The objective is to develop and verify a series of interdisciplinary modeling and analysis techniques that have been specialized to address three specific hot section components. These techniques will incorporate data as well as theoretical methods from many diverse areas including cycle and performance analysis, heat transfer analysis, linear and nonlinear stress analysis, and mission analysis. The new methods developed will be integrated to provide an accurate, efficient, and unified approach to analyzing combustor burner liners, hollow air-cooled turbine blades, and air-colled turbine vanes. For these components, the methods developed will predict temperature, deformation, stress, and strain histories throughout a complete flight mission

Mcknight, R. L.

Tipton, M. T.

English

NASA Technical Reports Server

N88- 11166
COMPONENT SPECIFIC MODELING*
R.L. McKnight and M.T. Tipton
Gene_'al Electric Company
Aircraft Engine Business Group
INTRODUCTION
The overall objective of this program is to develop and verify a series of
interdisciplinary modeling and analysis techniques that have been specialized
to address three specific hot section components. These techniques will
incorporate data as well as theoretical methods from many diverse areas
including cycle and performance analysis, heat transfer analysis, linear and
nonlinear stress analysis, and mission analysis. Building on the proven
techniques already available in these fields, the new methods developed
through this contract will be integrated to provide an accurate, efficient,
and unified approach to analyzing combustor burner liners, hollow air-cooled
turbine blades, and air-cooled turbine vanes. For these components, the
methods developed will predict temperature, deformation, stress, and strain
histories throughout a complete flight mission.
The base program for the component specific modeling effort is illustrated
in Figure (1). Nine separate tasks have been arranged into two parallel
activities. The component specific structural modeling activity in
Figure (2), is directed towards the development of the analytical techniques
and methodology required in the analysis of complex hot section components.
The component specific thermomechani cal load mission model ing effort
illustrated in Figure (3), provides for the development of approximate
numerical models for engine cycle, aerodynamic, and heat transfer analyses of
hot section components.
Thermomechani cal Load Mi ssion Model in_
In the thermomechanical load mission modeling portion of the program, we
developed the Thermodynamic Engine Model (TEM). The TEM is complete and has
been developed as a computational tool used to define mission station profiles
of gas path engine flow variables and rotor speeds as a function of defined
input conditions. Basic input variables for the model are mach number (M),
altitude (h) power level (PL). Generated within the model for select
aerodynamic stations in the combustor and high pressure gas flowpath are, gas
weight flow (_), temperature (t), pressure (p) and the associated fan (NI) and
core (N2) speeds.
The development of tlm TEM was presented at last years workshop so
attention is directed at the capability and accuracy of the model. The
accueacy of the model was evaluated relative to the steady state performance
computer code (a cycle deck) of a production engine. Noting that the model is
based upon multidimensional interpolation of stored data, tilemaximum error of
*Work done under NASA Contract NAS3-23687.
PR_'CEDLNG PAGS BLANK NOT FILMED
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https://ntrs.nasa.gov/search.jsp?R=19880001784 2020-03-20T08:34:41+00:00Z
T
Component-
Specific
Structural
Modeling
Task II
Task VI
Task VIII
Task I - ISurvey
T
Software
Development
Task IV
Component-
Specific
Thermomechanical
Load Mission
Modeling
Task III
Task V
Task VII
Task IX
Figure I. Component Specific Modeling Base Program.
Task III
Thermodynamic
Engine Model
Task V
Mission Model
Decomposition
r
Task VII
Thermomechanical Load
Mission Model
Development
Decomposition/Synthesis
Capability
Verification
Figure 2. Component Specific Thermomechanical Load
Mission Modeling.
246
Task VI
Structural Analysis
Methods Evaluation
Task II
Design Structural Analysis
Software Architecture
f
Task Vlll
Component Specific Modeling
Select Components for
Model Development
Develop Geometric
Modeling and Display
Develop Structural
Analysis Capability
