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DOE OSTI2020

Broadband Characterization and Circuit Model Development of Transmission-Scale Transformers

This report describes broadband measurements of transmission-scale transformers typical in the electric power grid. This work was performed as part of the EMP Resilient Grid LDRD project at Sandia National Laboratories to generate circuit models that can be used for high-altitude electromagnetic pulse (HEMP) coupling simulations and response predictions. The objective of the work was to obtain characterization data of substation yard equipment across a frequency range relevant to HEMP. Vector network analyzer measurements up to 100 MHz were performed on two power transformers at ABB-Hitachi and a single ITEC potential transformer. Custom cable breakouts were designed to interface with the transformer terminals and provide ground connections to the chassis at the base of the transformer bushings. The three-phase terminals of the power transformers were measured as a common mode impedance using a parallel resistive splitter, and the single-phase terminals of the potential transformer were measured directly. A vector fitting algorithm was used to empirically fit circuit models to the resulting two-port networks and input impedances of the measured objects. Simplified circuit representations of the input impedances were also generated to assess the degree of precision needed for high-altitude electromagnetic pulse response predictions, which were performed in Sandia's XYCE circuit simulator platform. HEMP coupling simulations using the transformer models showed significant reduction in the voltage peak and broadening in the pulse width seen at the power transformer compared to the traveling wave voltage. This indicated the importance of the load condition when defining the coupled insult in an electric power substation. Simplified circuit models showed a similar voltage at the transformer with a smoothed waveform. The presence of potential transformers in the simulation did not significantly change the simulated voltage at the power transformer. Single-port input impedance models were also developed to define load conditions when transfer characteristics were not necessary.

24 POWER TRANSMISSION AND DISTRIBUTION↗

NASA NTRS1994

Analysis of small-scale microwave background radiation anisotropy in the presence of foreground contamination

Many of the current round of experiments searching for anisotropies in the microwave background radiation (MBR) are confronting the problem of how to disentangle the cosmic signal from contamination due to Galactic and intergalactic foreground sources. Here we show how commonly used likelihood function techniques can be generalized to account for foreground. Specifically we set some restrictions on the spectrum of foreground contamination but allow the amplitude to vary arbitrarily. The likelihood function thus generalized gives reasonable limits on the MBR anisotropy which, in some cases, are not much less restrictive than what one would get from more detailed modeling of the foreground. Furthermore, the likelihood function is exactly the same as one would obtain by simply projecting out foreground contamination and looking at the reduced data set. We apply this generalized analysis to the recent medium-angle data sets of ACME-HEMT (Gaier et al. 1992; Schuster et al. 1993) and MAX (Meinhold et al. 1993; Gunderson et al. 1993). The resulting analysis constrains the one free parameter in the standard cold dark matter theory to be Q(sub rms-ps) = 18(sub -5 sup +8) microKelvin. This best fit value, although in striking agreement with the normalization from Cosmic Background Explorer (COBE), is not a very good fit, with an overall chi-squared/degrees of freedom = 208/168. We also argue against three commonly used methods of dealing with foreground: (1) ignoring it completely; (2) subtracting off a best-fit foreground and treating the residuals as if uncontaminated; and (3) culling data which appears to be contaminated by foreground.

Dodelson, Scott↗

DOE OSTI2022

Estimation of pipe failure frequencies in the absence of operational experience data: A pilot study

Probabilistic failure metrics such as leak frequency and rupture frequency are commonly used to characterize piping reliability. The methodologies for calculating the failure metrics rely on a complex set of input parameters. Operating experience data and experimental data play an important role in informing the different input parameters. The paper describes results and conclusions of a coordinated research project to benchmark three different reliability models using a four-step procedure: reference case definition of relevance to advanced reactor designs, input parameter calibration, validation of results, and application of different methodologies upon completion of the calibration and validation steps. The reference case is a weld consisting of nickel-base alloy 152/52 and located within a primary pressure boundary of an advanced reactor. This alloy is a class of structural materials known to be highly resistant to stress corrosion cracking. Synergies between the different methods are noted and the importance of a multi-disciplinary approach to input parameter development is underscored. A key conclusion is that the three methods are equally suitable for estimating failure frequencies. In any specific application, a selection of the most practical or effective computational tool can be considered. The comparison of alternative models confirms and helps to gain confidence in the computed failure frequency estimates. The study was part of a coordinated research project organized by the International Atomic Energy Agency.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2020

