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DOE OSTI2023

Aerodynamic Sensitivity of a Novel Data-Driven Airfoil Shape Representation Framework

We explore the aerodynamic implications of a novel data-driven separable shape tensor framework used to represent discrete airfoil shapes. In this study, we construct a data-driven parameter space defined by separable shape tensors and informed by tens of thousands of distinct airfoils. We use this design space to generate new airfoil designs to study parametric sensitivities with respect to various aerodynamic responses. We use a HAM2D RANS solver to approximate the lift, drag, and moment coefficients for the generated airfoils at two different angles-of-attack. We analyze the robustness and sensitivities of using the separable shape tensor design space by examining the coverage of the aerodynamic response space, uncovering low-dimensional polynomial ridge approximations, and computing various sensitivity metrics. The results show that the data-driven design space produce significant variation in target aerodynamic quantities and facilitate highly accurate approximations (R^2 > 0.96) of one- and two-dimensional structures in each aerodynamic response. This further reduces the effective dimension to enable simplified design and optimization tasks.

aerodynamics↗

DOE OSTI2022

Grassmannian Shape Representations for Aerodynamic Applications

Airfoil shape design is a classical problem in engineering, science, and manufacturing. Our motivation is to combine principled physics-based considerations for the shape design problem with modern computational techniques informed by a data-driven approach. Traditional analyses of airfoil shapes emphasize a flow-based sensitivity to deformations which can be represented generally by affine transformations (rotation, scaling, shearing, shifting). We present a novel representation of shapes which decouples affine-style deformations from a rich set of data-driven deformations over a submanifold of the Grassmannian. The Grassmannian representation, informed by a database of physically relevant airfoils, offers (i) a rich set of novel 2D airfoil deformations not previously captured in the data, (ii) improved low-dimensional parameter domain for inferential statistics, and (iii) consistent 3D blade representation and perturbation over a sequence of nominal shapes.

blade representation↗

DOE OSTI2022

Grassmannian Shape Representations for Aerodynamic Applications: Preprint

blade representation↗

DOE OSTI2021

INTEGRATE - Inverse Network Transformations for Efficient Generation of Robust Airfoil and Turbine Enhancements

The INTEGRATE (Inverse Network Transformations for Efficient Generation of Robust Airfoil and Turbine Enhancements) project is developing a new inverse-design capability for the aerodynamic design of wind turbine rotors using invertible neural networks. This AI-based design technology can capture complex non-linear aerodynamic effects while being 100 times faster than design approaches based on computational fluid dynamics. This project enables innovation in wind turbine design by accelerating time to market through higher-accuracy early design iterations to reduce the levelized cost of energy. INVERTIBLE NEURAL NETWORKS Researchers are leveraging a specialized invertible neural network (INN) architecture along with the novel dimension-reduction methods and airfoil/blade shape representations developed by collaborators at the National Institute of Standards and Technology (NIST) learns complex relationships between airfoil or blade shapes and their associated aerodynamic and structural properties. This INN architecture will accelerate designs by providing a cost-effective alternative to current industrial aerodynamic design processes, including: - Blade element momentum (BEM) theory models: limited effectiveness for design of offshore rotors with large, flexible blades where nonlinear aerodynamic effects dominate - Direct design using computational fluid dynamics (CFD): cost-prohibitive - Inverse-design models based on deep neural networks (DNNs): attractive alternative to CFD for 2D design problems, but quickly overwhelmed by the increased number of design variables in 3D problems AUTOMATED COMPUTATIONAL FLUID DYNAMICS FOR TRAINING DATA GENERATION - MERCURY FRAMEWORK The INN is trained on data obtained using the University of Marylands (UMD) Mercury Framework, which has with robust automated mesh generation capabilities and advanced turbulence and transition models validated for wind energy applications. Mercury is a multi-mesh paradigm, heterogeneous CPU-GPU framework. The framework incorporates three flow solvers at UMD, 1) OverTURNS, a structured solver on CPUs, 2) HAMSTR, a line based unstructured solver on CPUs, and 3) GARFIELD, a structured solver on GPUs. The framework is based on Python, that is often used to wrap C or Fortran codes for interoperability with other solvers. Communication between multiple solvers is accomplished with a Topology Independent Overset Grid Assembler (TIOGA). NOVEL AIRFOIL SHAPE REPRESENTATIONS USING GRASSMAN SPACES We developed a novel representation of shapes which decouples affine-style deformations from a rich set of data-driven deformations over a submanifold of the Grassmannian. The Grassmannian representation as an analytic generative model, informed by a database of physically relevant airfoils, offers (i) a rich set of novel 2D airfoil deformations not previously captured in the data , (ii) improved low-dimensional parameter domain for inferential statistics informing design/manufacturing, and (iii) consistent 3D blade representation and perturbation over a sequence of nominal shapes. TECHNOLOGY TRANSFER DEMONSTRATION - COUPLING WITH NREL WISDEM Researchers have integrated the inverse-design tool for 2D airfoils (INN-Airfoil) into WISDEM (Wind Plant Integrated Systems Design and Engineering Model), a multidisciplinary design and optimization framework for assessing the cost of energy, as part of tech-transfer demonstration. The integration of INN-Airfoil into WISDEM allows for the design of airfoils along with the blades that meet the dynamic design constraints on cost of energy, annual energy production, and the capital costs. Through preliminary studies, researchers have shown that the coupled INN-Airfoil + WISDEM approach reduces the cost of energy by around 1% compared to the conventional design approach. This page will serve as a place to easily access all the publications from this work and the repositories for the software developed and released through this pr...

