High-fidelity Aerodynamic Shape Optimization Research Articles

Improving transonic performance with adjoint-based NACA 0012 airfoil design optimization

This study delves into the discrete adjoint method, a powerful tool in high-fidelity aerodynamic shape optimization that efficiently computes derivatives of a target function for different design variables. It offers a theoretical exploration of its implementation as an innovative tool for calculating partial derivatives (sensitivities) related to objective functions and design variables. It is implemented to a NACA0012 airfoil at a transonic speed. This designated test case is qualitatively evaluated, considering specified Mach number and Reynolds number values of 0.7 and 15.96 million, respectively. The standard Spalart-Allmaras turbulence model is adapted to improve computational cost efficiency. The results validate the efficiency of Discrete Adjoint with OpenFOAM, showcasing its capability to generate optimal configurations. The achieved optimized performance is evidenced by minimizing the drag coefficient value (Cd) to an impressive value of 0.00871, 62.2 % lower than the previous studies, thus securing a novelty. While this research does not consider the post-processing of sensitivity calculations, it enables the potential for future research. The primary target of this paper is to assess the educational and training needs of researchers, engineers, and graduate students, offering a comprehensive introduction to discrete adjoint aerodynamic design optimization, presenting a novel methodology, and contributing to future advancements in the design optimization field.

Aerodynamic design optimization of a NACA 0012 airfoil: An introductory adjoint discrete tool for educational purposes

The adjoint method is a powerful tool in high-fidelity aerodynamic shape optimization, providing an efficient means to compute derivatives of a target function with respect to various design variables. This paper delves into the discrete adjoint method. It offers a theoretical exploration of its implementation as an innovative tool for calculating partial derivatives (sensitivities) related to objective functions and design variables, specifically applied to a subsonic NACA0012 airfoil. The study conducts a qualitative evaluation using a designated test case, considering specified Mach number and Reynolds number values of 0.297 and 6,667 million, respectively. The Spalart-Allmaras turbulence model is employed to enhance computational cost efficiency. The results affirm the efficacy of the introduced tool, DAFoam, showcasing its ability to generate optimal geometries. The achieved performance optimization is evidenced by minimizing the drag coefficient value (CD) to an impressive 0.0131. While this research does not delve into the post-processing of sensitivity calculations, it acknowledges the potential for future investigations. The primary objective and novelty of this study is to provide the elementary background of the state of the art test case (NACA0012) within the subsonic regime, introducing the pioneer discrete adjoint aerodynamic optimization methodology (DAFoam) with the potential to explore its higher order capabilities in other aerodynamic related studies. Furthermore, it caters the educational needs of both graduate students and engineers in this exciting field. By presenting this cutting-edge methodology, it contributes to future advancements for the aerodynamicists in terms of optimal solutions.

Effects of Static Stability Margin on Aerodynamic Design Optimization of Truss-Braced Wing Aircraft

Currently, the aviation industry is facing an oil and energy crisis and is contributing much more greenhouse gas emissions to the environment. Aircraft design approaches, such as aerodynamic shape optimization, new configuration concepts, and active control technology, have been the primary and effective means of achieving goals concerning fuel burn, noise, and emissions. For now, the design problems of relaxed static stability (RSS, an active control technique) and truss-braced wing (TBW) configurations with high-fidelity aerodynamic shape optimization methods have been investigated widely to promote aerodynamic performance. Nevertheless, they are studied almost always separately, and the combination of exploration and refined design is rarely presented. Therefore, the purposes of this work are to evaluate the benefits of RSS on a full TBW wing–body–tail configuration under various flight conditions and the effects on multi-components and to further explore the potential and analyze the aerodynamic features with the combination of shape optimization and RSS. To address these issues, on the one hand, a range of seven static stability margins are adopted to evaluate its effects with a high-fidelity Reynolds-averaged Navier–Stokes solver. On the other hand, seven cases of drag minimization multipoint aerodynamic design optimization are performed, which are with 600 shape variables and 13 twist variables, subject to lift coefficient, trim, and thickness constraints. The results indicate that with RSS only, the initial configuration has a 2.39% drag reduction under cruise conditions and a 3.01% and a 5.24% drag reduction under two off-design conditions. Additionally, the effects on the multi-components are observed and analyzed. Moreover, all of the optimized configurations with RSS have 2.13%, 2.42%, and 2.12% drag reductions under cruise conditions, drag divergence conditions, and near-buffet-onset conditions, respectively. The most promising optimized configuration has a lift-to-drag ratio of 24.48 with an aerodynamic efficiency of 17.14. The evaluations with a series of off-design points also present high-level aerodynamic efficiency.

