A Probabilistic Analysis of a High Pressure Turbine Pre-Swirl Cavity
and Capture System to Identify Input Variability of Design Parameters
by
Pamela Ann Gray
A Thesis Submitted to the Graduate
Faculty of Rensselaer Polytechnic Institute
in Partial Fulfillment of the
Requirements for the degree of
Master’s of Science of Mechanical Engineering
Approved:
_________________________________________
Dr. Timothy Wagner, Thesis Adviser
Rensselaer Polytechnic Institute
Hartford, Connecticut
December 2009
© Copyright 2009
by
Pamela Ann Gray
All Rights Reserved
ii
CONTENTS
Topic
page
CONTENTS ..................................................................................................................... iii
LIST OF SYMBOLS ......................................................................................................... v
LIST OF TABLES ........................................................................................................... vii
LIST OF FIGURES ........................................................................................................ viii
ACKNOWLEDGMENT .................................................................................................. ix
ABSTRACT ...................................................................................................................... x
1. Introduction.................................................................................................................. 1
1.1
The Secondary Flow System of a Gas Turbine Engine ..................................... 1
1.2
Problem Statement ............................................................................................. 5
1.3
Research Objectives ........................................................................................... 6
1.4
Overview of Expected Result Usage.................................................................. 7
2. Background .................................................................................................................. 9
2.1
2.2
Overview of Previous Analyses ......................................................................... 9
2.1.1
Sidwell & Darmofal ............................................................................. 11
2.1.2
Cloud & Stearns ................................................................................... 11
2.1.3
Stearns, Cloud & Filburn ..................................................................... 12
Relationship of Current Project to Existing Literature .................................... 12
3. Theory ........................................................................................................................ 13
3.1
Analytical Flow Model .................................................................................... 13
3.1.1
Flow Model Governing Equations and Assumptions .......................... 13
3.1.2
Flow Model Inputs ............................................................................... 15
3.1.3
Solution Technique .............................................................................. 16
3.1.4
Restrictions and Chambers ................................................................... 18
3.1.5
The Flow Network Solver .................................................................... 21
iii
3.2
Probabilistic Flow Model ................................................................................. 22
3.2.1
Probabilistic Flow Model Inputs and Outputs ..................................... 23
4. Methodology .............................................................................................................. 24
4.1
Method of Analysis .......................................................................................... 24
4.1.1
4.2
Output Data Types ............................................................................... 25
Probabilistic Variation Types ........................................................................... 26
4.2.1
Input File .............................................................................................. 26
5. Results of Latin Hypercube Analysis ........................................................................ 29
5.1
Output Data ...................................................................................................... 29
5.1.1
Significant Design Parameters ............................................................. 29
5.1.2
Identifying Significant Drivers of Sensitivity ...................................... 30
5.1.3
Summary of Results ............................................................................. 42
6. Conclusions................................................................................................................ 43
6.1
Key Design Parameters & Primary Drivers of the Sub-System ...................... 43
6.2
Significant Contributors of the Key Design Parameters .................................. 43
6.3
Importance of Findings .................................................................................... 44
7. References.................................................................................................................. 45
8. Appendix.................................................................................................................... 47
8.1
Flow Model Input File – Sample only, not complete....................................... 47
8.2
Complete Probabilistic Input File .................................................................... 52
iv
LIST OF SYMBOLS
Nomenclature
English Symbols
A
Area, in2
Area vector, in2
A
b
Number of knife edge teeth
bi
Number of units the output will change if the ith input increases by 1%
c
Labyrinth seal knife edge clearance, inch
Cd
Discharge coefficient
CDF Cumulative Density Function
ci
Quadratic regression coefficient of ith input variable
d
Relaxation factor for flow model convergence
d
Diameter, inch
d/dy Derivative
F
Force, lbm*ft/s2
F
Force vector, lbm*ft/s2
f(x) PDF as a funciton of x
g
Acceleration of gravity, ft/s2
H
Enthalpy, Btu/lbm
h
Labyrinth seal land step height, inch
HPC High Pressure Compressor
HPT High Pressure Turbine
HT
Total enthalpy, Btu/lbm
ID
Inner Diameter
LE
Leading Edge
LHS Latin Hypercube Sampling
M
Dimensional analysis constant for the number of repeating parameters
Mass flow rate, lb/s
m
N
Dimensional analysis constant for the number of repeating parameters
n
Number of variables
OD
Outer Diameter
P
Pressure, psia
P4
High pressure turbine inlet pressure, psia
P5
High pressure turbine exit pressure, psia
PDF Probability Density Function
pKE
Knife edge pitch, inch
PR
Pressure Ratio
q
Heat interaction per unit area, Btu/lbm*ft2
Q
Heat interaction rate, Btu/lbm*hr
r
Radius, inch
R
Vector of governing equations
r
Radius vector, inch
rKE
Knife edge radius, inch
s
Entropy, Btu/lbm R
v
LIST OF SYMBOLS (Continued)
T
t
TE
TOBI
u
U
V
V
v
V
wKE
W
x
Xi
Y
y
yo
z
Temperature, F or R
Time, sec
Trailing Edge
Tangential On Board Injection
Internal energy, Btu/lbm
Vector of unknown states
Volume, ft3
Velocity, ft/s
Specific volume, ft3/lbm
Velocity vector, ft/s
Knife edge thickness, inch
Work interaction rate, hp/sec
Input variable
Random value of the ith variable
Linear regression output coefficient
Output variable
Constant term in regression equation
Height, inch
Greek Symbols
i
Linear regression coefficient of ith input variable
Partial differential
Finite increment
Flow parameter
( y ) Cumulative density function as a function of y
i
Mean value of ith input variable
Summation
i
Standard deviation of ith input variable
i
Percent of total variance the ith variable contributes to the output
Density, lbm/ft3
Subscripts
b
Body
CS
Control Surface
CV
Control Volume
down Downstream
T
Total
up
Upstream
Superscripts
n
Number of variables
down Downstream
up
Upstream
vi
LIST OF TABLES
Table
page
Table 1 Output Parameters .............................................................................................. 27
Table 2 Input Parameters and Standard Deviation .......................................................... 27
Table 3 Rankings for Significant Contributors (in % of Total Variance) ....................... 31
Table 4 Output Parameters, Standard Mean, Min, Max and R2 Values .......................... 31
vii
LIST OF FIGURES
Figure 1 Turbofan engine components: inlet fan, low and high pressure compressors ... 1
Figure 2 Turbofan engine components: combustor, high and low pressure turbines,
nozzle and front cavity....................................................................................................... 2
Figure 3 Pre-swirl nozzle rotor and stator schematic ........................................................ 3
Figure 4 Flow paths of high pressure turbine area ............................................................ 5
Figure 5 TOBI area flow network solver ........................................................................... 7
Figure 6 Chambers and restrictors ................................................................................... 16
Figure 7 TOBI system areas varied ................................................................................. 18
Figure 8 Labyrinth seal knife edge geometry, inputs for flow model ............................. 20
Figure 9 Blade output parameters and locations .............................................................. 28
Figure 10 TOBI area output parameters and locations .................................................... 28
Figure 11 Blade LE cooling flow % of total variance contribution ................................ 32
Figure 12 CDF plot for blade LE cooling holes mass flow rate ...................................... 33
Figure 13 PDF histogram blade LE cooling holes mass flow rate .................................. 33
Figure 14 Blade mid-body cooling flow % of total variance contribution ...................... 34
Figure 15 CDF for blade mid-body cooling holes mass flow rate .................................. 35
Figure 16 PDF histogram of the mid-body cooling holes mass flow rate ....................... 35
Figure 17 Blade TE cooling flow % of total variance contribution ................................ 36
Figure 18 CDF plot for blade TE cooling holes mass flow rate ...................................... 37
Figure 19 PDF histogram of the blade TE cooling holes mass flow rate ........................ 37
Figure 20 Blade supply pressure % of total variance ...................................................... 38
Figure 21 CDF plot for blade supply pressure................................................................. 39
Figure 22 PDF histogram for blade supply pressure ....................................................... 40
Figure 23 Blade supply temperature % of total variance contribution ............................ 41
Figure 24 CDF plot for blade supply temperature ........................................................... 41
Figure 25 PDF histogram for blade supply temperature ................................................. 42
viii
ACKNOWLEDGMENT
I would like to think my advisor at RPI, Dr. Timothy Wagner, for his time and
guidance. I would like to honorably mention the late Dr. Frederick de Jong, who
encouraged me to begin this major undertaking. I would also like to thank my many
patient co-workers and managers at Pratt & Whitney. And finally I want to thank my
family for their unconditional support throughout the years, because without them I
never would have attempted to further my education.
ix
ABSTRACT
This paper describes a gas turbine pre-swirl cavity and capture system’s flow
sensitivity as predicted through a probabilistic analysis of a typical high pressure turbine
of a commercial turbofan engine. The results are used to describe the flow sensitivity in
the chamber and the effects of variability of the determined drivers. This study was
performed in order to enhance existing modeling techniques in industry. Pre-swirl
supply systems deliver cooling air axially from stationary nozzles to a rotating turbine
disk. The holes in the rotating disk are at a similar radius as the nozzles to reduce
mixing losses; however, existing engine and rig data show significant losses in total
pressure occurring in the cooling flow exchange.
This paper will demonstrate a probabilistic study method that explores flow
sensitivity of design parameters relative to the high pressure turbine single stage preswirl cooling air delivery and capture system of a turbofan engine. The analysis shows
that the areas of the blade cooling holes are the most significant driver for all three
sections of the blade cooling flow. Each section contributes over 50% to the total
variance for the blade cooling flows.
The area of the leading edge cooling holes
contributes 63.4% to the total variance of the of the leading edge mass flow rate. The
area of the mid-body cooling holes contributes 64% to the total variance of the mid body
mass flow rate. The area of the trailing edge cooling holes contributes 97.0% to the total
variance of the trailing edge mass flow rate. The range of flow rates identified for the
blade leading edge, mid-body, and trailing edge were found to be 0.15%, 0.14% and
0.16% of the reference flow rate, respectively.
x
1. Introduction
1.1 The Secondary Flow System of a Gas Turbine Engine
The gas turbine engine is widely used to power both commercial and military
aircraft today.
With just over 9.8 million domestic commercial flight departures
performed in 2007 [6], safety, system performance, component durability and reliability
are major concerns for the gas turbine engine manufacturer. These combined system
and component attributes, regulated by industry standards and customized to meet
customer requirements, contribute to a well-designed product. The major components of
a turbofan engine are shown in Figures 1 & 2. The major components are a low pressure
inlet fan and compressor, a high pressure compressor, a combustion chamber, a low
pressure turbine, a high pressure turbine and a nozzle.
Figure 1 Turbofan engine components:
compressors
1
inlet fan, low and high pressure
Figure 2 Turbofan engine components: combustor, high and low pressure turbines,
nozzle and front cavity
At the inlet of the engine the intake air flows through the fan and upon exiting is
split into two main flow paths; the by-pass flow and the primary or core flow. The bypass flow is about 80% of the inlet flow and its primary function is thrust. It is
channeled through the fan duct then enters the nozzle where it remixes with the core
flow before exiting the rear of the engine. The remaining 20% inlet air goes through the
compressors and then the combustor where it is mixed with fuel and ignited before
entering the turbines. Once the core flow exits the turbines it remixes with the by-pass
flow, just before entering the nozzle. A portion of the core flow is split off near the
compressor exit. This flow, called the secondary air system, bypasses the burner and is
used to perform a variety of functions that are critical for safe engine operation. Some of
these functions are ventilation, sealing and purging air to disks, shafts, cavities and
bearing compartments [4].
Some of the cooling air enters the high turbine inner
diameter area through the pre-swirl nozzle and some enters the front cavity. Figure 2
shows a simple cross-section of the high pressure turbine cooling air path from the
compressor exit to the high turbine inlet.
The cooling air system is designed to assure
the life of the hardware, to provide thermal conditioning for clearance control, customer
bleed flow, compressor starting and stability bleeds, and engine anti-icing protection [4].
The secondary air system also influences rotor thrust bearing loads, protects bearing
compartments, and assures an acceptable nacelle environment [4]. The internal air
system optimizes propulsion system performance while satisfying all of the above
2
demands. Although each portion of the secondary air system is needed for a balanced
system, this paper will focus on the cooling air supplied to the high pressure disk and
blades through a pre-swirl cooling air delivery system. This system is one of the most
important of the secondary sub-systems because without effective cooling air sent to the
blade, it would not survive the high temperatures of the primary core flow.
The basic function of a pre-swirl system is to supply cooling air to a disk and
blade, meeting the temperature, pressure, and leakage requirements of the system while
minimizing the losses and work input associated with bringing air on board a rotating
structure. The turbine cooling air is taken from appropriate compressor stage locations
where work has been done to increase pressure. The path of the diverted high pressure
secondary air is a complex configuration consisting of orifices, cavities, and component
interfaces. Upon entering the pre-swirl nozzle, the high pressure cooling air typically
traverses a set of static tangentially inclined nozzles, called a cascade, which turn the air
in the direction of disk rotation. Turning the air imparts a tangential component to the
velocity of the cooling air, thereby minimizing the heat up generated when the air comes
on board the rotating structure, as defined by Euler’s equations [5]. The pre-swirl cavity
cooling air and delivery system is also known as the Tangential On Board Injection
(TOBI) system. See Figure 3 for a pre-swirl nozzle rotor and stator system schematic.