aerodynamics↗

NASA NTRS1976

Numerical Airfoil Optimization Using a Reduced Number of Design Coordinates

A method is presented for numerical airfoil optimization whereby a reduced number of design coordinates are used to define the airfoil shape. The approach is to define the airfoil as a linear combination of shapes. These basic shapes may be analytically or numerically defined, allowing the designer to use his insight to propose candidate designs. The design problem becomes one of determining the participation of each such function in defining the optimum airfoil. Examples are presented for two-dimensional airfoil design and are compared with previous results based on a polynomial representation of the airfoil shape. Four existing NACA airfoils are used as basic shapes. Solutions equivalent to previous results are achieved with a factor of more than 3 improvements in efficiency, while superior designs are demonstrated with an efficiency greater than 2 over previous methods. With this shape definition, the optimization process is shown to exploit the simplifying assumptions in the inviscid aerodynamic analysis used here, thus demonstrating the need to use more advanced aerodynamics for airfoil optimization.

Vanderplaats, G. N.↗

DOE OSTI2025

Aerodynamic Sensitivities over Separable Shape Tensors

Here, we present a comprehensive aerodynamic sensitivity analysis of airfoil parameterization informed by separable shape tensors. This parameterization approach uniquely benefits the design process by isolating various well-studied shape characteristics, such as airfoil thickness, and providing a well-regulated low-dimensional parameter domain for aerodynamic designs. Exploring the aerodynamic sensitivities of this novel parameterization can provide valuable insights for more robust designs and future manufacturing efforts. We construct a data-driven parameter space of airfoils using principal geodesic analysis of separable shape tensors informed by a curated database containing almost 20,000 suitable engineering airfoils. Analyzing the shape reconstruction error and the maximum mean discrepancy between joint distributions of aerodynamic quantities, we study the dimensionality of the learned parameter space. This simple numerical experiment demonstrates a dramatic dimension reduction that retains design effectiveness and promotes regularity of the shape representations. Finally, we generate new airfoils and use the HAM2D Reynolds-averaged Navier–Stokes solver to predict lift, drag, and moment coefficients. We compute multiple sensitivity metrics to quantify and assert the consistency of parameter influence on the aerodynamic quantities. We also explore low-dimensional polynomial ridge approximations to motivate physical intuitions and offer explanations of the approximated sensitivities.

17 WIND ENERGY↗

NASA NTRS2014

Computational Aerodynamic Analysis of Three-Dimensional Ice Shapes on a NACA 23012 Airfoil

The present study identifies a process for performing computational fluid dynamic calculations of the flow over full three-dimensional (3D) representations of complex ice shapes deposited on aircraft surfaces. Rime and glaze icing geometries formed on a NACA23012 airfoil were obtained during testing in the NASA Glenn Research Center's Icing Research Tunnel (IRT). The ice shape geometries were scanned as a cloud of data points using a 3D laser scanner. The data point clouds were meshed using Geomagic software to create highly accurate models of the ice surface. The surface data was imported into Pointwise grid generation software to create the CFD surface and volume grids. It was determined that generating grids in Pointwise for complex 3D icing geometries was possible using various techniques that depended on the ice shape. Computations of the flow fields over these ice shapes were performed using the NASA National Combustion Code (NCC). Results for a rime ice shape for angle of attack conditions ranging from 0 to 10 degrees and for freestream Mach numbers of 0.10 and 0.18 are presented. For validation of the computational results, comparisons were made to test results from rapid-prototype models of the selected ice accretion shapes, obtained from a separate study in a subsonic wind tunnel at the University of Illinois at Urbana-Champaign. The computational and experimental results were compared for values of pressure coefficient and lift. Initial results show fairly good agreement for rime ice accretion simulations across the range of conditions examined. The glaze ice results are promising but require some further examination.

