Species Transport¶

Overview¶

The species transport module (mod_species.f90) enables simulation of dissimilar metal mixing in additive manufacturing. It solves a convection-diffusion equation for concentration and provides composition-dependent material properties through two-way coupling.

Concentration Convention¶

Value	Meaning	Properties Source
C = 1	Pure primary (base) material	`&material_properties` in `input_param.txt`
C = 0	Pure secondary material	Named constants in `mod_species.f90`
0 < C < 1	Mixed region	`mix(prop1, prop2, C) = prop1C + prop2(1-C)`

Enabling Species Transport¶

In input_param.txt:

&output_control ... species_flag=1 /

When species_flag=0 (default), the species module is completely inert — no arrays allocated, no computation, no overhead.

Physics¶

Transport Equation¶

\[\frac{\partial (\rho C)}{\partial t} + \nabla \cdot (\rho \vec{u} C) = \nabla \cdot (\Gamma \nabla C)\]

where \(\Gamma = \rho D_m\) is the mass diffusion coefficient, \(D_m = 5 \times 10^{-9}\) m\(^2\)/s.

In solid regions (\(T < T_s\)), \(\Gamma\) is set to a floor value (\(10^{-30}\)) to effectively freeze concentration.

Two-Way Coupling¶

When species_flag=1, material properties depend on local concentration:

Thermal: tsolid, tliquid, acpa, acpb, acpl, thconsa, thconsb, thconl
Mechanical: dens, denl, viscos
Powder: pden, pcpa, pcpb, pthcona, pthconb

All computed inline via mix() — no extra arrays needed.

Properties that remain scalar (same for both materials):

beta (thermal expansion), emiss (emissivity)
hlatnt (latent heat), dgdt (thermal Marangoni)

Solutal Marangoni¶

Surface tension depends on concentration: \(\gamma = \gamma_0 + \frac{d\gamma}{dT}(T - T_{ref}) + \frac{d\gamma}{dC}(C - C_{ref})\)

The solutal Marangoni stress drives flow from low-C to high-C regions (when dgdc < 0):

\[\tau_C = \frac{d\gamma}{dC} \frac{\partial C}{\partial x}\]

Currently dgdc_const = -0.3 N/m (typical for liquid metal binary alloys).

Initial Conditions¶

Substrate (below powder layer): C = 1 (base material)
Powder layer, y >= y_mid: C = 1 (base material)
Powder layer, y < y_mid: C = 0 (secondary material)

This represents a half-and-half powder bed configuration for dissimilar metal testing.

Secondary Material Properties¶

Defined as named constants in mod_species.f90:

Property	Primary	Secondary	Unit
`dens/dens2`	8440	8880	kg/m^3
`denl/denl2`	7640	7800	kg/m^3
`viscos/viscos2`	0.007	0.003	Pa*s
`tsolid/tsolid2`	1563	1728	K
`tliquid/tliquid2`	1623	1803	K
`acpa/acpa2`	0.2441	0.3441	J/(kg*K^2)
`acpb/acpb2`	338.59	400	J/(kg*K)
`acpl/acpl2`	709.25	800	J/(kg*K)
`thconl/thconl2`	30.078	120	W/(m*K)
`D_m`	—	5e-9	m^2/s
`dgdc_const`	—	-0.3	N/m

Solver Details¶

Discretization: Power-law scheme (same as enthalpy)
Solver: Line-by-line TDMA with block correction
Domain: Melt pool region only (istatp1:iendm1, jstat:jend, kstat:nkm1)
Timing: Once per timestep, after iteration loop exits
Under-relaxation: urfspecies = 0.7
Clipping: concentration forced to [0, 1] after each solve
Transient: uses delt (not delt_eff) — species is always solved globally

Performance¶

Typical overhead with species enabled:

Metric	Impact
Species solver CPU	< 1% (solves only in melt pool)
Two-way coupling overhead	~16% (mix() calls in properties, enthalpy_to_temp, source)
Memory	+65 MB (two concentration arrays on 400x400x50 grid)

VTK Output¶

When species_flag=1, two additional scalar fields appear in vtkmov*.vtk:

concentration: mass fraction of primary material [0, 1]
tsolid_field: composition-dependent solidus temperature (K)