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Results for “nonlinear power flow equations”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRS1990

Analysis of unsteady compressible viscous layers

The development of an analysis to predict the unsteady compressible flows in blade boundary layers and wakes is presented. The equations that govern the flows in these regions are transformed using an unsteady turbulent generalization of the Levy-Lees transformation. The transformed equations are solved using a finite difference technique in which the solution proceeds by marching in time and in the streamwise direction. Both laminar and turbulent flows are studied, the latter using algebraic turbulence and transition models. Laminar solutions for a flat plate are shown to approach classical asymptotic results for both high and low frequency unsteady motions. Turbulent flat-plate results are in qualitative agreement with previous predictions and measurements. Finally, the numerical technique is also applied to the stator and rotor of a low-speed turbine stage to determine unsteady effects on surface heating. The results compare reasonably well with measured heat transfer data and indicate that nonlinear effects have minimal impact on the mean and unsteady components of the flow.

Power, G. D.↗

DOE OSTI2021

Additively Manufactured Compliant Hybrid Gas Thrust Bearing for Supercritical Carbon Dioxide Turbomachinery: Experimental Evaluation and Fluid–Structure Model Predictions

This paper presents rotating test results and advances an analytical predictive fluid–structure model for a new type of gas-lubricated thrust bearing fabricated using direct metal laser melting. The bearing concept in this study is a compliant hybrid gas thrust bearing that uses external pressurization to increase load carrying capacity, where the testing campaign in this study was only focused on steady-state static performance. The need for the bearing concept comes from enabling highly efficient supercritical carbon dioxide (sCO2) turbomachinery by replacing oil-lubricated bearings with process gas lubrication. Leveraging the process gas of the turbomachine for bearing lubrication results in lowered bearing power loss, simplified mechanical design, and allows for novel oil-free hermetic drivetrains resulting in an efficient emission-free system. The new concept utilizes hydrostatic pressurization on individual tilting pads flexibly mounted with hermetic squeeze film dampers (HSFDs). This paper focuses on rotating tests of a 173 mm outer diameter gas thrust bearing in air up to 10 krpm and hydrostatic inlet pressures to 365 psi (2.52 MPa). The influence of thrust runner speed and bearing inlet pressure on force deflection characteristics and load carrying capability of the gas film were experimentally evaluated. This work also advances a predictive fluid–structure thrust bearing model using an isothermal ideal-gas-based compressible Reynolds flow equation directly coupled to a lumped stiffness element possessing axial and rotational degrees-of-freedom. The rotating testing demonstrated load capability of 1816 lbs (8.1 kN), which equates to a thrust bearing unit load of 67 psi (0.46 MPa). Gas film force–deflection curves reveal a nonlinear relationship between thrust load and film clearance. Comparison of film thickness values with the predictive model show good agreement under high load and inlet pressure, however deviate as load and pressure decrease. Load capability was shown to increase with increasing hydrostatic inlet pressure, while the increase in thrust runner speed revealed a small decrease in load capacity.

Engineering↗

DOE OSTI2024

Divide and conquer: Learning chaotic dynamical systems with multistep penalty neural ordinary differential equations

Forecasting high-dimensional dynamical systems is a fundamental challenge in various fields, such as geosciences and engineering. Neural Ordinary Differential Equations (NODEs), which combine the power of neural networks and numerical solvers, have emerged as a promising algorithm for forecasting complex nonlinear dynamical systems. However, classical techniques used for NODE training are ineffective for learning chaotic dynamical systems. In this work, we propose a novel NODE-training approach that allows for robust learning of chaotic dynamical systems. Here, our method addresses the challenges of non-convexity and exploding gradients associated with underlying chaotic dynamics. Training data trajectories from such systems are split into multiple, non-overlapping time windows. In addition to the deviation from the training data, the optimization loss term further penalizes the discontinuities of the predicted trajectory between the time windows. The window size is selected based on the fastest Lyapunov time scale of the system. Multi-step penalty(MP) method is first demonstrated on Lorenz equation, to illustrate how it improves the loss landscape and thereby accelerates the optimization convergence. MP method can optimize chaotic systems in a manner similar to least-squares shadowing with significantly lower computational costs. Our proposed algorithm, denoted the Multistep Penalty NODE, is applied to chaotic systems such as the Kuramoto-Sivashinsky equation, the two-dimensional Kolmogorov flow, and ERA5 reanalysis data for the atmosphere. It is observed that MP-NODE provide viable performance for such chaotic systems, not only for short-term trajectory predictions but also for invariant statistics that are hallmarks of the chaotic nature of these dynamics.