Receiver Holes
Rotating
Minidisk
Stationary PreSwirl Nozzle
Figure 3 Pre-swirl nozzle rotor and stator schematic
3
The flow paths of the high pressure turbine TOBI area are shown in Figure 4. The
high pressure cooling air is expanded through the stationary pre-swirl nozzles where the
majority of the air passes through a chamber and then is delivered to receiver holes on
the rotating mini disk. The higher the pre-swirl nozzle exit tangential velocity, the colder
the cooling air will be as it is delivered to the blade, maximizing cooling effectiveness.
The swirled cooling air exiting the pre-swirl nozzles splits and follows three paths,
fulfilling separate tasks. The majority of the flow delivered to the receiver holes on the
rotating mini disk is split into two directions, outward towards the gas path and inward
towards the bore. As the flow travels outboard, cooling flow is delivered to the rotating
blade meeting a supply pressure requirement at a particular flow level and temperature.
These requirements ensure the blade will meet its life goal and satisfy rear blade
attachment leakages. Blade supply pressure, temperature, and flow requirements are met
at the condition where the majority of blade damage occurs, which is take-off for most
engine applications. The inward path taken once exiting the receiver holes provides the
flow needed to meet the requirement for high pressure turbine bore flow. This flow path
has little impact on the TOBI system and will not be discussed in detail. The remaining
cooling air, once exiting the pre-swirl nozzles, goes through the outer diameter labyrinth
seal to supply attachment leaks and front rim cavity purge.
4
OD Seal-Dead rim cooling air
and front rim cavity purge
Pre-swirl
cooling air
Blade cooling air
and attachment
leaks
From HPC
rear hub
#4 bearing
compartment air
HPT bore
cooling air
Figure 4 Flow paths of high pressure turbine area
1.2 Problem Statement
The cooling air delivered to the turbine is critical for flight safety; without it,
parts would not meet life requirements and hardware failures would occur. The core
flow turbine inlet air exiting the combustor is quite high and can reach temperatures over
3000oF. The high pressure turbine first stage purge flow cooling air prevents excessive
hot gas ingestion, keeping the metal coatings on the vane and blade platforms from being
burned off before reaching life goals. The cooling air supplied to the rotating disk and
blade by the pre-swirl nozzle system is also critical to part life. The intention of this
thesis is to demonstrate a method to perform a probabilistic secondary flow analysis for
a high pressure turbine pre-swirl cavity capture and delivery cooling air system of the
turbofan engine. The analysis will be used to quantify the variability of the cooling air
delivery system due to inherent uncertainty in manufacturing processes and engine
performance.
In addition to quantifying the variability of the cooling air delivery
system, the sensitivity of the design parameters will be determined.
5
1.3 Research Objectives
The probabilistic flow analysis performed on the high pressure turbine secondary
flow system is done using an enhanced deterministic flow model. The outputs of interest
are the flow through the pre-swirl nozzle, the nozzle exit pressure and temperature, the
cooling flow to the blade, rim cavity purge flow, flow to the bore, the blade supply
pressure and temperature, and the pre-swirl cavity temperature. The probabilistic input
is applied by adding a variation to the input parameters of the flow network solver by
use of an input file; input values are presented in the Appendix. For example, the high
pressure turbine inlet and exit pressures have a standard deviation of 0.5% of the average
pressure with a 2 sigma variation applied to each.
These variations are based on
manufacturing tolerances and engineering experience gained through testing and
performance analysis. A complete list of the parameters that will be varied can be found
in Section 3.
The flow solver program consists of networks that mathematically model the entire
engine, from the fan inlet to the nozzle. A flow network consists of restrictors that
represent pressure losses such as orifices, labyrinth seals, frictional losses in pipes, and
vortexes. These restrictors are connected to chambers representing large plenums of air
[2]. Each of the restrictors and chambers is defined by their associated pressure loss.
See Figure 5 for an example of a flow solver network showing restrictors and chambers
of the TOBI system.
6
Figure 5 TOBI area flow network solver
The probabilistic flow analysis is executed with variability in engine
performance (day to day variability) and hardware geometry (engine to engine
variability) yielding the variability in mass flow rates and air temperatures. After all
correct and assumed deviations have been entered, and all desired outputs have been
identified, the model is used to generate regression output, Cumulative Density
Functions (CDF), and Probability Density Functions (PDF). The cumulative density
functions are useful for determining how likely a range of values is, and probability
density functions show the distribution of output variables, the mean, minimum and
maximum values.
1.4 Overview of Expected Result Usage
The results of the analysis will be used to efficiently determine sources of
variability in the secondary flow system while identifying the most influential geometric
parameters. This will allow known performance capabilities to be established promoting
a more reliable and inexpensive engine.
This paper will demonstrate a probabilistic study method that explores flow
sensitivity of design parameters relative to the subsystem high pressure turbine single
7
stage pre-swirl cooling air delivery and capture system of a turbofan engine.
Probabilistic analysis has many applications in cost reduction, engine design,
optimization, and root cause analysis and has been discussed by Cloud & Stearns and
others [1-3]. The results of those analyses will be discussed in Section 2.
8
2. Background
2.1 Overview of Previous Analyses
In order to better understand how input variability or uncertainty may impact design
features of a commercial turbofan engine, probabilistic analyses have been performed
[1-3]. These types of analyses describe the variability of a system by applying variation
to the inputs of that system. This is an enhancement to current flow modeling practices
that use a deterministic model with single value inputs and outputs where the single
answer contains no measureable probability. The key to performing a probabilistic
analysis centers on the ability to propagate input variability through the system. The
previously performed probabilistic studies [1-3] and this one as well, use a proprietary
one dimensional flow network solver that simulates the behavior of the entire auxiliary
flow system for the engine. The flow solver contains additional modifications that make
it possible to evaluate output variability and sensitivity. This design tool allows the user
to input variables with a nominal value, a standard deviation, a distribution type and a
variance by means of an input file which propagates the variability through the flow
model.
Quadratic regressions are then fit to the probabilistic data to post process the results
by the method of least squares. Each regression output variable is represented by the
following sets of equations. The output variable, Y, is shown below.
Y = y0 + bi(Xi) + ci(Xi)2
(1)
Where
Y = output variable
y0 = constant regression coefficient
bi = linear regression term, which is a measure of how input variability affects
output variability
ci = quadratic regression term, which is a measure of how input variability affects
the output mean value
Xi = input variable
= finite increment
9
The following regression output variable, i, shows the expected change in the output
variable for a 1% change in the input variable, Xi. If the ith variable changes by 1% the
output variable will change by %.
i = (bi*i/i)/100
(2)
Where
i = mean value of the ith input variable
i = deviation value of the ith input variable.
The following linear regression output variable, i, represents the percent of the total
variance on the output parameter.
i = bi2/bi2
(3)
The ith variable contributes % of the total variance on that output.
In addition to the linear regression output, cumulative and probability density
functions are generated. The following is the cumulative density function equation,
y
( y) f ( x)dx
(4)
Where
y = output variable
x = input variable
( y ) = CDF as a function of y
f(x) = PDF as a function of x,
Or, equivalently if CDF is differentiable,
d/dy () = PDF
(5)
The cumulative density function is useful for determining how likely a range of
values are. The probability density function or, equivalently if the cumulative density
function is differentiable,
d/dy (CDF) = PDF
(6)
This means that the probability density function is a measure of how fast the probability
changes relative to the output variable [13].
10
2.1.1
Sidwell & Darmofal
Sidwell & Darmafol [1] demonstrated how a Monte Carlo probabilistic method is
used to estimate the distribution of oxidation failure probability of turbo-fan engines for
two different airlines operating the same engine model in different environments. To
model the statistical behavior of turbine blade oxidation life, two different types of input
variability were used for the flow network solver: day to day variability and engine to
engine variability. Day to day variability included the environmental condition of the
ambient temperature. Engine to engine variability included engine conditions, blade to
blade variations and manufacturing variations.
Engine conditions varied were
component inlet and exit temperatures and rotor speeds, which were based on field
experience. The blade to blade variations included film cooling hole effective areas that
are relevant to placement, which were derived from flow measurements performed
during manufacturing. The manufacturing variations such as machining tolerances on
TOBI seal radii and discharge coefficients of the cooling air system were assumed to
have a +/- two sigma variation. A least squares regression analysis, as described above,
was applied to the probabilistic results to identify input variables for which a decrease in
tolerance would result in an increase in life. Regression analysis determined the effect
of the variability of each input on typical and minimum engine oxidation life to be a
10% decrease in the tolerance on the blade’s leading edge effective flow area for both
airlines.
2.1.2
Cloud & Stearns
In 2004 Cloud & Stearns [2] documented a methodology for analyzing turbofan
secondary flow systems probabilistically using the Latin hypercube method [2, 3]
instead of the Monte Carlo method as was done by Sidwell & Darmofol [1]. The benefit
is that a smaller sample size is used that allows a faster convergence. The method was
applied in order to find variability in the total turbine cooling and leakage air of the
secondary flow system and the high and low rotor axial bearing loads of a turbofan
engine. Two probabilistic analyses were generated and analyzed. The first run results
allowed identification of significant system drivers. The second probabilistic run
incorporated more specific manufacturing tolerances for the significant drivers
11
determined, which were identified by interrogating drawings. The evaluation of thermal
and centrifugal growth effects were accomplished by including a percent deviation to
labyrinth seals and vortex radii. Cloud & Stearns [2, 3] concluded that absolute
deviations should be applied when manufacturing tolerances are to be analyzed. The
results showed the system behaved linearly, resulting in negligible mean shifts due to
input variation.
2.1.3
Stearns, Cloud & Filburn
In 2006 Stearns, Cloud & Filburn [3] documented the initial development of a
method to perform a thermal probabilistic analysis of gas turbine internal hardware. The
turbine inter-stage seal of turbofan engine was used as an example. The objective was to
investigate the variability of steady state metal temperature due to variability in the
secondary flow system as well as the sensitivity of the metal temperature. This was
accomplished by taking the results of the probabilistic analysis and using them as input
or boundary conditions for the thermal analysis. The thermal analysis was performed
using the commercial software known as ANSYS [3]. The results showed the variability
in metal temperature is ultimately caused by labyrinth seal clearance.
2.2 Relationship of Current Project to Existing Literature
This project will use the Latin hypercube method as was done and discussed by
others [2, 3]. The input variables will have similar standard deviations as described
above by Sidwell and Darmofal [1]. The investigation will focus on the pre-swirl cavity
cooling air capture and delivery system of the high pressure turbine.
12
3. Theory
3.1 Analytical Flow Model
The analytical secondary flow model used for this probabilistic study is a one
dimensional data-matched commercial turbofan engine model that represents build of
material hardware. The one dimensional flow model is run via a graphical user interface
(GUI). The flow model calculates the internal engine cavity pressures and temperatures,
internal cooling and leakage fluid flow rates, and the axial load on the thrust bearings.
The secondary flow model is a one-dimensional proprietary analytical tool used to
design the secondary flow system at Pratt & Whitney, Mechanical Components
Department.
The Air Systems Design and Integration group is responsible for
maintaining the in-house code that runs the program. The flow model software is
written in FORTRAN code and contains the mathematics required to accurately simulate
the secondary flow system of a commercial turbofan engine. The tool has many uses,
and one of particular interest is that it allows system designers to predict the effect of
over or under machined parts on the secondary flow system. The flow model is also
used to validate the secondary flow system, verifying the system requirements are met.
The results of the flow model are also used as input for other analyses such as thermal
analysis of the rotors, disks, blades and life estimates for bearings.
Secondary flow system requirements of interest for this analysis are the mass flow
rate through the pre-swirl nozzles of the high pressure turbine, the pressure and
temperature supplied to the blade for cooling. The flow model can solve a flow system
for a steady state case, a transient case and a statistical sensitivity or probabilistic
analysis case. Only the steady state and probabilistic features will be discussed. The
statistical probabilistic analysis used for this study is the nonlinear Latin hypercube
sampling method as described in Section 2.
3.1.1
Flow Model Governing Equations and Assumptions
The physics of the secondary flow system are governed by the conservation of mass,
the conservation of momentum and the first and second laws of thermodynamics. The
flow solver assumptions are as follows: air is treated as an ideal fluid, steady state flow,
fluid is a continuum, fluid is Newtonian (whenever viscosity is not assumed negligible),
13
internal flow and subsonic flow. Each of these laws may be addressed at a different level of
modeling fidelity, even within the same flow component.
3.1.1.1 Conservation of Mass (Continuity Equation)
Integral equation [14, 16]:
V dA
CS
dv
t
CV
(7)
Assuming steady state flow, with constant velocity and density over areas, and
velocities normal to areas:
AV
AllControl
Surfaces
m 0
(8)
AllControl
Surfaces
Reducing this to two control surfaces, one inlet and one exit:
2 m
1 m
m
(9)
3.1.1.2 Newton’s 2nd Law of Motion (Conservation of Momentum)
Linear momentum [14, 16]:
FS Fb dv Vdv VV dA
t CV
CV
CS
Assuming an ideal fluid, steady state:
FS VV dA
(10)
(11)
CS
Angular momentum:
r
F
r
F
dv
r
V
dv
r
VV dA
S
b
t
CS
CV
CV
CS
Assuming an ideal fluid, steady state:
r
F
r
S VV dA
CS
CS
3.1.1.3 First Law of Thermodynamics (Conservation of Energy)
Integral equation [15, 16]:
14
(12)
(13)
2
V
V
Q W u gz dv H
gz V dA
t CV
2
2
CS
(14)
Assuming an ideal fluid; steady state; 1D flow, constant enthalpy, velocity and density
over area; velocities normal to areas:
V2
V2
dV dA m H
m H T
Q W H
2
2 AllContro
AllControl
CS
Surfaces
(15)
Surfaces
Where for this one dimensional flow,
HT H
V2
2
(16)
3.1.1.4 Second Law of Thermodynamics
Integral equation [15, 16]:
q
sdv sVxyz dA dA 0
t
T
CV
CS
CS
(17)
Steady State:
q
sVxyz dA 0
T
CS
CS
(18)
Further details can be found in FABL++ Manual [16].
