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A Review of Aerodynamic Flow Models, Solution Methods and Solvers – and Their Applicability to Aircraft Conceptual Design Literature Study Report

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A Review of Aerodynamic Flow Models, Solution Methods and Solvers – and Their Applicability to Aircraft Conceptual Design Literature Study Report A review of aerodynamic flow models, solution methods and solvers – and their applicability to aircraft conceptual design Literature study report B. Peerlings November 1, 2018 Delft University of Technology A review of aerodynamic flow models, solution methods and solvers – and their applicability to aircraft conceptual design Literature study report by B. (Bram) Peerlings in partial fulfilment of the requirements for the degrees of Master of Science in Aerospace Engineering Student number 4079388 Project duration June 4, 2018 – September 5, 2018 October 8, 2018 – November 1, 2018 Department Flight Performance & Propulsion, faculty of Aerospace Engineering Supervisor dr. ir. R. Vos Electronic versions of this document suitable for screen and print are available at bram.peerlings.me/en/literature-study/, using the password ‘AE4020-2018’. Contents Preface v Summary vii List of figures ix List of tables xi List of abbreviations xiv List of symbols xviii 1 Introduction 1 2 Overview of flow models 3 2.1 Navier-Stokes equations . 5 2.1.1 Direct numerical simulation (DNS). 8 2.1.2 Large eddy simulation (LES). 8 2.1.3 Unsteady Reynolds-averaged Navier-Stokes equations (URANS) . 8 2.1.4 Reynolds-averaged Navier-Stokes equations (RANS) . 9 2.1.5 Thin-layer Navier-Stokes equations (TLNS). 9 2.1.6 Turbulence modelling . 10 2.2 Boundary layer equations . 10 2.3 Euler equations . 11 2.4 Full potential equation . 12 2.5 Linearised potential equation . 13 2.6 Laplace’s equation . 14 2.7 Empirical methods . 14 3 Overview of solution methods 15 3.1 Non-linear solution methods . 15 3.1.1 Finite difference methods (FDM). 15 3.1.2 Finite element methods (FEM). 16 3.1.3 Finite volume methods (FVM) . 16 3.2 Linear solution methods . 16 3.2.1 Lifting line and lifting surface theory (LLT / LST) . 17 3.2.2 Vortex lattice method (VLM) . 18 3.2.3 Panel method . 18 3.3 Boundary conditions . 19 3.3.1 Far-field boundary conditions . 20 3.3.2 Surface boundary conditions. 20 3.3.3 Numerical implementation . 21 4 Overview of solvers 23 4.1 Two-dimensional solvers . 26 4.1.1 XFOIL . 26 4.1.2 Viscous Garabedian and Korn (VGK) . 30 4.1.3 MSES . 37 4.1.4 Ames Research Center 2D (ARC2D) . 39 4.1.5 Comparative review . 43 iii iv Contents 4.2 Three-dimensional solvers . 45 4.2.1 Athena Vortex Lattice (AVL) . 45 4.2.2 Tornado . 46 4.2.3 Vortex Separation Aerodynamics (VSAERO) . 49 4.2.4 MATRICS / -V. 53 4.2.5 Stanford University Unstructured (SU2) . 59 4.2.6 Comparative review . 64 4.3 Hybrid two-/three-dimensional solvers . 67 4.3.1 XFLR5. 67 4.3.2 Quasi-three-dimensional aerodynamic solver (Q3D) . 69 4.3.3 Comparative review . 72 5 Applicability to conceptual design 73 6 Conclusions 77 7 Discussion 81 7.1 Limitations of current research. 81 7.2 Recommendations for future research and development . 81 8 Research outlook 83 8.1 Research goal and questions . 83 8.2 Methodology . 84 8.3 Planning. 86 Bibliography 89 Preface To many a student, having to do a literature review is – simply put – a pain and something they dread. Telling friends how I have started the work on this review before summer, I am often greeted with some- what of a pitiful look. And, to be honest, I had not exactly been looking forward to it myself. Luckily, things turned out quite different and I am happy with as well as proud of the report that currently lies before you. Fellow students at Science Communication showed me how to best go about an as- signment like this and even managed to get me to like doing these reviews. Browsing older or newer reports or articles, coming across other researchers struggling with the same problem as yourself, or having found a solution idea you so desperately needed turns out to be very rewarding! Most of the days working on this review, I found myself going home feeling a little smarter and better understanding the subject matter – aerodynamic flow models, solution methods and aerodynamic solver codes. I man- aged to shine a light in (most of) these previously black boxes and uncovered similarities, differences and trends. Particularly fascinating was to review how various researchers think about the use of these models and tools in the conceptual design phase and how they see that field of engineering developing. As you will more formally read in the introduction, these four topics form the pillars of this report. Two other things about reading this report I would like to discuss in this preface. First of all: the report is best viewed in colour. There are some figures so densely packed with information, that it was simply impossible to not use colour to discern between different data sets. A further advantage is that reading this document in colour makes the in-text citations stand out, so