Heat Transfer

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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



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