This paper presents a multidisciplinary design optimization of a turbocharger radial turbine for automotive applications with the aim to improve two major manufacturer requirements: the total-to-static efficiency and the moment of inertia of the radial turbine impeller. The search for the best design is constrained by mechanical stress limitations, by the mass flow and power, and by aerodynamic constraints related to the isentropic Mach number distribution on the rotor blade. The optimization of the radial turbine is performed with a two-level optimization algorithm developed at the von Karman Institute for Fluid Dynamics. The system makes use of a differential evolution algorithm, an artificial neural network (ANN), and a database as a compromise between accuracy and computational cost. The ANN performance predictions are periodically validated by means of accurate steady state 3D Navier-Stokes and centrifugal stress computations. The results show that it is possible to improve the efficiency and the moment of inertia only in a few numbers of iterations while limiting the stresses to a maximum value. Based on the large number of evaluated designs during the optimization, this paper provides design recommendations of a turbocharger radial turbine at least for a good preliminary design.

Superior rotor tip geometries possess the potential to simultaneously mitigate aerodynamic losses and severe thermal loads onto the rotor overtip region. However, classical design strategies are usually constrained to a specific type of geometry, narrowing the spread of shape topologies considered during the design phase. The current paper presents two novel multi-objective optimization methodologies that enable the exploration of a broad range of distinct tip configurations for unshrouded rotor blades. The first methodology is a shape optimization process that creates a fully carved blade tip shape defined through a Bezier surface controlled by 40 parameters. Combined with a differential evolution (DE) optimization strategy, this approach is applied to a rotor blade for two tip gap sizes: 0.85% (tight) and 1.38% (design) of the blade span. The second methodology is based on a topology optimization process that targets the creation of arbitrary tip shapes comprising one or multiple rims with a fixed height. The tip section of the blade has been divided into more than 200 separate zones, where each zone can be either part of an upstanding rim or part of the cavity floor. This methodology was tested with a level-set approach in combination with a DE optimizer and coupled to an optimization routine based on genetic algorithms (GAs). The current study was carried out on a modern high-pressure turbine operating at engine-like Reynolds and high subsonic outlet Mach numbers. A fully hexahedral unstructured mesh was used to discretize the fluid domain. The aerothermal performance of each tip profile was evaluated accurately through Reynolds-averaged Navier–Stokes (RANS) simulations adopting the shear-stress transport (SST) turbulence model. Multi-objective optimizations were set for both design strategies that target higher aerodynamic rotor efficiencies and simultaneous minimization of the heat load. This paper illustrates a wide variety of profiles obtained throughout the optimization and compares the performance of the different strategies. The research shows the potential of such novel methodologies to reach new unexplored types of blade tip designs with enhanced aerothermal performances.

This two-part paper addresses the design of a U-bend for serpentine internal cooling channels optimized for minimal pressure loss. The total pressure loss for the flow in a U-bend is a critical design parameter, as it augments the pressure required at the inlet of the cooling system, resulting in a lower global efficiency. In this first part of the paper, the design methodology of the cooling channel is presented. The minimization of the total pressure loss is achieved by means of a numerical optimization method that uses a metamodel-assisted differential evolution algorithm in combination with an incompressible Navier–Stokes solver. The profiles of the internal and external side of the bend are parameterized using piece-wise Bezier curves. This allows for a wide variety of shapes, respecting the manufacturability constraints of the design. The pressure loss is computed by the Navier–Stokes solver, which is based on a two-equation turbulence model and is available from the open source software OpenFOAM. The numerical method predicts an improvement of 36% in total pressure drop with respect to a circular U-bend, mainly due to the reduction of the separated flow region along the internal side of the bend. The resulting design is subjected to experimental validation, presented in Part II of the paper.

This second paper presents the aerothermal optimization of the first stage rotor blade of an axial high pressure (HP) turbine by means of the conjugate heat transfer (CHT) method and lifetime model described in Paper I. The optimization system defines the position and diameter of the cooling channels leading to the maximum lifetime of the blade while limiting the amount of cooling flow. It is driven by the results of a CHT and subsequent stress analysis of each newly designed geometry. Both temperature and stress distributions are the input for the Larson–Miller material model to predict the lifetime of the blade. The optimization procedure makes use of a genetic algorithm (GA) and requires the aerothermal analysis of a large number of geometries. Because of the large computational cost of each CHT analysis, this results in a prohibitive computational effort. The latter has been remediated by using a more elaborate optimization system, in which a large part of the CHT analyzes is replaced by approximated predictions by means of a metamodel. Two metamodels, an artificial neural network and a radial basis function network, have been tested and their merits have been discussed. It is shown how this optimization procedure based on CHT calculations, a GA, and a metamodel can lead to a considerable extension of the blade lifetime without an increase in the amount of cooling flow or the complexity of the cooling geometry.

This paper presents a 3-D optimization of a moderately loaded transonic compressor rotor by means of a multiobjective optimization system. The latter makes use of a differential evolutionary algorithm in combination with an Artificial Neural Network and a 3D Navier-Stokes solver. Operating it on a cluster of 30 processors enabled the evaluation of the off-design performance and the exploration of a large design space composed of the camber line and spanwise distribution of sweep and chord length. Objectives were an increase of efficiency at unchanged stall margin by controlling the shock waves and off-design performance curve. First designs of single blade rows allowed a better understanding of the impact of the different design parameters. Forward sweep with unchanged camber improved the peak efficiency by only 0.3% with the same stall margin. Backward sweep with an optimized S shaped camber line improved the efficiency by 0.6% at unchanged stall margin. It is explained how the camber line control can introduce the same effect as forward sweep and compensate the expected negative effects of backward sweep. The best results (0.7% increase in efficiency and unchanged stall margin) have been obtained by a stage optimization that allows also a spanwise redistribution of the rotor flow and an increase of loading by extra flow turning. The latter compensates the loading shift induced by the backward sweep in order to reduce the inlet Mach number at the downstream stator hub.

This first paper describes the conjugate heat transfer (CHT) method and its application to the performance and lifetime prediction of a high pressure turbine blade operating at a very high inlet temperature. It is the analysis tool for the aerothermal optimization described in a second paper. The CHT method uses three separate solvers: a Navier–Stokes solver to predict the nonadiabatic external flow and heat flux, a finite element analysis (FEA) to compute the heat conduction and stress within the solid, and a 1D aerothermal model based on friction and heat transfer correlations for smooth and rib-roughened cooling channels. Special attention is given to the boundary conditions linking these solvers and to the stability of the complete CHT calculation procedure. The Larson–Miller parameter model is used to determine the creep-to-rupture failure lifetime of the blade. This model requires both the temperature and thermal stress inside the blade, calculated by the CHT and FEA. The CHT method is validated on two test cases: a gas turbine rotor blade without cooling and one with five cooling channels evenly distributed along the camber line. The metal temperature and thermal stress distribution in both blades are presented and the impact of the cooling channel geometry on lifetime is discussed.