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NASA NTRS2012

Constructing an Efficient Self-Tuning Aircraft Engine Model for Control and Health Management Applications

Self-tuning aircraft engine models can be applied for control and health management applications. The self-tuning feature of these models minimizes the mismatch between any given engine and the underlying engineering model describing an engine family. This paper provides details of the construction of a self-tuning engine model centered on a piecewise linear Kalman filter design. Starting from a nonlinear transient aerothermal model, a piecewise linear representation is first extracted. The linearization procedure creates a database of trim vectors and state-space matrices that are subsequently scheduled for interpolation based on engine operating point. A series of steady-state Kalman gains can next be constructed from a reduced-order form of the piecewise linear model. Reduction of the piecewise linear model to an observable dimension with respect to available sensed engine measurements can be achieved using either a subset or an optimal linear combination of "health" parameters, which describe engine performance. The resulting piecewise linear Kalman filter is then implemented for faster-than-real-time processing of sensed engine measurements, generating outputs appropriate for trending engine performance, estimating both measured and unmeasured parameters for control purposes, and performing on-board gas-path fault diagnostics. Computational efficiency is achieved by designing multidimensional interpolation algorithms that exploit the shared scheduling of multiple trim vectors and system matrices. An example application illustrates the accuracy of a self-tuning piecewise linear Kalman filter model when applied to a nonlinear turbofan engine simulation. Additional discussions focus on the issue of transient response accuracy and the advantages of a piecewise linear Kalman filter in the context of validation and verification. The techniques described provide a framework for constructing efficient self-tuning aircraft engine models from complex nonlinear simulations.Self-tuning aircraft engine models can be applied for control and health management applications. The self-tuning feature of these models minimizes the mismatch between any given engine and the underlying engineering model describing an engine family. This paper provides details of the construction of a self-tuning engine model centered on a piecewise linear Kalman filter design. Starting from a nonlinear transient aerothermal model, a piecewise linear representation is first extracted. The linearization procedure creates a database of trim vectors and state-space matrices that are subsequently scheduled for interpolation based on engine operating point. A series of steady-state Kalman gains can next be constructed from a reduced-order form of the piecewise linear model. Reduction of the piecewise linear model to an observable dimension with respect to available sensed engine measurements can be achieved using either a subset or an optimal linear combination of "health" parameters, which describe engine performance. The resulting piecewise linear Kalman filter is then implemented for faster-than-real-time processing of sensed engine measurements, generating outputs appropriate for trending engine performance, estimating both measured and unmeasured parameters for control purposes, and performing on-board gas-path fault diagnostics. Computational efficiency is achieved by designing multidimensional interpolation algorithms that exploit the shared scheduling of multiple trim vectors and system matrices. An example application illustrates the accuracy of a self-tuning piecewise linear Kalman filter model when applied to a nonlinear turbofan engine simulation. Additional discussions focus on the issue of transient response accuracy and the advantages of a piecewise linear Kalman filter in the context of validation and verification. The techniques described provide a framework for constructing efficient self-tuning aircraft engine models from complex nonlinear simulatns.

Armstrong, Jeffrey B.↗

DOE OSTI2024

Understanding the Origin of Negative Temperature Dependence and Activity of N-Coordinated Cobalt Sites During Ethylene Dimerization

The on-demand production of short-chain linear alpha olefins (LAOs; C4-C8) via C2H4 dimerization and oligomerization is industrially attractive, prompting extensive research on designing active, selective, and stable catalysts for industrial use. Cobalt supported on ammoniated carbon (Co(NH3)x/C) catalysts have shown remarkable activity and selectivity in this process. However, critical aspects such as the active phase, active site structure, the role of the catalyst support, cobalt loading effects, and the inverse correlation of the reaction rate with temperature remain inadequately understood. This study systematically explores these factors using a combination of steady-state differential catalytic tests, in situ molecular characterization including diffuse reflectance UV-Vis (DR-UV-Vis), Infrared, and Raman spectroscopies, and ex situ X-ray diffraction (XRD) and high annular aberration-corrected dark field transmission electron microscopy (HAADF-STEM). Various supports (SiO2, Al2O3, NH4-ZSM-5, g-C3N4, and C) and cobalt loadings (1.0-3.0 Co nm-2) were studied to determine the optimal catalyst composition and identify the active phase and sites. Carbon-supported catalysts uniquely produce C4-8 LAOs during C2H4 dimerization, with site-time-yield remaining constant (~10-3 s-1) for 1.0-4.0 Co nm-2 at prolonged reaction times (24-48?h time-on-stream). At higher loadings of 6.0 Co nm-2, the formation of crystalline CoO and Co3O4 phases reduces catalytic activity and LAO selectivity. Our findings show that active catalysts lack crystalline cobalt oxides and instead feature dispersed Co2+ sites, tetra-coordinated to a mix of N/NH3 and O/H2O ligands, which catalyze C2H4 dimerization via the Cossee-Arlman mechanism, exhibiting 1st order dependence on C2H4 concentration. The observed inverse rate-temperature correlation is attributed to compensation effects (i.e., presence of Cremer-Constable relationship) linked to changes in adsorption enthalpic and entropic factors.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Techno-Economic Analysis of a Concentrating Solar Power Plant Using Redox-Active Metal Oxides as Heat Transfer Fluid and Storage Media

