Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “gradient methods”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,153 records · Page 64
All sourcesNASA NTRSDOE OSTI
NASA NTRS1998

Low Dissipative High Order Shock-Capturing Methods using Characteristic-Based Filters

An approach which closely maintains the non-dissipative nature of classical fourth or higher- order spatial differencing away from shock waves and steep gradient regions while being capable of accurately capturing discontinuities, steep gradient and fine scale turbulent structures in a stable and efficient manner is described. The approach is a generalization of the method of Gustafsson and Olsson and the artificial compression method (ACM) of Harten. Spatially non-dissipative fourth or higher-order compact and non-compact spatial differencings are used as the base schemes. Instead of applying a scalar filter as in Gustafsson and Olsson, an ACM like term is used to signal the appropriate amount of second or third-order TVD or ENO types of characteristic based numerical dissipation. This term acts as a characteristic filter to minimize numerical dissipation for the overall scheme. For time-accurate computations, time discretizations with low dissipation are used. Numerical experiments on 2-D vortical flows, vortex-shock interactions and compressible spatially and temporally evolving mixing layers showed that the proposed schemes have the desired property with only a 10% increase in operations count over standard second-order TVD schemes. Aside from the ability to accurately capture shock-turbulence interaction flows, this approach is also capable of accurately preserving vortex convection. Higher accuracy is achieved with fewer grid points when compared to that of standard second-order TVD or ENO schemes. To demonstrate the applicability of these schemes in sustaining turbulence where shock waves are absent, a simulation of 3-D compressible turbulent channel flow in a small domain is conducted.

Yee, H. C.↗
NASA NTRS1998

Low Dissipative High Order Shock-Capturing Methods Using Characteristic-Based Filters

An approach which closely maintains the non-dissipative nature of classical fourth or higher- order spatial differencing away from shock waves and steep gradient regions while being capable of accurately capturing discontinuities, steep gradient and fine scale turbulent structures in a stable and efficient manner is described. The approach is a generalization of the method of Gustafsson and Oisson and the artificial compression method (ACM) of Harten. Spatially non-dissipative fourth or higher-order compact and non-compact spatial differencings are used as the base schemes. Instead of applying a scalar filter as in Gustafsson and Olsson, an ACM like term is used to signal the appropriate amount of second or third-order TVD or ENO types of characteristic based numerical dissipation. This term acts as a characteristic filter to minimize numerical dissipation for the overall scheme. For time-accurate computations, time discretizations with low dissipation are used. Numerical experiments on 2-D vortical flows, vortex-shock interactions and compressible spatially and temporally evolving mixing layers showed that the proposed schemes have the desired property with only a 10% increase in operations count over standard second-order TVD schemes. Aside from the ability to accurately capture shock-turbulence interaction flows, this approach is also capable of accurately preserving vortex convection. Higher accuracy is achieved with fewer grid points when compared to that of standard second-order TVD or ENO schemes. To demonstrate the applicability of these schemes in sustaining turbulence where shock waves are absent, a simulation of 3-D compressible turbulent channel flow in a small domain is conducted.

Yee, H. C.↗
NASA NTRS1972

Numerical methods for reduction of topside ionograms

Several alternative methods for solving the group height equation are presented. Three of these are now in operation at Ames Research Center and use data contained in a single ionogram trace. From the data an electron density profile N(h) is computed. If the ionogram also exhibits other traces, reverse ionogram traces are computed, using the N(h) profile, for comparison with the redundant data. When agreement is poor, the initial data trace is reinterpreted, another N(h) profile computed, and the reverse traces generated once again. This process is repeated until a desired degree of consistency is achieved. To reduce the necessity for human intervention and eliminate decision making required in conjunction with the preceding methods, a method is proposed that accepts as input, all data from a single ionogram. In general, no electron density function will satisfy these data exactly, but a best N(h) profile can be computed. Finally, a method is described that eliminates the need to assume that the ionosphere is spherically stratified. Horizontal gradients in electron density are detected and accounted for by processing several ionograms from the same satellite pass simultaneously. This idea is derived as an extension of one of the basic methods.