Aerodynamic Shape Optimization of an S-Duct Intake for a Boundary-Layer Ingesting Engine

A high-fidelity aerodynamic shape optimization framework based on the Reynolds-averaged Navier–Stokes equations is applied to the optimization of a boundary-layer ingesting S-duct designed for embedded engines on a high-subsonic, unmanned flight vehicle. The optimizations initially target a cruise operating condition and are further extended to single-point and multipoint optimizations considering descent and climb. Two different composite objective functions are used. The first combines distortion and swirl at the fan interface plane as well as total pressure recovery, with user-defined weights for each objective, whereas the second involves pressure recovery, fan blade load variation, and fan blade incidence variation. Pareto fronts show the tradeoffs between objectives. The results indicate that compared to the baseline geometry, a simultaneous improvement in all objectives contained in the composite objective function can be obtained, depending on the priorities of each objective pre-assigned by the user. It was also found that if swirl can be ignored, then fan-face distortion can be greatly reduced while simultaneously reducing total pressure loss in the S-duct. Similarly, fan blade load variation and fan blade incidence variation can be significantly reduced while reducing total pressure loss. Finally, the multipoint optimization results show that a single S-duct geometry can perform well during cruise, climb, and descent conditions.

High-fidelity aerodynamic shape optimization using efficient orthogonal modal design variables with a constrained global optimizer

Abstract Aerodynamic shape optimization of aerofoils using efficient orthogonal design variables is considered using a global search algorithm. A novel approach is presented for deriving shape design variables, using a proper orthogonal decomposition of a set of training aerofoils to obtain an optimally efficient set of aerofoil deformation modes that represent typical design parameters such as thickness and camber. A major advantage of this extraction method is the production of orthogonal design variables, and this is particularly important in aerodynamic shape optimization. These design parameters have previously been tested on geometric shape recovery problems and been shown to be efficient at covering a large portion of the design space, hence the work is extended here to consider their use in aerodynamic shape optimization. A global search algorithm with an efficient constraint handling method has been developed and used here to optimize a suite of inviscid and viscous compressible aerofoil test cases using varying numbers of modal parameters. Often, an artefact of inviscid optimizations is an oscillatory pressure distribution, so to alleviate this drag minimization with a modulus of curvature penalty is also considered for the inviscid optimizations, where the penalty is used to force smoother pressure distributions; this is not necessary in the viscous optimizations. Results indicate that often fewer than 10 design parameters are required to obtain shock free solutions even from highly-loaded aerofoils with significant shocks.

High-Fidelity Aerodynamic Shape Optimization of a Lifting-Fuselage Concept for Regional Aircraft

High-fidelity aerodynamic shape optimization based on the Reynolds-averaged Navier–Stokes equations is used to optimize the aerodynamic performance of a conventional tube-and-wing design, a hybrid wing-body, and a novel lifting-fuselage concept for regional-class aircraft. Trim-constrained drag minimization is performed on a hybrid wing-body design, with an optimized conventional design serving as a performance reference. The optimized regional-class hybrid wing-body yields no drag savings when compared with the conventional reference aircraft. Starting from the optimized hybrid wing-body, an exploratory optimization with significant geometric freedom is then performed, resulting in a novel shape with a slender lifting fuselage and distinct wings. Based on this exploratory result, a new regional-class lifting-fuselage configuration is designed and optimized. With a span constrained by code “C” gate limits and having the same wing-only span as the conventional reference aircraft, this new design produces up to 10% lower drag than the reference aircraft. The effect of structural weight uncertainties, cruise altitude, and stability requirements are also examined.

High-Fidelity Hydrodynamic Shape Optimization of a 3-D Hydrofoil

With recent advances in high-performance computing, computational fluid dynamics (CFD) modeling has become an integral part in the engineering analysis and even in the design process of marine vessels and propulsors. In aircraft wing design, CFD has been integrated with numerical optimization and adjoint methods to enable high fidelity aerodynamic shape optimization with respect to large numbers of design variables. There is a potential to use some of these techniques for maritime applications, but there are new challenges that need to be addressed to realize that potential. This work presents a solution to some of those challenges by developing a CFD-based hydrodynamic shape optimization tool that considers cavitation and a wide range of operating conditions. A previously developed three-dimensional compressible Reynold saveraged Navier-Stokes (RANS) solver is extended to solve for nearly incompressible flows, using a low-speed preconditioner. An efficient gradient-based optimizer and the adjoint method are used to carry out the optimization. The modified CFD solver is validated and verified for a tapered NACA 0009 hydrofoil. The need for a large number of design variables is demonstrated by comparing the optimized solution obtained using different number of shape design variables. The results showed that at least 200 design variables are needed to get a converged optimal solution for the hydrofoil considered. The need for a high-fidelity hydrodynamic optimization tool is also demonstrated by comparing RANS-based optimization with Euler-based optimization. The results show that at high lift coefficient (CL) values, the Euler-based optimization leads to a geometry that cannot meet the required lift at the same angle of attack as the original foil due to inability of the Euler solver to predict viscous effects. Single-point optimization studies are conducted for various target CL values and compared with the geometry and performance of the original NACA 0009 hydrofoil, as well as with the results from a multipoint optimization study. A total of 210 design variables are used in the optimization studies. The optimized foil is found to have a much lower negative suction peak, and hence delayed cavitation inception, in addition to higher efficiency, compared to the original foil at the design CL value. The results show significantly different optimal geometry for each CL, which means an active morphing capability was needed to achieve the best possible performance for all conditions. For the single-point optimization, using the highest CL as the design point, the optimized foil yielded the best performance at the design point, but the performance degraded at the off-design CL points compared to the multipoint design. In particular, the foil optimized for the highest CL showed inferior performance even compared to the original foil at the lowest CL condition. On the other hand, the multipoint optimized hydrofoil was found to perform better than the original NACA 0009 hydrofoil over the entire operation profile, where the overall efficiency weighted by the probability of operation at each CL, is improved by 14.4%. For the multipoint optimized foil, the geometry remains fixed throughout the operation profile and the overall efficiency was only 1.5% lower than the hypothetical actively morphed foil with the optimal geometry at each CL. The new methodology presented herein has the potential to improve the design of hydrodynamic lifting surfaces such as propulsors, hydrofoils, and hulls.

