Parametric Analysis of Energy Requirements of
In-Flight Ice Protection Systems
Mahdi Pourbagian and Wagdi G. Habashi
NSERC-J.-Armand Bombardier-Bell Helicopter-CAE Industrial Research Chair
for Multi-disciplinary Analysis and Design of Aerospace Systems
CFD Lab, Department of Mechanical Engineering, McGill University,
Montreal, QC, Canada H3A 2S6
Email: [email protected]
ABSTRACT
Recent attention is being paid to optimizing the
performance of in-flight ice protection systems. This
requires a thorough understanding of the parameters
that control energy requirements, be they influenced
by atmospheric, meteorological, operational,
structural or geometrical parameters. Numerous
experimental analyses must be performed to
determine the influence of these parameters.
Numerical simulation can also be used as a
complementary analysis tool. The current CFD study
investigates
the
different
phenomena
and
mechanisms of energy transfer involved in anti-icing
systems and provides an estimate of the energy
requirements and their sensitivity with respect to
ambient temperature, airspeed, angle of attack, mean
volumetric diameter, liquid water content and wing
skin temperature. This study has relevance in the
design and optimization of hot-air and electrothermal ice protection systems.
1.
INTRODUCTION
In-flight icing has been a major concern since the
dawn of aviation. The NTSB (National
Transportation Safety Board), since 1997, has
classified icing among its “most wanted
transportation safety improvements” 1 , and the FAA
(Federal Aviation Administration) has recently
proposed additional certification rules for new
airplanes to deal with problems of supercooled large
droplets and of ice crystals 2. In-flight icing is defined
as ice accretion on an aircraft flying through a cloud
of supercooled water droplets at or below water
freezing temperature. Aircraft icing may result in
1
2
http://www.ntsb.gov/recs/mostwanted/aviation_issues.htm
http://edocket.access.gpo.gov/2010/2010-15726.htm
aerodynamic performance degradation, engine
failure, fuel consumption increase, etc. While several
parts of aircraft are affected by in-flight icing, the
wing’s leading edge is the most sensitive to ice
accretion. Ice contamination of the leading edge
increases surface roughness, inducing earlier
boundary layer transition to turbulent flow.
Consequently, it may cause an increase in drag and
stall speed and a decrease of lift and stall angle (Fig.
1).
Figure 1. Aerodynamic effects of icing on a wing3
Today, most if not all, commercial aircraft are
equipped with, chemical-based, mechanical-based, or
thermal-based
ice
protection
systems.
A
comprehensive description of the different types can
be found in [1]. Among these, thermal-based systems
such as hot-air and electro-thermal systems are
currently the most common. The latter are touted to
be more efficient and controllable. Thermal-based
systems can act as either anti-icing or de-icing; antiicing refers to the prevention of ice accretion on the
surface (by keeping the airfoil skin temperature over
the water freezing point), and de-icing denotes the
removal of the accreted ice on the surface. Energy
requirements for both hot-air and electro-thermal
systems need to be carefully examined to avoid
3
http://iopara.ca/research.html
operational degradation and/or excessive energy
usage. The present study is an investigation of the
energy transferred by different mechanisms during
anti-icing, and of the influence of various parameters
on the energy requirements of anti-icing systems.
There are many parameters affecting the energy
requirements. These parameters can be classified into
four main categories; atmospheric (altitude
temperature and pressure), meteorological (droplet
mean volumetric diameter and liquid water content,
relative humidity), functional (airspeed, angle of
attack, airfoil skin temperature), structural (types of
materials used in airfoil or ice protection system), and
geometrical (sweep angle, geometry of ice protection
system). In this study, some of the most important
parameters are being considered. These parameters
include ambient temperature, airspeed, angle of
attack, droplet mean volumetric diameter and liquid
water content, and airfoil skin temperature.
2.
detailed in the next sub-section. In the presence of a
thermal-based ice protection system, the conjugate
heat transfer problem between the fluid and solid is
solved by making the various disciplines reach
equilibrium using a fixed-point iteration (FPI)
process via exchanging the thermal boundary
conditions among the external airflow, water film and
airfoil solid skin [7].