Mcculley, L.↗
DOE OSTI2022

Two-Stage Reinforcement Learning Policy Search for Grid-Interactive Building Control

This paper develops an intelligent grid-interactive building controller, which optimizes building operation during both normal hours and demand response (DR) events. To avoid costly on-demand computation and to adapt to non-linear building models, the controller utilizes reinforcement learning (RL) and makes real-time decisions based on a near-optimal control policy. Learning such a policy typically amounts to solving a hard non-convex optimization problem. We propose to address this problem with a novel global-local policy search method. In the first stage, an RL algorithm based on zero-order gradient estimation is leveraged to search for the optimal policy globally, due to its scalability and the potential to escape some poor performing local optima. The obtained policy is then fine-tuned locally to bring the first-stage solution closer to that of the original unsmoothed problem. Experiments on a simulated five-zone commercial building demonstrate the advantages of the proposed method over existing learning approaches. They also show that the learned control policy outperforms a pragmatic linear model predictive controller (MPC) and approaches the performance of an oracle MPC in testing scenarios. Using a state-of-the-art advanced computing system, we demonstrate that the controller can be learned and deployed within hours of training.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2020

Novel strategies for modal-based structural material identification

Here, we present modal-based methods for model calibration in structural dynamics, and address several key challenges in the solution of gradient-based optimization problems with eigenvalues and eigenvectors, including the solution of singular Helmholtz problems encountered in sensitivity calculations, non-differentiable objective functions caused by mode swapping during optimization, and cases with repeated eigenvalues. Unlike previous literature that relied on direct solution of the eigenvector adjoint equations, we present a parallel iterative domain decomposition strategy (Adjoint Computation via Modal Superposition with Truncation Augmentation) for the solution of the singular Helmholtz problems. For problems with repeated eigenvalues we present a novel Mode Separation via Projection algorithm, and in order to address mode swapping between inverse iterations we present a novel Injective mode ordering metric. We present the implementation of these methods in a massively parallel finite element framework with the ability to use measured modal data to extract unknown structural model parameters from large complex problems. A series of increasingly complex numerical examples are presented that demonstrate the implementation and performance of the methods in a massively parallel finite element framework [7], [5], using gradient-based optimization techniques in the Rapid Optimization Library (ROL) [21].

36 MATERIALS SCIENCE↗
DOE OSTI2021

Droplet and Particle Methods to Investigate Turbulent Particle Laden Jets

The SARS-CoV-2 pandemic has heightened the interest in particle-laden turbulent jets generated by breathing, talking, coughing and sneezing, and how these can contribute to disease transmission. We present quantitative measurement methods for such flows, while exploring and offering improvements for common shortcomings. We generate jets consisting of either liquid droplets or solid particles in an isothermal, quiescent and electrically isopotential experimental chamber that was constructed to control the effects of ambient forcing on jet behavior. For liquid droplets, we find promise in surface deposition analysis based on fluorescent tracer use. For particles, we explore the performance of commercially available adhesive sampling strips and develop conductive grounded carbon tape based sampling strips. We explore ways in which the smallest of thermal gradients or electrostatic charge issues can affect particle dispersion, and suggest practical methods to address these issues. The developed methods are applied to study the simultaneous deposition of (Formula presented.) 25, 50 and 200 μm solid particles from a particle laden turbulent jet with a mean velocity of 33.2 m/s. The deposition location as a function of particle size was compared to results from a simple numerical RANS model, and illustrates ways in which imprecise initial or boundary conditions can lead to a notable deviation from experimental results. The differences in deposition pattern seen in experimental and numerical results despite a carefully controlled environment and characterized particle ejection indicate the need for a more stringent numerical model validation, especially when studying fate and transport of mid-range (neither purely aerosol or ballistic) sized particles.

