Marcel Aulich

Automated multiobjective optimisation in axial compressor blade design

This paper presents an automated multiobjective design methodology for the aerodynamic optimisation of turbomachinery blades. In this approach several operating-points of the compressor are considered and the flow-characteristics of the different flow-solutions are combined to one or more objective functions. The optimisation strategy is based on multiobjective asynchronous evolutionary algorithms (MOEA’S) which are accelerated using additive local neural networks and kriging procedures. Common operators: Mutation, Crossover and Differential-Evolution are used to create a new population. In addition to these common operators the optimisation runs temporarily on the response-surface created by the neural networks and/or kriging-processes respectively. Only the Pareto-optimal solutions obtained from this metamodel are evaluated using the numerical expensive flow-solver. Therefore, the response-surface is just a new operator that creates auspicious members. One of the main differences between the presented code to usual and traditional MOEA’S is the selection of parents. While traditional codes choose potential parents of a new population from the previous population, the current method selects parents from the database of all evaluated members. This approach allows the user to run the optimisation asynchronously and with a smaller size of population, treducing numerical costs, without influencing the diversity of the optimal solutions over the whole Pareto-front. This aspect is very important when evaluating very complex and/or discontinuous fronts.

High-Dimensional Constrained Multiobjective Optimization of a Fan Stage

A high-dimensional design space, different objectives, many constraints and a time-consuming process chain result in a complex task for any optimization tool. This paper shows methods and strategies used at DLR, Institute of Propulsion Technology, to handle this kind of problem. The present optimization task is a rotor-stator configuration with more than two hundred free design variables, two objective functions (efficiency, stall margin) and mechanical and aerodynamic constraints (mass flow, eigenfrequencies, etc.). The process chain consists of geometry and mesh generation, FEM-and 3D-CFD calculations for different operating points. After defining the setup and explaining the initial already 3-D-preoptimized configuration, the CFD/FEM optimization tool is described. This tool calculates the complete CFD/FEM process chain and creates new designs (also called members) by using an evolutionary algorithms. Parallel to the CFD/FEM optimization a program based on surrogate models is running. By using surrogate models a fast evaluation of new members is enabled. So a database of new members can be created quickly. Based on this database a set of new members is built. This is send to the CFD/FEM optimization tool, where the complete CFD/FEM process chain is applied. After the CFD/FEM evaluation process, these member are used to train the surrogate models again. This procedure repeats until the optimization goals are reached. In the next part of this paper the implemented surrogate models are discussed. Both neural networks and Kriging models have advantages and disadvantages compared to each other. It is important to understand them to choose the right model at the right time of optimization. The main focus of this paper is on the selection criterion for new members. This criterion has two targets: push the performance of the fan stage and enhance the surrogate models. At first sight these targets seem to be contrary, but the surrogate models do not predict a single mean value for an objective. They offer a density distribution of the potential objective values. That allows calculation of the Paretofront enhancement (ParetoEnSet) for a set of new members. ParetoEnSet is the expected area gain of a set of members to the current Paretofront. This criterion based on the already known expected improvement. It is shown, that ParetoEnSet can rise, when the uncertainty of an prediction increases. The uncertainty is estimated by a surrogate model. So new members tend to explore the design space, where the predicted uncertainty is huge. These members are favorable for improving the surrogate models. In addition, it is easy to couple constraints with ParetoEnSet. In the last section the results of the optimization are illustrated. Compared to baseline design the optimized stage accomplishes a notable improvement in efficiency by obtaining the stall margin and fulfilling multi aerodynamical and mechanical constraints.Copyright

Gradient Enhanced Surrogate Models Based on Adjoint CFD Methods for the Design of a Counter Rotating Turbofan

