Daedalus - A Software Package for the Design and Analysis of Airfoils

Transcription

1 First South-East European Conference on Computational Mechanics, SEECCM-06, (M. Kojic, M. Papadrakakis (Eds.)) June 28-30, 2006, Kragujevac, Serbia and Montenegro University of Kragujevac Daedalus - A Software Package for the Design and Analysis of Airfoils Eleftherios I. Amoiralis, Ioannis K. Nikolos Department of Production Engineering and Management, Technical University of Crete, University Campus, Kounoupidiana, GR-73100, Chania, Greece. jnikolo@dpem.tuc.gr Abstract: A software package named Daedalus is presented for the design and analysis of airfoils. Daedalus is a collection of integrated geometry, analysis, optimization and visualization tools, which provide the ability to interactively construct and analyze standard airfoils using the NACA analytical equations and non-standard airfoils using the NURBS equations. Additionally, a database incorporating hundreds of airfoils is linked to Daedalus. Computational Fluid Dynamics (CFD) and mesh generation tools have been integrated, providing the ability to produce fast flow field calculations. Additionally, a Differential Evolution algorithm is embedded, in order to iteratively solve the inverse airfoil design problem, using a prescribed pressure (or velocity) distribution. Concerning the standard airfoil profiles, Daedalus supports various NACA-series and symmetrical biconvex airfoils. Airfoils are produced in the form of a distribution of points with variable density, in order to provide densely spaced points near the leading and trailing edges. Furthermore, by providing the coordinates and weights of the corresponding control points, the user can design non-standard section profiles using the NURBS equations. Additionally, the proposed software incorporates the ability of interpolating an existing airfoil using B-Splines polynomials. In this way a section described with a small number of surface points can be reconstructed with a desired density of points for producing acceptable computational meshes. Moreover, a new airfoil can be produced by slightly modifying an existing standard airfoil, by displacing the corresponding B-Splines control points of the interpolated initial airfoil. Besides the geometrical tools, Daedalus provides the capability of calculating the flow field around any airfoil, under prescribed flow conditions, using embedded mesh generation and analysis tools. By incorporating the geometrical design, the mesh generation and the flow analysis tools within the same software package, the airfoil design and evaluation procedure becomes automated, without the need of interaction and data transfer between different software packages. The above mentioned tools can be used in conjunction with a Differential Evolution optimizer, integrated within the software package, in order to solve the inverse airfoil design problem. The cost function to be minimized is the area of the difference between the target pressure distribution and the calculated one for each candidate solution. Key words: airfoil design, NURBS, CFD, Differential Evolution optimizer, Free Form Deformation

2 1. Introduction One of the most important tasks in the optimum design of an aircraft is the correct construction (or selection) of airfoils. The motivation behind this work was to develop a userfriendly software package that combines airfoil design, analysis and optimization tools, useful for both design optimization and educational purposes. Over the past years, various software packages have been developed for the design and analysis of airfoils; some of them are presented in the following paragraphs. XFOIL [1] is an interactive program for the design and analysis of subsonic isolated airfoils; it consists of a collection of menu-driven routines which perform various functions. The software can implement viscous or inviscid analysis of an existing airfoil. In addition, it is able to design and redesign an airfoil by interactive modification of surface speed distributions using two methods: full-inverse method based on a complex-mapping formulation, and mixed-inverse method based on an extension of XFOIL's basic panel method. Moreover, XFOIL provides the ability to redesign an airfoil by interactive modifications to geometric parameters such as leading edge radius, trailing edge thickness, camber line via geometry specification, and so on. NVFoil [2] is a software package for the analysis of the 2D non viscous flow field (at M < 1 and Re = ) around any airfoil, at an assigned angle of attack. The airfoil to be analyzed can be either imported in the form of a text file or produced by the program; NACA 4 and 5 digits, or elliptic wing sections can be produced. Additionally, a database of airfoils is incorporated (containing approximately 1100 airfoils). Profili2 [3] is a software tool designed in order to help a wing designer to find the right airfoil by advanced search on more than airfoils and the analysis of their polars. Pablo [4] is a pedagogical low-speed airfoil analysis program written in MATLAB. It uses a one way coupled inviscid analysis (Panel Method) and a boundary layer model (with the inviscid flow velocity provided by the panel method). Finally, the drag coefficient is computed using the Squire-Young formula. PANDA [5] is a program for the analysis and design of airfoils. It computes and graphically displays the pressure distribution on airfoil sections in subsonic flows under prescribed conditions. For a given airfoil the program calculates the inviscid pressure distribution over the airfoil at a specified angle of attack and Mach number; lift and pitching moment about the 1/4- chord point are also computed. Additionally, the boundary layer properties, based on this inviscid pressure distribution, are provided. The location of transition, laminar or turbulent separation, and total drag are computed, based on integral boundary layer methods. It is possible to specify a position for "transition grit" on the upper and lower surfaces to force transition or model surface roughness. A major feature of the program is its provision for rapidly changing the airfoil geometry. FoilSim [6] was developed at the NASA Glenn Research Center; it is an interactive simulation software package that determines the airflow around various shapes of airfoils. The Airfoil View Panel is a simulated view of a wing being tested in a wind tunnel. Users change the position and shape of the wing by moving slider controls that vary the parameters of airspeed, altitude, angle of attack, thickness and curvature of the airfoil, and size of the wing area. The software displays plots of pressure or airspeed above and below the airfoil surface. A probe monitors air conditions (speed and pressure) at a particular point on or close to the surface of the airfoil. The software calculates the lift of the airfoils, allowing users to learn the factors that influence lift. A software package called Aerodynamics [7] provides a collection of computational tools for constructing numerical models for solving the problem of steady potential-flow over a twodimensional object using panel methods. The software consists of three Mathematica packages and supporting documentation. The primary package defines functions for geometric influence coefficients for commonly used source, doublet and vortex distributions. There are two support

