Aerodynamic Shape Optimization Research Articles

Aerodynamic shape optimization of H-VAWT blade airfoils considering a wide range of angles of attack

Abstract The current H-type vertical axis wind turbine (VAWT) airfoils are from horizontal axis wind turbine airfoils or symmetry airfoils that are designed at one angle of attack (such as α = 6°) rather than different angles of attack. As a consequence, it cannot, to a certain extent, increase wind power efficiency. Therefore, an optimal method of H-type VAWT blade airfoils in different ranges of angles of attack is presented. It can be expressed by airfoil integrated function. Then, an optimized mathematical model in which the objective function is the average of tangential force coefficients is established. The particle swarm optimization algorithm coupled with RFOIL program is introduced to optimize the H-type VAWT airfoil profiles with high aerodynamic performance. The optimized results show that the new HVAWT-00153 airfoil is more suitable to VAWTs than the other two new airfoils and NACA-0015 airfoil. Besides, by using computational fluid dynamics technology, the superiority of HVAWT-00153 airfoil over NCAC-0015 airfoil is reviewed. The results indicate that the H-type VAWT with new HVAWT-00153 airfoils could exhibit larger torque coefficients and higher power coefficients than that of the original H-type VAWT with NACA-0015 airfoils. The maximum power coefficient can reach 0.362, increased by 8.45% compared with that of the original one. This study has a good guidance to how to design the H-type VAWT airfoils with high wind energy power.

Multi-fidelity convolutional neural network surrogate model for aerodynamic optimization based on transfer learning

In aerodynamic shape optimization, a high-fidelity (HF) simulation is generally more accurate but more time-consuming than a low-fidelity (LF) simulation. To take advantage of both HF and LF simulations, a multi-fidelity convolutional neural network (CNN) surrogate model with transfer learning (MFCNN-TL) is proposed, which integrates different fidelity information through fine-tuning and adaptively learns their nonlinear mapping. The proposed surrogate model provides a new optimization framework, which maps the relation between shape parameters and aerodynamic performance. In the optimization framework, the HF model with a fine grid and the LF model with a coarse grid is used, respectively. In each optimization iteration, a multi-fidelity infilling strategy is adopted, and HF samples and LF samples are added to update the surrogate model. Finally, it is applied to the aerodynamic shape optimization of NACA0012 airfoil and RAE2822 airfoil. The optimization results show that the proposed MFCNN-TL surrogate model can significantly reduce the calculation cost and improve the optimization efficiency compared with the single-fidelity surrogate model.

Cyber-physical aerodynamic shape optimization of a tall building in a wind tunnel using an active fin system

This study explores the use of a cyber-physical systems (CPS) framework for the design and optimization of the aerodynamics of a tall building through aeroelastic boundary layer wind tunnel (BLWT) testing. The framework is a fully-automated combination of traditional experimental wind tunnel testing with numerical optimization strategies to evaluate a wide range of candidate designs both accurately and quickly. In this study, candidate designs are achieved through the physical adjustment of the aerodynamic shape of a multi-degree-of-freedom (MDOF) aeroelastic tall building model. BLWT testing is carried out at the University of Florida Natural Hazard Engineering Research Infrastructure (NHERI) Experimental Facility (EF). The specimen is equipped with an actuation system consisting of a series of individually-controllable slotted fins comprising an active fin system (AFS), which enable precise modifications of the aerodynamic shape of the envelope. The wind-induced building response of the specimen is directly captured using a series of accelerometers and laser displacement sensors. A stochastic optimization algorithm is then employed in the aerodynamic CPS framework to evaluate the fitness of each candidate design based on specified performance criterion related to either occupant comfort or building drift. Optimization results indicate that the CPS framework can reliably achieve the optimal solution which minimizes the response (i.e., horizontal accelerations and lateral displacements) of the aeroelastic specimen.

