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NASA NTRS2000

Thermal Conductivity Change Kinetics of Ceramic Thermal Barrier Coatings Determined by the Steady-State Laser Heat Flux Technique

A steady-state laser heat flux technique has been developed at the NASA Glenn Research Center at Lewis Field to obtain critical thermal conductivity data of ceramic thermal barrier coatings under the temperature and thermal gradients that are realistically expected to be encountered in advanced engine systems. In this study, thermal conductivity change kinetics of a plasma-sprayed, 254-mm-thick ZrO2-8 wt % Y2O3 ceramic coating were obtained at high temperatures. During the testing, the temperature gradients across the coating system were carefully measured by the surface and back pyrometers and an embedded miniature thermocouple in the substrate. The actual heat flux passing through the coating system was determined from the metal substrate temperature drop (measured by the embedded miniature thermocouple and the back pyrometer) combined with one-dimensional heat transfer models.

Zhu, Dongming↗

NASA NTRS1990

The steady state solutions of radiatively driven stellar winds for a non-Sobolev, pure absorption model

The steady state solution topology for absorption line-driven flows is investigated for the condition that the Sobolev approximation is not used to compute the line force. The solution topology near the sonic point is of the nodal type with two positive slope solutions. The shallower of these slopes applies to reasonable lower boundary conditions and realistic ion thermal speed v(th) and to the Sobolev limit of zero of the usual Castor, Abbott, and Klein model. At finite v(th), this solution consists of a family of very similar solutions converging on the sonic point. It is concluded that a non-Sobolev, absorption line-driven flow with a realistic values of v(th) has no uniquely defined steady state. To the extent that a pure absorption model of the outflow of stellar winds is applicable, radiatively driven winds should be intrinsically variable.

Poe, C. H.↗

DOE OSTI2024

Symbolic construction of the chemical Jacobian of quasi-steady state (QSS) chemistries for Exascale computing platforms

The Quasi-Steady State Approximation (QSSA) can be an effective tool for reducing the size and stiffness of chemical mechanisms for implementation in computational reacting flow solvers. However, for many applications, the resulting model still requires implicit methods for efficient time integration. Here, in this paper, we outline an approach to formulating the QSSA reduction that is coupled with a strategy to generate C++ source code to evaluate the net species production rates, and the chemical Jacobian. The code-generation component employs a symbolic approach enabling a simple and effective strategy to analytically compute the chemical Jacobian. For computational tractability, the symbolic approach needs to be paired with common subexpression elimination which can negatively affect memory usage. Several solutions are outlined and successfully tested on a 3D multipulse ignition problem, thus allowing portable application across chemical model sizes and GPU capabilities. The implementation of the proposed method is available at https://github.com/AMReX-Combustion/PelePhysics under an open-source license.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

NASA NTRS1978

Efficiency trade-offs of steady-state methods using FEM and FDM

The efficiency characteristics of finite element and finite difference approximations for the steady-state solution of the Navier-Stokes equations are examined. The finite element method discussed is a standard Galerkin formulation of the incompressible, steady-state Navier-Stokes equations. The finite difference formulation uses simple centered differences that are O(delta x-squared). Operation counts indicate that a rapidly converging Newton-Raphson-Kantorovitch iteration scheme is generally preferable over a Picard method. A split NOS Picard iterative algorithm for the finite difference method was most efficient.

Gartling, D. K.↗

NASA NTRS2009

Steady-State ALPS for Real-Valued Problems

The two objectives of this paper are to describe a steady-state version of the Age-Layered Population Structure (ALPS) Evolutionary Algorithm (EA) and to compare it against other GAs on real-valued problems. Motivation for this work comes from our previous success in demonstrating that a generational version of ALPS greatly improves search performance on a Genetic Programming problem. In making steady-state ALPS some modifications were made to the method for calculating age and the method for moving individuals up layers. To demonstrate that ALPS works well on real-valued problems we compare it against CMA-ES and Differential Evolution (DE) on five challenging, real-valued functions and on one real-world problem. While CMA-ES and DE outperform ALPS on the two unimodal test functions, ALPS is much better on the three multimodal test problems and on the real-world problem. Further examination shows that, unlike the other GAs, ALPS maintains a genotypically diverse population throughout the entire search process. These findings strongly suggest that the ALPS paradigm is better able to avoid premature convergence then the other GAs.

Hornby, Gregory S.↗

NASA NTRS1994

Numerical formulation of composition segregation at curved solid-liquid interface during steady state solidification process

The lateral solute segregation that results from a curved solid-liquid interface shape during steady state unidirectional solidification of a binary alloy system has been studied both analytically and numerically by Coriell, Bosivert, Rehm, and Sekerka. The system under their study is a two dimensional rectangular system. However, most real growth systems are cylindrical systems. Thus, in a previous study, we have followed Coriell etc. formalism and obtained analytical results for lateral solute segregation for an azimuthal symmetric cylindrical binary melt system during steady state solidification process. The solid-liquid interface shape is expressed as a series combination of Bessel functions. In this study a computer program has been developed to simulate the lateral solute segregation.