3.1.2
Flow Model Inputs
The flow and bearing load model is comprised of a series of “chambers”
interconnected by various types of “restrictions” to the gas path. These graphical
chambers and resistor icons allow the user to model cavities and restrictions that make
up an entire engine.
Chamber icons allow for the calculation of pressure and
temperature of a location, representing a large volume plenum where flow velocities are
assumed to be fully recovered and total pressure is equal to static pressure
Chamber pressures and temperatures can be either known or unknown and may be
input by a value or an equation, as in the case of data-matched locations. In order for the
model to solve, there must be at least one known chamber acting as a source and one
15
known chamber acting as a sink. The resistor icons model pressure losses and flows
between the chambers. There are 25 different types of restrictors available in the “GUI”,
the ones of most interest to the probabilistic analysis and ones pertinent to the TOBI
system’s design parameters are the flow parameter, orifice, labyrinth seal, vortex and
isentropic nozzle. Each type will be discussed in detail in section 3.1.4. The flow solver
then calculates the unknown chamber pressures and temperatures and restriction flow
rates through successive iterations until the flow rates are balanced.
The flow model used for this analysis is very detailed having hundreds of defined
chamber and resistor icons. The chambers and resistor icons are provided through an
input file that is generated using the flow model GUI. Every chamber and resistor has a
set of unknown states and governing equations that describe the local flow conditions
and are resolved by the flow solver. A coupled, nonlinear set of equations must be
solved to determine the flow in the flow network model. The flow solver uses a NewtonRaphson iterative method to solve the coupled equations [16].
3.1.3
Solution Technique
The flow network consists of the resistors and chambers with added interfaces
between every resistor and chamber. These interfaces are utilized to improve the
modularity of the underlying solver and are not controlled by the user. A simple flow
network structure is shown in Figure 6 where squares represent the chambers and circles
represent the restrictions.
Figure 6 Chambers and restrictors
Every chamber, resistor and interface has a set of unknown states and governing
equations that describe the local flow conditions and are determined by the flow and
bearing load solver. The states for chambers are pressure and temperature. If there is no
initial guess input for each pressure or temperature, the value is set to equal the average
16
of the known pressures or temperatures.
The states for restrictors are mass flow rate,
temperature at the intended upstream boundary and temperature at the downstream
boundary. The states for interfaces are mass flow rate, temperature and pressure.
The specific governing equations for chambers are:
1. Conservation of mass. In steady flow, the sum of the interface mass flow rates
connected to the chamber is required to be zero:
Number int
of erfaces
Interfaces
numberof
m
i 1
0
i
(19)
is the mass flow rate, or air flow.
Where m
For unsteady flow, appropriate time derivatives are added to account for a time rate
of change for the mass in the chamber.
2. Conservation of energy. In steady flow, the conservation of energy is given by:
Number
of erfaces
Interfaces
number
of int
m
i 1
i
H (Ti up ) 0
(20)
Where H is the stagnation enthalpy and Ti
up
is the temperature taken from the
upstream direction at interface i. In other words, if the interface is an inflow, this
temperature is equal to the interface temperature; however, at an outflow, this
temperature is equal to the chamber temperature. For unsteady flow, additional terms are
added to account for a time rate of change of energy in the chamber.
Resistor governing state laws:
1.
For most restrictors, the resistor mass flow rate is set up by a mass flow
relationship to the upstream and downstream pressures and temperatures that are taken
from the corresponding interfaces. However, for vortex resistors and fixed pressure ratio
resistors, a pressure ratio or pressure difference is set directly.
2.
Upstream temperature, which is based on the direction of flow, is set to the
upstream interface temperature value.
3.
The downstream temperature is set by the resistor model and may include a
temperature set by the user.
Interface governing state laws:
17
1.
The interface mass flow rate is set to the mass flow rate of the resistor it is
attached to.
2. The interface pressure
3. The
is set to the pressure of the chamber it is attached to.
interface temperature is set to the temperature from the upstream component,
for example the resistor or chamber which is upstream of the interface.
3.1.4
Restrictions and Chambers
The restrictors discussed here are the ones that will be varied in the input file
created for the probabilistic study and consist of the flow parameter, orifice, labyrinth
seal, vortex and isentropic nozzle. Figure 7 shows schematic of locations varied in high
pressure turbine TOBI area.
Isentropic nozzle restrictors
Flow parameter
restrictors
Labyrinth seal
restrictors
Orifice restrictor
Figure 7 TOBI system areas varied
Ideally, the flow model restrictors and chambers include inputs that represent the
physical description for the hardware being modeled. The standard output contains the
input items as well as the calculated output values including flow area, temperature,
pressure, pressure ratio, flow rates and reference values if input. Basic discussions are
18
presented here for the restrictor inputs of interest to the probabilistic analysis and for
brevity are simplified. The flow model calculates a flow parameter and pressure ratio
for each restrictor and chamber, and then uses these results for the iterations solving for
the sum of the mass flow rates.
3.1.4.1 Flow Parameter Restrictor
The flow parameter restrictor [16] is used to model the cooling hole passages of the
blade’s leading edge, mid-body, trailing edge, the trailing edge platform overhang and
the TOBI. The input is a flow parameter versus pressure ratio curve and is derived from
flow measurements taken during manufacturing. This restrictor is used where the
relationship between flow parameter and pressure ratio is known.
m T P
up
(21)
Where PR Pup
P
is known.
down
An effective area, discharge coefficient (Cd), can also be calculated based on the cold
flow data. If no discharge coefficient is entered the flow model assumes an effective
area of unity.
ACd
m T P
m T P A
up measured
up
(22)
isentropic
Where A is the area.
3.1.4.2 Orifice Restrictor
An orifice restrictor [16] is used to model the minidisk holes which feed the blades.
This restrictor is used where flow measurement or metering is done using a very short
passage with a sharp edge on the upstream side and beveling downstream, or a square
edge with no beveling such as a drilled hole. The input includes a required flow area A
and an optional discharge coefficient Cd. The flow area can be input as a value or an
equation.
19
3.1.4.3 Labyrinth Seal Restrictor
The labyrinth seal restrictor is used to model the outer diameter and inner diameter
TOBI seals. Definitions of a typical labyrinth seal knife edge geometry required for the
flow model are illustrated in Figure 8. The direction of the flow (up flow or down flow)
depends on the engine operating condition.
Figure 8 Labyrinth seal knife edge geometry, inputs for flow model
Where:
c = Seal Clearance
b = Number of Teeth
pKE = Knife Edge Pitch
wKE = Knife Edge thickness
h = Land Step Height
rKE = knife Edge Leading Edge Radius (illustrated in figure for Up Flow)
The flow area is calculated by the flow model using the supplied inputs.
3.1.4.4 Vortex Restrictor
The vortex restrictor [16] is used to simulate fluid motion involving rotation about
an axis. This simulation tool has no physical area restriction but can either increase or
decrease flows by imposing a pressure ratio on the adjacent chamber(s) with non-fixed
pressure(s). The flow model uses calculations for all the vortex motions that assume the
working fluid acts like a perfect gas and that the vortex is isentropic. These assumptions
20
are thought to provide a reasonable representation of a real vortex but if the vortex
pressure ratio is known it may be input directly.
3.1.4.5 Isentropic Nozzle
The isentropic nozzle restrictor [16] is used to model the rim cavities. Input
considerations include a required flow area, A, and an optional discharge coefficient, Cd.
The flow model assumes that the isentropic nozzle has an upstream area much larger
than the minimum flow area specified as input and uses the input flow area as the throat
for this restriction. The nozzle flow area must be input using the minimum passage area
known as the throat of the nozzle. The nozzle throat may have any cross-section shape;
the flow model will use the input flow area as the minimum flow area for the nozzle
throat.
3.1.4.6 Chamber
The flow model assumes 1-D flow, constant enthalpy, velocity and density over the
area [16]. Velocities are assumed normal to areas and no heat or work interactions with
surroundings occur. The air is assumed to be a perfect gas during the standard flow
model iteration loop, and it is assumed to be a real gas during the flow model iteration
loop in which the conservation of energy law is applied to each chamber using real fluid
properties. The chamber effectively acts as a mixing restriction with one or more control
surfaces.
3.1.5
The Flow Network Solver
The coupled, nonlinear set of equations must be solved to determine the flow in the
flow and bearing load network model. The flow solver uses a Newton-Raphson [16]
iterative method to solve the coupled equations. Specifically, the governing equations
and unknown states for every chamber, resistor, and interface in the flow network can be
combined into a residual form,
R (U ) 0
(23)
Where U is a vector containing all of the unknown states and R is the corresponding
vector containing all of the governing equations. A Newton-Rapshon method [16] for
21
solving this nonlinear set of equations is found by linearizing the residuals about a
current guess for the solution,
R(U n dU ) 0
R(U n )
R
dU 0
U
(24)
Then, by solving for dU, an update for the state vector is given by,
U n1 U n
R 1
R(U n )
U
(25)
In practice, however, the full Newton update is not taken at every iteration
especially early in the iterative process where the linearized update may result in nonphysical solutions. Thus, the Newton update is under-relaxed as follows,
U n1 U n d
U 1
R(U n )
U
(26)
Where d is a relaxation factor in the flow solver and is known as the drate.
The algorithm for determining the drate involves several parameters which may be
modified to control the convergence behavior of the flow solver. Two types of limiting
of the drate are used: (1) limiting based on the flow rate residual, and (2) limiting based
on the change in the states. For the flow rate residual limiting, the basic idea is to limit
the Newton update whenever the mass flow rate imbalance anywhere in the flow
network is large at the current iteration. For the state-based limiting, the basic idea is to
limit the changes in the state to guarantee that the states at the next iteration are
physically realistic. Thus, in both limiting procedures, as the solution converges, drate
should approach unity, while initially drate is less than unity.
3.2 Probabilistic Flow Model
The flow model’s sensitivity analysis permits the user to input variations of certain
parameters and then run a sensitivity study (linear or non-linear) to obtain statistical
variations for other defined parameters. The secondary flow model, as a design feature,
has an option for varying input values and propagating them through the flow model.
Typically the flow model takes single input values per chambers and restrictors in the
form of flow areas, pressures and temperatures. The probabilistic flow analysis allows
the user to input variability in engine performance (day to day variability) and hardware
22
geometry (engine to engine variability) yielding the variability in mass flow rates and air
temperatures and pressures.
3.2.1
Probabilistic Flow Model Inputs and Outputs
The input file for the probabilistic study needs to identify the parameter (chamber or
restrictor) being varied, the nominal value, the standard deviation, the distribution type
and the variance. The flow model probabilistic analysis generates regression output,
cumulative density functions, and probability density functions. After propagating input
variability through the model by means of an input file, it is possible to analyze the
model outcomes of means and deviations.
23
4. Methodology
4.1 Method of Analysis
The secondary flow model used for the probabilistic study is a data-matched
secondary flow model of a current production commercial turbofan engine
configuration. This flow model’s input parameters are a specified pressure, temperature
and flow rate for a standard day take off condition. A probabilistic analysis allows
variation of different input parameters (many at a time) in a random manner
independently which will generate the effect on several other output parameters with the
resulting probability or frequency distribution of each output parameter. By default, all
the input variables can be changed completely independent of each other [2, 8]. The
input values used for the probabilistic analysis are refined variations as determined from
tolerance dimensions identified from part drawings, experience and engineering
judgment.
The probabilistic analysis used the Latin hypercube [12] sampling method and is a
design feature of the flow model. The statistical method of Latin Hypercube Sampling
(LHS) was developed to generate a distribution of plausible collections of parameter
values from a multidimensional distribution. The technique was first described by
McKay in 1979 [8], it was further elaborated by Ronald L. Iman, and others [10] in
1981. Detailed computer codes and manuals were later published [11]. This method is
incorporated into the secondary flow model’s FORTRAN code.
The probabilistic
analysis was run for 4000 samples as recommended by Cloud & Stearns [2, 3].
In the context of statistical sampling, a square grid containing sample positions is a
Latin square if (and only if) there is only one sample in each row and each column. A
Latin hypercube is the generalization of this concept to an arbitrary number of
dimensions, whereby each sample is the only one in each axis-aligned hyper-plane
containing it. When sampling a function of
divided into
M equally probable intervals.
N variables, the range of each variable is
The same number of sample points are then
placed to satisfy the Latin hypercube requirements; note that this forces the number of
divisions, M, to be equal for each variable. Also note that this sampling scheme does not
require more samples for more dimensions (variables); this independence is one of the
24
main advantages of this sampling scheme. Another advantage is that random samples
can be taken one at a time, remembering which samples were taken so far.
maximum number of combinations for a Latin Hypercube of
M
The
divisions and
N
variables (i.e., dimensions) can be computed with the following formula:
(27)
For example, a Latin hypercube of
M = 4
divisions with
N = 2
square) will have 24 possible combinations. A Latin hypercube of M
variables (i.e., a
= 4 divisions with
N = 3 variables (i.e., a cube) will have 576 possible combinations [12].