High-Fidelity Hydrodynamic Shape Optimization of a 3-D Hydrofoil

With recent advances in high-performance computing, computational fluid dynamics (CFD) modeling has become an integral part in the engineering analysis and even in the design process of marine vessels and propulsors. In aircraft wing design, CFD has been integrated with numerical optimization and adjoint methods to enable high-fidelity aerodynamic shape optimization with respect to large numbers of design variables. There is a potential to use some of these techniques for maritime applications, but there are new challenges that need to be addressed to realize that potential. This work presents a solution to some of those challenges by developing a CFD-based hydrodynamic shape optimization tool that considers cavitation and a wide range of operating conditions. A previously developed three-dimensional compressible Reynolds-averaged Navier‐Stokes (RANS) solver is extended to solve for nearly incompressible flows, using a low-speed preconditioner. An efficient gradient-based optimizer and the adjoint method are used to carry out the optimization. The modified CFD solver is validated and verified for a tapered NACA 0009 hydrofoil. The need for a large number of design variables is demonstrated by comparing the optimized solution obtained using different number of shape design variables. The results showed that at least 200 design variables are needed to get a converged optimal solution for the hydrofoil considered. The need for a high-fidelity hydrodynamic optimization tool is also demonstrated by comparing RANS-based optimization with Euler-based optimization. The results show that at high lift coefficient (C L) values, the Euler-based optimization leads to a geometry that cannot meet the required lift at the same angle of attack as the original foil due to inability of the Euler solver to predict viscous effects. Single-point optimization studies are conducted for various target C L values and compared with the geometry and performance of the original NACA 0009 hydrofoil, as well as with the results from a multipoint optimization study. A total of 210 design variables are used in the optimization studies. The optimized foil is found to have a much lower negative suction peak, and hence delayed cavitation inception, in addition to higher efficiency, compared to the original foil at the design C L value. The results show significantly different optimal geometry for each C L, which means an active morphing capability was needed to achieve the best possible performance for all conditions. For the single-point optimization, using the highest C L as the design point, the optimized foil yielded the best performance at the design point, but the performance degraded at the off-design C L points compared to the multipoint design. In particular, the foil optimized for the highest C L showed inferior performance even compared to the original foil at the lowest C L condition. On the other hand, the multipoint optimized hydrofoil was found to perform better than the original NACA 0009 hydrofoil over the entire operation profile, where the overall efficiency weighted by the probability of operation at each C L, is improved by 14.4%. For the multipoint optimized foil, the geometry remains fixed throughout the operation profile and the overall efficiency was only 1.5% lower than the hypothetical actively morphed foil with the optimal geometry at each C L. The new methodology presented herein has the potential to improve the design of hydrodynamic lifting surfaces such as propulsors, hydrofoils, and hulls.

Two-Level Free-Form and Axial Deformation for Exploratory Aerodynamic Shape Optimization

An intuitive shape parameterization and control technique suitable for high-fidelity aerodynamic shape optimization is presented. It relies on the principles of free-form and axial deformation, enabling thorough exploration of the design space while keeping the number of design variables manageable. Surface sensitivities to the design variables are readily available; their inclusion in a highly efficient and robust adjoint-based optimization methodology involving linearly elastic volume mesh deformation and a Newton–Krylov solver for the Euler equations is described. The flexibility of the proposed approach is demonstrated through the exploratory shape optimization of a three-pronged feathered winglet, leading to a span efficiency of 1.19 under a height-to-span ratio constraint of 0.1, and an optimization of a regional jet wing at transonic speed where a winglet is allowed to develop starting from a planar wingtip extension, leading to an 18.8% reduction in drag.

