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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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At least 1,747 records · Page 97
All sourcesNASA NTRSDOE OSTI
DOE OSTI2018

RBMK Uranium-Erbium Fuel

The history of the development and adoption of erbium fuel in RBMK is described. Research performed at the end of the 1980s – beginning of 1990s led to the conclusion that the optimal method of decreasing the steam coefficient of reactivity in RBMK is to add a consumable absorber – erbium. Computational and experimental work on the safety validation of the new fuel made it possible to adopt this fuel first in RBMK-1500 and then in RBMK-1000. The use of uranium-erbium fuel in RBMK made it possible to increase reactor safety, provide the requisite conditions for modernizing control rods, reduce the acuteness of the problem of storing spent fuel, and improve the economic indices of the fuel cycle. Considering the heightened interest in the use of erbium as a consumable absorber in VVER and some other reactors, the experience gained in developing and operating uranium-erbium fuel for RBMK could be helpful.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2020

Hadronic contributions to (g - 2) µ

The Muon g-2 Experiment at Fermilab, which recently started running, plans to reduce the uncertain- ties on the already very precisely measured anomalous magnetic moment of the muon by a factor of four. The goal of this effort is to probe the observed difference of more than three standard deviations between Standard-Model theory and experiment, one of the few persistent hints for physics beyond the Standard Model. The Fermilab experiment collected data from their first run last year with statistics comparable to BNL E821. They expect to release the measurement result in 2019. On the theoretical side, because the muon g - 2 arises from quantum- mechanical loop contributions in the Standard Model, it is sensitive to virtual effects of new particles, and places important constraints on Standard-Model extensions. To leverage the anticipated reduction in experimental errors, and determine unambiguously whether or not new-physics effects contribute to this quantity, the theoretical errors must be made more reliable and reduced to a commensurate precision. The Muon g-2 Theory Initiative was created to facilitate this development. The dominant sources of uncertainty in the Standard-Model prediction of the muon g -2 are from the hadronic contributions. The hadronic vacuum polarization (HVP) provides the leading correction followed by hadronic light-by-light (HLbL) scattering. There are a number of complementary theoretical efforts underway to better understand and quantify these contributions, including dispersive and data driven methods, lattice QCD, and effective field theories. Given the precision goals and the phenomenological importance, it is important to have more than one independent method for each of the two hadronic corrections, each with fully quantified uncertainties. Fostering the development of such methods is a prime goal of the initiative, as this will enable critical cross checks, and, upon combination, may yield gains in precision, to maximize the impact of E989. An important aspect of the Muon g-2 Theory Initiative’s activities are providing platforms that facilitate interactions between the different groups, as well as between the theoretical and experimental g - 2 communities. To this end, several workshops were organized in 2017 and 2018. The first meeting, held at Fermilab (June 3–6, 2017, St. Charles, IL, USA), served to kick-off the Initiative’s activities. Two meetings in early 2018 were focused respectively on the HVP and HLbL corrections. The HVP meeting was held at KEK (February 12–14, 2018, Tsukuba, Japan) and the HLbL meeting at the University of Connecticut (March 12–14, 2018, Storrs, CT, USA). The most recent workshop, which served as the second plenary meeting of the Initiative, was held at the University of Mainz (June 18–22, 2018, Mainz, Germany). An important outcome of these meetings are concrete plans for a first white paper, which is currently being written. We aim to post the white paper just prior to the release of the first E989 measurement, to present a clean theoretical prediction. The first white paper is focused on assessing and improving the reliability of the SM prediction. The purpose of the INT workshop in September 2019 is to start the next stage of the Initiative, focusing on the development of strategies to improve the theory uncertainties beyond the current level towards the E989 precision goal. We aim to accelerate theoretical developments on the hadronic contributions to the muon g - 2 so that the Standard-Model theory error can be brought to the needed precision, again in advance of the next release from E989. Hence the workshop will provide crucial theory support for a US experiment with broad impact. The Muon g-2 Theory Initiative relies on input from representatives of all the different communities that are engaged in this effort. It is therefore important that all these areas are properly represented. The funds from this grant will be used to enable more people, especially early-career scientists, to participate and make essential contributions to the workshop discussions. Since the workshop’s main goal is to kick-off the next stage of the theory initiative’s activities, support for this workshop from the DOE will help the theory community provide crucial theoretical support to the Fermilab Muon g-2 Experiment.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1989

