This work focuses on the application of multi-fidelity methods for the robust design optimization of engine components. The robust design optimization approach yields geometric designs that have high efficiencies and are less sensitive to uncertainties from manufacturing and wear. However, the uncertainty quantification techniques required to evaluate the robustness are computationally expensive, which limits their use in robust optimization. Multi-fidelity methods offer a promising solution to reduce the computational cost while maintaining accuracy in both uncertainty quantification and optimization. A Kriging and a multi-fidelity recursive Cokriging framework are developed, implemented, and applied to a test function. In addition, a multi-fidelity super efficient global optimization algorithm is developed. The optimizer is surrogate model-based and can handle constraints. The developed methods are then applied to a compressor test case of a high pressure compressor blade row with 9 uncertainty and 24 design parameters of the geometry. The 2.5% quantile of the stage efficiency is used as a robustness measure and it is therefore optimized. Design bounds and performance constraints are applied. In addition, various uncertainty quantification techniques are analyzed. A multi-fidelity uncertainty quantification approach is developed that combines simplified coarse-grid low-fidelity results with high-fidelity results to reduce the computational cost while maintaining high accuracy. Uncertainty quantification techniques of three fidelity levels are then developed and used for the multi-fidelity approach in the design space. The robust design optimization of the compressor is performed and the optimal designs obtained from the multi-fidelity approach show superior performance compared to existing robust design optima in the literature.

The increasing demands on jet engines require progressive thermodynamic process parameters, which typically lead to higher aerothermal loadings and accordingly to designs with high complexity. State-of-the-art high-pressure turbine (HPT) nozzle guide vane (NGV) design involves vane profiles with three-dimensional features including a high amount of film cooling and profiled endwalls (PEWs). Typically, the specific mass flow, also called capacity, which governs the engine's operation, is set by the HPT NGV. Hence, geometric variations due to manufacturing scatter of the HPT NGV's passage can affect relevant aerodynamic quantities and the entire engine behavior. Within the traditional deterministic design approach, the influences of those geometric variations are covered by conservative assumptions and engineering experience. This paper addresses the consideration of variability due to the manufacturing of HPT NGVs through probabilistic CFD investigations. To establish a statistical database, 80 HPT NGVs are digitized with a high precision optical 3D scanning system to record the outer geometry. The vane profiles are parametrized by a section-based approach. For this purpose, traditional profile theory is combined with a novel method that enables the description of NGV profile variability taking the particular leading edge (LE) shape into account. Furthermore, the geometric variability of PEWs is incorporated by means of principle component analysis (PCA). On this basis, a probabilistic system assessment including a sensitivity analysis in terms of capacity and total pressure loss coefficient is realized. Sampling-based methods are applied to conduct a variety of 3D CFD simulations for a typical population of profile and endwall geometries. This probabilistic investigation using realistic input parameter distributions and correlations contributes to a robust NGV design in terms of relevant aerodynamic quantities.

The paper addresses a probabilistic approach to lifetime prediction of cooled gas turbine blades. Variations of load and material parameters are taken into account by a combination of a direct Monte Carlo Simulation and a Response Surface Method. The proposed approach allows a reduction in the number of finite element analyses especially for problems with low failure probability. Therefore, the computational effort becomes acceptable even for full-scale 3D and 2D analysis models. Results of a probabilistic life assessment are shown for two cooled turbine blades. The probability of failure and the sensitivity of material and loading parameters are presented.

