Common Research Model Wing Research Articles

Data-driven reduced-order modeling for nonlinear aerodynamics using an autoencoder neural network

The design of commercial air transportation vehicles heavily relies on understanding and modeling fluid flows, which pose computational challenges due to their complexity and high degrees of freedom. To overcome these challenges, we propose a novel approach based on machine learning (ML) to construct reduced-order models (ROMs) using an autoencoder neural network coupled with a discrete empirical interpolation method (DEIM). This methodology combines the interpolation of nonlinear functions identified based on selected interpolation points using DEIM with an ML-based clustering algorithm that provides accurate predictions by spanning a low-dimensional subspace at a significantly lower computational cost. In this study, we demonstrate the effectiveness of our approach by the calculation of transonic flows over the National Advisory Committee of Aeronautics 0012 airfoil and the National Aeronautics and Space Administration Common Research Model wing. All the results confirm that the ROM captures high-dimensional parameter variations efficiently and accurately in transonic regimes, in which the nonlinearities are induced by shock waves, demonstrating the feasibility of the ROM for nonlinear aerodynamics problems with varying flow conditions.

Efficient Global Aerodynamic Shape Optimization of a Full Aircraft Configuration Considering Trimming

Most existing aerodynamic shape optimization (ASO) studies do not take the balanced pitching moment into account and thus the optimized configuration has to be trimmed to ensure zero pitching moment, which causes additional drag and reduces the benefit of ASO remarkably. This article proposes an efficient global ASO method that directly enforces a zero pitching moment constraint. A free-form deformation (FFD) parameterization combing Laplacian smoothing method is implemented to parameterize a full aircraft configuration and ensure sufficiently smooth aerodynamic shapes. Reynolds-averaged Navier–Stokes (RANS) equations are solved to simulate transonic viscous flows. A surrogate-based multi-round optimization strategy is used to drive ASO towards the global optimum. To verify the effectiveness of the proposed method, we adopt two design optimization strategies for the NASA Common Research Model (CRM) wing–body–tail configuration. The first strategy is to optimize the configuration without considering balance of pitching moment, and then manually trim the optimized configuration by deflecting the horizontal tail. The second one is to directly enforce the zero pitching moment constraint in the optimization model and take the deflection angle of the horizontal tail as an additional design variable. Results show that: (1) for the first strategy, about 4-count drag-reducing benefits would be lost when manually trimming the optimal configuration; (2) the second strategy can achieve 3.2-count more drag-reducing benefits than the first strategy; (3) compared with gradient-based optimization (GBO), surrogate-based optimization (SBO) is more efficient than GBO for ASO problems with around 80 design variables, and the benefit of ASO achieved by SBO is comparable to that obtained by GBO.

An aeroelastic optimisation framework for manufacturable variable stiffness composite wings including critical gust loads

This work presents a new aeroelastic optimisation framework for the preliminary design of variable stiffness composite wing structures. The framework is constructed by sequentially and iteratively solving two sub-problems: aeroelastic tailoring and lay-up retrieval, using gradient-based algorithms with full-analytical sensitivities provided. During aeroelastic tailoring, the wing mass is minimised by optimising the lamination parameters and thickness of wing laminates together with wing jig twist distribution. The load cases cover not only static loads, but also the critical gust loads that are identified across the entire flight envelop at every iteration of optimisation. Further, a cruise shape constraint is included in addition to other aerostructural constraints, so that the optimal aircraft performance can be ensured. During lay-up retrieval, the manufacturable stacking sequence is retrieved according to the optimal lamination parameters with the consideration of minimal steering radius constraint. Moreover, to fix the possible constraint violations caused by lay-up retrieval, a correction strategy is incorporated to tighten the violated constraints for repeating aeroelastic tailoring. Finally, several case studies on the design of NASA common research model wing are carried out and investigated. The results indicate that the critical gust loads and cruise shape constraint have a large influence on the design of tow-steered composite wing structures, which therefore demonstrate the usefulness and benefits of the proposed optimisation framework.

