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Konstantinos G. Kyprianidis Module Development Backtracking is of particular importance in achieving very high accuracy i.e. very small residual tolerance, and in simulating the notorious regions of a system (for example in simulating ultra-high bypass ratio engines at idle conditions - where the hot nozzle pressure ratio approaches unity and component efficiencies drop significantly). The user can choose - via the library interface - between the original “standard” Newton-Raphson method or the quasi-Newton method described thoroughly in Broyden [158, 159]. A switch is provided for selecting one of the differentiation methods described earlier, as well as for reusing the inverted Jacobian from previous simulation points. The library integration also includes a quasi-Newton solver that utilises the Powell dogleg step procedure [160], namely MINPACK, described by Mor ́e et al. [161,162] and available under a freeware license through NetLib [163]. Therefore, MINPACK may also be selected for use during steady state simulations and it is worth noting that this is the solver of choice for the commercially available gas turbine performance simulation code PROOSIS. During dynamic simulations, the original steady state set of algebraic equa- tions representing the engine model is coupled with a set of Ordinary Differ- ential Equations (ODE) that describe the dynamics of the system, and is hence transformed into a set of Ordinary Algebraic Differential Equations (ODAE). Gro ̈nstedt [23,164] presents various strategies for solving ODAE systems for gas turbine dynamic simulations and after extended benchmarking concludes that the “direct approach” of treating differential and algebraic variables simultane- ously seems to perform best. Stamatis et al [157] also gives benchmarking results for implicit and explicit integration schemes, while Petzold [165] provides a good reference on solving ODAE sets. A large number of ODAE solvers, coupled with the SLATEC Common Mathe- matical Library, an extensive library of Fortran numerical routines, are together available under a freeware license through NetLib [163]. Three of these solvers (namely the DDASSL, the DDASPK and the DDASKR) have been integrated in the LISIS library together with some parts of the SLATEC library. In an attempt to reduce non-convergence cases, the FITPACK higher order sur- face splines routines were introduced in the LISIS library; these routines are available under a freeware license through NetLib [163] and described by Dier- ckx [166]. Surface splines can be used to approximate component maps (i.e. 69PDF Image | Multi-disciplinary conceptual design of future jet engine systems
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