We present results for a one-dimensional quasi-steady-state thermodynamic model developed for a 111.7 MW e concentrating solar power (CSP) system using a redox-active metal oxide as the heat storage media and heat transfer agent integrated with a combined cycle air Brayton power block. In the energy charging and discharging processes, the metal oxide CaAl 0.2 Mn 0.8 O 2.9-δ (CAM28) undergoes a reversible, high temperature redox cycle including an endothermic oxygen-releasing reaction and exothermic oxygen-incorporation reaction. Concentrated solar radiation heats the redox-active oxide particles under partial vacuum to drive the reduction extent deeper for increased energy density at a fixed temperature, thereby increasing storage capacity while limiting the required on sun temperature. Direct counter-current contact of the reduced particles with compressed air from the Brayton compressor releases stored chemical and sensible energy, heating the air to 1,200°C at the turbine inlet while cooling and reoxidizing the particles. The cool oxidized particles recirculate through the solar receiver subsystem for another cycle of heating and reduction (oxygen release). We applied the techno-economic model to 1) size components, 2) examine intraday operation with varying solar insolation, 3) estimate annual performance characteristics over a simulated year, 4) estimate the levelized cost of electricity (LCOE), and 5) perform sensitivity analyses to evaluate factors that affect performance and cost. Simulations use hourly solar radiation data from Barstow, California to assess the performance of a 111.7 MW e system with solar multiples (SMs) varying from 1.2 to 2.4 and storage capacities of 6–14 h. The baseline system with 6 h storage and SM of 1.8 has a capacity factor of 54.2%, an increase from 32.3% capacity factor with no storage, and an average annual energy efficiency of 20.6%. Calculations show a system with an output of 710 GWh e net electricity per year, 12 h storage, and SM of 2.4 to have an installed cost of $329 million, and an LCOE of 5.98 ¢/kWh e . This value meets the U.S. Department of Energy’s SunShot 2020 target of 6.0 ¢/kWh e ( U. S Department of Energy, 2012 ), but falls just shy of the 5.0 ¢/kWh e 2030 CSP target for dispatchable electricity ( U. S Department of Energy, 2017 ). The cost and performance results are minimally sensitive to most design parameters. However, a one-point change in the weighted annual cost of capital from 8 to 7% (better understood as a 12.5% change) translates directly to an 11% decrease (0.66 ¢/kWhe) in the LCOE.

Gorman, Brandon T.↗

NASA NTRS1977

ALTKAL: An optimum linear filter for GEOS-3 altimeter data

ALTKAL is a computer program designed to smooth sea surface height data obtained from the GEOS 3 altimeter, and to produce minimum variance estimates of sea surface height and sea surface slopes, along with their standard derivations. The program operates by processing the data through a Kalman filter in both the forward and backward directions, and optimally combining the results. The sea surface height signal is considered to have a geoid signal, modeled by a third order Gauss-Markov process, corrupted by additive white noise. The governing parameters for the signal and noise processes are the signal correlation length and the signal-to-noise ratio. Mathematical derivations of the filtering and smoothing algorithms are presented. The smoother characteristics are illustrated by giving the frequency response, the data weighting sequence and the transfer function of a realistic steady-state smoother example. Based on nominal estimates for geoidal undulation amplitude and correlation length, standard deviations for the estimated sea surface height and slope are 12 cm and 3 arc seconds, respectively.

