Wenping Song

Bilevel Adaptive Weighted Sum Method for Multidisciplinary Multi-Objective Optimization

The primary goal of this research is to develop a framework for dealing with multi-objective, multidisciplinary optimization problems with a large number of variables. The proposed method is expected to provide a relatively uniformly spaced, widely distributed Pareto front. To achieve this end, a novel integration of the adaptive weighted sum method within a concurrent subspace optimization framework is presented. In the bilevel framework of concurrent subspace optimization, the adaptive weighted sum is used to make tradeoffs among multiple, conflicting objectives. To obtain better distributed solutions, two modifications are made. First, an additional equality constraint in suboptimization for each expected solution is relaxed because it causes slow convergence within the bilevel optimization framework. The probability of entrapment in local minima can also be reduced. Second, the mesh of the Pareto front patches is modified due to the low efficiency of the original scheme. The proposed method is demonstrated with three multidisciplinary design optimization problems: 1) a numerical multidisciplinary design optimization test problem with a convex Pareto front, available within the NASA multidisciplinary design optimization Test Suite; 2) a test problem with a nonconvex Pareto front, which is not easily solved; and 3) a conceptual design of a subsonic passenger aircraft, which consists of two objectives, four design variables, five coupling behavior variables, seven constraints in aerodynamics, and weight discipline. The primary results show that the proposed method is promising with regard to obtaining a uniformly spaced, widely distributed, and smooth Pareto front and is applicable in the design of large-scale, complex engineering systems such as aircraft.

Coupled Aerodynamic/Structural Optimization of a Subsonic Transport Wing Using a Surrogate Model

[Abstract] Coupled aerodynamic and structural optimization is performed for the preliminary design of a high-subsonic transport-aircraft wing using surrogate models. The aerodynamic performance of wing/body combination in transonic flow is calculated with full-potential equation in conjunction with viscous correction method. Structural analysis is performed using finite-element method (FEM) to obtain stress and deform distribution. The span, taper ratio, sweep angle and linear twist angle are chosen as design variables that define the aerodynamic configuration of the wing. And another four representing thicknesses of spars and skin are selected as the design variables for structural discipline. After the aeroelastic analysis of the various candidate wings, the aerodynamic and structural performances are obtained such as the lift coefficient, the drag coefficient, and the deformation and equivalent stress of the wing. Based on these sample data, the approximation models for analyzing the aerodynamic and structural performances are established using surrogate models including quadratic response surface method (RSM), kriging model (KM) and radial-basis function (RBF) Network. The modeling accuracy is evaluated by numerical-error analysis. We aim to select the approximation models with best accuracy to replace the complicated and time-consuming analysis in optimization. It is found that KM and RSM has comparative high accuracy and both are more accurate than RBF. Multi-objective optimization for the supercritical wing is performed based on RSM, for maximizing lift-to-drag ratio and minimizing weight. And the optimization is constrained by lift, reference area, deform, equivalent stress. The performance of the optimal design is proven to be improved based on the initial design. And compared with the optimal design without considering aeroelastic effect, lift-to-drag ratio is increased by 5.77% and lift is increased by 19.55%. It is proven by practice that considering aeroelastic effect is necessary in priliminary design of aircraft when optimizing high-aspect-ratio wing.

Optimization of Active Flow Control over an Airfoil Using a Surrogate-Management Framework

An efficient method based on the surrogate-management framework has been excised to optimize the actuation parameters of active flow control over an airfoil via a synthetic jet. In this approach, sample points are chosen by the design of experiments method, and approximation models are built based on the sampled data obtained from unsteady Reynolds-averaged Navier―Stokes simulations. The accuracy of these approximation models is evaluated at some test points by comparing the approximated values with the accurate values obtained from unsteady Reynolds-averaged Navier―Stokes simulations. Three types of approximation models (quadratic response-surface model, kriging model, and radial-basis-function neutral network) are built from the same data set. The model with highest accuracy is chosen as the surrogate model to be used to replace the unsteady Reynolds-averaged Navier― Stokes analysis during optimization. The optimization objective is to maximize the lift coefficient of a NACA 0015 airfoil at given angles of attack (14 to 22°), with the jet momentum coefficient, nondimensional frequency, and jet angle being the design variables. The surrogate model is coupled with a simulated annealing genetic algorithm optimizer to efficiently obtain the global optimum. As a result of the optimization process, the lift coefficient at an angle of attack of 16° is increased by 16.9% and the corresponding drag is decreased by 13.4% with respect to the initial controlled flow. It is preliminarily shown that the presented method is efficient and applicable for optimization of active flow control via a synthetic jet.