42 ENGINEERING↗
NASA NTRS2015

Experimental and Finite Element Modeling of Near-Threshold Fatigue Crack Growth for the K-Decreasing Test Method

The experimental methods to determine near-threshold fatigue crack growth rate data are prescribed in ASTM standard E647. To produce near-threshold data at a constant stress ratio (R), the applied stress-intensity factor (K) is decreased as the crack grows based on a specified K-gradient. Consequently, as the fatigue crack growth rate threshold is approached and the crack tip opening displacement decreases, remote crack wake contact may occur due to the plastically deformed crack wake surfaces and shield the growing crack tip resulting in a reduced crack tip driving force and non-representative crack growth rate data. If such data are used to life a component, the evaluation could yield highly non-conservative predictions. Although this anomalous behavior has been shown to be affected by K-gradient, starting K level, residual stresses, environmental assisted cracking, specimen geometry, and material type, the specifications within the standard to avoid this effect are limited to a maximum fatigue crack growth rate and a suggestion for the K-gradient value. This paper provides parallel experimental and computational simulations for the K-decreasing method for two materials (an aluminum alloy, AA 2024-T3 and a titanium alloy, Ti 6-2-2-2-2) to aid in establishing clear understanding of appropriate testing requirements. These simulations investigate the effect of K-gradient, the maximum value of stress-intensity factor applied, and material type. A material independent term is developed to guide in the selection of appropriate test conditions for most engineering alloys. With the use of such a term, near-threshold fatigue crack growth rate tests can be performed at accelerated rates, near-threshold data can be acquired in days instead of weeks without having to establish testing criteria through trial and error, and these data can be acquired for most engineering materials, even those that are produced in relatively small product forms.

Smith, Stephen W.↗
DOE OSTI2022

Accurate parameterization of the kinetic energy functional for calculations using exact-exchange

In this report, electronic structure calculations based on Kohn-Sham density functional theory (KSDFT) that incorporate exact exchange or hybrid functionals are associated with large computational expense, a consequence of the inherent cubic scaling bottleneck and large associated prefactor, which limits the length and time scales that can be accessed. Though orbital-free density functional theory (OFDFT) calculations scale linearly with system size and are associated with significantly smaller prefactor, they are limited by the absence of accurate density-dependent kinetic energy functionals. Therefore, the development of accurate density-dependent kinetic energy functionals is important for OFDFT calculations of large realistic systems. To this end, we propose a method to train kinetic energy functional models at the exact-exchange level of theory by using a dictionary of physically relevant terms that have been proposed in the literature in conjunction with linear or nonlinear regression methods to obtain the fitting coefficients. For our dictionary, we use gradient expansion of the kinetic energy, nonlocal models proposed in the literature and their nonlinear combinations, such as a model that incorporates spatial correlations between higher order derivatives of electron density at two points. The predictive capabilities of these models are assessed by using a variety of model one-dimensional systems that exhibit diverse bonding characteristics, such as a chain of eight hydrogens, LiF, LiH, C 4 H 2 , C 4 N 2 and C 3 O 2 . We show that by using data from model one-dimensional KSDFT calculations performed using the exact-exchange functional for only a few neutral structures, it is possible to generate models with high accuracy for charged systems as well as electron and kinetic energy densities during self-consistent field iterations. In addition, we show that it possible to learn both the orbital dependent terms, i.e., the kinetic energy and the exact-exchange energy, and models that incorporate additional nonlinearities in spatial correlations, such as a quadratic model, are needed to capture subtle features of the kinetic energy density that are present in exact-exchange-based KSDFT calculations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