Wang, Jai-Ching↗

NASA NTRS1983

Implicit Total Variation Diminishing (TVD) schemes for steady-state calculations

The application of a new implicit unconditionally stable high resolution total variation diminishing (TVD) scheme to steady state calculations. It is a member of a one parameter family of explicit and implicit second order accurate schemes developed by Harten for the computation of weak solutions of hyperbolic conservation laws. This scheme is guaranteed not to generate spurious oscillations for a nonlinear scalar equation and a constant coefficient system. Numerical experiments show that this scheme not only has a rapid convergence rate, but also generates a highly resolved approximation to the steady state solution. A detailed implementation of the implicit scheme for the one and two dimensional compressible inviscid equations of gas dynamics is presented. Some numerical computations of one and two dimensional fluid flows containing shocks demonstrate the efficiency and accuracy of this new scheme.

Yee, H. C.↗

NASA NTRS1983

Implicit total variation diminishing (TVD) schemes for steady-state calculations

Yee, H. C.↗

NASA NTRS1992

A comparison and review of steady-state and time-varying reconnection

Extensions of Petschek's (1964) analysis are reviewed and used to investigate the steady-state and time-dependent reconnection in a current sheet geometry of the type observed at the magnetopause. It is shown that steady-state reconnection appears as a very special case in a time-dependent analysis. A single theoretical framework is proposed for interpreting reconnection phenomena at the magnetopause and for investigating the characteristics of dayside reconnection.

Semenov, V. S.↗

NASA NTRS1963

A STEADY-STATE, STAGNATION-POINT, HEAT-TRANSFER-RATE MEASURING DEVICE

Steady-state, stagnation-point, heat transfer rate measuring device

HEAT TRANSFER↗

NASA NTRS1974

Transient and steady-state velocity of domain walls for a complete range of drive fields

Approximate analytic solutions for transient and steady-state 180 deg domain wall motion in bulk magnetic material are obtained from the dynamic torque equations with a Gilbert damping term. The results for the Walker region in which the transient solution approaches the familiar Walker steady-state solution are presented in a slightly new form for completeness. An analytic solution corresponding to larger drive fields predicts an oscillatory motion with an average value which decreases with drive field for reasonable values of the damping parameter. These results agree with those obtained by a computer solution of the torque equation and those obtained with the assumption of a very large anisotropy field.

Bourne, H. C., Jr.↗

NASA NTRS1974

Transient and steady-state velocity of domain walls for a complete range of drive fields

Approximate analytic solutions for transient and steady-state 180 deg domain-wall motion in bulk magnetic material are obtained from the dynamic torque equations with a Gilbert damping term. The results for the Walker region in which the transient solution approaches the familiar Walker steady-state solution are presented in a slightly new form for completeness. An analytic solution corresponding to larger drive fields predicts an oscillatory motion with an average value of the velocity which decreases with drive field for reasonable values of the damping parameter. These results agree with those obtained by others from a computer solution of the torque equation and those obtained by others with the assumption of a very large anisotropy field.

Bourne, H. C., Jr.↗

NASA NTRS1983

Reduction methods for nonlinear steady-state thermal analysis

Hybrid analysis techniques and a problem adaptive computational algorithm are presented for predicting the nonlinear steady state temperature distribution in structures and solids. In the proposed techniques, the structure is discretized by using the finite element method. The vector of nodal temperatures is then expressed as a linear combination of a small number of global temperature modes (or basis vectors), and the Bubnov Galerkin technique is used to compute the amplitudes of the global modes. The global temperature modes (or basis vectors) are chosen to include the various order derivatives of the nodal temperature vector with respect to preselected path parameter(s). The potential of the proposed reduction methods for solution of large scale, nonlinear thermal problems is discussed and the effectiveness of the methods is demonstrated by means of numerical examples, including steady state conduction, convection, and radiation modes of heat transfer.

Noor, A. K.↗

NASA NTRS1996

Steady-State Dynamic Behavior of a Flexible Rotor With Auxiliary Support From a Clearance Bearing

This paper investigates the steady-state responses of a rotor system supported by auxiliary bearings in which there is a clearance between the rotor and the inner race of the bearing. A simulation model based upon the rotor of a production jet engine is developed and its steady-state behavior is explored over a wide range of operating conditions for various parametric configurations. Specifically, the influence of rotor imbalance, clearance, support stiffness and damping is studied. Bifurcation diagrams are used as a tool to examine the dynamic behavior of this system as a function of the afore mentioned parameters. The harmonic balance method is also employed for synchronous response cases. The observed dynamical responses is discussed and some insights into the behavior of such systems are presented.

