Aerodynamic Shape Optimization Research Articles

Efficient aerodynamic shape optimization through free-form mesh morphing and reduced order CFD modeling

Although computational power is increasingly available, high-fidelity simulation based aerodynamic shape optimization is still challenging for industrial applications. To make the simulation based optimization acceptable in the practice of engineering design, a technique combining mesh morphing and reduced order modeling is proposed for efficient aerodynamic optimization based on CFD simulations. The former technique avoids the time-consuming procedure of geometry discretization. And the latter speeds up the procedure of field solution by combining pre-computed solution snapshots. To test the efficiency of the proposed method, the windshield of a motorbike is analyzed and optimized. It is shown that even the total number of cells of the mesh is around 0.4 million, the CFD computation and the post processing of the results can be completed in less than 10 seconds if the reduced order model is adopted. Running on a personal computer, the generic algorithm is applied to optimize the profile of the windshield. A 8% reduction of the drag coefficient is achieved after 800 queries of the reduced order CFD model and the total CPU time is only around 2 hours.

A robust methodology for the design optimization of diffuser augmented wind turbine shrouds

Shrouded wind turbines represent an attractive solution of high potential that could improve significantly the feasibility of renewable energy production at sites characterized by poor wind resources. This work presents the development of a modular optimization scheme for the aerodynamic shape optimization of diffuser-augmented wind turbine (DAWT) shrouds. For the numerical simulation of the incompressible flow field, an axisymmetric RANS solver has been implemented, based on the artificial compressibility method and SST turbulence model. The major features of the RANS solver are demonstrated, while its validity is assessed against both numerical and experimental data. Mesh and geometry parameterization are simultaneously succeeded by employing an in-house developed computational tool, based on the well-known Free-Form Deformation (FFD) technique. The backbone of the optimization framework is formed by a parallel and asynchronous Differential Evolution (DE) algorithm, which is assisted by Artificial Neural Network (ANN) meta-models. The proposed methodology is applied to the design optimization of an axisymmetric shroud (diffuser) for a 15 kW wind turbine, aiming to maximize the mean velocity speed-up ratio and minimize drag, under geometrical constrains. The resulting designs are capable of providing high velocity accelerations, accompanied by considerable reduction in drag and volume.

Aerodynamic shape optimization of barriers for windblown sand mitigation using CFD analysis

Protection from windblown sand is one of the key engineering issues for construction and maintenance of human infrastructures in arid environments. In the last decades, a number of barrier-type Sand Mitigation Measures with different shapes have been proposed in order to overcome this problem. Sand barriers are often deployed alongside long line-like infrastructures crossing vast desert regions. It follows that highly optimized preliminary design of the barrier cross section is of paramount importance in the perspective of a large-scale production, in order to minimize the construction costs per unit length, and maximize the aerodynamic performances. The present computational study aims to adapt and apply aerodynamic optimization to a windblown sand barrier. The search for the optimum is carried out on Computational Fluid Dynamics simulations, without recourse to surrogate models. Both gradient-based method and genetic algorithm are used, in the light of the features of the goal function previously sampled by extensive sensitivity studies. The approach is applied to two constructive forms of the same barrier having increasing complexity. Results are critically discussed by combining complementary remarks on the optimization convergence, the phenomenological reading of the flow around the optimized barrier, and its design and construction.

Aerodynamic design of integrated propulsion–airframe configuration of a hybrid wing body aircraft

