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At least 1,729 records · Page 96
All sourcesNASA NTRSDOE OSTI
NASA NTRS1972

Viscel: A general purpose computer program for analysis of linear viscoelastic structures, volume 2

The VISCEL program is a general purpose computer program developed for equilibrium analysis of linear viscoelastic structures. The program is written in FORTRAN 5 language to operate on the Univac 1108 computer under the EXEC 8 operating system. The program, an extension of the linear equilibrium problem solver ELAS, is an updated and extended version of its earlier form written for the IBM 7094 computer. Finite element matrix displacement approach coupled with the synchronized material property concept, utilizing incremental time steps, was adopted for the solution presented. The step-by-step procedure involves solution of recursive equations in the time domain, which takes into account the memory of material properties. Incremental and accumulative displacements and stresses are obtained at the end of each time step. In order to minimize the extent of computations resulting from accumulative effects of material memory, the program provides an option which enables the employment of constant time steps in the logarithmic scale. Program documentation is presented.

Gupta, K. K.↗
NASA NTRS1986

Resistive ballooning modes in line-tied coronal arcades

The equations describing the linear evolution of resistive ballooning modes are obtained by using a modified WKB expansion in the short perpendicular wavelength, while variations of the perturbations along the field are described by a slowly varying amplitude, on which the tying boundary conditions are imposed. In general, given an equilibrium, there are certain ranges of magnetic surfaces for which the system predicts instability even without dissipation. The main conclusion is that within the resistive MHD approximation cylindrically symmetric arcades with pressure falling with radius are unstable to resistive localized modes; the growth rates, close to ideal marginal stability, are large, so that it would appear that energy could be released during 10 to 100 Alfven times. The wavelength of the modes is expected to be limited by the ion gyroradius, when stabilizing drift effects must be taken into account. The nonlinear evolution of resistive ballooning modes should be studied to assess their overall relevance to the violent and rapidly evolving phenomena observed on the sun.

Velli, Marco↗
NASA NTRS1987

Application of a sensitivity analysis technique to high-order digital flight control systems

A sensitivity analysis technique for multiloop flight control systems is studied. This technique uses the scaled singular values of the return difference matrix as a measure of the relative stability of a control system. It then uses the gradients of these singular values with respect to system and controller parameters to judge sensitivity. The sensitivity analysis technique is first reviewed; then it is extended to include digital systems, through the derivation of singular-value gradient equations. Gradients with respect to parameters which do not appear explicitly as control-system matrix elements are also derived, so that high-order systems can be studied. A complete review of the integrated technique is given by way of a simple example: the inverted pendulum problem. The technique is then demonstrated on the X-29 control laws. Results show linear models of real systems can be analyzed by this sensitivity technique, if it is applied with care. A computer program called SVA was written to accomplish the singular-value sensitivity analysis techniques. Thus computational methods and considerations form an integral part of many of the discussions. A user's guide to the program is included. The SVA is a fully public domain program, running on the NASA/Dryden Elxsi computer.

Paduano, James D.↗
NASA NTRS1994

Two-layer viscous instability in a rotating couette device

A novel experiment to study the interfacial shear instability between two liquids is described. Density-matched immiscible liquids are confined between concentric cylinders such that the interface is parallel to the cylinder walls. Interfacial waves that develop because of viscosity differences between the shearing fluids are studied as a function of rotation rate and depth ratio using optical techniques. Conditions neutral stability and the most unstable wavenumber agree reasonably well with predictions from linear stability analysis of the Navier-Stokes equations. Illumination using laser sheets allows precise measurement of the interface shape. Future experiments will verify the correctness of weakly nonlinear theories that describe energy transfer and saturation of wave growth by nonlinear effects. Measurements of solitary wave shapes, that occur far above neutral stability, will be compared to similar measurements for systems that have gravity as an important force to determine how gravity effects large disturbances. These results will be used to interpret slug and annular flow data that have been obtained in other mu g studies.