Calculation of nonequilibrium hydrogen-air reactions with implicit flux vector splitting method

Two methods, fully- and loosely-coupled, are developed to incorporate nonequilibrium hydrogen-air chemistry into the fluid dynamic implicit flux vector splitting code (F3D). The new code (F3D/Chem) is validated against other existing codes for two cases: nozzle expansion, and shock-induced combustion around a blunt body. The shock-induced combustion case is compared also with an experimental data. The reaction rate constants are varied in an effort to reproduce the experimental data. The fully- and loosely-coupled methods are found to yield comparable results, but the computation time is shorter using the loosely-coupled method. The present method is found to reproduce results obtained using different existing codes. The experimental data was not reproduced with any selected rate coefficients set.

Lee, Seung-Ho↗
NASA NTRS2015

Simplified Methodology to Estimate the Maximum Liquid Helium (LHe) Cryostat Pressure from a Vacuum Jacket Failure

The aircraft-based Stratospheric Observatory for Infrared Astronomy (SOFIA) is a platform for multiple infrared astronomical observation experiments. These experiments carry sensors cooled to liquid helium temperatures. The liquid helium supply is contained in large (i.e., 10 liters or more) vacuum-insulated dewars. Should the dewar vacuum insulation fail, the inrushing air will condense and freeze on the dewar wall, resulting in a large heat flux on the dewar's contents. The heat flux results in a rise in pressure and the actuation of the dewar pressure relief system. A previous NASA Engineering and Safety Center (NESC) assessment provided recommendations for the wall heat flux that would be expected from a loss of vacuum and detailed an appropriate method to use in calculating the maximum pressure that would occur in a loss of vacuum event. This method involved building a detailed supercritical helium compressible flow thermal/fluid model of the vent stack and exercising the model over the appropriate range of parameters. The experimenters designing science instruments for SOFIA are not experts in compressible supercritical flows and do not generally have access to the thermal/fluid modeling packages that are required to build detailed models of the vent stacks. Therefore, the SOFIA Program engaged the NESC to develop a simplified methodology to estimate the maximum pressure in a liquid helium dewar after the loss of vacuum insulation. The method would allow the university-based science instrument development teams to conservatively determine the cryostat's vent neck sizing during preliminary design of new SOFIA Science Instruments. This report details the development of the simplified method, the method itself, and the limits of its applicability. The simplified methodology provides an estimate of the dewar pressure after a loss of vacuum insulation that can be used for the initial design of the liquid helium dewar vent stacks. However, since it is not an exact tool, final verification of the dewar pressure vessel design requires a complete, detailed real fluid compressible flow model of the vent stack. The wall heat flux resulting from a loss of vacuum insulation increases the dewar pressure, which actuates the pressure relief mechanism and results in high-speed flow through the dewar vent stack. At high pressures, the flow can be choked at the vent stack inlet, at the exit, or at an intermediate transition or restriction. During previous SOFIA analyses, it was observed that there was generally a readily identifiable section of the vent stack that would limit the flow – e.g., a small diameter entrance or an orifice. It was also found that when the supercritical helium was approximated as an ideal gas at the dewar condition, the calculated mass flow rate based on choking at the limiting entrance or transition was less than the mass flow rate calculated using the detailed real fluid model2. Using this lower mass flow rate would yield a conservative prediction of the dewar’s wall heat flux capability. The simplified method of the current work was developed by building on this observation.

