Aerodynamic Shape Optimization - Dissertation Example

Aerodynamic shape optimization for morphing multi-element airfoil based on CFD by using adjoint method algorithm Issues in aerodynamic design The design of any aerodynamic components involved application of optimization approaches towards attaining very efficient systems. The general steps involved in any aircraft design process are conceptual design, preliminary design and detail design. These steps are explained here considering an aircraft that could be classified as a medium sized vehicle. The conceptual design step requires a manpower support to the tune of 20 to 25 personals and a definite time line could not be stated (McGill, n.d.). As the concept creation is the most vital part in the design process and all the subsequent steps need to follow this, this step is a very dynamic one that explores different options, technological support and future business potential etc. The finalizing the initial concept would be followed by the preliminary design requirements, which calls for the effort of 200 to 300 people spread over a period of 2 to 3 years. This phase need to support huge manpower cost and is estimated that nearly 200-300 million USD is required for this exercise (McGill, n.d.). The detailed design is the final step and this too demands large number of design engineers and also technicians. Nearly 3000 skilled manpower is expected to put in their effort for a time period of four to five years. Also, the budget expectation of this period is nearly 5-7 billion USD (McGill, n.d.). Thus the large-scale monetary demand in the design phase is followed by the huge manufacturing cost. Further, the studies undertaken earlier have shown that break-even normally starts at least 11 to 12 years after proposal has been put into action. Thus an effective design process that minimizes its cost of design as well as manufacturing is very essential. The multidisciplinary optimization of the aircraft structure is undertaken during the preliminary design phase itself. Thus the final objective of the aerodynamic design is, to arrive at the best aerodynamic configuration that gives the best operational performance given the constrains, irrespective of the method chosen to achieve this. One of the important techniques of design is by using the techniques of Computational Fluid Dynamics (CFD). The CFD based design approaches are normally classified into three different methods namely – inverse surface models, inverse field model and numerical optimization models (Othmer, 2006). When the design variables goes over 1,00,000 the conventional methods would soon approach its limits. The numerical models have been widely accepted in the design process and have clearly established their advantages over the conventional design process. But serious limitations have been observed on the use of numerical models in the aerodynamic design also. The major constrain experienced in this connection is the increased computational cost that limit the use of wide ranging parameters while exploring the design requirement. The non-compatibility of total design freedom and the parameterization of CAD is another problem facing the design operations. Thus the aforementioned reasons limit the large-scale use of CFD in the aerodynamic design process (McGill, n.d.). Importance of Adjoint method Thus various limitations discussed earlier could be easily overcome by using the advanced computational methods like adjoint methods. The importance of adjoint methods for the shape optimization in the aerospace applications have also been reported widely in the literature. The success of these methods in the aerospace industry have forced various automobile manufacturers to employ them in their design operations.  The application of adjoint method is being explained by the author for the drag reduction in the passenger car (Jameson. n.d.). The adjoint methods eliminates the cost attached to the design variables and hence the design variables could be made independent of the cost involved in it (Othmer, 2006) . The cost independence of adjoint method opens up wide opportunities in the design optimization. The earlier approaches in the computational methods are by using large scale CAD parameterisation. But it was experienced that server restrictions are imposed by CAD parameterisation route. Thus the restrictions imposed by the CAD parameterisation could be easily removed and various type of computational resources like surface meshing and volumetric meshing could be abundantly used in this connection. The adjoint method has been successfully implemented in the design of various automobile components. Othmer et al (2005) have successfully used them in the evaluation of various automotive objective functions that included dissipated power, equal flow of mass through the outlets, uniformity of flow and also the angular momentum of the flow. In a similar academic exercise, the Automatic Differentiation techniques were applied to a CFD code in order to form a discrete adjoint solver. But it was soon realized that these codes lacked the flexibility to be used in large industrial level applications. And later, when the similar methodology was used through the Continuous adjoint method into a CFD environment successfully for the design of a air flow segment (Othmer, 2006). The studies have shown that the topological optimization through these methods would result in the uneven surfaces of geometry obtained. The CFD simulation or computation carried out on such a model would not be very accurate as obtained using the model discretised using any body fitted mesh. Thus topological optimization would result in the efficient drafting of the geometry than putting the efforts in fine-tuning the geometry. Thus in this case the optimization techniques employing directly on shape of the body need to be given the importance. In the applications involving the design of aircraft components, highly developed CFD systems are effectively integrated into the multi-system optimization  that delivers their ability to address the complex geometry, multiple objective functions and geometric design constrains. Combined