3 packages, one defining a data type for a collection of vectors, and the other defining functions for the geometry of airfoils and their discretization. Fig. 1. The structure of Daedalus software. MultiElement Airfoils [8] is a unique software package authored for computing the lift, drag and moment coefficients for multiple interacting airfoil shapes. The software is designed to increase the productivity in aerodynamics conceptual design and analysis. The user can change the airfoil type, size, camber, thickness and orientation to quickly generate multiple test cases. The software can compute lift, drag and moments for any airfoil configuration. Additionally, it contains generators for NACA 4, 5, and 6-digit airfoils, the UIUC airfoil database, and provides tools to read-in and analyze custom airfoils. PCPANEL/PNLGRF [9] is a flow solver for single/multi-element airfoils and turbomachinery blade rows. It uses an integral equation methodology (panel method) to solve two dimensional fluid flow problems on a personal computer. PNLGRF is an interactive graphical interface program, written specifically to allow visual analysis of the flow solutions generated by PCPANEL. The working fluid is assumed to be inviscid, irrotational, and a perfect gas. The

4 integral equation solution provides the flow around single or multi-element airfoils that lie on a surface of revolution; additionally, flows through planar cascades or around isolated airfoils can be computed. PCPANEL's includes the effects of compressibility, radius change, blade-row rotation, and variable stream sheet thickness. The software package Daedalus presented in this paper was developed for the design and analysis of airfoils. The structure of the proposed software is illustrated in Fig. 1. Daedalus is a collection of integrated geometry, analysis, optimization and visualization tools, which provide the ability to interactively construct and analyze standard airfoils using the NACA analytical equations and non-standard airfoils using the NURBS equations. Additionally, a database incorporating hundreds of airfoils is linked to Daedalus which can be imported for analysis, evaluation or modification. 2. Airfoil Construction 2.1 Airfoil construction and modification NACA 4, NACA 5, NACA modified 4, NACA modified 5, NACA 6, -6A, NACA 16 series and symmetrical biconvex airfoils can be interactively constructed. Depending on the airfoil type, the designer designates the corresponding parameters, i.e. the maximum thickness, the position of maximum thickness, the mean-line camber, the distance from the leading edge to the location of the maximum camber, the design lift coefficient, etc. After the selection of the type of airfoil to be constructed, pop-up forms are used to define the airfoil parameters. The airfoil shape results from the corresponding analytical formulas [10]. NACA 6 and 6A series airfoils are constructed using Ladson et al. procedure [11], [12], [13]. Airfoils are produced in the form of a distribution of points with variable density, in order to provide densely spaced points near the leading and trailing edges (Fig. 2). Equal spacing of points, half cosine distribution with high density near the leading or trailing edge, and full cosine density distribution of points are supported. The user has the ability to save the produced airfoils in text files, which may added to the included database; these airfoils may be later re-introduced to the software for further modifications or analyses. Besides the standard airfoil types, Daedalus software provides the ability to construct nonstandard airfoils, using NURBS curves. In recent years NURBS (Non-Uniform Rational B- Splines) [14] have been widely used for the parametric modeling of airfoils. This methodology has been shown to have some distinct advantages, such as the ability to discretize the geometry to any level of fidelity, the inherent smoothing of the curve, and the ability to represent extremely complex shapes with remarkably little data i.e. the weights and coordinates of curve s control points. Using NURBS formulation multiple airfoils can be constructed (Fig. 3). The number of airfoils and the corresponding set of control points are introduced using standard text files. Each airfoil is defined as a single open NURBS curve, with its degree defined by the user. A graphical interactive interface is used in order to reshape each airfoil by displacing its control points, using the mouse (Fig. 3). The designer may either export the airfoil points or the control points in standard text files. Additionally, the proposed software incorporates the ability of interpolating an existing airfoil using B-Splines polynomials. In this way, a section described with a small number of surface points can be reconstructed with a desired density of points for producing acceptable computational meshes (Fig. 4). Moreover, a modified airfoil may be easily produced by slightly modifying an existing standard airfoil, by displacing the corresponding B-Splines control points of the interpolated airfoil.