Gradient-free aerodynamic shape optimization using Large Eddy Simulation

In this paper we demonstrate the ability to perform gradient-free aerodynamic shape optimization using Large Eddy Simulation (LES) with the Mesh Adaptive Direct Search (MADS) optimization algorithm. We first outline the challenges associated with performing gradient-based optimization using LES, specifically chaotic divergence of the adjoint. We then introduce a Dynamic Polynomial Approximation (DPA) procedure, which allows the high-order solution polynomial representation used by the flow solver to be increased, or decreased, depending on the poll size being used by MADS. This allows rapid convergence towards the optimal design space using lower-fidelity simulations, followed by automatic transition to higher-fidelity simulations when close to the optimal design point. We demonstrate the utility of MADS for optimization of simple chaotic problems, specifically the Lorenz system. We then demonstrate the utility of DPA for aerodynamic optimization of a low Reynolds SD7003 airfoil, highlighting the benefits of the binary DPA approach. Finally, we perform aerodynamic optimization of a turbulent SD7003 airfoil with a final design that increases the mean lift to drag ratio by 32% relative to experimental data, demonstrating that shape optimization using LES and MADS is feasible for aerodynamic design.

Aerodynamic Shape Optimization Method of Non-Smooth Surfaces for Aerodynamic Drag Reduction on A Minivan

To reduce aerodynamic drag of a minivan, non-smooth surfaces are applied to the minivan’s roof panel design. A steady computational fluid dynamics (CFD) method is used to investigate the aerodynamic drag characteristics. The accuracy of the numerical method is validated by wind tunnel test. The drag reduction effects of rectangle, rhombus and arithmetic progression arrangement for circular concaves are investigated numerically, and then the aerodynamic drag coefficient of the rectangle arrangement with a better drag reduction effect is chosen as the optimization objective. Three parameters, that is, the diameter D of the circular concave, the width W and the longitudinal distance L among the circular concaves, are selected as design variables. A 20-level design of an experimental study using a Latin Hypercube scheme is conducted. The responses of 20 groups of sample points are obtained by CFD simulation, based on which a Kriging model is chosen to create the surrogate-model. The multi-island genetic algorithm is employed to find the optimum solution. The result shows that maximum drag reduction effects up to 7.71% can be achieved with a rectangle circular concaves arrangement. The reduction mechanism of the roof with the circular concaves was discussed. The circular concaves decrease friction resistance of the roof and change the flow characteristics of the recirculation area in the wake of the minivan. The roof with the circular concaves reduces the differential pressure drag of the front and rear of the minivan.

Research on the Rapid Aerodynamic Shape Optimization of Canards of Gliding Guided Projectile

Research on the Rapid Aerodynamic Shape Optimization of Canards of Gliding Guided Projectile

Discrete Adjoint-Based Aerodynamic Shape Optimization Framework for Natural Laminar Flows

An adjoint-based aerodynamic shape optimization framework for natural laminar flows is developed. The laminar to turbulent-transition onset is predicted by the correlation-based Bas–Cakmakcioglu transition model that is coupled with the Spalart–Allmaras turbulence model. A discrete adjoint implementation is subsequently developed. Automatic differentiation is utilized to construct the partial derivatives in the discrete adjoint formulation. The turbulence and transition models are fully coupled into the sensitivity derivative evaluations, as well as into the objective function evaluations. The sensitivity derivatives evaluated by the discrete adjoint solver are validated against those of the finite central difference method. The discrete adjoint-based aerodynamic shape optimization framework developed for natural laminar flows is successfully employed to optimize aerodynamic characteristics of the NLF(1)-0416 airfoil and a low-aspect-ratio wing.

Aerodynamic Shape Optimization of Highly Nonplanar Raised and Drooped Wings

Aircraft wings are commonly designed with nonplanar geometry, such as winglets, in order to improve aerodynamic efficiency. This work presents a method for generating nonplanar wing designs through gradient-based optimization, which is then used to investigate the performance characteristics of nonplanar wings. The nonplanar parameterization is defined to give a large design space that allows the formation of highly nonplanar features and permits large changes to the geometry. Aerodynamic characteristics are captured using an inviscid three-dimensional panel method with approximations for viscous drag. The methodology is demonstrated by optimizing reference wings from literature and comparing aerodynamic performance. Investigations are also performed on the impact on performance when wings are raised or drooped, and the differences in aerodynamic behavior between the two designs. Results suggest that the converged designs and their performance are highly dependent on how the geometry is restricted. If a large design space is provided, both raised and drooped wings are able to produce designs with similar performance when only inviscid analysis is considered. When accounting for viscous effects, results suggest that drooped wings are not beneficial for drag reduction.

