Airfoil optimization using Design-by-Morphing with minimized design-space dimensionality

Manifold-guided multi-objective gradient algorithm combined with adjoint method for supersonic aircraft shape design

The Class-Shape function Transformation (CST) method is used to describe the parameterized airfoil geometry. The parameterized models for aerodynamic and stealthy performance of airfoil are constructed. The aerodynamic analysis model of airfoil is constructed by Computational Fluid Dynamics (CFD) method based on N-S equations. And the stealthy performance analysis model of airfoil is constructed by Computational Electromagnetic Method (CEM) based Method of Moments (MoM). The multi-objective aerodynamic and stealthy performance optimization method for airfoil using Kriging surrogate model is presented in this paper. The Latin hypercube method is employed to get a set of sample points. The aerodynamic and stealthy performance Kriging models are built. The multi-objective aerodynamic and stealthy performance optimization of airfoil is optimized by combining Pareto genetic algorithm with Kriging surrogate model. The presented method is validated by two applications. The results of the investigation show that the constructed analysis models are reasonable and the presented multi-objective optimization design method is feasible, which can improve the performance of airfoil and the efficiency of optimization effectively.

In this work, a multiobjective aerodynamic optimization of a high-speed train head was performed to improve the aerodynamic performance of the high-speed train running on an embankment under crosswinds. Seven optimization design variables were selected to control five regions on the train head. The total aerodynamic drag force, aerodynamic lift force, and aerodynamic side force of the head coach were set as the optimization objectives. The optimal Latin hypercube sampling method was used to obtain the values of the design variables of the sample points. The high-speed train head was deformed using the free-form deformation approach through which the mesh morphing was performed without remodeling and re-meshing. Then, the aerodynamic performances of the high-speed trains at the sample points were calculated using the computational fluid dynamics method. A Kriging surrogate model between the design variables and their optimization objectives was constructed. Then, the multiobjective aerodynamic optimization of the high-speed train head was performed using multiobjective genetic algorithms based on the Kriging model. Based on the results of the sample points, the relationships between the optimization design variables and the optimization objectives were analyzed, and the contributions of the primary factors to the optimization objectives were obtained. After optimization, a series of Pareto-optimal head shapes were obtained. The steady and unsteady aerodynamic performances of the train with an optimal head, which was selected from the Pareto-optimal head shapes, were compared with those of the original train.

A variable fidelity concept is introduced in a re-parameterization approach based on the proper orthogonal decomposition (POD) to efficiently solve multi-objective aerodynamic shape optimization problems. The re-parameterization approach enables to extract dominant shape deformation modes from a database of good designs and to reduce the number of design variables. The present variable fidelity approach is proposed by utilizing low-fidelity functional evaluations to select the good designs. The proposed approach is investigated in two multi-objective aerodynamic shape optimization problems of 2D airfoil in which the combinations of viscous/inviscid simulations or fine/coarse grid simulations are treated as the high/low-fidelity evaluation methods. It can be confirmed that dominant POD modes obtained from low-fidelity evaluations are qualitatively equivalent with that obtained from high-fidelity evaluations. Non-dominated solutions obtained from a conventional optimization approach can be reproduced with smaller numbers of design variables using the dominant POD modes. The computational costs to solve the multi-objective aerodynamic shape optimization problems can be dramatically reduced by introducing the variable fidelity concept.

Multi-objective aerodynamic optimization of expansion–deflection nozzle based on B-spline curves

Solving Stackelberg equilibrium for multi objective aerodynamic shape optimization

The present work is aiming at aerodynamic multi-point, inverse, optimization of airfoils as well as at aeroelastic, multi-disciplinary, optimization of the exposed X31 delta wing. Results are achieved by means of a multi-objective genetic algorithm (GA) utilizing a GUI-supported software being developed in the European-Union funded “FRONTIER” project.

Constraints handling in Nash/Adjoint optimization methods for multi-objective aerodynamic design

This study demonstrates the application of the discrete adjoint method for aerodynamic shape optimization of the NACA2412 airfoil used in Cessna 172R at moderate Reynolds numbers and low Mach numbers . The open-source CFD solver OpenFOAM is coupled with DAFoam-discrete adjoint with OpenFOAM to efficiently compute the sensitivities of the drag coefficient concerning shape design variables. The SST (Shear Stress Transport) turbulence model is employed for its superior performance in predicting flow separation over airfoils. The airfoil geometry is parameterized using B-spline curves with control points as design variables. A discrete adjoint method for a multidisciplinary optimization algorithm minimizes the drag coefficient subject to lift constraints by automatically adjusting the control point positions. The optimized airfoil exhibits significantly reduced drag compared to the baseline NACA2412. Optimizing the airfoil shape reduced drag coefficient by , increased lift coefficients, and increased lift-todrag ratios at different angles of attack over the original design.

