Aerodynamic Shape Optimization for a 3d Multi-Element Airfoil - Research Paper Example

Aerodynamic shape optimization for a 3d multi-element airfoil Aerodynamic shape optimization for a 3D multi-element airfoil ABSTRACT This paper discusses the uses of shape morphing/optimization in order to improve the lift to drag ratio for a typical 3D multi-element airfoil. A mesh morpher algorithm is used in conjunction to a direct search optimization algorithm in order to optimize the aerodynamics performance of a typical high-lift device. Navier stokes equations are solved for turbulent, steady-state, incompressible flow by using k-epsilon model and SIMPLE algorithm using the commercial code ANSYS Fluent. Detailed studies are done on take-off/landing flight conditions; the results show that the optimization is successful in improving the aerodynamic performance. Introduction Problems in 3-D dynamics are usually tackled using a combination of different fundamental approaches. These approaches include experimental fluid dynamics, theoretical fluid dynamics and computational fluid dynamics (CFD). CFD is what has opened the ‘three approach’ in the field of aerodynamics. CFD has had a big role to play in the analysis of aerodynamic configurations so as to aid the design process. The availability of high performance computing platforms have also aided in the development of aerodynamics (Reuther, Alonso & Jameson 1996). Both the mesh morpher algorithm and the direct search algorithm are gradient based optimization techniques. When using these designs in a 3D element optimization airfoil, the control function is parameterized with some set of design variables and a suitable cost function is either minimized or maximized. In order to show the dependence between the cost function and control function governing equations are introduced. The sensitivity derivatives of the cost function in retrospect to design variables are introduced in order to get a direction of improvement. The convergence to a minimum or maximum is achieved when the procedure is repeated. A fast and accurate way of calculating the necessary gradient information is imperative in developing a design that is effective and this is often the most time consuming part in the design algorithm. Therefore, this should be put into consideration when a very large number of design variables as in the case of the three dimensional wing shape design are concerned. 3D airfoil with flap Fully meshed 3D model RESEARCH STRATEGY PLAN The plan of this research strategy is to produce 3D multi-element airfoil design and optimization mechanism that can adapt a model (3D airfoil) delivering enhanced aerodynamic performance in terms of maximizing lift to drag ratio under landing and takeoff flight situation (Reuther, Alonso & Jameson 1996). Processing the multi-element airfoil optimization development can significantly reduce manufacturing product time duration and fetch into view better designs in contrast with the traditional planned design modification methodologies. A well-organized and efficient optimization method is initiated by an amalgamation of high-fidelity commercial CFD tools with numerical optimization methodologies. This organism not only presents a steady, computerized optimization device for design engineers, but furthermore significantly minimizes the expenditure and the production time for a design process. The plan will be to unite the high fidelity commercial CFD tools (Fluent) with mathematical optimization systems to morph high lift organization. In research plan as shown in figure (1) we carry out morphing (grid deformation) openly within the fluent code devoid of reconstruction of geometry and the mesh with a peripheral utensil. A direct search method algorithm (Torczon algorithm) is used. Research strategy plan FORMULATION Flow Solver FLUENT is a computational fluid dynamics (CFD) solver. It is a software package to simulate fluid flow problems. It is based on a finite-volume method to solve the governing equations for a fluid. It provides the capability to use different physical models such as incompressible or compressible, in viscid or viscous, laminar or turbulent, steady- state or transient analyses (Reuther, Alonso & Jameson 1996). In the CFD formulation as well, the conservative forms of continuity and Navier-Stoke’s equations in integral form for incompressible flow of constant viscosity were solved by the built-in functions of the Fluent 13 CFD software. The current work used two equation turbulent models: the realizable k-e model that solves one transport equation to allow the turbulent kinetic energy, and its dissipation rate to be independently determined. The realizable k-e model is particularly suitable for our model, as the model uses enhanced wall treatment based on the law of the wall. High lift designs have been realized by the careful wind tunnel testing. The approach is expensive and challenging due to extremely complex nature of flow interactions. Computational fluid dynamics analyses the incorporated high lift design process and tries to better them. The method that is recently used is the parallel implementation. This is due to the increased number of mesh points which are needed in order to resolve the boundary layer. This presents an additional cost to the computing of the viscous terms. The need to use a turbulence model therefore emerges. The slower convergence of the Navier-Stokes equations in the meshes are highly stretched and the computational costs for the viscous design are at least an order o magnitude and in viscid design. Therefore, the reduction of the computational costs means that if they are reduced the development of the practically effective viscous designs methods will be improved thereby creating low costs for the computation costs. In this paper, steady-state, incompressible three dimensional flow was assumed. The numerical simulations were carried out by solving the conservation equations for mass and momentum by using structured grid finite volume methodology (Reuther, Alonso & Jameson 1996). The sequential algorithm, semi-implicit method for pressure linked equation (SIMPLE), was used in solving all the scalar variables. For the convective terms of the continuity and momentum equations, and also for the turbulence equations, the first order upwind interpolating scheme was applied in order to achieve more accurate results. B. Objective functions A single-objective function can be stated as: Find X which Minimize f(X) = [f1(X)/ f2(X)] The symbols f1, f2 are drag and lift correspondingly, X is known as the design vectors. The vector of design variables, X, principally includes factors that manipulate the shape of the 3D multi-element airfoil. Relying