This paper studies the use of adjoint CFD solvers in combination with surrogate modelling in order to reduce the computational cost of the optimization of complex 3D turbomachinery components. The method is applied to a previously optimized counter rotating turbofan, with a shape parameterized by 104 CAD parameters.Through random changes on the reference design, a small number of design variations are created to serve as training samples for the surrogate models. A steady RANS solver and its discrete adjoint are then used to calculate objective function values and their corresponding sensitivities. Kriging and neural networks are used to build surrogate models from the training data. To study the impact of the additional information provided by the adjoint solver, each model is trained with and without the sensitivity information. The accuracy of the different surrogate model predictions is assessed by comparison against CFD calculations.The results show a considerable improvement of the fitness function approximation when the sensitivity information is taken into account. Through a gradient based optimization on one of the surrogate models, a design with higher isentropic efficiency at the aerodynamic design point is created. This application demonstrates that the improved surrogate models can be used for design and optimization.Copyright

MULTIDISCIPLINARY 3D-OPTIMIZATION OF A FAN STAGE PERFORMANCE MAP WITH CONSIDERATION OF THE STATIC AND DYNAMIC ROTOR MECHANICS

Achievement of an optimal compressor design with respect to its aerodynamic performance and feasible structural mechanics within an automated optimization process is subject of this paper. The compressor considered is a highly loaded, transonic fan stage, designed for achievement of a very high pressure ratio. To ensure operation in highly integrated installation conditions, a sufficient stability margin is of major concern. Multiple aerodynamic operating points at two rotational speeds allowed optimization of both the stability margin and the working line stage efficiency. On the part of structural mechanics, several static stress criteria were addressed for definite blade regions as well as the dynamic blade behavior in terms of the Campbell diagram. An optimization strategy was chosen, which targeted firstly on the fulfillment of multiple mechanical and aerodynamical constraints, while the aerodynamic performance was under constraint itself. Upon achievement, optimization aimed for maximum aerodynamic performance while keeping mechanics feasible. Response surfaces have been incorporated in the optimization process to reconcile costly high fidelity CFD and structural simulations with the large number of 114 free design parameters. Furthermore, optimization on these models enabled a successfully accomplishment of the constraint issue by a large number of numerically cheaper fitness evaluations. Starting from an already optimized baseline configuration, the current work targeted an improvement of the rotor aerodynamics in the transonic hub region and the resolution of previously unsolved problems concerning the rotor structural mechanics. Free design parameters were hub and casing contours in the rotor part, the shape of the leading and trailing blade edges and a high degree of freedom for rotor profile sections in the lower half of the blade.

Novel Performance Prediction of a Transonic 4.5 Stage Compressor

Computing capacities have grown exponentially in recent years and 3D-Navier-Stokes methods were developed widely. However it is still not feasible to design a multi-stage compressor directly in three dimensions. Instead, compressor design starts with 1D-design. In accordance with this approach, basic parameters such as the number of stages and stage pressure ratios are determined. In the following 2D-design, the geometry of the flow channel and the main parameters of the blade geometries can be determined. Afterwards in the 3D-design, unsteady and 3D-flow-effects are considered and the design optimized accordingly. Therefore, it is virtually impossible to correct conceptual faults in the 3D-design phase. Thus a robust and reliable 2D-Throughflow-solver including a performance prediction for modern airfoil geometries is necessary. So far there is no efficient methodology known which predicts the performance for all kinds of airfoil geometries, as it would be necessary in a 2D-Throughflow optimization process. In [1, 2] a novel methodology was presented, which is able to predict the performance for a large number of airfoil geometries accurately. This method is based on a large airfoil database which is used to train a surrogate model for airfoil performance prediction. The scope of this work is to validate and to document the progress of this new approach. In Schmitz et al. [1] it was validated on rotor 1 of the 4.5 stage transonic test compressor DLR-RIG250 of the Institute of Propulsion Technology. In this work all 4.5 stages were calculated at different speedlines and different vane positions. The results of the S2-solver are compared to experimental data and 3D-CFD calculations, obtained using the DLR in-house solver TRACE.Copyright

