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Softening the Gap between Wöhler and Paris – New Approaches for Fatigue Analysis –

Fatigue analysis tools can vary across industries. For example, automotive engineers often use the Wöhler (S-N) approach to design for safe-life, while aerospace engineers prioritize damage tolerance and inspection intervals, relying instead on crack growth models such as Paris’ law. Although both approaches may deal with the control of cracks in similar materials, their analysis tools and material characterizations are fundamentally distinct. This divide mirrors the classic split between stress-based strength analysis and linear elastic fracture mechanics. However, modern nonlinear models that incorporate material softening, such as cohesive laws, blur this boundary and capture fracture behaviors across scales. This presentation describes the CF23 fatigue model, which uses cohesive softening to link S-N crack initiation with crack propagation rates. CF23 spans the full fatigue spectrum, from initial propagation transients to steady-state growth and threshold conditions, offering a unified framework that bridges Wöhler and Paris-based methodologies. Example applications include fatigue crack propagation transients in adhesive interfaces and skin/stiffener separation.

cohesive elements

Microstructural Evolution and Mechanical Properties of LP-DED NASA HR-1 – A Hydrogen Resistant AM Superalloy for Space Propulsion Applications

The National Aeronautics and Space Administration (NASA) has actively pursued metal additive manufacturing (AM) technologies for spaceflight applications since the late 2000s. AM offers transformative advantages in cost, schedule, part consolidation, and design flexibility. Among the various AM techniques, laser powder directed energy deposition (LP-DED) is particularly well suited for fabricating complex geometries with fine feature resolution. In propulsion systems that utilize high-pressure gaseous hydrogen—such as liquid hydrogen rocket engines—hydrogen environment embrittlement (HEE) presents a serious threat to material performance 1,2 . Mechanical property degradation under these conditions can compromise component reliability, especially under cyclic loading. To address this challenge, NASA developed NASA HR-1 (Hydrogen Resistant-1) as a solution for liquid rocket engine components operating in hydrogen-rich environments, using the LP-DED technique 3-9 . A key component in a liquid rocket engine is the exhaust nozzle, which is typically regeneratively cooled (regen) due to the high heat flux. NASA HR-1 was specifically developed for regen nozzle applications using hydrogen as a propellant, providing resistance to HEE, a critical issue for many materials. The AM version of NASA HR-1 was also formulated to achieve high ultimate tensile strength, along with high yield strength and ductility in this environment 5,6 . Low-cycle fatigue (LCF) is another important consideration in nozzle design, as components are expected to endure multiple starts and missions. Additionally, the LP-DED version of the alloy exhibits improved thermal conductivity compared to its wrought counterpart, which benefits nozzle cooling. Overall, NASA HR-1 offers an excellent balance of high strength, HEE resistance, LCF performance, thermal conductivity, and ductility to meet the demanding requirements of channel-cooled nozzles and other components used with hydrogen and other propellants. The LP-DED–processed NASA HR-1 requires several post-processing heat treatment steps to achieve the material properties desirable for its intended application 6 . These steps include stress relief, homogenization, solution annealing, and aging for precipitation hardening. The stress relief treatment mitigates residual stresses accumulated during the LP-DED process and minimizes the potential for distortion. Homogenization, a common step for AM materials, reduces elemental segregation and promotes recrystallization to develop a more equiaxed grain structure. The subsequent solution annealing treatment heats the part to a solid solution temperature to dissolve the undesirable η-phase that forms during cooling from homogenization, followed by rapid cooling to retain an η-phase–free microstructure. Finally, aging promotes precipitation of the strengthening γ′ phase in the alloy. The integration of compositional design and optimized thermal processing enables high-quality LP-DED NASA HR-1 components with excellent microstructural and mechanical stability. Improved chemical and microstructure homogeneity enhances ductility and fatigue resistance—both critical for safe and reliable operation in high-pressure hydrogen environments. NASA has successfully fabricated and hot-fire tested multiple subscale and full-scale channel wall nozzles using LP-DED NASA HR-1 5,6, 9-14 . These efforts included process refinements to support thin-wall construction and various channel geometries. Throughout development, several key observations emerged. After homogenization, the as-built columnar grain structure transforms into a fully equiaxed microstructure. However, subsequent treatments—such as solution annealing and aging—result in changes that are more difficult to track. The grain structure remains largely unchanged, and the γ′ precipitates, typically 5–10 nm in diameter, are beyond the resolution of scanning electron microscopy (SEM). While transmission electron microscopy (TEM) can resolve these fine precipitates, TEM sample preparation is time-consuming and difficult for LP-DED material. As an alternative, differential scanning calorimetry (DSC) offers a useful, qualitative approach to monitor precipitate evolution throughout different stages of heat treatment. The overall goal is to improve the understanding of how heat treatment affects the microstructure and mechanical performance of LP-DED NASA HR-1. This paper presents heat treatment design considerations, microstructural characterization, mechanical testing – including tensile and LCF testing in both air and hydrogen environments.

