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

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All sourcesNASA NTRSDOE OSTI
NASA NTRS2017

A Parametric Study of Actuator Requirements for Active Turbine Tip Clearance Control of a Modern High Bypass Turbofan Engine

The efficiency of aircraft gas turbine engines is sensitive to the distance between the tips of its turbine blades and its shroud, which serves as its containment structure. Maintaining tighter clearance between these components has been shown to increase turbine efficiency, increase fuel efficiency, and reduce the turbine inlet temperature, and this correlates to a longer time-on-wing for the engine. Therefore, there is a desire to maintain a tight clearance in the turbine, which requires fast response active clearance control. Fast response active tip clearance control will require an actuator to modify the physical or effective tip clearance in the turbine. This paper evaluates the requirements of a generic active turbine tip clearance actuator for a modern commercial aircraft engine using the Commercial Modular Aero-Propulsion System Simulation 40k (C-MAPSS40k) software that has previously been integrated with a dynamic tip clearance model. A parametric study was performed in an attempt to evaluate requirements for control actuators in terms of bandwidth, rate limits, saturation limits, and deadband. Constraints on the weight of the actuation system and some considerations as to the force which the actuator must be capable of exerting and maintaining are also investigated. From the results, the relevant range of the evaluated actuator parameters can be extracted. Some additional discussion is provided on the challenges posed by the tip clearance control problem and the implications for future small core aircraft engines.

Turbine↗
NASA NTRS2011

Parametric Testing of Launch Vehicle FDDR Models

For the safe operation of a complex system like a (manned) launch vehicle, real-time information about the state of the system and potential faults is extremely important. The on-board FDDR (Failure Detection, Diagnostics, and Response) system is a software system to detect and identify failures, provide real-time diagnostics, and to initiate fault recovery and mitigation. The ERIS (Evaluation of Rocket Integrated Subsystems) failure simulation is a unified Matlab/Simulink model of the Ares I Launch Vehicle with modular, hierarchical subsystems and components. With this model, the nominal flight performance characteristics can be studied. Additionally, failures can be injected to see their effects on vehicle state and on vehicle behavior. A comprehensive test and analysis of such a complicated model is virtually impossible. In this paper, we will describe, how parametric testing (PT) can be used to support testing and analysis of the ERIS failure simulation. PT uses a combination of Monte Carlo techniques with n-factor combinatorial exploration to generate a small, yet comprehensive set of parameters for the test runs. For the analysis of the high-dimensional simulation data, we are using multivariate clustering to automatically find structure in this high-dimensional data space. Our tools can generate detailed HTML reports that facilitate the analysis.

Schumann, Johann↗
DOE OSTI2021

Microstructure based modeling of friction stir welded joint of dissimilar metals using crystal plasticity

We report the friction stir welding (FSW) process shows promising results in joining dissimilar metals which are otherwise almost impossible to join using traditional welding techniques. Being a new technique, the deformation and the failure mechanism of the joints made by the FSW process needs to be investigated. In this work, a joint between AZ31 Mg alloy and DP590 steel is modeled using phenomenological crystal plasticity formulation on the mesoscale in the form of a representative volume element (RVE). The interface of the two materials is modeled using a cohesive zone model. A parametric study has been performed to understand the effect of grain size and interface fracture toughness as well as strength on the mechanical performance of the joint. It was found that the grain size of AZ31 Mg alloy, as well as DP590 steel, has little effect on the overall joint performance. On the other hand, interface fracture toughness and strength have a significant impact on the mechanical properties of the joint

36 MATERIALS SCIENCE↗
DOE OSTI2021

Dissipative dark matter on FIRE – I. Structural and kinematic properties of dwarf galaxies

