TURBO EXPO 2002
ASME
Turbo Expo: Land, Sea & Air 2002
June
3-6
, 2002, Amsterdam, The Netherlands
GT
-2002-30500
A COMPUTER CODE FOR GAS TURBINE ENGINE WEIGHT
AND DISK LIFE ESTIMATION
Michael T. Tong
NASA Glenn Research Center
Cl
eveland, Ohio
Ian
Halliwe
ll
Mode
rn
Technolog
ie
s Corporation
Cl
evelan
d,
Ohio
Lo
ui
s J. Ghosn
Ohio Ae
ro
space Institute
Cl
eveland , Ohio
ABSTRACT
Reliable engine-weight estimation at the conceptual design
stage
is
critical to the development
of
new aircraft engines.
It
helps to identify the best engine concept amongst several
candidates. In this paper, the major enhancements to
NASA's
engine-weight estimate computer code (WATE) are described.
These enhancements include the incorporation
of
improved
weight-calculation routines for the compressor and turbine disks
using the finite-difference technique. Furthennore, the stress
distribution
for
various disk geometries was also incorporated,
for
a life-prediction module
to
calculate disk life. A material
database, consisting
of
the material data
of
most
of
the
commonly-used aerospace materials, has also been incorporated
into WATE. Collectively, these enhancements provide a more
realistic and systematic way
to
calculate the engine weight.
They also provide additional insight into the design trade-off
between engine life and engine weight. To demonstrate the new
capabilities, the enhanced WATE code
is
used
to
perfonn
an
engine weight/life trade-off assessment on a production aircraft
engine.
Keywords: Engine Weight, Finite Difference, Disk Life
IN
TRODUCTION
Engine weight is a key design parameter
fo
r any new
aircraft engine.
It
affects aircraft range and
is
a key element
in
fuel burn. Weight
is
also considered
an
indicator
of
engine cost.
Reliable engine-weight estimation at the conceptual design
stage
is
critical to the development
of
new aircraft engines.
It
helps to identify the best engine concept amongst several
candidates.
Equally important, aircraft engines must meet safety
demands. Fatigue loading
of
turbine components associated
with continuous aircraft take-offlcruise/landing cycles
is
a
principal source
of
degradation
in
turbomachinery. A disk burst
is
potentially the most catastrophic fai lure possible in an engine
and th
us
disks are designed with overspeed capability and low
cycle fatigue life
as
primary objectives. The requirement
fur
higher turbine stage work without additional stages has resulted
in increased turbine blade tip speeds and higher turbine inlet
temperatures in advanced commercial aircraft engines.
This
trend has resulted
in
significant increases
in
turbine stage disk
rim loading and a more severe thennal environment, thereby
making it more difficult
to
design turbine disks for a specific
life
requirement meeting
CWTent
goals.
CWTent
trend indicates that
both turbine blade tip speeds and turbine inlet temperatures will
continue to increase
in
advanced commercial engines
as
higher
turbine work levels are achieved. Advanced turbine disk
concepts are required
to
insure long life disks in commercial
engines, without resulting
in
severe weight, perfonnance, or
cost penalties.
At NASA Glenn Research Center (GRC) , the Weight
Analysis
of
Turbine Engines (WATE) computer code [I],
originally developed by Boeing Aircraft,
is
cWTent
ly used to
estimate the engine weight
of
various conceptual engine
designs. The code was originally developed for NASA
in
1979,
but since then, substantial improvements have been made
to
the
code
to
improve the weight calculations
for
most
of
the engine
components. Recently a series
of
efforts were perfonned at GRC
to
enhance the capability
of
the WATE code.
In
this paper,
these WATE code enhancements are described. The major
enhancements include the incorporation
of
improved weight-
calculation routines
for
the compressor and turbine disks using
the finite-difference technique. Furthennore, the stress
distribution
for
various disk geometries was also incorporated,
for
a
li
fe-prediction module
to
calculate disk life. A material
database, consisting
of
the material data
of
most
of
the
commonly-used aerospace materials, h
as
also been incorporated
into WATE. Co
ll
ectivel
y,
these enhancements provide a more
rea
li
stic and systematic way
to
calculate the engine weight.
They also provide additional insight into the design trade-off
between engine life, weight,
and
cost. The current effo
rt
paves
the way for an automated
engine
design tool, which
wo
uld
eas
il
y allow engine developers to perfonn d
esig
n trade-offs
between engine perfonnance, durability, and cost.
To
demonstrate the
new
capabilities, the impr
ove
d WATE code is
used to perfonn
an
engine weight/life
tra
de-o
ff
assessment on a
production aircraft engine.