The Sensitivity of Joint Inversions of Seismic and Geodynamic Data to Mantle Viscosity

Seismic tomography has revealed the existence of large-scale velocity heterogeneities in the mantle. The interpretation of seismic velocity anomalies in terms of temperature and chemical composition is nonunique. We use geodynamic observations including gravity, plate motions, dynamic topography, and excess ellipticity of the core-mantle boundary combined with seismic observations to investigate the thermo-chemical structure of the mantle through joint inversions. An outstanding issue, however, is the physical connection between mantle density anomalies and the surface geodynamic observations, which requires knowledge of the mantle viscosity structure. Here we perform joint inversions assuming different viscosity profiles and examine the dependence of the results on the viscosity. We first assume that mantle heterogeneity is due to thermal variations, which places a constraint on the relation between seismic velocity and density, and we subsequently relax the constraint to allow for potential nonthermal effects. In all of our joint inversions, a nonthermal origin of density anomalies is required to explain the geodynamic data, though the amount varies with the assumed viscosity structure. A common observation is a high-density chemical signal in the center of the large low-shear-velocity provinces at the base of the mantle resulting in a near neutral or slightly dense overall buoyancy there. Using the derived density models and their corresponding viscosity profiles, we also calculate instantaneous mantle flow fields. The predicted flow fields derived from joint inversions are generally similar but are quite different from flow fields using density models derived from a posteriori scaling of pure seismic tomography models.

58 GEOSCIENCES↗

DOE OSTI2023

The Potential Benefits of Handling Mixture Statistics via a Bi-Gaussian EnKF: Tests With All-Sky Satellite Infrared Radiances

The meteorological characteristics of cloudy atmospheric columns can be very different from their clear counterparts. Thus, when a forecast ensemble is uncertain about the presence/absence of clouds at a specific atmospheric column (i.e., some members are clear while others are cloudy), that column's ensemble statistics will contain a mixture of clear and cloudy statistics. Such mixtures are inconsistent with the ensemble data assimilation algorithms currently used in numerical weather prediction. Hence, ensemble data assimilation algorithms that can handle such mixtures can potentially outperform currently used algorithms. In this study, we demonstrate the potential benefits of addressing such mixtures through a bi-Gaussian extension of the ensemble Kalman filter (BGEnKF). The BGEnKF is compared against the commonly used ensemble Kalman filter (EnKF) using perfect model observing system simulated experiments (OSSEs) with a realistic weather model (the Weather Research and Forecast model). Synthetic all-sky infrared radiance observations are assimilated in this study. In these OSSEs, the BGEnKF outperforms the EnKF in terms of the horizontal wind components, temperature, specific humidity, and simulated upper tropospheric water vapor channel infrared brightness temperatures. This study is one of the first to demonstrate the potential of a Gaussian mixture model EnKF with a realistic weather model. Our results thus motivate future research toward improving numerical Earth system predictions though explicitly handling mixture statistics.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Powder diffraction

Powder diffraction is a non-destructive technique, which is experimentally simple in principle. Because the physics behind diffraction is well understood, an exceptionally large amount of information can be obtained from a single measurement. The positions and relative intensities of the peaks yield a fingerprint that can be used for qualitative phase analysis. Quantitative phase analysis can be obtained by detailed analysis of the intensities. Unit cells can be derived from the peak positions. Crystal structures can be solved using powder diffraction data and refined by the Rietveld method. The peak profiles contain information about crystallite size, strain and nanostructure. Non-idealities in the intensities give information on texture. Abandoning the crystallographic model provides information about local structure, by pair distribution function analysis. For powder diffraction, everything is a sample; the technique is commonly applied to characterize minerals, ceramics, metals and alloys, catalysts, polymers, pharmaceuticals, organic compounds, environmental and forensic samples, among others. The major features of contemporary laboratory powder diffractometers are described. Methods for obtaining suitable powder specimens are summarized. Major applications of qualitative and quantitative phase analysis, structure solution, size/strain/nanostructure analysis using peak profiles, texture analysis and pair distribution function analysis are introduced.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2020