Fang, B. T.↗

NASA NTRS1979

A theory of stationary long waves. III - Quasi-normal modes in a singular waveguide

The present paper deals with the fundamental issue of whether one can treat waves as normal modes when critical surface, where the phase speed of the wave matches the zonal wind speed, are present. In particular the question of whether a Rossby critical level (such as the zero-wind line for stationary waves) is absorbing or reflecting is raised and subsequently addressed. It is found that the critical level is never totally absorbing; Rossby waves are partially reflected even if the critical layer is dominated by dissipative processes. The relevance of nonlinearity in planetary-scale Rossby wave critical layers is also discussed and it is found to be the dominant mechanism. With the relative magnitudes of nonlinearity versus viscosity relevant to the earth's atmosphere it is found that the steady-state critical level should be almost perfectly reflecting to incident Rossby waves. Consequently, normal-mode solutions can be found; the quantization condition for these waves is also derived.

Tung, K. K.↗

NASA NTRS1985

Mephisto: Interfacial Destabilization in Metal Alloys

The destabilizing mechanisms at a solidification interface were studied to obtain information on the kinetics and morphologies in the transient and steady state, and to separate the influences of liquid phase instabilities from interfacial instabilities. A differential seebeck voltage measurements technique was developed to provide a continuous record of the solid-liquid interface temperature as the solidification rate is varied to determine the kinetic coefficients. Signal processing and noise suppression techniques allow nonovolt precision which corresponds to mK accuracy for the interfacial temperature.

Favier, J. J.↗

NASA NTRS2002

Dispersal of Disks Around Young Stars: Constraints on Kuiper Belt Formation

We review the evidence pertaining to the lifetimes of planet-forming disks and discuss possible disk dispersal mechanisms: 1) viscous accretion of material onto the central source; 2) close stellar encounters; 3) stellar winds; and 4) photoevaporation by ultraviolet radiation. We focus on 3) and 4) and describe the quasi-steady state appearance and the overall evolution of disks under the influence of winds and radiation from the central star and of radiation from external OB stars. Viscous accretion likely dominates disk dispersal in the inner disk (r approx. <= 10 AU), while photoevaporation is the principal process of disk dispersal outside of r approx. >= 10 AU for low mass stars. Disk dispersal timescales are compared and discussed in relation to theoretical estimates for planet formation timescales. Photoevaporation may explain the large differences in the hydrogen content of the giant planets in the solar system. The commonly held belief that our early sun's stellar wind dispersed the solar nebula is called into question. Finally, we study the constraints that the evaporation of the outer disk has on the formation of Kuiper belts in extrasolar planetary systems.

Hollenbach, David↗

NASA NTRS2005

Evolution of the Electron Yield Curves of Insulators as a Function of Impinging Electron Fluence and Energy

Electron emission and concomitant change accumulation near the surface of insulators in central to understanding spacecraft charging. We present a study of changes in electron emission yields as a result of internal charge build up due to electron dose. Evolution of total, backscattered and secondary yield results over a broad range of incident energies are presented for two representative insulators, Kapton(trademark) and Al2O3. Reliable yield curves for uncharged insulators are measured and quantifiable changes in yield are observed due to < 100 fC/sq mm fluences. We find excellent agreement with a phenomenological argument based on insulator charging predicted by the yield curve; this includes a decrease in the rate of change of the yield as incident energies approach the crossover energies and as accumulated internal charge reduces the landing energy to asymptotically approach a steady state surface charge and unity yield. We also find that the exponential decay of yield curves with fluence exhibit an energy dependent decay constant, alpha(E). Finally, we discuss physics based models for this energy dependence. To understand fluence and energy dependence of these charging processes requires knowledge of how charge is deposited within the insulator, the mechanisms for charge trapping and transport within the insulator, and how the profile of trapped charge affects the transport and emission of charges from insulators.

Sim, Alec↗

NASA NTRS2005

Promoted Metals Combustion at Ambient and Elevated Temperatures

Promoted combustion testing of materials, Test 17 of NASA STD-6001, has been used to assess metal propensity to burn in oxygen rich environments. An igniter is used at the bottom end of a rod to promote ignition, and if combustion is sustained, the burning progresses from the bottom to the top of the rod. The physical mechanisms are very similar to the upward flammability test, Test 1 of NASA STD-6001. The differences are in the normal environmental range of pressures, oxygen content, and sample geometry. Upward flammability testing of organic materials can exhibit a significant transitional region between no burning to complete quasi-state burning. In this transitional region, the burn process exhibits a probabilistic nature. This transitional region has been identified for metals using the promoted combustion testing method at ambient initial temperatures. The work given here is focused on examining the transitional region and the quasi-steady burning region both at conventional ambient testing conditions and at elevated temperatures. A new heated promoted combustion facility and equipment at Marshall Space Flight Center have just been completed to provide the basic data regarding the metals operating temperature limits in contact with oxygen rich atmospheres at high pressures. Initial data have been obtained for Stainless Steel 304L, Stainless Steel 321, Haynes 214, and Inconel 718 at elevated temperatures in 100-percent oxygen atmospheres. These data along with an extended data set at ambient initial temperature test conditions are examined. The pressure boundaries of acceptable, non-burning usage is found to be lowered at elevated temperature.

