Inverse Design of Axial-Flow Compressor Blades Using Elastic Surface Algorithm in Subsonic and Transonic Flow Regimes With Separation

In this study, a new inverse design method called Elastic Surface Algorithm (ESA) is developed and enhanced for axial-flow compressor blade design in subsonic and transonic flow regimes with separation. ESA is a physically based iterative inverse design method that uses a 2D flow analysis code to estimate the pressure distribution on the solid structure, i.e. airfoil, and a 2D solid beam finite element code to calculate the deflections due to the difference between the calculated and target pressure distributions. In order to enhance the ESA, the wall shear stress distribution, besides pressure distribution, is applied to deflect the shape of the airfoil. The enhanced method is validated through the inverse design of the rotor blade of the first stage of an axial-flow compressor in transonic viscous flow regime. In addition, some design examples are presented to prove the effectiveness and robustness of the method. The results of this study show that the enhanced Elastic Surface Algorithm is an effective inverse design method in flow regimes with separation and normal shock.

Efficient Multi-Objective Optimization of Labyrinth Seal Leakage in Steam Turbines Based on Hybrid Surrogate Models

The demand for energy is increasingly covered through renewable energy sources. As a consequence, conventional power plants need to respond to power fluctuations in the grid much more frequently than in the past. Additionally, steam turbine components are expected to deal with high loads due to this new kind of energy management. Changes in steam temperature caused by rapid load changes or fast starts lead to high levels of thermal stress in the turbine components. Therefore, todays energy market requires highly efficient power plants which can be operated under flexible conditions. In order to meet the current and future market requirements, turbine components are optimized with respect to multi-dimensional target functions. The development of steam turbine components is a complex process involving different engineering disciplines and time-consuming calculations. Currently, optimization is used most frequently for subtasks within the individual discipline. For a holistic approach, highly efficient calculation methods, which are able to deal with high dimensional and multidisciplinary systems, are needed. One approach to solve this problem is the usage of surrogate models using mathematical methods e.g. polynomial regression or the more sophisticated Kriging. With proper training, these methods can deliver results which are nearly as accurate as the full model calculations themselves in a fraction of time. Surrogate models have to face different requirements: the underlying outputs can be, for example, highly non-linear, noisy or discontinuous. In addition, the surrogate models need to be constructed out of a large number of variables, where often only a few parameters are important. In order to achieve good prognosis quality only the most important parameters should be used to create the surrogate models. Unimportant parameters do not improve the prognosis quality but generate additional noise to the approximation result. Another challenge is to achieve good results with as little design information as possible. This is important because in practice the necessary information is usually only obtained by very time-consuming simulations. This paper presents an efficient optimization procedure using a self-developed hybrid surrogate model consisting of moving least squares and anisotropic Kriging. With its maximized prognosis quality, it is capable of handling the challenges mentioned above. This enables time-efficient optimization. Additionally, a preceding sensitivity analysis identifies the most important parameters regarding the objectives. This leads to a fast convergence of the optimization and a more accurate surrogate model. An example of this method is shown for the optimization of a labyrinth shaft seal used in steam turbines. Within the optimization the opposed objectives of minimizing leakage mass flow and decreasing total enthalpy increase due to friction are considered.

Adaptive Mesh Refinement for DDES Simulation on Transonic Compressor Cascade With Unstructured Mesh

There are local flow phenomena like shock wave/boundary interaction and tip leakage flow which strongly influence the compressor performance and stability. AMR (Adaptive Mesh Refinement) strategy shows attractive property for automatically refining local mesh and predicting higher local phenomenon details. This paper develops the AMR strategy for turbomachinery with unstructured mesh. Curved surface boundary matching is focused in AMR process for achieving high level simulation accuracy. The developed AMR strategy is used to improve shock wave prediction in this paper. Firstly two dimensional RANS simulation of compressor cascade L030-4 is conducted to test the AMR strategy. Refined mesh shows better shock wave details compared with the almost none shock wave structure of baseline mesh. Then quasi-3D DDES (Delayed Detached Eddy Simulation) simulation of this compressor cascade is conducted. Shock wave oscillation phenomenon is clearly shown for this cascade. Local mesh of shock wave oscillation region is automatically refined by AMR. The refined mesh predicts better shock wave details and better turbulence motion comparing to the baseline mesh.

