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All sourcesNASA NTRSDOE OSTI
NASA NTRS2019

Ozone Vertical Profile Satellite Measurements by S-NPP OMPS, Aura MLS, and Sentinel-5P TROPOMI

NASA has been monitoring ozone variations from space since 1970 with the launch of the Backscatter Ultraviolet instrument (BUV) on Nimbus- 4. Ozone in the Earth’s stratosphere and troposphere plays a crucial role in protecting life from harmful solar UV radiation, and it also influences Earth’s climate. The vertical distribution of ozone is used in modeling forecasts, verifying model analysis and simulations, and improving the measurement of tropospheric ozone that is a toxic constituent of air pollution. The Microwave Limb Sounder (MLS) on the EOS Aura spacecraft has been monitoring long-term continuous stratosphere ozone vertical behaviors since 2004. The Ozone Mapper Profile Suite (OMPS) on the Suomi National Polar-orbiting Partnership (S-NPP) was launched in 2011. Two of its three instruments, the Limb Profiler (LP) and the Nadir Profiler (NP), are designed to map ozone profiles with full global coverage (~6 days for NP) and a high level of vertical accuracy (1-km reporting record for LP) in the stratosphere and upper troposphere. The TROPOspheric Monitoring Instrument (TROPOMI) on the Copernicus Sentinel-5 Precursor (S5P), launched in 2017, aims to retrieve ozone profiles in both the troposphere and up to top-of-atmosphere (TOA) by using UV radiation measurements in a spectral range of 270-320 nm. S5P/TROPOMI ozone profile products are planned to become available in April 2020. This presentation will concentrate on satellite ozone vertical profile data collections from OMPS and MLS which are archived at the NASA Goddard Earth Sciences Data and Information Services Center (GES DISC). TROPOMI ozone vertical profiles for the troposphere and to top-of-atmosphere will become available at NASA GES DISC in 2020. The presentation briefly explores their potential complementary usability in determining three-dimensional ozone global distributions with high temporal and spatial resolutions.

Zeng, Jian↗
DOE OSTI2021

Development of Mission Profiles for Humidity Models in the Reliability Testing of PV Inverters: Preprint

To understand the impacts of humidity on PV inverters, mission profiles were developed to accurately describe the different processes and rates based on the environmental factors of temperature, relative humidity, and irradiance. The operating environment of the device introduces stress factors dependent on component temperature, relative humidity, and component voltage. The development of profiles started from looking at historical climate conditions at Cocoa, