Design optimization and uncertainty quantification for aeromechanics forced response of a turbomachinery blade

• Main Author: Modgil, Girish A
• Format: Dissertation
• Language: English
• Published: ProQuest Dissertations & Theses 01-01-2013
• Subjects: Aerospace engineering; Applied Mathematics
• ISBN: 130332878X; 9781303328787

Gas turbine engines for aerospace applications have evolved dramatically over the last 50 years through the constant pursuit for better specific fuel consumption, higher thrust-to-weight ratio, lower noise and emissions all while maintaining reliability and affordability. An important step in enabling these improvements is a forced response aeromechanics analysis involving structural dynamics and aerodynamics of the turbine. It is well documented that forced response vibration is a very critical problem in aircraft engine design, causing High Cycle Fatigue (HCF). Pushing the envelope on engine design has led to increased forced response problems and subsequently an increased risk of HCF failure. Forced response analysis is used to assess design feasibility of turbine blades for HCF using a material limit boundary set by the Goodman Diagram envelope that combines the effects of steady and vibratory stresses. Forced response analysis is computationally expensive, time consuming and requires multi-domain experts to finalize a result. As a consequence, high-fidelity aeromechanics analysis is performed deterministically and is usually done at the end of the blade design process when it is very costly to make significant changes to geometry or aerodynamic design. To address uncertainties in the system (engine operating point, temperature distribution, mistuning, etc.) and variability in material properties, designers apply conservative safety factors in the traditional deterministic approach, which leads to bulky designs. Moreover, using a deterministic approach does not provide a calculated risk of HCF failure. This thesis describes a process that begins with the optimal aerodynamic design of a turbomachinery blade developed using surrogate models of high-fidelity analyses. The resulting optimal blade undergoes probabilistic evaluation to generate aeromechanics results that provide a calculated likelihood of failure from HCF. An existing Rolls-Royce High Work Single Stage (HWSS) turbine blisk provides a baseline to demonstrate the process. The generalized polynomial chaos (gPC) toolbox which was developed includes sampling methods and constructs polynomial approximations. The toolbox provides not only the means for uncertainty quantification of the final blade design, but also facilitates construction of the surrogate models used for the blade optimization. This paper shows that gPC , with a small number of samples, achieves very fast rates of convergence and high accuracy in describing probability distributions without loss of detail in the tails . First, an optimization problem maximizes stage efficiency using turbine aerodynamic design rules as constraints; the function evaluations for this optimization are surrogate models from detailed 3D steady Computational Fluid Dynamics (CFD) analyses. The resulting optimal shape provides a starting point for the 3D high-fidelity aeromechanics (unsteady CFD and 3D Finite Element Analysis (FEA)) UQ study assuming three uncertain input parameters. This investigation seeks to find the steady and vibratory stresses associated with the first torsion mode for the HWSS turbine blisk near maximum operating speed of the engine. Using gPC to provide uncertainty estimates of the steady and vibratory stresses enables the creation of a Probabilistic Goodman Diagram, which - to the authors' best knowledge - is the first of its kind using high fidelity aeromechanics for turbomachinery blades. The Probabilistic Goodman Diagram enables turbine blade designers to make more informed design decisions and it allows the aeromechanics expert to assess quantitatively the risk associated with HCF for any mode crossing based on high fidelity simulations.