The design of gas turbine engines is a complex problem. This complexity has led to the adoption of a modular design approach, in which a conceptual design phase fixes the values for some global parameters and dimensions in order to facilitate the subdivision of the overall task into a number of simpler subproblems. This approach, while making a complex problem more tractable, necessarily has to rely on designer experience and simple evaluations to specify these process-intrinsic constraints at a point in the design process where very little knowledge about the final design exists. Later phases of the design process, using higher-fidelity tools but acting on a limited region of the design space, can only refine an already established design. While substantial improvements in performance have been possible with the current approach, further gains are becoming increasingly hard to achieve. A gas turbine is a complex multidisciplinary system: a more integrated design approach can facilitate a better exploitation of the trade-offs between different modules and disciplines, postponing the setting of these critical interface parameters (such as flow areas, radii, etc.) to a point where more information exists, reducing their impact on the final design. In the resulting large, possibly multimodal, highly constrained design space, and with a large number of objectives to be considered simultaneously, finding an optimal solution by simple trial-and-error can prove extremely difficult. A more intelligent search approach, in which a numerical optimizer takes the place of the human designer in seeking optimal designs, can enable the design space to be explored significantly more effectively, while also yielding a substantial reduction in development times thanks to the automation of the design process. This paper describes the development of a system for the integrated design and optimization of gas turbine engines, linking a metaheuristic optimizer to a geometry modeler and to evaluation tools with different levels of fidelity. In recognition of the substantial increase in design space size required by the integrated approach, an improved parameterization based on the concept of principal components' analysis was implemented, allowing a rotation of the design space along its most significant directions and a reduction in its dimensionality, proving essential for a faster and more effective exploration of the design space.

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Gas turbine compression systems are required to perform adequately over a range of operating conditions. Complexity has encouraged the conventional design process for compressors to focus initially on one operating point, usually the most commonor arduous, to draw up an outline design. Generally, only as this initial design is refined is its offdesign performance assessed in detail. Not only does this necessarily introduce a potentially costly and timeconsuming extra loop in the design process, but it also may result in a design whose offdesign behavior is suboptimal. Aversion of nonintrusive polynomial chaos was previously developed in which a set of orthonormal polynomials was generated to facilitate a rapid analysis of robustness in the presence of generic uncertainties with good accuracy. In this paper, this analysis method is incorporated in real time into the design process for the compression system of a three-shaft gas turbine aeroengine. This approach to robust optimization is shown to lead to designs that exhibit consistently improved system performance with reduced sensitivity to offdesign operation.

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The complexity of modern gas turbine engines has led to the adoption of a modular design approach, in which a conceptual design phase fixes the values for a number of parameters and dimensions in order to facilitate the subdivision of the overall task into a number of simpler design problems. While making the overall problem more tractable, the introduction of these process-intrinsic constraints (such as flow areas and radii between adjacent stages) at a very early phase of the design process can limit the level of performance achievable, neglecting important regions of the design space and concealing important trade-offs between different modules or disciplines. While this approach has worked satisfactorily in the past, the continuous increase in components' efficiencies and performance makes further advances more difficult to achieve. Part I of this paper described the development of a system for the integrated design optimization of gas turbine engines: postponing the setting of the interface constraints to a point where more information is available facilitates better exploration of the available design space and better exploitation of the trade-offs between different disciplines and modules. In this second part of the paper, the proposed approach is applied to several test cases from the design of a three-spool gas turbine engine core compression system, demonstrating the risks associated with a modular design approach and the consistent gains achievable through the proposed integrated optimization approach.

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The design of a gas turbine, or one of its constituent modules, is generally approached with some specific operating condition in mind (its design point). Unfortunately, engine components seldom exactly meet their specifications and do not operate at just one condition, but over a range of power settings. This simplification can then lead to a product that exhibits performance worse than nominal in real-world conditions. The integration of some consideration of robustness as an active part of the design process can allow products less sensitive to the presence of the noise factors commonly found in real-world environments to be obtained. To become routinely used as a design tool, minimization of the time required for robustness analysis is paramount. In this study, a nonintrusive polynomial chaos formulation is used to evaluate the variability in the performance of a generic modular-core compression system for a three-spool modern gas turbine engine subject to uncertain operating conditions with a defined probability density function. The standard orthogonal polynomials from the Askey scheme are replaced by a set of orthonormal polynomials calculated relative to the specific probability density function, improving the convergence of the method.

