Adjoint Functors, Projectivization, and Differentiation Algorithms for Representations of Partially Ordered Sets

Adjoint functors and projectivization in representation theory of partially ordered sets are used to generalize the algorithms of differentiation by a maximal and by a minimal point. Conceptual explanations are given for the combinatorial construction of the derived set and for the differentiation functor

A homological approach to differentiation algorithms and dimensions of finite type for representations of partially ordered sets

The category of representations of a partially ordered set is studied from a homological point of view. This approach is used to generalize the differentiation algorithms for representations of partially ordered sets with respect to maximal respectively minimal elements. Homological methods and the differentiation procedure are further explored to study dimensions of finite type for representations of partially ordered sets

OPTIMIZATION OF COMPRESSOR VARIABLE GEOMETRY SETTINGS USING MULTI-FIDELITY SIMULATION

Variable geometry blade rows are a common instrument to avoid compressor instabilities which occur especially at low- and full-speed operation of gas turbines. The operating settings of variable stator vanes (VSVs) are typically obtained from expensive and time consuming performance rig tests and are not known during the early design phase of a gas turbine. During preliminary design of the overall engine it is common practice to use default component characteristics based on considerable engineering experience. These can deviate substantially at off-design and often do not properly account for the impact of changes in component geometry. As a solution, multi-fidelity simulation often referred to as zooming or variable complexity analysis is applied. This proceeding facilitates a transfer of single component performance characteristics obtained in mid- or high-fidelity analysis to a full gas turbine system analysis based on lower resolution level. The purpose of this study is to present a multidisciplinary numerical optimization methodology to define ideal blade row staggering of variable compressor stator vanes during the early preliminary design phase using multi-fidelity simulation. The objective of the resultant multi-dimensional constraint optimization is to find the best solution for the entire gas turbine system for a set of discrete operating points. For the assessment a generic turbofan engine model is designed by taking into account top level engine requirements from an assumed airframe and flight mission scenario. Based on the performance calculation a full 3-D axial multistage high pressure compressor (HPC) is designed. The assumed design considerations are summarized and the modelling techniques are presented. The optimization of VSV staggering mentioned above is carried out by re-staggering the variable geometry blade rows of the high-fidelity HPC and run a full 2-dimensional through-flow calculation. Results are then automatically transferred to the 0-dimensional engine model to calculate the engine overall performance. A Pareto optimized blade row staggering is found by taking into account the surge margin and the specific fuel consumption of the entire engine system as objective functions of the optimization process. Simultaneously several constraints such as DeHaller numbers and diffusion factors are considered. The optimization process chain and the tool coupling are summarized and described in detail. The resulting VSV staggering for a set of discrete operating points is shown

Design and Application of a Multi-Disciplinary Pre-Design Process for Novel Engine Concepts

The purpose of this paper is to present a multidisciplinary predesign process and its application to three aero-engine models. First, a twin spool mixed flow turbofan engine model is created for validation purposes. The second and third engine models investigated comprise future engine concepts: a counter rotating open rotor (CROR) and an ultrahigh bypass turbofan. The turbofan used for validation is based on publicly available reference data from manufacturing and emission certification. At first, the identified interfaces and constraints of the entire predesign process are presented. An important factor of complexity in this highly iterative procedure is the intricate data flow, as well as the extensive amount of data transferred between all involved disciplines and among different fidelity levels applied within the design phases. To cope with the inherent complexity, data modeling techniques have been applied to explicitly determine required data structures of those complex systems. The resulting data model characterizing the components of a gas turbine and their relationships in the design process is presented in detail. Based on the data model, the entire engine predesign process is presented. Starting with the definition of a flight mission scenario and resulting top level engine requirements, thermodynamic engine performance models are developed. By means of these thermodynamic models, a detailed engine component predesign is conducted. The aerodynamic and structural design of the engine components are executed using a stepwise increase in level of detail and are continuously evaluated in context of the overall engine system

Collaborative Aircraft Engine Preliminary Design using a Virtual Engine Platform, Part B: Application

Digitalization is of growing importance for industries and research institutions as it simplifies and accelerates product development. By that it also offers the ability to reduce risks and costs. Among others, also the aircraft engine sector is facing such a shift of paradigm, entailing a huge potential to support the preliminary design workflow of projected next generation engine concepts. For that purpose the German Aerospace Center (DLR) has started the development of the virtual engine platform GTlab (Gas Turbine Laboratory). It offers a high degree of usability and flexibility with its modular architecture comprising standardized interfaces and thus allows a simple integration of arbitrary user-defined tools. At the heart of the present paper is the application of GTlab in a realistic example of an ultra high bypass-ratio (BPR $\approx 16$) aircraft engine with an anticipated state of the art technology of 2028. The design workflow starts with a 0D thermodynamic performance model and continues with 1D and 2D mid-fidelity preliminary aerodynamic and structural design tools. In this context, challenges are highlighted that were encountered in the course of the process chains and during data handling processes between different fidelity-levels. The mid-fidelity preliminary component designs are carried out by various departments of the DLR and comprise the turbo-components as well as the combustor and structural parts. By that, also the iterative procedure is highlighted, since the initial performance model is updated everytime variations are encountered in the aerodynamic component designs. Also the assessment of fan noise is integrated into the preliminary engine design procedure summing up the multi-disciplinary design loop for the evaluation of future engine concepts

Design and Application of a Multi-Disciplinary Pre-Design Process for Novel Engine Concepts

Central targets for jet engine research activities comprise the evaluation of improved engine components and the assessment of novel engine concepts for enhanced overall engine performance in order to reduce the fuel consumption and emissions of future aircraft. Since CO2 emissions are directly related to engine fuel burn, a reduction in fuel consumption leads to lower CO2 emissions. Therefore improvements in engine technologies are still significant and a multi-disciplinary pre-design approach is essential in order to address all requirements and constraints associated with different engine concepts. Furthermore, an increase in effectiveness of the preliminary design process helps reduce the immense costs of the overall engine development. Within the DLR project PEGASUS (Preliminary Gas Turbine Assessment and Sizing) a multi-disciplinary pre-design and assessment competence of the DLR regarding aero engines and gas turbines was established. The application of modern preliminary design methods allows for the construction and evaluation of innovative next generation engine concepts. The purpose of this paper is to present the developed multi-disciplinary pre-design process and its application to three aero engine models. First, a state of the art twin spool mixed flow turbofan engine model is created for validation purposes. The second and third engine models investigated comprise future engine concepts: a Counter Rotating Open Rotor and an Ultra High Bypass Turbofan. The turbofan used for validation is based on publicly available reference data from manufacturing and emission certification. At first the identified interfaces and constraints of the entire pre-design process are presented. An important factor of complexity in this highly iterative procedure is the intricate data flow, as well as the extensive amount of data transferred between all involved disciplines and among the different fidelity levels applied within the smoothly connected design phases. To cope with the inherent complexity data modeling techniques have been applied to explicitly determine the required data structures of those complex systems. The resulting data model characterizing the components of a gas turbine and their relationships in the design process is presented in detail. Based on the established data model the entire engine pre-design process is presented. Starting with the definition of a flight mission scenario and the resulting top level engine requirements thermodynamic engine performance models are developed. By means of these thermodynamic models, a detailed engine component pre-design is conducted. The aerodynamic and structural design of the engine components are executed using a stepwise increase in level of detail and are continuously evaluated in the context of the overall engine system