Gas turbine engines for aircraft applications are required to meet multiple performance and sizing requirements, subject to constraints established by the best available technology level, that are both directly and indirectly associated with the aerothermodynamic cycle. The performance requirements and limiting values of constraints that are considered by the cycle analyst conducting an engine cycle design occur at multiple operating conditions. The traditional approach to cycle analysis chooses a single design point with which to perform the on-design analysis. Additional requirements and constraints not transpiring at the design point must be evaluated in off-design analysis and therefore do not influence the cycle design. Such an approach makes it difficult to design the cycle to meet more than a few requirements and limits the number of different aerothermodynamic cycle designs that can reasonably be evaluated.;Engine manufacturers have developed computational methods to create aerothermodynamic cycles that meet multiple requirements, but such methods are closely held secrets of their design process. This thesis presents a transparent and publicly available on-design cycle analysis method for gas turbine engines which generates aerothermodynamic cycles that simultaneously meet performance requirements and constraints at numerous design points. Such a method provides the cycle analyst the means to control all aspects of the aerothermodynamic cycle and provides the ability to parametrically create candidate engine cycles in greater numbers to comprehensively populate the cycle design space. The cycle design space represents all of the candidate engine cycles that meet the performance requirements for a particular application from which a "best" engine can be selected.;This thesis develops the multi-design point on-design cycle analysis method labeled simultaneous MDP. The method is divided into three different phases resulting in an 11 step process to generate a cycle design space for a particular application. The first phase is the requirements and technology definition phase which defines the engine cycle problem to be analyzed through the establishment of requisite performance requirements and technology rules at the different design points and determines the overall engine architecture. The second phase is the MDP setup phase which establishes a set of nonlinear equations by formulating a system of nonlinear equations at on-design mode from design rules that couple the design points, performance requirements, technology rules and design variables. The key to the method is the understanding of the coupling of the performance between the different design points. The equations are divided into three categories; user defined equations specified by the cycle analyst based on the chosen design rules, engine component matching relations to ensure that conservation of mass and energy is maintained at each of the design points, and constraint relations which determine the feasibility of the candidate engines. The third phase is the MDP execution phase which populates the cycle design space by parametrically varying cycle design variables and then simultaneously finds the solution to the entire set of nonlinear equations with a modified version of the Newton-Raphson solver. For a specific cycle design problem, the first two phases are only performed once and the third phase repeated for each unique combination of design variables to create the cycle design space.;Through implementation of simultaneous MDP, a comprehensive cycle design space can be created quickly for the most complex of cycle design problems. Furthermore, the process documents the creation of each candidate engine providing transparency as to how each engine cycle was designed to meet all of the requirements. The cycle analyst is intricately involved in the simultaneous MDP method using their knowledge and expertise in the first two phases to define and setup the cycle design space, but are removed from the more time consuming task of finding each design that meets all of the requirements. As this process is left to the solver, the computational efficiency of the Newton-Raphson solver allows for the creation of numerous candidate engines to comprehensively cover the cycle design space.;The simultaneous MDP method is demonstrated in this thesis on a high bypass ratio, separate flow turbofan with up to 25 requirements and constraints and 9 design points derived from a notional 300 passenger aircraft with a large civil transport engine. Five separate experiments are designed to test different aspects of the simultaneous MDP method. The experiments highlight the transformation of the design rules into a system of nonlinear equations to be solved using the modified Newton-Raphson solver. The sensitivity of the solver to its initial iterate necessitated the development of a systematic approach to the generation of the initial iterate for a particular cycle design space. To ensure the highest solver convergence success rate possible, a multi-design point repair algorithm was devised for feasible candidate engines that initially fail to converge to the solution.
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