Structural optimization of an aeroelastic wind tunnel model for unsteady transonic testing

The reduction of loads, ultimately leading to a weight reduction and thus an increase in aircraft performance, plays an important role in the design of modern aircraft. To this end, two aeroelastic tailoring methodologies, independently developed at ONERA and DLR and aiming at load reduction by means of a sophisticated application of composite materials, were applied to a common model geometry. A choice was made in favor of the publicly available NASA Common Research Model (CRM) wing, featuring a comprehensive database with respect to geometry, as well as analytical and experimental research results. The span of the wing half to be investigated was set to 0.55 m, limited by the test section dimensions. While wind tunnel testing was part of ONERA’s workshare, the model building was performed by DLR. This paper at hand focuses on the structural, aeroelastic optimization of the DLR wing. It is based on an optimization framework developed and constantly being enhanced and extended at the DLR - Institute of Aeroelasticity (DLR-AE). The paper describes the consideration of different structural objective functions, structural and aeroelastic constraint combinations, design field considerations, as well as the application of an aero load correction applied in the course of the optimization. The final results consist of the selection of an appropriate fiber type, optimized fiber layers represented as stacking sequence tables for the upper and lower wing skins, and the corresponding optimized jig twist distribution, required for manufacturing the lamination molds; in summary, all data required to start the construction of the wind tunnel model.

Invariant Vortex-Force Theory Extending Classical Aerodynamic Theories to Transonic Flows

Recent studies about the Lamb vector have led to the development of the vortex-force theory: a formulation able to predict the aerodynamic force in compressible flows and decompose it into lift, lift-induced drag, and profile drag. Here, a revised formulation of the vortex-force theory developed at ONERA in collaboration with the University of Naples is presented and applied to steady transonic flows. In the mathematical developments, special care is given to the presence of shock wave discontinuities within the flowfield. The equivalence between the new definition, the Kutta–Joukowski lift theorem, Maskell’s lift-induced drag formula (“Progress Towards a Method for the Measurement of the Components of the Drag of a Wing of Finite Span,” Procurement Executive, Ministry of Defence, Royal Aircraft Establishment TR 72232, Farnborough, England, U.K., 1972) and Betz’s profile drag formula (“A Method for the Direct Determination of Wing-Section Drag,” NACA TM 337, 1925) are emphasized. The revised formulation also presents several practical advantages: the decomposition is naturally invariant to the reference point chosen for the calculation of moment transformations, and the computation can be performed in a fine part of the grid, close to the body skin. The formulation is finally tested on the NASA Common Research Model wing–fuselage configuration in cruise flight conditions.

Transonic small disturbance unsteady potential flow over very high aspect ratio wings

AbstractIn this paper, the prediction of the unsteady flow field over typical high aspect ratio (AR) wings in the transonic flow regime but below the sonic Mach number is of interest. The methodology adopted is a computational approach based on the transonic small disturbance unsteady potential equation. It is shown that the higher AR wings generally have a higher lift coefficient as well as a higher lift-to-drag ratio. With NASA’s common research model (CRM) wing, there is an increase in maximum lift with increasing AR while the induced drag is almost the same. There is also an optimum sweep angle, which is different for each angle-of-attack so that variable sweep lifting surfaces may be designed to provide optimum solutions. The computed flutter speeds indicate an expected reduction with increasing AR.

Skin Panel Optimization of the Common Research Model Wing Using Sandwich Composites

This paper presents an approach for optimizing practical commercial-scale aircraft wings using sandwich composites in a preliminary design stage. The approach uses lamination parameters as design variables in a continuous optimization step. Structural constraints for classic composite laminate design such as material failure and buckling, and for sandwich design such as crimping, wrinkling, dimpling, and core shear failure are accounted for using industrial-standard and empirical methods driven by finite element analyses. As an application case, optimization studies are performed at a skin panel level on the open-source Common Research Model wing. Optimization trends show areas of the wingbox where sandwich composites offer superior structural performance, as well as potential cost savings by requiring lesser number of stringers. The aim and novelty of this work is to present performance gains that can be achieved using sandwich composites in primary load-carrying aircraft structures when compared with monolithic composite designs and, through this, to provide a motivation for further research and development in sandwich composites and their applications.

Application of femtosecond-laser tagging for unseeded velocimetry in a large-scale transonic cryogenic wind tunnel

Femtosecond laser electronic excitation tagging (FLEET) velocimetry was applied in the National Transonic Facility and assessed for its use in providing quantitative velocity measurements in a large-scale cryogenic wind tunnel. Comparisons of freestream results with theory and existing tunnel measurements indicate that FLEET velocity measurements agree within 1% of the tunnel reference, while the largest error among all conditions remained within 2.5%. For single-shot velocity measurements, binning of the FLEET intensity data improved the signal-to-noise ratio sufficiently to provide measurement precisions on the order of 1% of the freestream velocity. After confirmation of system performance, spatially resolved velocity profile measurements were obtained in the wake downstream of the Common Research Model wing. Effects of the model angle-of-attack on velocity deficit profiles were explored, and a two-dimensional, one-component velocity map resolving the wake region was constructed by scanning the laser’s position within the test section. The experimental campaign described herein represents the first non-intrusive, quantitative measurements of velocity made in this facility since its inception in 1984.

