-
Research ArticleNumerical Simulation of Unsteady Conjugate Heat
Transfer ofElectrothermal Deicing Process
Zuodong Mu , Guiping Lin, Xiaobin Shen , Xueqin Bu, and Ying
Zhou
Laboratory of Fundamental Science on Ergonomics and
Environmental Control, Beihang University, Beijing 100191,
China
Correspondence should be addressed to Xiaobin Shen;
[email protected]
Received 2 June 2017; Accepted 28 November 2017; Published 29
January 2018
Academic Editor: Paul Williams
Copyright © 2018 Zuodong Mu et al. This is an open access
article distributed under the Creative Commons Attribution
License,which permits unrestricted use, distribution, and
reproduction in any medium, provided the original work is properly
cited.
A novel 3-D unsteady model of in-flight electrothermal deicing
process is presented in this paper to simulate the conjugate
massand heat transfer phenomena of water film runback, phase
change, and solid heat conduction. Mathematical models of waterfilm
runback and phase change are established and solved by means of a
loosely coupled method. At the current time step, solidheat
conduction, water film runback, and phase change are iteratively
solved until the heat boundary condition reachesconvergence, then
the temperature distribution and ice shape at the moment are
obtained, and the calculation of the next timestep begins
subsequently. A deicing process is numerically simulated using the
present model following an icing tunnelexperiment, and the results
match well with those in the literatures, which validate the
present model. Then, an in-flight deicingprocess is numerically
studied to analyze the effect of heating sequence.
1. Introduction
The water droplet in clouds may remain in a liquid state evenif
the temperature is below freezing point due to the surfacetension
and a lack of condensation nucleus. Supercooledwater droplet would
solidify when impinging on windwardsurfaces of aircraft, which
would cause the deterioration inthe aerodynamic performance due to
the change of aerody-namic configuration [1]. Aircraft icing would
impose seriousadverse effects on flight safety, which has long been
recog-nized as an important issue to prevent.
In view of the serious threats that ice accretion wouldimpose on
flight safety, ice protection methods must beapplied to prevent or
control the ice accretion. Hot air anti-icing method is widely
applied in commercial jets. The bleedair from engine compressor
impinges on the structure to heatthe surface, so that the water
evaporates or stays in a liquidstate rather than freezes.
Electrothermal ice protectionmethod uses heating pads, which are
incorporated in themultilayer structure, to heat the surfaces.
Electrothermalpads are available in both anti-icing mode with a
constantpower density and deicing mode with a periodic
powerdensity. Besides, some other deicing methods have been
developed, such as the thermomechanical expulsion deicingmethod
[2], while they are not widely applied. A largeamount of bleed air
is needed in hot air anti-icing system,which would significantly
affect the performance of anengine, especially during the takeoff
or landing period.Meanwhile, the jet flow would cause excessive
temperatureat the impingement point, which may damage the
compositematerials that are widely used in a modern aircraft [3] or
eventhe aluminum skin. The electrothermal ice protectionmethod has
a higher heating efficiency and a lower powerdensity, which results
in the advantages in structure safetyand energy efficiency. As the
concepts of more-electric-aircraft and all-electric-aircraft are
increasingly employed ina modern aircraft design, the
electrothermal ice protectionmethod is drawing more attention. The
ice protection systemof B-787 [4], which is based on the
electrothermal method,serves as an example.
Since the icing tunnel experiments and the flight experi-ments
are complex, expensive, and not able to cover all envi-ronment
conditions, the investigation of a deicing process byan
experimental method is quite limited and seldom reportedto date.
The numerical simulation method, which is time-efficient and
cost-effective, becomes an important tool for
HindawiInternational Journal of Aerospace EngineeringVolume
2018, Article ID 5362541, 16
pageshttps://doi.org/10.1155/2018/5362541
http://orcid.org/0000-0001-9684-2250http://orcid.org/0000-0002-0735-5774https://doi.org/10.1155/2018/5362541
-
the design of the ice protection system. The in-flightdeicing
process is a conjugate mass and heat transfer phe-nomenon, which is
very complex and consists of a varietyof coupled processes such as
the air-droplet flow, waterfilm runback and phase transition, and
multilayer solidheat conduction. The phase state varies with both
spatiallocations and time. Due to the periodic power density,
spatialdistribution of heaters, and sustained droplet
impingement,phase transition phenomena, such as evaporation,
solidifica-tion, liquefaction, and sublimation, may coexist on
thesurface of the protection area, which makes it complex
andtypically unsteady.
The early study of electrothermal deicing concentratedon the
solution of multilayer structure heat conduction.Stallabrass [5]
numerically analyzed the heat conductionduring the deicing process,
focusing on the effects of multi-layer materials on the
distribution of skin temperature,especially the effects of inner
and outer insulating layers.Then, the latent heat was introduced to
simulate the phasechange during the deicing process by Baliga [6].
As theresearch went in depth, Marano [7] and Roelke et al.
[8]developed the “enthalpymethod,” in which the unified
energyequation was applied in the whole computational domain andthe
phase interface was determined by enthalpy distribution.Based on
the enthalpy method, plenty of researches wereconducted to simulate
the phase transition process. Chao[9], Leffel [10], and Masiulaniec
[11] applied the method to2-D cases and analyzed the effects of
surface curvature andheating pad spatial distribution. Chang [12,
13] numericallystudied the 2-D deicing process by a finite volume
methodand analyzed the effects of the heating sequence and
powerdensity. Yaslik et al. [14] studied a 3-D deicing process,
usinga Douglas method to discretize the heat conduction
equation.Xiao [15] applied a porous medium method to simulate
theice melting process. As is briefly reviewed above,
researchershave done much work on the study of multilayer
structureheat conduction and ice melting process based on
enthalpymethod, while the study of the in-flight deicing process,
whichinvolves sustained droplet impingement and water filmrunback,
is quite rare.