4.1.1
Output Data Types
There are three output files of interest generated by the probabilistic analysis; the
linear regression, the cumulative distribution function, and the probability density
function.
The regression is the most helpful for identifying significant parameters by
looking at the percent of the total variance a given input contributes. The pie charts show
the percent of total variance contribution, for each output parameter. These will help
identify which parameters are significant contributors. Another useful output of the
regression is the R2 value, which is given for each output parameter. This is an indicator
that measures how well the regression equation fits the data; the closer this value is to
one means that a good fit to the data was achieved [7].
The cumulative density functions are useful for determining how likely a range
of values are. The cumulative density function plots show how close the parameters are
to the normal distribution.
Probability density functions serve to represent a probability distribution in terms of
integrals and is the derivative of the cumulative density function.
The probability
density functions show the mean, minimum and maximum value for the output
parameters. This information can be used by designers when considering manufacturing
tolerances.
25
4.2 Probabilistic Variation Types
Two types of input parameters are varied in this study: day to day variation, which
are engine conditions, and engine to engine variation, which are manufacturing
tolerances. The day to day variations can be captured through the high pressure turbine
inlet and exit pressure and temperature. The standard deviation applied to the engine
performance was based on engine test data and engineering experience. The engine to
engine variations are accounted for by varying the geometry of the system’s hardware,
this includes areas and flow rates. Manufacturing tolerances for each significant input
were identified by interrogating current build of material drawings for the hardware such
as the knife edge seal clearances. The variation values are currently documented and can
be found on drawings and engineering standard work. Output parameters include flow
rate, pressure and temperature for the TOBI, the blade supply pressure, blade leading
edge rim cavity purge flow and cooling flow for the blade’s leading edge, trailing edge
and platform trailing edge.
4.2.1
Input File
The input file contains the input and output parameter names, which follows the
same naming convention as the flow model. The parameter input information includes
the nominal value, the standard deviation, the distribution type and the variance applied.
The flow network solver will then generate random values for each input within the
given distributions and solve the system for each sample. The convergence criteria for
the flow network solver is to solve all the unknown pressures, flows and temperatures
until all the mass flow rates summed are equal to zero. The flow model input file and the
probabilistic input file are located in the Appendix.
For this probabilistic study a 5% standard deviation was assumed on restrictor areas
and vortex RPMFs, a 15% standard deviation on the TOBI OD labyrinth seal clearance,
and a 25% standard deviation on the plat-form leakage areas, which are consistent with
average manufacturing tolerances. The standard deviation applied to the TOBI flow area
was based on the blueprint cold flow data and is 1.5%. The TOBI ID labyrinth seal
clearance was based on test data and engineering experience and was 5%. The standard
deviation applied to the performance was based on experience and test data and was
26
0.2%.
The distribution type chosen was a truncated normal distribution. Output
parameters will include flow rates, pressures and temperatures for the pre-swirl nozzle
and the blade. Table 1 provides a list of selected output parameters of the subsystem.
Table 1 Output Parameters
Component/Location
Parameters
TOBI Nozzle
ID and OD Labyrinth Seal Leakages, Flow
Rate, Discharge Pressure and Temperature
Platform Feather Seal, Front and Rear
Attachment Leakages, Cooling Hole
Areas, Supply Pressure, Supply
Temperature, Cooling Flow
Purge Flow and Pressures
Blade
Rim Cavity
The results of the analysis will be used to identify the significant drivers of variability of
the pre-swirl nozzle cooling air capture and delivery system. Unlike the previously
performed probabilistic analyses, the output parameters of this study are the mass flow
rates of the high pressure turbine blade cooling air, the blade supply air temperature and
pressure. Table 2 shows the standard deviations applied to each parameter.
Table 2 Input Parameters and Standard Deviation
Parameter
Probabilistic Input
TOBI OD Seal
= 15 % of Cd
TOBI ID Seal
= 5 % of Cd
Platform Leakages
= 25 % of Area
TOBI Area
= 1.5 % of Area
Vortices
= 5 % of RPMF
Blade Cooling Area
= 5 % of Area
Pressures
= 0.2 % of P4 & P5
27
See Figure 9 for a schematic of the blade output parameters and locations.
Leading Edge Cooling
Flow Restrictor
Trailing Edge Cooling
Flow Restrictor
Mid Body Cooling
Flow Restrictor
Blade Supply
Pressure Chamber
Figure 9 Blade output parameters and locations
See Figure 10 for a schematic of the TOBI area output parameters and locations.
TOBI OD
Labyrinth Seal
Restrictor
TOBI Flow
Area Restrictor
TOBI
Discharge
Temperature
Chamber
TOBI ID
Labyrinth Seal
Restrictor
Figure 10 TOBI area output parameters and locations
28
5. Results of Latin Hypercube Analysis
5.1 Output Data
A probabilistic analysis allows simultaneous variation of different input parameters
in a random manner independently. The results generated show the probability or
frequency distribution, the percent of total variance contribution and the mean, minimum
and maximum values for each output parameter. Identifying the significant drivers of
the pre-swirl nozzle cooling air capture and delivery system is determined by reviewing
the output data of the important secondary flow design parameters.
5.1.1
Significant Design Parameters
The important design parameters of the cooling air capture and delivery system are
pressure, temperature and flow of the high pressure turbine blade. This assumption is
based on experience learned from the airfoil flow process certification, which includes
cold flow testing of the hardware. During the cold flow testing the airfoils are connected
to a sonic nozzle that supplies flow through the blades. The particular blade analyzed
has three paths for the cooling air, with the supply pressure set, the flow dumps to
ambient and the flow rate is measured. From this information a flow parameter is
calculated. The upstream pressure and temperature are needed for this calculation.
m T P
up
Where
(28)
is the flow parameter,
m is the mass flow rate,
T is the upstream supply temperature and
Pup is the upstream supply pressure.
The mass flow rate, temperature and pressure are significant design parameters of
the pre-swirl nozzle and cooling air capture and delivery system. The manufacturing
tolerance of the blade airfoils is derived from the cold flow data and the standard
deviation is based on this information.
29
5.1.2
Identifying Significant Drivers of Sensitivity
Knowing the important design parameters helps to focus on the appropriate output
probabilistic flow data, limiting the review to include the blade supply pressure,
temperature and cooling airfoil flows. The linear regression output coefficient for
each design parameter reveals the significant drivers of the pre-swirl nozzle cooling air
capture and delivery system to be the blade cooling flow areas of the leading edge, mid
body and the trailing edge, the TOBI flow area, and the TOBI Outer Diameter (OD)
labyrinth seal clearance. The input file in the Appendix shows the areas for each
restrictor.
The results of the probabilistic run are shown through the normalized data plots
presented in Figures 11 through 25 for five key system design parameters: the blade
leading edge cooling flow, the blade mid-body cooling flow, the blade trailing edge
cooling flow, the blade supply pressure and the blade supply temperature. A summary
of these findings is shown in Table 3, and is easily observed by the pie charts presented
for each parameter. The top five significant drivers of the sub-system were identified by
the linear regression data: the area of the blade cooling holes for the leading edge, midbody and trailing edge, the TOBI flow area, and the TOBI OD labyrinth seal clearance.
The determination of these five drivers was based on the percent of the total variance,
i, results for each design parameter. Note that each important design parameter has the
same top five contributors of the total variance. The scale designation uses one for the
largest contributor, two represents the second largest contributor, three is the third
largest, and so on. The TOBI discharge temperature, which is representative of the blade
supply temperature, is not as significant as the blade supply pressure or the blade mass
flow rate as shown in Figures 23 through 25. The temperature does not have the same
top five contributors to the total variance. More significant to the temperature was the
TOBI OD cavity and mini-disk vortex RPMFs.
30
Table 3 Rankings for Significant Contributors (in % of Total Variance)
Significant Contributors
Key Design
Parameters
Blade LE
Cooling Flow
Blade MidBody Cooling
Flow
Blade TE
Cooling Flow
Blade Supply
Pressure
Blade Supply
Temperature
Blade LE
Cooling
Hole Area
Blade TE
Cooling
Hole Area
TOBI Flow
Area
1
Blade MidBody
Cooling
Hole Area
4
TOBI OD
Lab Seal
Clearance
2
3
5
63.4%
6.8%
10.9%
7.5%
5.7%
3
1
2
4
5
8.4%
64.0%
10.1%
6.9%
5.3%
2
4
1
3
5
2.4%
1.8%
90.7%
2.0%
1.5%
2
4
1
3
5
19.8%
12.4
23.9%
14.9%
10.2
-
-
5
3
5.7%
16.2%
Mini-disk
Vortex
RPMF
-
TOBI OD
Cavity
Vortex
RPMF
-
-
-
-
-
-
-
1
2
4
29.7%
26.5%
8.6%
A summary of the linear regression results are shown in Table 4 and show the mean,
minimum, maximum and R2 values for each output parameter. The R2 value shows
good fits for the data.
Table 4 Output Parameters, Standard Mean, Min, Max and R2 Values
Standard
Mean
Min
Max
R2 Value
Blade Supply Pressure
(% Reference Pressure)
54.42
52.51
56.47
0.9981
Blade Supply Temperature
(% Reference Temperature)
100.51
100.39
100.65
0.9943
Blade Leading Edge Mass Flow Rate
(% Reference Flow)
1.44
1.26
1.66
0.9994
Blade Mid-Body Mass Flow Rate
(% Reference Flow)
1.25
1.10
1.43
0.9994
Blade Trailing Edge Mass Flow Rate
(% Reference Flow)
1.59
1.43
1.77
0.9998
Output Parameters, Key Design Parameters
31
It is assumed that the nominal values for the 1st blade cooling flow, supply pressure
and temperature are the values that meet the system requirements and the manufacturing
tolerances are the minimum and maximum values.
5.1.2.1 Results for Blade Leading Edge Cooling Flow Output Parameter
The pie chart in Figure 11 shows the percent of total variance, , each parameter
contributes to the blade flow of the leading edge cooling holes. The highest contributor
at 63.4% is the flow area of blade leading edge cooling holes, which is followed by the
flow area of the blade trailing edge cooling holes at 10.9%, then the TOBI flow area
with a 7.5% contribution. The next most significant contributor is the flow area of the
blade mid-body cooling holes at 6.8% followed by the TOBI OD labyrinth seal
clearance with just a 5.7% contribution.
Blade Leading Edge Cooling Flow
% of Total Variance Contribution
0.1%
0.1%
Blade LE Cooling Flow Area
0.2%
Blade TE Cooling Flow Area
0.6%
TOBI Flow Area
4.7%
Blade Mid Body Cooling Flow Area
5.7%
TOBI OD Lab Seal Clearance
Mini Disk Vortex RPMF
0.0%
0.0%
6.8%
Blade Rear Side Plate Leakage
TOBI OD Lab Seal Radius
7.5%
TOBI OD Vortex RPMF
HPT OD Mini-disk Leak
10.9%
63.4%
OD Lab Seal Cavity Vortex RPMF
Blade Rear Side Plate Leakage
Figure 11 Blade LE cooling flow % of total variance contribution
The cumulative density function plot in Figure 12 shows the blade leading edge
cooling holes flow range probability. There is a 10% probability for values to fall below
1.37% of the reference flow rate. There is a 90% probability for values to be less than
1.52% of the reference flow rate.
32
Cumulative Density Function Plot for the
Blade Leading Edge Cooling Holes Mass Flow Rate
1.0
Frequency Distribution
0.9
0.8
0.7
0.6
0.5
90% of flow rates will
be less than this value
10% of flow rates will
be less than this value
0.4
0.3
0.2
0.1
0.0
1.25
1.30
1.35
1.40
1.45
1.50
1.55
1.60
1.65
% Reference Mass Flow Rate
Figure 12 CDF plot for blade LE cooling holes mass flow rate
Figure 13 is the probability density function histogram for the blade leading
edge. The mean, minimum and maximum for the blade leading edge is 1.44%, 1.26%
and 1.66% of the reference flow, respectively.
Probability Density Function Histogram for the
Blade Leading Edge Mass Flow Rate
Probability Distribution
6.0
5.0
4.0
3.0
2.0
1.0
% Reference Flow Rate
Figure 13 PDF histogram blade LE cooling holes mass flow rate
33
1.
65
1.
63
1.
60
1.
58
1.
55
1.
53
1.
50
1.
48
1.
45
1.
43
1.
41
1.
38
1.
36
1.
33
1.
31
1.
28
1.
26
0.0
5.1.2.2 Results for Blade Mid-Body Cooling Flow Output Parameter
The pie chart in Figure 14 shows the percent of total variance each parameter
contributes to the blade flow of the mid body cooling holes. The highest contributor at
64.0% is the flow area of the blade mid-body cooling holes, which is followed by the
flow area of the blade trailing edge cooling holes at 10.1% then the flow area of the
blade leading edge cooling holes with an 8.4% contribution. The next most significant
contributor is the TOBI flow area at 6.9% followed by TOBI OD labyrinth seal
clearance with just a 5.3% contribution.