Hf‐W chronology of a macrochondrule from the L5/6 chondrite Northwest Africa 8192

Abstract A large, igneous‐textured, and 2 cm‐sized spherical object from the L5/6 chondrite NWA 8192 was investigated for its chemical composition, petrography, O isotopic composition, and Hf‐W chronology. The petrography and chemical data indicate that this object closely resembles commonly found chondrules in ordinary chondrites and is therefore classified as a “macrochondrule.* As a result of metal loss during its formation, the macrochondrule exhibits elevated Hf/W, which makes it possible to date this object using the short‐lived 182 Hf‐ 182 W system. The Hf‐W data provide a two‐stage model age for metal–silicate fractionation of 1.4 ± 0.6 Ma after Ca‐Al‐rich inclusion (CAI) formation, indicating that the macrochondrule formed coevally to normal‐sized chondrules from ordinary chondrites. By contrast, Hf‐W data for metal from the host chondrite yield a younger model age of ~11 Ma after CAIs. This younger age agrees with Hf‐W ages of other type 5–6 ordinary chondrites, and corresponds to the time of cooling below the Hf‐W closure temperature during thermal metamorphism on the parent body. The Hf‐W model age difference between the macrochondrule and the host metal demonstrates that the Hf‐W systematics of the bulk macrochondrule were not disturbed during thermal metamorphism, and therefore, that the formation age of such objects can still be determined even in strongly metamorphosed samples. Collectively, this study illustrates that chondrule formation was not limited to mm‐size objects, implying that the rarity of macrochondrules reflects either that this process was very inefficient, that subsequent nebular size‐sorting decimated large chondrules, or that large precursors were rare.

58 GEOSCIENCES↗

DOE OSTI2024

Multiscale modeling of HBV infection integrating intra- and intercellular viral propagation to analyze extracellular viral markers

Chronic infection with hepatitis B virus (HBV) is caused by the persistence of closed circular DNA (cccDNA) in the nucleus of infected hepatocytes. Despite available therapeutic anti-HBV agents, eliminating the cccDNA remains challenging. Thus, quantifying and understanding the dynamics of cccDNA are essential for developing effective treatment strategies and new drugs. However, such study requires repeated liver biopsy to measure the intrahepatic cccDNA, which is basically not accepted because liver biopsy is potentially morbid and not common during hepatitis B treatment. We here aimed to develop a noninvasive method for quantifying cccDNA in the liver using surrogate markers in peripheral blood. We constructed a multiscale mathematical model that explicitly incorporates both intracellular and intercellular HBV infection processes. The model, based on age-structured partial differential equations, integrates experimental data from in vitro and in vivo investigations. By applying this model, we roughly predicted the amount and dynamics of intrahepatic cccDNA within a certain range using specific viral markers in serum samples, including HBV DNA, HBsAg, HBeAg, and HBcrAg. Our study represents a significant step towards advancing the understanding of chronic HBV infection. The noninvasive quantification of cccDNA using our proposed method holds promise for improving clinical analyses and treatment strategies. By comprehensively describing the interactions of all components involved in HBV infection, our multiscale mathematical model provides a valuable framework for further research and the development of targeted interventions.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2020

