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NASA NTRS1983

Evaluation of the effect of vibration nonlinearity on convergence behavior of adaptive higher harmonic controllers

Effect of nonlinearity on convergence of the local linear and global linear adaptive controllers is evaluated. A nonlinear helicopter vibration model is selected for the evaluation which has sufficient nonlinearity, including multiple minimum, to assess the vibration reduction capability of the adaptive controllers. The adaptive control algorithms are based upon a linear transfer matrix assumption and the presence of nonlinearity has a significant effect on algorithm behavior. Simulation results are presented which demonstrate the importance of the caution property in the global linear controller. Caution is represented by a time varying rate weighting term in the local linear controller and this improves the algorithm convergence. Nonlinearity in some cases causes Kalman filter divergence. Two forms of the Kalman filter covariance equation are investigated.

Molusis, J. A.↗

NASA NTRS1982

Convergence behavior that controls adaptive wind tunnel walls near the test section in the high angle of attack range

The NACA 0012 profile at Mach 0.5 was investigated in a wind tunnel with adaptive walls. It is found that adaptation of the flexible walls is possible in the high angle of attack range on both sides of maximum lift. Oil film photographs of the flow at the profile surface show three dimensional effects in the region of the corners between the profile and the sidewall. It is concluded that pure two dimensional separated flow is not possible.

Ziemann, J.↗

NASA NTRS1989

Separate visual representations for perception and for visually guided behavior

Converging evidence from several sources indicates that two distinct representations of visual space mediate perception and visually guided behavior, respectively. The two maps of visual space follow different rules; spatial values in either one can be biased without affecting the other. Ordinarily the two maps give equivalent responses because both are veridically in register with the world; special techniques are required to pull them apart. One such technique is saccadic suppression: small target displacements during saccadic eye movements are not preceived, though the displacements can change eye movements or pointing to the target. A second way to separate cognitive and motor-oriented maps is with induced motion: a slowly moving frame will make a fixed target appear to drift in the opposite direction, while motor behavior toward the target is unchanged. The same result occurs with stroboscopic induced motion, where the frame jump abruptly and the target seems to jump in the opposite direction. A third method of separating cognitive and motor maps, requiring no motion of target, background or eye, is the Roelofs effect: a target surrounded by an off-center rectangular frame will appear to be off-center in the direction opposite the frame. Again the effect influences perception, but in half of the subjects it does not influence pointing to the target. This experience also reveals more characteristics of the maps and their interactions with one another, the motor map apparently has little or no memory, and must be fed from the biased cognitive map if an enforced delay occurs between stimulus presentation and motor response. In designing spatial displays, the results mean that what you see isn't necessarily what you get. Displays must be designed with either perception or visually guided behavior in mind.

Bridgeman, Bruce↗

NASA NTRS2001

A Parallel Cartesian Approach for External Aerodynamics of Vehicles with Complex Geometry

This workshop paper presents the current status in the development of a new approach for the solution of the Euler equations on Cartesian meshes with embedded boundaries in three dimensions on distributed and shared memory architectures. The approach uses adaptively refined Cartesian hexahedra to fill the computational domain. Where these cells intersect the geometry, they are cut by the boundary into arbitrarily shaped polyhedra which receive special treatment by the solver. The presentation documents a newly developed multilevel upwind solver based on a flexible domain-decomposition strategy. One novel aspect of the work is its use of space-filling curves (SFC) for memory efficient on-the-fly parallelization, dynamic re-partitioning and automatic coarse mesh generation. Within each subdomain the approach employs a variety reordering techniques so that relevant data are on the same page in memory permitting high-performance on cache-based processors. Details of the on-the-fly SFC based partitioning are presented as are construction rules for the automatic coarse mesh generation. After describing the approach, the paper uses model problems and 3- D configurations to both verify and validate the solver. The model problems demonstrate that second-order accuracy is maintained despite the presence of the irregular cut-cells in the mesh. In addition, it examines both parallel efficiency and convergence behavior. These investigations demonstrate a parallel speed-up in excess of 28 on 32 processors of an SGI Origin 2000 system and confirm that mesh partitioning has no effect on convergence behavior.

