On the Evaluation of Common Design Metrics for the Optimization of Non-Axisymmetric Endwall Contours for a 1-stage Turbine Rotor - Bergh, Jonathan (Department of Mechanical Engineering, 2019)
With the continued economic and socio-political pressure on aircraft manufacturers to produce more profitable and environmentally-friendly aircraft, the drive towards increasingly more efficient aircraft engines remains of prime importance to aircraft engine manufacturers. While the majority of axial flow turbomachines use cylindrically shaped endwalls between the blades on the hub or shroud, non-axisymmetric endwall contouring is a reasonably recent technique which relaxes this constraint, and allows the geometry of the endwalls to depart from that of a plain cylinder. Although a number of studies have shown non-axisymmetric endwall contouring to be an effective mechanism for the reduction of secondary flows (and the losses associated with them), within the open literature there still remains a general lack of detailed information relating to the optimal design of these devices. Among some of the most important issues which remain unresolved, are uncertainties such as: “What is the best way to identify and thereafter quantify the strength of turbine secondary flows?”, and thereafter, as a natural progression from this, “Of the metrics which are currently found within the literature, which are best for use in the design of secondary loss mitigating endwall contours for a real turbine?”. Some of the reasons for the lack of information as described above, result from the undertaking of many of the investigations into the design of endwall contours by or on behalf of the major engine manufacturers, and therefore, a general inability or perhaps even unwillingness to divulge many of the specific details related to the methodologies and quantities used as a result of the commercial sensitivity of these investigations. In addition to this, as a result of the relatively large number and diverse nature of groups involved in non-axisymmetric endwall contouring research, within the literature which has been made available, there exists a wide variety of different test geometries as well as conditions which have been used, making a neutral determination of the most successful approach to endwall contouring considerably more difficult. This thesis documents the design and testing of a number of different non-axisymmetric endwall configurations intended to produce flow conditions optimized using a selection of the metrics commonly found in the literature, for the rotor of a low speed, research turbine, whose baseline as well as performance using contoured endwalls has been reported on previously, in order to establish which of these metrics is the most effective. As part of this process, a fully validated computational fluid dynamics model of the turbine downstream of the first nozzle was developed and incorporated into an automated non-axisymmetric end- wall design routine, capable of producing endwall contours optimized for various objective functions. Numerical testing showed that, in order to distinguish accurately between the various endwall configurations, relatively fine computational meshes were required and therefore, as a result of corresponding computational expense associated with these meshes, the implementation of a surrogate modelling procedure in which part of this computational cost is offset by mathematical modelling, was necessary. Altogether, a total of 8 endwall designs were produced - 6 using a single metric each as the basis of their objective functions (the ‘simple’ designs) and a further 2 so-called ‘compound’ designs. Of the simple designs, the best performing endwalls in terms of improvements to the rotor exit efficiency were the ηtt-, Cske- & βdev-based designs, which were based in turn on the rotor total-total efficiency (ηtt), coefficient of secondary kinetic energy (Cske) and flow deviation from design angle (βdev) respectively. All three of these designs were predicted to result in very similar changes to the secondary flow characteristics although the increasing bias towards flow correction was found to have an inverse correlation with the overall efficiencies predicted for each rotor. Of these designs, the numerical predictions for both the ηtt- & Cske-based designs (which were included in the experimental subset), were found to be validated, at both the rotor exit as well as downstream measurement planes. Further to this (with the exception of the Cp0,rel-based case), although the remainder of the simple designs (i.e. the SKEH & ηde-based designs) were also predicted to improve the overall rotor efficiency, either the form or the performance of these endwalls resulted in the final corresponding designs for these metrics being considered unsatisfactory. Finally, the two ‘compound’ metrics were both formulated to to include a term designed to target the secondary flow within the target blade row, as well as an additional term which was designed to promote improvement in the flow into the downstream blade row. While both designs produced using the compound design objective functions were predicted to improve both the conditions for the target blade row, as well as the flow quality at the exit of the blade row, flow separations at the exit of the contoured regions for both designs resulted in only partial validation of each design when tested experimentally. Finally, although both designs were once again predicted to perform very well at the ‘mixed-out’ measurement plane, these predictions were found to be only partially validated by the experiment.