We present the first set of cosmological baryonic zoom-in simulations of galaxies including dissipative self-interacting dark matter (dSIDM). These simulations utilize the Feedback In Realistic Environments galaxy formation physics, but allow the dark matter to have dissipative self-interactions analogous to standard model forces, parametrized by the self-interaction cross-section per unit mass, (σ/m), and the dimensionless degree of dissipation, 0 < f diss < 1. We survey this parameter space, including constant and velocity-dependent cross-sections, and focus on structural and kinematic properties of dwarf galaxies with $M_{\rm halo} \sim 10^{10-11}{\, \rm M_\odot }$ and $M_{\ast } \sim 10^{5-8}{\, \rm M_\odot }$. Central density profiles (parametrized as ρ ∝ rα) of simulated dwarfs become cuspy when $(\sigma /m)_{\rm eff} \gtrsim 0.1\, {\rm cm^{2}\, g^{-1}}$ (and f diss = 0.5 as fiducial). The power-law slopes asymptote to α ≈ -1.5 in low-mass dwarfs independent of cross-section, which arises from a dark matter ‘cooling flow’. Through comparisons with dark matter only simulations, we find the profile in this regime is insensitive to the inclusion of baryons. However, when $(\sigma /m)_{\rm eff} \ll 0.1\, {\rm cm^{2}\, g^{-1}}$, baryonic effects can produce cored density profiles comparable to non-dissipative cold dark matter (CDM) runs but at smaller radii. Simulated galaxies with $(\sigma /m) \gtrsim 10\, {\rm cm^{2}\, g^{-1}}$ and the fiducial fdiss develop significant coherent rotation of dark matter, accompanied by halo deformation, but this is unlike the well-defined thin ‘dark discs’ often attributed to baryon-like dSIDM. The density profiles in this high cross-section model exhibit lower normalizations given the onset of halo deformation. For our surveyed dSIDM parameters, halo masses and galaxy stellar masses do not show appreciable difference from CDM, but dark matter kinematics and halo concentrations/shapes can differ.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2020

Probability of Decompression Sickness and Venous Gas Emboli from 49 NASA Hypobaric Chamber Tests with Reference to Exploration Atmosphere

Introduction: Decompression sickness (DCS) is a complex biophysical event; it combines human perception of pain, for instance, and the presence of a gas phase in the tissues. Living tissues are complex and dynamic. Micronuclei and later bubbles may or may not form given what appears to be the same conditions. Even when bubbles grow, symptoms may or may not develop under what appears to be the same conditions. Therefore, at this time it is appropriate to consider DCS as a probabilistic rather than a deterministic event. Methods: Probabilistic models about hypobaric DCS and venous gas emboli (VGE) require a large amount of quality research data, a definition of decompression dose using physical and physiologic variables, and a flexible analytical approach that can quantify the association between each outcome and all covariates of interest (assuming independence between DCS and VGE) and then ultimately be extended to acknowledge dependencies between DCS and VGE. Our DCS and VGE data are from 1,031 hypobaric decompressions from 1983 to 2016. A total of 577 humans participated in 49 hypobaric chamber tests to evaluate denitrogenation procedures used by astronauts in the Space Shuttle and International Space Station programs. We defined decompression dose as the ratio of computed nitrogen tension in a theoretical 360-minute half-time compartment to ambient pressure, which accounts for denitrogenation and exposure pressure as well as explanatory variables such as age, sex, body mass index, and the presence or absence of ambulation as part of exercise at the exposure pressure. A parametric survival model, using a log-logistic distribution, was used to quantify the time to development of DCS, VGE, and Grade IV VGE. Results: Our survival estimates are applicable to simple hypobaric decompressions, such as depressurizations in 5 to 30 minutes to exposure pressures between 4 and 10 pounds per square inch absolute (psia) and after minutes to hours of denitrogenation, either under resting or exercise conditions to accelerated denitrogenation. The regressions are applicable to exposures between 2 to 6 hours and under conditions of ambulation or no ambulation as part of exercise at the test pressure. We estimate that an exposure to 4.3 psia with simulated extravehicular activity (EVA) that includes ambulation after equilibration to the exploration atmosphere at 8.2 psia with a 34% oxygen atmosphere will result in 3.1% DCS (1.8% to 5.2 95% confidence interval), 23.2% VGE (16.7 to 31.2%), and 8.5% Grade IV VGE (4.7 to 14.7%) in equal samples of men and women exposed for 6 hours. Discussion: Probabilistic models for DCS, VGE, and Grade IV VGE can be used to inform those that plan future EVAs. Their applications are useful to quantify the risk of DCS and VGE in astronauts that perform EVAs in low-pressure space suits while in space or while exploring the surfaces of the moon or Mars.

