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At least 1,297 records · Page 72

Development of a Filtered CFD-DEM Drag Model with Multiscale Markers Using an Artificial Neural Network and Nonlinear Regression

Here, the accuracy of coarse-grained Euler-Lagrangian simulations of fluidized beds heavily depends on the mesoscale drag models to account for the influences of the unresolved sub-grid structures. Traditional filtered drag models are regressed with mesoscale markers such as voidage and slip velocities. In this research, a filtered drag was regressed with both mesoscale and macro-scale markers using fine grid Computational Fluid Dynamics - Discrete Element Method (CFD-DEM) simulations. The traditional non-linear regression method was compared with machine learning regression using an Artificial Neural Network (ANN) implemented in PyTorch and coupled with MFiX. The new drag showed higher accuracy than the Wen-Yu drag and another filtered drag derived from the two-fluid model. The nonlinear regression shows slightly better results than ANN regression in cases with similar R 2 values. The utilization of the gas inlet velocity as an additional macro-scale marker reduced the errors by up to 55.3% in the tested cases.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Three-Dimensional High Fidelity Progressive Failure Damage Modeling of NCF Composites

Performance prediction of off-axis laminates is of significant interest in designing composite structures for energy absorption. Phenomenological models available in most of the commercial programs, where the fiber and resin properties are smeared, are very efficient for large scale structural analysis, but lack the ability to model the complex nonlinear behavior of the resin and fail to capture the complex load transfer mechanisms between the fiber and the resin matrix. On the other hand, high fidelity mesoscale models, where the fiber tows and matrix regions are explicitly modeled, have the ability to account for the complex behavior in each of the constituents of the composite. However, creating a finite element model of a larger scale composite component could be very time consuming and computationally very expensive. In the present study, a three-dimensional mesoscale model of non-crimp composite laminates was developed for various laminate schemes. The resin material was modeled as an elastic-plastic material with nonlinear hardening. The fiber tows were modeled with an orthotropic material model with brittle failure. In parallel, new stress based failure criteria combined with several damage evolution laws for matrix stresses were proposed for a phenomenological model. The results from both the mesoscale and phenomenological models were compared with the experiments for a variety of off-axis laminates.

Aitharaju, Venkat↗

Application of the MAT 213 Composite Impact Model to NASA Problems of Interest

A material model has been developed which incorporates several key capabilities which have been identified as lacking in currently available composite impact models. The material model utilizes experimentally based tabulated input to define the evolution of plasticity and damage as opposed to specifying discrete input parameters (such as modulus and strength). The material model has been implemented into LS-DYNA® as MAT 213. The model can simulate the nonlinear deformation, damage and failure that takes place in a composite under dynamic loading conditions. The deformation model utilizes an orthotropic plasticity formulation. For the damage model, the nonlinear unloading response that is observed prior to the point where the peak stress is reached can be simulated, as well as the stress degradation response that occurs after the peak stress is reached. A variety of failure models, including a generalized tabulated failure model which facilitates the utilization of general failure surfaces, have been implemented into MAT 213. Recent studies at NASA have concentrated on using MAT 213 to analyze both the impact and crush response of a variety of laminated and textile architectures. Several of these studies will be discussed in the presented paper. For example, a woven carbon/Kevlar composite is currently being examined for use in an energy absorber system for rotorcraft structures. MAT 213 analyses have been conducted to examine the ability of the model to accurately simulate the dynamic crush response of this material. Studies are also being conducted to examine the ability of MAT 213 to simulate the ballistic impact response of representative laminated and woven thermoplastic and thermoset matrix composites. NASA efforts are also concentrated on developing methods and processes for improving characterization methods and developing “best practices” for using MAT 213, a summary of which will be discussed in the paper.

