Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “cylindrical coordinates”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 127 records · Page 7

Towards and FVE-FAC Method for Determining Thermocapillary Effects on Weld Pool Shape

Several practical materials processes, e.g., welding, float-zone purification, and Czochralski crystal growth, involve a pool of molten metal with a free surface, with strong temperature gradients along the surface. In some cases, the resulting thermocapillary flow is vigorous enough to convect heat toward the edges of the pool, increasing the driving force in a sort of positive feedback. In this work we examine this mechanism and its effect on the solid-liquid interface through a model problem: a half space of pure substance with concentrated axisymmetric surface heating, where surface tension is strong enough to keep the liquid free surface flat. The numerical method proposed for this problem utilizes a finite volume element (FVE) discretization in cylindrical coordinates. Because of the axisymmetric nature of the model problem, the control volumes used are torroidal prisms, formed by taking a polygonal cross-section in the (r, z) plane and sweeping it completely around the z-axis. Conservation of energy (in the solid), and conservation of energy, momentum, and mass (in the liquid) are enforced globally by integrating these quantities and enforcing conservation over each control volume. Judicious application of the Divergence Theorem and Stokes' Theorem, combined with a Crank-Nicolson time-stepping scheme leads to an implicit algebraic system to be solved at each time step. It is known that near the boundary of the pool, that is, near the solid-liquid interface, the full conduction-convection solution will require extremely fine length scales to resolve the physical behavior of the system. Furthermore, this boundary moves as a function of time. Accordingly, we develop the foundation of an adaptive refinement scheme based on the principles of Fast Adaptive Composite Grid methods (FAC). Implementation of the method and numerical results will appear in a later report.

Canright, David↗

Turbulence Measurements in the Near Field of a Wingtip Vortex

The roll-up of a wingtip vortex, at Reynolds number based on chord of 4.6 million was studied with an emphasis on suction side and near wake measurements. The research was conducted in a 32 in. x 48 in. low-speed wind tunnel. The half-wing model had a semi-span of 36 in. a chord of 48 in. and a rounded tip. Seven-hole pressure probe measurements of the velocity field surrounding the wingtip showed that a large axial velocity of up to 1.77 U(sub infinity) developed in the vortex core. This level of axial velocity has not been previously measured. Triple-wire probes have been used to measure all components of the Reynolds stress tensor. It was determined from correlation measurements that meandering of the vortex was small and did not appreciably contribute to the turbulence measurements. The flow was found to be turbulent in the near-field (as high as 24 percent RMS w - velocity on the edge of the core) and the turbulence decayed quickly with streamwise distance because of the nearly solid body rotation of the vortex core mean flow. A streamwise variation of the location of peak levels of turbulence, relative to the core centerline, was also found. Close to the trailing edge of the wing, the peak shear stress levels were found at the edge of the vortex core, whereas in the most downstream wake planes they occurred at a radius roughly equal to one-third of the vortex core radius. The Reynolds shear stresses were not aligned with the mean strain rate, indicating that an isotropic-eddy-viscosity based prediction method cannot accurately model the turbulence in the cortex. In cylindrical coordinates, with the origin at the vortex centerline, the radial normal stress was found to be larger than the circumferential.