Superalloy

Thermal Data-driven Model Reduction for Enhanced Battery Health Monitoring

Electric aviation faces a major challenge of avoiding potentially catastrophic consequences of the battery’s thermal runaway while keeping the weight of the battery low. Detection of early warning signals of battery failures requires accurate monitoring of the battery’s health throughout its lifespan. However, identifying the parameters of the battery from field data is notoriously difficult. We investigate this problem within the framework of modeling the temperature dynamics of a Li-ion cell during tests simulating loading in electric aircraft flights. It is found that the parameters of a higher-fidelity physics-based thermal model cannot be identified from the simulated flight data. To resolve this issue, we reduce the higher-fidelity thermal model to a model with fewer parameters. The resulting reduced-order model can predict temperature dynamics accurately and is identifiable throughout the cell’s lifespan which allows using the model’s parameters to monitor the state-of-health of the aging cell and detect anomalies in thermal behavior.

Li ion batteries

Single-Drop Reactive Extraction/Extractive Reaction with Forced Convective Diffusion and Interphase Mass Transfer

An algorithm has been developed for the forced convective diffusion-reaction problem for convection inside and outside a droplet by a recirculating flow field hydrodynamically coupled at the droplet interface with an external flow field that at infinity becomes a uniform streaming flow. The concentration field inside the droplet is likewise coupled with that outside by boundary conditions at the interface. A chemical reaction can take place either inside or outside the droplet or reactions can take place in both phases. The algorithm has been implemented and results are shown here for the case of no reaction and for the case of an external first order reaction, both for unsteady behavior. For pure interphase mass transfer, concentration isocontours, local and average Sherwood numbers, and average droplet concentrations have been obtained as a function of the physical properties and external flow field. For mass transfer enhanced by an external reaction, in addition to the above forms of results, we present the enhancement factor, with the results now also depending upon the (dimensionless) rate of reaction.

Leonid S Kleinman

Solid Inflammability Boundary at Low Speed (SIBAL)

This research program is concerned with the effect of low-speed, concurrent flow on the spreading and extinction processes of flames over solid fuels. The primary objective is to verify the theoretically predicted extinction boundary, using oxygen percentage and flow velocity as coordinates. In particular, we are interested in the low-speed quenching limits and the existence of the critical oxygen flammability limit. Detailed flame spread characteristics, including flame spread rate, flame size, and flame structure are sought. Since the predicted flame behavior depends on the inclusion of flame and surface radiation, the measured results will also be used to assess the importance of radiative heat transfer by direct comparison to a comprehensive numerical model. This project passed the Science Concept Review (SCR) in 1996. As a result, the experiment continues on the flight definition path, and is currently scheduled to be performed in the Space Station Combustion Integrated Rack (CIR). We present an overview of recent and ongoing work, including selected experimental and theoretical topics.

James S T'ien

Single-Drop Reactive Extraction/Extractive Reaction With Forced Convective Diffusion and Interphase Mass Transfer

An algorithm has been developed for time-dependent forced convective diffusion-reaction having convection by a recirculating flow field within the drop that is hydrodynamically coupled at the interface with a convective external flow field that at infinity becomes a uniform free-streaming flow. The concentration field inside the droplet is likewise coupled with that outside by boundary conditions at the interface. A chemical reaction can take place either inside or outside the droplet, or reactions can take place in both phases. The algorithm has been implemented, and for comparison results are shown here for the case of no reaction in either phase and for the case of an external first order reaction, both for unsteady behavior. For pure interphase mass transfer, concentration isocontours, local and average Sherwood numbers, and average droplet concentrations have been obtained as a function of the physical properties and external flow field. For mass transfer enhanced by an external reaction, in addition to the above forms of results, we present the enhancement factor, with the results now also depending upon the (dimensionless) rate of reaction.