Further progress in the development of modern gas turbines for aircraft engines and electric power stations requires both continuous optimization on component and system level as well as the use of new and innovative technology. Thereby, the design is often pushed closer to the physical limits, which demands an outstanding understanding and predictability of the structural behavior under different design and off-design conditions. Due to the considerable costs of real component testing, the knowledge on structural behavior and failure mechanisms of gas turbine components is often gained from validated numerical models. To obtain a realistic computational image of reality, the uncertainties inherent in the design, the material properties, the loading and the operation conditions have to be considered in the modeling process. The effect of variations in key input design parameters on critical results such as the predicted component life can be evaluated on the basis of probabilistic analyses. The paper addresses first general aspects of applying probabilistic Finite-Element analyses in the turbine blade design process. Then, probabilistic design methods are applied to investigate the lifetime of a single crystal (SX) turbine blade submodel. Thereby, variations in three SX orientations as well as different load positions and variations in the creep properties are investigated by Monte-Carlo-Simulation (MCS) techniques.

Modern high-pressure turbine (HPT) blade design stands out due to its high complexity comprising three-dimensional blade features, multipassage cooling system (MPCS), and film cooling to allow for progressive thermodynamic process parameters. During the last decade, probabilistic design approaches have become increasingly important in turbomachinery to incorporate uncertainties such as geometric variations caused by manufacturing scatter and deterioration. Within this scope, the first part of this two-part article introduces parametric models for cooled turbine blades that enable probabilistic finite element (FE) analysis taking geometric variability into account to aim at sensitivity and robustness evaluation. The statistical database is represented by a population of more than 400 blades whose external geometry is captured by optical measurement techniques and 34 blades that are digitized by computed tomography (CT) to record the internal geometry and the associated variability, respectively. Based on these data, parametric models for airfoil, profiled endwall (PEW), wedge surface (WSF), and MPCS are presented. The parametric airfoil model that is based on the traditional profile theory is briefly described. In this regard, a methodology is presented that enables to adapt this airfoil model to a given population of blades by means of Monte Carlo-based optimization. The endwall variability of hub and shroud are parametrized by radial offsets that are applied to the respective median endwall geometry. WSFs are analytically represented by planes. Variations of the MPCS are quantified based on the radial distribution of cooling passage centroids. Thus, an individual MPCS can be replicated by applying adapted displacement functions to the core passage centroids. For each feature that is considered within this study, the accuracy of the parametric model is discussed with respect to the variability that is present in the investigated blade population and the measurement uncertainty. Within the scope of the second part of this article, the parametric models are used for a comprehensive statistical analysis to reveal the parameter correlation structure and probability density functions (PDFs). This is required for the subsequent probabilistic finite element analysis involving real geometry effects.

Modern high-pressure turbine (HPT) blade design stands out due to high complexity comprising three-dimensional blade features, multipassage cooling system (MPCS), and film cooling to allow for progressive thermodynamic process parameters. During the last decade, probabilistic design approaches have become increasingly important in turbomachinery to incorporate uncertainties such as geometric variations caused by manufacturing scatter. In Part B of this two-part article, real geometry effects are considered within a probabilistic finite element (FE) analysis that aims at sensitivity evaluation. The knowledge about the geometric variability is derived based on a blade population of more than 400 individuals by means of parametric models that are introduced in Part A. The HPT blade population is statistically assessed, which allows for reliable sensitivity analysis and robustness evaluation taking the variability of the airfoil, profiled endwalls (PEWs) at hub and shroud, wedge surfaces (WSFs), and the MPCS into account. The probabilistic method—Monte Carlo simulation (MCS) using an extended Latin hypercube sampling (eLHS) technique—is presented subsequently. Afterward, the FE model that involves thermal, linear-elastic stress, and creep analysis is described briefly. Based on this, the fully automated process chain involving computer-aided design (CAD) model creation, FE mesh morphing, FE analysis, and postprocessing is executed. Here, the mesh morphing process is presented involving a discussion of the mesh quality. The process robustness is assessed and quantified referring to the impact on input parameter correlation. Finally, the result quantities of the probabilistic FE simulation are evaluated in terms of sensitivities. For this purpose, regions of interest are determined, wherein the statistical analysis is conducted to achieve the sensitivity ranking. A significant influence of the considered geometric uncertainties onto mechanical output quantities is observed, which motivates to incorporate these in modern design strategies or robust optimization.