the course of a run, especially when the .... for the answers to these two questions .... 0.100000. 0.005800. IS THE INPUT DATA SATISFACTORY? ANSWER.
NASA
DOT/FAA/CT-TN92/33
Contractor
Report
4530
User's Manual for the NASA Lewis Accretion/Heat Transfer Prediction Code with Electrothermal Deicer
Konstanty
Ice
Input
C. Masiulaniec
University of Toledo Toledo, Ohio and William
B. Wright
Sverdrup Lewis Brook
Technology,
Research Center Park, Ohio
Inc. Group
Prepared for Lewis Research
Center
Under
Contract
NAS3-25517
Grant
NAG3-72
National
Aeronautics
Space
Administration
O_ce
of Management
Scientific Information 1994
and
and Technical Program
and
US.DeoQrtrr_nl of Transportation r-edeml Aviation Administration
SUMMARY
A
version
of
LEWlCE
electrothermal
deicer
accomplished,
in essence,
has
been
code, developed
developed
at the University
by replacing
a subroutine
energies
at the ice surface,
with a subroutine
balance,
as well as handles
all the time-temperature
layers
of a composite
blade
This new addition heater
chordwise
may be cycled addition, Thus,
with periods
the user
the new
installed
capability,
addition
be noted it can
downstream
(which
The
of each other.
number
heaters
balanced
this same
the ice surface,
may
The heater
of layers
and
the
energy
for all of the
in modeling
that the model
simulates
both
any number be fired
intensity
thicknesses
flexibility
simulate
the
would
where
anti-icing
virtually
be equivalent
the heaters
in the prediction
determine
the effects
there
of heaters,
in unison,
any
or they
may also be varied.
depthwise
into
In
the blade.
any electrothermal
version
ice shapes.
The
deicer
on the ice accretion
1, no conduction
are firing.
agreement may
process.
the runback
as detect
icing
of the airfoil.
with subsequent
code
With
as well
of LEWICE).
but no heaters
identical
runback.
performance,
In mode
is modeled,
is virtually
and
portions
modes.
by conduction,
of accreted
of conduction
of heater
to the original
are engaged
run in the first mode,
shedding
in unprotected
can be run in three
to be caused
LEWlCE
mode
due to runback
of LEWICE
is considered
heat transfer
When
any
performs
that a user may specify
has maximum
of the heaters
This version
transfer
specify
which
This was
itself.
gap desired.
independent
below
developed
B. Wright.
EBAL,
UTICE
transients
recently
by William called
UTICE.
a
into any airfoil.
It should
modeled
may
in LEWICE,
as well as the ice layer
and any heater
incorporates
of Toledo
called
is set up in such a fashion
length,
that
heat transfer
In mode In mode
is
2, all heat
3, conduction
ice shedding.
with the original be run in the second
version
of
mode
to
Work
has
been
selected
temperature
specific
depth.
locations
in expanding
distributions
This
making
done
would
allow
use of existing
either
the subroutines depthwise
in LEWICE's at a specific
intermediate.time-temperature capabilities
and hardware
PLOT3D
routines
chord
location
results
to be inspected
with a minimum
to graph
or chordwise
at a
at specific
of new coding.
_II_T_ODUCTJ&_
The formation performance,
as it increases
equipment
necessary
be classified
The times.
of ice on the exterior
Typical
through
principle anti-icing
channels
below
involves
the periodic
systems,
attention
on
the
among
of
the more
The
surface.
boots,
boot Boots
a considerable
an aircraft
Basically,
the prevention make
use
on which
of accreted
also be given
common
The pneumatic iced.
methods
non-uniform
pneumatic
lift. Thus,
or prevention.
involves
removal
can have
must
aircraft
effect
on flight
be designed
ice protection
with the
systems
can
or de-icing.
the surface
must
dangers
including
anti-icing
of aircraft
and decreases
for ice removal
as either
anti-icing
drag
surfaces
of chemicals
on the protected
and/or
the passage
ice formation
is to be prevented.
ice by mechanical
or thermal
to uniform
shedding.
of ice formation
removal
Various
electro-expulsive,
de-icing
pneumatic
impulse,
In contrast,
have
air
de-icing
For ice removal
(reference
methods
at all
of hot bleed
means.
of ice. Itagaki
area
1) elaborates
been
investigated,
and electrothermal,
which
are
concepts.
boot is essentially
an exterior
"skin"
which
is a flexible,
rubber-like
material
which,
are relatively
simple
efficient,
but
and
is laminated
when require
to the surface
inflated,
breaks
frequent
the
to be deice off
maintenance
the
to ensure
reliability.