Aftosmis, M. J.↗

NASA NTRS1991

Approximate effect of parameter pseudonoise intensity on rate of convergence for EKF parameter estimators

When using parameter estimation methods based on extended Kalman filter (EKF) theory, it is common practice to assume that the unknown parameter values behave like a random process, such as a random walk, in order to guarantee their identifiability by the filter. The present work is the result of an ongoing effort to quantitatively describe the effect that the assumption of a fictitious noise (called pseudonoise) driving the unknown parameter values has on the parameter estimate convergence rate in filter-based parameter estimators. The initial approach is to examine a first-order system described by one state variable with one parameter to be estimated. The intent is to derive analytical results for this simple system that might offer insight into the effect of the pseudonoise assumption for more complex systems. Such results would make it possible to predict the estimator error convergence behavior as a function of the assumed pseudonoise intensity, and this leads to the natural application of the results to the design of filter-based parameter estimators. The results obtained show that the analytical description of the convergence behavior is very difficult.

Hill, Bryon K.↗

NASA NTRS2019

Weighted Least-Squares Cell-Average Gradient Construction Methods for the VULCAN-CFD Second-Order Accurate Unstructured-Grid Cell-Centered Finite-Volume Solver

White, Jeffery A.↗

NASA NTRS2008

An Initial Investigation of the Effects of Turbulence Models on the Convergence of the RK/Implicit Scheme

A three-stage Runge-Kutta (RK) scheme with multigrid and an implicit preconditioner has been shown to be an effective solver for the fluid dynamic equations. This scheme has been applied to both the compressible and essentially incompressible Reynolds-averaged Navier-Stokes (RANS) equations using the algebraic turbulence model of Baldwin and Lomax (BL). In this paper we focus on the convergence of the RK/implicit scheme when the effects of turbulence are represented by either the Spalart-Allmaras model or the Wilcox k-! model, which are frequently used models in practical fluid dynamic applications. Convergence behavior of the scheme with these turbulence models and the BL model are directly compared. For this initial investigation we solve the flow equations and the partial differential equations of the turbulence models indirectly coupled. With this approach we examine the convergence behavior of each system. Both point and line symmetric Gauss-Seidel are considered for approximating the inverse of the implicit operator of the flow solver. To solve the turbulence equations we use a diagonally dominant alternating direction implicit (DDADI) scheme. Computational results are presented for three airfoil flow cases and comparisons are made with experimental data. We demonstrate that the two-dimensional RANS equations and transport-type equations for turbulence modeling can be efficiently solved with an indirectly coupled algorithm that uses the RK/implicit scheme for the flow equations.

Swanson, R. C.↗

NASA NTRS2019

Efficient and Robust Weighted Least-Squares Cell-Average Gradient Construction Methods for the Simulation of Scramjet Flows

White, Jeffery A.↗

NASA NTRS1993

Convergence acceleration of implicit schemes in the presence of high aspect ratio grid cells