Engel, Carl D.↗

NASA NTRS1999

Bubble Dynamics on a Heated Surface

In this work, we study steady and oscillatory thermocapillary and natural convective flows generated by a bubble on a heated solid surface. The interaction between gas and vapor bubbles with the surrounding fluid is of interest for both space and ground-based processing. A combined numerical-experimental approach is adopted here. The temperature field is visualized using Mach-Zehnder and/or Wollaston Prism Interferometry and the flow field is observed by a laser sheet flow visualization technique. A finite element numerical model is developed which solves the transient two-dimensional continuity, momentum, and energy equations and includes the effects of temperature-dependent surface tension and bubble surface deformation. Below the critical Marangoni number, the steady state low-g and 1-g temperature and velocity fields predicted by the finite element model are in excellent agreement with both the visualization experiments in our laboratory and recently published experimental results in the literature. Above the critical Marangoni number, the model predicts an oscillatory flow which is also closely confirmed by experiments. It is shown that the dynamics of the oscillatory flow are directly controlled by the thermal and hydrodynamic interactions brought about by combined natural and thermocapillary convection. Therefore, as numerical simulations show, there are considerable differences between the 1-g and low-g temperature and flow fields at both low and high Marangoni numbers. This has serious implications for both materials processing and fluid management in space.

Kassemi, M.↗

DOE OSTI2021

Towards a reliable assessment of charging effects during surface analysis: Accurate spectral shapes of ZrO 2 and Pd/ZrO 2 via X-ray Photoelectron Spectroscopy

X-ray Photoelectron Spectroscopy of large bandgap or insulating material surfaces relies on an effective mechanism that compensates for the emission (loss) of electrons by maintaining the material surface at a steady-state uniform potential. While a steady-state may be attained by utilizing an active compensation, such as low power electron emitting filament, there is the possibility that the surface potential is not uniform over the area analyzed, leading to peak shifts and incorrect spectral interpretation. Here, in this work, a spectral data processing method based on mapping the ZrO 2 and Pd/ZrO 2 surfaces utilizing photoemission peak binding energy is proposed, which provides information about the response of specific material surfaces to charge compensation. Spectromicroscopy of ZrO 2 and Pd/ZrO 2 surfaces without spatial information is used to monitor the efficacy of charge compensation. Exploiting counts distributed over many bins require the use of procedures and algorithms essential to practical mapping peak positions. Iterative singular value decomposition is therefore introduced and utilized as a means of efficiently delivering spatially resolved spectra from which binding energy for peaks is computed. The concepts developed in this work result in robust and accurate peak models of ZrO 2 and Pd/ZrO 2 that can be applied in XPS analysis of not only ZrO 2 but other large bandgap or insulating material surfaces. Supporting arguments for a peak model representing signal from Zr 3p and Pd 3d are developed within this work are presented.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Dioctyl ether radiolysis under used nuclear fuel reprocessing conditions: Foundational knowledge for the development of sacrificial ligand grafts