(U) PRAD0697 & PRAD0698: Complex Loading of CeO₂ Powder

Cerium(IV) oxide (CeO₂) powder is shock compressed using the Precision High Energy-density Liner Implosion eXperiment (PHELIX) platform. Experimental results are compared against several modeling approaches. Compaction behavior is best captured with a P-∝ model, which calculates CeO₂ powder bulk densities within 80-99% of experimental values but overpredicts densi cation at the cylindrical target's outer radius and center by up to 20%. Preliminary calculations suggest that accuracy could be increased with the inclusion of a coupled strength model. Several common computational modeling approaches for the shock compression response of granular materials and the magnetohydrodynamic (MHD) force upon the impactor/liner in pulsed power compression experiments are investigated and analyzed for their validity. The Bi-linear Ramp, P-∝ PACXP, and P-∝ Menikoff-Kober continuum compaction models are calibrated to planar impact Hugoniot data for CeO₂ powder and used to predict the powder's shock compaction response under non-planar shock wave compression. MHD calculations of the PHELIX pulsed power driver are performed using an idealized resistor-inductor-capacitor (RLC) circuit calibrated to previous experiments. All simulations are performed using the LANL code FLAG. Two validation experiments are computationally designed using the calibrated compaction and circuit models, executed using the PHELIX platform on CeO₂ targets with initial porous densities of 3.95 and 4.03 g/cm³, measured with proton radiography, and analyzed against the model predictions. The two P-∝ models more accurately describe CeO₂ powder densi cation than the Bi-linear Ramp model. However, the two P-∝ models overpredict bulk density of the shock compressed CeO₂ powder by up to 20% when the appropriate impact velocities are applied. MHD calculations for both validation experiments underpredict liner impact velocities by 4-11% when using the idealized RLC circuit model calibrated to previous experiments. Compensating underpredictions of impact velocity and overpredictions of powder densication lead to a false accuracy in pre-shot calculations compared to experimental data. To improve correlation between simulations and experiments, the following improvements are suggested: 1. A coupled strength model for CeO₂ powder that updates strength as a function of porosity and applied stress. 2. An improved MHD circuit model that more accurately captures the PHELIX machine.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Multi-phenomenology Yield Characterization

This report serves as the first delivery of a four-year applied science effort to transform and advance the error bounds for the yield estimate of an explosion. Each year’s delivery will be in this form, culminating in the submission of this work for peer review to a scientific journal. Importantly, the yearly progress reports can then also be viewed as expanding drafts working towards a formal journal article submission. For the first tranche of funding, we collaborated with Air Force Technical Applications Center (AFTAC) scientists to identify unclassified real-world data that demonstrate and validate our advanced error propagation methods. Collaboration includes visits to AFTAC and telecons. For this development, we illustrate the fusion of seismic, acoustic, optical, and surface effect signatures from an explosion. The mathematics and code being adapted to this specific application (Williams et al., 2021) involves physics models of multiple sensor signatures. We have also identified related physics models and have integrated them into code. Current methods of underground explosion yield estimation for the Threshold Test Ban Treaty (TTBT) have served the US treaty monitoring mission well for decades. A research objective of the Defense Nuclear Nonproliferation Research and Development (DNN R&D) office of the National Nuclear Security Administration (NNSA) has always been to provide new technical capabilities for monitoring lower thresholds. The general model and error propagation code to be developed in this project is based on significant advances in error modeling and propagation needed to analyze data at lower detection thresholds. The second tranche of funding for this project began on May 1, 2022, and planned work for the second tranche includes: i) completing the integration of physical model code into the general error model framework; this code accommodates a wide range of linear/nonlinear source models, fixed/ random effects, and frequentist/Bayesian analyses (the purpose of which is not to dictate to users how to analyze data, but instead to allow users the maximum flexibility in their work); ii) illustrative application of code to identified data, and; iii) initial planning with AFTAC researchers on delivery of code to the Common Development Environment at AFTAC, and continued writing of the planned final journal article submission (year two of this progress report), with particular emphasis on descriptions of data identified for this effort.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗

DOE OSTI2022

Prescreening-Based Subset Selection for Improving Predictions of Earth System Models With Application to Regional Prediction of Red Tide

We present the ensemble method of prescreening-based subset selection to improve ensemble predictions of Earth system models (ESMs). In the prescreening step, the independent ensemble members are categorized based on their ability to reproduce physically-interpretable features of interest that are regional and problem-specific. The ensemble size is then updated by selecting the subsets that improve the performance of the ensemble prediction using decision relevant metrics. We apply the method to improve the prediction of red tide along the West Florida Shelf in the Gulf of Mexico, which affects coastal water quality and has substantial environmental and socioeconomic impacts on the State of Florida. Red tide is a common name for harmful algal blooms that occur worldwide, which result from large concentrations of aquatic microorganisms, such as dinoflagellate Karenia brevis, a toxic single celled protist. We present ensemble method for improving red tide prediction using the high resolution ESMs of the Coupled Model Intercomparison Project Phase 6 (CMIP6) and reanalysis data. The study results highlight the importance of prescreening-based subset selection with decision relevant metrics in identifying non-representative models, understanding their impact on ensemble prediction, and improving the ensemble prediction. These findings are pertinent to other regional environmental management applications and climate services. Additionally, our analysis follows the FAIR Guiding Principles for scientific data management and stewardship such that data and analysis tools are findable, accessible, interoperable, and reusable. As such, the interactive Colab notebooks developed for data analysis are annotated in the paper. This allows for efficient and transparent testing of the results’ sensitivity to different modeling assumptions. Moreover, this research serves as a starting point to build upon for red tide management, using the publicly available CMIP, Coordinated Regional Downscaling Experiment (CORDEX), and reanalysis data.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