The performance of Navier-Stokes codes are influenced by several phenomena. For example, the robustness of the code may be compromised by the lack of grid resolution, by a need for more precise initial conditions or because all or part of the flowfield lies outside the flow regime in which the algorithm converges efficiently. A primary example of the latter effect is the presence of extended low Mach number and/or low Reynolds number regions which cause convergence deterioration of time marching algorithms. Recent research into this problem by several workers including the present authors has largely negated this difficulty through the introduction of time-derivative preconditioning. In the present paper, we employ the preconditioned algorithm to address convergence difficulties arising from sensitivity to grid stretching and high aspect ratio grid cells. Strong grid stretching is particularly characteristic of turbulent flow calculations where the grid must be refined very tightly in the dimension normal to the wall, without a similar refinement in the tangential direction. High aspect ratio grid cells also arise in problems that involve high aspect ratio domains such as combustor coolant channels. In both situations, the high aspect ratio cells can lead to extreme deterioration in convergence. It is the purpose of the present paper to address the reasons for this adverse response to grid stretching and to suggest methods for enhancing convergence under such circumstances. Numerical algorithms typically possess a maximum allowable or optimum value for the time step size, expressed in non-dimensional terms as a CFL number or vonNeumann number (VNN). In the presence of high aspect ratio cells, the smallest dimension of the grid cell controls the time step size causing it to be extremely small, which in turn results in the deterioration of convergence behavior. For explicit schemes, this time step limitation cannot be exceeded without violating stability restrictions of the scheme. On the other hand, for implicit schemes, which are typically unconditionally stable, there appears to be room for improvement through careful tailoring of the time step definition based on results of linear stability analyses. In the present paper, we focus on the central-differenced alternating direction implicit (ADI) scheme. The understanding garnered from this analyses can then be applied to other implicit schemes. In order to systematically study the effects of aspect ratio and the methods of mitigating the associated problems, we use a two pronged approach. We use stability analyses as a tool for predicting numerical convergence behavior and numerical experiments on simple model problems to verify predicted trends. Based on these analyses, we determine that efficient convergence may be obtained at all aspect ratios by getting a combination of things right. Primary among these are the proper definition of the time step size, proper selection of viscous preconditioner and the precise treatment of boundary conditions. These algorithmic improvements are then applied to a variety of test cases to demonstrate uniform convergence at all aspect ratios.

Buelow, B. E. O.↗

NASA NTRS2017

Geometrically Flexible and Efficient Flow Analysis of High Speed Vehicles Via Domain Decomposition, Part 1: Unstructured-Grid Solver for High Speed Flows

The ability to solve the equations governing the hypersonic turbulent flow of a real gas on unstructured grids using a spatially-elliptic, 2nd-order accurate, cell-centered, finite-volume method has been recently implemented in the VULCAN-CFD code. This paper describes the key numerical methods and techniques that were found to be required to robustly obtain accurate solutions to hypersonic flows on non-hex-dominant unstructured grids. The methods and techniques described include: an augmented stencil, weighted linear least squares, cell-average gradient method, a robust multidimensional cell-average gradient-limiter process that is consistent with the augmented stencil of the cell-average gradient method and a cell-face gradient method that contains a cell skewness sensitive damping term derived using hyperbolic diffusion based concepts. A data-parallel matrix-based symmetric Gauss-Seidel point-implicit scheme, used to solve the governing equations, is described and shown to be more robust and efficient than a matrix-free alternative. In addition, a y+ adaptive turbulent wall boundary condition methodology is presented. This boundary condition methodology is deigned to automatically switch between a solve-to-the-wall and a wall-matching-function boundary condition based on the local y+ of the 1st cell center off the wall. The aforementioned methods and techniques are then applied to a series of hypersonic and supersonic turbulent flat plate unit tests to examine the efficiency, robustness and convergence behavior of the implicit scheme and to determine the ability of the solve-to-the-wall and y+ adaptive turbulent wall boundary conditions to reproduce the turbulent law-of-the-wall. Finally, the thermally perfect, chemically frozen, Mach 7.8 turbulent flow of air through a scramjet flow-path is computed and compared with experimental data to demonstrate the robustness, accuracy and convergence behavior of the unstructured-grid solver for a realistic 3-D geometry on a non-hex-dominant grid.