Wright et al. [16] developed a 2-D deicing model, whichwas based
on the classic Messinger mass and energy balancemodels [17]. The
mass and energy balance equations tookinto account the input water
caused by droplet impingement,
but the water film runback mechanism was not taken
intoconsideration. Habashi et al. [18–20] developed a
conjugatemodel for the in-flight deicing process. The airflow
anddroplet impingement were calculated as initial solutions,and the
solid conduction was solved, which was coupled witha water phase
transition in a loosely coupled way. Finite ele-ment solvers were
applied to the solution as the modules ofthe commercial software
FENSAP-ICE, while the detailedsolution method was not available in
the open literature.
As electrothermal deicing method is increasinglyemployed in the
new generation of aircraft, the study on themechanism and
simulation methods is urgently needed.Whilemost current studies on
the deicing process concentrated onthe multilayer structure heat
conduction and ice melting pro-cess, studies available on the
in-flight deicing were quite rare.
This paper focuses on the conjugate heat transfer mecha-nism of
the in-flight electrothermal deicing. A novel 3-Dunsteady model is
established based on the water film run-back dynamic mechanism and
phase transition thermody-namic model and solved by a loosely
coupled method.Using the present model, the deicing process is
numericallyinvestigated, which contributes to a better
understanding ofelectrothermal deicing so as to guide the design
and optimi-zation of an aircraft ice protection system.
2. Mathematical Model
The in-flight deicing process is a conjugate mass and
heattransfer process, which involves air-droplet flow, solid
heatconduction, water film runback, and the phase transition.The
mass and energy balance, as is briefly shown inFigure 1, is
determined by a variety of factors including con-vection, droplet
impingement, evaporation, solidification,heat conduction, and film
runback. Due to the periodicpower density and spatial distribution
of heaters, the phasetransition process is typically unsteady.
2.1. Air-Droplet Flow. Since the volume fraction of droplet
isvery small, typically under 10−6 for icing conditions, the
air-droplet flow can be solved by a one-way coupled method[21].
Reynolds-averaged Navier–Stokes equations (RANS)are applied to
solve the air flow field. The mass and momen-tum equations are
expressed as (1), and the energy equationis expressed as (2):
∂ρa∂t
+ ∂ ρauixi
= 0,1
∂∂t
ρaui +∂∂xj
ρauiuj = −∂p∂xi
+ ∂∂xj
μ∂ui∂xj
+∂uj∂xi
−23 δij
∂ul∂xl
+ ∂∂xj
−ρaui′uj′ ,
∂∂t
ρaE +∂∂xi
ui ρaE + p =∂∂xj
λ +cpμ
Pr∂T∂xj
+ ∂∂xj
ui μ + μt∂ui∂xj
+∂uj∂xi
−23 δi,j
∂ul∂xl
, 2
2 International Journal of Aerospace Engineering
-
where the Reynolds stress is defined by Boussinesq as
−ρui′uj′ = μt∂ui∂xj
+∂uj∂xi
−23 ρk + μt
∂uk∂xk
δij, 3
where μt is the turbulent viscosity, ui is the average
velocity,and k is the turbulence kinetic energy.
The continuity and momentum equations of droplet floware
expressed as [22]
∂ ρα∂t
+ ∇ ⋅ ραu = 0, 4
∂ ραu∂t
+ ∇ ⋅ ραuu = ραK ua − u + ραF, 5
where ρ is the density of water, α is the droplet
volumefraction, u is the velocity vector of droplet, ua is the
velocityvector of air, ραF is the external body forces exerted
ondroplet, such as the gravity or inertial force, and K is
theair-droplet momentum exchanger coefficient defined as
K =18μf dragρd2p
, 6
where μ is the dynamic viscosity of air, dp is the diameter
ofdroplet, and f drag is the drag function. The Schiller andNaumann
model is adopted here.
f drag =CDRer24
CD =24 1 + 0 15Re0 687r
Rer, Rer ≤ 1000,
0 44, Rer > 1000
7
Rer is the relative Reynolds number and is given as
Rer =ρa∣ua − u∣dp
μ8
2.2. Water Film Runback and Phase Transition. The differen-tial
form of continuity equation for runback water film on thesurface of
ice protection area is expressed as
∂ρ∂t
+ div ρv =mimp −mice −mevap, 9
where v is the velocity of water film,mimp is the water mass
ofdroplet impingement, mice is the icing rate, and mevap is
theevaporation rate. The water film is incompressible, and
thedevelopment of water film is quick due to a quite small
thick-ness. Therefore, the unsteady water mass term is
neglected,and the continuity equation is derived by integrating
thedifferential form in a control volume.
〠min,n +mimp =〠mout,n +mice +mevap, 10
where ∑min,n is the total mass of water entering the
currentcontrol volume from adjacent ones per unit time, ∑mout,n
isthe total mass of water flowing out of the control volume,and the
mass flux through a face n can be expressed as
mout,n = ρlnh v ⋅ nn , 11
where h is the film thickness, ln is the edge length, and
nnrepresents the unit vector normal to face n.
The mass flux of droplet impingement is determined bylocal
collection efficiency β, as expressed as
mimp = u∞ ⋅ LWC ⋅ β ⋅ A, 12
where u∞ is the velocity of droplet at far field, LWC is
theliquid water content, and A is the area of control volume.
The evaporation rate is determined by the Chilton-Colburn
analogy theory where the convective mass transfer
Heat conduction,water film runback, and phase transition
Solidificationand melting
Heat generationand conduction
Heater
Convection
EvaporationDroplet
impingement
Film runback
Air flow
Droplet
Figure 1: Mass and energy balance of deicing process.