An optimization method for chaotic turbulent flow

Evidence indicates that quantities-of-interest in some turbulent flows can be controlled despite the overall chaotic dynamics. It is typically thought that this is via relatively deterministic, larger-scale components of the turbulence. However, finding such controls, if they exist, is challenging because chaos causes sensitivity gradients to explode and the search space to become intractably non-convex. This challenge is analyzed, and a penalty method is introduced to cope with it. In the new approach, the time domain is broken into segments approximately matching the chaos time scales, so that the solution within each segment is both physical and relatively deterministic. The initial condition of each segment is included in an adjoint-based gradient optimization, which temporarily introduces artificial Δq discontinuities in the overall solution. The optimization then proceeds in stages with increasing penalization of Δq. The method is developed and illustrated for a logistic map, the Lorenz Equation, and an advection augmented Kuramoto–Sivashinsky Equation. These examples show how the Δq temporarily increases the search scale prior to the strong Δq → 0 penalization that recovers a physical solution. It is then applied to turbulent Kolmogorov flow, for which it also far outperforms a standard adjoint-based gradient search. Finally, the utility of such an optimized chaotic solution is discussed.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

System and method thermopile energy harvesting for subsurface well bore sensors

A system and method for powering a borehole sensor with thermal energy is disclosed. The system includes a tubular pipe inserted into a subsurface borehole. A borehole casing is coaxially disposed with the tubular pipe. An annular space between the casing and the tubular pipe has a power source placed in the borehole to power a sensor in response to a temperature gradient between a surface of the casing and a surface of the tubular pipe. The method includes attaching thermopiles on the borehole casing or tubing; placing the thermopile in the annulus between the casing and the tubing; inducing a thermal gradient across the thermopile; generating an electrical energy in response to the temperature gradient; powering the sensor from the generated energy; and monitoring vertical expansion of a CO2 plume.

Bryan, Charles R.↗
DOE OSTI2025

Jipole: A Differentiable ipole-based Code for Radiative Transfer in Curved Spacetimes

Recent imaging of supermassive black holes by the Event Horizon Telescope has relied on exhaustive parameter-space searches, matching observations to large, precomputed libraries of theoretical models. As observational data become increasingly precise, the limitations of this computationally expensive approach grow more acute, creating a pressing need for more efficient methods. In this work, we present Jipole, an automatically differentiable (AD), ipole-based code for radiative transfer in curved spacetimes, designed to compute image gradients with respect to underlying model parameters. These gradients quantify how parameter changes—such as the black hole’s spin or the observer’s inclination—affect the image, enabling more efficient parameter estimation and reducing the number of required images. We validate Jipole against ipole in two analytical tests and then compare pixelwise intensity derivatives from AD with those from finite-difference methods. We then demonstrate the utility of these gradients by performing parameter recovery for an analytical model in three increasingly complex cases for the injected image: ideal, blurred, and blurred with added noise. In most cases, high-accuracy fits are obtained in only a few optimization steps, failing only in cases with extremely low signal-to-noise ratios. These results highlight the potential of AD-based methods to accelerate robust, high-fidelity model-data comparisons in current and future black hole imaging efforts.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1997

Constrained Multipoint Aerodynamic Shape Optimization Using an Adjoint Formulation and Parallel Computers

An aerodynamic shape optimization method that treats the design of complex aircraft configurations subject to high fidelity computational fluid dynamics (CFD), geometric constraints and multiple design points is described. The design process will be greatly accelerated through the use of both control theory and distributed memory computer architectures. Control theory is employed to derive the adjoint differential equations whose solution allows for the evaluation of design gradient information at a fraction of the computational cost required by previous design methods. The resulting problem is implemented on parallel distributed memory architectures using a domain decomposition approach, an optimized communication schedule, and the MPI (Message Passing Interface) standard for portability and efficiency. The final result achieves very rapid aerodynamic design based on a higher order CFD method. In order to facilitate the integration of these high fidelity CFD approaches into future multi-disciplinary optimization (NW) applications, new methods must be developed which are capable of simultaneously addressing complex geometries, multiple objective functions, and geometric design constraints. In our earlier studies, we coupled the adjoint based design formulations with unconstrained optimization algorithms and showed that the approach was effective for the aerodynamic design of airfoils, wings, wing-bodies, and complex aircraft configurations. In many of the results presented in these earlier works, geometric constraints were satisfied either by a projection into feasible space or by posing the design space parameterization such that it automatically satisfied constraints. Furthermore, with the exception of reference 9 where the second author initially explored the use of multipoint design in conjunction with adjoint formulations, our earlier works have focused on single point design efforts. Here we demonstrate that the same methodology may be extended to treat complete configuration designs subject to multiple design points and geometric constraints. Examples are presented for both transonic and supersonic configurations ranging from wing alone designs to complex configuration designs involving wing, fuselage, nacelles and pylons.