White, Jeffery A.↗

NASA NTRS2018

Characterizing Material Scalability for Ultralight Lattice Design

Stiff yet ultra-light lattice structures constructed using digital materials have many practical applications as the building block for aircraft and other structures. By furthering our understanding of how material configuration affects the structural properties of an ultralight lattice, we can intelligently design these structures based on their intended function. Here we compare the behavior of ultralight lattice structures when fabricated by different materials. The individual unit cells of the lattice structures are referred to as voxels. The stiffness, elastic modulus, and yield strength of the specimens in compression and tension are determined through mechanical testing. Specimens are tested both as single voxel as well as 4x4x4 voxel constructions on an Instron 5982 Universal Testing System until failure. Each voxel is manufactured in bulk through injection molding, with a unit cell pitch of 76.2 mm. Individual voxels are fastened with machine screws and nuts to create assemblies. Four separate materials are used as voxel compositions in this experiment. These include a homogeneous polymer referred to as Ultem 1000, a glass-fiber reinforced polymer referred to as Ultem 2200, a polymer with chopped carbon fibers as 30% of its fill, and homogenous polypropylene. This work compares mechanical behavior, as well as the convergence behavior of the lattice as the size of the lattice assembly increases for various materials. The goal of this study is to characterize the behavior of homogenous lattices such that heterogenous lattices can be designed with different material voxels to achieve target material properties for ultralight space applications.

Sajjadi, Afsheen↗

NASA NTRS1981

Self-adaptive predictor-corrector algorithm for static nonlinear structural analysis

A multiphase selfadaptive predictor corrector type algorithm was developed. This algorithm enables the solution of highly nonlinear structural responses including kinematic, kinetic and material effects as well as pro/post buckling behavior. The strategy involves three main phases: (1) the use of a warpable hyperelliptic constraint surface which serves to upperbound dependent iterate excursions during successive incremental Newton Ramphson (INR) type iterations; (20 uses an energy constraint to scale the generation of successive iterates so as to maintain the appropriate form of local convergence behavior; (3) the use of quality of convergence checks which enable various self adaptive modifications of the algorithmic structure when necessary. The restructuring is achieved by tightening various conditioning parameters as well as switch to different algorithmic levels to improve the convergence process. The capabilities of the procedure to handle various types of static nonlinear structural behavior are illustrated.

Padovan, J.↗

NASA NTRSDate not supplied

Effect of Geometric Granularity on the Noise Signature of a Full-Scale Large Civil Transport Nose Landing Gear

Results from a comprehensive simulation campaign focused on characterizing the air-frame noise signature of a full-scale Boeing 777-300ER nose landing gear are presented. The as-flown, installed nose gear geometry was used to assess how accurately the selected computational methodology can predict far-field noise before extending the simulation approach to the complete B777-300ER aircraft in landing configuration. To facilitate direct comparisons with experimental data, the simulations were conducted for conditions matching those recorded for a flyby of the same aircraft over the ground-based phased microphone array used during the 2005 Quiet Technology Demonstrator II test. The far-field acoustic footprint of the nose landing gear was computed via a Ffowcs-Williams and Hawkings integral approach, with pressures on the model solid surface or flow quantities on a permeable data surface enclosing the gear used as input. A grid refinement study performed for the baseline gear con-figuration to establish the convergence behavior of the far-field spectrum indicated that the sound pressure levels had converged at frequencies slightly beyond 5 kHz for the finest spatial resolution attempted. To ascertain the effects of geometric granularity on far-field noise, simulations of a defeatured version of the nose gear were undertaken. Comparisons with fully-dressed gear results indicated that finer geometric details add 2–4 dB to the sound pressure levels at mid- to high-frequencies (800 Hz to 5 kHz), suggesting that for accurate noise prediction such details cannot be neglected.

airframe noise↗

NASA NTRS1980

Application of fully stressed design procedures to redundant and non-isotropic structures