that it becomes much easier to skip over the citation and quickly get back on track with the remainder of the sentence. It is hoped that this improves the readability of the report and makes the citations distract as little as possible. Citations form a second aspect relevant to discuss in this reading guide. Contrary to the numerical citations customary in the aerospace industry (especially in publications by the American Institute of Aeronautics and Astronautics), I have chosen for author-year-citations. I feel having this information in-text is a massive benefit, as it immediately shows how recent (or old) a reference is (and, by extension, how recent an idea or development is) and allows to identify authors throughout reading this report. Also, some additional references are included that point to a more extensive discussion of the topic at hand. In most of these cases, the citation also includes reference to a chapter, section or page, to help find the relevant information sooner. Last, I would like to take the opportunity to express my gratitude to a number of people – without whom this review would not have been as complete, thorough or focused. First of all, thanks to Roelof Vos, Maurice Hoogreef and Martijn Roeloefs for suggesting aerodynamic solvers to include. A second and well-deserved word of appreciation goes out to Martijn, for his extensive and valuable feedback on an earlier version of this report, which has especially helped me in further improving the various comparative reviews. Last, I would like to thank Roderick Schildkamp, for pointing me to the wonderful book on com- putational aerodynamics by Cummings et al.. It has helped solve many mysteries and was instrumental in the aforementioned moments of increased understanding of the subject matter that is presented here. Bram Peerlings Delft, November 1, 2018 v Summary This literature study report is written in preparation for a subsequent graduation research project that aims to develop a methodology for uncertainty quantification in (aerodynamic) models, in order to contribute to improve decisions made in the conceptual aircraft design process. In the current text, the assumptions, simplifications and limitations of various aerodynamic solvers have been investigated, as well as their performance compared. A more fundamental discussion of flow models (from Navier-Stokes to Laplace’s equation) and non-linear (FDM, FEM, FVM) and linear (LLT, VLM, panel methods) solution methods precede an analysis of 11 solvers of different fidelity levels. Of the two-dimensional codes, XFOIL (panel method and boundary layer model), VGK (full potential FDM and BL model), MSES (Euler FVM and BL model) and ARC2D (thin-layer NS using FDM) were investigated. In three dimensions, the research comprised vortex lattice methods VLM and Tornado, VSAERO (panel method and BL model), MATRICS-V (full potential FVM and BL model) and SU2 (Euler, inviscid NS and turbulent RANS using FVM or FEM). XFLR5 and Q3D, combining 2D boundary layer models with 3D linear potential codes, were classified as ‘hybrid’ solvers and analysed. Given their different flow models, these codes most notably vary in terms of including viscosity, the applicable Mach number range and limitations to geometry modelling. Unsurprisingly, it was concluded that the higher-fidelity codes generally match experimental results best. In 2D codes, predicting shock strength and shock location were found to be most difficult. The 3D codes mostly differentiated themselves based on the geometric detail that could be modelled. In this case, higher-fidelity models more clearly outperformed lower-fidelity codes. Problems with accurately predicting transition and separation (insofar supported by the computational tool in question) were – to a greater or lesser extent – seen throughout the entire range of solvers considered. The downside of these higher-fidelity codes is their increased computational cost – both directly in terms of computer time and indirectly because of preparatory work, such as geometry modelling and mesh- ing. Although various authors see application of more advanced CFD codes earlier in the (conceptual) design process as a key towards enabling technologies such as early MDO, others believe conceptual design should remain focused on the high-level parameters and not pay too much attention the details. Also, scholars feel that current (drafting-based) CAD-software suitable for generating detailed enough geometries required by advanced simulations are unsuitable for rapid design and iteration common in conceptual design. In conclusion, it is felt a lower limit is set by the requirement that a solver should be able to definitively distinguish between concepts and a (currently fairly stringent) upper limit by compu- tational cost and geometry requirements. vii List of figures 2.1 Hierarchical overview of aerodynamic flow models ...................... 4 2.2 Boundary layer properties .................................... 11 3.1 Elementary flow solutions ...................................
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