High-Temperature Thermodynamics of Uranium from Ab Initio Modeling

We present high-temperature thermodynamic properties for uranium in its γ phase (γ-U) from first-principles, relativistic, and anharmonic theory. The results are compared to CALPHAD modeling. The ab initio electronic structure is obtained from density-functional theory (DFT) that includes spin–orbit coupling and an added self-consistent orbital-polarization (OP) mechanism for more accurate treatment of magnetism. The first-principles method is coupled to a lattice dynamics scheme that is used to model anharmonic lattice vibrations, namely, Self-Consistent Ab Initio Lattice Dynamics (SCAILD). The methodology can be summarized in the acronym DFT + OP + SCAILD. Upon thermal expansion, γ-U develops non-negligible magnetic moments that are included for the first time in thermodynamic theory. The all-electron DFT approach is shown to model γ-U better than the commonly used pseudopotential method. In addition to CALPHAD, DFT + OP + SCAILD thermodynamic properties are compared with other ab initio and semiempirical modeling and experiments. Our first-principles approach produces Gibbs free energy that is essentially identical to CALPHAD. The DFT + OP + SCAILD heat capacity is close to CALPHAD and most experimental data and is predicted to have a significant thermal dependence due to the electronic contribution.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

Evaluation of obstacle modelling approaches for resource assessment and small wind turbine siting: case study in the northern Netherlands

Abstract. Growth in adoption of distributed wind turbines for energy generation is significantly impacted by challenges associated with siting and accurate estimation of the wind resource. Small turbines, at hub heights of 40 m or less, are greatly impacted by terrestrial obstacles such as built structures and vegetation that can cause complex wake effects. While some progress in high-fidelity complex fluid dynamics (CFD) models has increased the potential accuracy for modelling the impacts of obstacles on turbulent wind flow, these models are too computationally expensive for practical siting and resource assessment applications. To understand the efficacy of available models in situ, this study evaluates classic and commonly used methods alongside new state-of-the-art lower-order models derived from CFD simulations and machine learning approaches. This evaluation is conducted using a subset of an extensive original dataset of measurements from more than 300 operational wind turbines in the northern Netherlands. The results show that data-driven methods (e.g. machine learning and statistical modelling) are most effective at predicting production at real sites with an average error in annual energy production of 2.5 %. When sufficient data may not be available de novo to support these data-driven approaches, models derived from high-fidelity simulations show promise and reliably outperform classic methods. On average these models have 6.3 %–11.5 % error compared with 26 % for classic methods and 27 % baseline error for reanalysis data without obstacle correction. While more performant on average, these methods are also sensitive to the quality of obstacle descriptions and reanalysis inputs.

17 WIND ENERGY↗

NASA NTRS1973

Supersonic turbulent boundary-layer flows with tangential slot injection.

An implicit finite-difference method has been developed for the solution of the compressible boundary-layer equations. This method is applied to tangential slot injection into supersonic turbulent boundary-layer flows. In addition, the effects induced by the interaction between the boundary-layer displacement thickness and the external pressure field are considered. Three different eddy viscosity models have been used to specify the turbulent momentum exchange. One model depends on the species concentration profile, and the species conservation equation has been included in the system of governing partial differential equations. For air injected into air, the freestream and injected gases are treated as separate species which have common fluid properties. Calculations were made and results were compared with experimental data at freestream Mach numbers of 2.4 and 6.0 and with results of another finite-difference method. Good agreement was obtained for the reduction of wall skin friction with slot injection.