An evaluation is presented of fully stressed design procedures for sizing highly redundant structures including structures made of composite materials. The evaluation is carried out by sizing three structures: a simple box beam of either composite or metal construction; a low aspect ratio titanium wing; and a titanium arrow wing for a conceptual supersonic cruise aircraft. All three structures are sized by ordinary fully-stressed design (FSD) and thermal fully stressed design (TFSD) for combined mechanical and thermal loads. Where possible, designs are checked by applying rigorous mathematical programming techniques to the structures. It is found that FSD and TFSD produce optimum designs for the metal box beam, but produce highly non-optimum designs for the composite box beam. Results from the delta wing and arrow wing indicate that FSD and TFSD exhibits slow convergence for highly redundant metal structures. Further, TFSD exhibits slow oscillatory convergence behavior for the arrow wing for very high temperatures. In all cases where FSD and TFSD perform poorly either in obtaining nonoptimum designs or in converging slowly, the assumptions on which the algorithms are based are grossly violated. The use of scaling, however, is found to be very effective in obtaining fast convergence and efficiently produces safe designs even for those cases when FSD and TFSD alone are ineffective.

Adelman, H. M.↗

NASA NTRSDate not supplied

Using the Dimensionality Reduction (DR) Approach to Treat Singular and Near-Singular Source and Test Integrals on Triangles for Moment Methods

Recently, the authors presented preliminary results of an initial study of a dimensional reduction scheme for treating (near-)singular integrals (D. R. Wilton et al., “Dimensionality Reduction Approach for Treating Singular and Near-Singular Multidimensional Integrals of Electromagnetics,” 2022 URSI USNC National Radio Science Meeting, Boulder, CO, Jan. 2022). The approach reported there refined and extended several ideas appearing in a recent paper (R. R. Chang, Z. Wang, and Q. Xie, "Fast Convergent Quadrature Method for Evaluating the RWG- and SWG-Related Convolutional Integrals," IEEE Trans. Antennas Propagat., 69, Dec. 2021). That paper reported a curated collection of important, previously published results all leading to very efficient and accurate line integral methods for handling the most common (near-)singular integrals associated with triangles and tetrahedrons with RWG and SWG bases, respectively. Our contributions provided a simpler exposition as well as a more unified, systematic, and robust overall framework for deriving and applying the approach. This presentation further elucidates our extensions to the approach and broadens our initial study to examine the convergence behaviors of the various potential forms over a wider range of triangular source element shape and observation point parameters for various smoothing transformations; we also examine convergence, not just at the subtriangle level, but also overcomplete triangles. In addition, we investigate the application of the recently reported “vertex function” concept to develop faster converging test integrals (Rivero et al., “Acceleration of the Surface Test Integral Using Vertex Functions,” 2021 IEEE Int’l Symp. Ant. Propagat. and USNC-URSI Rad. Sci. Meeting,” Singapore, 4-10 Dec. 2021). Combining these separate schemes has the potential for yielding a near-optimal approach for accurately evaluating singular and near-singular integrals for moment methods.

Singular Integrals↗

NASA NTRSDate not supplied

Aeroacoustic Computations of a Transonic Truss-Braced Wing Aircraft: Part 2 – Acoustic Signature and Noise Source Identification

High-fidelity, time-dependent simulations of a Boeing-designed, transonic, truss-braced-wing aircraft in cruise (clean) and landing configurations are leveraged to generate synthetic microphone-phased-array data for airframe noise prediction and assessment. These data sets are used to compute source localization (beamform) maps to determine the location and strength of primary and secondary airframe noise sources associated with this unique configuration. The synthetic phased-array implementation mimics the setup of a flight test. As this study is ongoing, preliminary integrated far-field spectra for the cruise configuration obtained at multiple spatial resolutions revealed significant tonal content that lacked convergence with increased resolution. The origin of several of these tones and their unusual convergence behavior was traced to the larger-than-normal trailing-edge thickness of the “as-tested” cruise model being simulated. Reducing the trailing-edge thickness to more realistic values eliminated most of the tones at low to moderate frequencies and improved spectrum convergence significantly. Applying lessons learned from the cruise simulations, several modifications to the geometry of the landing configuration were made and are described in this work. Results from permeable and solid Ffowcs-Williams and Hawkings surfaces at two different spatial resolutions (coarse and medium) are used to illustrate the major noise sources and determine convergence of the CLEAN integrated noise levels for the entire aircraft as well as major subcomponents. We demonstrate that the low-frequency content of the far-field spectrum is dominated by noise generated from the main landing gear, while the medium- and high-frequency content is dominated by the wing-leading-edge Krueger flaps. Since analysis of the acoustic maps for the landing configuration revealed several clusters of multiple sources along the wing leading edge, “high resolution” processing of the array data was used to distinguish more accurately the locations of sources.

