Compressor Blade Optimization Using a Continuous Adjoint Formulation

In this paper, a constrained optimization algorithm is formulated and utilized to improve the aerodynamic performance of a 3D peripheral compressor blade cascade. The cascade efficiency is measured in terms of entropy generation along the developed flowfield, which defines the field objective functional to be minimized. Its gradient with respect to the design variables, which are the coordinates of the Non-Uniform Rational B-Spline (NURBS) control points defining the blade, is computed through a continuous adjoint formulation of the Navier-Stokes equations based on the aforementioned functional. The steepest descent algorithm is used to locate the optimal set of design variables, i.e. the optimal blade shape. In addition to the well-known advantages of the adjoint method, the current formulation has even less CPU cost for the gradient computation as it leads to gradient expression which is free of field variations in geometrical quantities (such as derivatives of interior grid node coordinates with respect to the design variables); the computation of the latter would be costly since it requires remeshing anew the computational domain for each bifurcated design variable. The geometrical constraints, which depend solely on the blade parameterization, are handled by a quadratic penalty method by introducing additional Lagrange multipliers.

Optimisation Techniques Applied to the Design of Gas Turbine Blades Cooling Systems

This paper addresses the methodology used to design the layout of the tip cooling nozzles of a high pressure rotor blade turbine. The methodology used is through a complete CAE approach, by means of a parametric CFD model which is run several times for the exploration of several designs by an optimizer. Hence the design is carried out automatically by parallel computations, with the optimization algorithms taking the decisions rather than the design engineer. The engineer instead takes decision regarding the physical settings of the CFD model to employ, the number and the extension of the geometrical parameters of the blade tip holes and the optimization algorithms to be employed. From CFD validation the final design of the tip cooling geometry found by the optimizer has proved to be better than the base design, which used mean values of all input parameters, and than the design proposed by an experienced heat transfer AVIO engineer, who used standard best practice methods. Furthermore the large number of experiences gained by the simulations run by the optimizer allowed the designer to find laws, functions and correlation between input parameters and performance output, with a further and deeper insight on this specific design problem.

The Development of an Aerodynamic Performance Prediction Tool for Modern Axial Flow Compressor Profiles

The development of a computational tool (MP-LOS) for the aerodynamic loss modeling and prediction for axial-flow compressor blade sections is presented in this paper. A state-of-the-art quasi 3-D flow solver, MISES, has been used for the flow analysis on existing airfoil geometries in many working conditions. Different values of inlet flow angle, inlet Mach number, AVDR, Reynolds number and solidity have been chosen to investigate a possible working range. The target is a loss prediction formulation that will be introduced into throughflow or axisymmetric Navier-Stokes codes for the performance prediction of multistage axial flow compressors. The loss coefficient has been correlated to the flow parameters that have shown an influence on the profile loss for the blades under study. The proposed correlation, using the described computational approach, can be extended to any profile family with the aid of any code for the parametric design of blade profiles.

Assessing Convergence in Predictions of Periodic-Unsteady Flowfields

Predictions of time-resolved flowfields are now commonplace within the gas-turbine industry, and the results of such simulations are often used to make design decisions during the development of new products. Hence it is necessary for design engineers to have a robust method to determine the level of convergence in design predictions. Here we report on a method developed to determine the level of convergence in a predicted flowfield that is characterized by periodic-unsteadiness. The method relies on fundamental concepts from digital signal processing including the discrete Fourier transform, cross-correlation, and Parseval’s theorem. Often in predictions of vane-blade interaction in turbomachines, the period of the unsteady fluctuations is expected. In this method, the development of time-mean quantities. Fourier components (both magnitude and phase), cross-correlations, and integrated signal power are tracked at locations of interest from one period to the next as the solution progresses. Each of these separate quantities yields some relative measure of convergence that is subsequently processed to form a fuzzy set. Thus the overall level of convergence in the solution is given by the intersection of these sets. Examples of the application of this technique to several predictions of unsteady flows from two separate solvers are given. These include a prediction of hot-streak migration as well as more typical cases. It is shown that the method yields a robust determination of convergence. Also, the results of the technique can guide further analysis and/or post-processing of the flowfield. Finally, the method is useful for the detection of inherent unsteadiness in the flowfield, and as such it can be used to prevent design escapes.

Effect of the Leakage Flows and the Upstream Platform Geometry on the Endwall Flows of a Turbine Cascade

This work describes the effect that the injection of leakage flow from a cavity into the mainstream has on the endwall flows and their interaction with a large pressure surface separation bubble in a low-pressure turbine. The effect of a step in hub diameter ahead of the blade row is also simulated. The blade profile under consideration is a typical design of modern low-pressure turbines. The tests are conducted in a low speed linear cascade. These are complemented by numerical simulations. Two different step geometries are investigated, i.e., a backward-facing step and a forward-facing step. The leakage tangential velocity and the leakage mass flow rate are also modified. It was found that the injection of leakage mass flow gives rise to a strengthening of the endwall flows independently of the leakage mass flow rate and the leakage tangential velocity. The experimental results have shown that below a critical value of the leakage tangential velocity, the net mixed-out endwall losses are not significantly altered by a change in the leakage tangential velocity. For these cases, the effect of the leakage mass flow is confined to the wall, as the inlet endwall boundary layer is pushed further away from the wall by the leakage flow. However, for values of the leakage tangential velocity around 100% of the wheelspeed, there is a large increase in losses due to a stronger interaction between the endwall flows and the leakage mass flow. This gives rise to a change in the endwall flows structure. In all cases, the presence of a forward-facing step produces a strengthening of the endwall flows and an increase of the net mixed-out endwall losses when compared with a backward-facing step. This is because of a strong interaction with the pressure surface separation bubble.