This work performs a multi-objective aerodynamic optimization for a high-vacuum centrifugal vacuum pump. The hub and shroud profiles of the impeller were chosen as the geometrical factors for the optimization and were parameterized using the Bezier curves. The total pressure ratio (πtt) and polytropic efficiency (η) were set as the optimization objectives. The sample models were generated using the Reynolds-averaged Navier–Stokes simulations based on the Latin hypercubic sampling method. The backpropagation neural network was employed as the surrogate model, and the multi-objective optimization was performed using the non-dominated sorting genetic algorithm. The Pareto front of the optimization was obtained, and two optimized models, named OPT1 and OPT2, were selected for the simulation and analysis of the internal flow. The numerical results reveal that compared with the baseline model, the two optimized models improve πtt by 1.009% and 1.863%, respectively, and the absolute magnitude of η by 1.206% and 1.019%, respectively. The analysis of the internal flow of the baseline and optimized centrifugal vacuum pumps demonstrates that the optimized hub and shroud produce a comparably better uniform flow in the impeller, with remarkably reduced separation and reduced Mach number. The significant static entropy and entropy generation formed near the shroud are substantially weakened in magnitude and size. The flow in the radial vaneless region of the optimized models presents uniform distributions of flow angle and Mach number over the whole circumference. The reduced energy loss and uniform flow field contribute to the improved performance of the centrifugal vacuum pump.

A comparative study of multi-objective expected improvement for aerodynamic design

This text describes methods to organize a large set of optimized airfoils in a relational database and its application in throughflow design. Optimized airfoils are structured in five dimensions: inlet Mach number, blade stagger angle, pitch-chord ratio, maximum thickness-chord ratio and a parameter for aerodynamic loading. In this space, a high number of airfoil geometries is generated by means of numerical optimization. Each airfoil geometry is tailored to its specific requirements and optimized for a wide working range as well as low losses. During the optimization of each airfoil, performance in design and off-design conditions is evaluated with the blade-to-blade flow solver MISES. Together with airfoil geometry, the database stores automatically calibrated correlations which describe cascade performance in throughflow calculation. Based on these methods, two subsonic stages of a 4.5-stage transonic research compressor are redesigned. Performance of baseline and updated geometries is evaluated with 3D CFD. The overall approach offers accurate throughflow design incorporating optimized airfoil shapes and a fast transition from throughflow to 3D CFD design.

Aiming at shortening the design period and improve the design efficiency of the nose shape of high speed trains, a parametric shape optimization method is developed for the design of the nose shape has been proposed in the present paper based on the VMF parametric approach, NURBS curves and discrete control point method. 33 design variables have been utilized to control the nose shape, and totally different shapes could be obtained by varying the values of design variables. Based on the above parametric method, multi-objective particle swarm algorithm, CFD numerical simulation and supported vector machine regression model, multi-objective aerodynamic shape optimization has been performed. Results reveal that the parametric shape design method proposed here could precisely describe the three-dimensional nose shape of high speed trains and could be applied to the concept design and optimization of the nose shape. Besides, the SVM regression model based the multi-points criterion could accurately describe the non-linear relationship between the design variables and objectives, and could be generally utilized in other fields. No matter the simplified model or the real model, the aerodynamic performance of the model after optimization has been greatly improved. Based on the SVR model, the nonlinear relation between the aerodynamic drag and the design variables is obtained, which could provide guidance for the engineering design and optimization.

Uncertainties in design variables and problem parameters are often inevitable in multi-objective optimizations, and they must be considered in an optimization task if reliable Pareto optimal solutions are to be sought. Multi-objective reliability-based design optimization has been raised as a question in design for reliability, but the disadvantages of fixed evolutionary parameters, nonuniformly distributed Pareto optimal solutions and high computational cost hinder engineering applications of reliability-based design. To deal with it, this work proposes an integrated multi-objective cultural-based particle swarm algorithm to solve the double-loop reliability-based design optimization. In the inner optimization loop, the cultural space is composed of the elitism, situational and normative knowledge to adjust the parameters for swarm space, and the crowding distance ranking is introduced to update the global and local optimum and control the maximum number of solutions in elitism knowledge. The hybrid mean value method is improved to perform reliability analysis in the outer loop to suit both concave and convex types of performance functions. In addition, the car side-impact and the injection molding machine are chosen as multi-objective reliability design examples to demonstrate the effectiveness of the proposed approach. Simultaneously, results of car side-impact problem are compared with two traditional multi-objective reliability optimization algorithms, i.e., nondominated sorting genetic algorithm and crowding distance ranking-based multi-objective particle swarm optimizer, to assess the efficiency of the proposed approach. The results denote the proposed cultural-based multi-objective particle swarm optimizer is effective and feasible to solve the reliability-based design optimization problems.

In this paper, we propose the concept of the flexibility of design variables to Pareto-optimal solutions in multi-objective optimization problems. In addition, we introduce a method for measurement of the flexibility of design variables to Pareto-optimal solutions. Increases in the number of design variables usually result in a wide variety of optimum solutions. However, when the flexibilities of some design variables are small, the contributions of these design variables are also very small. This means that the same Pareto-optimal solutions can be derived without these parameters. Therefore, it is very important to find the flexibility of the design variables to the Pareto-optimal solutions. To find the flexibility, the values of one of the design variables are changed, while those of the remaining parameters are fixed. In this procedure, it is very important to determine the fixed values. We describe these procedures to determine the flexibility of the design variable to the Pareto-optimal solutions. Finally, we illustrate using the diesel engine fuel emission scheduling problem that the Pareto- optimal solutions can be derived with only the design variables whose flexibilities are high.