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.

Optical flow provides an opportunity to elevate the resolution and sensitivity of deflection sensing in background-oriented schlieren (BOS). Despite extensive relevant literature within the field of computer vision, there is a lack of proper quantification of its abilities and limitations with regard to the state-of-the-art BOS experiments. Thus, this study performs an assessment of accuracy and resolution limits in different flow field scenarios utilizing background patterns generated with random dot and wavelet noise distributions. Accordingly, a synthetic assessment over a theoretically generated Prandtl–Meyer expansion fan is conducted with variations introduced in the background patterns and operational parameters of optical flow. A clear superiority of accuracy and resolvable range of density gradient amplitudes over cross-correlation is demonstrated. Moreover, an experimental assessment of supersonic flow features over multiple wind tunnel models is performed. The influence of experimental constraints, limitations and uncertainties related to the application of optical flow in BOS and its comparative performance against the block-matching counterpart is characterized. Graphical

Blade tip design and tip leakage flows are crucial aspects for the development of modern aero-engines. The inevitable clearance between stationary and rotating parts in turbine stages generates high-enthalpy unsteady leakage flows that strongly reduce the engine efficiency and can cause thermally induced blade failures. An improved understanding of the tip flow physics is essential to refine the current design strategies and achieve increased turbine aerothermal performance. However, while past studies have mainly focused on conventional tip shapes (flat tip or squealer geometries), the open literature suffers from a shortage of experimental and numerical data on advanced blade tip configurations of unshrouded rotors. This work presents a complete numerical and experimental investigation on the unsteady flow field of a high-pressure turbine, adopting three different blade tip profiles. The aerothermal characteristics of two novel high-performance tip geometries, one with a fully contoured shape and the other presenting a multicavity squealer-like tip with partially open external rims, are compared against the baseline performance of a regular squealer geometry. The turbine stage is tested at engine-representative conditions in the high-speed turbine facility of the von Karman Institute. A rainbow rotor is mounted for simultaneous aerothermal testing of multiple blade tip geometries. On the rotor disk, the blades are arranged in sectors operating at two different clearance levels. A numerical campaign of full-stage simulations was also conducted on all the investigated tip designs to model the secondary flows development and identify the tip loss and heat transfer mechanisms. In the first part of this work, we describe the experimental setup, instrumentation, and data processing techniques used to measure the unsteady aerothermal field of multiple blade tip geometries using the rainbow rotor approach. We report the time-average and time-resolved static pressure and heat transfer measured on the shroud of the turbine rotor. The experimental data are compared against numerical predictions. These numerical results are then used in the second part of the paper to analyze the tip flow physics, model the tip loss mechanisms, and quantify the aero-thermal performance of each tip geometry.

In high-speed, unshrouded turbines, tip leakage flows generate large aerodynamic losses and intense unsteady thermal loads over the rotor blade tip and casing. The stage-loading and rotational speeds are steadily increased to achieve higher turbine efficiency, and hence, the overtip leakage flow may exceed the transonic regime. However, conventional blade tip geometries are not designed to cope with supersonic tip flow velocities. A great potential lies in the modification and optimization of the blade tip shape as a means to control the tip leakage flow aerodynamics, limit the entropy production in the overtip gap, manage the heat-load distribution over the blade tip, and improve the turbine efficiency at high-stage loading coefficients. The present paper develops an optimization strategy to produce a set of blade tip profiles with enhanced aerothermal performance for a number of tip gap flow conditions. The tip clearance flow was numerically simulated through two-dimensional compressible Reynolds-averaged Navier–Stokes (RANS) calculations that reproduce an idealized overtip flow along streamlines. A multiobjective optimization tool, based on differential evolution combined with surrogate models (artificial neural networks), was used to obtain optimized 2D tip profiles with reduced aerodynamic losses and minimum heat transfer variations and mean levels over the blade tip and casing. Optimized tip shapes were obtained for relevant tip gap flow conditions in terms of blade thickness to tip gap height ratios (between 5 and 25) and blade pressure loads (from subsonic to supersonic tip leakage flow regimes), imposing fixed inlet conditions. We demonstrated that tip geometries that perform superior in subsonic conditions are not optimal for supersonic tip gap flows. Prime tip profiles exist, depending on the tip flow conditions. The numerical study yielded a deeper insight on the physics of tip leakage flows of unshrouded rotors with arbitrary tip shapes, providing the necessary knowledge to guide the design and optimization strategy of a full blade tip surface in a real 3D turbine environment.