Radiation-induced ligand destruction and concomitant degradation product formation is unavoidable under envisioned used nuclear fuel reprocessing conditions, and ultimately limits the recyclability of a given solvent system formulation. With this in mind, a novel approach to ligand innovation for advanced separations processes is in the design of tailored “protomolecules,” which when exposed to ionizing radiation undergo desired chemical transformations, thereby allowing for a reprocessing solvent system to advantageously evolve with absorbed radiation dose. Here we provide foundational knowledge for the time-resolved (electron pulse) and steady-state (cobalt-60 gamma) radiolytic behavior of dioctyl ether, a protomolecule grafting surrogate. Gamma irradiation of single-phase solutions of dioctyl ether (5–100 vol.%) in n-dodecane resulted in the loss of dioctyl ether (G = -0.72 µmol J –1 ) and the formation of octane (G = 0.11 µmol J –1 ) and octanol (G = 0.15 µmol J –1 ) degradation products, the latter of which is a known reprocessing phase modifier and radioprotectant. Further, these radiation-induced changes were attributed to direct radiation effects, for more concentrated dioctyl ether solutions, and indirect radiation effects, predominantly driven by the reaction of dioctyl ether with the dodecane radical cation, for which we report a second-order rate coefficient of k = (1.53 ± 0.05) × 10 10 L mol –1 s –1 . Under typical biphasic extraction (4.0 mol L –1 HNO 3 ) and strip (0.1 mol L –1 HNO 3 ) reprocessing conditions, gamma irradiation of 5 vol.% dioctyl ether solvent systems afforded negligible change in the rate of parent molecule destruction but promoted significant differences in the radiolytic behavior of its degradation products. These differences are attributed to their respective interactions with [dioctyl ether/HNO 3 /H 2 O] and [octanol/HNO 3 /H 2 O] adducts extracted into the organic phase. Overall, these results support the grafting of ether linkages to advanced separations ligands (e.g., modified diglycolamides).

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗

DOE OSTI2025

Design and Analysis of an Integrated Additively Manufactured Test Article for Plasma-Facing Components

Current plasma-facing components (PFCs) used in helium-cooled divertor modules are complex structures with tungsten tile, steel sleeve components, and cartridges, all assembled in a helium-cooled multiple jet (HEMJ) structure. The goal of this project is to simplify the complex PFC design using additive manufacturing techniques to create a single integrated tungsten test article. Apart from the flexibility this opens up in exploring a wide array of geometries for the article, having a single integrated article significantly reduces the number of joints and parts in the article, thus reducing chances of leaks. A process called electron beam melting has shown to produce very high-density samples and unique geometries, enabling HEMJ or similar designs. To validate and optimize this novel design, the model underwent a series of computational fluid dynamics and finite element analysis simulations to replicate steady-state heat flux in the divertors. The simulations presented in this study consider a steady-state base heat flux of 5 MW/m 2 , with water serving as the coolant. Future research will explore the use of helium as a coolant, simulate edge-localized-mode conditions, and include experimental validation. Since 3D-printed tungsten is anisotropic, the build direction versus build plane of the article are taken into consideration for the test article strength. Because of the high operating temperatures and low ductility of tungsten, thermal creep and brittle fracture are important failure mechanisms to consider. In conclusion, the cap is evaluated with various flow velocities and nozzle diameters, and an optimal design choice is made for which this cap will survive the divertor conditions with a conservative safety margin.

Divertor↗

NASA NTRS1988

Control-augmented structural synthesis

A control-augmented structural synthesis methodology is presented in which the structural member sizes and active control system feedback gains are treated simultaneously as independent design variables. Multiple static and harmonic dynamic loading conditions are considered. Constraints are imposed on static displacements, natural frequencies, and the magnitudes of the steady-state dynamic displacements and actuator forces to ensure acceptable system behavior. Side constraints imposed on the design variables protect against the generation of unrealizable designs. Example problems are presented that demonstrate the method and underscore the importance of integrating the structural and active control system design process.

Lust, R. V.↗

NASA NTRS1995

Diamond and diamondlike carbon as wear-resistant, self-lubricating coatings for silicon nitride

Recent work on the friction and wear properties of as-deposited fine-grain diamond, polished coarse-grain diamond, and as-deposited diamondlike carbon (DLC) films in humid air at a relative humidity of approximately 40 percent and in dry nitrogen is reviewed. Two types of chemical vapor deposition (CVD) processes are used to deposit diamond films on silicon nitride (Si3N4) substrates: microwave-plasma and hot-filament. Ion beams are used to deposit DLC films of Si3N4 substrates. The diamond and DLC films in sliding contact with hemispherical bare Si3N4 pins have low steady-state coefficients of friction (less than 0.2) and low wear rates (less than 10(exp -7) mm(exp 2)/N-m), and thus, can be used effectively as wear-resistant, self-lubricating coatings for Si3N4 in the aforementioned two environments.