Gallagher, Christopher↗
NASA NTRS2018

Fuzzy Modeling and Parallel Distributed Compensation for Aircraft Flight Control from Simulated Flight Data

A method is described that combines fuzzy system identification techniques with Parallel Distributed Compensation (PDC) to develop nonlinear control methods for aircraft using minimal a priori knowledge, as part of NASA’s Learn-to-Fly initiative. A fuzzy model was generated with simulated flight data, and consisted of a weighted average of multiple linear time invariant state-space cells having parameters estimated using the equation-error approach and a least-squares estimator. A compensator was designed for each subsystem using Linear Matrix Inequalities (LMI) to guarantee closed-loop stability and performance requirements. This approach is demonstrated using simulated flight data to automatically develop a fuzzy model and design control laws for a simplified longitudinal approximation of the F-16 nonlinear flight dynamics simulation. Results include a comparison of flight data with the estimated fuzzy models and simulations that illustrate the feasibility and utility of the combined fuzzy modeling and control approach.

Weinstein, Rose↗
DOE OSTI2026

A Scalable Reduced‐Order Model for the Steady Navier–Stokes Equations

Scaling up new scientific technologies from laboratory to industry often involves demonstrating performance on a larger scale. Computer simulations can accelerate design and predictions in the deployment process, though traditional numerical methods are computationally intractable even for intermediate pilot plant scales. Recently, the component reduced order modeling method has been developed to tackle this challenge by combining projection reduced order modeling and discontinuous Galerkin domain decomposition. However, while many scientific or engineering applications involve nonlinear physics, this method has only been demonstrated for various linear systems. In this work, the component reduced order modeling method is extended to steady Navier–Stokes flow, with application to general nonlinear physics in view. The large‐scale, global domain is decomposed into a combination of small‐scale unit component. Linear subspaces for flow velocity and pressure are identified via proper orthogonal decomposition over sample snapshots collected from each small‐scale unit component. Velocity bases are augmented with a pressure supremizer to satisfy the inf–sup condition for stable pressure prediction. Two different nonlinear reduced order modeling methods are employed and compared for efficient evaluation of nonlinear advection: A third‐order tensor projection operator and the empirical quadrature procedure. The proposed method is demonstrated on the flow over arrays of five different unit objects, achieving a 23‐fold speedup with less than 4% relative error in domains up to 256 times larger than the unit components. Furthermore, a numerical experiment with the pressure supremizer strongly indicates the need for a supremizer for stable pressure prediction. A comparison between the tensorial approach and the empirical quadrature procedure revealed a slight advantage of the empirical quadrature procedure. The framework is compared with an alternating Schwarz‐based reduced‐order approach, demonstrating improved efficiency and robustness for the DG‐based global solver while retaining flexibility for sub‐scale iterative solvers. The method is further extended to a coupled advection–diffusion and Navier–Stokes system, illustrating its applicability to multi‐physics problems and its potential for more general, inter‐coupled nonlinear systems.

42 ENGINEERING↗
DOE OSTI2023

Anticipating gelation and vitrification with medium amplitude parallel superposition (MAPS) rheology and artificial neural networks

Abstract Anticipating qualitative changes in the rheological response of complex fluids (e.g., a gelation or vitrification transition) is an important capability for processing operations that utilize such materials in real-world environments. One class of complex fluids that exhibits distinct rheological states are soft glassy materials such as colloidal gels and clay dispersions, which can be well characterized by the soft glassy rheology (SGR) model. We first solve the model equations for the time-dependent, weakly nonlinear response of the SGR model. With this analytical solution, we show that the weak nonlinearities measured via medium amplitude parallel superposition (MAPS) rheology can be used to anticipate the rheological aging transitions in the linear response of soft glassy materials. This is a rheological version of a technique called structural health monitoring used widely in civil and aerospace engineering. We design and train artificial neural networks (ANNs) that are capable of quickly inferring the parameters of the SGR model from the results of sequential MAPS experiments. The combination of these data-rich experiments and machine learning tools to provide a surrogate for computationally expensive viscoelastic constitutive equations allows for rapid experimental characterization of the rheological state of soft glassy materials. We apply this technique to an aging dispersion of Laponite ® clay particles approaching the gel point and demonstrate that a trained ANN can provide real-time detection of transitions in the nonlinear response well in advance of incipient changes in the linear viscoelastic response of the system.