Miner, E. W.↗

NASA NTRS1974

An integrated PCM data system for full scale aeronautics testing

An integrated PCM data system is being developed at Ames Research Center to gather test data on advanced STOL propulsive lift, VTOL, rotary wing, and V/STOL control systems concepts as they pass through wind-tunnel, test-stand, flight-simulator and flight-test phases. Identical airborne signal conditioning and PCM encoding is used on test aircraft and wind tunnel models. An 80,000 word/second PCM installation will be the first all PCM-instrumented rotary wing development project. The system uses both dedicated and time-shared computers for fast data analysis with maximum use of resources. This system development shows one way to bring separate data user groups together over a common data base, while sharing computing resources for minimum cost.-

Reynolds, D. R.↗

NASA NTRS1975

Gravimetric investigations on the North American Datum (1972 - 1973)

All the available unclassified gravity data on the North American Datum (NAD) and in the surrounding oceans was assembled late in 1972 for the investigation of the gravity field in North America and its relation to North American Datum 1927 (NAD 27). The gravity data in Canada and the United States was compiled on a common datum compatible with the International Gravity Standardization Network 1971 (IGSN 71). The variation in the error of representation in the region is studied along with the correlation characteristics of gravity anomalies with elevation. A free air geoid (FAG 73) was computed from a combination of surface gravity data and Goddard Earth Model (GEM) 4 and this was used as the basis for the computation of the non-Stokesian contributions to the height anomaly. The geocentric orientation parameters obtained by this astrogravimetric method are compared with those obtained by satellite techniques. The differences are found to be no greater than those between individual satellite solutions. The differences between the astrogravimetric solution and satellite solutions GSFC 73 and GEM 6 are studied in detail with a view to obtaining a better understanding of these discrepancies.

Mather, R. S.↗

NASA NTRS1983

An investigation of wing leading-edge vortices at supersonic speeds

Studies at subsonic and transonic speeds of the fundamental vortex behavior on the leeward surface of wings have led to the design of several unique and novel leading-edge devices commonly referred to as 'vortex flaps'. The present investigation has the objective to provide some fundamental vortex-flow results obtained at supersonic speeds. Experimental studies were performed in which pressure data and several types of flow visualization data were obtained on the leeward surface of a series of flat delta-wing models to identify the various flow mechanisms which can occur and to determine the effect of leading-edge sweep, Mach number, and angle of attack on the vortex strength and location. The reported investigation forms part of a study which is to explore the use of wing leading-edge vortex technology as a supersonic wing-design tool. The obtained results indicate that the procedure of distributing the vortex force as a pressure variation about a vortex action line is a promising concept.

Miller, D. S.↗

NASA NTRS1994

Dynamic modeling of orographically induced precipitation

Local orography governs the triggering of cloud formation and the enhancement of processes such as condensation and hydrometeor nucleation and growth in mountainous regions. Intense, lengthy precipitation events are typical upwind of the topographic divide, with sharply decreasing magnitude and duration on the lee side. Differences in mean annual precipitation of several hundred percent between windward slopes of orographic barriers and adjacent valleys or lee side slopes are not unusual. Because much of the streamflow in areas such as the western United States is derived from mountainous areas that are remote and often poorly instrumented, modeling of orographic precipitation has important implications for water resources management. Models of orographically induced precipitation differ by their treatment of atmospheric dynamics and by the extent to which they rely on bulk parameterization of cloud and precipitation physics. Adiabatic ascent and a direct proportionality between efficiency and orographically magnified updrafts are the most frequent assumptions in orographic precipitation modeling. Space-time discretization (i.e., resolution) is a major issue because of the high spatial variability of orographic precipitation. For a specific storm, relative errors as large as 50 to 100% are common in the forecast/hindcast of precipitation intensity and can be even larger in the case of catastrophic storms. When monthly or seasonal timescales are used to evaluate model performance, the magnitude of such errors decreases dramatically, reaching values as low as 10 to 15%. Current research is focusing on the development of data assimilation techniques to incorporate radar and satellite observations, and on the development of aggregation and disaggregation methodologies to address the implications of modeling a multiscale problem at restricted spatial and temporal resolutions.

Barros, Ana Paula↗