Electro-expulsive applications. shield.
The
aerodynamic
Pneumatic here shock
In this system flexing forces
of this acting
impulse
is the same wave
de-icers
are
a series shield
a relatively of electromagnets cracks
de-icers
down
any
development is pulsed
surface
ice,
that
in cycles,
causing
is beginning flexing
to find
a metal
it to be easily
abrasion
shed
by the
on the surface.
are also a relatively
as in the electro-expulsive
moving
new
a series
system,
of branching
new except
tubes,
3
development.
The
that the abrasion
ultimately
guiding
shedding
mechanism
shield
is flexed
the shock
wave
by a to the
abrasionshieldsurface.The shockwaveis generatedby a pulseof high pressureair releasedby a quick actionsolenoidvalve.This systemshouldbefinding applicationsin thenearfuture. Electrothermalde-icing consistsof cyclic heating of discrete elementsby electrothermal means.The energyrequirementsaresignificantlylessfor de-icingsystemsthan theyarefor antiicing systems. From experimental studies, Stallabrass(reference 2) concluded that the electrothermalmethodhasthe mostadvantagesasa de-icing mechanism,althoughit doeshave some maintainability/reliability problems. Werner (reference 3) has also reported that the electrothermalde-icingtechniqueis the mostcommonlyusedmethod,andthatit hasbeenapplied to bothfixed-wing androtary-wingaircraft. The objectiveof an electrothermalde-icingsystemis to raisethe compositebladesurface/ice interfacetemperatureabovethemeltingtemperatureof ice, resultingin avery thin interfaciallayer of liquid which reducesthe ice adhesionto the blade surface.Aerodynamicand/orcentrifugal forcescanthenreadily sweepthe unmeltedice from the surface.A typical electrothermalde-icer padis essentiallya compositebodyconsistingof (1) a metalsubstrate(the main structureof the aircraft blade), (2) an inner layer of insulation, (3) a heating element,(4) an outer layer of insulation,and(5) anabrasionshield.Dependingupontheconstructionandapplicationof a blade/ heatermat combination,theremay be additionallayers.In a thermalanalysisof the composite constructionany glue or adhesivebonding the layers togethermay itself be consideredlayer. Figure 1depictsa two-dimensionalcut-awayview of thetypicalconstructionof anelectrothermal de-icer pad,as well asa representativesetof materialsandthicknessesusedfor fabrication.The cross-sectionshownrepresentsaview of the heaterpadnormalto therun of the heatingelements. The heatingelementusuallyemployedin an electrothermalde-icerpad consistseither of a wovenmatof wiresandglassfibersor of multiplestripsof resistanceribbon.Thegapswhich exist betweenthe individual rows of matsor ribbonscanreducetheeffectivenessof the heatingpad's de-icing performance,causingnonuniformmelting of the ice. The two insulation layers,which usually consistof a resin impregnatedglasscloth, serveto provide electricalinsulation for the
Ice Water Shield Heater
Insulation
Substrate
Material
Layer
Substrate
755-T6
Inner Insulation
Aluminum
Diffusivity ft2/hr
Thickness Inches 0.087
1.65
Epoxy/Glass
0.050
0.0087
Heater
N ic hrome
0.004
0.138
Outer Insulation
Epoxy/Glass
0.010
0.0087
S ubstrate
304 Stainless
0.012
0.15
0.250
0.0445
Ice
Figure
1 - Typical
materials and construction
of an electrothermal
de-icer
pad.
heating
element.
greater
thickness
to protect uniform
In order
for the inner
the de-icer heating,
The ability
pad
and subsequent
fabrication
time-temperature
history
the nature
qualitative
representation
center,
the direction
drops
model
icing
problem,
each
constant
To accomplish
material
throughout
composite
of a typical under
model
but even
In this model, location assumed
properties.
analytical
solutions
for relatively
interface
on the temperature
2 provides
the
a pictorial indication
of
is three-dimensional,
temperature
provides
is highest
is thickest)
a
at the
and less rapidly
in
throughout thermal
2) appears
using
finite difference
method.
