UNIVERSITY OF SOUTHAMPTON FACULTY OF ENGINEERING AND THE ENVIRONMENT Aeronautics, Astronautics and Computational Engineering Computational Engineering & Design Group ON DEVELOPING EFFICIENT PARAMETRIC GEOMETRY MODELS FOR WAVERIDER-BASED HYPERSONIC AIRCRAFT by Konstantinos Kontogiannis Thesis for the degree of Doctor of Philosophy November 2017 UNIVERSITY OF SOUTHAMPTON FACULTY OF ENGINEERING AND THE ENVIRONMENT Computational Engineering & Design Group Thesis for the degree of Doctor of Philosophy ON DEVELOPING EFFICIENT PARAMETRIC GEOMETRY MODELS FOR WAVERIDER-BASED HYPERSONIC AIRCRAFT Konstantinos Kontogiannis ABSTRACT This work is focused on tackling the high dimensionality and complex nature of waverider- based high speed aircraft design through the development of effective and efficiently parameterized parametric geometry models. The first part of the work is focused on the parameterization and handling of waverider forebody geometries. Different design approaches and a novel design method are presented, each offering direct control of different aspects of the geometry. This can be utilized to directly implement any design constraints or to enable straightforward interfacing with additional geometry components. The new three-dimensional leading edge waverider design method that is proposed is a step away from inverse and one towards direct waverider design. A series of requirements for designing valid three-dimensional leading edge curves are also highlighted. A method to compare different parameterization schemes in order to avoid over or under-parameterizing the geometries and assist in deciding on the number of degrees of freedom and control points for the design-driving curves of the inverse design methods is also presented. This enables the designer to make better educated decisions during the parametric model development phase and when parameterizing hypersonic-design-specific components for which we have limited experience and detailed data in the literature. Complementing the waverider forebody component of the aircraft are a series of blunt leading edge shape formulations. Their effectiveness and efficiency compared to other blunting approaches is highlighted. They are suitable for generating blunt shapes for any wedge-like geometry and they can also be used for inlet cowls, sidewalls, control surfaces, etc. They also offer second order continuity at the interface between the blunt part and the original geometry, which can have a favourable effect on the receptivity and turbulent transition mechanism. Finally, a parametric geometry model development framework consisting of a revised aerodynamic design process that involves design loops to better tune the parametric model, and a geometry engine developed to enable these early design loops, is presented. This is complimented by a number of implementation specific findings and proposed features such as an interactive GUI with real-time updates and dynamically controlled resolution of the generated geometries. Table of Contents Table of Contents .......................................................................................................... i List of Tables ................................................................................................................. v List of Figures .............................................................................................................. vii DECLARATION OF AUTHORSHIP .................................................................................. xix Acknowledgements .................................................................................................... xxi Definitions and Abbreviations ................................................................................... xxiii English letters ................................................................................................................ xxiii Greek letters .................................................................................................................. xxiv Subscripts .......................................................................................................................xxv Abbreviations .................................................................................................................xxv Chapter 1: Introduction ....................................................................................... 1 Chapter 2: Background ........................................................................................ 5 2.1 Hypersonic Aircraft Design ...................................................................................... 5 2.2 Waveriders ............................................................................................................. 10 2.2.1 Base Flowfields for Inverse Design .......................................................... 11 2.2.2 Waverider Adoption ................................................................................ 16 2.3 Computational Geometry for Engineering Applications ....................................... 20 2.3.1 Bézier curves and splines ......................................................................... 22 2.3.2 B-splines and Non-Uniform Rational B-splines ........................................ 24 2.3.3 Surfaces .................................................................................................... 25 2.3.4 Free-Form Deformation ........................................................................... 27 2.4 Parameterization of Waverider-based Hypersonic Aircraft Configurations ......... 29 2.5 Motivation & Approach ......................................................................................... 34 Chapter 3: Waverider Forebody Parameterization ............................................. 37 3.1 Different Approaches to Inverse Design Methods ................................................ 39 3.1.1 Upper Surface Profile Definition (USPD) ................................................. 39 3.1.2 Planform Leading Edge Definition (PLED) ................................................ 40 3.1.3 Lower Surface Profile Definition (LSPD) .................................................. 42 i 3.1.4 Hybrid Design Approach .......................................................................... 43 3.2 Waverider Design Based on 3D Leading Edge Shapes .......................................... 46 3.2.1 Method Description ................................................................................ 47 3.2.2 Additional Considerations ....................................................................... 50 3.2.3 CFD Validation ......................................................................................... 56 3.3 Flexibility of the Design-Driving Curves ................................................................. 58 3.3.1 Methodology ........................................................................................... 59 3.3.2 Case 1 ...................................................................................................... 61 3.3.3 Case 2 ...................................................................................................... 64 Chapter 4: Blunt Leading Edge Shape Parameterization ...................................... 69 4.1 Leading Edge Geometry Parameterization ........................................................... 71 4.1.1 Quadratic Rational Bézier Leading Edge ................................................. 71 4.1.2 Cubic Rational Bézier Leading Edge ........................................................ 72 4.1.3 Fourth Order Rational Bézier Leading Edge ............................................ 75 4.2 2D CFD Analysis of Shapes ..................................................................................... 77 4.2.1 Cold Wall Simulations .............................................................................. 78 4.2.2 Equilibrium Temperature Simulations .................................................... 82 4.3 Preliminary Receptivity – Transition Investigation ............................................... 85 4.4 Integration on 3D Waverider Geometries ............................................................. 89 Chapter 5: A Geometry Tool for the Waverider-based Hypersonic Aircraft Design Process ........................................................................................................ 95 5.1 Waverider-based Hypersonic Aircraft Design Process .......................................... 96 5.1.1 Differences to Conventional Aircraft Design ........................................... 96 5.1.2 Overview of a Generic Aerodynamic Design Process ............................. 99 5.1.3 The Revised Hypersonic Aerodynamic Design Process ......................... 101 5.2 The Parametric Geometry Generation Tool ........................................................ 105 5.2.1 Requirements ........................................................................................ 106 5.2.2 Overview ................................................................................................ 108 5.3 Specialized Features ............................................................................................ 109 ii 5.3.1 Interactive Graphical User Interface (GUI) ............................................ 109 5.3.2 Aerodynamic Performance Evaluation Tool .......................................... 113 5.3.3 Design-Driving Curves ............................................................................ 115