Aerodynamics↗

NASA NTRS2014

Computational Aerodynamic Analysis of Three-Dimensional Ice Shapes on a NACA 23012 Airfoil

The present study identifies a process for performing computational fluid dynamic calculations of the flow over full three-dimensional (3D) representations of complex ice shapes deposited on aircraft surfaces. Rime and glaze icing geometries formed on a NACA23012 airfoil were obtained during testing in the NASA Glenn Research Centers Icing Research Tunnel (IRT). The ice shape geometries were scanned as a cloud of data points using a 3D laser scanner. The data point clouds were meshed using Geomagic software to create highly accurate models of the ice surface. The surface data was imported into Pointwise grid generation software to create the CFD surface and volume grids. It was determined that generating grids in Pointwise for complex 3D icing geometries was possible using various techniques that depended on the ice shape. Computations of the flow fields over these ice shapes were performed using the NASA National Combustion Code (NCC). Results for a rime ice shape for angle of attack conditions ranging from 0 to 10 degrees and for freestream Mach numbers of 0.10 and 0.18 are presented. For validation of the computational results, comparisons were made to test results from rapid-prototype models of the selected ice accretion shapes, obtained from a separate study in a subsonic wind tunnel at the University of Illinois at Urbana-Champaign. The computational and experimental results were compared for values of pressure coefficient and lift. Initial results show fairly good agreement for rime ice accretion simulations across the range of conditions examined. The glaze ice results are promising but require some further examination.

Aerodynamics↗

DOE OSTI2023

Separable shape tensors for aerodynamic design

Airfoil shape design is a classical problem in engineering and manufacturing. In this work, we combine principled physics-based considerations for the shape design problem with modern computational techniques using a data-driven approach. Modern and traditional analyses of two-dimensional (2D) and three-dimensional (3D) aerodynamic shapes reveal a flow-based sensitivity to specific deformations that can be represented generally by affine transformations (rotation, scaling, shearing, and translation). We present a novel representation of shapes that decouples affine-style deformations over a submanifold and a product submanifold principally of the Grassmannian. As an analytic generative model, the separable representation, informed by a database of physically relevant airfoils, offers: (i) a rich set of novel 2D airfoil deformations not previously captured in the data, (ii) an improved low-dimensional parameter domain for inferential statistics informing design/manufacturing, and (iii) consistent 3D blade representation and perturbation over a sequence of nominal 2D shapes.

42 ENGINEERING↗

NASA NTRS2013

Assessment of Ice Shape Roughness Using a Self-Orgainizing Map Approach

Self-organizing maps are neural-network techniques for representing noisy, multidimensional data aligned along a lower-dimensional and nonlinear manifold. For a large set of noisy data, each element of a finite set of codebook vectors is iteratively moved in the direction of the data closest to the winner codebook vector. Through successive iterations, the codebook vectors begin to align with the trends of the higher-dimensional data. Prior investigations of ice shapes have focused on using self-organizing maps to characterize mean ice forms. The Icing Research Branch has recently acquired a high resolution three dimensional scanner system capable of resolving ice shape surface roughness. A method is presented for the evaluation of surface roughness variations using high-resolution surface scans based on a self-organizing map representation of the mean ice shape. The new method is demonstrated for 1) an 18-in. NACA 23012 airfoil 2 AOA just after the initial ice coverage of the leading 5 of the suction surface of the airfoil, 2) a 21-in. NACA 0012 at 0AOA following coverage of the leading 10 of the airfoil surface, and 3) a cold-soaked 21-in.NACA 0012 airfoil without ice. The SOM method resulted in descriptions of the statistical coverage limits and a quantitative representation of early stages of ice roughness formation on the airfoils. Limitations of the SOM method are explored, and the uncertainty limits of the method are investigated using the non-iced NACA 0012 airfoil measurements.