Chow, Jim↗

Validation of an Accurate Three-Dimensional Helical Slow-Wave Circuit Model

The helical slow-wave circuit embodies a helical coil of rectangular tape supported in a metal barrel by dielectric support rods. Although the helix slow-wave circuit remains the mainstay of the traveling-wave tube (TWT) industry because of its exceptionally wide bandwidth, a full helical circuit, without significant dimensional approximations, has not been successfully modeled until now. Numerous attempts have been made to analyze the helical slow-wave circuit so that the performance could be accurately predicted without actually building it, but because of its complex geometry, many geometrical approximations became necessary rendering the previous models inaccurate. In the course of this research it has been demonstrated that using the simulation code, MAFIA, the helical structure can be modeled with actual tape width and thickness, dielectric support rod geometry and materials. To demonstrate the accuracy of the MAFIA model, the cold-test parameters including dispersion, on-axis interaction impedance and attenuation have been calculated for several helical TWT slow-wave circuits with a variety of support rod geometries including rectangular and T-shaped rods, as well as various support rod materials including isotropic, anisotropic and partially metal coated dielectrics. Compared with experimentally measured results, the agreement is excellent. With the accuracy of the MAFIA helical model validated, the code was used to investigate several conventional geometric approximations in an attempt to obtain the most computationally efficient model. Several simplifications were made to a standard model including replacing the helical tape with filaments, and replacing rectangular support rods with shapes conforming to the cylindrical coordinate system with effective permittivity. The approximate models are compared with the standard model in terms of cold-test characteristics and computational time. The model was also used to determine the sensitivity of various circuit parameters including typical manufacturing dimensional tolerances and support rod permittivity. By varying the circuit parameters of an accurate model using MAFIA, these sensitivities can be computed for manufacturing concerns, and design optimization previous to fabrication, thus eliminating the need for costly experimental iterations. Several variations were made to a standard helical circuit using MAFIA to investigate the effect that variations on helical tape and support rod width, metallized loading height and support rod permittivity, have on TWT cold-test characteristics.

Kory, Carol L.↗

Response of High Subsonic Jet to Nonaxisymmetric Disturbances

A model of sound generated in a high subsonic (Mach 0.9) circular jet is solved numerically in cylindrical coordinates for nonaxisymmetric disturbances. The jet is excited by transient mass injection by a finite duration pulse via a modulated ring source. The nonaxisymmetric solution is computed for long times after the initial disturbance has exited the computational domain. The long time behavior of the jet is dominated by vorticity and pressure disturbances generated at the nozzle lip and growing as they convect down-stream in the jet. These disturbances generate sound as they propagate. The primary non-axisymmetric effect that we simulate is that of a flapping mode where regions of high and low pressure alternate on opposite sides of the jet. The predominant feature of this mode is the appearance of relatively large deviations of the pressure from the ambient pressure on opposite sides of the jet and the convection of these regions downstream. We illustrate flow field, near field and far field data. Important nonaxisymmetric characteristics of the near and flow field disturbances include roughly periodic pressure elevations and depressions at opposite values of the azimuthal angle psi. These correspond to pressure disturbances propagating in the axial direction. The azimuthal velocity exhibits a sinusoidal dependence on psi with similar roughly periodic disturbances. For every azimuthal angle psi, the jet radiation peaks about 30 deg. from the jet axis, however there is now a pronounced dependence of the far field radiation pattern on psi.

Bayliss, A.↗

Radiation Losses Due to Tapering of a Double-Core Optical Waveguide

The theoretical model we designed parameterizes the power losses as a function of .the profile shape for a tapered, single mode, optical dielectric coupler. The focus of this project is to produce a working model that determines the power losses experienced by the fibers when light crosses a taper region. This phenomenon can be examined using coupled mode theory. The optical directional coupler consists of a parallel, dual-channel, waveguide with minimal spacing between the channels to permit energy exchange. Thus, power transfer is essentially a function of the taper profile. To find the fields in the fibers, the approach used was that of solving the Helmholtz equation in cylindrical coordinates involving Bessel and modified Bessel functions depending on the location.

