Mauro Minervino, Pier Luigi Vitagliano and Domenico Quagliarella
The paper aims to reduce the aerodynamic drag of a rotorcraft stabilizer in forward flight by taking into account downwash effects from the main rotor wake (power-on conditions).
Abstract
Purpose
The paper aims to reduce the aerodynamic drag of a rotorcraft stabilizer in forward flight by taking into account downwash effects from the main rotor wake (power-on conditions).
Design/methodology/approach
A shape design methodology based on numerical optimization, CAD-in-the-loop (CAD: computer-aided design) approach and high-fidelity Computational Fluid Dynamics (CFD) tools was set-up and applied to modify the horizontal empennage of a rotorcraft configuration. This included the integration of both commercial and in-house computer-aided engineering tools for parametric geometry handling, adaptive mesh generation, CFD solution and evolutionary optimization within a robust evaluation chain for the aerodynamic simulation of the different design candidates generated during the automatic design loop. Geometrical modifications addressed both the stabilizer planform and sections, together with its setting angle in cruise configuration, accounting for impacts on the equilibrium, stability and control characteristics of the empennage.
Findings
An overall improvement of 11.1 per cent over the rotorcraft drag was estimated at the design condition (cruise flight; power-on) for the stabilizer configuration with optimized planform shape, which is increased to 11.4 per cent when combined with the redesigned airfoil to generate the stabilizer surface.
Research limitations/implications
Critical design considerations are introduced with regard to structural and systems integration issues, and a design candidate alternative is identified and proposed as a compromise solution, achieving 8.3 per cent reduction of the rotorcraft configuration drag in cruise conditions with limited increase in the empennage aspect ratio and leading edge sweep angle when compared to the pure aerodynamic optimal design obtained from genetic algorithm evolution.
Originality/value
The proposed methodology faces the empennage design problem by explicitly taking into account the effects of main rotor wake impinging the stabilizer surface in forward flight conditions and using an automated optimization approach which directly incorporates professional CAD tools in the design loop.
Details
Keywords
Massimiliano Vasile, Edmondo Minisci and Domenico Quagliarella
Luciano Andrea Catalano, Domenico Quagliarella and Pier Luigi Vitagliano
The purpose of this paper is to propose an accurate and efficient technique for computing flow sensitivities by finite differences of perturbed flow fields. It relies on computing…
Abstract
Purpose
The purpose of this paper is to propose an accurate and efficient technique for computing flow sensitivities by finite differences of perturbed flow fields. It relies on computing the perturbed flows on coarser grid levels only: to achieve the same fine-grid accuracy, the approximate value of the relative local truncation error between coarser and finest grids unperturbed flow fields, provided by a standard multigrid method, is added to the coarse grid equations. The gradient computation is introduced in a hybrid genetic algorithm (HGA) that takes advantage of the presented method to accelerate the gradient-based search. An application to a classical transonic airfoil design is reported.
Design/methodology/approach
Genetic optimization algorithm hybridized with classical gradient-based search techniques; usage of fast and accurate gradient computation technique.
Findings
The new variant of the prolongation operator with weighting terms based on the volume of grid cells improves the accuracy of the MAFD method for turbulent viscous flows. The hybrid GA is capable to efficiently handle and compensate for the error that, although very limited, is present in the multigrid-aided finite-difference (MAFD) gradient evaluation method.
Research limitations/implications
The proposed new variants of HGA, while outperforming the simple genetic algorithm, still require tuning and validation to further improve performance.
Practical implications
Significant speedup of CFD-based optimization loops.
Originality/value
Introduction of new multigrid prolongation operator that improves the accuracy of MAFD method for turbulent viscous flows. First application of MAFD evaluation of flow sensitivities within a hybrid optimization framework.
Details
Keywords
Frédéric Moens and Christelle Wervaecke
Today, the design process of high‐lift configurations in industry mainly relies on experts' knowledge, and lacks a simple exploration of the design space. Therefore, the…
Abstract
Purpose
Today, the design process of high‐lift configurations in industry mainly relies on experts' knowledge, and lacks a simple exploration of the design space. Therefore, the introduction of high‐fidelity tools in an optimization chain is now envisaged. The purpose of this paper is to define and solve a realistic high‐lift design problem by the use of a constrained evolutionary algorithm, coupled to a Navier‐Stokes (RANS) solver. The complete optimization (shape and settings) of a 3‐element configuration has been carried out for landing and take‐off configurations using a sequential approach.
Design/methodology/approach
In a first step, the elements' shapes and settings of the landing configuration have been optimized simultaneously. Then, shapes have been frozen and settings have been optimized for take‐off conditions. The flow evaluation during the optimization process is made through 2.5D Navier‐Stokes computations on chimera grids. The optimization technique used is an evolutionary algorithm, with a dynamic adaptation of the covariance matrix (CMA‐ES). Geometric and aerodynamic constraints have been considered through a dynamic penalization technique of the cost function.
Findings
Solutions obtained have been analyzed and compared to the reference initial configuration. In term of cost functions improvement, 5.71 per cent drag reduction has been obtained for landing, and 2.89 per cent improvement on climb index at take‐off.