Optimization of Robust Transonic Compressor Blades

Surface degradation in an axial compressor during its lifetime can have a considerable adverse effect on its performance. The present study investigates how the optimized design of compressor blades in a single compressor stage is affected by considering a high level of surface roughness on a level representative of a long period of in-service use. It is shown that including surface roughness in the optimization process is of relatively little importance, however, matching of compressor stages is shown to require consideration as the rotational speed must be increased to reach the design point as surface quality decrease. An increased surface roughness in itself is shown to have a large effect on performance. Two optimization approaches are compared. The first approach considers the compressor blades to be hydraulically smooth. The designs obtained from this approach are subsequently degraded by increasing the level of surface roughness. The compressor blades from the first approach are compared to designs obtained from a second optimization approach, which considers a high level of surface roughness from the outset. The degraded compressor stages from the first approach are shown to be among the best performing designs in terms of polytropic efficiency and stability when compared to designs obtained with the second approach.

Automated Thermal and Stress Preliminary Analyses Applied to a Turbine Rotor

The use of Multidisciplinary Design Optimization (MDO) techniques at the preliminary design phase (PMDO) of a gas turbine engine allows investing more effort at the pre-detailed phase in order to prevent the selection of an unsatisfactory concept early in the design process. Considering the impact of the turbine tip clearance on an engine’s efficiency, an accurate tool to predict the tip gap is a mandatory step towards the implementation of a full PMDO system for the turbine design. Tip clearance calculation is a good candidate for PMDO technique implementation considering that it implies various analyses conducted on both the rotor and stator. As a first step to the development of such tip clearance calculator satisfying PMDO principles, the present work explores the automation feasibility of the whole analysis phase of a turbine rotor preliminary design process and the potential increase in the accuracy of results and time gains. The proposed conceptual system integrates a thermal boundary conditions automated calculator and interacts with a simplified air system generator and with several conception tools based on parameterized CAD models. Great improvements were found when comparing this work’s analysis results with regular pre-detailed level tools, as they revealed to be close to the one generated by the detailed design tools used as target. Moreover, this design process revealed to be faster than a common preliminary design phase while leading to a reduction of time spent at the detailed design phase. By requiring fewer user inputs, this system decreases the risk of human errors while entirely leaving the important decisions to the designer.

Body Force Modeling of the Aerodynamics of the Fan of a Turbofan at Windmill

The windmilling regime of a turbofan corresponds to a freewheeling mode of the fan rotor, driven by the ram pressure at the inlet. Early in the design process, determination of the windmilling rotational speed of the fan can be critical in the design of the supporting structure of the engine. Therefore, prediction of key parameters in windmilling is an important part of engine design. In particular, given the very high bypass ratio obtained at windmill (typically around 50), the flow in the fan stage and bypass duct is of prime interest, as it drives the establishment of the rotational speed of the low pressure spool and the overall drag. Classical CFD simulations have been shown to provide an adequate representation of the flow, but extensive parametric studies can be needed, which underlines the need for reduced-cost modeling of the flow in the engine. In this context, a body force modeling (BFM) approach to windmilling simulations is examined in the present contribution. The main objective is to assess the capability of the BFM approach to reproduce the aerodynamics of the flow in the fan rotor of a turbofan at windmill, and to propose a method to predict the rotational speed of the fan. The test case considered is a high-bypass ratio geared turbofan (the DGEN 380), which has been tested in an experimental facility designed to reproduce ground level windmilling conditions. The available global and local experimental data are used to validate the model. Furthermore, classical RANS simulations are also provided as reference simulations to assess the accuracy of the BFM results. It is found that the overall performance of the fan is well predicted by the BFM simulations, in particular at the low rotational regime associated to windmilling. In terms of local validation, radial profiles are also found to be in good agreement, except close to the shroud. Analysis of the CFD results shows this can be traced back to massive flow separation in the rotor tip area. In terms of cost, a BFM simulation is about 80 times faster than the baseline CFD computation, making this approach very efficient in term of accuracy-to-cost ratio. Finally, assuming zero-work exchange across the rotor, a transient equation for the rotational speed is derived and included in the time-marching process to the steady state. As a result, the rotational speed of the fan becomes an output of the simulations. The rotational speed predicted by the present model shows good agreement with engine experimental data. However, as only the rotor is modeled, the internal losses are not fully accounted for, and the massflow has to be specified from the experimental data. Further improvement of the approach will consist in modeling the stator and the complete secondary duct so that the loss, and therefore the massflow, can be predicted.