5 Fig. 2. Software s main form with a NACA airfoil (left). The same airfoil with an aileron flap deflection 7 o, hinge at 75% of chord (right). Fig. 3. A two-element airfoil constructed using NURBS curves (left). The displacement of control points using the mouse, allows for easy airfoil modifications (right). A second modification tool, incorporated in the software, is the import of an aileron flap. The flap is formed by hinging the rearmost part of the airfoil about a point within the contour (Fig.2). The user defines the position of the hinge in chordwise and normal to chord directions as fractions of chord length, along with the angle of deflection. Downward deflections are positive flap deflections. The graphical interface was designed in order to provide the user with useful tools for the manipulation of airfoil geometry and discretization meshes. Most of the functions are menu-

6 driven, while the mouse is used in order to perform various tasks, such as zooming operations, selection and displacement of control points etc. 2.2 Database A database incorporating hundreds of airfoils in the form of text files is linked to Daedalus; these airfoils have been collected from the open literature or the Internet [15], [16] [17] and the corresponding text files have been transformed to a common format for use with Daedalus software. Airfoils are selected using graphical interfaces and their geometry is automatically illustrated in the main form of the software (Fig. 4). Additionally, the designation of the corresponding airfoil is presented in a text box, along with other related information contained in the corresponding text file. All database airfoils can be analyzed using the grid generation and analysis software integrated to Daedalus; additionally, modifications to their shape may be introduced, using the aforementioned geometry tools. Fig. 4. An airfoil retrieved from the Database [Eppler E1098] (left). The same airfoil with denser distribution of points, after interpolation with a B-Splines curve (right). 3. Analysis and Optimization Tools 3.1 Analysis tools Besides the geometrical tools, Daedalus provides the capability of calculating the flow field around any airfoil, under prescribed flow conditions, using embedded mesh generation and analysis tools (Fig. 5, 6). The first evaluation software which has been integrated to Daedalus is Bijan Mohamadi s [18] NSC2KE solver. It is a finite-volume Galerkin solver, designed for the computation of 2D and axisymmetric flows on unstructured meshes. These meshes are constructed using the DELAUNDO software, developed by Jens-Dominik Muller [19]. This software has been also integrated to Daedalus and the mesh construction is fully automated. The software uses the Frontal Delaunay method, which incorporates ideas from the frontal vertex placement strategy of the Advancing Front method and the Delaunay triangulation method, providing high quality point cloud with optimal connectivity. The second evaluation software

7 integrated to Daedalus is M. Drela s [20] XFOIL design and analysis software, which combines the speed and accuracy of high order panel methods with a fully-coupled viscous-inviscid interaction method, and is capable for solving low-reynolds flows. A Karman-Tsien compressibility correction is incorporated, allowing good compressible predictions all the way to sonic conditions, but without the ability to deal with shocked-flows. These computational tools are external executables, which are called by Daedalus software to perform the relevant tasks; the required information is passed to the executables through the use of appropriate text files, which are automatically composed by Daedalus software, using appropriate information provided by the user through the graphical interface. The structure of Daedalus allows for the integration of various solvers with minor modifications to the code. Fig. 5. Unstructured mesh around NACA with aileron flap. Fig. 6. Mach contours around NACA with aileron flap (left), as calculated using the integrated Euler solver, and the Cp diagram at Mach 0.7 and zero angle of attack (right).