Lossy compression techniques supporting unsteady adjoint on 2D/3D unstructured grids

This paper proposes and assesses remedies to the significant storage requirements of unsteady adjoint methods used in gradient-based optimization, in multi-dimensional problems modeled by unsteady PDEs. Even if the application domain of the proposed technique(s) is wide, these remedies are herein demonstrated in shape optimization problems with unsteady fluid flows. In these cases, the adjoint equations are integrated backwards in time, requiring the instantaneous flow fields to be available at each time-step of the adjoint solver, and this noticeably increases storage requirements. To avoid extreme treatments, such as the full storage of the computed instantaneous flow fields or their recomputations from scratch during the solution of the adjoint equations, or even the widely used check-pointing technique, lossy compression techniques are proposed. These are implemented within OpenFOAM, which is used to solve the flow and adjoint equations and conduct the optimization. In this paper, (a) the ZFP compression library, (b) the incremental Proper Generalized Decomposition (iPGD) algorithm and (c) an efficient hybridization of them are used. The compression strategies are assessed on aerodynamic shape optimization problems. Their effectiveness in data reduction, computational overhead and representation accuracy is considered, in relation to the continuous adjoint method which uses the decompressed fields to compute the gradient of objective functions as the reference method.

Adjoint-based aerodynamic drag minimisation with trim penalty

AbstractThe aerodynamic performance of conventional aircraft configurations are mainly affected by the wing and horizontal tail. Drag reduction by shape optimisation of the wing, while taking into account the aircraft trimmed constraint, has more benefit than focusing solely on the wing. So in order to evaluate this approach, the following study presents results of a single and multipoint aerodynamic shape optimisation of the wing-body-tail configuration, defined by the Aerodynamic Design Discussion Group (ADODG). Most of the aerodynamic shape optimisation problems published in the last years are focused mainly on the wing as the main driver for performance improvement, with no trim constraint and/or excess drag obtained from the fuselage, fins or other parts. This work partially fills this gap by an investigation of RANS-based aerodynamic optimisation for transonic trimmed flight. Mesh warping and geometry parametrisation is accomplished by fitting the multi-block structured grid to a B-spline volumes and performing the mesh movement by using surface control points embedded within the free-form deformation (FFD) volumes. A gradient-based optimisation algorithm is used with an adjoint method in order to compute the derivatives of the objective and constraint functions with respect to the design variables. In this work the aerodynamic shape optimisation of the CRM wing-body-tail configuration is investigated, including a trim constraint that is satisfied by rotating the horizontal tail. The shape optimisation is driven by 432 design variables that envelope the wing surface, and 120 shape variables for the tail, as well as the angle of attack and tail rotation angles. The constraints are the lift coefficient, wing’s thickness controlled by 1,000 control points, and the wing’s volume. For the untrimmed configuration the drag coefficient is reduced by 5.76%. Optimising the wing with a trim condition by tail rotation results in shock-free design with a considerably improved drag, even better than the untrimmed-optimised case. The second optimisation problem studied is a single and multi-point lift constraint drag minimisation of a gliding configuration wing in transonic viscous flow. The shock is eliminated, reducing the drag of the untrimmed configuration by more than 60%, using 192 design variables. Further robustness is achieved through a multi-point optimisation with more than 45% drag reduction.