on the problem of concern, supplementary design variables may comprise of the angle of attack, the parallel and perpendicular transformation design variables that administer the place of flaps in multi-element configurations as shown in figure (2). In this work, the objective function is processed by C++ language encoding & programming and constructed on the User Defined Function (UDF) library which considers control points and angle of attack as input factors, and value of drag to lift ratio is output result. Figure 2 reveals the parallel (overlap) and perpendicular (gap) transformation design variables in multi-element configurations. Comparison between 2D and 3D A 2D airfoil is an infinite wing while a 3D wing is a finite wing. A 3D airfoil enables air to travel up, down and around the wingtip producing trailing vortices. The flow on a 2D airfoil on the other hand does not create a vortex and thus it is not able to move in this third dimension. Aerodynamically, the effect of the trailing vortices of 3D reduces the slope of the co-efficient lift versus the angle of attack curve. This means that in a 3D wing the lower the aspect ratio of the wing, the more the lift curve slope is reduced. In 2D however, the higher the aspect ratio of the wing the more the lift curve is increased. The ideal lift curve for 2D airfoil is 2pi. When the lift curve gets less than 2pi the overall lift wing reduces. Other differences between 2D and 3D include wing loading and optimization techniques. The difference in 3D loading is less than 10% compared to nearly 300% for the 2D loading. This shows that 3D loading is more effective because it ranges from 0.20 powered miniatures at 3 ounces with 150sq. as compared to 2D which has to have a bigger wing in order for it to experience the power lift. The optimization techniques are also different in these two designs; they require different algorithms and their optimization points are different. The costs between the two different designs are also a factor to consider. Cost is an essential part in airfoil design and thus without mentioning it one would be making a detrimental mistake. 3D airfoils need more complex and expensive techniques as compared to 2D airfoils. results and discussion in this section please discuss the results in the table and figures below. alpha (L/D)before (L/D)after improvement % 0 10.495 12.387 16.533 4 20.557 23.052 11.446 8 17.441 20.279 15.044 16 9.178 10.796 16.203 When alpha is 0 the L/D before is 10.495, the L/D after is 12.387 therefore, it can be seen that there is an improvement of 16.533%. The alpha before is calculated by the stall speed which is given by Vstall = s 2W ½1ACLmax. The speed is lowest lowest when the aircraft is able to generate an amount lift L which is equal to its weight. As it can be seen from the table above when apha is 0 the greatest improvement is achieved. This consequently means that in order to reduce stall speed and minimize the take off and running runway length, a value of C L max is desirable. When alpha increases to 4 the improvement percentage decreases by 5% to 11.446. This pattern can be observed because in the landing condition, the steeper approach angle is desirable because the three dimensional wing needs a lower angle of incidence on its mesh morpher algorithm (Reuther, Alonso & Jameson 1996). When alpha is increased to 8 the improvement increases because the portion of trailing edge section of the airfoil that is deflected downwards in an effort to increase the effective camber of the section of the airfoil. This consequently increases the lift co-efficient enabling a dynamic power lift. It can be seen that after 3D optimization the optimization gradually increases and then decreases. It is optimum when the L/D ratio is 24 and the angle of attack 5. It can thus be seen that for complete optimization of a 3D airfoil the angle of attack should be not more than 10. This is because when the angle of attack increases the pressure difference between the upper wing and the lower wing decreases thereby decreasing the power lift of the plane. Figure . Final shape optimization for 3D Summary It can be seen that optimization of analytical model is a process used to develop better wing designs that enable power lifts. CFD has been demonstrated to allow computation of optimal shapes of an airfoil for any particular application. The sensitivity of the final optimal design has been establisehd as an important concern in the shape of optimziation of airfoils (Reuther, Alonso & Jameson 1996). The agrresiveness of an optimal solution is achieved by incorporating the rating of variability of operating conditions directly into the problem formulation in order for optimization. The applications above show that a statistical approach leads to smooth airfoil geometries and drag profiles. The mesh morpher algorithm is computationally similar to the existing multi piont optimiztion, which has been widely accepted in the airline industry. This therefore increases the likelihood of acceptance by both heorists and designers alike. The relative likelihood of each operating condition being taken into accout is depends on the the randomized intergration scheme which ensures the optimizer does not in any way exploit the approximation errors that are as a result of descrtization. Conclusion can be made that optimization on the basis of the shape of the wing needs candidate designs which when included need more realistic pressure distributions. Nomenclature Symmetrical airfoil – the chord line is a line of symmetry that cuts the airfoil into two equal parts. Angle ot attack- this is the angle between relative wind and the chord line. 1) the lift is perpendicular to the freestream velocity 2) the drag is parallel to the freestream velocity. 3) The moment is positve nose up. Center of pressure- this is the point that on the airfoil that the moment due to the aerodynamics is 0. It should be noted that increasing the angle of attack causes the pressure center to move forward and decreasing the angle of attack moves pressure backwards. Aerodynamic center- the point on the airfoil which is indepent of the angle of attack. Acknowledement Am highly indebted to the following authors Sharon L. Padula of the NASA reseach centre multidislinary optimizitation branch and William of the purdue university school. I would also like to thank my professor for his insightful suggestions and comments wchich were hugely beneficial to the writing of this paper. References Kaurather Jameson, P. R. (1996). Aerodynamic Shape optimization of supersonic aircraft configurations via an adjoint formulation on parallel computer. symposium on multidisciplinary Analysis and Optimization , 96-4045. Read More