8 3.2 Optimization tools A Differential Evolution algorithm [21] (Fig. 7) in conjunction with FreeForm Deformation (FFD) technique [22] is embedded in Daedalus, in order to iteratively solve the inverse airfoil design problem, using a prescribed pressure distribution. The problem is defined as a minimization one and the cost function to be minimized is the area of the difference between the target pressure distribution and the calculated one for each candidate solution (airfoil). FFD technique is a recently proposed method, initially used to deform geometrical entities for 3-D animation applications. The basic FFD concept is the deformation of an initial object. While other commonly used techniques manipulate an object directly, FFD deforms a lattice that is built around the object (the initial airfoil), and, consequently, manipulates the whole space in which the object is embedded (Fig. 8). The lattice has the topology of a rectangle when deforming 2D objects; it consists of B-Splines or NURBS control points, which when displaced, deform the embedded object. The strong point of the method is that, by deforming the whole volume around (or inside) the object, the computational grids are also being automatically deformed with the object, which is a valuable characteristic for automated design optimization procedures. Fig. 7. The form used for the Differential Evolution optimizer. The parameters of the lattice, such as the number of rows and columns of control points, the degrees of B-Spline polynomials in the two directions etc., are provided by the user. The control points of the parametric lattice around the initial airfoil are uniformly distributed along chordwise direction (between leading and trailing edges). Their normal to chordwise position is automatically calculated, in such a way that the lower and upper boundaries of the lattice are tangential to the lower and upper surfaces of the initial airfoil (Fig. 8). Additionally, a row of control points is always placed along the airfoil chord, in case that the number of rows is odd and greater than 2. Only the normal coordinates of the parametric lattice control points will serve as

9 design variables in the optimization procedure, with the cordwise coordinates being fixed during the procedure. Each candidate solution, during the optimization procedure, produces a deformed parametric lattice, which produces a deformed airfoil (embedded in the lattice), using FFD formulation. Having the deformed airfoil, the analysis software can be used in order to compute the corresponding pressure distribution around it. Subsequently, the area between the target pressure distribution and the calculated one is calculated, which serves as the cost function to be minimized in the optimization procedure initial lattice initial airfoil before the deformation deformed lattice deformed airfoil Fig. 8. The Free Form Deformation concept: The initial airfoil embedded inside a lattice of control points (upper), and the resulting airfoil after the deformation of the control lattice (lower). 4. Conclusions The motivation behind this work was to develop a user-friendly software package that combines airfoil design, analysis and optimization tools, useful for both design optimization and educational purposes. Daedalus, the resulted software, provides the ability to interactively construct and analyze standard and non standard airfoils, using analytical equations or NURBS formulation respectively. Additionally, the embedded Differential Evolution optimizer, combined with Free Form Deformation technique, provide a handy tool for the inverse airfoil design problem. Daedalus software has been successfully applied in many cases of real world aerodynamic design problems, where fast and accurate solutions were needed. Using a unique software for all tasks (design, evaluation and optimization), without the need to care about

10 interfaces or data exchange between different software, results in minimization of the required effort and maximization of the productivity of the designer. The software package is under continuous development and various new functions are being studied for integration within Daedalus. The priorities are in the direction of multi element airfoil design and optimization and the work is currently focused towards this direction. Acknowledgments This work was partially funded by the Greek Ministry of Education under a PYTHAGORAS II project. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] Abbott, I.H., A.E. Von Doenhoff, Theory of Wing Sections, Dover Publications, Inc., New York, [11] Ladson, C.L., C.W. Brooks, Jr., Development of a Computer Program to Obtain Ordinates for NACA 6- and 6A-Series Airfoils, NASA TM X-3069, pp. 106, [12] Ladson, C.L., C.W. Brooks, Jr., Development of a Computer Program to Obtain Ordinates for NACA 4-Digit, 4-Digit Modified 5-Digit, and 16-Series Airfoils, NASA TM X- 3284, [13] Ladson, C.L., C.W. Brooks, Jr., and A.S. Hill, Computer Program to Obtain Ordinates for NACA Airfoils, NASA TM-4741, [14] Piegl, L., W. Tiller, The NURBS Book, Springer, 2nd Edition, [15] [16] [17] [18] Mohamadi, B., Fluid Dynamics Computation with NSC2KE, A User-Guide, Release 1.0, INRIA RT-0164, [19] Muller, J.D., On Triangles and Flow, Ph.D. Thesis, The University of Michigan, [20] Drela M., XFOIL: An Analysis and Design System for Low Reynolds Number Airfoils, in Proceedings of the Conference on Low Reynolds Number Airfoil Aerodynamics, University of Notre Dame, [21] Nikolos, I.K., Inverse Design of Aerodynamic Shapes using Differential Evolution coupled with Artificial Neural Network, in Proceedings of the ERCOFTAC Conference in Design Optimization: Methods and Applications, Athens, Mar. 31- Apr. 2, [22] Amoiralis, E.I., I.K. Nikolos, Freeform Deformation vs. B-Spline Representation in Inverse Airfoil Design, in Proceedings of the 8th Biennial Conference on Engineering Systems Design and Analysis, ASME-ESDA06, Torino, Italy, July 4-7, 2006, paper ESDA