A hybrid wing body (HWB) concept is being considered by NASA as a potential subsonic transport aircraft that meets aerodynamic, fuel, emission, and noise goals in the time frame beyond 2035. While the concept promises advantages over a conventional wing-and-tube aircraft, it poses unknowns and risks, thus requiring in-depth and broad assessments. Specifically, the configuration entails a tight integration of the airframe and propulsion geometries; the aerodynamic impact has to be carefully evaluated. With the propulsion nacelle installed on the (upper) body, the lift and drag are affected by the mutual interference effects between the airframe and nacelle. The static margin for longitudinal stability is also adversely changed. In the present paper, a design approach is developed in which the integrated geometries of airframe (HWB) and propulsion are accounted for simultaneously in a simple algebraic manner, via parameterization of the planform and airfoils at the design sections of the wing body. This paper presents a design of a 300-passenger aircraft that employs distributed electric fans for the propulsion. The trim condition for stability is achieved through the use of the wing tip twist angle. The geometric shape variables are determined through the adjoint optimization method by minimizing the drag while subjecting them to lift, pitching moment, and geometry constraints. An Euler model-based aerodynamic shape optimization is employed to save the design cost for the evaluation of the static margin and longitudinal stability, while the performance of the optimized configuration is evaluated by the RANS model coupled with a drag decomposition method to assess the true aerodynamic performance. The design results clearly show the influence on the aerodynamic characteristics of the installed nacelle and trimming for stability. A drag minimization with the trim constraint yields a reduction of 10 counts in the drag coefficient from the baseline design N3-X configuration, which is comparable with 2000 lbs more payload on a conventional subsonic civil transport airplane.

Study on Optimization of Drag Characteristics of Large Civil Airliners

In order to reduce the drag of large civil airliners and improve the economy of their operation, this paper chooses the shape of a typical large civil airliner as the research object, analyses the causes and classifications of the drag of large civil airliners, and puts forward the drag reduction measures for different sources of drag by means of numerical simulation. The results show that the frictional drag can be reduced by installing vortex generator on the rear body of the fuselage, the form drag can be significantly reduced by installing the after body end plate, improving high angle of Attack Performance and the induced drag can be further reduced by using the vertical section add to the lateral section of the winglets. The results can lay a theoretical foundation for aerodynamic shape design and optimization of large civil airliners.

Hybrid inverse/optimization design method for rigid coaxial rotor airfoils considering reverse flow

Double-ended airfoils with round leading and trailing edges outperform conventional round-nose and sharp trailing-edge airfoils when used for the inboard part of a rigid coaxial rotor operating in forward flight, as reverse flow can occupy 80% surface of the retreating blade. However, aerodynamic design optimization for this kind of airfoils is challenging, since it is required to achieve drag reduction over a wider lift range in both forward and reverse flows but there is no method available currently. To address this problem, this article proposes an efficient hybrid inverse/optimization design method that combines inverse design and direct optimization within a surrogate-based optimization (SBO) framework. The weighted objective function consists of two components: prescribed pressure distributions and total drag. The resulting constrained optimization problem is solved by using kriging surrogate model and dedicated infill-sampling method. The proposed method is demonstrated by aerodynamic shape optimizations of a DBLN-526 airfoil and an elliptical airfoil and compared with direct optimization method. For DBLN-526 airfoil case, 7%–30% drag reduction is achieved in the range from zero lift to maximum lift and the optimum airfoil features better stall characteristics. For the case of elliptical airfoil of 40% thickness, significant drag reduction is achieved in both forward and reverse flows and the optimum airfoil features more robust aerodynamic performance at off-design Mach numbers. The results confirm that the proposed method outperforms the conventional direct optimization method and more practical for aerodynamic shape optimization of double-ended airfoils.