Figure 3. Component Specific Structural Modeling.
247
the model silould occur at a position the greatest distance from Known data
points. Illustrated in Figure (4) is an example of a situation in whicll a
region is bounded by four data points with the test point at its center. The
region is then subdivided into four rectangles eac_ possessing its own
interpolation logic and associated error. Error curves imposed on such a
figure iIIustrate two facts:
(1) The error surface is approximately parabolic and attains its maximum
value at the center of the region.
(2) Each quadrant has its own error surface and discontinuities occur
where they meet.
Table l shows a brief summary of the accuracy level achieved for the TEi_.
Column 2 shows the average of all test point errors. Columns 3, 4, and 5 show
the value that is exceeded 2, 4 and II times (1%, 2%, and 5% of the 220 error
values). Note that all data in this figure refers to the worst-case test
points. Since the error surfaces are approximately parabolic in shape, the
average error in each quadrant is approximately half of the maximum error, and
the overall error is approximately half of the average error listed.
Table l Validation Case Error Analysis
Error Exceeded N Times
Average N = 2 N = 4 N = II
P2 0.03% I% I% I%
P3 0.23% 1.3% 1.2% 1.0%
FNINI 0.49% 1.8% 1.8% 1.8%
XN25 0.17% 0.7% 0.6% 0.5%
T2 0.08% 5 ° 5 ° 5°
T3 2.1 ° 10 ° 10 ° i0 °
T41 11 ° 47 ° 47 ° 35 °
Component Specific Structural Modeling
The concepts and techniques developed in the NASA supported ESMOSS program
i}ave provided the basis to create an efficient modeling system for specific
hot section engine components. The modeling and subsequent discretization of
model geometries is component dependent and follows either a recipe or a data
point/curve fit format. The capability to create geometric and discretized
models of these components is well under development and examples of such are
illustrated in Figure (5).
Finite Element Methods
This phase of the program centers on the development, implementation and
evaluation of both new and existing analytical methods for the non-linear
stress analysis of select hot section components. Within the structural
248
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,-4
d
o
4_
o
4_
c_
c_
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249
Typical Nugget
rl
LI
Physical Input Parameters
Master Region Definition 2D Model
5///
3D Model Turbine Blade with Cavities
Figure 5. Examples of Component Specific Structural Modeling Capabilities.
250
analysis software exist several new and innovative concepts. Embedded in the
code are several classical solution algorithms, three constitutive models,
"self-adaptive" type solution techniques, and the capability for remeshing and
mesh refinement.
As noted, several classical solution techniques have been included in the
code. It is intended that such a selection of solution algorithms will afford
the user (and the programmer) a choice as to method of solution as well as to
provide for adaptability of the code to problem definition and machine
residency. Solution algorithms currently include:
(A) SESOL
- A sparse matrix solver witil a skyline storage scheme.
(B) COLSOL
- A vectorized column solver.
(C) Frontal Method
- Currently under development.
In addition to our library of select solution techniques, we have included
in our analysis code an alternate method for defining convergence of the
numerical solution. Our current work has focused upon vector norms due to
their structure, computational simplicity and potential applicability to
self-adaptive solution strategies and techniques. Vector norms provide the
means by which both quantitative and qualitative statements can be made
between associated vectors. Noting that our current solution scheme is an
iterative technique, we are looking at the convergence of a series of vectors
(i.e. displacements). In such an application it is necessary to determine
when a solution has been obtained as well as to determine the quality of that
sol uti on.
Convergence of the numerical solution can be determined on either the
local or global level. Currently within our code we use a local or point-by-
point method and the present work represents an effort to see if a global
scheme has applicability.
There can be defined infinitely many norms but the three most common norms
are the _p norm_II'IIP for P = l, 2, ands.
I1-11 " + Ii I + 1i31 + ..... I NI