Johnny Conkin↗
NASA NTRS2018

Pterodactyl: Integrated Control Design for Precision Targeting of Deployable Entry Vehicles

Deployable Entry Vehicles (DEVs) enable in-situ scientific exploration at destinations with atmospheres across the solar system. Because they stow in a compact form and deploy only when ready to enter the atmosphere, DEVs relax the volume constraint imposed by rigid aeroshells. This work seeks to do for a DEV what the Wright Brothers did to propel modern day aviation: develop the guidance and control (G&C) methods that will make maneuvering and precision landing of DEV a reality. The Pterodactyl project objective is to deliver an integrated G&C methodology for a DEV, based on a detailed analysis that utilizes a Multi-disciplinary, Design, Analysis and Optimization (MDAO) framework. The current state-of-the-art for blunt body entry, G&C is rooted in the precision landing of vehicles such as Mars Science Laboratory (MSL) and Apollo, which used a propulsive reaction control system (RCS) to steer. Recent research has taken a particular interest in non-propulsive control for DEVs, including direct force control (angle of attack modulation via control surfaces or mass movement) and drag modulation (discrete change in ballistic coefficient). Using the MDAO framework that includes a guidance and control model to explore multiple control concepts for a DEV will shed light on the best design approach for these vehicles. In Pterodactyl, we will complete this study for a novel DEV concept, and then we will fabricate a functional prototype to help validate the design. The project is expected to down-select to a final control architecture by the end of 2018, and complete fabrication of the prototype by the end of 2019.The DEV chosen for detailed study in this project is the Adaptable Deployable Entry and Placement Technology (ADEPT). ADEPT uses a revolutionary 3D-woven carbon fabric that is foldable, can serve as primary structure, and can survive the extreme heating environment of atmospheric entry. The specific configuration of ADEPT under investigation is called Lifting Nano-ADEPT (LNA). LNA is designed for secondary payloads missions that require precision landing either for scientific objectives at a target destination or for payload recovery at Earth.The MDAO framework being created through this research, called COBRA-Pt (Composite Beam Roll-Up Solar Array-Prototype), will combine three critical elements of the system design: a guidance algorithm with Monte Carlo, a parametric control model, and vehicle geometry details. Novel control models being studied are deployable aerodynamic surfaces as well as shape morphing. These concepts will be compared at the system level with a more traditional propulsive RCS by comparing several key performance parameters. Upon completion of the design study, a functional prototype of LNA will be fabricated that will include the integration of guidance software and relevant control actuators. We expect this study will provide critical data that could feed into the development of an Earth-based flight test of LNA. The COBRA-Pt framework will provide a modular system by which to study any DEV concept in any atmosphere.

Smith, Brandon↗
NASA NTRSDate not supplied

Development of a Cold-Walled Molten Regolith Electrolysis Reactor for Lunar Oxygen Production

