15 In-flight Icing: Modeling, Prediction, and Uncertainty
487
15.3.4.5 An Improved Myers Model
A new modified Myers model derived from the Stefan problem introduced by
Parma et al. [78] explicitly accounts for the mass flux related to sublimation. Here,
an improved method of describing the liquid film flow above the ice surface is
introduced; permitting not only water flowing from one glaze cell into another
adjacent glaze cell but also mass transfer from a glaze to a rime cell. This ensures to
maintain the mass transfer criterion. To model this mass transfer an additional term
is included for rime ice accretion.
Finally, the third modification concerns the description of the heat diffusion
problem through the ice phase in the glaze regime. It introduces a modification in
the temperature distribution within the ice layer which better respects the hypothesis
of the high thermal conductivity of the wall. The linear temperature profile is
replaced by an assigned parabolic shape function, namely T (z) = a
√
z + b, where
a and b are two coefficients defined by the boundary conditions T (0) = T wall and
T (B) = T f reezing to obtain,
T (z) = T wall +
T f reezing − T wall
√
B
√
z.
(15.30)
The new modified model for the ice accretion law for the rime regime hence reads
as,
Rime :
∂B
∂t
=
˙
m d + ˙
m in − ˙
m s
Aρ ri
,
(15.31)
where ˙
m d accounts for the mass rate of impinging droplets, ˙
m in is the runback water
mass rate coming into a control volume, and ˙
m s is the mass rate lost due sublimation.
A modified ice accretion law for the glaze regime is defined as,
Glaze :
∂B
∂t
=
1
ρ g L F
K i
(T f reezing − T wall )
2B
+
( ˙
Q c + ˙
Q e + ˙
Q d − ˙
Q k − ˙
Q a )
A
,
(15.32)
where the limiting thickness can now be defined as,
Rime limit thickness :
A K i
T f reezing − T wall
2
L F
β LWC V ∞ A − ˙
Q s L
−1
s
−
˙
Q c + ˙
Q s + ˙
Q d − ˙
Q k − ˙
Q a
.
(15.33)
487
15.3.4.5 An Improved Myers Model
A new modified Myers model derived from the Stefan problem introduced by
Parma et al. [78] explicitly accounts for the mass flux related to sublimation. Here,
an improved method of describing the liquid film flow above the ice surface is
introduced; permitting not only water flowing from one glaze cell into another
adjacent glaze cell but also mass transfer from a glaze to a rime cell. This ensures to
maintain the mass transfer criterion. To model this mass transfer an additional term
is included for rime ice accretion.
Finally, the third modification concerns the description of the heat diffusion
problem through the ice phase in the glaze regime. It introduces a modification in
the temperature distribution within the ice layer which better respects the hypothesis
of the high thermal conductivity of the wall. The linear temperature profile is
replaced by an assigned parabolic shape function, namely T (z) = a
√
z + b, where
a and b are two coefficients defined by the boundary conditions T (0) = T wall and
T (B) = T f reezing to obtain,
T (z) = T wall +
T f reezing − T wall
√
B
√
z.
(15.30)
The new modified model for the ice accretion law for the rime regime hence reads
as,
Rime :
∂B
∂t
=
˙
m d + ˙
m in − ˙
m s
Aρ ri
,
(15.31)
where ˙
m d accounts for the mass rate of impinging droplets, ˙
m in is the runback water
mass rate coming into a control volume, and ˙
m s is the mass rate lost due sublimation.
A modified ice accretion law for the glaze regime is defined as,
Glaze :
∂B
∂t
=
1
ρ g L F
K i
(T f reezing − T wall )
2B
+
( ˙
Q c + ˙
Q e + ˙
Q d − ˙
Q k − ˙
Q a )
A
,
(15.32)
where the limiting thickness can now be defined as,
Rime limit thickness :
A K i
T f reezing − T wall
2
L F
β LWC V ∞ A − ˙
Q s L
−1
s
−
˙
Q c + ˙
Q s + ˙
Q d − ˙
Q k − ˙
Q a
.
(15.33)