Technique for Adequate CFD-Modeling of the Pump With Hydro-Drive of the Low-Pressure Stage

This article describes the technique for CFD-modeling of a powerful two-stage pump with the following main parameters: main rotor speed is 13,300 rpm, inlet pressure is 0.2 MPa, pressure head is more than 3,000 meters with mass flow of 250 kg/s. The main feature of investigated pump is the hydro-drive of the low-pressure stage of turbine with variable rotational speed. There are two highlights in this work in comparison with the previous ones. The first one is how to choose the rotating speed of hydro-turbine. The second one is the CFD-modeling of cavitation processes. The core part of proposed technique is the determination of rotational speed during CFD-simulation by special methodology. Another feature is the cavitation modeling to be sure that there is no cavitation in pre-pump at quite low inlet pressure and variable rotor speed. Also, recommendations about program tools (ANSYS CFX, NUMECA AutoGrid5, ANSYS ICEM CFD) are a significant part of the discussed technique, as well as modeling features (fluid domain restriction, meshing, turbulence models choosing, convergence checking, post-processing). The adequacy of CFD-model was evaluated by comparing predicted characteristics of the pump with the experimental ones derived from the test rig. The differences amounted to less than 10%. The obtained technique can be used in the future research for performance improving and efficiency increasing of pumps with hydro-drive of the low-pressure stage by CFD-tools.

Adjoint-Response Surface Method in Aerodynamic Shape Optimization of Turbomachinery Blades

An adjoint-response surface method is developed to give global representation of cost function in a parametrized design space for turbomachinery blades. Radial basis function (RBF) based and quadratic polynomial (QP) based response surface models are constructed using both the values of cost function and its adjoint gradients with respect to geometry control parameters. The method is tested on a quasi-three dimensional NACA0012 blade row, then applied to the transonic Rotor 67. In preliminary design optimization stage, when the number of undetermined control parameters is large, the QP based model can provide a global image of the cost function in high dimensional design space with a small amount of sample points. In two-parameter fine optimization stage, high resolution can be achieved with the RBF based models. This gradient-enhanced response surface method is useful in guiding designers to discover the global optimum which may be missed by local gradient methods in a complicated design space. It may also be used as substitute of CFD flow solver in time consuming iterative design and optimization.

Application of High-Resolution Large Eddy Simulation to Simplified Turbomachinery Flows

Fully resolved large eddy simulation (LES) is applied to two simple geometry flowfields with well-defined boundary conditions. The LES results are compared with simulations based on a Reynolds-averaged Navier-Stokes (RANS) model with turbulence, and pros and cons of using high-resolution LES for turbomachinery flows are discussed. One flow is a linear compressor cascade flow composed of the tip section of GE rotor B at Rec = 4 × 105 with a clearance, and the other is a Mach 1.76 supersonic turbulent boundary layer at Reδ = 5000 that laminerizes through a 12-degree expansion corner. The grids are prepared fine enough to resolve the turbulent boundary layer through a grid sensitivity study. The liner cascade result shows that all the turbulent shear layers and boundary layers including those in the small tip clearance are well resolved with 800 million grid points. The Reynolds stress derived from the LES results are compared directly with those predicted from the Spalart-Allmaras one-equation RANS turbulence model. The two results agreed qualitatively well except for the shear layer surrounding the tip leakage vortex, demonstrating that the RANS model performs well at least for flowfields near the design condition. From the simulation of the turbulent boundary layer experiencing sudden expansion, noticeable decreases of both Reynolds stress and local friction coefficient were observed, showing that the turbulent boundary layer has relaminarized through the sudden expansion. The boundary layer downstream of the expansion exhibits a nonequilibrium condition and was different from the laminar boundary layer.

Development of an Improved Streamline Curvature Approach for Transonic Axial Compressor

In this paper, an improved streamline curvature (SLC) approach is presented to obtain the internal flow fields and evaluate the performance of transonic axial compressors. The approach includes some semi-empirical correlations established based on previous literatures, such as minimum loss incidence angle model, deviation model and total pressure loss model. Several developments have been made in this paper for the purpose of considering the influences of three-dimensional (3D) flow in high-loaded multistage compressors with high accuracy. A revised deviation model is applied to predict the cascade with large deflection range. The method for predicting the shock loss is also discussed in detail. In order to validate the reliability of the approach, two test cases including a two-stage transonic fan and a three-stage transonic compressor are conducted. The overall performance and distribution of spanwise aerodynamic parameters are illustrated in this paper. Compared with both the experimental and computational fluid dynamic (CFD) data at design and a number of different off-design condition, the SLC results give reasonable characteristic curves. The validation demonstrates that this improved approach can serve as a fast and reliable tool for flow field analysis and performance prediction in preliminary design stage of axial compressors.