On the lunar surface, production of commodi-ties to support human presence, such as water, food and oxygen, and sustain the growth of a per-manent outpostwill likely require the use oflocal resources. The moon is covered almost entirely withfragmented oxide minerals known as regolithhundreds of meter thick.As a resource, it is rich in oxygen (> 42 wt.%) bound in a solid state with a variety of metals. The molten regolith electrolysis (MRE)reactor is a promising technology for the production of gaseous oxygen from the lunar reg-olithin a simple, single-stepreaction that requires minimalconsumable materials, produces oxygen and metals with high electrical efficiency and high yields from any regolithcomposition.This process involvesmelting regolith to~1600°C then electro-lyzing the molten pool to separate metal and oxy-gen ions that are then collected as liquid metal and gaseous oxygen at the respective electrodes. Lab-scale demonstrations of the MRE technology have previously reliedon external heating sources to bring the entirety of the reactor up to the operating temperaturewhich creates corrosive interfaces be-tween the molten regolith and the containment ma-terial in the reactor, limiting the overall lifespan of a reactor[1]. The Gaseous Lunar Oxygen from Regolith Electrolysis (GaLORE) project is focused on the development of a “cold-walled” or “Joule-heated” reactor design in which an internal heating source is used to selectively melt a pool of regolith between the electrodes of the reactor, leaving a shell of solidified regolith between the molten pool and the containment vessel of the reactor. This next generation reactor concept has been under development as molten oxide electrolysis (MOE) by MIT and Boston Metal for the production of iron from pure ores for terrestrial application [2]. The GaLORE project in engaged in early development of the technology for use with varying lunar regolith compositionsin the lunar environment. Thermal modelling of a proposed cold-walledreac-tor design were used as a scaffold to develop pa-rameters for a feasible reactor shape and size as well as target energy consumption[3]. The current development effort for the cold-walled reactor de-sign will be presented as a trade study of the most promising techniques for melting regolithwithin the constraints imposed by the lunar environment.Heater devices are designed to accommodate lim-ited electrical power availabilityon the moon, a wide range of regolith compositions that may be seen on the moon, limited metals available for re-placing consumed parts,and the low thermal con-ductivity of granular regolith in vacuum.Heater de-vices will be down-selectedbased on performance measurements within the above operationalcon-straints,and selected devices will be integrated into a reactor with electrodes to begin producing oxygen. [1]Sibille,L.,Sadoway, D.R.,Sirk, A., Tripathy,P.,Melendez, O., Standish, E., Dominguez, J. A., Stefanescu, D.M.,Curreri, P.A., Poizeau,S.,2009. “Recent Advancesin Scale-up Development of Molten Regolith Electrolysis for Oxygen Production in support of a Lunar Base.”AIAA 2009-659, 47th AIAA Aerospace Sciences Meeting, 5 -8 January 2009, Orlando, FL. [2] Boston Metal, https://www.boston-metal.com/moe-technology/#moe-process[3]Schreiner, S.S.,Sibille, L., Dominguez, J.A., Hoffman, J.A., 2016. "A parametric sizing model for Molten Regolith Electrolysis reactors to pro-duce oxygen on the Moon." Advances in Space Research 57.,7,1585-1603.

K D Grossman↗
NASA NTRS2019

Blind Validation Study of Parametric Cost Estimation Tool SEER-H for NASA Space Missions

One of the primary parametric cost modeling tools used by NASA and the aerospace industry to estimate the development and production cost of future spacecraft hardware is SEER-H by Galorath. To date, no independent validation of this tool for cost estimation of space missions has been reported in the literature. In the present validation study, cost estimators used SEER-H to estimate the cost of twelve different past NASA science missions. The estimators were prevented from knowing the actual cost of the missions in an effort to minimize cognitive biases. The point estimates of SEER-H had an average error of 23%, median error of -0.3%, and a standard deviation of 43%. Nine of the twelve mission's actual costs fell within the 80% confidence interval of SEER's probabilistic estimates. Several factors independent of SEER that may have affected the accuracy of the results have been identified and are discussed; these include: uncertainty in the technical data used for the estimates, the methods used to estimate uncertainty in spacecraft component mass and numbers of prototypes, and the experience of the estimators.

SEER-H↗
DOE OSTI2021

A microstructure-based modeling approach to predict the mechanical properties of Zr alloy with hydride precipitates

In nuclear reactors, hydrides can form in fuel cladding due to hydrogen absorption in ZIrcaloy and cause embrittlement. This work presents a microstructure-based finite element model to predict the stress-strain response of Zircaloy containing hydrides. Quantitative microstructural details extracted from scanning electron microscopy (SEM) images were used to generate heterogeneous microstructures including the morphology and spatial distribution of hydrides. The constitutive material model for zircaloy in this study is based on crystal plasticity theory which considers the hexagonal close-packed (HCP) atomic structure of Zircaloy material. The hydrides were modeled as brittle material along with a damage model. Hydride formation inside the zircoloy matrix results in residual stress. This phenomenon is also captured in this model. A parametric study has been conducted to understand the effect of volume fraction, orientation, and lamellae thickness of the hydride phase on the mechanical properties of the overall material.