New Approach to High-Fidelity Aerodynamic Design Optimization of a Wind Turbine Blade

A new approach to high-fidelity aerodynamic design optimization of a wind turbine blade configuration is offered. This method combines Blade Element Momentum (BEM) theory with the high fidelity aerodynamic shape optimization of an airfoil. The chord length and the twist angle of the blade at various radiuses have been calculated by BEM. The Navier Stokes equations are solved to simulate both two and three dimensional flows. The Results which are obtained from 2D Computational Fluid Dynamics (CFD) have been utilized to train a Neural Network (NN). E387Eppler is used as the base cross section of the blade. In the process of airfoil optimization, Genetic Algorithm (GA) is coupled with trained NN to attain the best airfoil shape at each angle of the attack. The simulation and validation of the base wind turbine with calculated pitch angle, twist angle, chord profile and base airfoil have been performed. The comparison of the results of this turbine with optimized one, illustrates a significant improvement in power factor.

High‐fidelity aerodynamic shape optimization of modern transport wing using efficient hierarchical parameterization

AbstractAerodynamic shape optimization technology is presented, using an efficient domain element parameterization approach. This provides a method that allows geometries to be parameterized at various levels, ranging from gross three‐dimensional planform alterations to detailed local surface changes. Design parameters control the domain element point locations and, through efficient global interpolation functions, deform both the surface geometry and corresponding computational fluid dynamics volume mesh, in a fast, high quality, and robust fashion. This results in total independence from the mesh type (structured or unstructured), and optimization independence from the flow‐solver is achieved by obtaining gradient information for an advanced gradient‐based optimizer by finite‐differences. Hence, the optimization tool can be used in conjunction with any flow‐solver and/or mesh generator. Results have been presented recently for two‐dimensional aerofoil cases, and shown impressive results; drag reductions of up to 45% were demonstrated using only 22 active design parameters. This paper presents the extension of these methods to three dimensions, with results for highly constrained optimization of a modern aircraft wing in transonic cruise. The optimization uses combined global and local parameters, giving 388 design variables, and produces a shock‐free geometry with an 18% reduction in drag, with the added advantage of significantly reduced root moments. Copyright © 2009 John Wiley & Sons, Ltd.

Two-Level Multifidelity Design Optimization Studies for Supersonic Jets

The conceptual/preliminary design of supersonic jet configurations requires multidisciplinary analyses tools, which are able to provide a level of flexibility that permits the exploration of large areas of the design space. High-fidelity analysis for each discipline is desired for credible results; however, the corresponding computational cost can be prohibitively expensive, often limiting the ability to make drastic modifications to the aircraft configuration in question. Our work has progressed in this area, and we have introduced a truly hybrid, multifidelity approach in multidisciplinary analyses and demonstrated, in previous work, its application to the design optimization of a low-boom supersonic business jet. In this paper, we extend our multifidelity approach to the design procedure and present a two-level design of a supersonic business-jet configuration, in which we combine a conceptual low-fidelity optimization tool with a hierarchy of flow solvers of increasing fidelity and advanced adjoint-based sequential quadratic programming optimization approaches. In this work, we focus on the aerodynamic performance aspects alone: no attempt is made to reduce the acoustic signature. The results show that this particular combination of modeling and design techniques is quite effective for our design problem and the ones in general and that high-fidelity aerodynamic shape optimization techniques for complex configurations (such as the adjoint method) can be effectively used within the context of a truly multidisciplinary design environment. Detailed configuration results of our optimizations are also presented.

Design of a Morphing Airfoil Using Aerodynamic Shape Optimization

An in-house high-fidelity aerodynamic shape optimization computer program based on a computational fluid dynamics solver with the Spalart-Allmaras turbulence model and a sequential-quadratic-programming algorithm is used to obtain a set of optimal airfoils at the different flight conditions of a light unmanned air vehicle. For this study, the airfoil requirements at stall, takeoff run, climb gradient, rate of climb, cruise, and loiter conditions are obtained. Then, the aerodynamic shape optimization program is used to obtain the airfoil that has the optimal aerodynamic characteristics at each one of these flight conditions. Once the optimal airfoils at each flight condition are obtained, the results are analyzed to gain a better understanding of the most efficient initial airfoil configuration and the possible mechanisms that could be used to morph the single element airfoil. The results show that a very thin airfoil could be used as the initial configuration. Furthermore, a morphing mechanism that controls the camber and leading-edge thickness of the airfoil will almost suffice to obtain the optimal airfoil at most operating conditions. Lastly, the use of the optimal airfoils at the different flight conditions significantly reduces the installed power requirements, thus enabling a greater flexibility in the mission profile of the unmanned air vehicle.