Master Thesis For the degree of Master of Science in Aerospace Engineering at Delft University of Technology Multi-fidelity Method for Aerodynamic Shape Optimisation of Axial Compressor Blades by Lennart Verheij Supervisors: Dr. Robert Grewe, Siemens AG (Division Power and Gas) Dr.ir. Matteo Pini, TU Delft (Faculty of Aerospace Engineering) Completed in: Siemens AG (Division Power and Gas) Mu¨lheim an der Ruhr Exam committee: Prof.dr.ir. P. Colonna di Paliano, TU Delft (Faculty of AE) Dr.ir. M. Pini, TU Delft (Faculty of AE) Dr. R. P. Dwight, TU Delft (Faculty of AE) Dr.ir. R. Pecnik, TU Delft (Faculty of 3ME) Thesis registration number: 166#17#MT#FPP Matriculation number: 4142306 Date of submission: October 2017 Statement of originality I hereby confirm that the content of this thesis is my own work, without contributions from any sources other than those cited in the text and acknowledgements. This also applies to graphics, drawings and images included. Lennart Verheij Mu¨lheim an der Ruhr, 27th of October, 2017 Abstract In turbomachinery optimisation problems, run time is often a critical factor due to high dimensionality of the design search space. This work explores the use of the multi-fidelity method to speed up an aerodynamic optimisation algorithm applied to axial compressor blades. A rotor blade is optimised in a two-stage blade geometry for maximum isentropic efficiency. The single-fidelity reference optimisation usesahigh-fidelityevaluationprocessemployingMenterSSTturbulenceequationsandameshof903,000 cells. Five multi-fidelity optimisation setups are tested, which employ the same high-fidelity process, but distinct low-fidelity processes ranging from a fine mesh and RANS turbulence equations to a coarse mesh and inviscid Euler equations. It is found that multi-fidelity optimisation could cause a delay in run time of up to 39.9%, equivalent to almost three days and a loss in optimum efficiency of 0.11%. The best result is a speed-up of 14.1%, equivalent to 1 day of time savings and an improvement in efficiency of 0.02%. The speed-up of 50% demonstrated in literature could not be achieved since the high-fidelity model in this work is much cheaper. The best cost ratio achieved in this work is comparable with 0.14, but the correlation coefficient of 0.46 is insufficient. It is shown that at their optimum efficiencies, two selected single-fidelity and multi-fidelity optima have different geometries and aerodynamic behaviour. For improving performance using the multi-fidelity method, it is recommended to increase the fidelity gap between the low-fidelity and the high-fidelity processes. The cost ratio of a new low-fidelity process can be estimated with an error of at most 5%, by using 10 member designs. Furthermore, the correlation coefficient can be estimated with an error of at worst 35%, using 20 blade designs. From the results in this thesis, it is recommended to employ a cheaper low-fidelity process using for instance through-flow calculations or to make the high-fidelity process more expensive by adding more design features. Keywords: multi-fidelity method, aerodynamic optimisation, axial compressor blade, fidelity reduction, Kriging, Co-Kriging, RANS turbulence modelling, Euler equations Preface This thesis considers the implementation of a new method to improve aerodynamic shape optimisation of compressor blades. The method is applied to an industrial four-row compressor design and measured against test results from reference works. This research project was issued by the R&D department of Materials and Technology for large industrial gas turbines of Siemens A/G. This report is written to fulfil the graduation requirements of the Master in Aerospace Engineering at Delft University of Technology in the Netherlands. I was engaged in writing this thesis from February 2017 to October 2017 at Siemens Power and Gas in Mu¨lheim an der Ruhr. Over a period of nine months, I have been given the chance to manage a unique collaborative project between my university and a frontrunner in the energy industry. Not only it has been an incredible experience to work with knowledgeable colleagues in a high-tech environment, I have also learned much about the German culture, customs and the inspiring work mentality. With deep respect for the peopleIhavegottoknowwithinandoutsideofmydepartment,IfeelfortunatethatIwasgiventhischance. I would like to express my gratitude to a number of people that have helped me to push my boundaries. First and foremost, I would like to thank my supervisor Robert Grewe, who has been a major support during the entire project. It was a great pleasure unravelling the mysteries of this method together and achieving major breakthroughs, even after periods of seemingly small progress. Furthermore, I like to thank my university supervisor Matteo Pini for his enthusiasm and for taking the responsibility to evaluate my work from an academic perspective. I say thanks to my colleagues Matthias Hu¨ls and Gregor Schmid, for sharing their knowledge and advice on setting up the surrogate model and the aerodynamic simulation process. Furthermore, I appreciate how my colleagues and interns have made my time at Siemens pleasant and worthwhile. Finally, I say thanks to my family and close friends for their enjoyable visits to Germany, their vast support and boundless interest. Lennart Verheij Mu¨lheim an der Ruhr, October 2017 Contents Abstract IV Preface V Nomenclature VIII 1 Introduction 1 1.1 Industrial context . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Aerodynamic optimisation of compressors . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Thesis objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.4 Report structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 2 Fundamentals of compressor design and modelling 5 2.1 Compressor performance and operating principles . . . . . . . . . . . . . . . . . . . . . . 5 2.2 Design philosophy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.3 Basics of CFD simulation for compressors . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3 Theory on aerodynamic shape optimisation 12 3.1 AutoOpti and optimisation terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 3.2 Optimisation architectures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.3 Evolutionary algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 3.4 Surrogate modelling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 3.4-1 Kriging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.4-2 Co-Kriging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.5 Decision function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.6 Optimisation progress quantification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 3.7 Potential metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 3.8 Literature review on multi-fidelity compressor optimisations . . . . . . . . . . . . . . . . . 