Kulkarni, Shank S.↗
DOE OSTI2026

Process-level cost analysis of hybrid manufacturing pathways for aerospace structural components

Hybrid manufacturing is a promising route for producing complex aerospace components, yet systematic cost benchmarking across multiple additive-subtractive pathways remains limited. This study presents a comprehensive process-based cost analysis of seven hybrid manufacturing routes, including laser powder bed fusion (L-PBF), powder- and wire-directed energy deposition (DED), wire arc additive manufacturing (WAAM), additive friction stir deposition (AFSD), metal binder jetting (MBJ), and agility forging, followed by scanning and finish machining. Parametric cost models incorporating direct material, labor, and energy costs were developed. L-PBF results are discussed in detail for a pickle fork component and directly compared with commercial pricing. Across all hybrid routes, labor emerged as the dominant cost driver, contributing more than 70% of total manufacturing cost in some cases. AFSD exhibited the lowest cost for aluminum components, with MBJ being its 316 L stainless steel counterpart, after accounting for geometric scaling. Benchmarking against industrial quotes suggests that hybrid manufacturing can achieve cost levels comparable to those of commercial services, although labor-intensive processes exhibit greater deviation. The analysis highlights automation of material handling, setup, and supervision as key opportunities for improving economic competitiveness. Overall, the proposed framework provides a quantitative basis for evaluating and optimizing hybrid manufacturing pathways for aerospace applications.

Baruah, Sweta [ORNL] (ORCID:0009000174256207)↗
DOE OSTI2025

Coupled beam-target-moderator optimization for the Second Target Station

To support the design of the Second Target Station, that aims to provide the world’s highest peak brightness of cold neutrons, studies that optimize the dimensions of the target and moderators are invaluable. In this work, we investigate the influence of the target dimensions and beam profile on the performance and optimal size of the moderators. We perform optimization runs with detailed MCNP6.2 simulations using high-fidelity unstructured mesh geometries generated from parametrized CAD models. We demonstrate that small changes in target height do not influence the moderator performance if the beam dimensions are chosen adequately. We quantify the effect of beam footprint and target width on the moderator performance and show that the optimal moderator dimensions are insensitive to limited changes in target and beam profile.

Dakota↗
DOE OSTI2021

Directly probing the Higgs-top coupling at high scales

We explore the sensitivity to new physics for the coupling of the Higgs boson (h) and top quark (t) at high energy scales with the process ${pp}$→ $t\bar{t}h$ at the high-luminosity LHC. This process probes the coupling in both the space-like and time-like domains at a high scale, complementary to the off-shell Higgs processes in the time-like domain. The effects from physics beyond the Standard Model are parametrized in terms of the effective field theory framework and a non-local Higgs-top form factor. Focusing on the boosted Higgs regime in association with jet substructure techniques, we show that the present search can directly probe the Higgs-top coupling to good precision, providing a strong sensitivity to the new physics scale

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Characterization of partial wetting by CMAS droplets using multiphase many-body dissipative particle dynamics and data-driven discovery based on PINNs

The molten sand that is a mixture of calcia, magnesia, alumina and silicate, known as CMAS, is characterized by its high viscosity, density and surface tension. The unique properties of CMAS make it a challenging material to deal with in high-temperature applications, requiring innovative solutions and materials to prevent its buildup and damage to critical equipment. Here, we use multiphase many-body dissipative particle dynamics simulations to study the wetting dynamics of highly viscous molten CMAS droplets. The simulations are performed in three dimensions, with varying initial droplet sizes and equilibrium contact angles. We propose a parametric ordinary differential equation (ODE) that captures the spreading radius behaviour of the CMAS droplets. The ODE parameters are then identified based on the physics-informed neural network (PINN) framework. Subsequently, the closed-form dependency of parameter values found by the PINN on the initial radii and contact angles are given using symbolic regression. Finally, we employ Bayesian PINNs (B-PINNs) to assess and quantify the uncertainty associated with the discovered parameters. In brief, this study provides insight into spreading dynamics of CMAS droplets by fusing simple parametric ODE modelling and state-of-the-art machine-learning techniques.

Mechanics↗
DOE OSTI2026

Coherent and Dynamic Small Polaron Delocalization in CuFeO 2

Small polarons remain a bottleneck in realizing efficient transition metal oxide devices. Routes to engineer small polaron coupling to electronic states and lattice modes to control carrier localization remain unclear. Here, we measure small polaron formation in CuFeO 2 using transient extreme ultraviolet reflection spectroscopy and compare to theoretical predictions in realistically parametrized Holstein models, demonstrating that polaron localization depends on coupling to high-frequency versus low-frequency phonon bath components. We measure small polaron formation on a comparable ∼100 fs timescale to other Fe(III) compounds. Dynamic delocalization of the polaron follows formation through a coherent lattice expansion between Fe–O layers and charge-sharing with surrounding Fe(IV) states. Simulations reveal two major factors dictate polaron formation timescales: phonon density and reorganization energy distributions between acoustic and optical modes, matching experimental findings. Our work shows how electronic-structural coupling in a polaron-host material can be leveraged to suppress polaronic effects for various applications.