Blade Mid-Body Cooling Flow
% of Total Variance Contribution
0.1%
0.2%
0.5%
Blade Mid Body Cooling Flow Area
4.4%
Blade TE Cooling Flow Area
Blade LE Cooling Flow Area
5.3%
TOBI Flow Area
0.1%
0.0%
0.0%
6.9%
TOBI OD Lab Seal Clearance
Mini Disk Vortext RPMF
Blade Rear Side Plate Leakage
8.4%
TOBI OD Lab Seal Radius
TOBI OD Cavity Vortex RPMF
HPT OD Mini-disk Leak
10.1%
64.0%
OD Lab Seal Cavity Vortex RPMF
Blade Rear Side Plate Leakage
Figure 14 Blade mid-body cooling flow % of total variance contribution
The cumulative density function plot of the blade mid body cooling holes shown in
Figure 15, shows the probability band (10% to 90%) for the flow to lie between 1.18%
and 1.32% of the reference flow rate.
34
Cumulative Density Function Plot for the
Blade Mid-Body Cooling Holes Mass Flow Rate
1.0
Frequency Distribution
0.9
0.8
0.7
0.6
0.5
90% of flow rates will
be less than this value
10% of flow rates will
be less than this value
0.4
0.3
0.2
0.1
0.0
1.05
1.10
1.15
1.20
1.25
1.30
1.35
1.40
1.45
% Reference Mass Flow Rate
Figure 15 CDF for blade mid-body cooling holes mass flow rate
Figure 16 is the probability density function histogram for the blade mid-body
cooling holes. This plot shows the mean, minimum and maximum values are 1.25%,
1.1% and 1.43% of the reference mass flow rate, respectively.
Probability Density Fucntion Histogram for the
Blade Mid-Body Cooling Holes Mass Flow Rate
Probability Distribution
7.0
6.0
5.0
4.0
3.0
2.0
1.0
0.0
0
1.1
2
1.1
4
1.1
6
1.1
8
1.1
0
1.2
2
1.2
4
1.2
6
1.2
8
1.2
0
1.3
2
1.3
4
1.3
6
1.3
8
1.3
% Reference Mass Flow Rate
Figure 16 PDF histogram of the mid-body cooling holes mass flow rate
35
0
1.4
2
1.4
5.1.2.3 Results for Blade Trailing Edge Cooling Flow Output Parameter
Figure 17 shows the percent of total variance each parameter contributes to the
blade flow of the trailing edge cooling holes. The highest contributor at 90.7% is the
flow area of the blade trailing edge cooling holes, which is followed by the flow area of
the blade leading edge cooling holes at 2.4% then the TOBI flow with a 2.0%
contribution. The next most significant contributor is the flow area of the blade midbody cooling holes at 1.8% followed by TOBI OD labyrinth seal clearance with just a
1.5% contribution.
Blade Trailing Edge Cooling Flow
% of Total Variance Contribution
0.2%
1.2%
Blade TE Cooling Flow Area
1.5%
Blade LE Cooling Flow Area
1.8%
TOBI Flow Area
2.0%
Blade Mid Body Cooling Flow Area
2.4%
TOBI OD Lab Seal Clearance
0.1%
0.0%
0.0%
0.0%
Mini Disk Vortex RPMF
Blade Rear Side Plate Leakage
TOBI OD Lab Seal Radius
TOBI OD Cavity Vortex RPMF
HPT OD Mini-disk Leak
OD Lab Seal Cavity Vortex RPMF
90.7%
Figure 17 Blade TE cooling flow % of total variance contribution
Figure 18 is the cumulative density function plot and shows the probability band for
the trailing edge cooling holes to be from 1.51% to 1.67% of the reference flow rate.
36
Cumulative Density Function Plot of the
Blade Trailing Edge Cooling Holes Mass Flow Rate
1.0
Frequency Distribution
0.9
0.8
0.7
0.6
0.5
0.4
90% of flow rates will
be less than this value
10% of flow rates will
be less than this value
0.3
0.2
0.1
0.0
1.40
1.45
1.50
1.55
1.60
1.65
1.70
1.75
1.80
% Reference Mass Flow Rate
Figure 18 CDF plot for blade TE cooling holes mass flow rate
Figure 19 is the probability density function histogram for the blade leading edge
and shows the mean, minimum and maximum values to be 1.59%, 1.43% and 1.77% of
the reference flow rate.
Probability Density Function Histogram of the
Blade Trailing Edge Cooling Holes Mass Flow Rate
Probability Distribution
6.0
5.0
4.0
3.0
2.0
1.0
0.0
3
1.4
5
1.4
7
1.4
9
1.4
1
1.5
3
1.5
5
1.5
7
1.5
9
1.5
1
1.6
3
1.6
6
1.6
8
1.6
0
1.7
2
1.7
% Reference Flow
Figure 19 PDF histogram of the blade TE cooling holes mass flow rate
37
4
1.7
6
1.7
5.1.2.4 Results for Blade Supply Pressure Output Parameter
The pie chart in Figure 20 shows the percent of total variance each parameter
contributes to the blade flow of the blade supply pressure. The highest contributor at
23.9% is the flow area of the blade trailing edge cooling holes, which is followed by the
flow area of the blade leading edge cooling holes at 19.8% then the TOBI flow area with
a 16.4% contribution. The next most significant contributor is the flow area of the blade
mid-body cooling holes at 14.9% followed by TOBI OD labyrinth seal clearance with
just a 12.4% contribution.
Blade Supply Pressure % of Total Variance Contribution
0.2%
0.3%
Blade Trailing Edge Cooling Flow Area
0.5%
Blade Leading Edge Cooling Flow area
1.2%
TOBI Flow Area
0.0%
10.2%
Blade Mid-Body Cooling Flow Area
23.9%
TOBI OD Lab Seal Clearance
12.4%
Mini-disk Vortex RPMF
Blade Rear Side Plate Leakage
TOBI OD Lad Seal Radius
TOBI OD Cavity Vortex RPMF
14.9%
19.8%
HPT OD Mini-disk Leak
OD Lab Seal Cavity Vortex RPMF
16.4%
Figure 20 Blade supply pressure % of total variance
Figure 21 shows the blade supply pressure has a probability band that ranges from
53.65% to 55.2% of the reference pressure.
38
Cumulative Density Function Plot for
Blade Supply Pressure
1.0
Frequency Distribution
0.9
0.8
0.7
0.6
0.5
0.4
90% of pressures will
be less than this value
10% of pressures will
be less than this value
0.3
0.2
0.1
0.0
52.5
53.0
53.5
54.0
54.5
55.0
55.5
56.0
56.5
% Reference Pressure
Figure 21 CDF plot for blade supply pressure
Figure 22 is the probability density function plot for the blade supply pressure
and shows the mean, minimum and maximum values to be 54.42%, 52.51% and 56.41%
of the reference pressure respectively.
39
0.20
0.15
0.10
0.05
0.00
52
.
52 51
.
52 67
.
53 83
.
53 00
.
53 16
.
53 32
.
53 48
.
53 64
.
53 80
.
54 96
.
54 13
.
54 29
.
54 45
.
54 61
.
54 77
.
55 93
.
55 10
.
55 26
.
55 42
.
55 58
.
55 74
.
56 90
.
56 06
.
56 23
.3
9
Probability Distribution
Probability Density Function Histogram for
Blade Supply Pressure
% Reference Pressure
Figure 22 PDF histogram for blade supply pressure
5.1.2.5 Results for Blade Supply Temperature Output Parameter
The pie chart in Figure 23 shows the percent of total variance each parameter
contributes to the TOBI discharge temperature and blade supply temperature. The
highest contributor at 29.7% is the TOBI OD labyrinth seal clearance, which is followed
by the mini-disk vortex RPMF at 26.5%, then the TOBI flow area with a 16.2%
contribution. The next most significant contributor is the TOBI OD vortex RPMF at
8.6%, followed by the flow area of the blade trailing edge cooling holes with just a 5.7%
contribution.
40
TOBI Discharge Temperature/Blade Supply Temperature
% of Total Variance Contribution
0.3%
0.6%
TOBI OD Lab Seal Clearance
1.2%
Mini-Disk Vortex RPMF
3.0%
TOBI Flow Area
3.5%
TOBI OD Vortex RPMF
0.1%
4.6%
Blade TE Cooling Flow Area
29.7%
5.7%
Blade Mid-Body Cooling Flow Area
Blade LE Cooling Flow Area
8.6%
TOBI ID Lab Seal Clearance
TOBI OD Lab Seal Radius
TOBI ID Lab Seal Radius
16.2%
Blade Rear Side Plate Leakage
TOBI OD Lab Seal OD Vortex RPMF
26.5%
Figure 23 Blade supply temperature % of total variance contribution
Figure 24 is the cumulative density function plot and shows the probability band
ranges from 100.46% to 100.56% of the reference temperature.
Cumulative Density Function Plot for the
TOBI Discharge Temperature/Blade Supply Temperature
1.0
Probability Distribution
0.9
0.8
0.7
0.6
0.5
0.4
0.3
90% of temperatures
will be less than this
value
10% of temperatures
will be less than this
value
0.2
0.1
0.0
100.40
100.42
100.44
100.46
100.48
100.50
100.52
100.54
100.56
100.58
100.60
100.62
100.64
% Reference Temperature
Figure 24 CDF plot for blade supply temperature
Figure 25 is the probability density function histogram that shows the blade
supply temperature mean, minimum and maximum values to be 100.51%, 100.39% and
100.65% of the reference temperature.
41
Probability Density Function Histogram for
TOBI Discharge Temperature/Blade Supply Temperature
Probability Distribution
1.20
1.00
0.80
0.60
0.40
0.20
10
0.
10 39
0.
10 40
0.
10 41
0.
10 42
0.
10 43
0.
10 44
0.
10 45
0.
10 46
0.
10 47
0.
10 48
0.
10 49
0.
10 50
0.
10 52
0.
10 53
0.
10 54
0.
10 55
0.
10 56
0.
10 57
0.
10 58
0.
10 59
0.
10 60
0.
10 61
0.
10 62
0.
10 63
0.
64
0.00
% Reference Temperature
Figure 25 PDF histogram for blade supply temperature
5.1.3
Summary of Results
The results of the analysis identified sources of variability in the secondary flow
system and determined the most influential geometric parameters. The cooling hole
flow areas, the TOBI flow area and TOBI OD labyrinth seal clearance were identified as
being the most significant drivers of the pre-swirl nozzle cooling air capture and delivery
system.
42
6. Conclusions
6.1 Key Design Parameters & Primary Drivers of the Sub-System
This probabilistic study of the pre-swirl nozzle and cooling air capture and delivery
system identified the significant drivers of the sub-system’s key design parameters. The
key sub-system design parameters are the blade’s cooling flow, which are the LE, midbody and TE flows, the blade supply pressure and the blade supply temperature. The
primary drivers of the blade flows and supply pressure design parameters were found to
be the area of the blade cooling holes (the LE, mid-body and TE), the TOBI flow area,
and the TOBI OD labyrinth seal clearance. The primary drivers for the TOBI discharge
temperature, which is representative of the blade supply temperature, were found to be
the TOBI OD labyrinth seal clearance, the mini-disk vortex RPMF, the TOBI flow area,
the TOBI OD cavity vortex RPMF and the blade trailing edge cooling holes area.
The following drivers were found to not have a significant impact on the subsystem’s total blade flow (i.e., the LE, mid-body and TE flows) and supply pressure: the
blade rear side plate leakage, the OD labyrinth seal cavity vortex RPMF, the HPT OD
mini-disk leakages, TOBI OD vortex RPMF and the TOBI lab seal radius. The analysis
also showed that the following drivers had no impact on the blade supply temperature:
the TOBI OD labyrinth seal OD vortex RPMF, the blade rear side plate leakage, the
TOBI ID labyrinth seal radius, the TOBI OD labyrinth seal radius and the TOBI ID
labyrinth seal clearance. Note that these findings are based on variances that were
defined by manufacturing tolerances.
6.2 Significant Contributors of the Key Design Parameters
The linear regression output showed that for the blade flows the most significant
contributor was the area of the cooling holes. The blade mid-body cooling flow design
parameter had a 64.0% contribution of the total variance by the area of the mid-body
cooling holes. The blade leading edge cooling flow design parameter had a 63.4%
contribution of the total variance by the leading edge cooling hole area. The trailing
edge cooling flow design parameter had a 63.4% contribution of the total variance by the
area of the leading edge cooling holes.
43
The supply pressure key design parameter’s most significant contributor to the total
variance is the area of the blade trailing edge cooling holes with 23.9% of the
contribution.
The supply temperature key design parameter’s most significant contributor is the
TOBI OD lab seal clearance with 29.7% of the total variance, which is the 5th most
significant contributor to the other four key design parameters.
6.3 Importance of Findings
The pre-swirl nozzle cooling air and capture sub-system is an important part of
turbine cooling air delivery systems. This analysis provides the understanding of the key
design parameters of the TOBI and the impact of their variations on system cooling
flow, pressure and temperature. The results of this study can provide guidanc for
designers to indicate where to decrease tolerances to achieve design improvement and
where to relax the tolerances for cost reduction.
44
7. References
[1] Sidvell, V., Darmofal, D., 2003. “Probabilistic Analysis of a Turbine Cooling Air
Supply System: The Effect on Airfoil Oxidation Life,” ASME Paper GT2003-38119.
[2] Stearns, E., Cloud, D., 2004. “Probabilistic Analysis of a Turbofan Secondary Flow
System, “ASME Pater GT2004-53197.