3International Journal of Aerospace Engineering
-
coefficient kc is obtained from the convective heat
transfercoefficient hc as shown below.
hccp
Pr2/3 = kcSc2/3, 13
where Sc is the Schmidt number. The convective heat trans-fer
coefficient hc is calculated according to the surface heatflux and
the temperature difference.
hc =q
A ⋅ T − T∞ 1 + f rec γ − 1/2 Ma2, 14
where f rec is the recovery coefficient; γ is the air specific
heatratio, of which the value is 1.4; and Ma is the Mach numberof
air flow. Then the evaporation rate is derived as
mevap =hcAcp,air
⋅MWwaterMWair
⋅PrSc
2/3
⋅pv,satpT
⋅TTT
⋅pTp
1/γ−pv,∞,satrh
p∞,
15
whereMW is the air molecular weight, cp,air is the air
specificheat, pv,sat is the vapor saturated pressure, pT is the
totalpressure, TT is the total temperature, and rh is the
relativehumidity, of which the value on water film surface is
1.
The momentum equation of water film runback is givenby
incompressible Navier–Stokes equation as
∂∂t
ρv + ∇ ⋅ ρvv + pI = ∂∂y
μ∂v∂y
+ ρg, 16
where p is the pressure, I is the unit tensor, y is the
coordinatenormal to surface, and g is the gravitational
acceleration.
The air-film boundary condition is defined as
μ∂v∂y
= τ + σκ, y = h, 17
where τ is the shear stress, σ is the coefficient of tension,
andκ is the water film surface curvature which is given by
κ = − ∂2h
∂x2j1 + ∂h
∂xj
2 −3/2
18
The solid-film boundary is depicted under the nonslipboundary
condition.
v = 0,y = 0
19
Previous studies suggest that the effects of pressure gradi-ent
should only be considered for water film with a largethickness
[23]. During the deicing process, the water film isvery thin;
therefore, the terms of gradient and gravity arenegligible, of
which the effect is slight compared with otherterms such as shear
stress. The tangential velocity gradientis also very small;
therefore, the momentum diffusion termis negligible [24]. The value
of surface curvature is generallyvery small for film which entirely
wets the surface, and theshear stress is the dominant factor at the
air-film interface.Under such condition, the momentum equation and
bound-ary condition of water film are simplified as
∂∂y
μ∂v∂y
= 0,
μ∂v∂y
= τ, y = h,
v = 0, y = 0
20
The velocity distribution normal to the surface isderived as
v = yμτ 21
Air flow Droplet flow
Unsteady time step
Update ice accretion state
Coupled iteration
Icing/melting rateBoundary convergence
Water film runbackand phase transition
Multilayer heatconduction
Figure 2: Diagram of coupling solution method.
4 International Journal of Aerospace Engineering
-
The average velocity V is obtained by integrating theabove
equation along the film thickness direction, asexpressed as
V = h2μ τ 22
The energy balance of water film is described by the fol-lowing
differential equation:
∂ ρcwT∂t
+ div ρcwTV =Himp + Eice −Qc −Hevap +Qcond23
Integrating the above equation, the energy balance in acontrol
volume is expressed as
ρAhcw T − TpreΔt +〠n
Hout,n −〠n
Hin,n =H imp + Eice −Qc
−Hevap +Qcond,24
where cw is the specific heat of water, T and Tpre are the
tem-perature at current time step and previous time step, Qcond
isthe deicing heat flux from solid, obtained from the calcula-tion
of solid heat conduction during the iterations, and
Start Calculate the airflowCalculate thedroplet flow Assume Ts =
T0
Use Ts to calculate f, solveenergy balance equition
Find the stagnation point andboundary
Interpolationand store data
Export localcollectionefficiency
Export shearstress and heatflux
0
-
Hin,n is the energy carried by runback water entering thecurrent
control volume through the face n, and it can beexpressed as
Hin,n =min,ncw T in,n − T0 25
Himp is the energy of impinging water, which consists oftwo
parts: the internal energy and the kinetic energy, asexpressed
below.
Himp =mimp cw T∞ − T0 +12 u
2∞ 26
Qc is the convective heat flux obtained by the con-vective heat
transfer coefficient hc and the temperaturedifference between
surface temperature T and recovertemperature Trec.
Qc = hcA T − T rec 27
The latent heat of solidification Eice, the out-flow
energyHout,n, and the latent heat of evaporation Hevap are
relatedto the phase condition of the control volume, which
arediscussed as follows by considering the freezing fractionf ,
namely the ratio of icing mass to the total enteringwater mass.
If f = 0 and the surface is clean, which means currentlythat
there is no ice accretion, the water in the control volumeremains
at a liquid state, icing rate is zero, and the energy ofrunback
water and evaporation can be expressed as
mice = 0,Eice = 0,
Hout,n =mout,ncw Ts − T0 +12mout,nV
2,
Hevap =mevap Levap + cw Ts − T0 ,
28
where Levap is the latent heat of water evaporation.If f = 0 and
there is ice accretion in the current volume,
the ice melts at a liquid-solid mixed state and the
controlvolume remains at the phase transition temperature.
Ts = T0,Eice =mmeltLs,
Hout,n = 1/2mout,nV2,Hevap =mevapLevap,
29
where mmelt is the melting rate and Ls is the
solidificationlatent heat.
If 0< f< 1, part of water freezes, and the control volume
isat the phase transition temperature.
Ts = T0,Eice =miceLs,
Hout,n = 1/2mout,nV2,Hevap =mevapLevap
30
If f = 1, all the water freezes and the energy terms can
beexpressed as
Eice =mice Ls + cice T0 − Ts ,mout,n = 0,Hout,n = 0,Hevap =mevap
Lsub + cice Ts − T0 − Ls ,
31
Heater
Heater
12
3
4
5
Erosion shield0.2 mm
Elastomer0.56 mm
Fiberglass0.89 mm
Silicone foam3.4 mm
6 7
Figure 4: Material and structure of ice protection area.