Hematite↗
DOE OSTI2021

Data-driven optimized control of the COVID-19 epidemics

Optimizing the impact on the economy of control strategies aiming at containing the spread of COVID-19 is a critical challenge. We use daily new case counts of COVID-19 patients reported by local health administrations from different Metropolitan Statistical Areas (MSAs) within the US to parametrize a model that well describes the propagation of the disease in each area. We then introduce a time-varying control input that represents the level of social distancing imposed on the population of a given area and solve an optimal control problem with the goal of minimizing the impact of social distancing on the economy in the presence of relevant constraints, such as a desired level of suppression for the epidemics at a terminal time. We find that with the exception of the initial time and of the final time, the optimal control input is well approximated by a constant, specific to each area, which contrasts with the implemented system of reopening ‘in phases’. For all the areas considered, this optimal level corresponds to stricter social distancing than the level estimated from data. Proper selection of the time period for application of the control action optimally is important: depending on the particular MSA this period should be either short or long or intermediate. We also consider the case that the transmissibility increases in time (due e.g. to increasingly colder weather), for which we find that the optimal control solution yields progressively stricter measures of social distancing. We finally compute the optimal control solution for a model modified to incorporate the effects of vaccinations on the population and we see that depending on a number of factors, social distancing measures could be optimally reduced during the period over which vaccines are administered to the population.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2025

Emulators for Scarce and Noisy Data: Application to Auxiliary-Field Diffusion Monte Carlo for Neutron Matter

Understanding the equation of state (EOS) of pure neutron matter is necessary for interpreting multimessenger observations of neutron stars. Reliable data analyses of these observations require well-quantified uncertainties for the EOS input, ideally propagating uncertainties from nuclear interactions directly to the EOS. This, however, requires calculations of the EOS for a prohibitively larger number of nuclear Hamiltonians, solving the nuclear many-body problem for each one. Quantum Monte Carlo methods, such as auxiliary-field diffusion Monte Carlo (AFDMC), provide precise and accurate results for the neutron matter EOS, but they are very computationally expensive, making them unsuitable for the fast evaluations necessary for uncertainty propagation. Here, we employ parametric matrix models to develop fast emulators for AFDMC calculations of neutron matter and use them to directly propagate uncertainties of coupling constants in the Hamiltonian to the EOS. As these uncertainties include estimates of the effective field theory truncation uncertainty, this approach provides robust uncertainty estimates for use in astrophysical data analyses. In conclusion, this Letter will enable novel applications such as using astrophysical observations to put constraints on coupling constants for nuclear interactions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

A demonstration of improved constraints on primordial gravitational waves with delensing

We present a constraint on the tensor-to-scalar ratio, $r$, derived from measurements of cosmic microwave background (CMB) polarization $B$-modes with "delensing,'' whereby the uncertainty on $r$ contributed by the sample variance of the gravitational lensing $B$-modes is reduced by cross-correlating against a lensing $B$-mode template. This template is constructed by combining an estimate of the polarized CMB with a tracer of the projected large-scale structure. The large-scale-structure tracer used is a map of the cosmic infrared background derived from Planck satellite data, while the polarized CMB map comes from a combination of South Pole Telescope, BICEP/Keck, and Planck data. We expand the BICEP/Keck likelihood analysis framework to accept a lensing template and apply it to the BICEP/Keck data set collected through 2014 using the same parametric foreground modelling as in the previous analysis. From simulations, we find that the uncertainty on $r$ is reduced by $\sim10\%$, from $\sigma(r)$= 0.024 to 0.022, which can be compared with a $\sim26\%$ reduction obtained when using a perfect lensing template. Applying the technique to the real data, the constraint on $r$ is improved from $r_{0.05} < 0.090$ to $r_{0.05} < 0.082$ (95% C.L.). Furthermore, this is the first demonstration of improvement in an $r$ constraint through delensing.

79 ASTRONOMY AND ASTROPHYSICS↗