Reuther, James↗
DOE OSTI2023

HD-Bind: Encoding of Molecular Structure with Low Precision, Hyperdimensional Binary Representations

Publicly available collections of drug-like molecules have grown to comprise tens of billions of compounds due to advances in combinatorial chemistry. Traditional methods for identifying "hit" molecules from a large collection of potential drug-like candidates have relied on biophysical theory to compute approximations to the Gibbs free energy of the binding interaction between the drug and its protein target. These approaches have the major drawback that they require exceptional computing capabilities for even relatively small collections of molecules. Hyperdimensional Computing (HDC) is a recently-proposed learning paradigm that represents data with high-dimension binary vectors; this allows the use of low-precision binary vector arithmetic to create models of the data that can be learned without the need for the gradient-based optimization required in many conventional machine learning and deep learning methods. This algorithmic simplicity allows for acceleration in hardware that has been previously demonstrated in a range of application areas. We consider existing HDC approaches for molecular property classification and introduce two novel encodings of a commonly-used molecular representation, the extended connectivity fingerprint (ECFP). We show that HDC-based inference methods are as much as 91 times more efficient than traditional machine learning methods, and achieve an acceleration of nearly nine orders of magnitude compared to molecular docking. Our results show that HDC accelerated methods retain competitive accuracy on a number of well-studied tasks such as molecular property predictions using the MoleculeNet dataset, and bind/no-bind activity classification using the DUD-E and LIT-PCBA datasets. Our work thus motivates further investigation into molecular representation learning to develop ultraefficient pre-screening tools.

Jones, William↗
DOE OSTI2020

A scalable matrix-free spectral element approach for unsteady PDE constrained optimization using PETSc/TAO

In this work, we provide a new approach for the efficient matrix-free application of the transpose of the Jacobian for the spectral element method for the adjoint-based solution of partial differential equation (PDE) constrained optimization. This results in optimizations of nonlinear PDEs using explicit integrators where the integration of the adjoint problem is not more expensive than the forward simulation. Solving PDE constrained optimization problems entails combining expertise from multiple areas, including simulation, computation of derivatives, and optimization. The Portable, Extensible Toolkit for Scientific computation (PETSc) together with its companion package, the Toolkit for Advanced Optimization (TAO), is an integrated numerical software library that contains an algorithmic/software stack for solving linear systems, nonlinear systems, ordinary differential equations, differential algebraic equations, and large-scale optimization problems and, as such, is an ideal tool for performing PDE-constrained optimization. This paper describes an efficient approach in which the software stack provided by PETSc/TAO can be used for large-scale nonlinear time-dependent problems. Time integration can involve a range of high-order methods, both implicit and explicit. The PDE-constrained optimization algorithm used is gradient-based and seamlessly integrated with the simulation of the physical problem.

