Aircraft wings are a compromise that allows the aircraft to fly at a range of flight conditions, but the performance at each condition is sub-optimal. The ability of a wing surface to change its geometry during flight has interested researchers and designers over the years as this reduces the design compromises required. Morphing is the short form for metamorphose; however, there is neither an exact definition nor an agreement between the researchers about the type or the extent of the geometrical changes necessary to qualify an aircraft for the title ‘shape morphing.’ Geometrical parameters that can be affected by morphing solutions can be categorized into: planform alteration (span, sweep, and chord), out-of-plane transformation (twist, dihedral/gull, and span-wise bending), and airfoil adjustment (camber and thickness). Changing the wing shape or geometry is not new. Historically, morphing solutions always led to penalties in terms of cost, complexity, or weight, although in certain circumstances, thes...

A Review of Morphing Aircraft

andsimplemathematicalfunctionshavingeasilyobservedphysicalfeatures.Thefundamentalparametricgeometry representation method is shown to describe an essentially limitless design space composed entirely of analytically smooth geometries. The class function/shape function methodology is then extended to more general threedimensional applications such as wing, body, ducts, and nacelles. It is shown that a general three-dimensional geometry can be represented by a distribution of fundamental shapes, and that the class function/shape function methodology can be used to describe the fundamental shapes as well as the distributions of the fundamental shapes. Withthisveryrobust,versatile,andsimplemethod, athree-dimensional geometry isdefinedinadesignspacebythe distribution of class functions and the shape functions. This design space geometry is then transformed into the physical space in which the actual geometry definition is obtained. A number of applications of the class function/ shape function transformation method to nacelles, ducts, wings, and bodies are presented to illustrate the versatility of this new methodology. It is shown that relatively few numbers of variables are required to represent arbitrary three-dimensional geometries such as an aircraft wing, nacelle, or body.

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Universal Parametric Geometry Representation Method

The Kriging-based genetic algorithm is applied to aerodynamic design problems. The Kriging model, one of the response surface models, represents a relationship between the objective function (output) and design variables (input) using stochastic process. The kriging model drastically reduces the computational time required for objective function evaluation in the optimization (optimum searching) process. ‘Expected improvement (EI)’ is used as a criterion to select additional sample points. This makes it possible not only to improve the accuracy of the response surface but also to explore the global optimum efficiently. The functional analysis of variance (ANOVA) is conducted to evaluate the influence of each design variable and their interactions to the objective function. Based on the result of the functional ANOVA, designers can reduce the number of design variables by eliminating those that have small effect on the objective function. In this paper, the present method is applied to a two-dimensional airfoil design and the prediction of flap’s position in a multi-element airfoil, where the lift-to-drag ratio (L/D) is maximized.

Efficient Optimization Design Method Using Kriging Model

Explicit mathematical functions are used for 2D curve definition for airfoil design. Flowphe-nomena-oriented parameters control geometrical and aerodynamic properties. Airfoil shapes are blended with known analytical section formulae. Generic variable camber wing sections and multicomponent airfoils are generated. For 3D wing definition all parameters are made functions of a third spanwise coordinate. High lift systems are defined kinematically by modelled track gear geometries, translation and rotation in 3D space. Examples for parameter variation in numerical optimization, mechanical adaptation and for unsteady coupling of flow and configuration are presented.

Parametric Airfoils and Wings

Notes on numerical fluid mechanics

This chapter is intended to combine the knowledge bases of applied geometry with those of hydrodynamics and aerodynamics, including the modest additions presented in the two previous book chapters focusing on the interaction between compressible flow with shock waves and flow boundary conditions. The need to have flexible tools for effectively influencing the phenomena occurring in high speed flow calls for development of fast and flexible software to create shapes in a way to have easy access to the crucial shape-generating parameters controlling these flow phenomena, and at the same time observe the constraints given by structural and other practical limitations.

Geometry Generator for CFD and Applied Aerodynamics

The present paper describes two different experiments performed in a transonic wind tunnel facility at DLR-Goettingen. The first experiment was conducted in order to study compressible vortices behind a cylinder and investigating the feasibility of combining two different measuring techniques: the Background Oriented Schlieren (BOS) technique and the Particle Image Velocimetry (PIV) which allow respectively to measure both density and velocity fields. The second experiment described in the present paper is done in the same wind tunnel facility where a new test section has been developed to investigate the unsteady flow about oscillating models under dynamic stall conditions. Dynamic stall is characterized by the development, movement and shedding of one or more concentrated vortices on the blade upper surface, the hysteresis loops of lift-, drag- and pitching moment are highly influenced by these vortices. To understand the very complicated unsteady flow involved, a detailed knowledge of the instantaneous flow fields is of crucial importance. With the application of the described measuring techniques it is expected to gain more insight into the problem. In recent years numerical codes based on the time-accurate solution of the Reynolds-Averaged Navier-Stokes equations (RANS) have been developed. Results from these codes are ready for comparison with experimental data. A section of the present paper is dedicated to the comparison of numerical with corresponding experimental data.

New Rotor Airfoil Design Procedure for Unsteady Flow Control

Airfoil designs for helicopter rotors are based on compromises: On the advancing side the blade encounters high speed transonic flows including moving shock waves, on the retreating side, however, the high incidence of the blade may lead to dynamic stall with strong hysteresis effects in force and moment loops. It is the aim of the present numerical investigation to systematically develop airfoils which are changing their shape during operation. With specially designed dynamically deforming airfoil sections the dynamic stall characteristics can successfully be influenced. Rather small airfoil modifications show already considerable benefits with respect to a reduction of the negative (nose-down) pitching moment peak as well as with the avoidance of negative aerodynamic damping.

Unsteady flow control on rotor airfoils

A new design principle for transonic aerodynamics has led to several operational computer codes for shock-free flow. The method is described with emphasis on theoretical variable geometry definition of transonic airfoils and wings for efficient supercritical flight.

Helmut Sobieczky

Papers

Parametric Airfoils and Wings

Geometry Generator for CFD and Applied Aerodynamics

New Rotor Airfoil Design Procedure for Unsteady Flow Control

Unsteady flow control on rotor airfoils

Computational Methods for the Design of Adaptive Airfoils and Wings