RBF-based morphing of B-Rep models for use in aerodynamic shape optimization

This paper presents a shape parameterization method based on morphing that acts directly on CAD-compatible Boundary-Representations (B-Rep), effectively integrated into aerodynamic shape optimization. The proposed technique requires the definition of a small number of ”handles”, which are strategically placed around or on the B-Rep shapes to be optimized. Displacement vectors associated with these handles are used as design variables in the optimization method. Using Radial Basis Functions (RBF) as an interpolation method, these displacements are transferred from the handles to the Non-Uniform Rational Basis-Splines (NURBS) control points of the B-Rep model; this approach offers the advantage that the updated surface remains in CAD format and is thus exportable to a STEP file. The proposed method combines two successive deformation steps. Each deformation is controlled by an independent set of handles, increasing the flexibility of the morphing action. A strategy for updating the CFD surface grid to the already changed B-Rep models enables the seamless inclusion of the proposed method into any optimization loop, avoiding any into-the-loop dependence on grid generation packages. The surface grid is updated by computing new nodal coordinates based on the updated NURBS parametric coordinates; these are computed according to changes in the parametric domain of trimmed surfaces by an RBF-based interpolation. The displacement of the surface nodes is then used to displace the CFD volume grid. The tool is differentiated and integrated into gradient-based optimization loops using the adjoint method to compute the gradient of the objective and constraint functions with respect to the surface nodal positions. The performance of the proposed method is assessed in four aerodynamic shape optimization problems, concerning a 2D airfoil, a duct, an aircraft model and a compressor stationary blading. An assessment of the proposed method based on parametric effectiveness, in the 2D case, is also presented.

RBF-based morphing of B-Rep models for use in aerodynamic shape optimization

RBF-based morphing of B-Rep models for use in aerodynamic shape optimization

Performance improvement of horizontal axis wind turbines by aerodynamic shape optimization including aeroealstic deformation

Aerodynamic shape optimization of horizontal axis wind turbines was performed to minimize the cost of energy. The optimum blade was obtained by modifying the blade section contours at selected blade radial stations. For the optimization, the design variables were defined as the coordinates of the blade section contours perpendicular to the chord. An aerodynamic performance database was constructed for those blade configurations defined by random combinations of design variables selected within a given range by Latin-Hypercube sampling. An artificial neural network was applied to derive the approximate functions between the design variables and the aerodynamic performance of the database. By utilizing the approximate functions, a genetic algorithm was adopted to search for an optimized blade. To construct the database, a CFD flow solver based on unstructured meshes was utilized. To consider the effects of aeroelastic deformation of the structurally flexible blades, a coupled CFD-CSD method was also adopted. The applications were made for the NREL phase VI and NREL 5 MW reference wind turbine rotor blades. After optimization, the cost of energy was reduced by 0.82% for the NREL phase VI rotor blade and one percent for the NREL 5 MW reference wind turbine blade, respectively.

Gradient-based Pareto front approximation applied to turbomachinery shape optimization

Multi-objective optimization has been rising in popularity, especially within an industrial environment, where several cost functions often need to be considered during the design phase. Traditional gradient-free approaches, such as evolutionary algorithms, can be employed to compute a front of equally suitable solutions a designer can choose from, with a high computational cost though, particularly in high-dimensional design spaces. In this paper, a gradient-based algorithm is developed for efficiently tracing the Pareto front in bi-objective aerodynamic shape optimization problems, where an adjoint method is used for the computation of the objective functions’ gradients with respect to the design variables. After obtaining a starting point on the front, a prediction–correction approach is employed to compute new Pareto points. Satisfying the Karush–Kuhn–Tucker conditions provides a prediction for the next point, which is, then, corrected by solving a minimum distance problem. The prediction step, though, requires the costly computation of the Hessian matrix. This is avoided here using the BFGS (Nocedal and Wright in Numerical optimization, Springer, New York, 2006) technique. The proposed method is first demonstrated in a less expensive lift/drag optimization of an isolated airfoil and then applied to the bi-objective optimization of a 3D compressor stator. The extension of the proposed method to cases with more than two objectives is straightforward, on condition that an algorithm is found to coordinate the way the Pareto front is swept.

Surrogate-based aerodynamic shape optimization of hypersonic flows considering transonic performance

