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 Proposal Submitted to the Graduate
Faculty of Rensselaer Polytechnic Institute
in Partial Fulfillment of the
Requirements for the degree of
MASTER OF SCIENCE
Major Subject: MECHANICAL ENGINEERING
Approved:
_________________________________________
Timothy Wagner, RPI Thesis Advisor
_________________________________________
Roger Paollilo, Pratt and Whitney Thesis Advisor
Rensselaer Polytechnic Institute
Hartford, Connecticut
Abstract:
This paper will demonstrate a probabilistic study method that explores flow sensitivity of
design parameters relative to the high pressure turbine single stage pre-swirl cooling air
delivery and capture system of a turbofan engine. The goal of the proposed research is to
describe the drivers of variability of the subsystem and determine the variability of those
drivers. Probabilistic flow analysis has many applications in cost reduction, engine
design, optimization, and root cause analysis and has been discussed by others [1-3].
Introduction:
Among proprietary one dimensional secondary flow network solvers where the values of
the inputs are assumed to be exact, probabilistic analysis tools are being developed. The
inputs of probabilistic analysis methods such as Monte Carlo, Latin hypercube and others
assume a distribution of probable values rather than single values. The post processed
output will be used to determine variability and sensitivity of the design parameters in
hopes of identifying tolerances that can be loosened and possibly some that might require
tightening. This may be an iterative process.
Review of the previous work in the field indicates that there has been some work done
regarding probabilistic studies of secondary flow system’s sensitivity impacts on; overall
turbine cooling air system and bearing loads (Latin hypercube analysis), metal
temperatures (Latin hypercube analysis), and oxidation lifing (Monte Carlo analysis).
The proposed research will investigate a subsystem of the secondary flow system using
the Latin hypercube analysis, which is the pre-swirl capture and cooling air delivery
system of the high pressure turbine’s first stage. An attempt at identifying the variability
of the subsystem’s design parameters while still meeting system requirements will be
made.
Problem Statement:
It is the intention of this thesis to develop a method to perform a probabilistic secondary
flow analysis for a turbofan engine subsystem. The development of input parameters will
provide distribution (linear regression) of output parameters of the pre-swirl cavity
capture and delivery cooling air system. The output will be used to determine variability
of manufacturing tolerances of the pre-swirl cavity capture and delivery system that will
allow the secondary flow system to still meet system requirements.
Methodology:
Establish requirements for probabilistic model output. Determine what inputs will be
varied, what condition, and what model outputs will be needed. Examples of output
parameters are mass flow rates, supply pressures, air temperatures, windage, and heat
generation to name a few.
Step 1: Analytical Flow Model Definition.
Conduct extensive literature review on secondary flow system. Review the effects of
secondary air system not meeting requirement of cooling air flow; brush seal erosion,
over heated airfoils and platforms.
Step 2:
Determine the variation that will be applied to all selected inputs (2 sigma variation).
Engine to engine variability (manufacturing tolerances) and day to day (environment
condition) variability will need to be determined. Variability and uncertainty should be
given, from hardware owner to secondary flow analyst, separately, and then combined
statistically.
Step 3:
Modify steady state secondary flow model to accept probabilistic input.
Step 4:
Run secondary flow model with variation applied to selected inputs.
Step 5:
Verify secondary flow model and performance model calculations and applied input
variation versus expectations and deterministic model results.
Step 6:
Post-process output to determine output variability and sensitivity.
Step 7:
Collect data to validate assumptions on input variability (validation and verification
phase only unless component data is available during detailed design).
Step 8:
Collect data to validate system level output variability.
Goal:
The intention of the research proposed is to help identify ways to reduce manufacturing
cost, enhance engine design and component optimization and aid in root cause analysis of
the secondary flow system. The development of a standardized method for practitioners
to perform secondary flow analyses for subsystems will also be accomplished.
Tentative Thesis Milestones:
(October 20) Complete literature and analytical model review of commercial 1-D
deterministic flow models and develop probabilistic model input file draft. Run initial
probabilistic model.
(October 21) Provide reference material to advisor.
(October 26) Create draft intro/background.
(November 15th) Submit draft proposal, revised intro/background.
(November 18) Identify input parameters and variability, and output parameters to be
included in final analysis. Create final input file for probabilistic analysis. Run
probabilistic model. Identify main drivers of variability and compare to first pass.
Revise inputs/outputs if necessary.
(November 26) Create draft analysis portion of thesis.
(November 31) Refine method, and analysis.
(December 11) Submit approved Thesis.
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] Jarzombek, K., Dohmen, H. J., Benra, F.-K., Schneider, O., 2006. “Flow Analysis in
Gas Turbine Pre-Swirl Cooling Air Systems – Variation of Geometric Parameters,”
ASME Paper 2006-90445.
[5] United Technology Corporation, Reprinted with revisions in 1988, The Aircraft Gas
Turbine Engine and It’s Operation. Pratt and Whitney Operating Instructions 200.
[6] Kerrebrock, J.L., 1992, Aircraft Engines and Gas Turbines, The MIT Press,
Cambridge.
[7] Alexiou, A., Mathioudakis, K., 2009. “Secondary Air System Component Modeling
for Engine Performance Simulations, “ ASME Journal of Engineering for Gas Turbines
and Power, 131. pp. 031202-1 – 031202-9.