Table 2: Material properties of NASA experiment.
MaterialDensity(kg/m3)
Heat conductivity(W/mK)
Heat capacity(J/kgK)
Erosionshield
8025.25 16.26 502.4
Elastomer 1383.96 0.2561 1256.0
Fiberglass 1794 0.294 1570.1
Siliconefoam
648.75 0.121 1130.4
6 International Journal of Aerospace Engineering
-
where cice is the specific heat of ice and Lsub is the
sublimationlatent heat.
2.3. Heat Conduction. The unsteady heat conduction throughthe
multilayer materials is expressed as
∂H∂t
= ∇ ⋅ λ∇T + S, 32
where H is the enthalpy of the material, λ is the thermal
con-ductivity, and S is the heat source term. For
electrothermaldeicing process, the source term is determined by the
spatiallocation of heaters and the power sequence.
The Dirichlet heat boundary condition of heat conduc-tion is
provided by the solution of water film runback andphase transition
during the coupled solution. In return, thedeicing heat flux is
calculated and sent to the calculation ofwater film. The deicing
heat flux is obtained at the boundaryof a solid structure as shown
in
Qcond = −Aλ∂T∂n , 33
where n is the normal vector of the boundary surface.
Temperature of heater 3295
290
285
280
T (K
)
275
270
265
2600 100 200 300
Time (s)400 500 600
PresentExperimentFENSAP
Figure 8: Comparison of temperature of heater 3.
NASA
0.6
0.5
0.4
Dro
plet
colle
ctio
n effi
cien
cy
0.3
0.2
0.1
0.0−0
.12
−0.1
0
−0.0
8
−0.0
6
−0.0
4
−0.0
2
0.00
0.02
Curve length (m)
0.04
0.06
0.08
0.10
0.12
Present—mesh aPresent—mesh bPresent—mesh c
Figure 7: Comparison of droplet collection efficiency.
280260240220200180160
Con
vect
ive h
eat t
rans
fer c
oeffi
cien
t (W
/m2 K
)
140120100
80604020
0−0.10 −0.05 0.00
Curve length0.05
LEWICEExperimentPresent—mesh a
Present—mesh bPresent—mesh c
0.10
Figure 6: Comparison of convective heat transfer
coefficient.
7 0 0 124006 0 0 124005 0 15500 04 7750 7750 77503 0 15500 02 0
0 124001 0 0 12400
Heater 100 s 10 s 10 sTime
Figure 5: Heating sequence of NASA experiment (power in
W/m2).
7International Journal of Aerospace Engineering
-
X
Y
Z
Ice shapet = 100 s
0.05
Ice 100 sWall
0.040.030.020.01
0
0 0.02 0.04X
0.06 0.08 0.1
Y
−0.01−0.02−0.03−0.04−0.05
(a) t = 100 s
Ice shapet = 110 s
X
Y
Z0.05
Ice 110 sWall
0.040.030.020.01
0
0 0.02 0.04X
0.06 0.08 0.1
Y
−0.01−0.02−0.03−0.04−0.05
(b) t = 110 s
Ice shapet = 120 s
X
Y
Z 0.05
Ice 120 sWall
0.040.030.020.01
0
0 0.02 0.04X
0.06 0.08 0.1
Y
−0.01−0.02−0.03−0.04−0.05
(c) t = 120 s
Figure 9: Simulated ice shape following NASA experiment.
8 International Journal of Aerospace Engineering
-
3. Solution Procedure
During the solution of the above unsteady conjugate heattransfer
model, the water film runback and phase transitionare coupled with
the solid heat conduction, due to the factthat the solution of the
solid heat conduction provides theinterface heat flux which is
needed in the water film energybalance equation; on the other hand,
the boundary conditionof the solid heat conduction is provided by
the solution of thefilm runback and phase transition. A loosely
coupled methodis applied to solve the present model, in which both
the waterfilm runback and the heat conduction are iteratively
calcu-lated until the heat boundary condition reaches
convergence,and during each iteration, the surface temperature T
and heatflux Qcond are exchanged, as briefly shown in Figure 2.
Considering that the ice thickness during deicing processis
typically controlled at a very small value, the effect of theice
shape on air-droplet flow is slight. As a result, the steadyairflow
solution is computed as an initial condition and isassumed
unchanged during the simulation. Besides, it isaccurate as long as
the ice thickness does not exceed a certainlimit due to a
protection failure. The RANS equations of air-flow are discretized,
using a finite volume method in a secondorder upwind scheme. To
simulate the turbulent flow, thetransition SST model, which is
shown to obtain good resultsfor wall-bounded flows, such as the
airfoil, is utilized. A CFDsolver FLUENT is used to solve the
governing equations. Thegoverning equations of droplet flow field
are solved by thefinite volume method using the User-Defined Scalar
(UDS)transport equation. The droplet volume fraction and
velocitycomponents are set as the UDS, and the convective
terms,diffusion terms, and source terms are defined by codes
whichare programmed using the User-Defined Functions (UDF).The
solution of air-droplet flow is the initial condition ofwater film
runback and solid heat conduction, and the dataexchange is achieved
by interpolation due to the differencebetween flow field mesh and
solid mesh.
A loosely coupled method is applied to solve the deicingmodel.
At the current time step, both the solid heat conduc-tion and the
water film runback are iteratively calculateduntil convergence.
During each iteration, the surface temper-ature and heat flux are
exchanged, and the boundary condi-tions are updated. The ice shape
is obtained by the icingrate or melting rate, and the calculation
of the next time stepthen begins. The flowchart is shown in Figure
3, and somebrief introduction is provided below for the
flowchart.