NOMENCLATURE
D true tensile ductility =
In
[
(
l
O~~~~)
]
E modulus
of
elasticity
N
r
cycles to fatigue crack initiation failure
RA
reduction in area at failure
6.T
reference temperature = room temperature
T
max
-
6.T
maximum
di
sk
metal te
mp
erature, assumed to be at
the rim; user input
temperature difference between disk rim and bore;
user
input
c axial chord at the blade hub
number
of
blades
mass
of
one blade
radius
of
the c.
g.
of
the dead weight
radial distance
r
I ,r2, .. r6 various radial location al
ong
the
disk
rl
outer radius
of
the live di
sk
ri inner radius (di
sk
bore)
ro
outer
radius (disk rim)
6.r
change
in
radius
sf
1.1
, safety factor
t local
disk
thickness
at
r
6.t
change
in
disk thickness
u radial displacement
p disk material density
ill
rotational speed, (rad/sec)
a coefficient
oft
h
ennal
expansion
v
Poison's
ratio
(J
y yield
stre
ngth
of
the
disk
material at the
lo
cal
temperature
(J
e
equivalent
or
Von Mises stress
(J
eavg average tangential
st
ress
of
the disk
(J
uls ultimate tensile
st
r
ength
(J
,.
radial stress
2
+---
I
Dead
we
igh
L
Live
T--:
1--:;;"':;""-
-;
we
ight
Cav
it
y
----~
Se
ctio
n A
-A
Figure
1.-Disk/blade
assemb
l
y.
(J
o
6.£1
6.£e/
6.£ill
tangential
st
re
ss
total
st
rain r
ange
elastic strain range
in
elastic strain ran
ge
OBJECTIVE
The
objective
of
the current
work
is to e
nh
ance the current
engine
flow-path d
esign
tool
so
that
it will allow engine
developers to easily perfonn design trade-offs
betwe
en engine
weight
, durability, and eventually, cost.
TURBOMACHINERY DISK DESIGN METHODOLOGY
A typical di
sk
de
sign is based
on
the
blading
geometry,
weight
, and rotational speed th
at
will already have been
specified in the design
of
the turbomacbinery flowpatb.
Fig
ure 1
shows bow blades are typically attached
to
a disk, and
introduces some
of
the nomencl
at
ure.
The
ty
pic
al three disk
models
(ring, web, and hy
perbolic
) are s
hown
in figures 2 to
4.
The
flowp
at
h heig
ht
or
blade span is defin
ed
via the blade tip
and hub radii,
which
are
prim
ary
input
s to t
he
WATE code.
The
disk
rim
thickness is
assumed
to be
eq
ual to the axial
chord at the
hub
of
the blade.
The
height
of
the
blade
root
is
also specified within the program, as a percentage
of
the airfo
il
height, and it
de
fines the out
er
limit
of
the live disk.
Note
that
so
me allowance mu
st
be
made for the cavity, since this is not
modeled s
pe
cifica
ll
y.
Movin
g inw
ar
ds towards the centerline,
ad
ditional rim height is then required to supp
ort
the stresses
ge
nerated by the dead weight, and this is specified as a function
of
the rim thickness. Regardless
of
the
disk
type, the
distribution
of
thickness for the remainder
of
the di
sk
is
specified initially by
minimum
default values
at
key
radial
/r-
r6
~----------
----
~
/
r-
r
5
/r-
r4
/r-
r3
/
'--
r2
/
'--
r1
Cen
ter
li
ne
--
-
--
-
--
-
--
-
--
-
--
-
--
---
Fi
gu
re 2.
--Radi
al
stations
and
locations
of
de
si
gn
con
trol
cal
culations
in
a
ring
disk.
locations. Stresses are calc
ul
ated at these and
ot
her radii using a
finite difference m
et
hod, and compared against a design stress
that includes a safety
ma
rgin for a specific mate
ri
a
l.
If
the
calc
ul
ated stress is above the design crit
er
i
a,
some disk
thickness is increased
seq
uentia
ll
y in an iterative manner un
ti
l
the stress design
cr
iteria are satisfied at a
ll
radial
sta
ti
on
s.
A di
sk
must
be desi
gned
to withstand the centrifugal
stresses generated by the rotating blades at
th
e maximum
rota
ti
onal speed
of
the spool and to trans
mi
t the torque
generated by the tur
bi.ne
blading to the appropriate co
mpr
essor
rotor.