Lyons, Donald R.↗

The Dynamics of Miscible Interfaces: Simulations

The goal of this experimental/computational investigation (joint with Prof Maxworthy at USC) has been to study the dynamics of miscible interfaces, both from a scientific and a practical point of view, and to prepare a related experiment to be flown on the International Space Station. In order to address these effects, we have focused experimental and computational investigations on miscible displacements in cylindrical capillary tubes, as well as in Hele-Shaw cells. Regarding the flow in a capillary tube, the question was addressed as to whether Korteweg stresses and/or divergence effects can potentially account for discrepancies observed between conventional Stokes flow simulations and experiments for miscible flows in capillary tubes. An estimate of the vorticity and streamfunction fields induced by the Kortewegs stresses was derived, which shows these stresses to result in the formation of a vortex ring structure near the tip of the concentration front. Through this mechanism the propagation velocity of the concentration front is reduced, in agreement with the experimental observations. Divergence effects, on the other hand, were seen to be very small, and they have a negligible influence on the tip velocity. As a result, it can be concluded that they are not responsible for the discrepancies between experiments and conventional Stokes simulations. A further part of our investigation focussed on the development of high-accuracy three-dimensional spectral element simulation techniques for miscible flows in capillary tubes, including the effects of variable density and viscosity. Towards this end, the conservation equations are treated in cylindrical coordinates.

Meiburg, Eckart↗

Nonaxisymmetric Disturbances in a Jet and Their Effect on Structural Loading

A model of sound generated in a high subsonic (Mach 0.9) circular jet is solved numerically in cylindrical coordinates for nonaxisymmetric disturbances. The jet is excited by transient mass injection by a finite duration pulse via a rotating ring source. The flow field, near field and far field pressure disturbances corresponding to these sources are described. In particular, the resulting pressure field, which would serve to excite nearby panels, is illustrated together with preliminary results on the excitation of thin slices of nearby panels. We consider both the short time behavior of the jet and the long time behavior, after the initial excitation pulse has exited the computational domain. The long time behavior of the jet is dominated by vorticity and pressure disturbances generated at the nozzle lip and growing as they convect downstream in the jet. These disturbances generate sound as they propagate. We find that rotating nonaxisymmetric disturbances persist for long times. Furthermore, depending on location, both in phase and out of phase behavior can be found upon reflection across the jet axis.

Bayliss, A.↗

Stability of Supersonic Boundary Layers on a Cone at an Angle of Attack

The stability and receptivity of three-dimensional supersonic boundary layers over a 7deg sharp tipped straight cone at an angle of attack of 4.2deg is numerically investigated at a free stream Mach number of 3.5 and at two high Reynolds numbers, 0.25 and 0.50x10(exp 6)/inch. The generation and evolution of stationary crossflow vortices are also investigated by performing simulations with three-dimensional roughness elements located on the surface of the cone. The flow fields with and without the roughness elements are obtained by solving the full Navier-Stokes equations in cylindrical coordinates using the fifth-order accurate weighted essentially non-oscillatory (WENO) scheme for spatial discretization and using the third-order total-variation-diminishing (TVD) Runge-Kutta scheme for temporal integration. Stability computations reveal that the azimuthal wavenumbers are in the range of m approx. 25-50 for the most amplified traveling disturbances and in the range of m approx. 40-70 for the stationary disturbances. The N-Factor computations predicted that transition would occur further forward in the middle of the cone compared to the transition fronts near the windward and the leeward planes. The simulations revealed that the crossflow vortices originating from the nose region propagate towards the leeward plane. No perturbations were observed in the lower part of the cone.

Balakumar, Ponnampalam↗

Stability of Hypersonic Boundary Layers on a Cone at an Angle of Attack

The stability and receptivity of a three-dimensional hypersonic boundary layer over a 7deg half-angle straight cone at an angle of attack of 6deg is numerically investigated at a freestream Mach number of 6.0 and a Reynolds number of 10.4x10(exp 6)/m. The generation and evolution of stationary crossflow vortices are also investigated by performing simulations with three-dimensional roughness elements located on the surface of the cone. The flow fields with and without the roughness elements are obtained by solving the full Navier- Stokes equations in cylindrical coordinates using a fifth-order accurate weighted essentially non-oscillatory (WENO) scheme for spatial discretization and a third-order total-variation-diminishing (TVD) Runge-Kutta scheme for temporal integration. Stability computations produced azimuthal wavenumbers in the range of m approx. 20-50 for the most amplified traveling disturbances and in the range of m approx.30-70 for the stationary disturbances. The frequency of the unstable second-mode ranges from 400 kHz to 900 kHz along the windward ray. The N-Factor computations predicted transition would occur more forward on the sides of the cone as compared to the transition fronts near the windward and the leeward rays. The simulations also show the crossflow vortices originating from the nose region propagate towards the leeward ray. No perturbations were observed toward the windward half of the cone.