Aerodynamic Design Optimization of a Transonic Strut-Braced-Wing Regional Aircraft

The aerodynamic design and fuel burn performance of a Mach-0.78 strut-braced-wing regional jet is investigated through aerodynamic shape optimization based on the Reynolds-averaged Navier–Stokes equations. Conceptual-level multidisciplinary design optimization is first performed to size the strut-braced-wing aircraft for a design mission similar to the Embraer E190-E2, with a design range of 3100 nmi at a maximum capacity of 104 passengers, and a maximum payload of 30,200 lb. For direct performance comparisons, a conventional tube-and-wing regional jet is also sized and optimized based on the same reference aircraft. Gradient-based aerodynamic shape optimization is then performed on wing–body–tail models of each aircraft, with the objective of drag minimization at cruise over a 500 nmi nominal mission. Design variables include twist and section shape degrees of freedom, which are realized through a free-form and axial deformation geometry control system, whereas nonlinear constraints include constant lift, zero pitching moment, minimum wing volume, and minimum maximum thickness-to-chord ratios. Results indicate that the optimizer is capable of mitigating shock formation, boundary-layer separation, and other flow interference effects from each wing design, including those within the wing–strut junction of the strut-braced wing. With year 2020 technology levels, the strut-braced-wing regional jet offers a 12.9% improvement in cruise lift-to-drag ratio over an Embraer E190-E2-like conventional tube-and-wing aircraft, which translates to a 7.6% reduction in block fuel for the nominal mission.

Machine learning for adjoint vector in aerodynamic shape optimization

Adjoint method is widely used in aerodynamic design because only once solution of flow field is required for it to obtain the gradients of all design variables. However, the computational cost of adjoint vector is approximately equal to that of flow computation. In order to accelerate the solution of adjoint vector and improve the efficiency of adjoint-based optimization, machine learning for adjoint vector modeling is presented. Deep neural network (DNN) is employed to construct the mapping between the adjoint vector and the local flow variables. DNN can efficiently predict adjoint vector and its generalization is examined by a transonic drag reduction of NACA0012 airfoil. The results indicate that with negligible computational cost of the adjoint vector, the proposed DNN-based adjoint method can achieve the same optimization results as the traditional adjoint method.Graphical abstract

An exploitation-enhanced multi-objective efficient global optimization algorithm for expensive aerodynamic shape optimizations

The traditional multi-objective efficient global optimization (EGO) algorithms have been hybridized and adapted to solving the expensive aerodynamic shape optimization problems based on high-fidelity numerical simulations. Although the traditional EGO algorithms are highly efficient in solving some of the optimization problems with very complex landscape, it is not preferred to solve most of the aerodynamic shape optimization problems with relatively low-degree multi-modal design spaces. A new infill criterion encouraging more local exploitation has been proposed by hybridizing two traditional multi-objective expected improvements (EIs), namely, statistical multi-objective EI and expected hypervolume improvement, in order to improve their robustness and efficiency in aerodynamic shape optimization. Different analytical test problems and aerodynamic shape optimization problems have been investigated. In comparison with traditional multi-objective EI algorithms and a standard evolutionary multi-objective optimization algorithm, the proposed method is shown to be more robust and efficient in the tests due to its hybrid characteristics, easier handling of sub-optimization problems, and enhanced exploitation capability.

Dual-convolutional neural network based aerodynamic prediction and multi-objective optimization of a compact turbine rotor

With the development of neural network technology, surrogate models and dimensionality reduction strategies based on machine learning have become the research hotspots of aerodynamic shape optimization recently. In order to further improve the accuracy and interpretability of the traditional surrogate models, this research establishes a deep learning model, named Dual Convolutional Neural Network (Dual-CNN) for the aero-engine turbines. The aerodynamic performances are predicted and the pressure, temperature fields are reconstructed for multiple rotor profile conditions. The prediction of efficiency is compared with the accuracy of Gaussian Process Regression (GPR) and Artificial Neural Network (ANN) models. The results show that the proposed Dual-CNN model can accurately reconstruct the fields, thus interpreting the mechanism for the change of aerodynamic performance. Dual-CNN is more accurate than GPR and ANN in predicting efficiency and torque, whose error is within an acceptable range of optimization. Then, efficiency and torque are selected as the objective functions to perform a gradient-based multi-objective optimization by the automatic differentiation method and a Pareto solution is obtained. The trained Dual-CNN provides rapid and accurate prediction of performance without CFD calculation in the optimization. Finally, the sensitivity to train size is analyzed for the Dual-CNN model, which indicates that the sampling of 1500 cases for eight design variables in this dataset enables Dual-CNN to achieve favorable effect of field reconstruction and performance prediction.

