478
B. Arizmendi et al.
Each RANS simulation requires the correct turbulence model dependent upon
the properties and behavior of the flow. Ice accretion is highly sensitive to the
flow field thus, modeling it accurately is crucial. Moreover, with different types
of ice formation comes different flow characteristics and such is the case that one
type of turbulence model may not be appropriate for all icing scenarios. Some
models such as the Spalart-Allmaras turbulence model maybe a good compromise
between stability and accuracy, however, it may also over predict heat fluxes if
assumptions such as fully turbulent flow are made. Hence, understanding the flow
is essential to apprehend which turbulence model is best suited for accurately
simulating ice accretion. Dunn et al. [75] investigated large droplet ice shapes on
airfoil aerodynamics with the one equation Spalart-Allmaras turbulence model and
found that lift and drag predictions were in good agreement with the experimental
results of Lee et al. [76] until the point where the flow was fully separated. The
results worsened with increasing incidence and were ascribed to the turbulence
models inadequately in predicting the amount of entrainment in the shear layer. A
further study from Marques et al. [77] on the same experimental data from Lee
et al. [76] later found the discrepancies in the Spalart-Allmaras and the k − ω
turbulence models at high angles of incidence. It found that generally the k − ω
turbulence model under predicted the suction peak downstream of the ice shape and
both models demonstrate difficulties in capturing the correct suction levels upstream
of the ice shape.
15.3.2 Governing Equations for Multiphase Flows
Modeling the mass, momentum, and energy balance properties of the incoming
supercooled water droplets on a surface will now be discussed taking into consideration the conservation of both mass and momentum. Aforesaid, the incoming liquid
may not instantaneously freeze upon impact but run downstream until freezing
in certain conditions, known as glaze ice. This process is strongly related to
the mass and heat transfer, surface roughness, skin friction, etc. over cells. The
freezing fraction over a control volume can be computed applying the first law of
thermodynamics with knowledge of the mass flux and a heat balance. This, together
with the droplet impingement rates are required to estimate the ice thickness.
15.3.2.1 Mass Balance
The ambient temperature determines the ice type. At low temperature Rime Ice
conditions dominate and the surface is effectively dry, as the water droplets freeze
on impact. At higher temperatures, however, Glaze is the primary source of icing.
At Glaze conditions, there are mass and energy flows on the surface of the airfoil
that should be accounted for. Consequently, the motion of the droplets on impact
as runback water is important. An illustration of a control volume impacted by
B. Arizmendi et al.
Each RANS simulation requires the correct turbulence model dependent upon
the properties and behavior of the flow. Ice accretion is highly sensitive to the
flow field thus, modeling it accurately is crucial. Moreover, with different types
of ice formation comes different flow characteristics and such is the case that one
type of turbulence model may not be appropriate for all icing scenarios. Some
models such as the Spalart-Allmaras turbulence model maybe a good compromise
between stability and accuracy, however, it may also over predict heat fluxes if
assumptions such as fully turbulent flow are made. Hence, understanding the flow
is essential to apprehend which turbulence model is best suited for accurately
simulating ice accretion. Dunn et al. [75] investigated large droplet ice shapes on
airfoil aerodynamics with the one equation Spalart-Allmaras turbulence model and
found that lift and drag predictions were in good agreement with the experimental
results of Lee et al. [76] until the point where the flow was fully separated. The
results worsened with increasing incidence and were ascribed to the turbulence
models inadequately in predicting the amount of entrainment in the shear layer. A
further study from Marques et al. [77] on the same experimental data from Lee
et al. [76] later found the discrepancies in the Spalart-Allmaras and the k − ω
turbulence models at high angles of incidence. It found that generally the k − ω
turbulence model under predicted the suction peak downstream of the ice shape and
both models demonstrate difficulties in capturing the correct suction levels upstream
of the ice shape.
15.3.2 Governing Equations for Multiphase Flows
Modeling the mass, momentum, and energy balance properties of the incoming
supercooled water droplets on a surface will now be discussed taking into consideration the conservation of both mass and momentum. Aforesaid, the incoming liquid
may not instantaneously freeze upon impact but run downstream until freezing
in certain conditions, known as glaze ice. This process is strongly related to
the mass and heat transfer, surface roughness, skin friction, etc. over cells. The
freezing fraction over a control volume can be computed applying the first law of
thermodynamics with knowledge of the mass flux and a heat balance. This, together
with the droplet impingement rates are required to estimate the ice thickness.
15.3.2.1 Mass Balance
The ambient temperature determines the ice type. At low temperature Rime Ice
conditions dominate and the surface is effectively dry, as the water droplets freeze
on impact. At higher temperatures, however, Glaze is the primary source of icing.
At Glaze conditions, there are mass and energy flows on the surface of the airfoil
that should be accounted for. Consequently, the motion of the droplets on impact
as runback water is important. An illustration of a control volume impacted by