Aerodynamics of a Common Research Model Wing with Leading-Edge Ice Shape

Icing on three-dimensional lifting surfaces has been shown to produce highly complex flowfields. However, there is a lack of experimental and computational information in the public domain regarding three-dimensional aerodynamics for iced commercial aircraft wing geometries. Recent work completed at NASA Glenn Research Center’s Icing Research Tunnel has developed realistic ice shapes for the leading edge of a 65% scale Common Research Model (CRM65). These ice shapes were then converted into artificial ice shapes that were used in aerodynamic testing at the Wichita State University’s Walter H. Beech Wind Tunnel on an 8.9% scale CRM65. RANS simulations were computed for one large leading-edge ice shape to assess the ability to predict the aerodynamic performance parameters and to better understand the flow physics. In general, RANS reasonably captures the complex “swept stall” flow features, which are dominated by strong spanwise flow and separation line breaks. Despite the flow complexity, the simulations are able to generally predict the chordwise pressure distributions even at high angles of attack. While the coefficients of lift, drag, and moment are more accurately captured at lower angles of attack than higher angles of attack, the agreement with experimental data is quite reasonable given the complexity of the flow around this iced swept wing.

Adjoint State of Nonlinear Vortex-Lattice Method for Aerodynamic Design and Control

The adjoint state of a nonlinear vortex-lattice method, coupled with sectional polars obtained with an infinite swept-wing (2.5D) Reynolds-averaged Navier–Stokes (RANS) solver, is presented as an interactive method for preliminary aerodynamic design and control of moderate-to-high aspect ratio wings in subsonic and transonic flows. First, the nonlinear vortex-lattice method is described, augmented with a Prandtl–Glauert compressibility correction and regularized so that poststall solutions can be recovered. The linearization of the coupled system of equations is formulated using a Newton method, and the adjoint state is obtained for lift, drag, and inverse design functionals. Numerical results show that the aerodynamic model approximates well the forces predicted by three-dimensional (3D) RANS simulations for the Common Research Model wing, and that the adjoint-state gradients agree well with finite difference tests for a plethora of test cases. More interesting examples are shown, ranging from the optimal unstalling of wings to the assimilation of 3D RANS data into the present model, as well as its ability to extrapolate.

Adjoint-Free Aerodynamic Shape Optimization of the Common Research Model Wing

Adjoint-free methods are required in aerodynamic shape design optimization if an adjoint solver is unavailable. However, their performance is highly criticized in high-dimensional problems like wing shape design optimization. This work proposes an adjoint-free optimization method using deep-learning techniques to address the issue. A deep-learning-based optimal sampling method is developed to generate various wing shapes subject to both geometric validity and feasibility constraints. To address the curse of dimensionality in adjoint-free optimization, a compact wing shape parameterization method is presented by deriving global wing mode shapes from the sample wings. The proposed method is compared with the adjoint-based optimization method in both single-point and multipoint design of the Common Research Model wing. The proposed adjoint-free optimization method converges within 1000 objective function evaluations. The optimized shapes are close to those obtained by the adjoint-based optimization, and the differences in are all within 0.5 counts. The results show that the proposed adjoint-free optimization method has almost the same efficiency and effectiveness as the adjoint-based optimization method in high-dimensional wing shape design.

Aeroelastic scaling of flying demonstrator: flutter matching

The traditional approach for the design of aeroelastically scaled models assumes that either there exists flow similarity between the full-size aircraft and the model, or that flow non-similarities have a negligible effect. However, when trying to reproduce the behavior of an airliner that flies at transonic conditions using a scaled model that flies at nearly-incompressible flow conditions, this assumption is no longer valid and both flutter speed and static aerodynamic loading are subject to large discrepancies. To address this issue, we present an optimization-based approach for wing planform design that matches the scaled flutter speeds and modes of the reference aircraft when the Mach number cannot be matched. This is achieved by minimizing the squared error between the full-size and scaled aerodynamic models. This method is validated using the Common Research Model wing at the reference aircraft Mach number. The error in flutter speed is computed using the same wing at model conditions, which are in the nearly-incompressible regime. Starting from the baseline wing, its planform is optimized to match the reference response despite different conditions, achieving a reduction of the error in the predicted flutter speed from 7.79% to 2.13%.