Ungar, Eugene K.↗
DOE OSTI2020

Thermodynamic Modeling of the Al-Ce-Cu-Mg-Si System and Its Application to Aluminum-Cerium Alloy Design

Recently discovered AlCe alloys have shown promise in a number of applications, but the propensity of Ce to react with Al and other alloying elements can complicate the phase equilibria and design approach. To solve this, the CALPHAD method is used to explore an alloy within the quinary Al-Ce-Cu-Mg-Si system by developing a thermodynamic database with self-consistent parameters. The database includes a description of all 10 binary systems and 8 ternary systems consisting of: (i) 6 Al-containing ternaries (Al-Ce-Cu, Al-Ce-Mg, Al-Ce-Si, Al-Cu-Mg, Al-Cu-Si and Al-Mg-Si); and (ii) 2 additional ternaries that include Mg and Si (i.e., Ce-Mg-Si and Cu-Mg-Si). The thermodynamic description for the Al-Ce-Mg and Al-Mg-Si systems were reassessed to ensure consistency with the binary systems and the Ce-Mg-Si system is presented for the first time and compared to theoretical data from DFT (Density Functional Theory). In addition to the ternary interactions, the quaternary compound Al3Cu2Mg9Si7 and solid solution extending from the ternary Al2CuMg phase (Al,Si)2CuMg are incorporated. The CALPHAD method is employed and leveraged through the use of a Materials Design Simulator (MDS) to accelerate the design of novel aluminum-cerium-based alloys. The combination of a CALPHAD-based framework with experimental efforts and industrial insight permits the development of three new Al-Ce alloys: Al-3.5Ce-0.4Mg-7Si (Ce-modified A356), Al-5Ce-1Cu-0.5Mg-10Si and Al-19Ce-0.9Mg-1.1Si.

36 MATERIALS SCIENCE↗
NASA NTRS2001

Grid Convergence of High Order Methods for Multiscale Complex Unsteady Viscous Compressible Flows

Grid convergence of several high order methods for the computation of rapidly developing complex unsteady viscous compressible flows with a wide range of physical scales is studied. The recently developed adaptive numerical dissipation control high order methods referred to as the ACM and wavelet filter schemes are compared with a fifth-order weighted ENO (WENO) scheme. The two 2-D compressible full Navier-Stokes models considered do not possess known analytical and experimental data. Fine grid solutions from a standard second-order TVD scheme and a MUSCL scheme with limiters are used as reference solutions. The first model is a 2-D viscous analogue of a shock tube problem which involves complex shock/shear/boundary-layer interactions. The second model is a supersonic reactive flow concerning fuel breakup. The fuel mixing involves circular hydrogen bubbles in air interacting with a planar moving shock wave. Both models contain fine scale structures and are stiff in the sense that even though the unsteadiness of the flows are rapidly developing, extreme grid refinement and time step restrictions are needed to resolve all the flow scales as well as the chemical reaction scales.

Sjoegreen, B.↗
DOE OSTI2019

Multi-scale simulation of reaction, transport and deactivation in a SBA-16 supported catalyst for the conversion of ethanol to butadiene

Effective design of heterogeneous catalytic systems requires careful coordination of physiochemical phenomena that span orders or magnitude in length and time scales. Multiscale modelling and simulation tools can provide useful insight for understanding and improving the performance of such systems. Mesoporous silica catalyst support materials present a versatile platform wherein support attributes may be tuned to control transport phenomena throughout the system. In this study we develop an integrated multiscale modelling approach for the conversion of ethanol to butadiene over a SBA-16 mesoporous silica supported catalyst. We use molecular dynamics simulations to calculate domain specific diffusivities of reactants and products in the various domains of SBA-16's nanostructure. This is used to calculate a resultant effective diffusivity through its microstructure using finite element method (FEM) models of the tessellated unit cell. The resultant intraparticle effective diffusivity enables the development of a reduced-order reactor level FEM model that is able to implicitly account for the SBA-16's transport effects without the explicit consideration of its detailed geometry. Experimental bench-scale conversion data for the ethanol to butadiene process over SBA-16 is used to extract intrinsic kinetic rate constants for a simplified reaction mechanism using this reduced order bench-scale reactor FEM model. The model is able to reproduce experimental trends in conversion and activity lifetimes. The impact of varying key support attributes such as pore-size and particle size on catalytic activity lifetimes is then explored. We demonstrate the utility of this multi-scale modelling strategy in guiding catalyst design for the development of rational strategies to improve the performance of heterogeneous supported catalytic systems.

