] [target usage]
0.1
# Coefficient for initial dimension of field nTupel
#  [minimum usage] [target usage]
0.1

# Phase data
# ==========
# Number of distinct solid phases?
1
#
# Data for phase 1:
# -----------------
# Simulation of recrystallisation in phase 1?
# Options:   recrystall     no_recrystall   [verbose|no_verbose]
no_recrystall
# Is phase 1 anisotrop?
# Options: isotropic  anisotropic  faceted_a faceted_b  antifaceted
anisotropic
# Crystal symmetry of the phase?
# Options:   none  cubic  hexagonal  tetragonal orthorhombic
cubic
# Should grains of phase 1 be reduced to categories?
# Options:   categorize no_categorize
no_categorize
#
# Orientation
# -----------
# How shall grain orientations be defined?
# Options:  angle_2d  euler_zxz  angle_axis  miller_indices  quaternion
angle_2d
#
#
# Grain input
# ===========
# Type of grain positioning?
# Options:  deterministic   random [deterministic_infile]   from_file
deterministic
# NB: the origin of coordinate system is the bottom left-hand corner,
#     all points within the simulation domain having positive coordinates.
# Number of grains at the beginning?
1
# Input data for grain number 1:
# Geometry?
# Options:  round  rectangular  elliptic  round_inverse
rectangular
# Center x,z coordinates [micrometers], grain number 1?
9.975
0.00000
# Length along x-axis [micrometers]
19.95
# Length along z-axis [micrometers]
1.5
# Should the Voronoi criterion be applied?
# Options:    voronoi     no_voronoi
no_voronoi
# Phase number?   (integer)
1
# Rotation angle? [Degree]
0.000000000000000E+000
#
#
# Data for further nucleation
# ===========================
# Enable further nucleation?
# Options:  nucleation   nucleation_symm   no_nucleation  [verbose|no_verbose]
no_nucleation verbose
#
# Concentration data
# ==================
# Number of dissolved constituents?   (int)
2
# Type of concentration?
# Options:     atom_percent    (at%)
#              weight_percent  (wt%)
weight_percent
#
#
# Phase diagram - input data
# ==========================
#
# List of phases and components which are stoichiometric:
#  phase and component(s) numbers
# List of concentration limits (at%):
#  <limits>, phase number and component number
# List for ternary extrapolation (2 elements + main comp.):
#  <interaction>, component 1, component 2
# Switches: <stoich_enhanced_{on|off}> <solubility_{on|off}>
# List of relative criteria on phase composition
#  <criterion_higher | criterion_lower>, phase No 1,  phase No 2, component No
# List of source changes for diffusion data
#  <switch_diff_data>, Phase-No., reference phase
# Switch: Add composition sets for calculation of diffusion/volume/enthalpy data
#  <diff_comp_sets | vol_comp_sets | enth_comp_sets>, phase list
# End with 'no_more_stoichio' or 'no_stoichio'
no_more_stoichio
#
#
# Is a thermodynamic database to be used?
# Options: database   database_verbose   database_consistent   no_database
database
#
# Name of Thermo-Calc *.GES5 file without extension?
GES_Files/AlSiMg
# Which global relinearisation mode shall be used?
# Options:  manual   from_file   none
manual 1E-3
# Input of the phase diagram of phase 0 and phase 1:
# --------------------------------------------------
# Which phase diagram is to be used?
# Options:  database [local|global[F]|globalG[F]] [start_value_{1|2}]
#           linear     linearTQ
database globalGF
# Relinearisation mode for interface 0 / 1
# Options:  automatic   manual   from_file   none
manual 1E-3
# Please specify the redistribution behaviour of each component:
# Format: forward [backward]
# Options: nple  para  paratq  normal [mob_corr]  atc [mob_corr]  [verbose]
# Component 1:
atc mob_corr
# Component 2:
atc mob_corr
# Reading GES5 workspace ...
# Index relations between TC and MICRESS
# --------------------------------------
# The database contains the following components:
# 1: AL
# 2: MG
# 3: SI
# Specify relation between component indices Micress -> TC!
# The main component has in MICRESS the index 0
# Thermo-Calc index of (MICRESS) component 0?
1
# Thermo-Calc index of (MICRESS) component 1?
2
# Thermo-Calc index of (MICRESS) component 2?
3
# 0 -> AL
# 1 -> MG
# 2 -> SI
# The database contains 4 phases:
# 1: DIAMOND_A4
# 2: FCC_L12
# 3: LIQUID
# 4: MG2SI_C1
# Specify relation between phase indices Micress -> TC!
# The matrix phase has in MICRESS the index 0
# Thermo-Calc index of the (MICRESS) phase 0  [ name ('#'-->'$') ]?
3
# Thermo-Calc index of the (MICRESS) phase 1  [ name ('#'-->'$') ]?
2
# 0 -> LIQUID
# 1 -> FCC_L12
#
# Molar volume of phase 0 (LIQUID)? [cm**3/mol]
# Options: manual database [temp_extrapol] [conc_extrapol]
database
# Molar volume of phase 1 (FCC_L12)? [cm**3/mol]
# Options: manual database [temp_extrapol] [conc_extrapol]
database
# TQ update-interval for molar volumes [s] ?
1.0000
# Temperature at which the initial equilibrium
# will be calculated? [K]
920.0000
#
#
# Initial concentrations
# ======================
# How shall initial concentrations be set?
# Options:  input  equilibrium  from_file     [phase number]
equilibrium
# Initial concentration of component 1 (MG) in phase 0 (LIQUID) ? [wt%]
0.4100000000
# Initial concentration of component 2 (SI) in phase 0 (LIQUID) ? [wt%]
1.010000000
# 1D far-field diffusion approximation was set.
# From which distance from the front should the diffusion be
# solved as 1D?  [micrometers]
10.0000000000000
# This distance is equivalent to 143 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
#
#
# Parameters for latent heat and 1D temperature field
# ===================================================
# Simulate release of latent heat?
# Options: lat_heat  lat_heat_3d[matrix phase]  no_lat_heat  no_lat_heat_dsc
no_lat_heat
#
#
# Boundary conditions
# ===================
# Type of temperature trend?
# Options:   linear     linear_from_file     profiles_from_file
linear
# Number of connecting points?    (integer)
0
# Initial temperature at the bottom?  (real)  [K]
920.0000
# Temperature gradient in z-direction?  [K/cm]
727.00
# Cooling rate? [K/s]
-14515
# Moving-frame system in z-direction?
# Options:      moving_frame      no_moving_frame
no_moving_frame
#
# Boundary conditions for phase field in each direction
# Options: i (insulation) s (symmetric) p (periodic/wrap-around)
#          g (gradient)   f (fixed)     w (wetting)
# Sequence: W E (S N, if 3D) B T borders
ssii
#
# Boundary conditions for concentration field in each direction
# Options: i (insulation) s (symmetric) p (periodic/wrap-around) g (gradient) f (fixed)
# Sequence: W E (S N, if 3D) B T borders
sssf
# Fixed value for concentration field for component 1 in T-direction
0.41000
# Fixed value for concentration field for component 2 in T-direction
1.0100
# Unit-cell model symmetric with respect to the x/y diagonal plane?
# Options:    unit_cell_symm   no_unit_cell_symm
no_unit_cell_symm
#
#
# Other numerical parameters
# ==========================
# Phase minimum?
1.00E-04
# Interface thickness (in cells)?
3.00
Thanks in advance and best regards,
Yongliang Ou