Icing↗

DOE OSTI2023

G2Aero: A Python package for separable shape tensors

G2Aero is a Python package for the design and deformation of discrete planar curves and tubular surfaces using a geometric data-driven approach. G2Aero utilizes a topology of product manifolds: the Grassmannian, $\mathcal{G}$($\mathcal{n}$, 2) - the set of 2-dimensional subspaces in $\mathbb{R}$ $\mathcal{n}$ - and the symmetric positive-definite (SPD) manifold, $\mathcal{S}^{2}_{++}$ - the set of 2x2 SPD matrices. The package provides a novel framework for representing separable deformations to shapes, which consist of stretching, scaling, rotating, and translating - also known as affine deformations - and a set of complementary deformations - which we refer to as undulation-type deformations. We focus on airfoil and blade design applications to emphasize the utility of the methods in an environment where the separation of affine and undulation-type deformations is critical. Notable functionalities of the framework for blade design include: 1) generating novel 2D (airfoil) shapes informed by a database of physically relevant airfoils, 2) building 3D blades by interpolating sequences of 2D airfoil cross-sections, and 3) generating blades with consistent perturbations along the blade span. We discuss the framework and provide examples in the context of wind energy applications, specifically wind turbine blade design. Figure 1 shows the wire frame obtained by interpolating airfoils defining the IEA 15-MW wind turbine blade and applying affine transformations corresponding to twist, chordal scaling, and bending. This, and all other figures in the paper, can be reproduced following examples and referencing supporting documentation provided in the G2Aero package.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2015

Three-Dimensional Piecewise-Continuous Class-Shape Transformation of Wings

Class-Shape Transformation (CST) is a popular method for creating analytical representations of the surface coordinates of various components of aerospace vehicles. A wide variety of two- and three-dimensional shapes can be represented analytically using only a modest number of parameters, and the surface representation is smooth and continuous to as fine a degree as desired. This paper expands upon the original two-dimensional representation of airfoils to develop a generalized three-dimensional CST parametrization scheme that is suitable for a wider range of aircraft wings than previous formulations, including wings with significant non-planar shapes such as blended winglets and box wings. The method uses individual functions for the spanwise variation of airfoil shape, chord, thickness, twist, and reference axis coordinates to build up the complete wing shape. An alternative formulation parameterizes the slopes of the reference axis coordinates in order to relate the spanwise variation to the tangents of the sweep and dihedral angles. Also discussed are methods for fitting existing wing surface coordinates, including the use of piecewise equations to handle discontinuities, and mathematical formulations of geometric continuity constraints. A subsonic transport wing model is used as an example problem to illustrate the application of the methodology and to quantify the effects of piecewise representation and curvature constraints.

Olson, Erik D.↗

NASA NTRS1992

Methodology for sensitivity analysis, approximate analysis, and design optimization in CFD for multidisciplinary applications

Fundamental equations of aerodynamic sensitivity analysis and approximate analysis for the two dimensional thin layer Navier-Stokes equations are reviewed, and special boundary condition considerations necessary to apply these equations to isolated lifting airfoils on 'C' and 'O' meshes are discussed in detail. An efficient strategy which is based on the finite element method and an elastic membrane representation of the computational domain is successfully tested, which circumvents the costly 'brute force' method of obtaining grid sensitivity derivatives, and is also useful in mesh regeneration. The issue of turbulence modeling is addressed in a preliminary study. Aerodynamic shape sensitivity derivatives are efficiently calculated, and their accuracy is validated on two viscous test problems, including: (1) internal flow through a double throat nozzle, and (2) external flow over a NACA 4-digit airfoil. An automated aerodynamic design optimization strategy is outlined which includes the use of a design optimization program, an aerodynamic flow analysis code, an aerodynamic sensitivity and approximate analysis code, and a mesh regeneration and grid sensitivity analysis code. Application of the optimization methodology to the two test problems in each case resulted in a new design having a significantly improved performance in the aerodynamic response of interest.

Taylor, Arthur C., III↗

NASA NTRS1994

Sensitivity of lag-damping correlations to structural and aerodynamic approximations of isolated experimental rotors in forward flight