Aeroelastic optimisation of manufacturable tow-steered composite wings with cruise shape constraint and gust loads

In the structural design of aircraft wings, aeroelastic tailoring is used to control the aeroelastic deformation to improve the aerostructural performance by making use of directional stiffness. Recently, tow-steered composites, where the fibre angles continuously vary within each ply, have been proven to have the potential to further expand the advantages of aeroelastic tailoring. This work extends TU Delft aeroelastic tailoring framework PROTEUS by introducing a lay-up retrieval step, so that it can be used for the conceptual design of tow-steered composite wing structures. In the extended framework, aeroelastic tailoring and lay-up retrieval are sequentially and iteratively performed to take static and dynamic loads, manufacturing and cruise shape constraints into consideration. The first step is carried out using PROTEUS, in which the lamination parameters and thickness of the wing sections are optimised under manoeuvre and gust load conditions. Further, for ensuring optimal aircraft performance in cruise flight conditions, the jig twist distribution is allowed to be optimised to maintain a desired prescribed cruise shape. In the second step, the stacking sequence, including minimum steering radius constraint, is retrieved. Since the lamination parameters cannot be matched exactly during the retrieval step, the constraints are checked, and tightened to take the performance loss during retrieval into account. The first step is repeated until all constraints are satisfied after fibre angle retrieval. To demonstrate the usefulness of the proposed optimisation framework, it is applied to the design of the NASA Common Research Model (CRM) wing, of which the objective is minimizing wing mass subjected to aerostructural design constraints, such as aeroelastic stability, aileron effectiveness, material strength and buckling load.

Aerodynamic Data Fusion Toward the Digital Twin Paradigm

This paper considers the fusion of two aerodynamic data sets originating from differing types of physical or computer experiments. This paper specifically addresses the fusion of 1) noisy and in-complete fields from wind-tunnel measurements and 2) deterministic but biased fields from numerical simulations. These two data sources are fused in order to estimate the true field that best matches measured quantities that serve as the ground truth. For example, two sources of pressure fields about an aircraft are fused based on measured forces and moments from a wind-tunnel experiment. A fundamental challenge in this problem is that the true field is unknown and cannot be estimated with 100% certainty. A Bayesian framework is employed to infer the true fields conditioned on measured quantities of interest; essentially a statistical correction to the data is performed. The fused data may then be used to construct more accurate surrogate models suitable for early stages of aerospace design. An extension of the proper orthogonal decomposition with constraints is also introduced to solve the same problem. Both methods are demonstrated on fusing the pressure distributions for flow past the RAE2822 airfoil and the Common Research Model wing at transonic conditions. Comparison of both methods reveals that the Bayesian method is more robust when data are scarce and capable of also accounting for uncertainties in the data. Furthermore, given adequate data, the proper-orthogonal-decomposition-based and Bayesian approaches lead to surprisingly similar results.

Aeroelastic optimization of composite wings including fatigue loading requirements

An analytical model to predict the fatigue life of a composite laminate is formulated. The model calculates stresses in each ply using classical lamination theory, degrades the residual strength using the linear wear-out law and predicts failure based on Tsai Wu failure theory. The cycles to failure are predicted using the updated cycle-by-cycle probability of failure. The predictions are validated for both a constant amplitude and a variable amplitude loading on a Glass/Epoxy laminate. Additionally the analytical model is extended to work with laminates described using lamination parameters instead of ply angles and stacking sequence. The analytical fatigue model is then integrated in the TU Delft aeroelastic and structural optimization tool PROTEUS. A thickness and stiffness optimization of the NASA Common Research Model (CRM) wing has been carried out. Results show that fatigue, strength and stiffness are the design drivers in the aeroelastic optimization of a composite wing. Furthermore, by including the analytical fatigue model instead of using a traditional knockdown factor to account for fatigue, a lighter wing is obtained.

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.