use of adjoint method with unconstrained optimization have been found to be very effective in the aerodynamic design of airfoils , wings, wing bodies and complex aircraft configurations (Reuther et al, 1997). The authors clearly establish the complete configuration design subject multiple design points and geometric constrains. These methods have been illustrated for the transonic and supersonic configuration ranging from wing alone de signs to complex configuration designs that incorporates the wing , fuselage, nacelles and pylons (Reuther et al, 1997). The advances in the computational facilities using CFD and the development in the computing power of modern computers the aerodynamic design optimization methods using CFD codes have become a design necessity. Among the various techniques that have been used the gradient based technique have been often preferred due to its robust numerical models developed using them besides the relatively low burden in the computational effort (Kim et al, 2001). The biggest concern in using them in these applications were the accurate and efficient calculation involved in an aerodynamic derivative function. Though finite difference approximation have been used in the determination of the sensitivity, the accuracy of such an approach rests entirely on the perturbation size of design variables and flow initialization. Adjoint method have been found to be very economical in these circumstances when the number of design variables increases much beyond that specified by the objective function and the constrains. Researchers have also attempted to design the aircraft configurations using continuous adjoint method along with the Euler equations in block system that is highly structured (Kim et al, 2001). But it is realized that in the case of aerodynamic problems the unstructured grid offers considerable advantages when compared with the structured grid approach. Unstructured approaches could treat any complex geometry with great efficiency and also with relatively lesser effort.   In addition, this is also said to offer greater advantage in the adaptive refinement or unrefinement and total grid point hence could be reduced significantly. The authors have used direct and adjoint sensitivity codes from three-dimensional Euler solver using finite volume method. These codes were used in the design of supersonic transport wings, wing body nacelle and wing body configurations (Kim et al, 2001). Multi objective constrained problem related to the numerical optimization of aerodynamic design have been reported in the literature (Wild, 2008). The author clearly describes the design targets and constrains related to the high lift wings. The research also highlights the analysis undertaken in the analysis of flow in the optimization problem and attempts to establish various algorithms related to the optimization in the problem considered. The validation and application of numerical optimization relating to the aerodynamic design of the wings are also presented in detail (Wild, 2008). In an effort to understand the improvements that could be made in the take off and landing performance the utility of computational fluid dynamics have been incorporated. The CFD combined with the gradient optimization techniques have helped to remove the difficulties associated with the design decision-making process. But it has been found that computationally efficient option is to use the control theory approach to optimal aerodynamic design where the gradient information is obtained through solution of adjoint formulation (Jameson, 1988) . Such an approach was first applied to transonic flow and has now been most preferred choice of design problems. The advantages of the adjoint method can be understood from the reason that the cost of computation in the gradient determination is independent of the design variables (Kim et al, n.d. ). Design of multi element airfoils The multi element airfoil throws an additional challenge to the adjoint method. The method would be able to capture the influence of the change in the one element by the other elements in the system. The preliminary studies undertaken in this domain have given optimistic results (Kim et al, n.d.)). In an another research undertaken, the researchers have tried to undertake the aerodynamic optimization of multi-element airfoil designed to operate in the transonic regime (Alexandro et al, 2000).The investigations undertaken consists of using low fidelity physics models. Thus the detailed research is necessary to further validate the application of adjoint method in the analysis of airfoil. References Alexandrov, N.M., Nielsen, E.J., Lewis, R.M. and Anderson, W.K (2000), First-order model management with variable-fidelity physics, American Institute of Aeronautics & Astronautics Giles, M.B. and Pierce, N.A., (2000), An introduction to the adjoint approach to design, Flow, Turbulance and Cumbustion., 65, 393 - 415 Jameson, A. (1988). Aerodynamic design via control theory. Journal of Scientific Computing, 3:233–260. Jameson, A. , Optimum aerodynamic design using CFD and Control Theory, Retrieved from 23 November 2008 Kim H, J., Sasaki, D., Obayashi, S., Nakahashi, K. (2001), Aerodynamic optimization of supersonic transport wing using unstructured adjoint method, AIAA Journal, 39(6). Kim,S., Alonso, J.J. and Jameson, A. (2004) Two-dimensional High-Lift Aerodynamic Optimization Using the Continuous Adjoint Method, Journal of aircraft, 41(1). McGill (n.d.) , Introduction to aerodynamic shape optimization , Retrieved from on 22 November 2008 Othmer, C (2006), CFD Topology and shape optimization with adjoint methods,Retrieved from < http://www.wire.tu-bs.de/mitarbeiter/cothmer/docs/vdi.pdf>, on 22 November 2008 Othmer, C., Ravier, P and Pierrot, G. (2005), adjoint methods for automotive CFD optimization, PUCA 2005, Tokyo. Reuther, J, Jameson, A., Alonso, J.J., Rimlinger M.J., Sauders, D (1997) Constrained multipoint aerodynamic shape optimization using an adjoint formulation and parallel computers, americal Institute of Aeronautics and Astronautics Inc  Aeroscience meeting and exhibition ,Retrieved from on 22 November 2008 Read More