Only
that portion
of
the di
sk
inb
oa
rd
of
the blade
root
is
cons
id
ered to carry the stresses, and this
is
r
efer
r
ed
to as the live
disk. The parts
of
the di
sk
between the blade roots (posts), as
we
ll
as the blade roots themselves and the airfoils, cons
ti
t
ut
e
d
ead
weigh
t.
Although it
is
the design
of
the
li
ve disk which is
bei
ng
addressed here, the posts mu
st
n
ot
be neglected when the
total disk weight
is
quoted.
The
dead weight produces the pull
stresses on the r
im
of
the live disk, but as one moves
in
war
ds
through the disk towards the bore, the disk
mu
st also support
3
Airfoil
Blade
root
+
Post
Outer
rim
Outer
Shou
lder
Web
Inner rim
Inner
Shoulder
Bore
1------
t6
--
----
---;..
"
'--
r6
Lt1
Centerline
--------------
-
--
-
---
--
-
---
Figure
3.-Radial
stations
and
locations
of
design
control
calculations
in
a
web
disk
.
an increasing
pr
oportion
oft
he centrifugal stress generated by its
ow
n
we
igh
t.
The average stress at the outer radius
of
the
li
ve disk is
estimated by smearing the total centrifugal
fo
rce
of
the dead
we
ight around the c
i.r
c
um
ference. The weight
of
th
e blades,
including platfo
nn
s and roots, a
nd
the axial chord at the root
should already be known from the flowpath
des
ign. The radial
location
of
the center
of
gravity
of
the
co
mbined dead weight
must be kn
ow
n, however,
in
order to calculate the radial
pull
I~
Airfoil
Blade
root
+
Post
Outer
rim
Shoulder
Outer
web
Inner
web
Inner rim
Bo
re
Centerline
t2
/
.r-
r2
t1
/
.r-
r1
Figure
4.-Radial
stations
and
l
ocations
of
design
control
calculations
in
a
hyperbolic
disk.
stress
at
the
live rim,
and
consequently
certain
assumptions
are
made
regarding
the
height
and
weight
of
the blade root, and the
weight
of
the posts.
The
assumptions
are as follows, where the
term
"total blade" refers to the "airfoil+platform+root".
For
the
ring
disk
:
Height
of
the
blade
root
Weight
of
the
blade
root
Weight
of
the
post
= 17.65% airfoil height
=
20
% total
blade
weight
= 1 0% total blade
weight
4
For
the
web
disk:
Height
of
the blade
root
Weight
of
the blade root
Weight
of
the
post
For
the
hyperbolic
disk:
Height
of
the blade
root
Weight
of
the
blade
root
Weight
of
the
post
DISK STRESS
ANALYSIS
= 25.00% airfoil
height
=
20
% total
blade
weight
=
20
% total
blade
we
ig
ht
= 53 .85% airfoil height
=
50
% total
blade
weig
ht
=
20
% total
blade
weight
The
differential equation
of
equilibrium [2] takes the form:
d
()
2 2
- tra
r
-toe+tpw
r
=0
dr
(1)
where
E
[dU
U ]
Or
= -
..
--
--
+v
-
-(l+v
)
aT
l-v
2
dr r
(2)
E
[u
du ]
Oe=-
..
- -2 -
+v
-
-(I+v)aT
1-
V r dr
(3)
The
radial steady-state temperature distribution for a
disk
is
given
by
Fourier
's law
of
conduction
from [3]:
!1.T
(r)
T=
T
bo
re
+
(r
o)
In
Ij
-T
O
In
-
r·
I
(4)
For
a thin slice
of
disk
material, the
disk
thiclmess, t, can
be
approximated
by:
t = mr + n
!1.t
m = slope
=-
M
!1.t
n=t-m
-
!1.r
Substitute
equations
(2) to (4)
and
the
disk
thicknes
s t
into
equation
(1) results in a
single
differential
equation
with one
var
iable, displacement:
d2~
+(
2n~r+n
_
~)
dU
+[_~_~+~
(
2
/
~r+n
)
]u=
dr
mr
+ nr r dr r r r mr + nr
(1
)[
dT
(2mr
+ n
a + v - + 2
dr mr
+nr
Equation
(5) is solved l1Lunerically
usmg
finite difference
method
with
boundary
conditions:
0,.=Oatr='j
;
du
u
thus, -
+ v - -
(l
+
v)cxT
= 0
dr r
0
,.