Structural Optimization of Internal Structure of Aircraft Wings with Curvilinear Spars and Ribs

A new framework for optimization of the internal structure of transport aircraft wings having curvilinear spars and ribs (SpaRibs) is described. SpaRibs are parameterized by third-order B-splines with constraints on the starting, ending, and various control points. A broad range of SpaRibs topologies can be created using a limited number of parameters. For local size optimization, panels are generated from the wing finite element model by an algorithm that is independent of the nodal coordinates and the order in which the elements are distributed, and which can be used for a broad range of aircraft wings. The local panel thicknesses are optimized to satisfy buckling and stress constraints of the wing using an algorithm that increases the thickness of the panels that are found to be vulnerable to buckling or wherein the stress is higher than the maximum permissible stress. This algorithm has been integrated with the particle swarm algorithm to optimize the SpaRibs topology for multiple objectives (weight and flutter velocity). The code is demonstrated by optimizing the internal structure of the NASA Common Research Model wing model with SpaRibs considering stress and buckling constraints at trim condition at Mach number equal to 0.85 for two different angles of attack ( and 6 deg).

A dynamically deflated GMRES adjoint solver for aerodynamic shape optimization

An essential step in adjoint-based aerodynamic shape optimization is to obtain the Lagrange multiplier by solving a sparse linear adjoint system of equations based on the Jacobian matrices from the converged flow states. Such an approach has been applied widely within the aerospace community for the design of aircraft and other optimization problems for aerospace applications. However, the need to resolve the flow over complex geometries often requires highly stretched grids and gives rise to anisotropic flow fields which increase the stiffness of the discrete Jacobian needed for the solution of the adjoint system. When a GMRES algorithm preconditioned by an Incomplete LU factorization is used, this stiff linear system requires the use of a large number of Krylov subspace vectors and a high level of fill-in; both require an increase in the amount of memory. Deflated restarting, which distributes spectral eigenpairs, has proven to be an effective method to enhance the convergence rates when solving an ill-conditioned linear system of equations. In this paper, we propose an algorithm to dynamically determine the number of deflated vectors and to deactivate deflation to reduce memory utilization. We demonstrate its efficiency for a two-dimensional NACA 0012 airfoil, the three-dimensional Common Research Model (CRM) wing, and two three-dimensional complete aircraft configurations in viscous flow.

Benchmark Aerostructural Models for the Study of Transonic Aircraft Wings

Since its introduction, the NASA Common Research Model has proved a useful aerodynamic benchmark for predicting computational-fluid-dynamics-based drag and aerodynamic design optimization. The model was originally conceived as a purely aerodynamic benchmark, and as such the wing geometry corresponds to the deflected shape at its nominal flight condition. However, interest has been growing to extend this model to aeroelastic studies. Unfortunately, because of its predefined deflection, the model is not suitable for aeroelastic analysis and design. To address this issue, an undeflected Common Research Model is defined through an inverse design procedure that includes the outer mold line geometry of the undeflected wing and the corresponding internal wingbox structure. Additionally, because modern transport aircraft are trending toward higher-aspect-ratio wing designs, a higher-aspect-ratio variant of the Common Research Model wing is developed to assess next-generation wing designs. This variant has an aspect ratio of 13.5 and is designed by using buffet-constrained multipoint aerostructural optimization. The purpose of these models is to provide publicly available benchmarks for aeroelastic wing analysis and design optimization.

On the influence of optimization algorithm and initial design on wing aerodynamic shape optimization

Aerodynamic shape optimization is a useful tool in wing design, but the impact of the choice of optimization algorithm and the multimodality of the design space in wing design optimization is still poorly understood. To address this, we benchmark both gradient-based and gradient-free optimization algorithms for computational fluid dynamics based aerodynamic shape optimization problems based on the Common Research Model wing geometry. The aerodynamic model solves the Reynolds-averaged Navier–Stokes equations with a Spalart–Allmaras turbulence model. The drag coefficient is minimized subject to lift, pitching moment, and geometry constraints, with up to 720 shape variables and 11 twist variables for two mesh sizes. We benchmark six gradient-based and three gradient-free algorithms by comparing both the accuracy of the optima and the computational cost. Most of the optimizers reach similar optima, but the gradient-based methods converge to more accurate solutions at a much lower computational cost. Since multimodality and nonsmoothness of the design space are common arguments for the use of gradient-free methods, we investigate these issues by solving the same optimization problem starting from a series of randomly generated initial geometries, as well as a wing based on the NACA 0012 airfoil with zero twist and constant thickness-to-chord ratio. All the optimizations consistently converge to practically identical results, where the differences in drag are within 0.05%, and the shapes and pressure distributions are very similar. Our overall conclusion is that the design space for wing design optimization with a fixed planform is largely convex, with a very small flat region that is multimodal because of numerical errors. However, this region is so small, and the differences in drag so minor, that the design space can be considered unimodal for all practical purposes.