09 BIOMASS FUELS↗
DOE OSTI2019

Prolonged dipyridamole administration reduces myocardial perfusion defects in experimental chronic Chagas cardiomyopathy

Background: Myocardial perfusion defects (MPD) due to coronary microvascular dysfunction is frequent in chronic Chagas cardiomyopathy (CCC) and may be involved with development of myocardial damage. We investigated whether MPD precedes left ventricular systolic dysfunction and tested the hypothesis that prolonged use of dipyridamole (DIPY) could reduce MPD in an experimental model of CCC in hamsters. Methods and results: We investigated female hamsters 6-months after T. cruzi infection (baseline condition) and control animals, divided into T. cruzi-infected animals treated with DIPY (CH + DIPY) or placebo (CH + PLB); and uninfected animals treated with DIPY (CO + DIPY) or placebo (CO + PLB). The animals were submitted to echocardiogram and rest SPECT-Sestamibi-Tc99m myocardial perfusion scintigraphy. Next, the animals were treated with DIPY (4 mg/kg bid, intraperitoneal) or saline for 30 days, and reevaluated with the same imaging methods. At baseline, the CH + PLB and CH + DIPY groups showed larger areas of perfusion defect (13.2 ± 13.2% and 17.3 ± 13.2%, respectively) compared with CO + PLB and CO + DIPY (3.8 ± 2.2% e 3.5 ± 2.7%, respectively), P < .05. After treatment, we observed: reduction of perfusion defects only in the CH + DIPY group (17.3 ± 13.2% to 6.8 ± 7.6%, P = .001) and reduction of LVEF in CH + DIPY and CH + PLB groups (from 65.3 ± 9.0% to 53.6 ± 6.9% and from 69.3 ± 5.0% to 54.4 ± 8.6%, respectively, P < .001). Quantitative histology revealed greater extents of inflammation and interstitial fibrosis in both Chagas groups, compared with control group (P < .001), but no difference between Chagas groups (P > .05). Conclusions: The prolonged use of DIPY in this experimental model of CCC has reduced the rest myocardial perfusion defects, supporting the notion that those areas correspond to viable hypoperfused myocardium.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2026

Ripening of Rh Nanoparticle Catalysts in Reverse Water–Gas Shift via a Data-Driven Model Combining Physics, Theory, and Experiment

Degradation via sintering is an ongoing challenge that impedes the broad commercial success of supported metallic nanoparticle catalysts. To mitigate degradation via informed catalyst design and process operations, here we aim to disambiguate the underlying mechanisms of sintering by combining theory and experiment in a quantitative framework. While mechanistic sintering models exist, they only model a single sintering pathway, even though multiple sintering mechanisms can occur simultaneously or dominate at different stages of the process. Data-driven machine learning models have emerged as a means to represent complex processes through data regression. However, machine learning models have very large data needs and lack mechanistic insights due to their black-box encoding. To develop an interpretive model of catalyst degradation via sintering, we constructed a hybrid model combining mechanistic “physics-based” models and data-driven methods to obtain both reliable predictions and mechanistic insights regarding experimentally observed sintering phenomena. Focusing on nanoparticle sintering in the Rh–TiO 2 catalyst for the reverse water–gas shift (RWGS) reaction, the hybrid model couples a mechanistic term for Ostwald ripening with energy values calculated via density functional theory (DFT) with a parametric, data-driven discrepancy function term for unmodeled mechanisms. The hybrid model is trained using Bayesian inference with data collected from small-angle X-ray scattering (SAXS) in situ experiments wherein average nanoparticle diameter versus time was measured at three relevant operating temperatures. The calibrated hybrid model results show that an Ostwald ripening-only model parameterized with fixed DFT energies does not fully capture the time and temperature dependence of the SAXS-observed sintering kinetics, and that an additional functional contribution, or DFT energy calibration, is required to reconcile simulation and experiment. Analysis of the hybrid-model error confirms that the hybrid model outperforms both the purely mechanistic and purely data-driven alternatives in terms of expected predictive accuracy for time-evolving average particle sizes. Furthermore, the results support the hypothesis that the Ostwald ripening mechanism is less important for explaining the sintering phenomena as operating temperature increases under an assumed fixed DFT parameterization. This could be explained in one of two ways: either latent, unmodeled sintering mechanisms dominate at higher temperatures, or the DFT uncertainty increases with temperature. The proposed modeling approach directly links theory to experiments and simulations via a statistical hybrid modeling framework and can be extended to other catalytic systems to improve predictive models and mechanistic understanding.