(1) Solve the air-droplet flow and transfer the data
byinterpolation;
(2) Loop all the surface control volumes and check them.If the
input water mass is already known, assume aninitial temperature,
solve the mass and energybalance equations, update the value of
temperatureand phase state, and provide input conditions
foradjacent volumes. Keep the calculation of water filmrunback and
phase transition until the calculationsof all control volumes are
done; the temperaturedistribution at boundary surface is
obtained;
(3) Set Dirichlet boundary condition for solid heatconduction
using the temperature distribution ofstep (2) and solve the heat
conduction; calculate thedeicing heat flux at boundary.
(4) Update the deicing heat flux of water film energyequation
using the data of step (3).
(5) Repeat steps (2)–(4) until convergence, calculate
iceaccretion at the moment, and advance to the nexttime step.
4. Results and Discussion
Validations of the present model are conducted, and theresults
are compared with the experimental data. Then, asimulation of
in-flight deicing process is conducted tooptimize the heating
sequence.
4.1. NASA Deicing Experiment in the Lewis Icing ResearchTunnel.
In order to perform the in-flight deicing simulation,a deicing
experiment model is selected in the very rarerecords available in
the open literature, which is conductedin the NASA Lewis Icing
Research Tunnel (IRT) byAl-Khalil et al. [25].
The experiment model is a NACA 0012 airfoil with achord of
0.914m (36 in), and the environment conditionsare listed in Table
1. The multilayer structure at the leadingedge protection area is
composed of four different layers,which are the erosion shield, the
elastomer, the fiberglass,and the silicone foam, with a thickness
of 0.2mm, 0.56mm,0.89mm, and 3.4mm, respectively. The structure is
shownin Figure 4, and the material properties are listed inTable 2.
Seven heating pads are arranged in the elastomerlayer, of which the
heating sequence and power density arecontrolled independently. The
length is 1.905 cm for heater4; 2.54 cm for heaters 2, 3, 5, and 6;
and 3.81 cm for heaters1 and 7. The heating sequence is shown in
Figure 5. Heater4 acts as the heat blade, which keeps activated
during thewhole cycle to avoid ice accretion on the leading edge.
Therear heating pads are activated alternately after 100 s.
The steady air-droplet flow was solved to obtain parame-ters
such as the convective heat flux, the shear stress, and thelocal
droplet collection efficiency. Then, the data weretransferred to
solid mesh by interpolation, and the unsteadydeicing process was
coupled solved. Structured grids weregenerated for the solution of
air-droplet flow. To verify themesh independence of the solution,
three mesh files wereapplied, and the normal distance of the first
layer is0.01mm (mesh a), 0.0075mm (mesh b), and 0.005mm(mesh c),
respectively. The y+ at the ice protection area ofall three mesh
files was controlled around or lower than 1.
Table 3: Environment conditions of in-flight case.
Temperature(K)
Velocity(m/s)
LWC(g/m3)
MVD(μm)
AoA
263 97.6 1 20 0
9International Journal of Aerospace Engineering
-
The simulated convective heat transfer coefficient curvesare
shown in Figure 6, which show good agreement with theexperimental
data and LEWICE solution. The results of threemesh files match
well, indicating that the solutions are meshindependent. The
convective heat transfer coefficient reachesthe peak at the
stagnation point and drops rapidly as it moves
backwards due to the development of boundary layer.
Theexperimental value is slightly larger than that of the
simu-lated results, and the turbulence intensity of the icing
tunneltest might be a possible explanation. The droplet
collectionefficiency was not recorded during the experiment, while
itwas simulated by NASA LEWICE code in the literature.
7 0 0 150006 0 0 150005 0 15000 04 10000 10000 100003 0 15000 02
0 0 150001 0 0 15000
Heater Time 75 s 25 s 25 s
Figure 10: Initial heating sequence of in-flight case (power in
W/m2).
X
Y
Z
Heat transfercoefficient
2602502402302202102001901801701601501401301201101009080
(a) Convective heat transfer coefficient (W/m2K)
X
Y
Z
Beta0.55
0.5
0.45
0.4
0.35
0.3
0.25
0.2
0.15
0.1
0.05
(b) Local collection efficiency
Figure 11: Contour of convective heat transfer and droplet
impingement.
10 International Journal of Aerospace Engineering
-
X
Y
Z
Temperature289288287286285284283282281280279278277276275274273272271
(a) t = 75 s
X
Y
Z
Temperature298296294292290288286284282280278276274272
(b) t = 100 s
X
YTemperature
312310308306304302300298296294292290288286284282280278276274
Z
(c) t = 125 s
Figure 12: Temperature distribution at cross section (K).
11International Journal of Aerospace Engineering
-
X
Y
Z
Ice shapet = 75 s
Ice 75 sWall
0.050.040.030.020.01
0Y
0 0.02 0.04X
0.06 0.08 0.1
−0.01−0.02−0.03−0.04−0.05
(a) t = 75 s
X
Y
Z
Ice shapet = 100 s
0.050.040.030.020.01
0Y
0 0.02 0.04X
0.06 0.08 0.1
−0.01−0.02−0.03−0.04−0.05
Ice 100 sWall
(b) t = 100 s
X
Y
Z
Ice shapet = 125 s
0.050.040.030.020.01
0Y
0 0.02 0.04X
0.06 0.08 0.1
−0.01−0.02−0.03−0.04−0.05
Ice 125 sWall
(c) t = 125 s
Figure 13: Simulated ice shape of in-flight case.
12 International Journal of Aerospace Engineering
-
The collection efficiency of the present model and LEWICE
isshown in Figure 7, and the results match well. The valuereaches
its maximum at the stagnation point, and then thevalue decreases as
it moves backwards. There is a dropletshadowed zone when the wrap
distance exceeds 0.03m,where the local collection efficiency is
zero.
The simulated temperature of heater 3 is shown inFigure 8 with
the experimental result and FENSAP simulatedresult provided in
[18]. The temperature variation curve ofeach cycle is similar
except for the beginning period whenthe solid structure starts to
warm up. The result of the presentmodel shows good agreement with
the experimental data andFENSAP. The simulated ice shapes at 100 s,
110 s, and 120 s(the moment when heaters are turned on or off) are
shownin Figure 9.