Results
short real times
into the problem.
within the composite temperature
6
simplifications
The
one
the plane
been
and
until the estimated
in extent.
The
containing
that
that they
have
model.
a His
well with approximate
To account
blade,
dimensional
the first to attempt
a one-dimensional agreed
are
to the full de-
infinite
contact
to have
A numerical
alterations
to be planes
in perfect
(reference
three
some
simplification.
are assumed
are
impossible.
unless
problem
was held at the freezing
to the design
with some
is virtually
de-icing
transients
more
of determining
Figure
The
3 illustrates
to be constant
that the layers
used an explicit
method
of energy
impractical,
of problem
all layers
is assumed
scheme
to provide
plot to the right of the figure
a problem
Figure
degrees
of an electrothermal
serves
is the thinnest).
for such
Stallabrass
shield
pad is essential
this, some
the insulation
this is somewhat
different
de-icer
distribution.
(where
and
to use a
gaps.
the conduction
temperature
the insulation
erosion,
that is part of an airfoil,
Clearly,
the heater
it is necessary
The abrasion
to be developed.
body. The temperature
numerical
shield
section
involved.
solution
change
the pad needs heater
numerical
phase
units.
insulation.
the heater
of these
having
at a given
It is generally
above
and the thermophysics.
is the simplest.
temperature point.
cold spots
the ice layer,
as dust/sand
of an electrothermal
realizable,
to the geometry
erosion
the performance
rapidly
made
model
as well
of an analytical
is more
toward
rain
from
of the ice (where
Development
flow
than for the outer
of the thermophysics in a curved,
heat
insulation
of an electrothermal
and occurs
heater
more
thus minimizing
to predict
representation
to direct
for the effect of the
the node at the ice-abrasion heat
flux into the control
Qy
T
Q×
QZ
Figure 2.--Qualitative
:-:'J"
representation electrothermal
of the thermophysics de-icer pad.
""i'':""
involved
in an
"'."-:
[_,. _-""[.'._ '.." _. I'". __''_/_ it """."'" ," -" ",':
'-'" [ ,"-: :: _',".'-::
I-D Figure 3.--Degrees
Simplified of simplification
2-D
to the true thermophysics
Full 2-D of the de-icing problem.
volume
containing
Baliga using
(reference
a high
method
the node
4) modelled
heat
capacity
to model
problem
numerical the effect
(reference
were initially
results
revealed
problem.
melting.
by handling (reference
Gent
change),
of the heater
and
the phase
5) applied
Cansdale
and obtained
8). Chao's
and
change
the
(reference
nearly
heat
transfer
so-called
enthalpy
6) solved
the same
the same
detailed
on deicing
experimental
results
the layers
found
that
wattages,
code there
are
material
and in the region
rotor
as Marano
two
excellent regions
properties,
of large curvature
etc.).
dimensions.
blade
at the leading
of Marano's
numerically.
transients
induced
These
experimental
section. and Marano.
over
most
substantial
are at the immediate edge of the blade
by
The experimental
thin, and the curvature results
by
Of fundamental
was studied
of potentially These
3, was solved
extension
of the thermal
by Chao
are sufficiently
yields
was a direct
to two
results
developed
of a blade
in figure
performance
helicopter
the codes
schematic
work
procedures
gap width
one-dimensional
on heater
by the middle
unit on a UH1H
that when
it was
banks,
represented
used to validate
Marano's
Furthermore,
heater
Marano
formulation
de-icing
results
(depending
problem
et al. (reference
9) provided
an electrothermal
gradual,
problem,
7) and DeWitt,
one-dimensional
Leffel
change
to cause
only.