Bayesian hybrid modeling↗
DOE OSTI2026

Design and simulation of a muon detector to characterize geological overburden

This study presents the design, construction, and simulation of a mobile muon detector tailored for geological overburden characterization. The detector employs plastic scintillator paddles with silicon photomultipliers (SiPMs) and a QuarkNet data acquisition system, offering a portable solution suitable for remote field deployment. The simulator’s modular aluminum frame allows for adjustable geometry and directional sensitivity, while its battery system supports over a week of autonomous operation. Preliminary experimental tests confirmed that its muon flux measurements were consistent with theoretical expectations. A comprehensive simulation framework using Geant4 and CORSIKA was developed to model detector response and overburden effects. Analytical and Monte Carlo methods were used to assess quadrant resolution and infer muon directionality. This work lays the foundation for future overburden mapping and supports the development of reconstruction algorithms for geological applications.

72 - PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Experimental 3-dimensional tracking of the dynamics of a single electron in the Fermilab Integrable Optics Test Accelerator (IOTA)

We present the results of experimental studies on the transverse and longitudinal dynamics of a single electron in the IOTA storage ring. IOTA is a flexible machine dedicated to beam physics experiments with electrons and protons. A method was developed to reliably inject and circulate a controlled number of electrons in the ring. A key beam diagnostic system is the set of sensitive high-resolution digital cameras for the detection of synchrotron light emitted by the electrons. With 60–130 electrons in the machine, we measured beam lifetime and derived an absolute calibration of the optical system. At exposure times of 0.5 s, the cameras were sensitive to individual electrons. Camera images were used to reconstruct the time evolution of oscillation amplitudes of a single electron in all 3 degrees of freedom. The evolution of amplitudes directly showed the interplay between synchrotron-radiation damping, quantum excitations, and scattering with the residual gas. From the distribution of measured single-electron oscillation amplitudes, we deduced transverse emittances, momentum spread, damping times, and beam energy. Estimates of residual-gas density and composition were calculated from the measured distributions of vertical scattering angles. Combining scattering and lifetime data, we also provide an estimate of the aperture of the ring. To our knowledge, this is the first time that the dynamics of a single electron are tracked in all three dimensions with digital cameras in a storage ring.

43 PARTICLE ACCELERATORS↗
DOE OSTI2024

Deep probabilistic direction prediction in 3D with applications to directional dark matter detectors

Abstract We present the first method to probabilistically predict 3D direction in a deep neural network model. The probabilistic predictions are modeled as a heteroscedastic von Mises-Fisher distribution on the sphere S 2 , giving a simple way to quantify aleatoric uncertainty. This approach generalizes the cosine distance loss which is a special case of our loss function when the uncertainty is assumed to be uniform across samples. We develop approximations required to make the likelihood function and gradient calculations stable. The method is applied to the task of predicting the 3D directions of electrons, the most complex signal in a class of experimental particle physics detectors designed to demonstrate the particle nature of dark matter and study solar neutrinos. Using simulated Monte Carlo data, the initial direction of recoiling electrons is inferred from their tortuous trajectories, as captured by the 3D detectors. For 40 keV electrons in a 70% He 30% CO 2 gas mixture at STP, the new approach achieves a mean cosine distance of 0.104 (26 ∘ ) compared to 0.556 (64 ∘ ) achieved by a non-machine learning algorithm. We show that the model is well-calibrated and accuracy can be increased further by removing samples with high predicted uncertainty. This advancement in probabilistic 3D directional learning could increase the sensitivity of directional dark matter detectors.