97 MATHEMATICS AND COMPUTING↗
NASA NTRSDate not supplied

Flight Dynamics Modeling for a Rapid Conceptual Development Environment

This paper presents the integration of flight dynamics modeling (FDM) within an aircraft conceptual development framework. Within this framework, FDM and simulation are used for the preliminary analysis of the takeoff, landing, and critical loss of thrust performance of early-stage aircraft concepts. The aerodynamic and propulsive models are built using the XML-based DAVE-ML model exchange. Automated integration of these models is achieved using the Simulink® model generation available through the DAVEtools Java package in addition to Simulink®-based flight simulation blocks. Results demonstrating the established methods are presented for the analysis of a twin-engine light transport example aircraft. This work establishes methods that will be used to perform trade studies of aircraft designed for Regional Air Mobility operations. These aircraft will require short takeoff and landing distances in addition to steep climb and descent gradients, each of which can be estimated and applied as design space constraints using the current methods.

Flight Dynamics↗
DOE OSTI2026

Sub-Doppler Cooling of a Trapped Ion in a Phase-Stable Polarization Gradient

Trapped ions provide a highly controlled platform for quantum sensors, clocks, simulators, and computers, all of which depend on cooling ions close to their motional ground state. Existing methods like Doppler, resolved sideband, and dark resonance cooling balance trade-offs between the final temperature and cooling rate. A traveling polarization gradient has been shown to cool multiple modes quickly and in parallel, but utilizing a stable polarization gradient can achieve lower ion energies, while also allowing tailorable light-matter interactions in the sub-wavelength regime. In this Letter, we demonstrate cooling of a trapped ion below the Doppler limit using a phase-stable polarization gradient created using trap-integrated photonic devices. At an axial frequency of 2⁢𝜋×1.45 MHz we achieve ⟨𝑛⟩=1.56±0.07 in 150 μ⁢s and cooling rates of ∼0.3 quanta/μ⁢s. Here, we examine ion dynamics under different polarization gradient phases, detunings, and intensities, showing reasonable agreement between experimental results and a multilevel model. Cooling is fast and power efficient, with lower average motional Fock state occupation when compared to simulated operation under the corresponding running wave configuration. Our results demonstrate a well-controlled test bed for studying the dynamics of multilevel atomic systems in a phase-stable polarization gradient.

Atom & ion cooling↗
DOE OSTI2021

Evaluation of the Large-Scale and Regional Climatic Response Across North Africa to Natural Variability in Oceanic Modes and Terrestrial Vegetation Among the CMIP5 Models

Hydrologic variability is a serious threat to the poverty-stricken regions of North Africa. Meanwhile, the scientific community struggles to attribute these extreme climatic episodes to specific oceanic and land drivers. Prior modeling studies have not assessed simulated feedbacks over North Africa against an established observational benchmark, so their results are considered as untested, model-specific findings. The Coupled Model Intercomparison Project Phase Five (CMIP5) archive represents the state-of-the-art in climate projections, with most CMIP5 models now containing interactive vegetation phenology; however, there have been no studies to date of their simulated vegetation feedbacks. The capability of CMIP5 models at accurately simulating the forcing of both sea-surface temperature (SST) and regional leaf area index (LAI) anomalies on North African climate needs to be a key consideration in assessing the models’ overall credibility and determining appropriate model weighting for developing climate projections. The Generalized Equilibrium Feedback Assessment (GEFA) is a promising statistical method, which can be applied to either model output or observations, for isolating the local and remote impacts of individual oceanic or terrestrial forcings on regional climate. We performed a combined observational and modeling assessment of land-ocean-atmosphere interactions across the distinct ecological and moisture gradients of North Africa. We evaluated and demonstrated the reliability of the GEFA statistical method over North Africa using the Community Earth System Model (CESM), applied GEFA to observational data to quantify the observed forcing of ocean basin SST anomalies and regional LAI anomalies on North African climate, evaluated the CMIP5 models’ performance in terms of representing these key observed feedbacks, and formulated CMIP5 feedback performance metrics for weighting North African climate projections. Our study represented the first attempt to separate the observed roles of oceanic and vegetation feedbacks across North Africa, the first systematic assessment and intercomparison of land-ocean-atmosphere feedbacks in CMIP5, and the first exploration of vegetation feedbacks among CMIP5 models. The following work was accomplished. (1) The team generated 14 scientific publications and 30 presentations based on the DOE-funded research. (2) A stepwise version of the GEFA statistical method was developed in which unimportant forcings were dropped to increase the reliability of the results. (3) SGEFA was successfully validated through experiments with CESM in terms of its ability to isolate the atmospheric responses to individual oceanic or land forcings. (4) Observational evidence was revealed for the Sahel’s positive vegetation-rainfall feedback on the seasonal to interannual time scale, and it was attributed to a moisture recycling mechanism rather than an albedo mechanism. (5) An approach with SGEFA was developed in which the individual contributions of soil moisture versus vegetation forcings could be separated, revealing that the former forcing outweighed the latter for sub-Saharan Africa. (6) Tropical ocean temperatures were found to be key regulators of pan-tropical vegetation variability, especially for arid and semi-arid regions, including sub-Saharan Africa. (7) The CMIP5 models largely underestimated the importance of land feedbacks across the Sahel. (8) The general consensus among CMIP5 models indicates, for the late 21st century, a diminished seasonal predictability of sub-Saharan African regional climate and an elevated role of the land surface compared to oceanic drivers in regulating regional climate variability. (9) Land-ocean-atmosphere interactions were demonstrated to be key contributors to the seasonal predictability of African wildfire activity. (10) The El Djouf was determined to be of greater importance than the Bodélé depression in terms of providing trans-Atlantic dust transport to the Americas.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2005