Xie, Huajun↗

DOE OSTI2026

Electrochemical Modeling of PID Leakage Current of PV Modules: Steady-State Current, Transient Current, and RC-Equivalent Circuit

Potential-induced degradation (PID) remains a significant reliability concern for photovoltaic (PV) modules, arising when a voltage difference between the module frame and the solar cells drives unintended leakage current through the glass-encapsulant stack. Although PID ultimately manifests as PID-s, PID-p, or PID-c, the underlying behavior of the leakage current-its magnitude and time dependence-requires clearer electrochemical interpretation. Traditional explanations attribute the initial transient current to bulk capacitive elements of the glass, encapsulant, and antireflection coatings, and the steady-state current according to their effective ohmic resistance. More recent studies, however, indicate that electrochemical charge-transfer processes at the encapsulant-metallization interface can play a dominant role in defining the leakage-current path. This paper develops a unified electrochemical framework for modeling PID leakage current. First, an RC-equivalent circuit is formulated by combining conventional RC elements with a Randles-type interface to capture transient leakage current through double-layer capacitance and faradaic processes at ionic-electronic boundaries. Second, the steady-state current-voltage behavior is explained using a linearized Butler-Volmer relationship, showing that the measured ohmic response corresponds to the low-overpotential limit of charge-transfer kinetics. Analytical results demonstrate that, for typical module materials-3.2-mm soda-lime glass and 0.45-mm encapsulant-the dominant modulators to PID leakage current are the glass surface resistance (under dry-surface conditions), the glass bulk capacitance, and the encapsulant resistance (under wet-surface conditions), with soda lime glass surface and EVA/POE encapsulant resistances primarily governing steady-state current. The proposed electrochemical model is validated against measured leakage-current data, showing good agreement in both the magnitude and the time-dependent evolution of PID leakage current.

14 SOLAR ENERGY↗

NASA NTRS1967

Steady-state and dynamic properties of the floating-ring journal bearing.

Steady state and dynamic properties of cylindrical floating ring journal bearing with pressurized lubricant supply, considering turbulent flow and whirl instability

WHIRL INSTABILITY↗

DOE OSTI2024

Dodecane Radiolysis Yields by Time-Resolved and Steady-State Methods

Liquid organic molecules are present as solvents, complexing ligands, and additives in both used nuclear fuel reprocessing solvent systems and in their subsequent nuclear waste streams. Under these extreme environments, these organic molecules are constantly exposed to ionizing radiation which promotes their radiolysis, forming a variety of short-lived, highly energetic, excited state and radical species.1-4 Here, we demonstrate new experimental results for the steady-state and time-resolved irradiations of dodecane (C12H26), a long chain, liquid, aliphatic hydrocarbon that is the prototypical solvent used for benchtop studies of aqueous-organic solvent extraction systems. When ionizing radiation interacts with neat dodecane, the energy transfer can result in molecular ionization, to give the dodecane radical cation (C12H26+•) and the solvated electron (eS–), and molecular electronic excitation (C12H26*), which rapidly produces transient carbon-centered radical fragments (CxHy•) and hydrogen atoms (H•).1-4 Studies on the initial yields of the ionization and excitation products were performed using time-resolved picosecond electron pulse radiolysis with the use of molecular probes. Using steady-state cobalt-60 gamma irradiations, the suite of products formed by dodecane radiolysis in aerated and deaerated solutions was determined. Then, using iodine as an alkyl radical scavenger, the loss of molecular iodine with dose was quantified, and by correlating with the molecular hydrogen yields of the system, the initial yields of the various carbon-centered radicals were also determined. Finally, the rates of reactions of the C12H26+• and eS– with ligands proposed for use in spent nuclear fuel reprocessing were studied as a function of temperature from 10 – 40 °C.

38 - RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCL↗

NASA NTRS1995

Dynamical Approach Study of Spurious Steady-State Numerical Solutions of Nonlinear Differential Equations: Global Asymptotic Behavior of Time Discretizations - 2

The global asymptotic nonlinear behavior of 1 1 explicit and implicit time discretizations for four 2 x 2 systems of first-order autonomous nonlinear ordinary differential equations (ODES) is analyzed. The objectives are to gain a basic understanding of the difference in the dynamics of numerics between the scalars and systems of nonlinear autonomous ODEs and to set a baseline global asymptotic solution behavior of these schemes for practical computations in computational fluid dynamics. We show how 'numerical' basins of attraction can complement the bifurcation diagrams in gaining more detailed global asymptotic behavior of time discretizations for nonlinear differential equations (DEs). We show how in the presence of spurious asymptotes the basins of the true stable steady states can be segmented by the basins of the spurious stable and unstable asymptotes. One major consequence of this phenomenon which is not commonly known is that this spurious behavior can result in a dramatic distortion and, in most cases, a dramatic shrinkage and segmentation of the basin of attraction of the true solution for finite time steps. Such distortion, shrinkage and segmentation of the numerical basins of attraction will occur regardless of the stability of the spurious asymptotes, and will occur for unconditionally stable implicit linear multistep methods. In other words, for the same (common) steady-state solution the associated basin of attraction of the DE might be very different from the discretized counterparts and the numerical basin of attraction can be very different from numerical method to numerical method. The results can be used as an explanation for possible causes of error, and slow convergence and nonconvergence of steady-state numerical solutions when using the time-dependent approach for nonlinear hyperbolic or parabolic PDES.

Yee, H. C.↗