Aerodynamic shape optimization of a hypersonic transport aircraft over a wide Mach-number range is challenging. The difficulty is not only associated with the large computational cost of high-fidelity CFD (computational fluid dynamics) simulations but also linked to the reasonable compromise between aerodynamic performances of aircraft at different speed ranges. This article proposes to use efficient global optimization based on surrogate models to address this type of problems. A RANS (Reynolds averaged Navier-Stokes) flow solver is adopted to evaluate objective and constraint functions; Kriging surrogate model combined with a parallel infill-sampling method and a multi-round strategy are employed to find the global optimum. First, a profile optimization with baseline airfoil of NACA64A-204 is conducted to achieve high lift-to-drag ratio (L/D) at both hypersonic (Ma=6.0) and transonic (Ma=0.8) regimes with up to 18 design variables, and significant improvement has been observed. Then, multi-objective wing optimizations of maximizing both hypersonic and transonic L/Ds with up to 54 design variables are performed and multiple optimizations with various sets of weight coefficients are investigated. The optimized wings are further evaluated and compared with the baseline wing at the flow regimes from subsonic to hypersonic speeds. Results show that by using the optimized profile, hypersonic and transonic L/Ds of a typical wing configuration are increased by 13.85% and 7.32%, respectively. After 3-D optimizations, the L/Ds at hypersonic and transonic design points are further improved by 4.47% and 3.19%, respectively, and a better performance over a wide Mach-number range is obtained. It is shown that a multi-round surrogated-based optimization is feasible and effective for aerodynamic shape optimization of hypersonic transport aircrafts over a wide Mach-number range.

Study on aerodynamic shape optimization of tall buildings using architectural modifications in order to reduce wake region

One of the most important factors in tall buildings design in urban spaces is wind. The present study aims to investigate the aerodynamic behavior in the square and triangular footprint forms through aerodynamic modifications including rounded corners, chamfered corners and recessed corners in order to reduce the length of tall buildings wake region. The method used was similar to wind tunnel numerical simulation conducted on 16 building models through Autodesk Flow Design 2014 software. The findings revealed that in order to design tall 50 story buildings with a height of about 150 meters, the model in triangular footprint with aerodynamic modification of chamfered corner facing wind direction came out to have the best aerodynamic behavior comparing the other models. In comparison to the related reference model (i.e., the triangular footprint with sharp corners and no aerodynamic modification), it could reduce the length of the wake region about 50% in general. Also, the model with square footprint and aerodynamic modification of chamfered corner with the corner facing the wind could present favorable aerodynamic behavior comparing the other models of the same cluster. In comparison to the related reference model (i.e., the square footprint with sharp corners and no aerodynamic modification), it could decrease the wake region up to 30% lengthwise.

Rotor blade aerodynamic shape optimization based on high-efficient optimization method

In order to design a high-performance rotor, a high-efficient optimization method is established by coupling Kriging model and sequential quadratic programming with high-accuracy computational fluid dynamics method. In order to obtain the global optimal design point, the initial blade shape is optimized by using the Kriging model coupled with genetic algorithm based on the baseline rotor blade (Helishape 7A rotor). After that, the modified sequential quadratic programming method is employed to search the final blade shape based on the initial blade shape deeply. In the optimal process, the regions of design variables are restricted considering rotor dynamic characteristics. As a result, a new shape of rotor blade with characters of nonlinear twist, variational chord length, complex swept, and anhedral distributions is obtained. Compared with the baseline rotor, blade-tip vortex of the final optimized rotor is significantly weakened, the figure of merit of the final optimized rotor increases about 3.42%, and the peak of sound pressure decreases about 16.9%. At the same time, it is demonstrated that the final optimized rotor has better forward flight characteristics.

Conceptual Aerodynamic Design of Pintle Nozzle for Variable-Thrust Propulsion

Comprehensive theoretical studies have been carried out for the geometry optimization of a pintle nozzle for variable-thrust propulsion. We designed the pintle such that, at the final pintle position, the integrated shape facilitates the scaled-down version of the shockless main nozzle. Numerical studies have been carried out using a validated two-dimensional transient, an implicit Reynolds-averaged Navier–Stokes equations (RANS) solver with a k–ω Menter’s shear stress transport (SST) turbulence model. At the quasi-steady and dynamic conditions, the numerical results have shown excellent agreement with the theoretical results. In the dynamic condition, the effects of shock train, shock impinging, and the shock location on the overall thrust are studied, and we observed a monotonic increase in thrust during the pintle movement toward the exit and achieved the maximum thrust at the highest area ratio (nozzle exit area to throat area) position. The diminishing of the shock–strength pattern and the movement of the shock-impinging point towards the nozzle exit are captured in the numerical simulation and reported herein. We concluded that the prudent aerodynamic shape optimization of the external surface contour of the pintle and the inner surface contour of its associated nozzle ensures improved performance for the variable-thrust propulsion of aerospace vehicles.

