3D shape optimisation of a low-pressure turbine stage

Abstract

The possibility of reducing the flow losses in low-pressure turbine stage has been investigated in an iterative process using a novel hybrid optimisation algorithm. Values of the maximised objective function that is isentropic efficiency are found from 3D RANS computation of the flowpath geometry, which was being changed during the optimisation process. To secure the global flow conditions, the constraints have been imposed on the mass flow rate and reaction. Among the optimised parameters are stator and rotor twist angles, stator sweep and lean, both straight and compound. Blade profiles remained unchanged during the optimisation. A new hybrid stochastic-deterministic algorithm was used for the optimisation of the flowpath. In the proposed algorithm, the bat algorithm was combined with the direct search method of Nelder-Mead in order to refine the best obtained solution from the standard bat algorithm. The method was tested on a wide variety of well-known test functions. Also, the results of the optimisation of the other stochastic and deterministic methods were compared and discussed. The optimisation gives new 3D-stage designs with increased efficiency comparing to the original design. Keywords: CFD, efficiency, hybrid method, low pressure steam turbine, optimisation, swarm intelligence. INTRODUCTIONThe performance and profitability of energetic systems depend fundamentally on turbine characteristics -the lower the turbine efficiency, the lower the system efficiency e.g. steam power plant efficiency [1, 2], ORC efficiency [3], energy storage efficiency [4]. Consequently, system efficiency basically depends on the expander design. The computational fluid dynamics (CFD) tools are extremely useful in the design of high-efficiency turbines because of inaccuracy of empirical loss correlation models [5]. The most important component of the total loss is usually connected with the losses within the blade passages -mainly profile loss and secondary (endwall) loss. Despite the significant amount of models, none of them by far has proven to be really general [6]. This leads to the use of computational fluid dynamics in an intensive way for turbomachinery blade design, but this higher performance must be achieved with fast prototyping and lower cost. The largest computational power cost during efficiency optimisation of turbine is connected with the calculation of values of the objective function, which is obtained from a RANS solver.Novel methods must be used in order to obtain the global minimum with lower number of calls of the objective function. Among these methods are neural network metamodels [7,8], Kriging and co-Kriging methods [9] and hybrid stochastic-deterministic algorithms [2,[10][11][12][13][14].In this work, the new hybrid stochastic-deterministic optimisation method was used. The method is a combination of Bat algorithm [15] and Nelder-Mead method [16]. Also, a parametric stator and rotor geometry model has been developed. As shown in this paper, these methods allow one for efficient optimisatio...