Leonid S Kleinman

Development of a Digital Twin for Electrified Aircraft Powertrain Health Management

The augmentation of aircraft powertrains with electrical power systems is a promising path to reducing aircraft fuel consumption, emissions, and noise. Like conventional propulsion systems, electrified aircraft propulsion (EAP) systems will be subject to wear and tear throughout their lifecycles. System health management for EAP will enable efficient flight and maintenance scheduling, realizing economic, safety, and reliability benefits. A digital twin is, broadly, a dynamically updated virtual representation of an individual physical asset. This paper presents a Kalman filter-based approach for the development of a digital twin for an electrified powertrain and applies the approach to an EAP controls testbed. Measurements from nominal testbed operations are used to update a nonlinear model of the testbed. A Kalman filter is then created and used to identify and isolate anomalous testbed behavior based on measurements from off- nominal operations. Results show that the Kalman filter-based digital twin can monitor individual powertrain components’ health for degradation or other changes in performance. The applicability of the presented digital twin approach to any hybrid- or fully-electrified powertrain is emphasized.

Electrified Aircraft Propulsion

A Multi-Tier Autonomous Aerial Architecture for Wildfire Detection, Characterization, and Communication in Infrastructure-Denied Environments

Wildfire response depends on how fast an ignition can be confirmed and located, especially in remote regions where ground-based communication and monitoring may be limited. Geostationary sensors provide frequent observations but at kilometer-scale resolution, which is too coarse to resolve small fires in remote terrain. Ground camera networks require sightlines and infrastructure that back-country areas lack. To address these limitations, this work proposes a Multi-Tier Autonomous Wildfire Intelligence System that combines wide-area monitoring with targeted, high-resolution sensing. A solar-powered high-altitude long endurance (HALE) platform operating at approximately 60,000 ft provides persistent wide-area thermal and optical surveillance, running onboard edge inference to screen candidate ignitions and reduce false positives and downlink bandwidth. When a candidate ignition is detected, low-altitude uncrewed aircraft systems (UAS) can be deployed to conduct localized observations, including high-resolution imaging and atmospheric measurements such as wind and plume observation. By combining persistent detection with local sensing, the proposed architecture is designed to provide first responders with timely, high-resolution information about fire location and behavior to aid in emergency decision making.

Wildfire management, UAS, drones

Extensional Flow Convecting a Reactant Undergoing a First Order Homogeneous Reaction and Diffusional Mass Transfer From a Sphere at Low to Intermediate Peclet and Damkohler Numbers

Forced convective diffusion-reaction is considered for viscous axisymmetric extensional convecting velocity in the neighborhood of a sphere. For Peclet numbers in the range 0.1 ≤ Pe ≤ 500 and for Damkohler numbers increasing with increasing Pe but in the overall range 0.02 ≤ Da ≤ 10, average and local Sherwood numbers have been computed. By introducing the eigenfunction expansion c(r,Θ) = Σ c n (r)P n (cosΘ) into the forced convective diffusion equation for the concentration of a chemical species undergoing a first order homogeneous reaction and by using properties of the Legendre functions P n (cosΘ), the variable coefficient PDE can be reduced to a system of N+1 second order ODEs for the radial functions C n (r), n=0,1,2, ... ,N. The adaptive grid algorithm of Pereyra and Lentini can be used to solve the corresponding 2(N+ 1) first order differential equations as a two-point boundary value problem on 1 ≤ r ≤ r •• . Convergence of the expansion for a specific value of N can thus be established and provides "spectral" behavior as well as the full concentration field c(r,Θ).

N Y Shah

Life cycle test results of a bipolar nickel hydrogen battery

A history is given of low Earth orbit (LEO) laboratory test data on a 6.5 ampere-hour bipolar nickel hydrogen battery designed and built at the NASA Lewis Research Center. The bipolar concept is a means of achieving the goal of producing an acceptable battery, of higher energy density, able to withstand the demands of low-Earth-orbit regimes. Over 4100 LEO cycles were established on a ten cell battery. It seems that any perturbation on normal cycling effects the cells performance. Explanations and theories of the battery's behavior are varied and widespread among those closely associated with it. Deep discharging does provide a reconditioning effect and further experimentation is planned in this area. The battery watt-hour efficiency is about 75 percent and the time averaged, discharge voltage is about 1.26 volts for all cells at both the C/4 and LEO rate. Since a significant portion of the electrode capacity has degraded, the LEO cycle discharges are approaching depths of 90 to 100 percent of the high rate capacity. Therefore, the low end-of-discharge voltages occur precipitously after the knee of the discharge curve and is more an indication of electrode capacity and is a lesser indicator of overall cell performance.

Cataldo, R. L.