2.1
Heat Transfer Mechanisms
Several mechanisms contribute to the mass and heat
transfer during ice accretion. The heat transfer
mechanisms mainly include kinetic, convection,
radiation, sensible, evaporation, fusion, and
conduction (Figures 2 and 3).
CFD SIMULATION OF IN-FLIGHT
ICING
A number of in-flight icing codes have been
developed and applied, such as LEWICE, ONICE,
TRAJICE, CANICE, I2CE, CRREL, ICECREMO
and FENSAP-ICE [2]; the latter being used in the
present research. Most icing codes have three main
modules: airflow solution, water impingement
calculation, and ice accretion prediction.
For the numerical simulation of in-flight icing, the
airflow solution must first be obtained. Several
methods have been used to solve the flow field [3]. In
this study, the airflow is solved via a 3D RANS
(compressible, turbulent) with the Spalart-Allmaras
turbulence model, by a finite element method (FEM)
for spatial discretization, a Newton method for
linearization, an implicit Gear scheme for time
discretization, and a generalized minimal residual
(GMRES) method for solving the matrix system.
Heat fluxes at the walls are computed using a
consistent Galerkin FEM method, i.e. Gresho’s
method [4]. After the airflow solution, water
impingement can be determined by considering the
forces (inertial, drag, gravitational, and buoyancy)
balance on the droplets. The major output of this step
[5] is the local water collection efficiency, i.e. the
normalized flux of water on a wall surface. Following
the dry airflow solution and water impingement
calculation, mass and energy conservation partial
differential equations, based on the Messinger model
[6], are solved over the surface to obtain the local
mass of accreted ice and water film as well as the
surface temperature. The different heat transfer
mechanisms involved in the energy equation are
Figure 2. Mass transfer mechanisms during ice accretion,
1: sublimation, 2: evaporation, 3: water impingement,
4: ice accretion
Figure 3. Heat transfer mechanisms in ice accretion,
1: sublimation, 2: evaporation, 3: kinetic, 4: sensible,
5: convection, 6: radiation, 7: fusion, 8: conduction
When brought to rest at the body surface, the water
droplets and airflow carry the kinetic energy to the
control volume, thus heating up the surface. The
energy transferred by the water droplets is given by
′′ = m imp
′′
Q kin
ud 2
2
(1)
′′ the
where ud is the water impact velocity, and m imp
impinging mass flux of water, calculated using the
local collection efficiency ( β ) and liquid water
content ( LWC ). The kinetic energy transferred by
the airflow (aerodynamic heating) can be implicitly
taken into account by calculating the convective heat
transfer as follows
′′
=
Q conv
hc (Trec − Ts )
1
′′ =
′′ ( Levap + Lsub )
Q evap
− m evap
2
(3)
are the latent heat of
′′
evaporation and sublimation, respectively and m evap
is the evaporative mass flux of water, calculated by
the following parametric model
′′ =
m evap
′′ the mass rate of
of water and ice, respectively, m ice
ice accretion, and T f the freezing temperature of
water. It should be noted that in case of anti-icing
where there is no ice on the surface, the second term
in Eq. (6) is eliminated. The heat of fusion, given by
the following equation, is also omitted in anti-icing
′′ = m ice
′′ L fusion
Q fusion
(2)
where hc is the convective heat transfer coefficient,
and Trec and Ts are the recovery and surface
temperatures, respectively. The recovery temperature
comes from the incomplete recovery of the kinetic
energy transferred by the airflow. Another form of
the heat transfer takes place through evaporation
where Levap and Lsub
where c p , w and c p ,ice are the specific heat capacities
0.7 hc  Pv , p (T ) − H r , ∞ Pv , ∞ 


c p , air 
Pwall

(4)
(6)
where L fusion is the latent heat of fusion. The last
mechanism is the heat conduction through the solid.
This heat flux is provided by the ice protection
system.
2.2
Analysis Approach Overview
To keep the airfoil surface free of ice, an appropriate
amount of heat flux must be provided by the ice
protection system to keep the surface above the
melting point. This heat flux can be obtained by an
energy balance for each surface element on the
airfoil. As the most critical zone is the leading edge,
the results are demonstrated for 1/5 of the airfoil
chord length. It is worth mentioning that after the
point where runback water is completely evaporated,
no more heat flux is required.
3.
where Pv , p is the saturation vapour pressure at the
RESULTS
surface, Pv , ∞ the saturation vapour pressure of water
3.1
in ambient air, Pwall is the absolute pressure above the
control volume outside the boundary layer, H r , ∞ the
A NACA 0012 airfoil with a chord length of
0.9144 𝑚 has been used as the test case to
demonstrate the numerical results. A structured grid
is used for the simulations (Fig. 4).
relative humidity, and c p , air the specific heat capacity
of air. If the surface temperature is above the freezing
temperature of water, there will be no ice on the
surface (anti-icing), and therefore the evaporative
′′ Levap ) . Given that
heat flux is simply given by ( −m evap
the surface temperature in a typical operation of an
ice protection system is not very high, the irradiative
heat flux, calculated as follows, does not play an
important role compared to the other mechanisms
′′
=
Q rad
σε (T∞ 4 − Ts 4 )
(5)
where σ is the Stefan-Boltzmann constant, ε the
solid emissivity, and T∞ the ambient temperature.
The next mechanism is the sensible energy that is due
to the temperature change of water (when impacting
on the surface) and ice
′′
′′ c p , w (T∞ − Ts ) + m ice
′′ c p ,ice (Ts − T f
=
Q sens
m imp
)
(6)
Reference Conditions
Figure 4. Structured mesh for the NACA 0012 airfoil
To investigate the effects of the parameters, first a
reference set of icing conditions is selected (Table 1).
Figure 6 shows the heat flux distributions for the
different mechanisms (the kinetic and irradiative are
plotted in a separate graph to suitably show their
small magnitudes). In these icing conditions, as can
be seen, the maximum energy must be provided at
the stagnation point. Comparing the different heat
transfer mechanisms, we find out that convection and
then evaporation are the dominant mechanisms. The
irradiative heat flux is constant, as the surface
temperature does not change over the surface. The
kinetic and sensible heat flux distributions, according
to the collection efficiency distribution (Fig. 6), drop
down along the leading edge. Evaporation and
convection, on the other hand, have a profile similar
to that of the heat transfer coefficient (Fig. 7).
T∞
(K)
Va
(m/s)
LWC
(g/m3)
MVD
(μm)
AoA
(deg)
Ts
(K)
261
70
0.27
25
0
280
Figure 6. Collection efficiency distribution
Table 1. Reference icing conditions
Figure 7. Heat transfer coefficient distribution
T∞
(K)
Va
(m/s)
LWC
(g/m3)
MVD
(μm)
AoA
(deg)
Ts
(K)
251~
269
45~90
0.1~
0.7
15~40
-9~0
276~
294
Table 2. Range of variation of the different parameters
Figure 5. Heat flux distributions
3.2
Individual Effects
To examine the individual effect of each parameter,
the parameter is perturbed while all other parameters
remain constant. The range of variation of each
parameter is provided in Table 2. For each parameter,
10 simulations have been performed for 10 sample
points within the corresponding range. As there is
only one variable, the solutions for other values
within the range are interpolated by a cubic spline
method.
Figures 8 to 13 show the different heat flux
distributions changing with the parameters being
investigated. As can be seen, MVD and LWC do not
have a significant effect on the evaporative and
convective heat transfer, as they do not affect the
surface pressure distribution and convective heat
transfer coefficient. However, they do affect the
collection efficiency and droplet impact velocity.
Hence, the kinetic and sensible heat fluxes increase
as MVD or LWC increase. The variation of heat flux
distributions with respect to the surface temperature,
ambient temperature, and airspeed can be similarly
explained. Figure 13, however, needs more
explanation. As the angles of attack (AoA) examined
here are negative, the stagnation point occurs on the
upper surface, thus the collection efficiency and
droplet impact velocity are larger compared to the
lower surface (Fig. 14). Therefore, the kinetic and
sensible heat fluxes increase when the absolute value
of AoA increases. Increasing AoA also affects the
convective heat transfer coefficient, making it
decrease on the upper surface and increase on the
lower surface (Fig. 15). The surface pressure,
however, increases on the upper surface and
decreases on the lower surface when increasing AoA.
(Fig. 16). Recalling equations 2, 3 and 4, we can now
explain the variation of the evaporative and
convective heat flux distributions in Fig. 13. The total
heat flux distributions changing with the different
parameters are illustrated in Fig. 17. Normalizing the
value of the different parameters within the range
mentioned in Table (2), we can show the variation of
the total heating energy (integration of the total heat
flux over the surface) with respect to the different
parameters (Fig. 18). As shown, MVD, LWC, and
angle of attack, have a small influence on the total
energy within their range. Surface temperature,
ambient temperature and airspeed, on the other hand,
significantly affect the total energy.
Figure 10. Heat flux distributions changing with Ts,
a: kinetic, b: sensible, c: evaporative, d: convective
Figure 11. Heat flux distributions changing with T∞,
a: kinetic, b: sensible, c: evaporative, d: convective
Figure 8. Heat flux distributions changing with MVD,
a: kinetic, b: sensible, c: evaporative, d: convective
Figure 12. Heat flux distributions changing with Va,
a: kinetic, b: sensible, c: evaporative, d: convective
Figure p. Heat flux distributions changing with LWC,
a: kinetic, b: sensible, c: evaporative, d: convective
Figure 13. Heat flux distributions changing with AoA,
a: kinetic, b: sensible, c: evaporative, d: convective
Figure 17. Total heat flux distributions changing with the
different parameters
Figure 14. Liquid water content distribution at AoA = -5o
Figure 15. Convective heat transfer coefficient distribution
for two different AoA’s
Figure 18. Variation of the total heating energy with respect
to the different parameters
3.3
Figure 16. Surface pressure distribution for two different
AoA’s
Multiple Effects
APPENDIX C of the FAR 25 regulations for
continuous icing conditions [8] (Fig. 19) is a suitable
case to investigate the multiple effects of the different
parameters. It includes a wide range of icing
conditions used to verify aircraft certification. As
shown in Fig. 19, MVD and LWC are independent
variables, while ambient temperature is a dependent
variable. 40 sample points are selected to be used for
interpolation. Uniformity and diversity of these
snapshots significantly influence the accuracy of the
interpolation. A good sample selection increases the
chance of extracting useful information from the
data. Here we use the Centroidal Voronoi
Tessellation (CVT) method [9]. The sample points
generated by CVT are shown in Fig. 19. After
performing the CFD simulation for each sample
point, we need to use an interpolation method to
estimate the solutions for other points. As there are
two variables, cubic spline may generate unnatural
wiggles. To overcome this issue, the Akima
interpolation method [10] is applied. It uses thirdorder polynomials, but is more like a hand-drawing
interpolation scheme. Figure 20 illustrates the heating
energy distributions for the different mechanisms.
The pattern of kinetic energy distribution is clearly
similar to that of the mass caught distribution (Fig.
21). The sensible energy depends on both the mass
caught and ambient temperature, and therefore its
intensity at the left-top of the APPENDIX C can be
explained. The decrease of the convective and
especially the evaporative heating energy in the rightdown area of the APPENDIX C is due to the fact that
the mass caught is very small, and so runback water
is completely evaporated at some point near the
leading edge. Finally, the total heating energy
distribution is demonstrated in Fig. 22. As expected,
it is similar to that of the evaporative and convective
heating energy distributions, being largest at some
areas near the left-down of the APPENDIX C.
content, surface temperature, ambient temperature,
airspeed, and the angle of attack are also investigated.
These investigations ought to be useful for designing
and optimizing thermal-based anti-icing systems.
Figure 20. Heating energy (W) distribution for the different
heat transfer mechanisms, a: kinetic, b: sensible,
c: evaporative, d: convective
Figure 21. Mass caught distribution
Figure 19. Continuous icing conditions (APPENDIX C)
and the sample points generated by the CVT method
4.
CONCLUSION
Energy requirements for thermal-based airfoil antiicing systems are parametrically analysed, based on a
constant surface temperature. The contribution of the
different heat transfer mechanisms during ice
accretion is demonstrated. The individual and
multiple effects of different parameters, including
droplet mean volumetric diameter, liquid water
Figure 22. Total heating energy distribution
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