(reference
importance,
the same
only (no phase
The two-dimensional Chao
sufficient
formulation.
the phase
for conduction
for conduction
was deemed
sufficiently of
the
blade.
inaccuracies edges
that wraps
of the around
the nose block.
Masiulaniec
(reference
dimensional
airfoil,
Masiulaniec
used
connected,
reducing a body
rectangular
with the solution for this procedure
10) and Huang
the possibilities
fitted
coordinate
computational
then being
(reference
were prohibitive.
of inaccuracies
transformation
zones.
'unmapped'
11) have successfully
A solution
Techniques
in the regions
that mapped was obtained
into real coordinates. to numerically
modelled
the full two-
of high
the airfoil
curvature.
into a series
in this transformed
The computational accelerate
times
the computations
of
domain, required need
to be applied modeled
before
the same
This approach points
the code problem
provides
are included
Although
concurrent which
Wright
affecting
from
covered
assumed based not,
new
technique allows
the transient
solve
assumptions.
This is first
the equations
is also required the electrothermal
which
gaps,
although
sector.
Huang
the curvilinear if a sufficient
this approach
has
effects. number
also becomes
of
too slow for
to model
seen
control
in the open
literature
upgrade
change
models
in accounting
numerically
model
direction
method
volumes
in the work
at each node. NASA
9
control
the method
are changing
of Roelke
solution
and phase.
(reference
is possible.
It is Wright's Lewis's
the solution volume
model
ice accretion
was
in a multilayered
ice and water,
are correct,
the
and ice shedding
occurring
between
of each
such that a direct
to LEWICE,
alternating
pad.
of a curvilinear
ice accretion,
equations
assumptions
no more
phase
transfer,
effect
deicer
a state for each node and then calculates
until
to find the correct heater
assumes
state
to be linearized
His algorithms
and accretion
as to the
is repeated
heat
for the
than previous
pad. An implicit
the phase
of the electrothermal
not allow
profiles.
transient
the heat transfer
made
does
temperature
If all these phase
are
a model
more comprehensive
the use of an electrothermal
assumptions
recalculated.
one,
was used. This method
on those
to capture
times,
12) has developed
it is much
with ice. In order
states
approach
the heater
of two-dimensional
used to simultaneously body
(reference
is a rectangular
phenomena
arise
element
computational
simulate
on the heat transfer,
for the physics
for use by the commercial
sector.
his model
geometry
reasonable
to accurately
recently,
be considered
but with a finite
more
use in the commercial
More
would
a solution
is complete.
If
the
solution
The
use of this
13). This
An iterative that forms code.
of
is
method
procedure the basis
for
HCMBHCLATURB
A
Area(f t)
CD
Coefficient
C C
Mass
Cp
Heat
C S
Mass
D
Length
e
Evaporative
F
Force
H
Enthalpy
of drag
(dimensionless)
concentration
capacity
Heat
of water
of rotor
of water
in air at the surface
arm (ft)
pressure
per unit span
(psia)
(lbf/ft)
per unit volume
transfer
of the boundary
(BTU/Ib°F)
concentration
transfer
in air at the edge
coefficient
3)
(BTU/ft2-hr-°F)
hm
Mass
coefficient
k
Thermal
L
Lewis
number
Lf
Latent
heat of fusion
L V
Latent
heat of vaporization
LWC
Liquid
water
M
Mach
number
conductivity
(BTU/ft
(ft/hr)
(BTU/ft-hr-°F)
(dimensionless)
content
(BTU/lb)
(BTU/lb)
of air (lb/ft 3)
(dimensionless)
10
(lb/ft 3)
layer
(lb/ft 3)
m
Mass
(lb)
MW
Molecular
N
Mass
Nf
Freezing
q"
Heat
q"'
Volumetric
R
Ideal
gas constant
Rrb
Mass
flux of runback
Rw
Mass
flux of impinging
weight
(lb/mol)
flux (lb/ft2-hr)
fraction
(dimensionless)
flux (BTU/ft2-hr)
heat source
Recovery
factor
T