At the first stage (0–100 s), only the heat blade isactivated.
Due to the solid conduction and the runback liquidwater, the
temperature of heater 3 rises. Figure 9(a) showsthat water remains
liquid on the surface over the heat blade,and ice forms downstream
where the heater is turned off. Therunback ice covers part of the
protection area. At the secondstage (100–110 s), heaters 3 and 5
are activated and the tem-perature of heater 3 rapidly rises to
290K. From Figure 9(b),it is observed that the ice over heater 3
melts and the run-back ice area moves backward, due to the fact
that theheating enlarges the water runback area. At the third
stage(110–120 s), heater 3 is turned off and the temperaturedrops.
Figure 9(c) shows that the runback ice, whichforms during the
second stage, melts and ice forms overheater 3 as it is turned
off.
The simulated temperature of heater 3 is slightly higherthan
that of the experimental data. When heater 3 is off,
theexperimental temperature is around 270K, and it is about3K lower
than the simulated results. At this period, thesurface is under a
runback icing condition, which means awater-ice mixed state, and
the temperature of such conditionis set at 273.15K (the freezing
point) in the thermodynamicmodel during simulation. The possible
reasons for the tem-perature difference between experiment and
simulation areas follows: (1) The supercooled water film runback
phenom-enon, which is observed in the experiments [26–28], has
notbeen considered in the present model. In simulation,
thetemperature of the runback water film would not be lowerthan the
freezing point temperature (273.15K). (2) Therunback water might
form beads or rivulet flow and doesnot completely wet the surface.
Part of the surface is exposedto air convection, and the
temperature is lower than thatwhen the surface is completely
wetted. (3) The temperaturemeasuring point in the experiment is
beneath the heatingpad, and the precise location is not mentioned
in the report;
while in simulation, the average value of the heater area
iscalculated as the result. The average value might be largerwhen
the heater is turned off, because the temperature atthe margin is
higher due to the heating of the adjacentheating pads.
4.2. Deicing Simulation under Different Heating Sequences.The
above simulations validate the present model and thesolution
method. In this section, another deicing simulationis conducted
under in-flight environment conditions to ana-lyze the deicing
performance of different heating sequences.The environment
conditions are listed in Table 3. Comparedwith NASA icing tunnel
experiment, the temperature islower, and the air velocity and
liquid water content are larger,which would lead to a severer ice
protection condition.
The heating sequence is shown in Figure 10, with a cycleof 125
s. The heat blade (heating pad 4, at the leading edge) iskept
activated during the whole cycle; heaters 3 and 5 areactivated
during 75–100 s, and other heaters are activatedduring 100–125 s.
The ice protection structure model andthe materials are the same
with those in Section 4.2.
The convective heat transfer coefficient distribution isshown in
Figure 11(a), and the contour of droplet collectionefficiency is
shown in Figure 11(b). The convective heattransfer intensity
reaches its peak at the stagnation pointand drops rapidly as it
moves backwards due to the develop-ment of the boundary layer.
Similarly, the droplet collectionefficiency reaches its maximum at
the stagnation point, andthe value decreases as it moves backwards.
There is nodroplet impingement at the rear part.
Figures 12 and 13 show the solid temperature distribu-tion of
the cross section and the ice shapes at t=75 s, 100 s,and 125 s,
which are the end time of the three stages. Duringthe first stage
(0–75 s), the structure temperature at the lead-ing edge increases
due to the activated heat blade, and thetemperature of the heat
blade reaches 289K as is shown inFigure 12(a). The temperature of
the adjacent area alsoincreases due to heat conduction, while the
value is lowerthan that of the heat blade and the heated area is
limited,because the thermal conductivity of the structure
materialsis low. The water remains at a liquid state over the heat
blade,as shown in Figure 13(a), and ice forms downstream. Com-pared
with the result of Section 4.2, the ice accretion areaand the ice
thickness are larger in this case. All the ice protec-tion area is
covered by ice, because the air velocity and liquidwater content
are larger and the temperature is lower in thiscase. Later in the
second stage (75–100 s), heaters 3 and 5 areturned on, ice starts
to melt, and solid temperature increases.At 100 s, ice over the
rear part of heaters 3 and 5 meltscompletely, and the surface
temperature exceeds 273.15K
7 0 0 150006 0 0 150005 0 15000 04 10000 10000 100003 0 15000 02
0 0 150001 0 0 15000
Heater Time 75 s 30 s 20 s
Figure 14: Altered heating sequence.
13International Journal of Aerospace Engineering
-
as shown in Figures 12(b) and 13(b). While there is ice left
inthe front of heaters 3 and 5, the accrete ice thickness is
largethere and the power is insufficient for all the accrete ice
tomelt. The ice continues to form on the nonheating surfacearea. In
the third stage (100–125 s), the temperature atheaters 3 and 5
drops rapidly when the heaters are turnedoff, and runback water
freezes over heaters 3 and 5, as shownin Figures 12(c) and 13(c).
Ice over heaters 1, 2, 6, and 7melts, and the temperature there
increases to a high levelsince the convective heat dissipation
there is relatively weak.
At the end of the second heating stage (t=100 s), there isice
left unmelted in the front of the surface over heaters 3 and
5, which would lead to ice accretion on that area. Accordingthe
discussion above, we know that the deicing power neededin the front
is larger than that in the rear part. Therefore, theheating
sequence is altered by extending the second stage to30 seconds and
shorten the third stage to 20 s, as shown inFigure 14. The total
time of a cycle remains the same, whilethe power needed for a cycle
is reduced, because the area ofheaters 1, 2, 6, and 7 is larger.
