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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 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

(U) A Theoretical Study of Asay Foil Trajectories (V.02)

We consider the trajectory of a generic Asay foil ejecta momentum diagnostic sensor, for scenarios where ejecta are produced at a planar surface and fly ballistically through a perfect vacuum to the sensor. To do so, we build upon a previously established mathematical formalism derived for the analytic study of stationary sensors (i.e., piezopins). First, we derive the momentum conservation equation for the problem, in a form amenable to accelerating sensors, in terms of a generic ejecta source areal mass function (“source model”). This defines an integro-differential equation (IDE) for the foil trajectory. When ejecta production is instantaneous - as is generally assumed in momentum diagnostic data analyses - the IDE leads to an implicit and easily calculable closed-form solution for the foil trajectory in a perfect system, as long as the ejecta particle velocity distribution is twice-integrable. General properties of the instant-production trajectory solution indicate the existence of a boundary condition the particle velocity distribution must satisfy in order for the analytically predicted foil trajectories to be compatible with certain features commonly observed in foil data. This boundary condition is identical to one derived previously from a consideration of piezopin data. Armed with the analytic solution for instant production, we also consider various techniques used to extract time-dependent cumulative ejecta masses from foil trajectories, and derive an expression for the error imposed by using an approximated equation of motion. This analytic trajectory solution furthermore makes it possible to examine the common practice of presenting inferred cumulative ejecta masses as a function of a normalized implied velocity; we derive conditions under which this methodology is and is not meaningful. We also propose a strategy for extending the instant-production trajectory solution to time-dependent source functions.

42 ENGINEERING↗
DOE OSTI2021

Error Analysis on Numerical Integration Algorithms in a Hypoelasticity Framework

This report determines local truncation errors for common stress integration algorithms used in explicit finite element codes with hypoelastic material models. The hypoelastic integration algorithms in question utilize an operator splitting procedure in a rotation neutralized configuration, where the stress response is determined from de- coupling the total deformation into rotational and strain dependent components. This document analyzes the error in evolving the stress given a one-step time increment Δt and compares the errors associated with both the rotational and strain components of the operator splitting method. A slight modification to a traditional algorithm is proposed and studied, where the rate of deformation is appropriately rotated from the midstep configuration at t n+1/2 to the end step configuration at t n+1 before the constitutive evaluation. The proposed modification either completely eliminates the error associated with the rotation rate or is of the same order of magnitude as the original algorithm for the three test cases considered in this report. These cases consist of an unaxial stretch with a constant true strain rate with a rigid body rotation, an uniaxial stretch with a constant engineering strain rate with a rigid body rotation, and a simple shear deformation. All three cases are compared to a closed form solution, and in almost every test case the alternative algorithm yields the most accurate one-step local truncation error.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Fabrication and Preliminary Demonstration of Microwave Resonant Cavity Transducer Performance

We are investigating a microwave cavity-based transducer for in-core high-temperature fluid flow sensing in molten salt cooled reactors (MSCR) and sodium fast reactors (SFR). This sensor is a hollow metallic cylindrical cavity, which can be fabricated from stainless steel, and as such is expected to be resilient to radiation, high temperature and corrosive environment of MSCR and SFR. The principle of sensing consists of making one wall of the cylindrical cavity flexible enough so that dynamic pressure, which is proportional to fluid velocity, will cause membrane deflection. Membrane deflection causes cavity volume change, which leads to a shift in the resonant frequency. We have developed an initial design for proof-of-principle testing of the flow sensor performance in microwave K-band. A cylindrical resonator prototype was fabricated from brass for initial tests in water. The cavity size is matched to the flange of a standard WR-42 waveguide. Microwave field is coupled into the resonant cavity through a subwavelength-size aperture. A test article was developed, consisting of a piping Tee with bulkhead WR-42 microwave waveguide installed in leak-proof design. In the test article, the cylindrical cavity is positioned in the center of the pipe. A microwave waveguide circulator was installed in the setup to suppress microwave reflections at the cavity entrance. Preliminary spectral characterization of cavity spectral response was performed with microwave VNA. Applying mechanical pressure to cavity membrane showed a measurable shift in the microwave resonant frequency. We also investigate mechanical integrity of the flowmeter’s membrane through computer simulations. By calculating the stress on the plate due to deflection and, comparing the stress to the material ultimate tensile strength and yield strength, it can be estimated if the plate will fail. The stress on the plate was calculated with an analytic closed form solution model, and with COMSOL Structural Mechanics Module which does not involve any approximations. Both the analytic model and COMSOL model showed that maximum stresses on the plate, which are at the radial boundary of the plate, are three orders of magnitude smaller than the yield strength and ultimate tensile strength. This indicates that the sensor is at a low risk of mechanical failure.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2021