Temperature
t
Time
V
Velocity
x
Parallel
y
Perpendicular
Greek
Letters:
ot
Thermal
13
Collection
(BTU/ft3-hr)
(BTU/mol-°R)
(lb/ft2-hr)
water
(lb/ft2-hr)
(dimensionless)
(°F)
(hr)
(ft/hr)
to the blade surface
to the blade
diffusivity
efficiency
(ft)
surface
(ft)
(ft2/hr)
(dimensionless)
11
'y
Ratio
p
Density
f_
Rotor
of heat capacities
Cp/Cv
(dimensionless)
(lb/ft 3)
speed
(rpm)
Subscripts
a
accretion
aero
aerodynamic
air
air
c
centrifugal
conv
convection
edge
of boundary
evap
evaporation
fh
frictional
i
node
ice
ice
in
amount
k
layer
ke
kinetic
lat
latent
layer
heat
number
going
in
number
energy
heat
12
1
liquid
phase
m
melt phase
nc
net amount
new
new
of convection
total property
old
old
out
amount
r
melt range
rec
recovery
s
surface
sol
solid phase
w
water
x
x-dependent
y
y-dependent
,_
free-stream
going
out
property
property
13
The previouselectrothermalmodelsthat werediscussedareaccuratefor the caseswhen deicing occursafterthe ice accretionprocesshasoccurred,with no further buildup of ice. They fail, however,to describethe phenomenaof ice accretionduring de-icing(or anti-icing), which representsthe morerealistic casethatneedsto be simulated.The discussionthatfollows explainshow this additionalphysicsis imbeddedwithin the algorithmsthatnumericallysimulatethe deicer. Messinger(reference14)appearsto havebeenthe first to developa model for the prediction of ice accretionon airfoils. His model assumessteady-state,incompressibleflow. Since then, Bragg(reference15),Gent(reference6) andRuff andBerkowitz(reference16)haveupdatedthis analysisto include two-dimensional,compressibleflow. It is Ruff and Berkowitz's model that was containedwithin LEWICE prior to its upgradewith the electrothermaldeicer.All of the abovemodelsconsiderthe surfaceof the airfoil to beinsulated.However,whenanelectrothermal deviceis activatedduring ice accretion,thereis significantheattransferthroughoutthe bladeand the ice. Clearly,thereis a needto combinethesetwo approachessuchthat thecompletephenomenaof icing can be modeled.The phenomenaof ice accretionwith heat sourceswould not be complete,however,without an analysisof how the ice is removedandan analysisof where it travelsafterward.Again, much of the early work in ice adhesionwasperformedby Stallabrass (reference2). Recently,Scavuzzo(references 17and18) hasdevelopeda moreadvancedtheoreticalmodel for the predictionof ice sheddingusinga finite elementanalysisof the ice stresses.He alsofound expeimentallythe relationof ice adhesionasa functionof surfacetemperature.The methodused in this work to predictsheddingis basedon Scavuzzo'sexperiments. The solutionmethodusedin this studyis anextensionof theADI method,which wasshown by Wright (reference19)to bethemostefficient for thetwo-dimensionaltransientheattransferin an electrothermaldeicer pad. The ADI methodis a direct solution methodfirst developedby
15 1=_
PAGE
IILANK
HOT
FILMED
?;:,3E
---!';_
_'' '--=
:
'_"
Peaceman
and Rachford
(reference
20). However,
a direct
solution
method
requires
a linear
solu-
tion matrix.
There
are two nonlinearities
the phase ing),
change
of the water
the enthalpy
found
in the
formed
by using
with a very ture
range
enthalpy
is assumed
control
volume
which
capacity
at each is then
the freezing
there
exists
magnitude the accretion
and then
and
the latent
pressure
is given
do not change
combines
equation,
The which
all of the previous
replaced
to LEWlCE
analysis
16
in order
between
and
mush.
phase
second
A
of each
nonlinearity equation
of the impinging by a high heat
the evaporation relationship is highly
Therefore,
the heat lost caused
of this enhancement
The
this tempera-
in the governing
such that changes drastically.
