Multidisciplinary design optimization (MDO) of a typical low aspect ratio wing using Isight

Transcription

1 Multidisciplinary design optimization (MDO) of a typical low aspect ratio wing using Isight Mahadesh Kumar A 1 and Ravishankar Mariayyah 2 1 Aeronautical Development Agency and 2 Dassault Systemes India (P) Ltd. Abstract: The design of wing is the most important activity in aircraft development. The two major factors considered in a wing design are the lift to drag (L/D) ratio and the weight. The problem was multidisciplinary in nature since both aerodynamic and structural performances were considered. In this paper, the multi-objective problem of maximizing L/D ratio and minimizing weight is explored using Isight as the MDO framework. An aerodynamic analysis code called AVLM developed in-house at ADA and the commercially available structural analysis code MSC/NASTRAN were used for the study, along with CATIA V5 for parametric modeling. The entire workflow was automated and integrated seamlessly using Isight. The automated MDO process was able to provide optimum values of wing design parameters by simultaneously meeting target specifications from both aerodynamics and structural disciplines. Keywords: aerodynamic, L/D, Isight, MDO, wing, weight. 1. Introduction Wing design and development is one of the most critical and important phases in any aircraft development process. The objective of any wing design is to provide a higher lift force with minimum drag force and the lowest possible weight. The aerodynamic performance of an aircraft depends significantly on the wing design. This means that a typical wing development process involves a variety of engineering problems that are multidisciplinary in nature. A typical wing design has to meet stringent design requirements of both structures and aerodynamics disciplines. Often the requirements from both these disciplines are competing and require careful and simultaneous consideration in a wing design process. Multidisciplinary Design Optimization (MDO) is a very powerful and an indispensable tool during the conceptual and preliminary design phases of a wing. In today s environment, a variety of computer-aided tools are used by designers and engineers for design and simulation of any product, and wing design is no exception. Different levels of analyses ranging from simple empirical expressions to complex finite element analyses are involved in its design process. This means that one has to invoke different types of tools ranging from in-house tools to wellestablished commercial CAD/CAE tools to come up with the optimum design. Each of these tools has its own advantages depending on the type of analysis that needs to be performed. If we SIMULIA India Regional Users Meeting 11 Page 1 of 10

2 look at an MDO framework that would cater to a wing design process, the following features are desired: (i) Automation of the execution of each tool involved in the process (ii) Automated and seamless exchange of data between the different tools (iii) Fast, powerful, and robust design exploration capabilities to quickly identify the optimal set of design parameters that satisfy the constraints Isight as a framework has exactly the desired features listed above which would help set up an MDO problem for a wing design with minimum effort. Isight has the capabilities to combine models across disciplines and automate the execution of the resulting simulation workflow, otherwise called as a simflow. Moreover, Isight provides an open component framework through which any simulation tool can be integrated and executed directly from within the environment. Isight has components for many commonly used CAD and CAE tools. In this paper an attempt has been made to couple CAD, CAE and in-house codes using Isight to perform an MDO for design and development of a typical low aspect ratio aircraft wing. 2. MDO Simflow set up and key challenges CAD applications are very commonly used for parametric modeling and design of an aircraft wing. In this work, the popular 3D CAD software, CATIA V5, was used to generate a parametric model of the wing. The critical geometric design parameters considered in this work were the sweep back angle (Λ), the tip chord length (C T ) and the root chord length (C R ), as shown in Figure 1. The sweep back angle (Λ) is one of the most important parameters which help in delaying shock formation on wing at transonic speeds. The other two geometric parameters, chord lengths, (C T ) and (C R ), control the shape as well as the weight of the wing. The parameter mean aerodynamic chord length is also based on these two chord lengths, (C T ) and (C R ). The ratio of the mean aerodynamic chord length to the span of the wing is called the aspect ratio, and this significantly affects the L/D ratio. The entire 3D wing model was generated automatically based on these three independent parameters. All the other features of the wing model such as generation of the airfoil ordinates and drawing of airfoil section were automatically calculated with these three independent parameters. The three parameters were linked to a design table defined in an Excel spreadsheet. SIMULIA India Regional Users Meeting 11 Page 2 of 10