Bernd
Posts: 1179
Joined: Mon Jun 23, 2008 9:29 pm

Re: High cooling rate and high resolution simulations

Post by Bernd » Mon Dec 21, 2020 3:03 pm

Hi Yongliang Ou,

When you say that "the driving force of the dendrite tip varies a lot during the dendrite growth process", you probably mean that it is decreasing constantly to more and more negative values. I think the reason is a too low interface mobility. The value you set in the phase interaction data has the meaning of a "physical" value, while the numerical value, which is calculated according to the "mob_corr" option, is written to the .mueS (mobility) output. If you assume diffusion limited growth (which is reasonable for metallic systems), you should chose a value which is sufficiently high. Please try 1 or even 10 cm4/(Js) instead of 0.1.

The round liquid inclusions in first place appear realistic, given the fact that at least at the position close to the dendrite tip you should not expect complete solidification. Indeed, for the given temperature gradient, the solidification range is much "bigger" than your simulation domain, so that if you would use "moving_frame" to follow the dendrite tip, you would never get to a temperature where you could expect complete solidification.
However, without moving frame or - given the extremely high and unrealistic tip undercooling as explained above - you could get to complete solidification, but only if you include Si and Mg2Si as potential precipitation phases.

The diffusion coefficients in the solid are about 3 orders of magnitude lower than those in the melt, which is realistic. However, what is strange is that the diffusivity of Si in the melt increases with decreasing temperature - probably an artefact of not calculating updates: I propose to reduce the interval for updating diffusion coefficients data down to at least 10-3 seconds.

A further hint: If you want to include Si and Mg2Si, you should nucleate them at the solid-liquid interface using liquid as reference phase. Then you should also switch from "double_obstacle" to "multi_obstacle".

Best regards
Bernd

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