[3] Stearns, E., Filburn, T., Cloud, D., 2006. “Probabilistic Thermal Analysis of Gas
Turbine Internal Hardware, “ ASME Paper GT2006-90881.
[4] Mercandante, A., Engineering Technical University, Pratt & Whitney, Flow 101,
Introduction to Flow Analysis.
[5] Moore, C., Engineering Technical University, Pratt & Whitney, Heat Transfer 303,
TOBI Flow Optimization.
[6] Research and Innovative Technology Administration, Bureau of Transportation
Statistics, found on the Federal Aviation Administration website, link to follow:
http://www.bts.gov/xml/air_traffic/src/datadisp.xml
[7] Saber, G.A.F., and Wild, C.J., 2003 Nonlinear Regression, Wiley-Interscience, N.Y.
[8] McKay, M.D.; Beckman, R.J.; Conover, W.J. (May 1979). "A Comparison of Three
Methods for Selecting Values of Input Variables in the Analysis of Output from a
Computer Code" (JSTOR Abstract). Technometrics Journal (American Statistical
Association) 21 (2): 239–245.
[9] Shapiro, Samuel S., and Gross, Alan J., 1981, Statistical Modeling Techniques,
Marcel Dekker, Inc. New York.
[10] Iman, R.L.; Helton, J.C.; and Campbell, J.E. (1981). "An approach to sensitivity
analysis of computer models, Part 1. Introduction, input variable selection and
preliminary variable assessment". Journal of Quality Technology 13 (3): 174–183.
[11] Iman, R.L.; Davenport, J.M. ; Zeigler, D.K. (1980). Latin hypercube sampling
(program user's guide).
[12] http://en.wikipedia.org/wiki/Latin_hypercube_sampling
[13] http://en.wikipedia.org/wiki/Linear_regression
[14] Fox, R.W., McDonald, A.T., Pritchard, P.J. 2004 Introduction to Fluid Mechanics,
John Wiley & Sons, Inc.
45
[15] Shapiro, A. H. 1953 The Dynamics and Thermodynamics of Compressible Fluid
Flow, John Wiley & Sons, New York, Chichester, Brisbane, Toronto, Singapore
[16] FABL++ Manual, February 15, 2008, PowerVision.
46
8. Appendix
8.1 Flow Model Input File – Sample only, not complete
** TITLE Revisions to final FBIN94A2 from xxxx to make final FBIN94A2
R4079 RPMF changed from 0.4 to 0.46 R4020,R4019 RPMF changed from 0.4
to 0.48 R4018 RPMF changed from 0.4 to 0.5 R8557 HPC OD seal Cl
adjusted from 0.0051 to 0.0075 to match PRHOS (C8504) R8559 HPC ID Seal
Cl adjusted from 0.021 to 0.0275 to match PRHIS (C8506) R4015 TOBI OD
seal cl adjusted from 0.013 to 0.012 R4011 TOBI ID Seal Cl adjusted
from 0.009 to 0.011 Updations in the model - mail by xxxxx dated 16 Apr
2004 (to xxxxx) - in comparison with FBINM22B R4010 TOBI changed from
Type-4 to Type-1 restrictor with Flow parameter curve points sent by
John (w.r.txxxxxxx mail) R4061 Changed from Type-2 to Type 4 with an
area of 0.5986 and Cd = 0.9 R4013 Created a restrictor (Type 4) with an
area of 0.0841 and Cd = 1.0 R4013 Deleted C4001 Deleted R4028 RPMF =
1.23 and N = 0.98(Vortex Exponent) introduced w.r.t RPM2 R4033 Relative
RPMF changed from 0.35 to 0.33 -------------------------------------------------------------------- Revisions to FBIN94A2 from xxxxx to make
final FBIN94A2 Change from Block 4 to Block 2 LPT C8509 .265 KT to
match T5BGS R5052 Clearance .0468 --> .052 to match P5BGS C659 Kp .4372
--> .4352 to match P9MAN R5529 .19 --> .229 to match P2VOC R5526 .0925
--> .112 to match P2VOC R5528 .17425 --> .210 to match P2VOC OAS area
based on X877-2 changes from D. Kane R4704 Cd .8 --> .9 Nozzle R4739
.001 --> .0025 Brush seal gap R4710 .004 --> .001 Coordal gap R4703
.001 --> .0005 Rear W seal TOBI Mach # ------------------------------------------------ xxxxxxxxxxxxxxxxxxxxxxx 03/11/2004. Revisions to
FBIN94A1 to FBIN94A2 (Datamatch) Performance data from ADR # 204 (X87904a) Gas path Statics data from xxxxxxxxxxxxxxxx 2/26/2004 LPT gas path
statics from spreadsheet from xxxxxx 3/3/04 ------ Low Shaft Flow
System R5052 LPT KE Seal Clearance 0.017 to 0.0468 to match P5BGS
(C8509) ------ TOBI Flow System C612 Kp 0.8712 to 0.8538 to match P11TO
(C612) Kt 1.047 to 1.072 to match T11TO R3034 RPMF 0.7 to 0.1 to match
P11TI (C8511) R8556 RPMF 0.8 to 0.19 to match P11TI C8511 Constant
value in equation is adjusted from +110 to +77 to match T11TI R8557 KE
Clr 0.0138 to 0.0051 to match PRHOS (C8504) C8504 Constant Temp value
in eqn is adjusted from +170 to +222.5 to match TRHOS R8559 RPMF value
0.1 to 0.48 to match PRHIS & TRHIS (C8506)
R8561 KE Cl 0.035 to 0.021 to match PDIWR (C8519) --- To match PTOBD
(C4004) R4011 KE Cl 0.02 to 0.009 R4015 KE Cl 0.01145 to 0.013 R4018
RPMF 0.5 to 0.1 R4019 RPMF 0.48 to 0.1 R4020 RPMF 0.46 to 0.1 R4079
RPMF 0.46 to 0.1 C702 Kp from 0.3169 to 0.3190 to match P1VITL (Gas
path Statics reads Kp = 0.3225) ------ Rotor ID Bleed Flow System C609
Kp from 0.4385 to 0.3927 to match P9MCI (C3007) Kt from 0.7315 to
0.7748 to match P9MCI (C3007) --To match PLFSF (C5012) R4073 RPMF from
0.36 to 0.1,free to forced R4074 RPMF from 0.5 to 0.1, free to forced
R4075 RPMF from 0.5 to 0.1, free to forced C5009 Kp from 0.364 to 0.667
to match PLFSR (C5005) R5021 LT KE Cl 0.0381 to 0.03 to match PLFSR
R5011 LT KE Cl 0.0213 to 0.029 to match PLFSR C802 Kp 0.5716 to 0.6176
to match P2SIR C753 Kp -0.0802 to -0.0562 to match P1BRR C5002 Kp from
0.667 to 0.5 to match PHLIC (C5001) R5001 Area 0.286 to 0.25 to match
PHLIC R5002 Area 0.37 to 1.23 to match PHLIC R5006 Area 0.11 to 0.093
to match PHLIC Flow direction reversed - R5072,5007,4073,4074 & 4075. ----- TCA & LT Case Cooling Flow System C659 Kp 0.4456 to 0.4372 to
match P9MAN (C3578) Kt 0.7667 to 0.7119 to match T9MAN (C3578) R5521
Area 0.075 to 0.0919 to match P2VOC (C5506) R5526 Area 0.335 to 0.4104
47
to match P2VOC (C5506) R5528 Area 0.070 to 0.0858 to match P2VOC
(C5506) - 22.5% C851 Kp 0.8712 to 0.78 to match P2VOF (C851) ------ HT
& BOAS Flow System C649 Constant value from 0.976 to 0.9785 C752 Kp
from 0.4587 to 0.4633 as per GasPath Statics (C752 - As per measured
data Kp = 0.4612 - Reverse flow noticed in R4705) ------ Miscellaneous
Chambers C657 Kp from 0.2742 to 0.2771 to match P8MAN (C3500) R3009
RPMF from 0.4 to 0.64 to match P3BGS (C3055) ------------------------------------------------------- X879-04 Pretest TCOOL. Based on FBINM08B
HPT Aero per xxxxxxxxxxxx 12/12/03 Blade curve per xxxxxxxxxxxx e-mail.
Revisions to FBINM04B to produce TCOOL FBINM08B: Performance ----------- DT2455.1 (3/26/02) PT#159 (SL/0.25/+27F) Fan & LPC
---------- No updates. HPC ---- HPC flow network modeled to reflect MTU
V01 HPC. HPC gaspath static pressures were originally updated per MTU
CM#6E-MP-6121. However, due to discrepancies between the streamline and
X872-9 data, the data was used for the OD pressures. The ID pressures
were ratioed based on the ratio between pressures from the OD
streamline vs OD data. The gaspath pressure at S11 LE was further
updated to reflect a higher pressure, which is more consistent with
MTU's original streamline assessment. HPC ID Bleed system was updated
using P966 gui to account for RPMF thru various cavities. RPMF from
p966 were found to match MTU's RPMFs from CFD. Filename:
FBINM08B_all.p966gui Updated TBS ID 3KE seal to 2KE and KE radius per
UG x-section (9/20/02) Sized Thrust balance holes to meet nominal 4000
lbs target (R8560). Corrected lab seal clearance for S11 (R3005) to
0.0150", instead of 0.150". Added flow network to account for flow thru
HPC shielding holes and flow moving forward of giggle tube to HPC oil
weep holes. Sized giggle tube system to meet 0.88% W25 intershaft flow.
HPT ---- xxxxxxxx - 12/17/02 Updated blade platform sealing
configuration per redesign: New Restrictions 4057, 4060, 4058, 4062,
4063 New Chambers 4010, 4029 (ps from Block 2 Navier Stokes, aero)
Modified Restrictions 4038, 4082, 4040, 4042, 4044, 4043 Additional
flow splits 4010 to 702, 4029 to 703 Modified Flow Splits 4000 to 703
Updated blade curves and dump pressures from xxxxxxxxxxx (TMC
durability), 12/16/02 Base-Line is scheme 2 Modified Restrictions 4034,
4035, 4036 Modified Chambers 960, 961, 962 Updated TOBI flow system to
maintain nominal blade supply pressure (0.987 Ps/Pt4.1rel) Modified
Restrictions 4010, 4013, 4027, 4028 Modified Chamber 4003 Updated
gaspath statics & corresponding info per xxxxxx for 0.025" clearance
(7/30/02). Flow model was passed to ASDI from xxxxxxxx. See xxxxxx
section (below) for detailed HPT updates.