GCRO with dynamic deflated restarting for solving adjoint systems of equations for aerodynamic shape optimization

Purpose This paper aims to present a dynamically adjusted deflated restarting procedure for the generalized conjugate residual method with an inner orthogonalization (GCRO) method. Design/methodology/approach The proposed method uses a GCR solver for the outer iteration and the generalized minimal residual (GMRES) with deflated restarting in the inner iteration. Approximate eigenpairs are evaluated at the end of each inner GMRES restart cycle. The approach determines the number of vectors to be deflated from the spectrum based on the number of negative Ritz values, k∗. Findings The authors show that the approach restores convergence to cases where GMRES with restart failed and compare the approach against standard GMRES with restarts and deflated restarting. Efficiency is demonstrated for a 2D NACA 0012 airfoil and a 3D common research model wing. In addition, numerical experiments confirm the scalability of the solver. Originality/value This paper proposes an extension of dynamic deflated restarting into the traditional GCRO method to improve convergence performance with a significant reduction in the memory usage. The novel deflation strategy involves selecting the number of deflated vectors per restart cycle based on the number of negative harmonic Ritz eigenpairs and defaulting to standard restarted GMRES within the inner loop if none, and restricts the deflated vectors to the smallest eigenvalues present in the modified Hessenberg matrix.

Turbocharger Axial Turbines for High Transient Response, Part 2: Genetic Algorithm Development for Axial Turbine Optimisation

In a previous paper [1], a preliminary design methodology was proposed for the design of an axial turbine, replacing a conventional radial turbine used in automotive turbochargers, to achieve improved transient response, due to the intrinsically lower moment of inertia. In this second part of the work, the focus is on the optimisation of this preliminary design to improve on the axial turbine efficiency using a genetic algorithm in order to make the axial turbine a more viable proposition for turbocharger turbine application. The implementation of multidisciplinary design optimisation is essential to the aerodynamic shape optimisation of turbocharger turbines, as changes in blade geometry lead to variations in both structural and aerodynamics performance. Due to the necessity to have multiple design objectives and a significant number of variables, genetic algorithms seem to offer significant advantages. However, large generation sizes and simulation run times could result in extensively long periods of time for the optimisation to be completed. This paper proposes a dimensioning of a multi-objective genetic algorithm, to improve on a preliminary blade design in a reasonable amount of time. The results achieved a significant improvement on safety factor of both blades whilst increasing the overall efficiency by 2.55%. This was achieved by testing a total of 399 configurations in just over 4 h using a cluster network, which equated to 2.73 days using a single computer.

Single/two-objective aerodynamic shape optimization by a Stackelberg/adjoint method

ABSTRACTIn this article, the Stackelberg game strategy is coupled with the adjoint method and applied in single-objective and two-objective aerodynamic shape optimizations. In the proposed method, two types of player (leader and follower) are involved, and each of these players is responsible for the optimization of one objective function by adjusting a subset of design variables. A Stackelberg equilibrium is reached when the leader cannot improve his/her objective function further. Note that the success of the proposed method is highly dependent on the choice of a few influential factors, including the maximal number of iterations for each player, the splitting and mapping schemes of design variables, and the allocation strategies of objective functions to different players. Therefore, the impacts of these factors are firstly assessed by a two-objective optimization case of the NACA0012 airfoil, and some useful inferences are produced for the choice of these factors. After that, single-objective and two-objective aerodynamic optimizations of the RAE2822 airfoil and the ONERA M6 wing are conducted to verify the usefulness of these inferences, and to validate the efficiency and effectiveness of the proposed method in optimization problems with a complex numerical model or a large number of design variables.

