Optimization of multistage turbines using a through-flow code

Abstract

Fast and accurate flow calculation and performance prediction of multistage axial flow turbines at design and off-design conditions were performed using a compressible steady state inviscid through-flow code with high fidelity loss and mixing models. The code is based on a stream function model and a finite element solution procedure. A new design system has been developed which optimizes hub and shroud geometry and inlet and exit flow field parameters for each blade row of a multistage axial flow turbine. Optimization was performed using a hybrid constrained optimization code that switches among the modules automatically in order to avoid local minima and to accelerate design convergence rate. By automatically varying a relatively small number of geometric variables per turbine stage it is possible to find an optimal radial distribution of flow parameters at the inlet and outlet of every blade row. Thus, an optimized meridional flow path can be found that is defined by the optimized shape of the hub and shroud while keeping blade shapes intact. The multistage design optimization system has been demonstrated using an actual two-stage axial gas turbine as an example. The comparison of computed performance of an already very high efficiency initial design and its optimized design demonstrates more than 1 per cent improvement in the turbine efficiency at design and significant off-design conditions. The entire design optimization process is feasible on a typical single-processor computer workstation or a personal computer.

Adjoint Method for Shape Optimization in Real-Gas Flow Applications

“…For steady-state problems, the governing equations can be symbolically expressed as B [o tp h y , u fo t p h y , Otge o ) , X ( o t g e o ) ] -0 ( 2 ) and can be regarded as an equality constraint for the minimization problem. For steady-state problems, the governing equations can be symbolically expressed as B [o tp h y , u fo t p h y , Otge o ) , X ( o t g e o ) ] -0 ( 2 ) and can be regarded as an equality constraint for the minimization problem.…”

“…However, in standard shape optimization problems, the physical variables appearing in expressions (1) and (2) are to be considered as fixed known parameters (i.e., are not considered variables in the design pro cess). However, in standard shape optimization problems, the physical variables appearing in expressions (1) and (2) are to be considered as fixed known parameters (i.e., are not considered variables in the design pro cess).…”

“…The final turbomachinery layout is then usually a complex combination of the outcomes provided by each optimization step, starting from the preliminary choice of the number of stages and of the stage arrangement [1], to the throughflow (or axisymmetric) design [2][3][4], up to the detailed blade shape definition [5,6]. The final turbomachinery layout is then usually a complex combination of the outcomes provided by each optimization step, starting from the preliminary choice of the number of stages and of the stage arrangement [1], to the throughflow (or axisymmetric) design [2][3][4], up to the detailed blade shape definition [5,6].…”

Aerodynamic optimization of through-flow design model of a high by-pass transonic aero-engine fan using genetic algorithm

“…There are two diffusion factors in the literature, diffusion factor and equivalent diffusion factor (D eq ). The latter is implemented within the SLC methodology, which is formulized in equation (20)…”

“…2,[16][17][18][19] However, reports on through-flow design optimization not only by genetic algorithm, but also by other stochastic methods are quite limited, even in the simplified case of single-stream compressor and turbines. The study of Petrovic et al 20 presents an application of genetic algorithm (hybridized with gradient method) on through-flow optimization of a turbine, where maximum efficiency is provided. In a similar through-flow optimization study, Park et al 21 obtained 0.5-1.5% increase in efficiency of a threestage low pressure compressor by perturbing booster hub and shroud geometries using hybrid genetic algorithm.…”