The simulated ice shape withthe altered heating sequence is shown
in Figure 15.Figure 15(a) shows that after the second stage the
surfaceover heaters 3 and 5 is clean with all accrete ice
melted.Figure 15(b) shows that after the whole deicing cycle,
most
X
Y
Z
Ice shapet = 105 s
t = 105 sWall
0.05
0.04
0.03
0.02
0.01
0Y
0 0.020.01−0.01−0.02 0.040.03X
0.060.05 0.07 0.08
−0.01
−0.02
−0.03
−0.04
−0.05
(a) t = 105 s
X
Y
Z
Ice shapet = 125 s
t = 125 sWall
0.05
0.04
0.03
0.02
0.01
0Y
0 0.020.01−0.01−0.02 0.040.03X
0.060.05 0.07 0.08
−0.01
−0.02
−0.03
−0.04
−0.05
(b) t = 125 s
Figure 15: Simulated ice shape under altered heating
sequence.
14 International Journal of Aerospace Engineering
-
part of the surface is clean, and only very slight ice
accretionoccurs at the location near the heat blade, which would
beremoved in the next cycle.
5. Conclusions
Based on the water film runback dynamics and energybalance
theory, an unsteady conjugate heat transfer modelfor electrothermal
deicing is established, and a looselycoupled solution method is
developed. The model is appliedin the simulation of deicing
process, and the conclusions areas follows:
(1) In-flight deicing process is very complex due tofactors such
as droplet impingement and water filmrunback. The present model is
capable of simulatingthe in-flight deicing process. Simulation
followingan icing tunnel experiment has been conducted tovalidate
the present model, and the results showgood agreement.
(2) The environment conditions would strongly affectthe solid
temperature distribution, the water filmrunback, and phase
transition. A larger velocity orliquid water content would
correspond to a largerrunback icing range, and a higher power of
longerheating duration is needed to perform the deicingprocess.
Water remains at a liquid state over the heatblade, and ice forms
on the surface where the heatingpower is insufficient.
(3) Heating sequence is a key factor for the deicingperformance.
A proper heating sequence not onlyleads to a better deicing
performance, but also savesenergy. The optimization of heat
sequence can beconducted by means of numerical simulation.
(4) However, there are several factors not yet
considered,including the ice shedding mechanism, the contactthermal
resistance between multilayer materials, andthe anisotropy of
material properties.
Conflicts of Interest
The authors declare that they have no conflicts of interest.
Acknowledgments
The work was supported by the National Natural ScienceFoundation
of China (Grant no. 51206008).
References
[1] G. Lin, X. Bu, and X. Shen, Aircraft Icing and
Anti-IcingMethod, Beihang University, Beijing, China, 2016.
[2] K. Al-khalil, “Thermo-mechanical expulsion deicing system
-TMEDS,” in 45th AIAA Aerospace Sciences Meeting andExhibit, Reno,
NV, USA, 2007American Institute of Aeronau-tics and
Astronautics.
[3] M. Sinnett, “787 no-bleed systems: saving fuel and
enhancingoperational efficiencies,” Aero Quarterly, vol. 18, pp.
6–11,2007.
[4] “Electro-thermal ice protection system for the B-787,”
AircraftEngineering and Aerospace Technology, vol. 79, no. 6,
2007.
[5] J. R. Stallabrass, “Thermal aspects of deicer design,” in
Interna-tional Helicopter Icing Conference, Ottawa, Canada, May
1972.
[6] G. Baliga, Numerical Simulation of One-Dimensional
HeatTransfer in Composite Bodies with Phase Change [Ph.D.
thesis],the University of Toledo, Toledo, OH, USA, 1980.
[7] J. J. Marano, Numerical Simulation of an
ElectrothermalDe-Icer Pad [Ph.D. thesis], the University of
Toledo,Toledo, OH, USA, 1982.
[8] R. J. Roelke, T. G. Keith, K. J. DE Witt, and W. B.
Wright,“Efficient numerical simulation of a one-dimensional
electro-thermal deicer pad,” Journal of Aircraft, vol. 25, no.
12,pp. 1097–1105, 1988.
[9] D. F. K. Chao, Numerical Simulation of Two-DimensionalHeat
Transfer in Composite Bodies with Application toDe-Icing of
Aircraft Components [Ph.D. thesis], the Universityof Toledo,
Toledo, OH, USA, 1983.
[10] K. L. Leffel, A Numerical and Experimental Investigation
ofElectrothermal Aircraft Deicing [Ph.D. thesis], the Universityof
Toledo, Toledo, OH, USA, 1986.
[11] K. C. Masiulaniec, A Numerical Simulation of the Full
Two-Dimensional Electrothermal De-Icer Pad [Ph.D. thesis],
theUniversity of Toledo, Toledo, OH, USA, 1987.
[12] S. Chang, S. Ai, X. Huo, and X. Yuan, “Improved simulation
ofelectrothermal de-icing system,” Journal of Aerospace Power,vol.
23, no. 10, pp. 1753–1758, 2008.
[13] J. Fu, W. Zhuang, B. Yang, and S. Chang, “Simulation of
heat-ing control law of electrothermal deicing of helicopter
rotorblade,” Journal of Beijing University of Aeronautics
andAstronautics, vol. 40, no. 9, pp. 1200–1207, 2014.
[14] A. D. Yaslik, K. J. De Witt, T. G. Keith, and W.
Boronow,“Three-dimensional simulation of electrothermal deicing
sys-tems,” Journal of Aircraft, vol. 29, no. 6, pp. 1035–1042,
1992.
[15] C. Xiao, Study on Heat Transfer Characteristics and Effects
ofElectrothermal Aircraft Deicing [Ph.D. thesis], China
Aerody-namics Research and Development Center, Sichuan,
China,2010.