Lennon, Kyle R. (ORCID:0000000212515461)↗
DOE OSTI2020

Learning and meta-learning of stochastic advection–diffusion–reaction systems from sparse measurements

Physics-informed neural networks (PINNs) were recently proposed in [18] as an alternative way to solve partial differential equations (PDEs). A neural network (NN) represents the solution, while a PDE-induced NN is coupled to the solution NN, and all differential operators are treated using automatic differentiation. Here, we first employ the standard PINN and a stochastic version, sPINN, to solve forward and inverse problems governed by a non-linear advection–diffusion–reaction (ADR) equation, assuming we have some sparse measurements of the concentration field at random or pre-selected locations. Subsequently, we attempt to optimise the hyper-parameters of sPINN by using the Bayesian optimisation method (meta-learning) and compare the results with the empirically selected hyper-parameters of sPINN. In particular, for the first part in solving the inverse deterministic ADR, we assume that we only have a few high-fidelity measurements, whereas the rest of the data is of lower fidelity. Hence, the PINN is trained using a composite multi-fidelity network, first introduced in [12], that learns the correlations between the multi-fidelity data and predicts the unknown values of diffusivity, transport velocity and two reaction constants as well as the concentration field. For the stochastic ADR, we employ a Karhunen–Loève (KL) expansion to represent the stochastic diffusivity, and arbitrary polynomial chaos (aPC) to represent the stochastic solution. Correspondingly, we design multiple NNs to represent the mean of the solution and learn each aPC mode separately, whereas we employ a separate NN to represent the mean of diffusivity and another NN to learn all modes of the KL expansion. For the inverse problem, in addition to stochastic diffusivity and concentration fields, we also aim to obtain the (unknown) deterministic values of transport velocity and reaction constants. The available data correspond to 7spatial points for the diffusivity and 20 space–time points for the solution, both sampled 2000 times. We obtain good accuracy for the deterministic parameters of the order of 1–2% and excellent accuracy for the mean and variance of the stochastic fields, better than three digits of accuracy. In the second part, we consider the previous stochastic inverse problem, and we use Bayesian optimisation to find five hyper-parameters of sPINN, namely the width, depth and learning rate of two NNs for learning the modes. Here, we obtain much deeper and wider optimal NNs compared to the manual tuning, leading to even better accuracy, i.e., errors less than 1% for the deterministic values, and about an order of magnitude less for the stochastic fields.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1971

On propagation of long waves in curved ducts.

Propagation of waves in curved ducts and pipes belong to the class of motion which is characterized by wave patterns totally different from those known in straight ducts or in unlimited space. The curvilinear boundaries are responsible for the appearance of a continuous standing radial wave which in turn affects the transmitted tangential waves. The purpose of this paper is to solve the problem of propagation of long acoustic waves in slightly and sharply bent ducts. This problem has been only partially analyzed by various authors. In this study two acoustic systems are considered which allow determination of the basic modes of motion and describe the transition and distortion of plane waves as they propagate down the curved channel. A detailed study of the behavior of waves in junctions between straight and curved ducts is also given. Solutions and expressions for principal modes of the wave are obtained by using the linearized equation of motion solved for its characteristic values. This original approach required a novel use of Bessel functions to determine the characteristic values of the steady and the decaying fields of motion.

Rostafinski, W.↗
NASA NTRS1975

Diagonalization and simultaneous symmetrization of the gas-dynamic matrices

The hyperbolic nature of the unsteady, inviscid, gas-dynamic equations implies the existence of a similarity transformation for diagonalizing an arbitrary linear combination of coefficient matrices. It is shown that the individual matrices are simultaneously symmetrized by the similarity transformation. The transformations and their norms can be applied to the well-posedness of the Cauchy problem, linear stability theory for finite-difference approximations, and simplification of block-tridiagonal systems that arise in implicit time-split algorithms.