Balakumar, P.↗

Full-field Deformation Measurement Techniques for a Rotating Composite Shaft

Test methods were developed to view global and local deformation in a composite tube during a test in which the tube is rotating at speeds and torques relevant to rotorcraft shafts. Digital image correlation (DIC) was used to provide quantitative displacement measurements during the tests. High speed cameras were used for the DIC measurements in order to capture images at sufficient frame rates and with sufficient resolution while the tube was rotating at speeds up to 5,000 rpm. Surface displacement data was resolved into cylindrical coordinates in order to measure rigid body rotation and global deformation of the tube. Tests were performed on both undamaged and impact damaged tubes in order to evaluate the capability to detect local deformation near an impact damaged site. Measurement of radial displacement clearly indicated a local buckling deformation near the impacted site in both dynamic and static tests. X-ray computed tomography (CT) was used to investigate variations in fiber architecture within the composite tube and to detect impact damage. No growth in the impact damage area was observed by DIC during dynamic testing or by x-ray CT in post test inspection of the composite tube.

Kohlman, Lee W.↗

Modeling Sound Propagation Through Non-Axisymmetric Jets

A method for computing the far-field adjoint Green's function of the generalized acoustic analogy equations under a locally parallel mean flow approximation is presented. The method is based on expanding the mean-flow-dependent coefficients in the governing equation and the scalar Green's function in truncated Fourier series in the azimuthal direction and a finite difference approximation in the radial direction in circular cylindrical coordinates. The combined spectral/finite difference method yields a highly banded system of algebraic equations that can be efficiently solved using a standard sparse system solver. The method is applied to test cases, with mean flow specified by analytical functions, corresponding to two noise reduction concepts of current interest: the offset jet and the fluid shield. Sample results for the Green's function are given for these two test cases and recommendations made as to the use of the method as part of a RANS-based jet noise prediction code.

Leib, Stewart J.↗

Density-conserving shape factors for particle simulations in cylindrical and spherical coordinates

It is established that a particle-to-grid weighting which is based on both conventional particle-in-cell (PIC) and cloud-in-cell (CIC) shape factors will yield nonuniform grid densities, even in the case of uniform particle distributions, in both cylindrical and spherical coordinates. In view of this, alternative density-conserving weighting schemes are discussed which encompass modified PIC and CIC weighting. These alternative shape factors are mathematically no more complicated than the conventional nondensity-conserving expressions.

Ruyten, Wilhelmus M.↗

Response-coefficient method for heat-conduction transients with time-dependent inputs

A theoretical overview of the response coefficient method for heat conduction transients with time-dependent input forcing functions is presented with a number of illustrative applications. The method may be the most convenient and economical if the same problem is to be solved many times with different input-time histories or if the solution time is relatively long. The method is applicable to a wide variety of problems, including irregular geometries, position-dependent boundary conditions, position-dependent physical properties, and nonperiodic irregular input histories. Nonuniform internal energy generation rates within the structure can also be handled by the method. The area of interest is long-time solutions, in which initial condition is unimportant, and not the early transient period. The method can be applied to one dimensional problems in cartesian, cylindrical, and spherical coordinates as well as to two dimensional problems in cartesian and cylindrical coordinates.