Analyzing Mechanical integrity of Microwave resonant Cavity flowmeter

The microwave resonant cavity flow sensor has been proposed to address the difficulties of measuring high-temperature molten salt flow in reactor vessels. The flow sensor consists of a metallic cylindrical cavity coupled to a microwave waveguide. The cylindrical cavity has one of the flat surfaces thin enough to undergo microscopic deflection due to dynamic pressure of the exerted by the flowing fluid. Deflection of the membrane causes a shift in the microwave resonant frequency. Fluid velocity can be estimated from the calibration curve. The objective of this report is to investigate mechanical integrity of the flowmeter’s membrane. The membrane is a thin stainless-steel circular plate with a clamped edge, subjected to uniform load. By calculating the stress on the plate due to deflection and, comparing the stress to the material ultimate tensile strength and yield strength, it can be estimated if the plate will fail. If the maximum stress is greater than the yield strength, the plate will undergo plastic deformation, and the sensor will be disabled. A stress greater than the ultimate tensile strength will cause the plate to fracture. The stress on the plate was calculated with an analytic closed form solution model, and with COMSOL Structural Mechanics Module which does not involve any approximations. Stresses in both the analytic model and COMSOL numerical model were calculated for stainless steel 316 thin circular plates under room temperature conditions, where the fluid is water. The diameter of the circular plate is approximately one inch, and thickness is 10mil. Fluid flow velocity is in the range from 0.5m/s to 1m/s. The results from the two models are similar. Both the analytic model and COMSOL model showed that maximum stresses on the plate, which are at the radial boundary of the plate, are three orders of magnitude smaller than the yield strength and ultimate tensile strength. This indicates that the sensor is at a low risk of mechanical failure.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2021

Equations of Motion for the Vertical Rigid-Body Rotor: Linear and Nonlinear Cases

Centuries ago, the prolific mathematician Leonhard Euler (1707–1783) wrote down the equations of motion (EOM) for the heavy symmetrical top with one point fixed. The resulting set of equations turned out to be nonlinear and had a limited number of closed-form solutions. Today, tools such as transfer matrix and finite elements enable the calculation of the rotor dynamic properties for rotor-bearing systems. Some of these tools rely on the “linearized” version of the EOM to calculate the eigenvalues, unbalance response, or transients in these systems. In fact, industry standards mandate that rotors be precisely balanced to have safe operational characteristics. However, in some cases, the nonlinear aspect of the EOM should be considered. The purpose of this paper is to show examples of how the linear vs. nonlinear formulations differ. This paper will also show how excessive unbalance is capable of dramatically altering the behavior of the system and can produce chaotic motions associated with the “jump” phenomenon.

42 ENGINEERING↗
DOE OSTI2025

Generalized Ginsparg-Wilson relations: Fermionic anomalies on the lattice

The Ginsparg-Wilson (GW) relation elegantly captures how the anomalous chiral symmetry of a Dirac fermion manifests on the lattice. In this talk, we discuss how the GW relation and its closed-form solution, the overlap operator, can be generalized to Majorana or Dirac fermions in any dimension for finite symmetry transformations (continuous or discrete). We find an exact symmetry which reproduces both perturbative and global anomalies on the lattice. These generalized GW fermions are boundary theories of various bulk symmetry-protected topological phases and thus provide an explicit lattice realization of the fermionic bulk-boundary correspondence central to recent proposals for chiral gauge theories on the lattice.

Singh, Hersh [Fermilab] (ORCID:0000000220026959)↗
NASA NTRS1962

One-Dimensional Heat Conduction Through the Skin of a Vehicle upon Entering a Planetary Atmosphere at Constant Velocity and Entry Angle

Closed-form solutions of the one-dimensional heat-conduction equations for the flow of heat into a plate with a laminar boundary layer have been obtained for a configuration entering a planetary atmosphere with constant velocity and negative entry angle. The atmospheric density was assumed to obey an exponential law and the temperature was assumed constant initially. The solution is in the form of a Fourier series expansion which, for most practical applications, can be approximated by retaining only one term of the expression. The solution applies to the initial part of the entry before the maximum heating conditions are encountered.

SKIN TEMPERATURE↗
NASA NTRS1971

Analysis of cavitation bubble dynamics in a liquid

General differential equations governing the dynamics of the cavitation bubbles in a liquid were derived. With the assumption of spherical symmetry the governing equations were simplified. Closed form solutions were obtained for simple cases, and numerical solutions were calculated for complicated ones. The growth and the collapse of the bubble were analyzed, oscillations of the bubbles were studied, and the stability of the cavitation bubbles were investigated. The results show that the cavitation bubbles are unstable, and the oscillation is not sinusoidal.

Fontenot, L. L.↗
NASA NTRS1972

Cross-spectral functions based on von Karman's spectral equation

Cross-spectral functions for the vertical and longitudinal components of turbulence of a two-dimensional gust field are derived from the point correlation function for turbulence due to von Karman. Closed form solutions in terms of Bessel functions of order 5/6 and 11/6 are found. An asymptotic expression for large values of the frequency argument, and series results for small values of frequency, are also given. These results now form the base for studying the effect of spanwise variations in turbulence for a turbulence environment which is characterized by the von Karman isotropic spectral relations. Previous studies were based mainly on the Dryden-type spectral representation.

Houbolt, J. C.↗
NASA NTRS1972

Diffusive and radiative effects on vaporization times of drops in film boiling

Diffusive and radiative effects are incorporated into an analysis for the vaporization time of drops in film boiling. The momentum, energy, and continuity equations are solved with some appropriate simplifications so as to obtain a simple closed form solution for the overall film boiling heat transfer coefficient. Next, a theoretical expression for the droplet vaporization time is developed and compared to the measured vaporization times of water droplets vaporizing into air, argon, nitrogen, and helium. The agreement between experiment and theory is good. Under the helium blanket, the diffusive evaporative component is significant in comparison to the film boiling component.

Baumeister, K. J.↗