Warming, R. F.↗
NASA NTRS1982

Methods of sequential estimation for determining initial data in numerical weather prediction

Numerical weather prediction (NWP) is an initial-value problem for a system of nonlinear differential equations, in which initial values are known incompletely and inaccurately. Observational data available at the initial time must therefore be supplemented by data available prior to the initial time, a problem known as meteorological data assimilation. A further complication in NWP is that solutions of the governing equations evolve on two different time scales, a fast one and a slow one, whereas fast scale motions in the atmosphere are not reliably observed. This leads to the so called initialization problem: initial values must be constrained to result in a slowly evolving forecast. The theory of estimation of stochastic dynamic systems provides a natural approach to such problems. For linear stochastic dynamic models, the Kalman-Bucy (KB) sequential filter is the optimal data assimilation method, for linear models, the optimal combined data assimilation-initialization method is a modified version of the KB filter.

Cohn, S. E.↗
NASA NTRS1988

Interface crack in a nonhomogeneous elastic medium

The linear elasticity problem for an interface crack between two bonded half planes is reconsidered. It is assumed that one of the half planes is homogeneous and the second is nonhomogeneous in such a way that the elastic properties are continuous throughout the plane and have discontinuous derivatives along the interface. The problem is formulated in terms of a system of integral equations and the asymptotic behavior of the stress state near the crack tip is determined. The results lead to the conclusion that the singular behavior of stresses in the nonhomogeneous medium is identical to that in a homogeneous material provided the spacial distribution of material properties is continuous near and at the crack tip. The problem is solved for various values of the nonhomogeneity parameter and for four different sets of crack surface tractions, and the corresponding stress intensity factors are tabulated.

Delale, F.↗
NASA NTRS1989

Stability and dynamic analysis of a slender column with curved longitudinal stiffeners

The results of a stability design study are presented for a slender column with curved longitudinal stiffeners for large space structure applications. Linear stability analyses are performed using a link-plate representation of the stiffeners to determine stiffener local buckling stresses. Results from a set of parametric analyses are used to determine an approximate explicit expression for stiffener local buckling in terms of its geometric parameters. This expression along with other equations governing column stability and mass are assembled into a determinate system describing minimum mass stiffened column design. An iterative solution is determined to solve this system and a computer program incorporating this routine is presented. Example design problems are presented which verify the solution accuracy and illustrate the implementation of the solution routine. Also, observations are made which lead to a greatly simplified first iteration design equation relating the percent increase in column mass to the percent increase in column buckling load. From this, generalizations are drawn as to the mass savings offered by the stiffened column concept. Finally, the percent increase in fundamental column vibration frequency due to the addition of deployable stiffeners is studied.

Lake, Mark S.↗
NASA NTRS1992

A comparison of lidar inversion methods for cirrus applications

Several methods for inverting the lidar equation are suggested as means to derive the cirrus optical properties (beta backscatter, alpha extinction coefficients, and delta optical depth) at one wavelength. The lidar equation can be inverted in a linear or logarithmic form; either solution assumes a linear relationship: beta = kappa(alpha), where kappa is the lidar ratio. A number of problems prevent us from calculating alpha (or beta) with a good accuracy. Some of these are as follows: (1) the multiple scattering effect (most authors neglect it); (2) an absolute calibration of the lidar system (difficult and sometimes not possible); (3) lack of accuracy on the lidar ratio k (taken as constant, but in fact it varies with range and cloud species); and (4) the determination of boundary condition for logarithmic solution which depends on signal to noise ration (SNR) at cloud top. An inversion in a linear form needs an absolute calibration of the system. In practice one uses molecular backscattering below the cloud to calibrate the system. This method is not permanent because the lower atmosphere turbidity is variable. For a logarithmic solution, a reference extinction coefficient (alpha(sub f)) at cloud top is required. Several methods to determine alpha(sub f) were suggested. We tested these methods at low SNR. This led us to propose two new methods referenced as S1 and S2.