Chaotic dynamical systems↗

NASA NTRS1995

Turbulence in the solar wind: Kinetic effects

Although a casual look at the fluctuating magnetic and velocity fields in the solar wind may be reminiscent of a chaotic and disordered flow, there is, nonetheless. considerable organization and structure in the temporal and spatial evolution of those fluctuations. Much of that evolution is controlled by processes operating on rather large scales for example, in the inner heliosphere, the fluctuations in magnetic and velocity are highly correlated in the sense of outward propagating Alfven waves. This correlation can be destroyed both in time and distance by the velocity gradients present between fast and slow streams and by other nonlinear processes which stir the medium, producing a turbulent cascade of energy from large to small scales. Many aspects of this turbulent evolution can be described using fluid models; however, at some scale the fluid approximation breaks down and a more detailed paradigm is necessary. The breakdown is evident in the power spectrum of magnetic fluctuations at scales approaching the wavelength of ion cyclotron waves. At those scales, as evident in Mariner 10 and other magnetometer data, the spectrum bends over and the fluctuations damp, possibly heating the ambient plasma. Some evidence for heating of the solar wind is present in the Voyager data. Fluid models can be modified to some extent to incorporate aspects of a kinetic treatment. This is done by modifying the dissipation terms in the fluid equations and by including extra terms, such as the Hall term. As the scale lengths of phenomena shrink further and approach the spatial and temporal scales characteristic of electron phenomena, the fluid description must be abandoned altogether and a fully kinetic treatment is required. One example is the generation of Langmuir solitons produced by the electron beams that generate type 3 solar radio bursts.

Goldstein, M. L.↗

DOE OSTI2024

NeuroSEM: A hybrid framework for simulating multiphysics problems by coupling PINNs and spectral elements

Multiphysics problems that are characterized by complex interactions among fluid dynamics, heat transfer, structural mechanics, and electromagnetics, are inherently challenging due to their coupled nature. While experimental data on certain state variables may be available, integrating these data with numerical solvers remains a significant challenge. Physics-informed neural networks (PINNs) have shown promising results in various engineering disciplines, particularly in handling noisy data and solving inverse problems in partial differential equations (PDEs). However, their effectiveness in forecasting nonlinear phenomena in multiphysics regimes, particularly involving turbulence, is yet to be fully established. Here, this study introduces NeuroSEM, a hybrid framework integrating PINNs with the highfidelity Spectral Element Method (SEM) solver, Nektar++. NeuroSEM leverages the strengths of both PINNs and SEM, providing robust solutions for multiphysics problems. PINNs are trained to assimilate data and model physical phenomena in specific subdomains, which are then integrated into the Nektar++ solver. We demonstrate the efficiency and accuracy of NeuroSEM for thermal convection in cavity flow and flow past a cylinder. The framework effectively handles data assimilation by addressing those subdomains and state variables where the data is available. We applied NeuroSEM to the Rayleigh-B´enard convection system, including cases with missing thermal boundary conditions and noisy datasets. Finally, we applied the proposed NeuroSEM framework to real particle image velocimetry (PIV) data to capture flow patterns characterized by horseshoe vortical structures. Our results indicate that NeuroSEM accurately models the physical phenomena and assimilates the data within the specified subdomains. The framework’s plug-and-play nature facilitates its extension to other multiphysics or multiscale problems. Furthermore, NeuroSEM is optimized for efficient execution on emerging integrated GPU-CPU architectures. This hybrid approach enhances the accuracy and efficiency of simulations, making it a powerful tool for tackling complex engineering challenges in various scientific domains.

42 ENGINEERING↗

DOE OSTI2022

Isotherm Modeling and Techno-Economic Analysis of Contactor Technologies for New Tetraamine-Appended MOF for NGCC Applications

Recently, a family of tetraamine-functionalized metal-organic frameworks (MOF) has been reported as promising sorbent materials for capturing CO2 from flue gas conditions relevant to natural gas combined cycle (NGCC) applications. The main advantages of these materials are their two-step cooperative CO2 adsorption, which gives rise to unusual two step-shaped CO2 adsorption profiles and their high thermal stability. This work presents the modelling of the two-transition isotherm of the tetraamine-appended MOF, N,N'-bis(3-aminopropyl)-1,4-diaminobutane (3-4-3)-appended Mg2(dobpdc), and the techno-economic analysis (TEA) of carbon capture processes utilizing this sorbent. Due to the unusual isotherm shapes of the experimental CO2 adsorption data for tetraamine-appended Mg2(dobpdc) and the strong nonlinearity of CO2 loading with respect to temperature and pressure, we tested two different models which use logistic functions for representing the different isotherm behaviors in the different pressure ranges. The first model uses the quadratic isotherm model in the low-pressure region, the Langmuir isotherm model in the middle pressure range, and the dual site Langmuir isotherm model in the high-pressure range. To model the transition between regions we used the arctangent functions independent of temperature and the thermal effect was accounted by using the Clausius-Clapeyron relation]. The second model is an extension of the weighted dual-site Langmuir isotherm model presented by Hughes et al.. In this extended model, the dual-site Langmuir isotherm is employed in the three transition regions, using temperature-dependent logistic functions to activate or deactivate the isotherm model in the low, middle, and high-pressure ranges. Both models fit the experimental data quite well with root mean squared errors (RMSE’s) of 0.41 and 0.17 for model 1 and model 2, respectively. Since model 2 resulted in a lower RMSE, it was leveraged for the development of the gas/solid contactor models used by the TEA. Specifically, two different contactor models, an axial-flow fixed bed and moving bed contactor, were developed as part of this work. These models are dynamic, pressure-driven, and consist of mass, energy, and momentum conservation equations. A kinetic model was also developed by performing parameter estimation using experimental fixed bed breakthrough data. These models are then used to simulate CO2 capture processes from the flue gas generated from a ~600 gross MW NGCC power plant. A cost model was developed which considers the capital cost of the reactors and the significant operating costs such as steam and electricity. Using NETL’s Framework for the Optimization and Quantification of Uncertainty of Uncertainty and Surrogates tool (FOQUS), which has the capability of linking models built using numerous modelling platforms with derivative-free optimization solvers, a techno-economic optimization of the carbon capture processes was performed which minimizes the cost of capture.