Ceylan, Tamer↗

Estimating Interplanetary Magnetic Field Conditions at Mercury's Orbit From MESSENGER Magnetosheath Observations Using a Feedforward Neural Network

Abstract Mercury's small magnetosphere is embedded in the dynamic and intense solar wind environment characteristic of the inner heliosphere. Both the magnitude and orientation of the interplanetary magnetic field (IMF) significantly influence the solar wind‐magnetospheric interaction at Mercury, driving phenomena such as magnetic reconnection. The MErcury Surface, Space Environment, Geochemistry and Ranging (MESSENGER) spacecraft provided in‐situ magnetic field measurements of the solar wind, the magnetosheath, and the magnetosphere along each orbit. However, it is a challenge to directly assess the IMF's impact on Mercury's plasma environment due to the temporal separation between observations within the solar wind and the magnetosphere, especially in the absence of an upstream monitor. Here, we present a feedforward neural network (FNN) trained on a subset of magnetosheath observations to estimate the strength and orientation of the IMF upstream of the bow shock. Utilizing magnetosheath magnetic field, cylindrical spatial coordinates, and heliocentric distance measurements, the FNN predicts upstream IMF conditions with an score of 0.70 and mean averaged error of 5.3 nT, thereby greatly decreasing the temporal separation between IMF estimates and magnetospheric measurements throughout the MESSENGER mission. This approach yields IMF estimates for all magnetosheath data measured by MESSENGER, providing a useful tool for future investigations of the IMF impact on Mercury's magnetosphere. This method will be integrable with the dual‐spacecraft BepiColombo magnetosheath measurements, providing useful estimates of upstream IMF conditions particularly during the extended periods in which neither spacecraft sample the solar wind. Our results demonstrate the utility of machine learning techniques on advancing space science research.

Bowers, Charles F.↗

Theoretical Assessment of the Transition Between Electron Emission Mechanisms for Nonplanar Diodes

Theoretically and computationally describing the operation of nanodiodes requires characterizing the transitions between multiple electron emission mechanisms for nanodiodes with complicated geometries. This motivates our development of techniques to determine when simplified theories for individual mechanisms suffice compared to more complete, but more computationally expensive, models. Leveraging recent theories that define a canonical gap distance to translate planar theory to nonplanar diodes, we derive the conditions for the transitions among thermal emission, field emission, and space-charge-limited current density (SCLCD) in vacuum and with collisions for non-Cartesian coordinate systems, including spherical, cylindrical, and prolate spheroidal coordinate systems. Particle-in-cell (PIC) simulations of the current density as a function of applied voltage for a tip-to-plate geometry in vacuum agreed qualitatively with the asymptotes for thermal emission at low voltage and SCLCD at higher voltage using the canonical gap distance. As a result, this demonstrates the utility of this approach for guiding system design and suggests future extensions to save simulation time for more realistic geometries that are more computationally expensive.

Conformal mapping↗

Initial Demonstration of New Griffin Technologies for Simulating the Running-In Phase of Pebble Bed Reactors

Griffin is a reactor multiphysics modeling application based on MOOSE (Multiphysics Object-Oriented Simulation Environment) and specifically targeting transient modeling of advanced reactors. Griffin has been used recently to model pebble-bed reactors for the Nuclear Regulatory Commission (NRC) Office of Nuclear Regulatory Research and the Advanced Reactor Technology program. This modeling work has focused thus far on the direct calculation of equilibrium cores. This report documents an initial demonstration of a new running-in simulation capability. The new running-in capability is verified using the existing direct equilibrium core calculation capability. A simplified pebble-bed reactor model is then used to demonstrate the running-in simulation capability. This demonstration shows that Griffin is able to simulate years of operation during the running-in phase efficiently with each depletion step taking only several seconds. Two new technologies are also presented in this report which have been developed in Griffin that will be essential for improved accuracy both of the direct equilibrium core computation and the new running-in simulation capability. The first technology is an online cross section generation capability specifically targeted for pebble-bed reactors. This will improve the accuracy of the depletion calculation as the cross sections are generated at the exact core status. This also avoids the difficult step of pre-generating a separate standalone multigroup cross section set. Secondly, a newly implemented discretization for discontinuous finite element method (DFEM) SN transport in cylindrical (RZ) coordinates, which can be solved efficiently using the existing SN sweep solver, is discussed and some results are shown demonstrating the usefulness of the additional accuracy transport provides over a diffusion approximation.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