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In real-world optimization problems, large design spaces and conflicting objectives are often combined with a large number of constraints, resulting in a highly multi-modal, challenging, fragmented landscape. The local search at the heart of Tabu Search, while being one of its strengths in highly constrained optimization problems, requires a large number of evaluations per optimization step. In this work, a modification of the pattern search algorithm is proposed: this modification, based on a Principal Components' Analysis of the approximation set, allows both a re-alignment of the search directions, thereby creating a more effective parametrization, and also an informed reduction of the size of the design space itself. These changes make the optimization process more computationally efficient and more effective - higher quality solutions are identified in fewer iterations. These advantages are demonstrated on a number of standard analytical test functions (from the ZDT and DTLZ families) and on a real-world problem (the optimization of an axial compressor preliminary design).@en

In the last 15 years, automatic design optimisation has been the subject of ever growing interest, thanks to the development of ever more reliable analysis software, efficient optimisation methods and powerful computers. Even in industrial environments, design optimisation is extensively used in a number of disciplines, such as aerodynamics, structures and many more applications. Better designs in shorter times and clearer trade-offs between different objectives and disciplines are the most generally recognised advantages.22 The parameterisation represents the " critical enabling factor" for an efficient exploration of the design space: it is essential to ensure that the parameterisation scheme is able to cover all feasible designs, in order not to lose potentially good designs, but also that the minimum possible number of parameters is used, since these affect the size of the design space and thus the convergence time of the optimiser. Irrespective of the specific parameterisation technique, the optimisation of complex products is likely to translate into a large design space and an a priori reduction is not advisable, as this could reduce the generality of the paramenterisation and lead to the loss of potentially good designs. Kipouros et al.16 have presented a method for selecting only the most significant components based on the results of a preliminary optimisation run. In the present study, a method based on Principal Components' Analysis is introduced: given a generic parameterisation, this allows an optimal representation to be derived that will facilitate a faster and more complete exploration of the design space. The advantages of this approach are demonstrated through two optimisation test cases from the design of a core compression system for a three-spool modern turbofan engine.@en

Engineering design commonly assumes nominal values for uncertain parameters to simplify the design process: the design of a gas turbine, or one of its modules, is generally approached with some specific operating conditions in mind (its design point). Unfortunately, engine components never exactly meet their specifications and do not operate at just one condition, but over a range of power settings. This simplification can then lead to a product that exhibits performance significantly worse than nominal in real-world conditions. This problem is exacerbated in the presence of heavily optimised designs, which tend to lie in extreme regions of the design space.15 In gas turbine design, safe and satisfactory off-design operation must be guaranteed and is generally evaluated before moving to the next phase of the design process. This approach, while guaranteeing that some minimum requirements are met, introduces a further loop in the design process and does not ensure the final design will be optimal with respect to this new requirement. The introduction of some robustness considerations into the design process can reduce the level of fragmentation and iteration typical of gas turbine engine design and produce further (and more robust) improvements relative to the traditional method. In this study, two approaches for dealing with off-design performance analysis are presented, integrated into an automatic optimisation system and applied to the preliminary design of a core compression system from a three-spool modern turbofan engine. Designs that are more robust than those found if only design-point performance is considered are successfully identified.@en

Modern turbofan engines are designed with pressure ratios as high as 40 and with bypass ratios in excess of 8. Multiple spools with substantial radial offset are essential to achieve the desired design and off-design performance and s-shaped ducts are necessary to deliver the flow from the exit of a turbomachine to the inlet of the following one in the minimum possible space to reduce the weight and the size of the gas turbine, without the risk of incurring in flow separation. In the absence of practical design rules or performance correlations for annular s-shaped ducts, a practical design approach could be the use of Computational Fluid Dynamics (CFD) for performance evaluation together with optimisation techniques for seeking the best design. Numerical optimisation methods (either deterministic or stochastic) can be linked to CFD solvers to provide a more thorough exploration of the design space, trying to produce a better design than the datum one, subject to a number of constraints. This paper reports the development and testing of an automatic framework for design optimisation of s-shaped ducts and its initial application to the optimisation of an axial-symmetric inter-compressor duct.

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