Improvements on the Computational Stability of Engine Performance Simulation at Low Rotating Speed

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The numerical model of engine performance is generally described as nonlinear equations solved by the Newton-Raphson method. The model runs well above idle rotating speed with a very high convergence rate. However, problems of astringency arise while solving the model below idle rotating speed, especially near the zero speed. Detailed debugging indicates two possible reasons caused the failure results. The first one is the incomplete definition of aerodynamic state of gas flow, and the second one is the incorrect initial value during the iteration of the Newton-Raphson method. Therefore, the efforts are made to improve the computational stability of these two problems in this paper.

Reverse flow often occurs in the nozzle while solving the nonlinear equations near zero rotating speed because of the abnormal gas flow state. The typical one is the total pressure at nozzle inlet less than the ambient pressure caused by the solver during iteration. A penalty function is constructed to extend the defining space of such aerodynamic process. This penalty function has no sense in aerodynamics but only forces the iteration to find its correct solution in mathematics. Compared with other treatments, the presented penalty function is more simple and effective.

The unsteady nature of the nonlinear model below starting speed determined that the solver should use the time stepping scheme. However, the analyses indicate that the inproper time step leads to a divergent result although the convergent result of last step is taken as the initial value for Newton-Raphson method. Therefore, the dual layer multi particle swarm optimization (DLMPSO) algorithm is proposed in this paper to optimize the initial value to speed up the convergence of iteration. Compared with standard PSO method, the DLMPSO algorithm avoids the local optimal solution and increases its global searching ability.

The full state model employs the backbone maps to represent compressors and turbines characteristics instead of the traditional maps. Correspondently, the independent variables of nonlinear equations are also set to match the backbone maps. By extending the backbone maps and using the proposed improvements, the low speed engine performances such as flaming out, ground and air starting are simulated. Partial comparisons and theoretical analysis indicate the validity of results. With the improvements, the numerical model is able to get a convergence result of engine performance simulation even below 1% high rotor speed.