A Preconditioned Multigrid Method for Efficient Simulation of Three-dimensional Compressible and Incompressible Flows

Abstract To develop an efficient and robust aerodynamic analysis method for numerical optimization designs of wing and complex configuration, a combination of matrix preconditioning and multigrid method is presented and investigated. The time derivatives of three-dimensional Navier-Stokes equations are preconditioned by Choi-Merkle preconditioning matrix that is originally designed for two-dimensional low Mach number viscous flows. An extension to three-dimensional viscous flow is implemented, and a method improving the convergence for transonic flow is proposed. The space discretizaition is performed by employing a finite-volume cell-centered scheme and using a central difference. The time marching is based on an explicit Runge-Kutta scheme proposed by Jameson. An efficient FAS multigrid method is used to accelerate the convergence to steady-state solutions. Viscous flows over ONERA M6 wing and M100 wing are numerically simulated with Mach numbers ranging from 0.010 to 0.839. The inviscid flow over the DLR-F4 wing-body configuration is also calculated to preliminarily examine the performance of the presented method for complex configuration. The computed results are compared with the experimental data and good agreement is achieved. It is shown that the presented method is efficient and robust for both compressible and incompressible flows and is very attractive for aerodynamic optimization designs of wing and complex configuration.

Surrogate-based Aerodynamic Shape Optimization with Application to Wind Turbine Airfoils

Design of airfoils specially tailored for wind turbine blades has dramatic influence on the performance of a wind turbine. The traditional way for wind turbine airfoil design is a kind of trial and error process. In order to improve the design efficiency was well as the performance of the design, numerical optimization methods coupling optimization algorithm with CFD codes in an automatic process chain are of great interest. This study is focused on the development of efficient numerical optimization design methods for wind turbine airfoils. The main feature is to use surrogate-based optimization. Surrogate-based optimization is very efficient and has the capability of finding global optima; it can be classified as the third-type optimization method other than the traditional gradient-based methods and gradient-free searching methods, such as evolutional algorithms. Optimization designs of FFA-W3-211, inverse design of NPU-WA-300 and realistic numerical optimization of NPU-WA-250 are exercised. Examples show that the developed methods are efficient and robust, with sufficient flexibility of handling both geometric and aerodynamic constraints, multi-points design and multi-objective design.

Prediction of Hovering Rotor Noise Based on Reynolds-Averaged Navier-Stokes Simulation

O VER the past decade, the hybrid method [coupling computational fluid dynamics (CFD) techniques with advanced analytic methods based on acoustic analogy, such as the Ffowcs Williams–Hawkings equation with penetrable data surface (FW–Hpds) method] has been successfully applied to predict the complicated acoustic field of helicopter rotors. The Ffowcs Williams–Hawkings (FW–H) equation [1], a rearrangement of Navier–Stokes equations by using generalfunction theory, provides an accurate theoretical model for describing the propagation of noise from a moving surface to the far field. The Farassat 1Amethod for solving the linear part of the FW–H equation was developed by Farassat and Succi [2]. It has been successfully applied in linear noise prediction [2,3] for more than 20 years. The Farassat 1A method predicts discrete frequency noise quite well, but it would run into complication when predicting nonlinear quadrupole noise of helicopter rotors, because the data surface is the blade itself and nonlinear effects are not included in the surface integral. To calculate the nonlinear noise [e.g., high-speed impulsive (HSI) noise], Farassat and Myers [4] derived the general form of the Kirchhoff equation and its solution (known as the Kirchhoff formulation) to describe the noise radiation from amoving surface. The data surface of the Kirchhoff formulation is fictitious and penetrable. The main benefit of the Kirchhoff method is that the nonlinear effect is accounted for by performing the integral on the data surface covering the nonlinear flow region. The Kirchhoff method coupled with the near-field CFD solution (called the CFD/ Kirchhoff method) has proven to be accurate and efficient when predicting impulsive noise. More recently, a new form of FW–H equation with a penetrable surface (called the FW–Hpds equation) was proposed by Crighton et al. [5] to improve the efficiency of solving the quadrupole noise. The method using a penetrable data surface for solving the FW–H equation with the Euler solution as input data was first implemented by di Francescantonio [6] for prediction of far-field noise from transonic helicopter rotors in hover. Brentner and Farassat [7] conducted an analytical comparison of the FW–Hpds method with the Kirchhoff method and concluded that the FW–Hpds method is more accurate and robust than the Kirchhoff method when the data surface is located in the nonlinear flow region. The FW–Hpds method rapidly showed promise in the studywork of a few researchers [7–10] when it was used for predicting the noise generated by helicopter rotors in hover and forward flight. More recently, Farassat and Casper [11] emphasized the role of analytical methods in computational aeroacoustics and recommended FW–Hpds as a very promising method for noise prediction of a complicated flowfield. To predict nonlinear noise generated by transonic rotors in hover, three-dimensional Euler equations were commonly used to consider the nonlinear effect related to shockwaves. To consider the influence of viscous effect in the near field and get more accurate information about noise sources, this paper uses Reynolds-Averaged Navier– Stokes (RANS) equations to model the nonlinear viscous flowfield near the rotor blades. The far-field noise is calculated by a retardedtime integral formula solving the FW–Hpds equation, with the solution of the RANS equations taken as input data.