Practical implications
Compared to the global optimization process, the use of a sequential approach can be quite efficient.
Originality/value
This paper presents a first step for the introduction of recent advanced methods into a design process of high‐lift configurations in an industrial environment.
Details
Keywords
Giovanni Petrone, John Axerio-Cilies, Domenico Quagliarella and Gianluca Iaccarino
A probabilistic non-dominated sorting genetic algorithm (P-NSGA) for multi-objective optimization under uncertainty is presented. The purpose of this algorithm is to create a…
Abstract
Purpose
A probabilistic non-dominated sorting genetic algorithm (P-NSGA) for multi-objective optimization under uncertainty is presented. The purpose of this algorithm is to create a tight coupling between the optimization and uncertainty procedures, use all of the possible probabilistic information to drive the optimizer, and leverage high-performance parallel computing.
Design/methodology/approach
This algorithm is a generalization of a classical genetic algorithm for multi-objective optimization (NSGA-II) by Deb et al. The proposed algorithm relies on the use of all possible information in the probabilistic domain summarized by the cumulative distribution functions (CDFs) of the objective functions. Several analytic test functions are used to benchmark this algorithm, but only the results of the Fonseca-Fleming test function are shown. An industrial application is presented to show that P-NSGA can be used for multi-objective shape optimization of a Formula 1 tire brake duct, taking into account the geometrical uncertainties associated with the rotating rubber tire and uncertain inflow conditions.
Findings
This algorithm is shown to have deterministic consistency (i.e. it turns back to the original NSGA-II) when the objective functions are deterministic. When the quality of the CDF is increased (either using more points or higher fidelity resolution), the convergence behavior improves. Since all the information regarding uncertainty quantification is preserved, all the different types of Pareto fronts that exist in the probabilistic framework (e.g. mean value Pareto, mean value penalty Pareto, etc.) are shown to be generated a posteriori. An adaptive sampling approach and parallel computing (in both the uncertainty and optimization algorithms) are shown to have several fold speed-up in selecting optimal solutions under uncertainty.
Originality/value
There are no existing algorithms that use the full probabilistic distribution to guide the optimizer. The method presented herein bases its sorting on real function evaluations, not merely measures (i.e. mean of the probabilistic distribution) that potentially do not exist.
Details
Keywords
Egidio D’Amato, Elia Daniele, Lina Mallozzi and Giovanni Petrone
The purpose of this paper is to propose a numerical algorithm able to describe the Stackelberg strategy for a multi level hierarchical three-person game via genetic algorithm (GA…
Abstract
Purpose
The purpose of this paper is to propose a numerical algorithm able to describe the Stackelberg strategy for a multi level hierarchical three-person game via genetic algorithm (GA) evolution process. There is only one player for each hierarchical level: there is an upper level leader (player L0), an intermediate level leader (player L1) who acts as a follower for L0 and as a leader for the lower level player (player F) that is the sole actual follower of this situation.
Design/methodology/approach
The paper presents a computational result via GA approach. The idea of the Stackelberg-GA is to bring together GAs and Stackelberg strategy in order to process a GA to build the Stackelberg strategy. Any player acting as a follower makes his decision at each step of the evolutionary process, playing a simple optimization problem whose solution is supposed to be unique.
Findings
A GA procedure to compute the Stackelberg equilibrium of the three-level hierarchical problem is given. An application to a Authority-Provider-User (APU) model in the context of wireless networks is discussed. The algorithm convergence is illustrated by means of some test cases.
Research limitations/implications
The solution to each level of hierarchy is supposed to be unique.
Originality/value
The paper demonstrates the possibility of using computational procedures based on GAs in hierarchical three level decision problems extending previous results obtained in the classical two level case.
Details
Keywords
Michiel H. Straathof, Giampietro Carpentieri and Michel J.L. van Tooren
An aerodynamic shape optimization algorithm is presented, which includes all aspects of the design process: parameterization, flow computation and optimization. The purpose of…
Abstract
Purpose
An aerodynamic shape optimization algorithm is presented, which includes all aspects of the design process: parameterization, flow computation and optimization. The purpose of this paper is to show that the Class‐Shape‐Refinement‐Transformation method in combination with an Euler/adjoint solver provides an efficient and intuitive way of optimizing aircraft shapes.
Design/methodology/approach
The Class‐Shape‐Transformation method was used to parameterize the aircraft shape and the flow was computed using an in‐house Euler code. An adjoint solver implemented into the Euler code was used to compute the required gradients and a trust‐region reflective algorithm was employed to perform the actual optimization.
Findings
The results of two aerodynamic shape optimization test cases are presented. Both cases used a blended‐wing‐body reference geometry as their initial input. It was shown that using a two‐step approach, a considerable improvement of the lift‐to‐drag ratio in the order of 20‐30 per cent could be achieved. The work presented in this paper proves that the CSRT method is a very intuitive and effective way of parameterizating aircraft shapes. It was also shown that using an adjoint algorithm provides the computational efficiency necessary to perform true three‐dimensional shape optimization.