Novel Approach for Loss and Flow-Turning Prediction Using Optimized Surrogate Models in Two-Dimensional Compressor Design

Two-dimensional (2D) streamline curvature methods are still an important tool in modern compressor design. In the past most of the streamline curvature methods made use of empirical correlations to approximate the blade row losses and deviation functions on which the accuracy of streamline curvature methods mainly depend. These empirical correlations are just accurate for a small set of geometric airfoil design parameters for which they where obtained and the prediction of airfoil performance at high Mach numbers or at off-design condition is inaccurate. Nowadays, a new approach is needed to consider highly customized, modern airfoil geometries with an increased number of design parameters. A new method with the possibility to predict the performance of these highly customized airfoils also at off-design condition and high Mach numbers is presented in this paper. This method uses a large airfoil database together with optimized surrogate models to accurately predict airfoil performance. The database consists of approximately 106 randomly created airfoils with randomly created inflow conditions and the airfoil performance which results from the 2D Euler-boundary layer code MISES [16]. The airfoil geometry in this database is described by ten geometrical parameters, e.g. stagger angle, chord length etc.. The flow condition is described by four flow parameters such as the relative inflow Mach number, MVDR, relative inflow angle and Reynolds number. Airfoil performance is represented by total pressure loss and flow-turning. This database was used to train neural networks that provides the relationship between the geometrical/flow parameters and the airfoil performance. The topology of the neural networks was optimized to achieve a model which represents this highly nonlinear functionality at best. This model was integrated in the DLR’s in-house streamline curvature tool ACDC which is based on the equations of MONIG et al. [12], GALLIMORE [8]. The code allows viscous throughflow calculations taking into account radial mixing by turbulent diffusion, endwall boundary layers and a model for tip clearance based on the work of DENTON [7], KROGER et al. [9].Copyright

Using automated optimisation to calibrate a correlation-based transition model

Transition models used in turbomachinery CFD are based on empirical correlations de-rived from a series of fundamental test cases. When these models are applied to complex configurations they often do not perform as desired and need to be tuned to the respec-tive area of application. In this paper, an approach to tune a correlation based transition model to a given set of turbine rigs using automated optimisation is presented. The model is optimised such that deviations from experiments in terms of blade pressure distribution and global losses are minimised. The optimisation strategy and results are analysed in detail showing strengths and weaknesses of the proposed approach. While the agreement with experimental data of the turbine rigs can be improved, an analysis of zero pressure gradient flat plate flow shows that the resulting models cannot be considered as general as the original model.

Automated Optimization of an Axial-Slot Type Casing Treatment for a Transonic Compressor

It has been shown in many cases that a notable aerodynamic stability enhancement can be achieved using casing treatments (CTs) on transonic compressors. This advantage, however, often involves degradation in efficiency at design point conditions. In order to analyze the correlations between efficiency, surge margin and other flow quantities on the one hand and the geometric parameters related to axial slots on the other, an automated multi objective geometry optimization of axial slots is performed. This involves the usage of time accurate URANS simulations for each new CT design the optimization tool proposes. The axial slots are generated using a parametric design, which can produce slots of different size, shape and position. Three operating points are simulated. One at design point (ADP) conditions, a second at reduced speed working line conditions and a third at reduced speed close to the stability limit. Based on the results of the CFD simulations two objective values are calculated. These are, first, an increased efficiency at working line conditions and, second, an increased surge margin at reduced speed. The test case used for the study is the first stage of DLR’s transonic research compressor Rig250. The rig is representative for the front stages of a heavy duty gasturbine compressor. The computational domain includes the IGV as well as the first rotor and stator. The rotor of the configuration is tip-critical for the studied part speed condition. The result of the optimization is a Pareto front with all optimal geometries regarding surge margin and efficiency. It is found that efficiency at design point can be exchanged against surge margin at reduced speed. The working principles and flow phenomena of the Pareto-optimal axial slots are analyzed in detail to obtain a better understanding of the mechanisms leading to the extension in surge margin.