Aerodynamic Design of Transonic Natural-Laminar-Flow (NLF) Wing via Surrogate-basedGlobal Optimization

This paper aims to develop an efficient global optimization method for design of transonic natural-laminar-flow (NLF) airfoils and wings, based on high-fidelity computational fluid dynamics (CFD) solver. The CFD solver features functionality of automatic transition prediction, by coupling Reynolds-averaged Navier-Stokes (RANS) equations with the linear-stability-theory-based dual e N method for Tollmien-Schlichting and crossflow instabilities. An A320-sized transonic NLF wing with a laminar supercritical airfoil is designed for cruise condition at Mach=0.74, Re=20 million, CL=0.515. In order to further improve the cruise efficiency, this NLF wing is optimized at higher Mach number of 0.75 via an in-house surrogate-based optimizer. The optimization is formulated as a drag minimization problem with constraints on lift, pitching moment and geometric thickness. Through only 130 CFD evaluations, 12.1 counts drag reduction is obtained, while all constraints are strictly satisfied. Further study shows that the drag reduction is contributed by both of shock-wave weakening and laminar-flow extension. On suction side, the favorable pressure gradient is maintained while shock wave is weakened; on pressure side, the crossflow (CF) instability is effectively suppressed and thereby the laminar flow region is dramatically extended. The improvement of aerodynamic performance is observed not only at design point but also over a certain range of off-design lift coefficients.

Bi-Level Adaptive Weighted Sum Method for Multidisciplinary Multi-Objective Optimization

The primary goal of this research is to develop a framework for dealing with multi-objective, multidisciplinary optimization problems with a large number of variables. The proposed method is expected to provide a relatively uniformly spaced, widely distributed Pareto front. To achieve this end, a novel integration of the adaptive weighted sum method within a concurrent subspace optimization framework is presented. In the bilevel framework of concurrent subspace optimization, the adaptive weighted sum is used to make tradeoffs among multiple, conflicting objectives. To obtain better distributed solutions, two modifications are made. First, an additional equality constraint in suboptimization for each expected solution is relaxed because it causes slow convergence within the bilevel optimization framework. The probability of entrapment in local minima can also be reduced. Second, the mesh of the Pareto front patches is modified due to the low efficiency of the original scheme. The proposed method is demonstrated with three multidisciplinary design optimization problems: 1) a numerical multidisciplinary design optimization test problem with a convex Pareto front, available within the NASA multidisciplinary design optimization Test Suite; 2) a test problem with a nonconvex Pareto front, which is not easily solved; and 3) a conceptual design of a subsonic passenger aircraft, which consists of two objectives, four design variables, five coupling behavior variables, seven constraints in aerodynamics, and weight discipline. The primary results show that the proposed method is promising with regard to obtaining a uniformly spaced, widely distributed, and smooth Pareto front and is applicable in the design of large-scale, complex engineering systems such as aircraft.

Surrogate-based robust design optimization of airfoil using inexpensive Monte Carlo method

This paper presents an efficient robust design optimization under the uncertainty quantification (UQ) of aleatory flight conditions using inexpensive Monte Carlo (IMC) method. Robust design optimization (RDO) technique is used to reduce the statistical moments of drag coefficient of an airfoil subject to some aerodynamic and geometric constraints. IMC approach with kriging surrogate model has been utilized to evaluate the robustness of a candidate design for prediction of statistical parameters and probability density functions of output response quantities. CFD calculations of RAE2822 airfoil have been evaluated using in-house code, PMNS2D. Combination of CFD input flight parameters such as free stream Mach number and angle of attack are varied and the propagation of their corresponding aleatory uncertainties on output properties of interest is studied. The reduction in objective function (Cd) is about 37.48% and 39.19% for combination of Mach and alpha uncertainties under Gaussian and LHS distributions respectively. Probability density function (PDF) of an output uncertainty is also compared with real PDF and found in good agreement with each other.

Effects of Proplet on Propeller Efficiency

Many studies have proved the validation of winglets on improving aerodynamic efficiency. Similar to winglet, a suitable proplet can improve the efficiency of a propeller. The effect of proplet on propeller performance is investigated in this paper. With a cell‐centered finite‐volume scheme, Reynolds‐Averaged Navier‐Stokes (RANS) equations are solved on a chimera grid system to simulate the flow around propeller to obtain the aerodynamic performance. A propeller designed for high altitude at 20 km with a diameter of 6.8 m is used as a baseline propeller. The effect of chord length and incidence angle of proplet tip on 8the efficiency of the propeller are also considered. The simulation results demonstrate that a proper proplet leads to weaker blade tip vortex, which is helpful to improve the efficiency of the propeller.