Hubble Space Telescope nickel-hydrogen flight spare battery test

For several years, MSFC has been engaged in a series of battery tests in support of the Hubble Space Telescope (HST) Program. Now that the HST is in orbit, many of these tests will continue in order to give those responsible for the HST a reasonable prediction on the performance of the flight batteries. These tests will also be a source of needed low earth orbit (LEO) data for nickel hydrogen (Ni-H2) batteries and cells. One of the tests currently in progress at MSFC is a mission simulation test on a 22-cell Ni-H2 battery. This battery is composed of spare cells taken from the lot of cells out of which the Flight Spare Module was assembled. This module is one of two modules launched on the HST. This battery has been on test since Jun. 1989 and has completed nearly 8000 LEO cycles. A series of characterization tests were run prior to the start of the mission simulation and a launch scenario test was run in Feb. and Mar. 1990 to test the behavior of the cells through a simulated launch. The results from these tests as well as the overall performance of the battery as it continues to cycle are reported.

Brewer, Jeffrey C.

Research and development of high thermal stability fuels

Increases in aircraft performance are leading to increases in the thermal stress on the primary aircraft coolant--the fuel. Fuel thermal stability limitations may offset future aircraft performance gains. The Air Force's Wright Laboratory is sponsoring several research programs to address this problem. The development of an additive package for JP-8 to improve its thermal stability is the primary focus of this paper. This program involves extensive testing of fuels and additives in a variety of test devices, culminating in tests in a fuel system simulator and engine tests. These tests involve Air Force personnel, on-site contractors (University of Dayton Research Institute, Systems Research Laboratories), Pratt and Whitney Aircraft Co., additive manufacturers, and Sandia National Laboratory. The test devices include several flowing and static tests, where the behavior of a fuel is investigated in a wide variety of environments. The study of several baseline fuels in these devices has led to some new insights into the mechanisms of fuel thermal (in)stability. It is becoming clear that a fuel's tendency to oxidize (to form peroxides, for example) is often inversely proportional to its tendency to form insoluble deposits.

T Edwards

Mitigating Grazing Flow Impedance Eduction Errors in Additively Manufactured Porous Liners

Additively manufactured porous metamaterials, including triply periodic minimal surface (TPMS) cores, are promising candidates for aeroengine liners but often behave as extended-reacting treatments under grazing flow. Standard impedance eduction procedures assume locally-reacting behavior and can yield physically inconsistent results for such materials. This study evaluates internal partitions (thin solid walls inserted at regular intervals along the liner’s streamwise extent) as a means of suppressing internal streamwise propagation to improve eduction consistency. Six TPMS configurations were tested in the NASA Langley Grazing Flow Impedance Tube (GFIT) at partition spacings of 4′′, 2′′, and 1′′, as well as unpartitioned, and at Mach numbers up to 0.3. For most geometries, 2′′ partition spacing eliminated impedance discontinuities and substantially improved Prony correlation, though effectiveness varied with core topology. Partitions also altered the acoustic response of the liners: resistance increased, resonance frequencies shifted downward, and peak attenuation decreased while bandwidth broadened in some cases. Because partitions modify the liner itself, the educed impedance characterizes the partitioned system rather than the original unpartitioned core. These results establish partitioning as a practical pathway toward liners that are more compatible with standard eduction methods, while demonstrating that the intervention is itself an acoustic design change.

liners

An Investigation Regarding the Effects of Volume Dynamics on Gas Turbine Engine Performance and Operability

This work explores the impact of adding volume dynamics to an electrified turbofan engine model. The zero-dimensional single-input single-output volume elements capture the physics of fluid compressibility of flow in the engine core gas path turbomachinery during transient operation with greater fidelity. Some background regarding the motivation for this effort is provided. A model of the volume element is developed from first principles. The baseline engine model is described and an explanation is given of the modifications made to incorporate the volume elements into the new model. Details of the simulated inputs, designed to elicit exaggerated dynamic responses and to facilitate comparison between the baseline and modified engine models, are explicated. The results of these simulations are presented and discussed, demonstrating that the transient performance and operability of the modified engine model, measured by parameters such as shaft speeds, thrust, and high-pressure compressor (HPC) stall margin, are impacted by the additional dynamics. Commentary is provided regarding potential explanations for the differences in behavior exhibited by the two models. Finally, suggestions are offered for future work that might improve the volume models developed in this effort and leverage the improved fidelity enabled by the modeling of turbomachinery volume dynamics.

Volume dynamics

CFD Modeling of Bi-Directional PMD inside Cryogenic Propellant Tanks Onboard Parabolic Flights

Future cryogenic propulsion systems will require efficient methods with which to transfer cryogenic propellants from a depot storage tank to a customer receiver tank to minimize cost and maximize reusability. The Reduced Gravity Cryogenic Transfer project is currently developing advanced cryogenic fluid management technology and developing and validating new numerical models for three phases of transfer: line chilldown, tank chilldown, and tank fill. Additionally, multiple liquid nitrogen (LN 2 ) parabolic flight transfer rigs are being designed by universities and NASA to investigate the gravitational sensitivities that exist in these three technologies. In order to maximize the collection of low-g data during flights, it is required to extract as much (LN 2 as possible from the supply tank, despite variable gravity levels. The purpose of this paper is to present computational fluid dynamics (CFD) volume of fluid simulations of (LN 2 behavior in the supply tank onboard parabolic flights to validate the optimal design of a bi-directional propellant management device (PMD) using the commercial software FLOW-3D. A parametric study is conducted on the effects of gravity level, fill level, pore size, open area, thickness, and type of baffle on PMD performance. Based on results, the PMD as designed exceeds the targeted expulsion efficiency.

