Page 63 - MSAM-4-1

Materials Science in Additive Manufacturing In situ electromagnetic field manipulation during LMD

cell depend on the volume fractions of each phase, which Where H is the enthalpy change of the material, h is
can be calculated using the volume-weighted average sensible enthalpy, ∆H is latent heat, L is the melting, latent
of each phase. In practical simulation studies, the VOF heat, and f is the liquid phase volume fraction.
l
method for tracking the interface can often be inaccurate, The enthalpy-porosity method is used to simulate the
leading to situations where local computational domains melting and solidification processes of materials. The mushy
within the substrate are incorrectly identified as gas-liquid zone (solid–liquid two-phase region) is treated as a porous
interfaces. In addition, it cannot accurately control the size medium, where the porosity in each cell equals the liquid
of the free interface region. phase fraction in that cell. The porosity is 0, and the velocity in
An improved method for tracking the interface using the region is reduced to 0 when fully solidified; the porosity is
volume fraction gradients based on the VOF method was 1 when completely melted. The mushy zone exists when the
proposed. This approach solves for the gradient of the porosity is between 0 and 1. The function expression for the
22
metal phase volume fraction in the computational domain liquid phase volume fraction is obtained from Equation VI: 26
at each iteration through a user-defined function. Since 
the internal region of the metal substrate contains only the  1, TT> l

metal phase, its volume fraction gradient is 0. Similarly, f = () =  TT− s , T ≤ T T (VI)
f x
≤
the gradient is also 0 for the argon gas phase in the argon l  T − T s s l
l
region. The change in phase volume fractions in different  0, TT<
directions causes a significant volume fraction gradient at  s
the metal-argon interface. The gradient value is related to Where T and T represent the liquidus and solidus lines
s
l
the mesh size; the position and size of the free interface can of the material, respectively.
be accurately captured by selecting an appropriate volume
fraction gradient value based on the model’s mesh size. 2.3.1. Mass addition equation
A more precise addition of mass, energy, and momentum The metal powder is ejected through a coaxial nozzle under
source terms can be achieved, leading to more accurate the conveying of powder feed gas in the process of LMD,
simulation results. and the spatial concentration distribution of the powder
2.3. Basic control equations approximates a Gaussian distribution. The synchronous
powder addition is implemented in the form of a mass
The model in the study calculates the pressure field, source term S , and the expression of the mass source
mass
velocity field, and temperature field of each element by term is expressed in Equation VII: 27
solving Equations I, II, and III, corresponding to the mass,
momentum, and energy conservation, respectively: 11,23-25 ωη m  ω    ( xv t) + y 2  
2
−

s


∂ρ +∇( ) = Sv (I) S mass = 1 r π p 2 s exp − r 2    (VII)
ρ


∂t mass p  b 
∂( ) Where ω represents the Gaussian distribution
ρv
1
µ
∂t +∇(ρvv ) =∇( ) −∇ +ρv p ρg + S mom (II) coefficient of the powder, ɳ denotes the powder utilization
p
efficiency, and m is the powder mass flow rate, r is the
p
s
∂ρH +∇( ) =∇ ∇ ) +H ρv h + S (III) radius of the powder Gaussian distribution region, and v
s
∂t (k T s energy represents the scanning speed of the laser head.
where ρ is the metal density, t is time, v is the fluid 2.3.2. Moving Gaussian heat source and thermal
velocity, S mass is the mass source term, μ is viscosity, g boundary conditions
is gravitational acceleration, p is pressure, S mom is the In the process of LMD, apart from the substrate’s
momentum source term, H is enthalpy, k is thermal absorption of laser heat, the heat flux density due to
conductivity, h is the enthalpy increment of external filling thermal convection and thermal radiation losses on the
s
materials, and S energy is the energy source term. substrate surface should also be included. The equation for
The enthalpy variation of the material in Equation IV S energy is as follows:
is the sum of sensible enthalpy and latent heat, where the S = Q -Q -Q (VIII)
melting latent heat ∆H can be represented by Equation V: energy laser con rad
Where Q represents the laser heat source, Q is
con
laser
H = h+∆H (IV) the energy loss due to convection, and Q represents the
∆H = Lf l (V) energy loss due to thermal radiation. rad
Volume 4 Issue 1 (2025) 4 doi: 10.36922/msam.8332