Transonic Truss-Braced Wing↗

NASA NTRS2011

A Universal Tare Load Prediction Algorithm for Strain-Gage Balance Calibration Data Analysis

An algorithm is discussed that may be used to estimate tare loads of wind tunnel strain-gage balance calibration data. The algorithm was originally developed by R. Galway of IAR/NRC Canada and has been described in the literature for the iterative analysis technique. Basic ideas of Galway's algorithm, however, are universally applicable and work for both the iterative and the non-iterative analysis technique. A recent modification of Galway's algorithm is presented that improves the convergence behavior of the tare load prediction process if it is used in combination with the non-iterative analysis technique. The modified algorithm allows an analyst to use an alternate method for the calculation of intermediate non-linear tare load estimates whenever Galway's original approach does not lead to a convergence of the tare load iterations. It is also shown in detail how Galway's algorithm may be applied to the non-iterative analysis technique. Hand load data from the calibration of a six-component force balance is used to illustrate the application of the original and modified tare load prediction method. During the analysis of the data both the iterative and the non-iterative analysis technique were applied. Overall, predicted tare loads for combinations of the two tare load prediction methods and the two balance data analysis techniques showed excellent agreement as long as the tare load iterations converged. The modified algorithm, however, appears to have an advantage over the original algorithm when absolute voltage measurements of gage outputs are processed using the non-iterative analysis technique. In these situations only the modified algorithm converged because it uses an exact solution of the intermediate non-linear tare load estimate for the tare load iteration.

balance calibration analysis↗

NASA NTRS2018

Convergence Analysis of Turbulent Flow Solutions

Data from the "Turbulence Modeling Resource" website for turbulent flow over an NACA-0012 airfoil is analyzed to determine the convergence behavior of three second-order CFD (Computational Fluid Dynamics) codes: CFL3D (Computational Fluids Lab 3 Dimensional flow solver), FUN3D (Fully Unstructured Navier-stokes flow solver), and TAU (German Aerospace Center (DLR) 2 dimensional code for unstructured hybrid grids solving the Reynolds-Averaged Navier-Stokes equations or the Euler equations). The convergence of both integrated properties and pointwise data are examined. Several different methods for estimating errors and computing convergence rates are compared. A high-order extension to the Richardson extrapolation is developed that improves the accuracy of the mesh limit values and provides a quantitative estimate of the threshold of the asymptotic regime. The coefficient of total drag exhibits second-order convergence for all three codes, and convergence is monotone over a sequence of 7 grids. Other force coefficients are not so well behaved. The convergence rates of the viscous component of drag on the three nest grids ranges from 3:0 for CFL3D to 1:0 for FUN3D. The three codes are converging to similar but not identical solutions. The largest differences between the codes are in the coefficient of lift for which the difference between CFL3D and FUN3D is greater than 10 (sup minus 4). The best agreement occurs in the viscous component of drag, which is the only force component for which all three codes are converging towards each other at a rate of second-order. The agreement between the two unstructured grid codes is good with all properties except lift converging towards common values at a rate of second-order. No one code was universally better than the other. The TAU code has the lowest error in total drag, FUN3D has the lowest error in lift, and CFL3D has the lowest error in the viscous component of drag.

Atkins, Harold L.↗