Ali Elham

Quasi-Three-Dimensional Aerodynamic Solver for Multidisciplinary Design Optimization of Lifting Surfaces

This paper presents the development of a quasi-three-dimensional aerodynamic solver, which provides accurate results for wing drag comparable to the higher-fidelity aerodynamic solvers at significantly lower computational costs. The proposed solver calculates the viscous wing drag using the combination of a two-dimensional airfoil analysis tool with a vortex lattice code. Validation results show that the results of the quasi-three-dimensional solver are in good agreement with higher-fidelity computational fluid dynamics solvers. The quasi-three-dimensional solver is used for a wing shape multidisciplinary design optimization. A multidisciplinary design optimization problem is formulated to design the wing shape of a typical passenger aircraft. The aircraft maximum takeoff weight is considered as the objective function. Two optimization algorithms, a local and a global optimum finder, are implemented in the multidisciplinary design optimization system. The optimization results indicate that the global opti...

Tool for preliminary structural sizing, weight estimation, and aeroelastic optimization of lifting surfaces*

This paper presents the development and implementation of a tool for wing structural sizing and aeroelastic optimization in early design steps, where the amount of available data about the wing structure is not enough to allow high-fidelity finite element analysis and optimization. The proposed tool consists of two levels. The first level is a quasi-analytical method for wing structural weight estimation and initially sizing of the wing box structure. The second level is an aeroelastic tool that uses a vortex lattice method and a finite beam element to compute the stress distribution in the wing box structure. The Newton method is used to solve the coupled system. The coupled adjoint sensitivity analysis method is used to compute the sensitivity of any function of interest with respect to the design variables. The tool was used for a series of wing aeroelastic optimizations to minimize the wing weight with a series of constraints on the wing structural failure modes and aileron effectiveness. Another series of optimizations is also used to find the wing jig shape for a predefined cruise shape. The outputs of the optimizations showed that the wing box weight varies quadratically with the required value for the aileron effectiveness.

Weight Indexing for Wing-Shape Multi-Objective Optimization

A method for wing-shape optimization is presented, in which the wing outer shape is optimized not only for the best aerodynamic efficiency but also for the minimum structural weight. The so-called airfoil effective distance is used to capture the influence of the wing outer shape on the wing-box structural weight. The airfoil weight index is defined based on the airfoil effective distance. Increasing the airfoil weight index results in decreasing the structural weight. The weight indexing method is used for airfoil multi-objective optimization for minimizing the aerodynamic drag as well as maximizing the weight index. The Pareto front for the drag and weight is found, and the airfoils on the Pareto front are used as the basis airfoils for a three-dimensional wing-shape optimization. The same method is applied to optimize the outer shape of three-dimensional wings for two objective functions: minimizing the wing drag and minimizing the wing structural weight. A response surface methodology is used to reduc...

Bilevel Optimization Strategy for Aircraft Wing Design Using Parallel Computing

A new bilevel optimization strategy for wing design is developed, in which the optimizations of the wing-planform and wing-airfoil shapes are decoupled from each other. The design of the wing-planform shape and the shape of the airfoils in several spanwise positions are considered as the goal of the optimization. In the new approach, the design problem is decomposed into a series of subproblems based on the design variables. The design variables defining the wing-planform shape are optimized in a top-level optimization, and the design variables defining the shape of airfoils in several spanwise positions are optimized in several sublevel optimizations. To take into account the influence of the airfoil shape in a specific spanwise position on the shape of the airfoils in other spanwise positions, a series of design variables are added to the design vector of the top-level optimization. The top-level optimizer is responsible for the consistency of the optimization. Using this approach, the number of design ...

Weight Indexing for Airfoil Multi-Objective Optimization

A new method for airfoil shape optimization is presented, in which the airfoil shape is optimized not only for the best aerodynamic efficiency but also for the minimum structural weight. To relate the structural weight to the airfoil shape a series of methods are prescribed for initial sizing of the wingbox structure. Based on these methods, a “weight index” is defined. The airfoil weight index is a mathematical equation that relates the structural weight of the wingbox to the airfoil shape. The structural weight of a wingbox reduces by increasing the weight index of the airfoil. A set of multi-objective optimizations is performed to find the Pareto front of the airfoil drag and the weight index.

Influence of weight modelling on the outcome of wing design using multidisciplinary design optimisation techniques

Weight estimation methods are categorised in different classes based on their level of fidelity. The lower class methods are based on statistical data, while higher class methods use physics based calculations. Statistical weight estimation methods are usually utilised in early design stages when the knowledge of designers about the new aircraft is limited. Higher class methods are applied in later design steps when the design is mature enough. Lower class methods are sometimes preferred in later design stages, even though the designers have enough knowledge about the design to use higher class methods. In high level multidisciplinary design optimisation (MDO) fidelity is often sacrificed to obtain models with shorter computation times. There is always a compromise required to select the proper weight estimation method for an MDO project. An investigation has been performed to study the effect of using different weight estimation methods, with low and medium levels of fidelity, on the results of a wing design using multidisciplinary design optimisation techniques. An MDO problem was formulated to design the wing planform of a typical turboprop and a turbofan passenger aircraft. The aircraft maximum take-off weight was selected as the objective function. A quasi-three-dimensional aerodynamic solver was developed to calculate the wing aerodynamic characteristics. Five various statistical methods and a quasi-analytical method are used to estimate the wing structural weight. These methods are compared to each other by analysing their accuracy and sensitivity to different design variables. The results of the optimisations showed that the optimum wing shape is affected by the method used to estimate the wing weight. Using different weight estimation methods also strongly affects the optimisation convergence history and computational time.