3 By modifying these parameter values in the spreadsheet, a modified 3D model could be automatically generated in CATIA V5. The parameterized 3D model was used as the basis for pre-processing and postprocessing of the downstream CAE models that would be integrated into the workflow without the need for any translators. Transferring data between CAD and CAE systems without any loss has been the biggest challenge for any MDO process that involves CAD-CAE integration. Within the CATIA V5 environment the user can create a finite element mesh and write out the node and element data in NASTRAN format. CATIA V5 has a useful add-on feature called DPS (Digital Product Simulation) with which the finite element mesh can be further augmented with material properties, loads and boundary conditions and can be converted to a complete NASTRAN finite element model. Hence a single parameterized 3D model was used in this study that catered to both CAD and CAE tools thereby preventing any loss of CAD data associated with a typical CAD-CAE integration process. With the availability of 3D wing finite element model, the workflow further branched out into two sub-flows downstream: one was the aerodynamic analysis sub-flow and the other was a structural analysis sub-flow. This can be clearly seen in Figure 2. Figure 1. CATIA V5 Wing model (a) geometry with the parameters and (b) 3D finite element model with restraints SIMULIA India Regional Users Meeting 11 Page 3 of 10

4 2.1 Aerodynamics workflow The CATIA V5 3D mesh model (in NASTRAN format) was read inside the PATRAN pre-processor. In PATRAN the mid-surface of the 3D finite element model was extracted as an element-based surface, which was then read by the in-house aerodynamic code AVLM. Depending on the shape of the extracted surface, AVLM calculates the (L/D) ratio (which directly depends on the wing aspect ratio) and the pressure load that needs to be input for the structural analysis workflow. The parameter (L/D) ratio was used as the first objective in the design exploration study. Integration of PATRAN in Isight was achieved using the SimCode component. AVLM codes were written using the mathematical software MATLAB and integrated within Isight framework using the MATLAB component. Figure 2. MDO setup for wing design 2.2Structural analysis workflow For the structural analysis workflow, the NASTRAN 3D finite element model output from DPS was imported inside the PATRAN pre-processor to setup the model for structural weight optimization. The pressure load input for the top skin was read from the SIMULIA India Regional Users Meeting 11 Page 4 of 10

5 AVLM code through Isight framework. The entire 3D model was divided into different zones for sizing optimization analysis using NASTRAN s SOL 200. The 3D finite element model from DPS and various zones used for sizing optimization are shown in Figure 3. The optimization problem in SOL 200 had an objective of minimum weight with thicknesses of the various zones being design variables and stress being a constraint. The resultant optimum weight was used as the second objective in the design exploration study. Figure3. Different zones for the wing model for sizing optimization 3. Design Exploration Strategy With the completion of the first two key requirements in the MDO setup: automation of each tool in the workflow, and seamless integration of the different tools in the workflow, the next logical step was to leverage Isight s powerful design exploration capabilities for design optimization, DFSS (Design for Six Sigma), approximations, and Design of Experiments (DOE). The design exploration strategy employed in this work has been described by the flow chart shown in Figure 4. The initial step was to create a DOE matrix with the three independent parameters (C T ), (C R ) and (Λ). A full-factorial based DOE approach was utilized with 3 levels SIMULIA India Regional Users Meeting 11 Page 5 of 10