Polymer Matrix Composites↗

Bayesian learning with Gaussian processes for low-dimensional representations of time-dependent nonlinear systems

This work presents a data-driven method for learning low-dimensional time-dependent physics-based surrogate models whose predictions are endowed with uncertainty estimates. We use the operator inference approach to model reduction that poses the problem of learning low-dimensional model terms as a regression of state space data and corresponding time derivatives by minimizing the residual of reduced system equations. Standard operator inference models perform well with accurate training data that are dense in time, but producing stable and accurate models when the state data are noisy and/or sparse in time remains a challenge. Another challenge is the lack of uncertainty estimation for the predictions from the operator inference models. Our approach addresses these challenges by incorporating Gaussian process surrogates into the operator inference framework to (1) probabilistically describe uncertainties in the state predictions and (2) procure analytical time derivative estimates with quantified uncertainties. The formulation leads to a generalized least-squares regression and, ultimately, reduced-order models that are described probabilistically with a closed-form expression for the posterior distribution of the operators. The resulting probabilistic surrogate model propagates uncertainties from the observed state data to reduced-order predictions. Furthermore, we demonstrate the method is effective for constructing low-dimensional models of two nonlinear partial differential equations representing a compressible flow and a nonlinear diffusion–reaction process, as well as for estimating the parameters of a low-dimensional system of nonlinear ordinary differential equations representing compartmental models in epidemiology.

Data-driven model reduction↗

Detecting and disentangling nonlinear structure from solar flux time series

Interest in solar activity has grown in the past two decades for many reasons. Most importantly for flight dynamics, solar activity changes the atmospheric density, which has important implications for spacecraft trajectory and lifetime prediction. Building upon the previously developed Rayleigh-Benard nonlinear dynamic solar model, which exhibits many dynamic behaviors observed in the Sun, this work introduces new chaotic solar forecasting techniques. Our attempt to use recently developed nonlinear chaotic techniques to model and forecast solar activity has uncovered highly entangled dynamics. Numerical techniques for decoupling additive and multiplicative white noise from deterministic dynamics and examines falloff of the power spectra at high frequencies as a possible means of distinguishing deterministic chaos from noise than spectrally white or colored are presented. The power spectral techniques presented are less cumbersome than current methods for identifying deterministic chaos, which require more computationally intensive calculations, such as those involving Lyapunov exponents and attractor dimension.

Ashrafi, S.↗

Nonlinear Visco-Elastic Response of Composites via Micro-Mechanical Models

Micro-mechanical models for a study of nonlinear visco-elastic response of composite laminae are developed and their performance compared. A single integral constitutive law proposed by Schapery and subsequently generalized to multi-axial states of stress is utilized in the study for the matrix material. This is used in conjunction with a computationally facile scheme in which hereditary strains are computed using a recursive relation suggested by Henriksen. Composite response is studied using two competing micro-models, viz. a simplified Square Cell Model (SSCM) and a Finite Element based self-consistent Cylindrical Model (FECM). The algorithm is developed assuming that the material response computations are carried out in a module attached to a general purpose finite element program used for composite structural analysis. It is shown that the SSCM as used in investigations of material nonlinearity can involve significant errors in the prediction of transverse Young's modulus and shear modulus. The errors in the elastic strains thus predicted are of the same order of magnitude as the creep strains accruing due to visco-elasticity. The FECM on the other hand does appear to perform better both in the prediction of elastic constants and the study of creep response.

Gates, Thomas S.↗

Development of a Control Co-Design Modeling Tool for Marine Hydrokinetic Turbines: Preprint

This report describes the ongoing and planned development of the software package CT-Opt (Current/Tidal Optimization), a control co-design modeling tool for marine hydrokinetic turbines. The commercialization of these turbines has faced significant challenges due to the complex, multidisciplinary nature of their design and the extreme environmental conditions of their operation. This project aims to create a modeling tool that will enable the efficient design of robust, cost-competitive hydrokinetic turbine systems. Rather than using traditional optimization methods, CT-Opt combines multiple models across a range of fidelities to enable coupled optimization of the system design and system controller via a control co-design approach. With this method, the parameters that affect system performance are considered more comprehensively at every stage of the design process. The lowest-fidelity, frequency-domain model called by CT-Opt is RAFT (Response Amplitudes of Floating Turbines), which was originally developed by the National Renewable Energy Laboratory (NREL) to model response amplitudes of floating offshore wind turbines. The highest-fidelity, time-domain model is OpenFAST, which was developed by NREL for land-based and offshore wind turbines. As part of the CT-Opt project, new functionalities will be added to RAFT and OpenFAST to enable the accurate simulation of fixed and floating marine hydrokinetic turbines. In addition to expanding the capabilities of RAFT and OpenFAST, new midfidelity models will be developed. These models will be based on RAFT and OpenFAST and will consist of linearized, state-space models derived from the fully coupled, nonlinear OpenFAST equations and derivative function surrogate models that approximate the nonlinear system behavior. Each model will be coupled with controllers to allow control co-design methods to be applied both within models and across fidelity levels, enabling efficient system optimization.