Miyoshi, Kazuhisa↗

NASA NTRS2002

Phase Transition in Dusty Plasmas: A Microphysical Description

Dust grains immersed in plasma discharges acquire a large negative charge and settle into a dust cloud at the edge of the sheath. In this region, the plasma ions stream toward the electrode at a velocity u approx. cs=(T(sub e)/m(sub i))(exp 1/2). Experimentally at sufficiently high gas pressure P, the random kinetic energy of the grains is damped by gas friction, and the grains are strongly coupled and self-organize into a crystalline configuration. For lower pressures despite the dissipation of grain kinetic energy to gas friction, the dust grains reach a steady-state kinetic temperature T(sub d) which is much larger than the temperature of any other component in the plasma. T(sub d) is so large that the dust acts like a fluid. We have used the dynamically shielded dust (DSD) model to simulate these physical processes. We find that the known experimental features are nicely reproduced in the simulations, and that additional features are revealed. In the figure we plot the variation of T(sub d) as P is continuously varied in a DSD code run. A marked difference is evident between the critical pressure P(sub m) for the melting transition as P is decreased, and the critical pressure P(sub c) for the condensation transition as P is increased. For P(sub m) is less than P is less than P(sub c), mixed phase states are seen. This hysteresis occurs because the instability which triggers melting is different from the instability that heats the dust in the fluid phase and inhibits freezing. At low pressure, the dust is subject to a two-stream instability with the ions. This instability is responsible for the high temperature of the dust at low pressure. The basic physics underlying the melting transition has been elucidated in a series of papers. We are developing a first-principles analytic approach to the melting transition, which embodies the same physics that is present in the DSD code.

Joyce, Glenn↗

NASA NTRS2003

Data and Modeling of Dendrites Subject to A Step Change in Pressure (TDSE)

There is considerable interest in dendritic solidification because of the influence dendrites have in the determination of microstructure, and thereby in the physical properties of cast metals and alloys. Current theories and models of dendritic growth generally couple diffusion effects in the melt with the physics of the interface. Data and subsequent analysis prior of the tip growth speed and radii of thermal succinonitrile dendrites in the near-convection free, on-orbit, free-fall environment demonstrate that these theories yield predictions that are reasonably in agreement with the results of experiment. However, data and analysis for assessing the interfacial physics component of theory are not sufficiently detailed or definitive. To study fundamental aspects of dendritic interface stability, we are measuring and modeling the kinetics and morphology of dendrites as they evolve from one well-defined steady state at a pre-set supercooling, through a transient stage, to a different well-defined steady state. More specifically, we subject succinonitrile dendrites, growing under steady-state conditions, to a rapid change in pressure. This leads to a rapid change in thermal driving force from the corresponding change in both the equilibrium melting temperature due to the Clapeyron effect, and a change in the far-field temperature due to adiabatic temperature changes in the bulk liquid and solid. Subsequently, we observe transformations from a well-characterized initial state into a new steady-state. Initial data reveal that the dendrite tip velocity changes almost as fast as the pressure charges, while the tip radius changes occur more slowly, taking from 10 60 seconds depending on the size of the step change and the final supercooling. Computer modeling of this process shows both agreements and disagreements with the experimental data. In making these observations and measurements, we are gaining new understandings of interfacial dynamics and state-selection physics.

Koss, Matthew B.↗

NASA NTRSDate not supplied

An Overview of the Patch Integral Method (PIM), a New Heat Transfer Analysis Tool for Hypersonic Wind Tunnel Facilities at NASA Langley

NASA Langley’s hypersonic wind tunnels are heavily leveraged for planetary missions. The data collection method in these tunnels is thermography, and surface temperature measurements of the model surface are collected and reduced to produce surface heating data, as seen in Fig 1. However, during model injection, no temperature data are collected, and thus conventional, integral heat transfer methods cannot be used to solve for surface heating. A method was developed in the 1990’s to reduce this data despite the data gap, known as the step approximation method. The method assumes that the film coefficient behaves as a step function, the model is semi-infinite, and thermal properties are constant. With these simplifying assumptions, a Laplace transform can be performed to result in an equation that takes the initial temperature of the model and a temperature at some point in time to back out the film coefficient at that time. This is the method that is used in the current thermographic data reduction software, IHEAT. While computationally light-weight, the step approximation has several issues associated with it. The time-history of temperature is not accounted for, which is vital as heat transfer is an integral process. Additionally, the required semi-infinite assumption is unnecessary and might be violated during runtime. Thermal variation of material properties can have a sizeable impact on heating results and are not modeled by the method. This method also takes multiple seconds to “collapse” to a steady state, which is undesirable from both a facility and data reduction standpoint. The method is also very sensitive to the “effective time” approximation, an approximation of when heating instantaneously starts (which is a nonphysical simplification), and a small variation in this value can result in an error in heating results.

J. S. Cheatwood↗