[16] W. B. Wright, K. J. WittDe, and T. Keith,
“Numericalsimulation of icing, deicing, and shedding,” in
29thAerospace Sciences Meeting, Reno, NV, USA, January
1991,American Institute of Aeronautics and Astronautics.
[17] T. G. Myers, “Extension to the Messinger model for
aircrafticing,” AIAA Journal, vol. 39, no. 2, pp. 211–218,
2001.
[18] T. Reid, G. S. Baruzzi, and W. G. Habashi,
“FENSAP-ICE:unsteady conjugate heat transfer simulation of
electrothermalde-icing,” Journal of Aircraft, vol. 49, no. 4, pp.
1101–1109,2012.
[19] M. Pourbagian and W. Habashi, “CFD-based optimization
ofelectro-thermal wing ice protection systems in de-icing mode,”in
51st AIAA Aerospace Sciences Meeting including the NewHorizons
Forum and Aerospace Exposition, Grapevine, TX,USA, January 2013,
American Institute of Aeronautics andAstronautics.
[20] M. Pourbagian and W. G. Habashi, “Aero-thermal
optimiza-tion of in-flight electro-thermal ice protection systems
intransient de-icing mode,” International Journal of Heat andFluid
Flow, vol. 54, pp. 167–182, 2015.
15International Journal of Aerospace Engineering
-
[21] C. T. Crowe, “Review—numerical models for dilute
gas-particle flows,” Journal of Fluids Engineering, vol. 104, no.
3,p. 297, 1982.
[22] S. Yang, G. Lin, and X. Shen, “An Eulerian method for
waterdroplet impingement prediction and its implementations,”
inProceedings of the 1st International Symposium on
AircraftAirworthiness, pp. 72–81, Beijing, China, 2009.
[23] A. P. Rothmayer and J. C. Tsao, “Water film runback on
anairfoil surface,” in 38th Aerospace Sciences Meeting andExhibit,
Reno, NV, USA, January 2000, American Institute ofAeronautics and
Astronautics.
[24] Newmerical Technologies Int, FENSAP-ICE, Software Pack-age,
Ver. 2011R1.0c, Newmerical Technologies International,Canada,
2011.
[25] K. Al-Khalil, C. Horvath, D. Miller, and W. Wright,
“Valida-tion of NASA thermal ice protection computer codes. III
-the validation of ANTICE,” in 35th Aerospace Sciences Meetingand
Exhibit, Reno, NV, USA, 1997, American Institute ofAeronautics and
Astronautics.
[26] R. List, F. Garcia-Garcia, R. Kuhn, and B. Greenan,
“Thesupercooling of surface water skins of spherical and
spheroidalhailstones,” Atmospheric Research, vol. 24, no. 1–4, pp.
83–87,1989.
[27] B. J. W. Greenan and R. List, “Experimental closure of the
heatand mass transfer theory of spheroidal hailstones,” Journal
ofthe Atmospheric Sciences, vol. 52, no. 21, pp. 3797–3815,
1995.
[28] A. R. Karev, M. Farzaneh, and L. E. Kollár,
“Measuringtemperature of the ice surface during its formation by
usinginfrared instrumentation,” International Journal of Heat
andMass Transfer, vol. 50, no. 3-4, pp. 566–579, 2007.
16 International Journal of Aerospace Engineering
-
International Journal of
AerospaceEngineeringHindawiwww.hindawi.com Volume 2018
RoboticsJournal of
Hindawiwww.hindawi.com Volume 2018
Hindawiwww.hindawi.com Volume 2018
Active and Passive Electronic Components
VLSI Design
Hindawiwww.hindawi.com Volume 2018
Hindawiwww.hindawi.com Volume 2018
Shock and Vibration
Hindawiwww.hindawi.com Volume 2018
Civil EngineeringAdvances in
Acoustics and VibrationAdvances in
Hindawiwww.hindawi.com Volume 2018
Hindawiwww.hindawi.com Volume 2018
Electrical and Computer Engineering
Journal of
Advances inOptoElectronics
Hindawiwww.hindawi.com
Volume 2018
Hindawi Publishing Corporation http://www.hindawi.com Volume
2013Hindawiwww.hindawi.com
The Scientific World Journal
Volume 2018
Control Scienceand Engineering
Journal of
Hindawiwww.hindawi.com Volume 2018
Hindawiwww.hindawi.com
Journal ofEngineeringVolume 2018
SensorsJournal of
Hindawiwww.hindawi.com Volume 2018
International Journal of
RotatingMachinery
Hindawiwww.hindawi.com Volume 2018
Modelling &Simulationin EngineeringHindawiwww.hindawi.com
Volume 2018
Hindawiwww.hindawi.com Volume 2018
Chemical EngineeringInternational Journal of Antennas and
Propagation
International Journal of
Hindawiwww.hindawi.com Volume 2018
Hindawiwww.hindawi.com Volume 2018
Navigation and Observation
International Journal of
Hindawi
www.hindawi.com Volume 2018
Advances in
Multimedia
Submit your manuscripts atwww.hindawi.com
https://www.hindawi.com/journals/ijae/https://www.hindawi.com/journals/jr/https://www.hindawi.com/journals/apec/https://www.hindawi.com/journals/vlsi/https://www.hindawi.com/journals/sv/https://www.hindawi.com/journals/ace/https://www.hindawi.com/journals/aav/https://www.hindawi.com/journals/jece/https://www.hindawi.com/journals/aoe/https://www.hindawi.com/journals/tswj/https://www.hindawi.com/journals/jcse/https://www.hindawi.com/journals/je/https://www.hindawi.com/journals/js/https://www.hindawi.com/journals/ijrm/https://www.hindawi.com/journals/mse/https://www.hindawi.com/journals/ijce/https://www.hindawi.com/journals/ijap/https://www.hindawi.com/journals/ijno/https://www.hindawi.com/journals/am/https://www.hindawi.com/https://www.hindawi.com/