Originality/value
The novelty of the algorithm lies in the use of the Class‐Shape‐Refinement‐Transformation method for parameterization and its coupling to the Euler and adjoint codes.
Details
Keywords
Hou Liqiang, Cai Yuanli, Zhang Rongzhi, Li Hengnian and Li Jisheng
A multi-disciplinary robust design optimization method for micro Mars entry probe (no more than 0.8 m in diameter) is proposed. The purpose of this paper is to design a Mars entry…
Abstract
Purpose
A multi-disciplinary robust design optimization method for micro Mars entry probe (no more than 0.8 m in diameter) is proposed. The purpose of this paper is to design a Mars entry probe, not only the geometric configuration, but the trajectory and thermal protection system (TPS). In the design optimization, the uncertainties of atmospheric and aerodynamic parameters are taken into account. The probability distribution information of the uncertainties are supposed to be unknown in the design. To ensure accuracy levels, time-consuming numerical models are coupled in the optimization. Multi-fidelity approach is designed for model management to balance the computational cost and accuracy.
Design/methodology/approach
Uncertainties which cannot defined by usual Gaussian probability distribution are modeled with degree of belief, and optimized through with multiple-objective optimization method. The optimization objectives are set to be the thermal performance of the probe TPS and the corresponding belief values. Robust Pareto front is obtained by an improved multi-objective density estimator algorithm. Multi-fidelity management is performed with an Artificial Neural Network (ANN) surrogate model. Analytical model is used first, and then with the improvement of accuracy, rather complex numerical models are activated. ANN updates the database during the optimization, and makes the solutions finally converge to a high-level accuracy.
Findings
The optimization method provides a way for conducting complex design optimization involving multi-discipline and multi-fidelity models. Uncertainty effects are analyzed and optimized through multi-disciplinary robust design. Because of the micro size, and uncertain impacts of aerodynamic and atmospheric parameters, simulation results show the performance trade-off by the uncertainties. Therefore an effective robust design is necessary for micro entry probe, particularly when details of model parameter are not available.
Originality/value
The optimization is performed through a new developed multi-objective density estimator algorithm. Affinity propagation algorithm partitions adaptively the samples by passing and analyzing messages between data points. Local principle component techniques are employed to resample and reproduce new individuals in each cluster. A strategy similar to NSGA-II selects data with better performance, and converges to the Pareto front. Models with different fidelity levels are incorporated in the multi-disciplinary design via ANN surrogate model. Database of aerodynamic coefficients is updated in an online manner. The computational time is greatly reduced while keeping nearly the same accuracy level of high fidelity model.
Details
Keywords
Pier Luigi Vitagliano, Mauro Minervino, Domenico Quagliarella and Pietro Catalano
– This paper aims to simulate unsteady flows with surfaces in relative motion using a multi-block structured flow solver.
Abstract
Purpose
This paper aims to simulate unsteady flows with surfaces in relative motion using a multi-block structured flow solver.
Design/methodology/approach
A procedure for simulating unsteady flows with surfaces in relative motion was developed, based upon a multi-block structured U-RANS flow solver1. Meshes produced in zones of the flow field with different rotation speed are connected by sliding boundaries. The procedure developed guarantees that the flux conservation properties of the original scheme are maintained across the sliding boundaries during the rotation at every time step.
Findings
The solver turns out to be very efficient, allowing computation in scalar mode with single core processors as well as in parallel. It was tested by simulating the unsteady flow on a propfan configuration with two counter-rotating rotors. The comparison of results and performances with respect to an existing commercial flow solver (unstructured) is reported.
Originality/value
This paper fulfils an identified need to allow for efficient unsteady flow computations (structured solver) with different bodies in relative motion.
Details
Keywords
Marc Guénot, Ingrid Lepot, Caroline Sainvitu, Jordan Goblet and Rajan Filomeno Coelho
The purpose of this paper is to propose a novel contribution to adaptive sampling strategies for non‐intrusive reduced order models based on Proper Orthogonal Decomposition (POD)…
Abstract
Purpose
The purpose of this paper is to propose a novel contribution to adaptive sampling strategies for non‐intrusive reduced order models based on Proper Orthogonal Decomposition (POD). These strategies aim at reducing the cost of optimization by improving the efficiency and accuracy of POD data‐fitting surrogate models to be used in an online surrogate‐assisted optimization framework for industrial design.
Design/methodology/approach
The effect of the strategies on the model accuracy is investigated considering the snapshot scaling, the design of experiment size and the truncation level of the POD basis and compared to a state‐of‐the‐art radial basis function network surrogate model on objectives and constraints. The selected test case is a Mach number and angle of attack domain exploration of the well‐known RAE2822 airfoil. Preliminary airfoil shape optimization results are also shown.
Findings
The numerical results demonstrate the potential of the capture/recapture schemes proposed for adequately filling the parametric space and maximizing the surrogates relevance at minimum computational cost.
Originality/value
The proposed approaches help in building POD‐based surrogate models more efficiently.