Elements of Design Aerodynamics

**10 lectures**

1. Introduction: Göttingen pioneering, motivation for this lecture series

Modern fluid mechanics and aerodynamics started a century ago in Göttingen. A few wellknown basics and early airfoil families developed there are highlighted. We are interested here in the classical beginnings of airfoil research and gasdynamics, leading to practical work in transonic, supersonic and hypersonic fluid mechanics which has been used to develop design tools for modern and future innovative aerospace vehicles and turbomachinery components. |

2. Geometry, the basic toolbox for creative design

The shaping of complex configurations today is carried out by CAD software. A rational definition of geometry parameters for creating flight vehicles with optimum aerodynamic performance requires the knowledge of fluid mechanic phenomena which are responsible for losses and environmental problems by high energy consumption. CAD software therefore has to be enhanced with special functions developed from analysis of fluid mechanical phenomena. |

3. Fluid mechanic basic equations adapted for design

Starting from the equations of motion for technologically relevant flows, successive simplifications will allow for an analytical treatment of complex phenomena in compressible fluids. Basic equations in potential and Euler form are shedding light on previously poorly understood effects in the higher speed regime. Rheoelectric analogy for subsonic flows and the method of characteristics for supersonic flows lay rational ground for fast computational design methods. |

4. Design methodology for wings and blades

Transonic flows are characterized be a simultanous occurrence of elliptic and hyperbolic partial differential equations. The near sonic border zone of these two domains allows for closed form analytic solutions which illustrate how subsonic and supersonic parts of the flow coexist. The methods to construct subsonic flow domains adjacent to the integration of locally supersonic flow patterns lead to design concepts for new generation transport aircraft in the flight regime close to Mach number unity as well for the components of high performance turbomachinery. |

5. Parameterized airfoils, wings and configurations

The new design concepts for wings and blades have taught us that the high speed regime responds dramatically to very small shape changes. Aerodynamic efficiency is influenced by characteristic shape parameters which are key input for new airfoil generators to be added in commercial CAD software used by the industry. While such practical applications are under way for conventional aircraft configurations, new ideas for future applications arise and seem to be well supported by the new tools. |

6. Analytical modeling of shock waves

Shock waves in supersonic flow are a significant source of losses resulting in high fuel consumption, as well as creating environmental unacceptably strong sonic booms. Gasdynamic relations lead to understanding the analytical structure of recompression shocks in transonic flow as well as of the bow waves in supersonic flow, guiding the development of inverse design methodology for shock strength control. Sonic boom analysis and minimization by geometric parameterization accelerates the design of supersonic aircraft with a chance of realization in the future. |

7. Configurations for Supersonic and Hypersonic flight

Geometric parameterization accelerates the design of supersonic aircraft forebodies with minimized sonic boom. The waverider principle, making use of a suitable selection of known supersonic flow fields, by this inverse approach more generally allows for prescribing a supersonic bow wave which emanates from the body to be designed. Hence the inverse approach finds bodies which are compatible with parameters defining lift and losses as design input, to be applied for supersonic inlets and hypersonic vehicles |

8. Design vs. CFD vs. Experiment

For a long time the development of numerical algorithms for computation of the (Navier-Stokes) equations of motion to describe realistic and practical flows was key agenda of fluid mechanic research organisations. At the same time, realistic experiments in wind tunnels to measure the flow past scaled-down aircraft models, claiming to represent original size flow, are very expensive. A mutual support and calibration of these two approaches is therefore to be seen sceptically. A specially designed wing with completely defined boundary conditions is investigated in a transonic wind tunnel and still serves as a test case for the refinement of computational methods. |

9. Adaptive Configurations

The capacity of geometry generation includes the definition of a parameter of a 4th dimension (e.g. time) to vary 3D shapes in a cyclic or arbitrary way. This is used to model unsteady and changing configurations, like the motion of rotor blades relative to the body and the flight direction of a helicopter. Using unsteady flow analysis in combination with transonic design, innovative blade sections are designed with adaptive sections to improve rotor performance through the whole circle. New fields of application are bionic models to learn from nature by simulating the movement of animals in water and air. |

10. Design Optimization

Fast parametric generation of variable configurations is needed for optimization cycles which require a large number of costly numerical analysis runs to compute a target function which needs to be driven toward an optimum by applying some strategy to modify certain geometry parameters. A reduction to select few but relevant parameters is made possible by applying the results of inverse design. Examples for multidisciplinary optimization, taking into account not only aerodynamics, but also structures, acoustics, thermodynamics and, last not least, economical considerations are all influencing what should be an over-all target function. |