Investigation of the Flow Field in a HP Turbine Stage for Two Stator-Rotor Axial Gaps: Part II — Unsteady Flow Field

An extensive experimental analysis was carried out at Politecnico di Milano on the subject of unsteady flow in high pressure (HP) turbine stages. In this paper the unsteady flow measured downstream of a modern HP turbine stage is discussed. Traverses in two planes downstream of the rotor are considered and, in one of them, the effects of two very different axial gaps are investigated: the maximum axial gap, equal to one stator axial chord, is chosen to “switch off” the rotor inlet unsteadiness, while the nominal gap, equal to 1/3 of the stator axial chord, is representative of actual engines. The experiments were performed by means of a fast-response pressure probe, allowing for two-dimensional phase-resolved flow measurements in a bandwidth of 80 kHz. The main properties of the probe and the data processing are described. The core of the paper is the analysis of the unsteady rotor aerodynamics; for this purpose, instantaneous snapshots of the rotor flow in the relative frame are used. The rotor mean flow and its interaction with the stator wakes and vortices are also described. In the outer part of the channel only the rotor cascade effects can be observed, with a dominant role played by the tip-leakage flow and by the rotor tip passage vortex. In the hub region, where the secondary flows downstream of the stator are stronger, the persistence of stator vortices is slightly visible in the maximum stator-rotor axial gap configuration, while in the minimum stator-rotor axial gap configuration the interaction with the rotor vortices dominates the flow field. A fair agreement with the wakes and vortices transport models has been achieved. A discussion of the interaction process is reported giving particular emphasis to the effects of the different cascade axial gaps. Some final considerations on the effects of the different axial gap over the stage performances are reported.

Numerical Simulations of Heat Transfer and Fluid Flow for a Rotating High-Pressure Turbine

In this work, a numerical study has been performed to simulate the heat transfer and fluid flow in a transonic high-pressure turbine stator vane passage. Four turbulence models (the Spalart-Allmaras model, the low-Reynolds-number realizable k-ε model, the shear-stress transport (SST) k-ω model and the v2-f model) are used in order to assess the capability of the models to predict the heat transfer and pressure distributions. The simulations are performed using the FLUENT commercial software package, but also two other codes, the in-house code VolSol and the commercial code CFX are used for comparison with FLUENT results. The results of the three-dimensional simulations are compared with experimental heat transfer and aerodynamic results available for the so-called MT1 turbine stage. It is observed that the predictions of the vane pressure field agree well with experimental data, and that the pressure distribution along the profile is not strongly affected by choice of turbulence model. It is also shown that the v2-f model yields the best agreement with the measurements. None of the tested models are able to predict transition correctly.

The Effect of Stator-Rotor Hub Sealing Flow on the Mainstream Aerodynamics of a Turbine

An investigation into the effect of stator-rotor hub gap sealing flow on turbine performance is presented. Efficiency measurements and rotor exit area traverse data from a low speed research turbine are reported. Tests carried out over a range of sealing flow conditions show that the turbine efficiency decreases with increasing sealant flow rate but that this penalty is reduced by swirling the sealant flow. Results from time-accurate and steady-state simulations using a three-dimensional multi-block RANS solver are presented with particular emphasis paid to the mechanisms of loss production. The contributions toward entropy generation of the mixing of the sealant fluid with the mainstream flow and of the perturbed rotor secondary flows are assessed. The importance of unsteady stator wake/sealant flow interactions is also highlighted.

Experimental Characterization of Vaneless Diffuser Rotating Stall: Part VI — Reduction of Three Impeller Results

Vaneless diffuser rotating stall is a major problem for centrifugal compressors since it is a limit to their working range. In the literature some good correlations for predicting stall inception can be found but they do not adequately cover the case of the last stage configuration, especially for very low blade-outlet-width-to-impeller-radius-ratio impellers typically used in high-pressure applications. Extensive research has been performed to define diffuser stall limits for this family of stages: three impellers characterized by different blade-outlet-width-to-impeller-radius-ratios have been tested with different diffuser configurations (different pinch shapes, diffuser widths and diffusion ratios). The basic configuration comprises a 1:1 geometrical scale stage with a return channel upstream, a 2D impeller with a vaneless diffuser and a volute with a constant cross sectional area downstream. Several diffuser types with different widths and diffusion ratios were tested. Detailed experimental results have been reported in previous works [1, 2, 3 and 4]. In this paper experimental data are reviewed in order to analyze impeller influence on diffuser stability and to develop some summarizing consideration on stall behavior of vaneless diffuser for impeller with low blade-outlet-width-to-impeller-radius-ratio.

The Performance of Air-Air Ejectors With Triangular Tabbed Driving Nozzles

This paper describes an experimental investigation into the effects of geometrical variations on ejector system performance when the driving nozzle includes delta mixing tabs. Mixing tabs have been shown to provide good mixing performance with comparable back-pressure penalties to other types of enhanced mixing nozzles. The performance parameters of most interest are pumping, mixing, and back-pressure. Geometric parameters studied include standoff distance, mixing-tube diameter, and tab angle. Experimental testing showed significant performance improvements in mixing and pumping with a decrease in tab angle. Maximum mixing was found to occur with tab angles positioned at 120°. Exceptional mixing was also observed with increased standoff. Back-pressure was shown to increase with increasing standoff and decreasing tab angle, but was not affected by mixing-tube diameter. In addition, a zone of recirculation was identified at the entrance to the mixing-tube. This zone is thought to have an influence on ejector performance.