11"112" [i 112 ÷ Ii212 + l_3i2 + ..... lINt2] !/2
251
The above norms are special cases of the vector norm:
N
To utilize the norms defined above the concept of relative and absolute
error can be defined (l) for any two vectors, the absolute error can be
written as:
-- I
. lliill-Ilxi_!li
And the relative error written as:
. _lx%-tE" IIi_II- '- f!
The expression for relative error tends to be far more applicable to our needs
and its structure lends itself conveniently to the formulation of convergence
criteria in iterative methods. Convergence can be assumed when the magnitude
of a norm, or the difference between norms of successive iterations is less
than some predefined tolerance. From the above, six separate norms were
defined, and then included in the code for evaluation.
Iii ill 2 - lli±-z !I2 !Ix_:llz - ll_±_jII2
4.
II_ II_ - iI___.II. II_.II. - l!__j. I!_
5. IIIj._j. II. 6. II_. ii®
To provide the user with a choice and offer some versatility in the
modeling of non-linear material behavior, three separate material constitutive
252
models have been coded into the analysis program. Ti_ese constitutive models
are:
(A) Haisler-Allen model
(B) Bodner's Model
(C) A Simplified Model
We are using remeshing and mesh refinement techniques in our self-adaptive
solution strategies. Work is focused on the examination of methods and
techniques required to upgrade the mesh and criteria by which this process is
activated. Methods of mesh refinement could include progressive subdivision,
mesh realignment and upgrade of element order. Criteria for mesh refinement
may include strain energy density, elemental stress/strain gradients,
inter-element stress/strain gradients and nodal stress comparisons. We are
currently in the evaluation phase of the above and our strategy for proceeding
in this area involves the following:
(a) Select an analytical model with Known solutions.
(b) Analyze several meshes of different density.
(c) Use the 20 noded brick element to evaluate remesning criteria.
For our initial work we have selected a semi-infinite plate with a circular
hole near the edge. Figure (6) shows the recipe parameters and master region
definition for the problem and Figure (7) illustrates tile coarse, medium and
refined meshes for such a model.
For a 2D plane stress conditions, the models were fixed at the left edge
and subjected to a uniform tensile stress at the right edge. Comparisons were
then made as to the adequacy of computed surface stresses and inter-element
stress distributions. A summary of the above appear in Figures (8) and (9).
CONCLUSIONS
When complete, this program will provide the engineer with a total
non-linear stress analysis system designed for hot section component parts.
The system will enable the engineer to address the effects of mission
variation and design cilanges on component response while demonstrating
efficiency and versatility in application. The system will provide new and
innovative technology in the area of non-linear iligt_temperature stress
analysis and in turn make a significant contribution to assessing hot section
component durability.
253
Master Region Model
53 54
7_
,
10
®
®
13
12 I
J
11
$9
S8
37
Parameters
f
A = Height
B = Relative Placement of Center
of Hole Relative to A
D = Diameter of Hole
Input: D as a Percentage of the Height
B as a Percentage of the Height
Note: The Hole Cannot be Placed Beyond the
Limits of the Beam
(Ex) Input = 20%, 23.334%
Set a 0.2A Hole
0.2334 A Center
Figure 6. Recipe Parameters and Master Region Model for Plate
with Hole.
254
J
I _
1
|
I
I
I
IllllllllillJ
Figure 7. Discretized Mesh Geometries for Semi-Infinite Plate Model.
255
400
370
310
280 |
O_
m 250
_D
220
190
160
130
i00
I i , ,
t
___ O = Density 1
I
_ i O, = Density 2
[--_ /_, = Density 3
_ _ " = AI/I Densityli• 2
I
__ • = AI/I Density 3
he
0 0.i 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 i.i 1.2
Wall Thickness
Figure 8. Effect of Mesh Density on Stress Prediction.
256
CG
F
E
MESH (Figure 33)
1 2 3 4
Points OMa x °Max OMa x l°Max OMa x °Max OMa x °Max
Diff
ModelIn ksiDiff °-_vgDiffxlO01 ksiDiff __DiffOAvgxlO0 ksiDiff °AvgDiffxlO0; ksIDiff O--_vg xlO0
A 71 42 58 30 42 20 34 15
B 46 42 38 37 26 30 20 35
C 29 38 19 26 ii 15 8 II
D 46 53 28 33 16 19 ii 13
E 46 41 18 16 ii 9 8
F 83 55 29 20 12 8 7 4
G 58 33 34 20 22 12 16 9
Figure 9. Results of the Effect of Mesh Density.
2.57


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