Computer Science↗
DOE OSTI2023

Combining protein sequences and structures with transformers and equivariant graph neural networks to predict protein function

Abstract Motivation Millions of protein sequences have been generated by numerous genome and transcriptome sequencing projects. However, experimentally determining the function of the proteins is still a time consuming, low-throughput, and expensive process, leading to a large protein sequence-function gap. Therefore, it is important to develop computational methods to accurately predict protein function to fill the gap. Even though many methods have been developed to use protein sequences as input to predict function, much fewer methods leverage protein structures in protein function prediction because there was lack of accurate protein structures for most proteins until recently. Results We developed TransFun—a method using a transformer-based protein language model and 3D-equivariant graph neural networks to distill information from both protein sequences and structures to predict protein function. It extracts feature embeddings from protein sequences using a pre-trained protein language model (ESM) via transfer learning and combines them with 3D structures of proteins predicted by AlphaFold2 through equivariant graph neural networks. Benchmarked on the CAFA3 test dataset and a new test dataset, TransFun outperforms several state-of-the-art methods, indicating that the language model and 3D-equivariant graph neural networks are effective methods to leverage protein sequences and structures to improve protein function prediction. Combining TransFun predictions and sequence similarity-based predictions can further increase prediction accuracy. Availability and implementation The source code of TransFun is available at https://github.com/jianlin-cheng/TransFun.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Exploring Dynamic P-Q Capability and Abnormal Operations of Inverter-Based Resources

Nowadays, inverter-based resources are rapidly growing in electric power systems. On the other side, abnormal inverter operations are also occurring more often. Traditionally, inverter PQ capability charts are employed by electric utility companies to ensure safe and reliable operations of inverter-based resources. However, it is found in this paper that existing inverter PQ capability charts do not address the operating characteristics of an inverter correctly, which can result in irregular and unstable inverter operations. Here in this paper, a novel study is conducted to investigate inverter PQ capability charts, where constraints that are specific to an inverter are considered. It is found in this paper that the inverter PQ capability charts exhibit a unique dynamic nature under uncertain grid conditions. This dynamic nature has not been considered by the industry in managing, designing, and controlling an inverter as well as in developing international standards for inverter-based resources. Via both electromagnetic transient simulation and hardware experimental investigations, it is found that the dynamic PQ capability nature, together with the limitations of the existing control methods, are the underlying causes of many unusual inverter operations that have been reported in the literature.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2019

Isomeric Cross Sections For 87 Y(n,$γ$) From Surrogate (p,d$γ$) Data

Cross sections for compound-nuclear reactions involving unstable targets are important for many applications, but can often not be measured directly. Recently, I developed a method for extracting cross sections for neutron-capture on unstable isotopes from indirect (surrogate) reaction data. I applied the method to $89$ Y(p,$γ$) data, which were supplied by the LLNL experimental nuclear physics program, to determine the $87$ Y(n,$γ$) (activation) cross section. Here, I extend the approach further, in order to determine cross sections for reactions that start and/or end at isomeric states. In particular, I determine cross sections, along with uncertainties, for seven additional reactions: $87$ Y(n,$γ$) $88gs$ Y, $87$ Y(n,$γ$) $88m1$ Y, $87$ Y(n,$γ$) $88m2$ Y, $87m$ Y(n,$γ$) $88$ Y (activation), $87m$ Y(n,$γ$) $88gs$ Y, $87m$ Y(n,$γ$) $88m1$ Y, $87m$ Y(n,$γ$) $88m2$ Y. These cross sections cannot be measured directly.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Evaluation of Neutron Detection Technology and Analysis Techniques to Support Fukushima Daiichi Decommissioning [Poster]

Decommissioning efforts and associated fuel debris retrieval from the damaged Units 1-3 require robust methods to monitor and assure subcriticality. These include adequate detection technologies capable to withstand high gamma radiation conditions within the units; as well as analysis methods capable to provide robust signatures to assure agile criticality monitoring in situation where material distribution is changing. This poster presents overview of experimental and analytical efforts focused on evaluation of neutronbased technologies and development of real-time analysis using state-of-the art capabilities available within the 1F Fuel Retrieval and Monitoring Experiments (1FRAME) project.

1FRAME↗
NASA NTRS1972

Coolant pressure and airflow distribution in a strut-supported transpiration-cooled vane for a gas turbine engine

An analysis to predict pressure and flow distribution in a strut-supported wire-cloth vane was developed. Results were compared with experimental data obtained from room-temperature airflow tests conducted over a range of vane inlet airflow rates from 10.7 to 40.4 g/sec (0.0235 to 0.0890 lb/sec). The analytical method yielded reasonably accurate predictions of vane coolant flow rate and pressure distribution.

Kaufman, A.↗