control co-design↗

Learning thermodynamic master equations for open quantum systems

The characterization of Hamiltonians and other components of open quantum dynamical systems plays a crucial role in quantum computing and other applications. Scientific machine learning techniques have been applied to this problem in a variety of ways, including by modeling with deep neural networks. However, the majority of mathematical models describing open quantum systems are linear, and the natural nonlinearities in learnable models have not been incorporated using physical principles. We present a data-driven model for open quantum systems that includes learnable, thermodynamically consistent terms. The trained model is interpretable, as it directly estimates the system Hamiltonian and linear components of coupling to the environment. We validate the model on synthetic two and three-level data, as well as experimental two-level data collected from a quantum device at Lawrence Livermore National Laboratory.

Mathematics and Computing↗

Integrated Control Modeling for Propulsion Systems Using NPSS

The Numerical Propulsion System Simulation (NPSS), an advanced engineering simulation environment used to design and analyze aircraft engines, has been enhanced by integrating control development tools into it. One of these tools is a generic controller interface that allows NPSS to communicate with control development software environments such as MATLAB and EASY5. The other tool is a linear model generator (LMG) that gives NPSS the ability to generate linear, time-invariant state-space models. Integrating these tools into NPSS enables it to be used for control system development. This paper will discuss the development and integration of these tools into NPSS. In addition, it will show a comparison of transient model results of a generic, dual-spool, military-type engine model that has been implemented in NPSS and Simulink. It will also show the linear model generator s ability to approximate the dynamics of a nonlinear NPSS engine model.

Parker, Khary I.↗

Additional Degree of Freedom for WEC Model

'Additional Degree of Freedom for WEC' - WEC-Sim numerical model from RFTS 1 TEAMER project. An increase in wave energy converter (WEC) efficiency requires not only consideration of the nonlinear effects in the WEC dynamics and the power take-off (PTO) mechanisms, but also more integrated treatment of the whole system, i.e., the buoy dynamics, the PTO system, and the control strategy. It results in an optimization formulation that has a nonquadratic and nonstandard cost functional. This model presents the application of real-time nonlinear model predictive controller (NMPC) to two degrees of freedom point absorber type WEC with highly nonlinear PTO characteristics. The nonlinear effects, such as the fluid viscous drag, are also included in the plant dynamics. The controller may be implemented on a real-time target machine, and the WEC device is emulated in real-time using the WECSIM toolbox. Please see the ‘ReadMe’ within the root directory for an explanation of how to set-up and run the model. An article covering the development of this model is attached as "Real-Time Nonlinear Model Predictive Controller for Multiple Degrees of Freedom Wave Energy Converters with Non-Ideal Power Take-Off"

16 TIDAL AND WAVE POWER↗

Recent Turbulence Model Advances Applied to Multielement Airfoil Computations

A one-equation linear turbulence model and a two-equation nonlinear explicit algebraic stress model (EASM) are applied to the flow over a multielement airfoil. The effect of the K-epsilon and K-omega forms of the two-equation model are explored, and the K-epsilon form is shown to be deficient in the wall-bounded regions of adverse pressure gradient flows. A new K-omega form of EASM is introduced. Nonlinear terms present in EASM are shown to improve predictions of turbulent shear stress behind the trailing edge of the main element and near midflap. Curvature corrections are applied to both the one- and two-equation turbulence models and yield only relatively small local differences in the flap region, where the flow field undergoes the greatest curvature. Predictions of maximum lift are essentially unaffected by the turbulence model variations studied.