= rims tress at r = '
a;
du u rims tress '
(1-
v
2
)
thu
s,
-'- +
v-
- - (I +
v)cxT
= 0
dr r E
rimstress
= average centrifugal stress at
th
e
li
ve rim
nb
mb
'cg 2
----"-CD
2n'ic
The
design criteria for the disk are:
and
0
y
---1.0
> 0
sf·G
e
l.0 > 0
DISK DESIGN PROCESS
Ring Disk
(design marg
in
)
(disk burst criteria)
(6)
(7)
The
ring disk model
is
shown
in
figure
2.
The design
process for a ring disk consists
of
the fo
ll
owing step
s:
1.
The thickness
of
the disk
is
set to the
bl
ade hub axi
al
chord.
2. The lower limit for the bore radius,
rl
,
is
calculated, based
on the disk rad
iu
s ratio provided
in
the input file a
nd
th
e
airfoil hub rad
iu
s.
It
should be noted that this will probably
not be reached.
3. All the six thickness va
lu
es are set to the value
of
the
di
sk
width
in
Step I.
4. The radial extent
of
the disk from the outer live disk radius
inwards
is
set
initially to 0. 1 inch.
5.
The
initial live disk height
is
div
id
ed into five equal
sections to obtain radii
r 1 through r6.
6. The stress calculations are carried out a
nd
the design is
checked for compliance with the design stress criteria
(eqs. (6) and (7)).
7.
If
the design criteria are not satisfied at every ra
di
al
lo
cation,
the disk inner radius
is
reduced and Steps 5 and 6
are
repeated.
8.
If
the design criteria are satisfied, disk weight
is
calculated
and the disk design process is completed.
9.
If
the lower limit on bore radius (established
in
Step 2) is
reached and the design criteria have still not been met, the
program prints an approp
ri
ate message and stop
s.
Web
Disk
The web di
sk
model
is
shown
in
figure
3.
The design
process for a web disk consists
of
the
fo
ll
owing step
s:
I . The thickness
of
the disk outer rim is set to the blade hub
axial chord.
5
2. The heights
of
the inner and outer rims and the inner
an
d
outer shoulders are specified by internal default
va
lue
s.
3. Minimum and maximum web and inner rim thickness
are
set by internal
def
ault
s.
4. Definition
of
the
li
ve
di
sk geometry is
in
it
iated. The bore
radius is fixed via the airfoil hub radius and
th
e input value
of
di
sk
radius ratio.
5. The six reference rad
ii
and thickness are set from the initial
di
sk geometry.
6.
The
stress calculations are carried out and the design
is
checked
for
compliance with the design stress c
ri
teria
(eqs. (6) and (7)).
7.
If
the design criteria are not satisfied at every ra
di
al
location,
the web thickness is he
ld
constant and the bore thickness is
increased sequentia
ll
y a
nd
Steps 5 and 6 are repeated.
If
the
design criteria rema
in
unsatisfied when the maximum
li
mit
on bore thickness is reached, the design process reverts to
the
minimum
bore
th
i
ckness
,
but
the
web
thicknes
s is
increased, a
nd
Steps 4 to 6 a
re
repeated.
8.
If
the design criteria are satisfied
wi
til
neither the maximum
bore thickness nor the maximum web thickness (established
in
Step 3) being exceeded, an acceptable web disk design is
achieved a
nd
its weight
is
calculated.
If
the design criteria
cannot be met within those limits, the program prints
an
appropriate message a
nd
stops.
Hyperbolic Disk
The hyperbolic
di
sk model is shown
in
figure 4. The
design process for a hyperbolic disk consists
of
the
fo
ll
owing
steps:
I . The width
of
the disk outer rim IS set to the hub axial
chord.
2. The initial disk geometry is set up, which consists
of
the
outer rim height, the shoulder height, the
mll1lmUm
outer
web thickness, and the inner rim heigh
t.
The maximum
bore width and height are also established.
3. The six
ref
erence radii and thickness are set from the initial
di
sk geometry.
4. Using a value
of
1.0 for the
di
sk shape factor, ds
f,
the inner
pOIiion
of
the initial
di
sk geometry
is
defined, with the
inner web thickness distribution being given b
y:
5.
The
stress analysis routine is called and comparisons
are
made with the design stress criteria (eqs. (6) and (7)) at a
ll
the radial location
s.
6.
If
the design criteria are not satisfied, the disk shape factor
is
increased and Steps 2 to 5 are repeate
d.
7.
If
the maximum limit on bore width
is
encou
nt
ered before a
satisfactory design is obtained, the value
of
th
e outer web
thickness
is
increased, the disk shape factor is reset to 1.0,
and Steps 2 to 5 are repeate
d.
8.
If
the design criteria are satisfied, disk weig
ht
is
calculated
and the disk design process
is
completed.