The predictions of regressive lag-mode damping levels are correlated with the database of an isolated, soft-inplane, three-blade rotor operated untrimmed. The database was generated at the Army Aeroflightdynamics Directorate at Ames. The correlation covers a broad range of data, from near-zero thrust conditions in hover to high-thrust and highly stalled conditions in forward flight with advance ratio as high as 0.55 and shaft angle as high as 20 degrees. In the experimental rotor, the airfoil or blade portion has essentially uniform mass and stiffness distributions, but the root flexure has highly nonuniform mass and stiffness distributions. Accordingly, the structural approximations refer to four models of root-flexure-blade assembly. They range from a rigid flap-lag model to three elastic flap-lag-torsion models, which differ in modeling the root flexure. The three models of root-flexure are: three root springs in which the bending-torsion couplings are fully accounted for; a finite-length beam element with some average mass and stiffness distributions such that the fundamental frequencies match those of the experimental model; and accurate modal representation in which the actual mass and stiffness distributions of the experimental root-flexure-blade assembly are used in calculating the nonrotating mode shapes. The four models of root-flexure-blade assembly are referred to as the rigid flap-lag model, spring model, modified model and modal model. For each of these four models of the root-flexure-blade assembly, the predictions are based on the following five aerodynamic theories: ear theory, which accounts for large angle-of-attack and reverse-flow effects on lift, and has constant drag and pitching moment; quasisteady stall theory, which includes quasisteady stall lift, drag and pitching moment characteristics of the airfoil section, dynamics stall theory, which uses the ONERA dynamic stall models of lift, drag and pitching moment; dynamic wake theory, which is based on a finite-state three-dimensional wake model and includes all wake effects including both shed and trailing vorticity; and dynamics and wake theory, which combines both dynamic stall theory and dynamic wake theory and is a relatively complete aerodynamic representation.

Gaonkar, G. H.↗

NASA NTRS1992

An interactive boundary-layer approach to multielement airfoils at high lift

A calculation method based on an interactive boundary-layer approach to multielement airfoils is described and is applied to three types of airfoil configurations with and without flap-wells in order to demonstrate the applicability of the method to general high-lift configurations. This method, well tested for single airfoils as a function of shape, angle of attack, and Reynolds number, is here shown to apply equally well to two-element airfoils and their wakes, to a flap-well region, and to a three-element arrangement which includes the effects of co-flowing regions, a flap well, and the wake of the elements. In addition to providing accurate representation of these flows, the method is general so that its extension to three-dimensional arrangements is likely to provide a practical, accurate and efficient tool to assist the design process.

Cebeci, Tuncer↗

NASA NTRS1937

Potential flow about arbitrary biplane wing sections

A rigorous treatment is given of the problem of determining the two-dimensional potential flow around arbitrary biplane cellules. The analysis involves the use of elliptic functions and is sufficiently general to include the effects of such elements as the section shapes, the chord ratio, gap, stagger, and decalage, which elements may be specified arbitrarily. The flow problem is resolved by making use of the methods of conformal representation. Thus the solution of the problem of transforming conformally two arbitrary contours into two circles is expressed by a pair of simultaneous integral equations, for which a method of numerical solution is outlined. As an example of the numerical process, the pressure distribution over certain arrangements of the NACA 4412 airfoil in biplane combinations is presented and compared with the monoplane pressure distribution.

Garrick, I E↗

NASA NTRS1997

The Development of a Tool for Semi-Automated Generation of Structured and Unstructured Grids about Isolated Rotorcraft Blades

The grid generation used to model rotorcraft configurations for Computational Fluid Dynamics (CFD) analysis is highly complicated and time consuming. The highly complex geometry and irregular shapes encountered in entire rotorcraft configurations are typically modeled using overset grids. Another promising approach is to utilize unstructured grid methods. With either approach the majority of time is spent manually setting up the topology. For less complicated geometries such as isolated rotor blades, less time is obviously required. This paper discusses the capabilities of a tool called Rotor blade Optimized Topology Organizer and Renderer(ROTOR) being developed to quickly generate block structured grids and unstructured tetrahedral grids about isolated blades. The key algorithm uses individual airfoil sections to construct a Non-Uniform Rational B-Spline(NURBS) surface representation of the rotor blade. This continuous surface definition can be queried to define the block topology used in constructing a structured mesh around the rotor blade. Alternatively, the surface definition can be used to define the surface patches and grid cell spacing requirements for generating unstructured surface and volume grids. Presently, the primary output for ROTOR is block structured grids using 0-H and H-H topologies suitable for full-potential solvers. This paper will discuss the present capabilities of the tool and highlight future work.

Shanmugasundaram, Ramakrishnan↗

NASA NTRS1985

Sidewall boundary-layer effects in two-dimensional airfoil testing

Theoretical studies required to evaluate and validate the streamlined wall test section of the 0.3 m transonic Cryogenic Tunnel were initiated. The various aspects that are being considered presently are deviations of the real wall shape from the true streamline shape, wall adjustment strategy, and the influence of the sidewall boundary layers. Since the top and bottom walls are supported at a finite number of jack points, the true wall shape will be different from the ideal streamline shape. This is determined by calculating the structural shape for cases for which the exact streamline shape can be calculated. For the structural shape calculations, the MSCNASTRAN code is being used. To start with, comparisons are made using simple singularities for model representation and also for a flat plate at angle of attack.

Murthy, A. V.↗