Robust Newton–Krylov Adjoint Solver for the Sensitivity Analysis of Turbomachinery Aerodynamics

Adjoint methods are widely used for turbomachinery aerodynamic shape optimization. However, for industrial applications, the degradation of robustness and efficiency of adjoint solvers for edge-of-the-envelope conditions still poses a challenge to the successful deployment of adjoint methods in the industry. This work attempts to alleviate such problems by using the Newton–Krylov method to solve both the flow and adjoint equations. The developed parallel adjoint solver reuses the Jacobian matrix computed by the flow solver and obtains the adjoint matrix–vector product via an accumulative parallel communication. Consequently, the development of an adjoint solver is significantly simplified, as reverse differentiation is not needed. Combining an already validated Newton–Krylov flow solver with the adjoint solver developed in this work, robust and efficient residual convergence is demonstrated for representative turbomachinery cases, including an axial and a centrifugal compressor. The compressor maps are first computed and adjoint solutions for both design and typical off-design conditions are calculated. Design sensitivities are computed using the adjoint approach and verified against finite differences. Compared with a representative implicit scheme, the Newton–Krylov approach allows the flow, adjoint, and sensitivities to be stably computed over a wider operating range, which facilitates whole-map adjoint aerodynamic shape optimization for turbomachinery components.

Aerodynamic shape optimization of an urban maglev train

With rapid development of urban rail transit, maglev trains, benefiting from its comfortable, energy-saving and environmentally friendly merits, have gradually entered people's horizons. In this paper, aiming at improving the aerodynamic performance of an urban maglev train, the aerodynamic optimization design has been performed. An improved two-point infill criterion has been adopted to construct the cross-validated Kriging model. Meanwhile, the multi-objective genetic algorithm and complex three-dimensional geometric parametrization method have been used, to optimize the streamlined head of the train. Several optimal shapes have been obtained. Results reveal that the optimization strategy used in this paper is sufficiently accurate and time-efficient for the optimization of the urban maglev train, and can be applied in practical engineering. Compared to the prototype of the train, optimal shape benefits from higher lift of the leading car and smaller drag of the whole train. Sensitivity analysis reveals that the length and height of the streamlined head have a great influence on the aerodynamic performance of the train, and strong nonlinear relationships exist between these design variables and aerodynamic performance. The conclusions drawn in this study offer the chance to derive critical reference values for the optimization of the aerodynamic characteristics of urban maglev trains.Graphic abstract

Variable-fidelity hypervolume-based expected improvement criteria for multi-objective efficient global optimization of expensive functions

Variable-fidelity surrogate-based efficient global optimization (EGO) method with the ability to adaptively select low-fidelity (LF) and high-fidelity (HF) infill point has emerged as an alternative to further save the computational cost of the single-fidelity EGO method. However, in terms of the variable-fidelity surrogate-assisted multi-objective optimization methods, existing methods rely on empirical parameters or are unable to adaptively select LF/HF sample in the optimal search process. In this paper, two variable-fidelity hypervolume-based expected improvement criteria with analytic expressions for variable-fidelity multi-objective EGO method are proposed. The first criterion relies on the concept of variable-fidelity expected improvement matrix (VFEIM) and is obtained by aggregating the VFEIM using a simplified hypervolume-based aggregation scheme. The second criterion termed as VFEMHVI is derived analytically based on a modified hypervolume definition. Both criteria can adaptively select new LF/HF samples in the iterative optimal search process to update the variable-fidelity models towards the HF Pareto front, distinguishing the proposed methods to the rests in the open literature. The constrained versions of the two criteria are also derived for problems with constraints. The effectiveness and efficiency of the proposed methods are verified and validated over analytic problems and demonstrated by two engineering problems including aerodynamic shape optimizations of the NACA0012 and RAE2822 airfoils. The results show that the VFEMHVI combined with the normalization-based strategy to define the reference point is the most efficient one over the compared methods.