6 for each of the parameters, thereby generating a design matrix of 27 experiments. The target output parameters for this DOE study were L/D ratio and weight. The objective of this particular DOE study was to find out the experiment which gives the maximum possible L/D ratio and the minimum possible weight as shown in Figure 5. This information helps choose an initial design point for subsequent optimization studies. The next step was to create a design approximation based on the results from the DOE. Approximations are mathematical models that mimic the behavior of the actual simulation codes. In many workflows involving MDO, approximations are a must since each design iteration involving simulation codes typically takes a long time to complete. Isight has a range of powerful approximation techniques available for the user to choose from. The efficiency of the approximation models generally depends upon the quality of the initial sampling points and the nature of applications. In our study, the RBF (Radial Basis Function) technique was used to create an approximation model. The relationship between the input parameters and the output parameters were obtained by examining the 3D graphs created by the approximations models, as shown in Figure 6. Once the approximation model was ready, a design search was performed by taking the parameters from the DOE run corresponding to the minimum possible weight. Examination of the 3D graphs from the approximations shows that the design space was smooth. Hence, the gradient-based optimization method NLPQL was used to drive optimization. The use of an approximate model for optimization enables rapid search of optimal parameters. However, since the optimal parameters were obtained from an approximate model, the same set of parameters was tested by running the complete simulation workflow without approximations. The values of the objective parameters, (L/D) ratio and weight, were then compared. If the results were close within an acceptable tolerance then it can be concluded that the optimum parameters obtained from approximation were indeed the optimum parameters. On the other hand, if there had been a significant difference between the results, then another approximation with a different strategy, such as more number of DOE runs or a different approximation technique, has to be implemented. SIMULIA India Regional Users Meeting 11 Page 6 of 10

7 Figure4. Design exploration strategy employed for obtaining optimum geometric parameters of the wing Figure5. DOE history showing the experiment that gave minimum weight (highlighted in green) and maximum L/D ratio (highlighted in blue) SIMULIA India Regional Users Meeting 11 Page 7 of 10

8 Figure 6. Variation of (C R ) and (Λ) with respect to (a) L/D ratio and (b) weight by RBF approximations SIMULIA India Regional Users Meeting 11 Page 8 of 10

9 Weight 4. Key observations from the design exploration studies From the design exploration studies that were performed, the following observations were made: 1. Increase in L/D ratio with increase in the magnitude of the sweep back angle (Λ) 2. Decrease in (C T ) and (C R ) values with increase in L/D ratio 3. Increase in the overall weight of the wing with increase in the sweep back angle (Λ) 4. The two objectives, L/D ratio and weight, were competing. The optimum weights for desired values of L/D ratio has been given in the figure 7. For example, if a wing design with a higher L/D ratio was desired then the objective of minimum weight is compromised accordingly L/D ratio vs weight 90, , , , , L/D ratio Figure7. Plot of L/D ratio versus weight 5. Summary and benefits of the MDO study 1. A highly automated process template for a wing design has been built and demonstrated in this study. It has been shown that the entire process flow right from the CAD model to CAE post-processing could be executed without any manual intervention. SIMULIA India Regional Users Meeting 11 Page 9 of 10

10 2. At least an order of magnitude reduction in design cycle time has been achieved in this study. A manual workflow for this process would have required at least a few weeks of engineering time to complete. In this workflow, 27 wing designs were generated in a day. 3. The key benefit of this MDO workflow setup was the achievement of seamless CAD/CAE integration, i.e. the same parameterized 3D model was used as a base for CAD as well as CAE. There was absolutely no data loss when transferring model from CAD to CAE environment. 4. In this particular study, only three design variables were considered. However, this can be easily extended to more number of variables for a more comprehensive characterization of wing design. In such a case, evaluating hundreds or even thousands of design would be necessary. With an automated process template, evaluating such huge number of design alternatives could be achieved quickly. 5. In this study, Isight s powerful design exploration capabilities were leveraged to quickly explore the design space and achieve the optimum design. 6. Acknowledgements The author would like to thank the managements of Aeronautical Development Agency and Dassault Systemes, India for their permission to publish this paper. The author would also like to express sincere gratitude to Mr. Bhatu Sonawane, Mr. Arun Yadurappa and Mr. Dayanidhi Panda from Dassault Systemes, India for their help in modeling 3D wing design in CATIA. SIMULIA India Regional Users Meeting 11 Page 10 of 10