Jason Hartwig

Thermostructural Testing of PICA-D for NASA Planetary Science Missions

Phenolic Impregnated Carbon Ablator–Domestic (PICA‑D) has been selected as the heatshield thermal protection system (TPS) material for two upcoming NASA planetary science missions: the Dragonfly mission to Titan and the Mars Sample Retrieval Lander (SRL). Early testing revealed differences between PICA‑D and heritage PICA, particularly in in‑plane (IP) tensile stiffness and thermal expansion. Thermostructural analyses using Finite Element Method (FEM) tools subsequently predicted the potential for IP compressive failure in the near‑surface layers of PICA‑D under both Dragonfly and SRL flight environments. Over the past three years, the Dragonfly and SRL teams have carried out an extensive thermostructural qualification campaign to address these concerns and validate PICA‑D for flight. This effort began with a comprehensive mechanical property characterization program at Kratos test laboratories, which significantly improved understanding of PICA‑D mechanical behavior and increased the fidelity of FEM predictions. The teams also conducted six large‑scale test entries at the National Solar Thermal Test Facility (NSTTF) solar tower, exposing PICA‑D articles—including gap fillers and representative design features or flaws—to combined thermal and mechanical loads. The talk will summarize key findings from these mechanical and thermostructural test campaigns and present the current status of PICA‑D qualification for NASA’s planetary science missions.

TPS

PROTECT: Production and Reuse of Thermally Efficient Ceramic Thermal Protection Systems

PROTECT (Production and Reuse Of Thermally Efficient Ceramic TPS) is a NASA Early Career Initiative focused on developing the next generation of reusable ceramic thermal protection systems (TPS). This project addresses key challenges in TPS design, including temperature capability, thermal stability, and refurbishment time, by integrating novel material development with predictive modeling. Leveraging enhanced capabilities in NASA’s Porous Microstructure Analysis (PuMA) software, PROTECT introduces new modeling tools to predict the thermal and mechanical behavior of fibrous ceramic materials. These tools enable accurate prediction of performance metrics such as thermal conductivity and structural integrity, reducing reliance on costly physical testing. Preliminary advances in these areas will be presented. To support model validation, PROTECT is building a comprehensive database of raw material properties using advanced characterization techniques, including micro computed tomography (CT) scanning in collaboration with the University of Illinois Urbana-Champaign (UIUC). The presentation will detail the sampling workflows and analysis methods used to generate this detailed microstructural data and how it is used to develop improved models in PuMA. This multi-center collaboration, spanning NASA (JSC, ARC, KSC, GRC), Oak Ridge National Laboratory, UIUC, and SpaceX, is developing tailored TPS solutions for LEO, lunar, and Martian missions. By bridging heritage systems with the demands of modern spaceflight, PROTECT contributes to the advancement of reusable TPS technologies for future exploration missions.

Propulsion, Refractory, and Coating Materials

Preliminary Dynamic Modeling of the Quarter-Scale Distributed Electric Propulsion Aircraft

This paper describes the early-stage modeling of a quarter-scale distributed electric propulsion aircraft, based on the SUbsonic Single Aft eNgine (SUSAN) Electrofan, a transformative concept aircraft for which a model exists. The full-scale 180 passenger SUSAN concept has a single turbofan engine in the tail that both produces thrust and provides electrical power to 16 electric fans distributed across the wings utilizing a series/parallel hybrid architecture. The quarter-scale version would have an internal combustion piston engine to provide power to 17 electric fans–16 on the wings, one in the tail–in a series hybrid configuration, and no vertical or horizontal stabilizers. It would also have a reduced flight envelope in terms of both altitude and speed. The initial modeling approach is to scale down the original airframe model to capture the dynamic behavior of a much smaller aircraft, albeit with an empennage. The original powertrain model is then replaced with one representing the physical components of that of the quarter-scale vehicle. This powertrain model is suitable for control design and analysis, and the fully integrated, although preliminary, aircraft model allows flight simulator testing and evaluation. Results from simulations are presented.

electrified aircraft propulsion