Rumsey, Christopher L.↗

A Nonlinear Schur Complement Solver for CFD-Based Multidisciplinary Models

CFD-based multidisciplinary models are the fundamental building blocks of multidis- ciplinary design optimization frameworks. Linear and nonlinear solutions of these coupled models are difficult, especially when the Jacobian matrices represent a saddle point problem, where a block-diagonal corresponding to a discipline is non-invertible. These scenarios necessitate the use of a coupled solver algorithm such as the Newton’s method instead of the popular block Gauss– Seidel-based methods because of this non-invertible block. To address this challenge, we introduce a nonlinear Schur complement solver suitable for CFD-based multidisciplinary models. The solver leverages the specialized linear and nonlinear solvers of the CFD code, and therefore, does not require the solution of a large coupled linear system as the coupled Newton’s method. Further- more, because the solver primarily uses the specialized linear and nonlinear solvers of the CFD code, it does not suffer from the same robustness limitations as the coupled Newton’s method. In this work, we will implement this solver in NASA’s OpenMDAO framework and demonstrate its effectiveness using a CFD-based aeropropulsive model. The solver will contribute to the develop- ment of aeropropulsive design optimization and CFD-based design optimization methods with the ultimate goal of accelerating the design and integration of advanced propulsion systems.

Nonlinear Solvers↗

Nonlinear quantum behavior of ultrashort-pulse optical parametric oscillators

The quantum features of ultrashort-pulse optical parametric oscillators (OPOs) are investigated theoretically in the nonlinear regime near and above threshold. Viewing the pulsed OPO as a multimode open quantum system, we rigorously derive a general input-output model that features nonlinear coupling among many cavity (i.e., system) signal modes and a broadband single-pass (i.e., reservoir) pump field. Under appropriate assumptions, our model produces a Lindblad master equation with multimode nonlinear Lindblad operators describing two-photon dissipation and a multimode four-wave-mixing Hamiltonian describing a broadband, dispersive optical cascade, which we show is required to preserve causality. To simplify the multimode complexity of the model, we employ a supermode decomposition to perform numerical simulations in the regime where the pulsed supermodes experience strong single-photon nonlinearity. We find that the quantum nonlinear dynamics induces pump depletion as well as corrections to the below-threshold squeezing spectrum predicted by linearized models. We also observe the formation of non-Gaussian states with Wigner-function negativity and show that the multimode interactions with the pump, both dissipative and dispersive, can act as effective decoherence channels. Finally, we briefly discuss some experimental considerations for potentially observing such quantum nonlinear phenomena with ultrashort-pulse OPOs on nonlinear nanophotonic platforms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

The weakly nonlinear response and nonaffine interpretation of the Johnson–Segalman/Gordon–Schowalter model

We derive new analytical solutions for the non-affine Johnson-Segalman/Gordon-Schowalter (JS/GS) constitutive equation with a general relaxation kernel in medium-amplitude oscillatory shear (MAOS) deformation. The results show time-strain separable (TSS) nonlinearity, therefore providing new physically-meaningful interpretation to the heuristic TSS nonlinear parameter in MAOS. The upper-convected, lower-convected, and corotational Maxwell models are all subsets of the results presented here. The model assumes that the microscale elements causing stress in the material slip compared to the continuum deformation. We introduce a visualization of the non-affine deformation field that acts on stress-generating elements to reinforce the hysical interpretation of the JS/GS class of models. Lastly, a case study is presented where previously published results, from fitting TSS models to MAOS data, can be re-interpreted based on the concept of non-affine motion of the JS/GS framework.

36 MATERIALS SCIENCE↗

Method for nonlinear exponential regression analysis

Two computer programs developed according to two general types of exponential models for conducting nonlinear exponential regression analysis are described. Least squares procedure is used in which the nonlinear problem is linearized by expanding in a Taylor series. Program is written in FORTRAN 5 for the Univac 1108 computer.

Junkin, B. G.↗

Constitutive Models Based on Compressible Plastic Flows

The need for describing materials under time or cycle dependent loading conditions has been emphasized in recent years by several investigators. In response to the need, various constitutive models describing the nonlinear behavior of materials under creep, fatigue, or other complex loading conditions were developed. The developed models for describing the fully dense (non-porous) materials were mostly based on uncoupled plasticity theory. The improved characterization of materials provides a better understanding of the structual response under complex loading conditions. The pesent studies demonstrate that the rate or time dependency of the response of a porous aggregate can be incorporated into the nonlinear constitutive behavior of a porous solid by appropriately modeling the incompressible matrix behavior. It is also sown that the yield function which wads determined by a continuum mechanics approach must be verified by appropriate experiments on void containing sintered materials in order to obtain meaningful numbers for the constants that appear in the yield function.

Rajendran, A. M.↗