The
it
for water
capacity,
temperature.
concerns
at the surface.
is small enough
time step to determine
the objective
equation
the results
been
liquid,
is found.
is the fraction
of the surface
by Antoine's
surface
which
which
in the ice accretion
solid,
phase.
fraction,
for in terms
an evaporative
phases:
nonlinearities
21).
heat of the ice and replaces
relationship
are two
is
is per-
and Raw (reference
a linear
profile
(or melt-
This
heat,
the assumed
heat has already
be removed.
showed
of the three
is
enthalpy
Wright
the latent
with
Since
range.
the temperature
There
the freezing
loss term
In summary,
each
compared
interface.
of this heat
ture at the previous
cal model
location
can be solved
and temperature
temperature
first of these
freezing
constant.
must
the latent
The
during
by Schneider
eliminates
small
within
because remains
developed
States
develops
since
nonlinearity
States,
a very
occurs
this non-linearity
10 -4 °F. By eliminating
found
However,
fraction
The other
pressure
over
The first concerns
freezes.
term,
of Assumed
for this process.
the temperature
for the ice,
the Method
at the ice accretion
this process.
while
of Assumed
temperature
phase
occurs
equations
to be, at most, and
to change
the Method
high heat
equations
into ice. This nonlinearity
continues
governing
Essentially,
in the governing
term.
between nonlinear.
in the surface this term
Within
this
evaporative However,
the
temperature
uses the tempera-
by evaporation.
is to develop to accurately
an efficient predict
numeri-
ice accretion,
at
ice shedding, HEAT
The
and two-dimensional CONDUCTION
following
conduction
assumptions
in a composite
1. The thermal different,
physical
anisotropic
layer
5. Thermal
isotropic
the ice as it melts
pad.
EQUATIONS
in the development
of the material
of a mathematical
contact
temperature
meaning
each
that
but that kx is not equal
between
model
for heat
layer
of the blade
may
be
to the effective
into account blade
direction
terms
in the
to ky.
because
the deicer
thickness
nor-
thickness.
are ignored.
and all heat transfer
due to melting
cross-derivative
layers.
are not taken
in the spanwise
change
composing
or orthotropic,
of the blade
transients
7. The density
made
in an electrothermal
on temperature.
is thin compared
6. The ambient
coefficients
is negligible,
are constant
i.e., the effect
with respect
of the volume
to time.
contraction
of
is neglected.
8. The phase true melting
were
thermal
effects
mal to the blade
CHANGE
are neglected,
is perfect
4. Curvature
PHASE
properties
is either
heat equation
3. There
transients
blade:
but do not depend
2. Each
With
AND
thermal
change
point
of the ice is assumed
rather
the above
than at the melting
assumptions,
conduction
in a chord-wise
represented
as:
aT (pCp)
at
k
point
c):aT
_.kax2
For the ice layer, the governing
k
over
a small
temperature
interval
formulation
composite
blade
for the problem with electrothermal
O_T+
of unsteady heating
heat can be
(1)
+ equation
near the
itself.
the mathematical
two-dimensional
=
to occur
in terms
17
of the enthalpy
is given
by
(2)
o.[Tx Oy- ) In order above
to solve
and replace
this problem,
it is necessary
it with temperature.
The
to remove
standard
enthalpy
relationship
from
between
the governing enthalpy
equation
and tempera-
ture is
(pCp) H =
(pCp) (pCp)
However, temperature linear
this relationship remains
relationship
plish this, ice is assumed instead
of at the melting
tIT Tm_ ]
are multiple
The numerical
so that the coefficient
temperature.
t(T-
range
requires
inverted.
near the melting
form of the enthalpy-
while
temperature
the
that a
To accomtemperature relationship
is:
(TH=
(PCp)'TmP+PILf _(pCp) Tmp
It is convenient
to define
a specific
heat capacity
(PL-P_)
'mush'
Pm is the density region.
Therefore,
lTmp < T < Trap + T_[ _ T>Tmp+T_ J
(4)
+ piLl + (pCp) l(T - Trap - T_
(Cp)
where
1r T