Caballero, Daison↗

NASA NTRS2010

Physics-Based Methods of Failure Analysis and Diagnostics in Human Space Flight

The Integrated Health Management (IHM) for the future aerospace systems requires to interface models of multiple subsystems in an efficient and accurate information environment at the earlier stages of system design. The complexity of modern aeronautic and aircraft systems (including e.g. the power distribution, flight control, solid and liquid motors) dictates employment of hybrid models and high-level reasoners for analysing mixed continuous and discrete information flow involving multiple modes of operation in uncertain environments, unknown state variables, heterogeneous software and hardware components. To provide the information link between key design/performance parameters and high-level reasoners we rely on development of multi-physics performance models, distributed sensors networks, and fault diagnostic and prognostic (FD&P) technologies in close collaboration with system designers. The main challenges of our research are related to the in-flight assessment of the structural stability, engine performance, and trajectory control. The main goal is to develop an intelligent IHM that not only enhances components and system reliability, but also provides a post-flight feedback helping to optimize design of the next generation of aerospace systems. Our efforts are concentrated on several directions of the research. One of the key components of our strategy is an innovative approach to the diagnostics/prognostics based on the real time dynamical inference (DI) technologies extended to encompass hybrid systems with hidden state trajectories. The major investments are into the multiphysics performance modelling that provides an access of the FD&P technologies to the main performance parameters of e.g. solid and liquid rocket motors and composite materials of the nozzle and case. Some of the recent results of our research are discussed in this chapter. We begin by introducing the problem of dynamical inference of stochastic nonlinear models and reviewing earlier results. Next, we present our analytical approach to the solution of this problem based on the path integral formulation. The resulting algorithm does not require an extensive global search for the model parameters, provides optimal compensation for the effects of dynamical noise, and is robust for a broad range of dynamical models. In the following Section the strengths of the algorithm are illustrated illustrated by inferring the parameters of the stochastic Lorenz system and comparing the results with those of earlier research. Next, we discuss a number of recent results in application to the development of the IHM for aerospace system. Firstly, we apply dynamical inference approach to a solution of classical three tank problems with mixed unknown continuous and binary parameters. The problem is considered in the context of ground support system for filling fuel tanks of liquid rocket motors. It is shown that the DI algorithm is well suited for successful solution of a hybrid version of this benchmark problem even in the presence of additional periodic and stochastic perturbation of unknown strength. Secondly, we illustrate our approach by its application to an analysis of the nozzle fault in a solid rocket motor (SRM). The internal ballistics of the SRM is modelled as a set of one-dimensional partial differential equations coupled to the dynamics of the propellant regression. In this example we are specifically focussed on the inference of discrete and continuous parameters of the nozzle blocking fault and on the possibility of an application of the DI algorithm to reducing the probability of "misses" of an on-board FD&P for SRM. In the next section re-contact problem caused by first stage/upper stage separation failure is discussed. The reaction forces imposed on the nozzle of the upper stage during the re-contact and their connection to the nozzle damage and to the thrust vector control (TVC) signal are obtained. It is shown that transient impact induced torquean be modelled as a response of an effective damped oscillator. A possible application of the DI algorithm to the inference of damage parameters and predicting fault dynamics ahead of time using the actuator signal is discussed. Finally, we formulate Bayesian inferential framework for development of the IHM system for in-flight structural health monitoring (SHM) of composite materials. We consider the signal generated by piezoelectric actuator mounted on composite structure generating elastic waves in it. The signal received by the sensor is than compared with the baseline signal. The possibility of damage inference is discussed in the context of development of the SHM.

Smelyanskiy, Vadim N.↗