Tip leakage flows in unshrouded high speed turbines cause large aerodynamic penalties, induce significant thermal loads and give rise to intense thermal stresses onto the blade tip and casing endwalls. In the pursuit of superior engine reliability and efficiency, the turbine blade tip design is of paramount importance and still poses an exceptional challenge to turbine designers. The ever-increasing rotational speeds and pressure loadings tend to accelerate the tip flow velocities beyond the transonic regime. Overtip supersonic flows are characterized by complex flow patterns, which determine the heat transfer signature. Hence, the physics of the overtip flow structures and the influence of the geometrical parameters require further understanding to develop innovative tip designs. Conventional blade tip shapes are not adequate for such high speed flows and hence, potential for enhanced performances lays in appropriate tip shaping. The present research aims to quantify the prospective gain offered by a fully contoured blade tip shape against conventional geometries such as a flat and squealer tip. A detailed numerical study was conducted on a modern rotor blade (Reynolds number of 5.5 × 10⁵ and a relative exit Mach number of 0.9) by means of three-dimensional (3D) Reynolds-averaged Navier–Stokes (RANS) calculations. Two novel contoured tip geometries were designed based on a two-dimensional (2D) tip shape optimization in which only the upper 2% of the blade span was modified. This study yields a deeper insight into the application of blade tip carving in high speed turbines and provides guidelines for future tip designs with enhanced aerothermal performances.

The leakage flows within the gap between the tips of unshrouded rotor blades and the stationary casing of high-speed turbines are the source of significant aerodynamic losses and thermal stresses. In the pursuit for higher component performance and reliability, shaping the tip geometry offers a considerable potential to modulate the rotor tip flows and to weaken the heat transfer onto the blade and casing. Nevertheless, a critical shortage of combined experimental and numerical studies addressing the flow and loss generation mechanisms of advanced tip profiles persists in the open literature. A comprehensive study is presented in this two-part paper that investigates the influence of blade tip geometry on the aerothermodynamics of a high-speed turbine. An experimental and numerical campaign has been performed on a high-pressure turbine stage adopting three different blade tip profiles. The aerothermal performance of two optimized tip geometries (one with a full three-dimensional contoured shape and the other featuring a multicavity squealer-like tip) is compared against that of a regular squealer geometry. In the second part of this paper, we report a detailed analysis on the aerodynamics of the turbine as a function of the blade tip geometry. Reynolds-averaged Navier-Stokes (RANS) simulations, adopting the Spalart–Allmaras turbulence model and experimental boundary conditions, were run on high-density unstructured meshes using the numecafine/open solver. The simulations were validated against time-averaged and time-resolved experimental data collected in an instrumented turbine stage specifically setup for the simultaneous testing of multiple blade tips at scaled engine-representative conditions. The tip flow physics is explored to explain variations in turbine performance as a function of the tip geometry. Denton's mixing loss model is applied to the predicted tip gap aerodynamic field to identify and quantify the loss reduction mechanisms of the alternative tip designs. An advanced method based on the local triple decomposition of relative motion is used to track the location, size and intensity of the vortical flow structures arising from the interaction between the tip leakage flow and the main gas path. Ultimately, the comparison between the unconventional tip profiles and the baseline squealer tip highlights distinct aerodynamic features in the associated gap flow field. The flow analysis provides guidelines for the designer to assess the impact of specific tip design strategies on the turbine aerodynamics and rotor heat transfer.