28 4 Methodology for shape optimisation 32 4.1 Problem specification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 4.2 Optimisation settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 4.3 Setup of optimisations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 4.3-1 Single-fidelity optimisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 4.3-2 Multi-fidelity optimisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 4.4 Low-fidelity model selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 4.4-1 Identification of fidelity reduction methods . . . . . . . . . . . . . . . . . . . . . . 40 4.4-2 Fidelity reduction study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 4.4-3 Down-selection of models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 4.5 Convergence criterion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4.6 Performance metrics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 VI 5 Results of the multi-fidelity method 54 5.1 Single-fidelity reference optimisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 5.2 Multi-fidelity results using variance decision function . . . . . . . . . . . . . . . . . . . . 55 5.2-1 Performance assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 5.2-2 Potential assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 5.2-3 Investigation of information transfer . . . . . . . . . . . . . . . . . . . . . . . . . . 63 5.3 Multi-fidelity results using constant decision function . . . . . . . . . . . . . . . . . . . . 65 5.3-1 Performance assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 5.3-2 Potential assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 5.4 Conclusions on multi-fidelity optimisation results . . . . . . . . . . . . . . . . . . . . . . . 68 5.5 Multi-fidelity performance forecasting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 5.5-1 Forecasting using one member . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 5.5-2 Forecasting using set of members . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 6 Aerodynamic analysis of optimum members 77 6.1 Three-dimensional blade shape . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 6.2 Radial distributions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 6.3 Distributions in the blade-to-blade plane . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 7 Conclusions 83 7.1 Answers to research questions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 7.2 Future work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 Appendix 87 VII Nomenclature Abbreviations B2B Blade-to-blade CFD Computational Fluid Dynamics DLR Deutsches Zentrum fu¨r Luft- und Raumfahrt HF High-fidelity GMC General Mesh Connector LF Low-fidelity MTU Motoren Turbinen Union RSL Radial streamlines RANS Reynolds Averaged Navier-Stokes SR Sampling resolution TRACE Turbomachinery Research Aerodynamic Computational Environment Greek symbols (cid:15) Turbulence dissipation rate m2/s3 η Efficiency % κ Turbulence kinetic energy m2/s2 µ Dynamic viscosity kg/(ms) Π Total pressure ratio - ρ Flow density kg/m3 f ρ Correlation - σ Standard deviation - σ2 Variance - Θ Hyperparameter - ω Specific turbulence dissipation rate 1/s VIII Latin symbols C Cost s C Cost ratio - r f Replacement ratio - r G Gain in CVG % K Covariance matrix - m˙ Mass flow kg/s N Rotational speed rpm p pressure N/m2 p Total pressure ratio - t r2 Correlation - R Correlation matrix - R Radial span % S Speed-up % T Temperature K t Time s U Velocity m/s w Weight coefficient - ∆x Mesh cell size m y Wall distance m y+ Dimensionless wall distance - IX 1 Introduction In the introduction chapter, the context of this master thesis is explained and the research question is motivated. This chapter starts by explaining the context of this work in Section 1.1. Afterwards, a short summary of the current state-of-the-art in compressor optimisation is given by Section 1.2. The objective of this thesis is explained in Section 1.3. At last, in Section 1.4, the structure of this report is outlined. 1.1 Industrial context Heavy-duty gas turbines have become an established means for power generation. The average power output of gas turbines has multiplied over a hundred-fold because of their rapid development in the last century. Primarily driven by advancements in the aerospace sector, the performance of stationary land-based gas turbines has seen a drastic increase, through increasing the overall pressure ratio and the firing temperature for combustion. In a combined cycle configuration, where waste heat from the gas turbine exhaust gasses is used to make steam and drive an additional steam turbine, an efficiency can be attained in the order of 50%. Recent demonstration has seen a combined efficiency of 60%. While gas turbines were initially used for emergency back-up in case of blackouts or peaking power in the USA and Europe, from 1980 there has been a trend to replace steam powered plants with gas turbines [2]. Gas turbines are now considered amongst the cleaner means to convert chemical energy from fossil fuel to electrical energy. In a forecast on the outlook of the world’s energy consumption by the International Energy Agency [14], the demand for natural gas is expected to rise by 50% in the year 2040. This rise will be mainly due to rapidly developing countries that share a large interest in power provision using industrial gas turbines. However, there is an increasing share of renewable energy sources expected to be introduced into the system. Moreover, energy production is expected to take place in decentralised systems, instead of in the centralised system effective today. These future challenges drive innovation with a focus to improve powerplant flexibility for scaling up or down the power output and to accommodate various types of fuels and easy adaptation in configuration. In order to stay competitive withanincreasingshareofcleanenergysources,themanufacturingandoperatingcostneedstobereduced. Major gas turbine engine manufacturers, such as Siemens are challenged to stay competitive in a global market. Over a broad portfolio of turbines ranging from 4 to 450 MW, Siemens has set goals to provide high reliability, load flexibility, low life cycle cost and environmental compatibility. Besides searching for innovative new concepts, the main components of the gas turbine are individually improved for delivering optimal efficiency. Those components are generally separately designed: the compressor, combustion chamber and turbine. Achieving small improvements in efficiency can result in huge savings in operating costspentonfuel. Thoseimprovementsalsocontributetotheobjectiveofloweringemissionsandreducing environmental impact. Within this context, in this thesis project, the optimisation of one blade row in an axial compressor is considered. 1