Elouragini, Salem↗
NASA NTRS2004

Variable Step Integration Coupled with the Method of Characteristics Solution for Water-Hammer Analysis, A Case Study

One-dimensional water-hammer modeling involves the solution of two coupled non-linear hyperbolic partial differential equations (PDEs). These equations result from applying the principles of conservation of mass and momentum to flow through a pipe, and usually the assumption that the speed at which pressure waves propagate through the pipe is constant. In order to solve these equations for the interested quantities (i.e. pressures and flow rates), they must first be converted to a system of ordinary differential equations (ODEs) by either approximating the spatial derivative terms with numerical techniques or using the Method of Characteristics (MOC). The MOC approach is ideal in that no numerical approximation errors are introduced in converting the original system of PDEs into an equivalent system of ODEs. Unfortunately this resulting system of ODEs is bound by a time step constraint so that when integrating the equations the solution can only be obtained at fixed time intervals. If the fluid system to be modeled also contains dynamic components (i.e. components that are best modeled by a system of ODEs), it may be necessary to take extremely small time steps during certain points of the model simulation in order to achieve stability and/or accuracy in the solution. Coupled together, the fixed time step constraint invoked by the MOC, and the occasional need for extremely small time steps in order to obtain stability and/or accuracy, can greatly increase simulation run times. As one solution to this problem, a method for combining variable step integration (VSI) algorithms with the MOC was developed for modeling water-hammer in systems with highly dynamic components. A case study is presented in which reverse flow through a dual-flapper check valve introduces a water-hammer event. The predicted pressure responses upstream of the check-valve are compared with test data.

Turpin, Jason B.↗
DOE OSTI2026

Linear-Scaling Asymmetric Triples Correction through the Solution of the DLPNO–CCSD Lambda Equations: DLPNO–CCSD(T) Λ

In this research, we derive equations for solving for the stationary points of the DLPNO–CCSD Lagrangian, in the t 1 -transformed formalism introduced earlier and as currently implemented in the P SI 4 quantum chemistry software package. These lambda equations in the local pair natural orbital basis allow for the evaluation of CCSD(T) Λ energetics with linear-scaling computational effort, also known as the asymmetric triples correction. This DLPNO–CCSD(T) Λ method allows for accurate triples contributions to be computed for larger molecules, especially in cases that CCSD(T) is known to be insufficient, such as with multireference systems and bond-breaking systems. We showcase the accuracy of our code on reaction energies, barrier heights, and noncovalent interaction energies. Also showcased are the capabilities of our code by evaluating DLPNO–CCSD(T) Λ energetics on large noncovalent dimers up to 112 atoms, as well as a rhodium catalyst complex containing 66 atoms.

Cluster chemistry↗
DOE OSTI2023

Large-scale molecular dynamics simulations of bubble collapse in water: Effects of system size, water model, and nitrogen

Molecular dynamics simulations in the microcanonical ensemble are performed to study the collapse of a bubble in liquid water using the single-site mW and the four-site TIP4P/2005 water models. To study system size effects, simulations for pure water systems are performed using periodically replicated simulation boxes with linear dimensions, L, ranging from 32 to 512 nm with the largest systems containing 8.7 × 10 6 and 4.5 × 10 9 molecules for the TIP4P/2005 and mW water models, respectively. The computationally more efficient mW water model allows us to reach converging behavior when the bubble dynamics results are plotted in reduced units, and the limiting behavior can be obtained through linear extrapolation in L –1 . Qualitative differences are observed between simulations with the mW and TIP4P/2005 water models, but they can be explained by the models’ differences in predicted viscosity and surface tension. Although bubble collapse occurs on time scales of only hundreds of picoseconds, the system sizes used here are sufficiently large to obtain bubble dynamics consistent with the Rayleigh–Plesset equation when using the models’ thermophysical properties as input. For the conditions explored here, extreme heating of the interfacial water molecules near the time of collapse is observed for the larger mW water systems (but the model underpredicts the viscosity), whereas heating is less pronounced for the TIP4P/2005 water systems because its larger viscosity contribution slows the collapse dynamics. The presence of nitrogen within the bubble only starts to affect bubble dynamics near the very end of the initial collapse, leading to an incomplete collapse and strong rebound for the mW water model. Although nitrogen is non-condensable at 300 K, it becomes highly compressed and reaches a liquid-like density near the collapse point. We find that the dissolution of nitrogen is much slower than the movement of the collapsing water front, and the re-expansion of the dense nitrogen droplet gives rise to bubble rebound. The incompatibility of the collapse and dissolution time scales should be considered for continuum-scale modeling of bubble dynamics. Finally, we also confirm that the diffusion coefficient for dissolved nitrogen is insensitive to pressure as the liquid transitions from a compressed to a stretched state.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