Disconnectd paired HPT Vanes OD to account for single set of 38
asymetric vanes: This included R4504, R4505, R4520, R4519, R4515,
R4516, R4517 & R4518 (R4004 was also changed in HPT ID). Updated 1st
vane flows per xxxxxxxxxx (9/09/02). Total flow = 10.823%W25. TOBI
bypass holes were sized to meet 0.500% W25 flow. Set TOBI ID seal
clearance to an average of 0.020" to meet thrust balance and blade
supply requirements and to minimize TOBI pollution flow. LPT ---Updated gaspath pressures with xxxxxx LPT gaspath pressures from
presentation sent 12/06/02. Updated all lab seals to reflect a 1/16"
honeycomb cell density and downstep seal designs (vs upstep). Nearly
all LPT restrictors were resized to match MTU's Block 4 flows in the
LPT case and rotor. Externals --------- TCA System - orifice sizes for
both 2nd (4 plcs) & 3rd vane have been resized to reflect MTU's case
flows. Buffer Cooler Hot Out fixed temperature (C8032) changed to Kt
Created restrictor to account for leakage in actuating solenoids for
start/stability & TCA valves from one of the buffer cooler pipes
(R8034). Removed restrictor (R7003) representing oil weep tube valve,
48
based on recommendation of design chiefs. Added changes from FBINM06B:
Remove extra restriction at front of TCA pipes R8000, 8001, 8002, 8003
Change area from 0.5(0) to 1.45 and make pipe orifice TCA orifices
R8017, 8018, 8019, 8020 change ACd to A=0.20 Cd=0.8 Jumper orifices
R8026, 8028 change ACd to A=0.047 Cd=0.8 Put in ACd for 2nd vane flow
R5524 A=0.549 Cd=1.0 Corrections to 6 stage bearing load section C612
inner radius 8.506 Remove chamber 901 (double book keeping) C3022 inner
radius 5.272 R3017, 3021 removed KE pitch (1 KE seal) R7503, Changed
start of FP curve from 0.0 0.0 to 1.0 0.0 ** TCHEADER
6024TC0336LH04FB94A16024 1265 X879-04 Pretest TCOOL ** FLSPLIT HTPIF702
4503 TCA HT01SLEI 701 TCA 1. 0 HTPO1751 4508 TCA HT01SLEO 751 TCA 1. 0
HTPO2751 4507 TCA HT01SLEO 751 TCA 1. 0 HTPO3751 4506 TCA HT01SLEO 751
TCA 1. 0 HTPO4751 4505 TCA HT01SLEO 751 TCA 1. 0 HTPO5751 4502 TCA
HT01SLEO 751 TCA 1. 0 HTPO6751 4500 TCA HT01SLEO 751 TCA 1. 0 HTBTIP01
4523 TCA HT01RLEO 752 TCA 1. 0 HTBTIP02 4524 TCA HT01RLEO 752 TCA 1. 0
HTBTIP03 4525 TCA HT01RLEO 752 TCA 1. 0 HTBTIP04 4526 TCA HT01RTEO 753
TCA 1. 0 HTBTIP05 4527 TCA HT01RTEO 753 TCA 1. 0 HTBTIP06 4528 TCA
HT01RTEO 753 TCA 1. 0 TDUCTID1 5002 TCA HT01RTEI 703 TCA 0.5LT01SLEI
801 TCA 0.5 0 TDUCTOD2 4533 TCA HT01RTEO 753 TCA 1. 0 TDUCTOD1 4532 TCA
HT01RTEO 753 TCA 1. 0 TDUCTOD3 4534 TCA LT01SLEO 851 TCA 1. 0 HT702703
4048 TCA HT01RTEI 703 TCA 0.7HT01RLEI 702 TCA 0.3 0 HT01PLE 4049 TCA
HT01RLEI 702 TCA 1. 0 HT1VTEI 4050 TCA HT01RLEI 702 TCA 1. 0 HT01PFLE
4010 TCA HT01RLEI 702 TCA 1. 0 HTPF702* 4000 TCA HT01RTEI 703 TCA 1. 0
HT01DFTE 4029 TCA HT01RTEI 703 TCA 1. 0 ** CONTROL PREF 409.81 WREF
113.54 TREF 948.51 SUMFLOWS 0.0008 ITERATIONS 500. TCOOL RSTART RESEQ
FMAP CONSERV_ITER 500. ** EQUATION BOASGAP = 0.025 TPERF6 = 1809.11
TREF45 = TPERF6
TPERF5 = 2742.01 TREF4 = TPERF5 CTMP4000 = 0.643*(TREF4-TREF45)+TREF45
TPERF4 = 948.513 CTMP4010 = 0.738*(TREF4-TREF45)+TREF45 CTMP4029 =
0.40754*(TREF4-TREF45)+TREF45 CTMP4048 = 0.40754*(TREF4-TREF45)+TREF45
CTMP4049 = 0.738*(TREF4-TREF45)+TREF45 CTMP4050 = TREF4 CTMP4500 =
TREF4 CTMP4502 = TREF4 CTMP4503 = TREF4 CTMP4504 = TREF4 CTMP4505 =
TREF4 CTMP4506 = TREF4 CTMP4507 = TREF4 CTMP4508 = TREF4 CTMP752 =
0.738*(TREF4-TREF45)+TREF45 CTMP753 = -0.027*(TREF4-TREF45)+TREF45
CTMP4523 = (CTMP752-CTMP753)*(6/7)+CTMP753 CTMP4524 = (CTMP752CTMP753)*(5/7)+CTMP753 CTMP4525 = (CTMP752-CTMP753)*(4/7)+CTMP753
CTMP4526 = (CTMP752-CTMP753)*(3/7)+CTMP753 CTMP4527 = (CTMP752CTMP753)*(2/7)+CTMP753 CTMP4528 = (CTMP752-CTMP753)*(1/7)+CTMP753
CTMP4532 = CTMP753 CTMP4533 = CTMP753 TPERF7 = 1219.51 TREF49 = TPERF7
TREF3 = TPERF4 CTMP4703 = TREF3+100 CTMP4704 = TREF3+100 CTMP4708 =
TREF3+100 CTMP801 = 0.999*(TREF45-TREF49)+TREF49 CTMP703 = 0.0788*(TREF4-TREF45)+TREF45 CTMP5002 = (CTMP703+CTMP801)/2 CTMP802 =
0.977*(TREF45-TREF49)+TREF49 CTMP5009 = (CTMP801+CTMP802)/2 CTMP804 =
0.711*(TREF45-TREF49)+TREF49 CTMP803 = 0.711*(TREF45-TREF49)+TREF49
CTMP5021 = (CTMP803+CTMP804)/2 CTMP806 = 0.375*(TREF45-TREF49)+TREF49
CTMP805 = 0.375*(TREF45-TREF49)+TREF49 CTMP5027 = (CTMP805+CTMP806)/2
CTMP5033 = (CTMP802+CTMP803)/2 CTMP5043 = (CTMP804+CTMP805)/2 CTMP807 =
-0.008*(TREF45-TREF49)+TREF49 CTMP5045 = (CTMP806+CTMP807)/2 TPERF2 =
35.011 TREF2 = TPERF2 TPERF3 = 220.391 TREF25 = TPERF3 CTMP510 = 0.000*(TREF25-TREF2)+TREF2 CTMP518 = 1.057*(TREF25-TREF2 )+TREF2
CTMP560 = 0.467*(TREF25-TREF2)+TREF2 CTMP568 = 565. CTMP600 =
0.000*(TREF3-TREF25)+TREF25
CTMP601 = 0.000*(TREF3-TREF25)+TREF25 CTMP602 = 0.1704*(TREF3TREF25)+TREF25 CTMP603 = 0.1704*(TREF3-TREF25)+TREF25 CTMP604 =
0.3508*(TREF3-TREF25)+TREF25 CTMP605 = 0.3508*(TREF3-TREF25)+TREF25
CTMP606 = 0.5497*(TREF3-TREF25)+TREF25 CTMP607 = 0.5497*(TREF3TREF25)+TREF25 CTMP608 = 0.7324*(TREF3-TREF25)+TREF25 CTMP609 =
49
0.7748*(TREF3-TREF25)+TREF25 CTMP610 = 0.8987*(TREF3-TREF25)+TREF25
CTMP611 = 0.8987*(TREF3-TREF25)+TREF25 CTMP649 = TREF3 CTMP650 =
0.000*(TREF3-TREF25)+TREF25 CTMP651 = -0.000*(TREF3-TREF25)+TREF25
CTMP652 = 0.1937*(TREF3-TREF25)+TREF25 CTMP653 = 0.1937*(TREF3TREF25)+TREF25 CTMP654 = 0.3893*(TREF3-TREF25)+TREF25 CTMP655 =
0.3893*(TREF3-TREF25)+TREF25 CTMP656 = 0.5927*(TREF3-TREF25)+TREF25
CTMP657 = 0.5901*(TREF3-TREF25)+TREF25 CTMP658 = 0.7692*(TREF3TREF25)+TREF25 CTMP660 = 0.9245*(TREF3-TREF25)+TREF25 CTMP661 =
0.9245*(TREF3-TREF25)+TREF25 CTMP662 = 1.0817*(TREF3-TREF25)+TREF25
CTMP698 = 0.152*(TREF3-TREF25)+TREF25 CTMP699 = TREF3 CTMP701 =
1.000*(TREF4-TREF45)+TREF45 CTMP751 = 1.000*(TREF4-TREF45)+TREF45
CTMP8030 = 0.152*(TREF3-TREF25)+TREF25 CTMP8032 = 0.152*(TREF3TREF25)+TREF25 CTMP8511 = TREF3 + 77 CTMP852 = 0.977*(TREF45TREF49)+TREF49 CTMP853 = 0.711*(TREF45-TREF49)+TREF49 CTMP854 =
0.7119*(TREF45-TREF49)+TREF49 CTMP855 = 0.375*(TREF45-TREF49)+TREF49
CTMP856 = 0.375*(TREF45-TREF49)+TREF49 CTMP857 = -0.008*(TREF45TREF49)+TREF49 TPERF1 = 35.011 CTMP901 = TPERF1 CTMP904 = TPERF1
CTMP950 = (CTMP701+CTMP751)/2 CTMP702 = 0.738*(TREF4-TREF45)+TREF45
CTMP951 = (CTMP702+CTMP752)/2 CTMP952 = CTMP751 CTMP953 = CTMP751
CTMP960 = 0.738*(TREF4-TREF45)+TREF45 CTMP961 = 0.40754*(TREF4TREF45)+TREF45 CTMP962 = (CTMP703+CTMP753)/2 CTMP964 = -0.027*(TREF4TREF45)+TREF45 CTMP982 = (CTMP802+CTMP852)/2 CTMP999 = 0.467*(TREF25TREF2)+TREF2 FANA = ( 549.8880 - ( -281.49)) / ( 1.7005 - 1.0) FANB = 281.49 - FANA HPTA = (-155.55- ( 6.962548))/ (4.02 - 1.0) HPTB =
6.962548 - HPTA PPERF2 = 14.707 PPERF14 = 25.940
LOADFN1 = FANA * PPERF14 + FANB * PPERF2 PREF2 = PPERF2 PPERF3 = 39.756
PREF25 = PPERF3 PRES510 = -0.125*(PREF25-PREF2)+PREF2 PSPIN = (PRES510
+ PREF2)/2 SPNAREA = 3.14*(9.323*9.323) LOADHC1 = -1*(SPNAREA * PSPIN)
PPERF4 = 409.81 PREF3 = PPERF4 P3OP25=PREF3/PREF25 LOADHC2 = (1.99*(P3OP25**2)+61.472*P3OP25-104.67)*PREF25 PPERF6 = 97.251 PPERF5 =
388.433 LOADHT2 = HPTA * PPERF5 + HPTB * PPERF6 LPCA = ( 185.9050 - (
7.5710)) / ( 2.7263 - 1.0) LPCB = 7.57100 - LPCA LOADLC1 = LPCA *
PPERF3 + LPCB * PPERF2 PPERF7 = 24.002 LPTA = ( -778.800 - (-81.6667))
/ ( 3.983950 - 1.0) LPTB = -81.6667 - LPTA LOADLT1 = LPTA * PPERF6 +
LPTB * PPERF7 PPERF8 = 14.707 PAMB = PPERF8
$======================================================================
$ BEGIN MISC. EQNS
$======================================================================
$$ airfoil cooling levels set as %W252(W25) PCTW252 = (113.541/100.) $
perf sta1 = 1 $ perf sta2 = 2 $ perf sta3 = 25 $ perf sta4 = 3 $ perf
sta5 = 4 $ perf sta6 = 45IL $ perf sta7 = 49 $ perf sta8 = AMB
$======================================================================
$ PERFORMANCE CONDITION PPERF1 = 14.707 PREF14 = PPERF14 PREF4 = PPERF5
PREF45 = PPERF6 PREF49 = PPERF7 PRES703 = (-0.0562*(PREF4PREF45)+PREF45)+M703*PREF3 PRES702 = (0.3190*(PREF4PREF45)+PREF45)+M702*PREF3 PRES4000 = ((0.4543+0.0906)/2)*(PRES702PRES703)+PRES703 PRES4010 = ((1.000+0.8180)/2)*(PRES702PRES703)+PRES703 PRES4029 = 0.4543*(PRES702-PRES703)+PRES703 PRES4048 =
0.2276*(PREF4-PREF45)+PREF45 PRES4049 = ((0.6363+0.4543)/2)*(PRES702PRES703)+PRES703 PRES701 = 0.9762*(PREF4-PREF45)+PREF45+M703*PREF3
PRES4050 = .3201*(PRES701-PRES702)+PRES702 PRES752 = 0.4633*(PREF4PREF45)+PREF45 PRES751 = 0.9734*(PREF4-PREF45)+PREF45 PRES4500 =
(3*PRES751+PRES752)/4 PRES4502 = .871*PREF3
PRES4503 = 0.786 * PREF3 PRES4504 = 0.2134*(PRES701-PRES702)+PRES702
PRES4505 = .842*PREF3 PRES4506 = .813*PREF3 PRES4507 = .784*PREF3
PRES4508 = .7549*PREF3 PRES753 = -0.1151*(PREF4-PREF45)+PREF45 PRES4523
= .9810*(PRES752-PRES753)+PRES753 PRES4524 = .9068*(PRES752-
50
PRES753)+PRES753 PRES4525 = .7707*(PRES752-PRES753)+PRES753 PRES4526 =
.4737*(PRES752-PRES753)+PRES753 PRES4527 = .0134*(PRES752PRES753)+PRES753 PRES4528 = .0085*(PRES752-PRES753)+PRES753 PRES851 =