Depth-Penetrating Luminescence Thermography of Thermal- Barrier Coatings

A thermographic method has been developed for measuring temperatures at predetermined depths within dielectric material layers . especially thermal-barrier coatings. This method will help satisfy a need for noncontact measurement of through-the-thickness temperature gradients for evaluating the effectiveness of thermal- barrier coatings designed to prevent overheating of turbine blades, combustor liners, and other engine parts. Heretofore, thermography has been limited to measurement of surface and near-surface temperatures. In the thermographic method that is the immediate predecessor of the present method, a thermographic phosphor is applied to the outer surface of a thermal barrier coating, luminescence in the phosphor is excited by illuminating the phosphor at a suitable wavelength, and either the time dependence of the intensity of luminescence or the intensities of luminescence spectral lines is measured. Then an emissivity-independent surface-temperature value is computed by use of either the known temperature dependence of the luminescence decay time or the known temperature dependence of ratios between intensities of selected luminescence spectral lines. Until now, depth-penetrating measurements have not been possible because light of the wavelengths needed to excite phosphors could not penetrate thermal-barrier coating materials to useful depths. In the present method as in the method described above, one exploits the temperature dependence of luminescence decay time. In this case, the phosphor is incorporated into the thermal-barrier coat at the depth at which temperature is to be measured. To be suitable for use in this method, a phosphor must (1) exhibit a temperature dependence of luminescence decay time in the desired range, (2) be thermochemically compatible with the thermal-barrier coating, and (3) exhibit at least a minor excitation spectral peak and an emission spectral peak, both peaks being at wavelengths at which the thermal-barrier coating is transparent or at least translucent. Conventional thermographic phosphors are not suitable because they are most efficiently excited by ultraviolet light, which does not penetrate thermal- barrier coating materials. (Typical thermal-barrier coating materials include or consist of various formulations of yttria-stabilized zirconia.) Only a small fraction of phosphor candidates have significant excitation at wavelengths long enough (>500 nm) for sufficient penetration of thermal-barrier coatings. One suitable phosphor material . yttria doped with europium (Y2O3:Eu) . has a minor excitation peak at 532 nm and an emission peak at 611 nm. In experiments, this material was incorporated beneath a 100-microns-thick thermal-barrier coating and subjected to excitation and measurement by the luminescence-decay-time technique. These experiments were found to yield reliable temperature values up to 1,100 C. At the time of reporting the information for this article, a search for suitable phosphors other than (Y2O3:Eu) was continuing.

Eldridge, Jeffrey↗