Beyond Quasi-Analytical Methods for Preliminary Structural Sizing and Weight Estimation of Lifting Surfaces

This paper presents the development and implementation of a tool for wing structural sizing and aeroelastic optimization in early design steps, where the amount of available data about the wing structure is not enough to allow high fidelity finite element analysis and optimization. The proposed tool consists of two levels. The first level is a quasianalytical method for wing structural weight estimation and initially sizing of the wing box structure. The second level is an aeroelastic tool that uses a vortex lattice method and a finite beam element to compute the stress distribution in the wing box structure. The Newton-Krylov method is used to solve the coupled system. The coupled adjoint sensitivity analysis method is used to compute the sensitivity of any function of interest with respect to the design variables. The tool was used for a series of wing aeroelastic optimizations to minimize the wing weight with a series of constraints on the wing structural failure modes and aileron effectiveness. Another series of optimizations is also used to find the wing jig shape for a predefined cruise shape. The outputs of the optimizations showed that the wing box weight varies quadratically with the required value for the aileron effectiveness.

Trust Region Filter-SQP Method for Multi-Fidelity Wing Aerostructural Optimization

A trust region filter-SQP method is used for wing multi-fidelity aerostructural optimization. Filter method eliminates the need for a merit function, and subsequently a penalty parameter. Besides, it can easily be modified to be used for multi-fidelity optimization. A low fidelity aerostructural analysis tool is presented, that computes the drag, weight, and structural deformation of lifting surfaces as well as their sensitivities with respect to the design variables using analytical methods. That tool is used for a mono-fidelity wing aerostructural optimization using a trust region filter-SQP method. In addition to that, a multi-fidelity aerostructural optimization has been performed, using a higher fidelity CFD code to calibrate the results of the lower fidelity model. In that case, the lower fidelity tool is used to compute the objective function, constraints, and their derivatives to construct the quadratic programming subproblem. The high fidelity model is used to compute the objective function and the constraints used to generate the filter. The results of the high fidelity analysis are also used to calibrate the results of the lower fidelity tool during the optimization. This method is applied to optimize the wing of an A320 like aircraft for minimum fuel burn. The results showed about 9 % reduction in the aircraft mission fuel burn.

Optimization of variable stiffness composite plates with cut-outs subjected to compression, tension and shear using an adjoint formulation

This paper presents an improved and extended version of a framework for the design of variable stiffness fiber composite panels developed by the authors. The framework supports the design of panels subjected to multiple load cases, each case a combination of compression or tension and shear. The framework consists of a finite element (FE) solver, an optimizer, a novel approach to relate design variables to the stiffness matrix in the FE module, constraint evaluation modules for manufacturing and buckling constraints and a postprocessor that translates the theoretical optimal result from the optimizer into discrete tow paths for each ply including a cut and restart function. The formulation of the design variables using a manufacturing mesh separate from the FE mesh limits the number of design variables while preserving smoothness of the solution and allows easy specification of manufacturing constraints enforced by the envisioned fiber steering process, for example the minimum course radius to prevent tow buckling. The framework is intended for inclusion in an MDO based aircraft wing weight estimation tool in which it is combined with aerodynamic analysis and optimization. Results obtained with the framework show the structural benefit of using variable stiffness also in case of multiple load cases. The design variable formulation and the adjoint based sensitivity analysis lead to acceptable calculation time while preserving accuracy and smoothness of the solution. Separation of optimizer and tow path planner allows multiple practical interpretations of the theoretical optimization result. This preserves the influence of the manufacturing engineer on the practical panel lay-up and enables the user to control overlaps and gaps using cut-and-restart functionality.

Wing Aerostructural Optimization Under Uncertain Aircraft Range and Payload Weight

An uncertainty-based approach is undertaken to deal with multipoint wing aerostructural optimization. The flight points are determined by the quadruple set of parameters: Mach number, cruise altitude, carried payload, and flight range. From this set, the payload and range are modeled as probabilistically uncertain based on U.S. flight data for the operations of an A320 aircraft. The fuel burn is selected as the performance metric to optimize. Structural failure criteria, aileron efficiency, and field performance considerations are formulated as constraints. The wing is parametrized by its planform, airfoil sections, and structural thickness. The analyses disciplines consist of an aerostructural solver and a surrogate-based mission analysis. For the optimization task, a gradient-based algorithm is used in conjunction with coupled adjoint methods and a fuel burn sensitivity analytical formula. Another key enabler is a cost-effective nonintrusive uncertainty propagator that allows optimization of an aircraft...