Aerodynamic shape optimization of rectangular and elliptical double-skin façades to mitigate wind-induced effects on tall buildings

Double-skin façades (DSFs) are high-efficiency systems traditionally used to improve the natural ventilation of buildings for energy-saving purposes and their aesthetic improvement. There are opportunities to enhance their functionality by applying them to improve building aerodynamics. This study aims at developing the preliminar data set that would assist with design of smart morphing facades (also known as Smorphacades). For this purpose the a DSF for rectangular and elliptical tall buildings is studied with the final goal of minimizing the aerodynamic loads on such structures. For this purpose, an integrated framework including numerical modeling and statistical analysis was developed. The design of experiment (DOE) method was applied to produce a sufficient dataset based on computational fluid dynamics (CFD) simulation of two-dimensional (2D) scaled models that were validated with available wind tunnel data. According to the data points recommended by the DOE method, a considerable number of CFD simulations were performed, and the drag coefficients of the building and double-skin façade were separately calculated. A prediction model based on the response surface methodology (RSM) was developed to estimate the drag coefficient for other cases inside the design space. Based on the fitted RSM, the Genetic algorithm was applied to search for the optimized Smorphacade shapes. The results indicated that the integrated smorphacade system could significantly mitigate wind-induced drag forces on the building at all attack angles by modifying wind-induced pressure around the building and weakening vortex shedding by interrupting flow separation and ejecting airflow into a lower-pressure area. This research proves that there are opportunitie to integarte the architectural and energy applications of smart double skin facades with wind-reducing effects as a promising solution for overcoming existing challenges for controlling wind-induced load and response of tall buildings.

Imposing C0 and C1 continuity constraints during CAD‐based adjoint optimization

AbstractThis article presents a method for performing adjoint‐based aerodynamic shape optimization by manipulating the standard CAD geometry of the shape to be optimized. A standard CAD file gives access to the boundary representation (BRep) of the shape and consequently its boundary surfaces which are usually trimmed patches. This is a sensible choice as the open format of such files is a requirement for the computation of the shape derivatives. The method addresses the continuity issues that emerge during the update of the shape by imposing up to C1 constraints between different CAD patches. A parameterization scheme based on NURBS surfaces is then defined, in which the aforementioned constraints are inherently satisfied. The proposed method is firstly demonstrated in a simple geometric case and then in the full‐scale optimization of industrial‐like cases such as the S‐section of a cooling duct and the tail surface of a passenger car.

CFD Analysis and Shape Optimization of Airfoils Using Class Shape Transformation and Genetic Algorithm—Part I

This paper presents the parameterization and optimization of two well-known airfoils. The aerodynamic shape optimization investigation includes the subsonic (NREL S-821) and transonic airfoils (RAE-2822). The class shape transformation is employed for parametrization while the genetic algorithm is used for optimization purposes. The absolute scheme of the optimization process is carried out for the minimization of the drag coefficient and maximization of lift to drag ratio. In-house MATLAB code is incorporated with a genetic algorithm to calculate the drag coefficient and lift to drag ratio of the resulting optimized airfoil. The panel method is utilized in genetic algorithm optimization code to calculate pressure distribution, lift coefficient, and lift to drag ratio for optimized airfoil shapes and validates with XFOIL and NREL experimental data. Furthermore, CFD analysis is conducted for both the original (NREL S-821) and optimized airfoil obtained. The present method shows that the optimized airfoil achieved an improvement in lift to drag ratio by 7.4% and 15.9% of S-821 and RAE-2822 airfoil, respectively, by the panel technique method and provides high design desirable stability parameters. These features significantly improve the overall aerodynamic performance of the newly optimized airfoils. Finally, the improved aerodynamics results are reported for the design of turbulence modeling and NREL phase II, Phase III, and Phase VI HAWT blades.