0.78*(PREF45-PREF49)+PREF49 PRES4532 = .927*(PRES753-PRES851)+PRES851
PRES4533 = .634*(PRES753-PRES851)+PRES851 PRES801 = 0.7239*(PREF45PREF49)+PREF49 PRES5002 = 0.5*(PRES703-PRES801)+PRES801 PRES802 =
0.6176*(PREF45-PREF49)+PREF49 PRES5009 = .667*(PRES801-PRES802)+PRES802
PRES804 = 0.2574*(PREF45-PREF49)+PREF49 PRES803 = 0.4200*(PREF45PREF49)+PREF49 PRES5021 = (PRES803+PRES804)/2 PRES806 = 0.0363*(PREF45PREF49)+PREF49 PRES805 = 0.1494*(PREF45-PREF49)+PREF49 PRES5027 =
(PRES805+PRES806)/2 PRES5033 = (PRES802+PRES803)/2 PRES5043 =
(PRES804+PRES805)/2 PRES807 = -0.0592*(PREF45-PREF49)+PREF49 PRES5045 =
(PRES806+PRES807)/2 PRES518 = 0.703*(PREF25-PREF2 )+PREF2 PRES560 =
0.198*(PREF25-PREF2)+PREF2 PRES568 = 0.746*(PREF25-PREF2 )+PREF2
PRES600 = -0.0097*(PREF3-PREF25)+PREF25 PRES601 = -0.0100*(PREF3PREF25)+PREF25 PRES602 = 0.0126*(PREF3-PREF25)+PREF25 PRES603 =
0.0513*(PREF3-PREF25)+PREF25 PRES604 = 0.0854*(PREF3-PREF25)+PREF25
PRES605 = 0.1396*(PREF3-PREF25)+PREF25 PRES606 = 0.1977*(PREF3PREF25)+PREF25 PRES607 = 0.2648*(PREF3-PREF25)+PREF25 PRES608 =
0.3699*(PREF3-PREF25)+PREF25 PRES609 = 0.3927*(PREF3-PREF25)+PREF25
PRES610 = 0.5849*(PREF3-PREF25)+PREF25 PRES611 = 0.6704*(PREF3PREF25)+PREF25 PRES649 = 0.9785 * PREF3+M649*(PREF3) PRES650 = 0.0168*(PREF3-PREF25)+PREF25 PRES651 = -0.0153*(PREF3-PREF25)+PREF25
PRES652 = 0.0270*(PREF3-PREF25)+PREF25 PRES653 = 0.0538*(PREF3PREF25)+PREF25 PRES654 = 0.0994*(PREF3-PREF25)+PREF25 PRES655 =
0.1462*(PREF3-PREF25)+PREF25 PRES656 = 0.2174*(PREF3-PREF25)+PREF25
PRES657 = 0.2771*(PREF3-PREF25)+PREF25 PRES658 = 0.3877*(PREF3PREF25)+PREF25 PRES660 = 0.5981*(PREF3-PREF25)+PREF25 PRES661 =
0.6694*(PREF3-PREF25)+PREF25
PRES662 = 0.8842*(PREF3-PREF25)+PREF25 PRES698 = PPERF4*.976 PRES699 =
PREF3*.976 PRES852 = 0.6964*(PREF45-PREF49)+PREF49 PRES853 =
0.4944*(PREF45-PREF49)+PREF49 PRES854 = 0.3467*(PREF45-PREF49)+PREF49
PRES855 = 0.2028*(PREF45-PREF49)+PREF49 PRES856 = 0.0753*(PREF45PREF49)+PREF49 PRES857 = -0.0364*(PREF45-PREF49)+PREF49 PRES899 =
.035*PREF3 PRES901 = PAMB+0.5 PRES904 = PAMB PRES905 = PAMB+0.5 PRES950
= 0.8568*PREF3 PRES951 = 0.6648*PREF3 PRES952 = 0.6338*PREF3 PRES953 =
0.6723*PREF3 PTREL4.1 = 0.542*PREF3 PRES960 = 0.87764*PTREL4.1 PRES961
= 0.81829*PTREL4.1 PRES962 = 0.59425*PTREL4.1 PRES964 = 0.163011*PPERF4
PRES982 = (PRES802+PRES852)/2 PRES999 = 0.198*(PREF25-PREF2)+PREF2
$======================================================================
$ RPM FACTORS RPM1 = 5539.86 RPM2 = 17537.5 RSAR4038 = 1.051/2*0.002*60
RSAR4058 = 0.014*0.025*60 RSAR4062 = 0.005*0.025*60 RSAR4063 =
0.078*0.002*60 RSAR4082 = 1.051/2*0.002*60 RSAR4600 =
36*9*.014*.014*3.14/4 RSAR4601 = 36*13*.014*.014*3.14/4 RSAR4602 =
36*13*.014*.014*3.14/4 RSAR4603 = 36*11*.014*.014*3.14/4 RSAR4604 =
36*9*.014*.014*3.14/4 RSAR4605 = 36*8*.014*.014*3.14/4 RSAR4606 =
36*2*.019*.019*3.14/4 RSAR4607 = 36*2*.019*.019*3.14/4 RSAR4608 =
36*2*.019*.019*3.14/4 RSAR4609 = 36*2*.019*.019*3.14/4 RSAR4610 =
36*2*.019*.019*3.14/4 RSAR4611 = 36*2*.019*.019*3.14/4 RSAR4612 =
36*2*3.14*.019*.019/4 RSAR4613 = 36*2*.019*.019*3.14/4 RSAR4616 =
.03*.6*36 RSAR4617 = 36*.03*.5 RSAR4618 = 36*.03*.6 RSAR4619 =
38*16*0.785*0.00000016**2 RSAR4620 =
38*.095/0.707*.0005*1.0+.5*.0005*1.0*38 VANEGAP = 0.017 RSAR4621 =
((.119*2+VANEGAP)*.030-.2*.030)*38 RSAR4622 =
38*.36*.002*1.+0.36*.002*1.*38 RSAR4623 =
38*VANEGAP*.095/0.707+38*(0.476*0.030-0.294*0.009) RSAR4624 =
38*VANEGAP*(0.045/0.707)
51
RSAR4625 = 12.55*2*3.14*.0005 SUPPGAP = 0.025 RSAR4626 = 18*.03*SUPPGAP
RSAR4627 = 38*6*.785*.07**2 RSAR4628 =
18*0.600**2*3.14/4+2*18*0.300**2*3.14/4 RSAR4629 = 180000*3.14*.5*.05
RSAR4630 = 18*.022*(2*0.16+SUPPGAP) RSAR4631 = 18*.128*0.0005 RSAR4632
= 18*0.18*0.003 RSAR4633 = 18*SUPPGAP*.02 RSAR4634 = 13.7*2*3.14*0.0005
RSAR4635 = .02*.4 RSAR4636 =
(2*3.14*13.7)/(1/(.0005**2)+1/(.0005**2)+1/(.0005**2))**(.5) RSAR4650 =
1.2*0.0005*18
8.2 Complete Probabilistic Input File
**
*
*
*
SENSITIVITY INPUT FILE FORMAT
Use '*' at first column for comments
PW6000 probabilistic study thesis, 3rd refinement
Questions: Ping Dang @7-2506
** INPUT PARAMETERS IN THE EQUATION/MUDS LIST (DONOT MODIFY THIS LINE
!)
* Parameter (exact as left hand of EQUATIONS) + standard deviation +
Distribution type + Truncated value
* note:
Distribution type: Uniform ( = 0), Normal ( = 1)
and Truncated Normal (= 2)
*
Truncated value if for Truncated Normal (= 2)
only
*
*Gaspath Pressures at stations 4, 45 (St.dev=0.1% of avg)
PPERF5
0.3884
2
0.7769 *(avg=388.40)
PPERF6
0.0973
2
0.1945 *(avg=97.30)
*TPERF5 (avg=3173.7)
*TPERF6 (avg=1955.5)
*
** INPUT PARAMETERS NOT IN THE EQATION/MUDS LIST (DONOT MODIFY THIS
LINE !)
* Parameter + mean value + standard deviation + Distribution type +
Truncated value
* note:
Distribution type: Uniform ( = 0), Normal ( = 1)
and Truncated Normal (= 2)
*
Truncated value if for Truncated Normal (= 2)
only
*
* CHAMBERS:
Parameter = PRESxxxx (xxxx is ID NUMBER)
*
CTMPxxxx
*
RxINRDxxxx (Inner Radius for rotor x chamber
xxxx)
*
RxOURDxxxx (Outer Radius for rotor x chamber
xxxx)
*
x is rotor real number!
*
*
RESISTOR TYPES APPLICABLE
* RESTRICTOR: Parameter = RSARxxxx
1, 2, 4(area)
*
RSCDxxxx
1, 2, 4(CD)
*
RSFLxxxx
2
(Flow)
*
MXRIxxxx
3
(Largest Radius of
labseal)
52
*
STHTxxxx
3
(step Height of
labseal)
*
CLEAxxxx
3
(Cleanrance)
*
UPRIxxxx
6
(upstream radius)
*
DWRIxxxx
6
(downstream radius)
*
RSRFxxxx
6
(RPMF)
*
RSEXxxxx
6
(Vortex exponent)
*
ORARxxxx
8
(Orifice area)
*
PIARxxxx
8
(Pipe area)
*
*Type 1,2,4 Restrictions (St.Dev 2-5% of Avg.)
RSAR7586
0.446
0.00892
2
0.01784
RSAR7584
0.1533
0.003066
2
0.006132
RSAR4092
1.644
0.03288
2
0.06576
RSAR4002
0.00181
0.0000362
2
0.0000724
RSAR4022
1
0.02
2
0.04
RSAR4061
0.5986
0.011972
2
0.023944
RSAR4017
0.003
0.00006
2
0.00012
RSAR4023
0.9923
0.019846
2
0.039692
RSAR8591
5.89
0.1178
2
0.2356
RSAR8503
38
0.76
2
1.52
RSAR7000
0.004
0.0002
2
0.0004
RSAR7001
0.004
0.0002
2
0.0004
RSAR7002
0.004
0.0002
2
0.0004
RSAR4027
9.204
0.18408
2
0.36816
RSAR4086
0.6675
0.033375
2
0.06675
RSAR4085
6.467
0.32335
2
0.6467
RSAR4037
5.658
0.2829
2
0.5658
RSAR4081
0.0001
0.000005
2
0.00001
RSAR4030
0.0815
0.004075
2
0.00815
RSAR4048
7.2
0.36
2
0.72
RSAR4069
0.0267
0.001335
2
0.00267
RSAR4072
0.02419
0.0012095
2
0.002419
RSAR4071
0.02419
0.0012095
2
0.002419
RSAR4049
0.2006
0.01003
2
0.02006
RSAR4053
0.092
0.0046
2
0.0092
RSAR4034
1
0.05
2
0.1
RSAR4035
1
0.05
2
0.1
RSAR4036
1
0.05
2
0.1
RSAR4077
60
3
2
6
RSAR4010
1
0.015
2
0.03
*
*TOBI ID/OD Lab Seals (St.dev 5-15% of CLR)
MXRI4011
6
0.12
2
0.24
CLEA4011
0.008
0.0004
2
0.0008
MXRI4015
7.56
0.1512
2
0.3024
CLEA4015
0.012
0.0018
2
0.0036
*
*Blade Platform Leakages (St.Dev 25% of Avg.)
RSAR4038
0.06306
0.015765
2
0.03153
RSAR4082
0.06306
0.015765
2
0.03153
RSAR4057
0.03
0.0075
2
0.015
RSAR4040
0.03024
0.00756
2
0.01512
RSAR4060
0.03
0.0075
2
0.015
RSAR4042
0.036
0.009
2
0.018
RSAR4076
6.721
1.68025
2
3.3605
RSAR4044
0.069
0.01725
2
0.0345
53
RSAR4043
0.012
0.003
2
0.006
RSAR4013
0.0841
0.021025
2
0.04205
RSAR4058
0.0021
0.000525
2
0.00105
RSAR4045
0.123
0.03075
2
0.0615
RSAR4063
0.00936
0.00234
2
0.00468
RSAR4062
0.0075
0.001875
2
0.00375
RSAR4047
0.42
0.105
2
0.21
RSAR4059
10.725
2.68125
2
5.3625
*
*Vane Platform Leakages (St.Dev 25% of Avg.)
RSAR4004
0.03968
0.00992
2
0.01984
RSAR4005
0.03366
0.008415
2
0.01683
RSAR4006
0.026281
0.00657025 2
0.0131405
RSAR4007
0.1347
0.033675
2
0.06735
RSAR4008
0.04864
0.01216
2
0.02432
RSAR4046
0.0627
0.015675
2
0.03135
RSAR4056
0.003602
0.0009005
2
0.001801
RSAR4055
0.0627
0.015675
2
0.03135
RSAR4009
0.0905
0.022625
2
0.04525
RSAR4054
0.04864
0.01216
2
0.02432
*
*RPM Factors Vortices (St.Dev 5% of Avg.)
RSRF4000
0.325
0.01625
2
0.0325
RSRF4001
0.12
0.006
2
0.012
RSRF4012
0.5
0.025
2
0.05
RSRF4014
0.7
0.035
2
0.07
RSRF4016
0.5
0.025
2
0.05
RSRF4018
0.5
0.025
2
0.05
RSRF4019
0.48
0.024
2
0.048
RSRF4020
0.48
0.024
2
0.048
RSRF4028
1.23
0.0615
2
0.123
RSRF4029
1
0.05
2
0.1
RSRF4079
0.46
0.023
2
0.046
RSRF4084
1
0.05
2
0.1
RSFR4052
1
0.05
2
0.1
RSRF4051
1
0.05
2
0.1
RSRF4050
1
0.05
2
0.1
RSRF4032
1
0.05
2
0.1
RSRF4068
1
0.05
2
0.1
RSRF4070
1
0.05
2
0.1
*
** OUTPUT PARAMETER (DO NOT MODIFY THIS LINE !)
* CHAMBER:
PRESxxxx / CTMPxxxx (xxxx is ID NUMBER)
* RESTRICTOR:
RSFLxxxx
* BEARING LOAD:
LOADx (x is the xth BL in the BL list. no always
the rotor number!)
*
*TOBI ID/OD Seal
RSFL4011
RSFL4015
RSFL4010
*Rim-cav
RSFL4085
RSFL4039
RSFL4076
*Blade Platform Leakage
RSFL4038
54
RSFL4082
RSFL4041
RSFL4057
RSFL4040
RSFL4060
RSFL4042
*Vane Platform Leakage
RSFL4004
RSFL4005
RSFL4006
RSFL4007
RSFL4008
RSFL4009
RSFL4046
RSFL4056
RSFL4055
RSFL4054
*Blade Cooling
RSFL4034
RSFL4035
RSFL4036
RSFL4077
*Blade Supply Pressures
PRES4003
PRES4004
CTMP4004
PRES4045
CTMP4045
PRES4013
CTMP4013
55