Data-driven constraint approach to ensure low-speed performance in transonic aerodynamic shape optimization

Aerodynamic shape optimization based on computational fluid dynamics has the potential to become more widely used in the industry; however, the optimized shapes are often criticized for not being practical. Techniques seeking more practical results, such as multipoint optimization and geometric constraints, are either ineffective or too time consuming because they require trial and error. We propose a data-driven constraint for the aerodynamic shape optimization of aircraft wings that ensures the overall practicality of the optimum shape, with a focus on achieving a good low-speed performance. The constraint is formulated by extracting the relevant features from an airfoil database via modal analysis, correlation analysis, and Gaussian mixture models. The optimization results demonstrated that this approach addresses the thin leading edge issue that had plagued previous optimization results, and further analysis demonstrated that this data-driven constraint ensures good low-speed off-design performance without sacrificing the transonic on-design performance. The proposed approach can use other airfoil databases and can even be generalized to other shape optimization and engineering design problems.

Efficient aerodynamic shape optimization using variable-fidelity surrogate models and multilevel computational grids

A variable-fidelity method can remarkably improve the efficiency of a design optimization based on a high-fidelity and expensive numerical simulation, with assistance of lower-fidelity and cheaper simulation(s). However, most existing works only incorporate “two” levels of fidelity, and thus efficiency improvement is very limited. In order to reduce the number of high-fidelity simulations as many as possible, there is a strong need to extend it to three or more fidelities. This article proposes a novel variable-fidelity optimization approach with application to aerodynamic design. Its key ingredient is the theory and algorithm of a Multi-level Hierarchical Kriging (MHK), which is referred to as a surrogate model that can incorporate simulation data with arbitrary levels of fidelity. The high-fidelity model is defined as a CFD simulation using a fine grid and the lower-fidelity models are defined as the same CFD model but with coarser grids, which are determined through a grid convergence study. First, sampling shapes are selected for each level of fidelity via technique of Design of Experiments (DoE). Then, CFD simulations are conducted and the output data of varying fidelity is used to build initial MHK models for objective (e.g. CD) and constraint (e.g. CL, Cm) functions. Next, new samples are selected through infill-sampling criteria and the surrogate models are repetitively updated until a global optimum is found. The proposed method is validated by analytical test cases and applied to aerodynamic shape optimization of a NACA0012 airfoil and an ONERA M6 wing in transonic flows. The results confirm that the proposed method can significantly improve the optimization efficiency and apparently outperforms the existing single-fidelity or two-level-fidelity method.

Morphing control of a new bionic morphing UAV with deep reinforcement learning

With rapid development of aviation technology, materials science and artificial intelligence, aircraft design is pursuing higher requirements both in civil and military fields. The new generation of aircraft should have the autonomous capable of performing a variety of tasks (such as take-off and landing, cruising, maneuvering, hover, attack, etc.) under a highly variable flight environment (height, Mach number, etc.) and meanwhile maintaining good performance. Morphing aircraft can use smart materials and actuators to autonomously deform the shape according to the changes in flight environment and mission, and always maintain an optimal aerodynamic shape, therefore get flourished developments. Based on the ability of birds to stretch wings when flying at low speed and to constrict wings at high speed, a new bionic morphing UAV has been designed and developed as the study model by our team. In order to make this new aircraft be able to complete rapid autonomous morphing and aerodynamic performance optimization under different missions and flight conditions, we developed deep neural networks and reinforcement learning techniques as a control strategy. Considering the continuity of the state and action spaces for model, the Deep Deterministic Policy Gradient (DDPG) algorithm based on the actor-critic, model-free algorithm was adopted and verified on the classic nonlinear Pendulum model and Cart Pole game. After the feasibility was verified, morphing aircraft model was controlled to complete prescribed deformation using DDPG algorithm. Furthermore, on the condition that the DDPG algorithm can control morphing well, through training and testing on model using simulation data from wind tunnel tests and actual flight, the autonomous morphing control for the shape optimization of the bionic morphing UAV model could be realized.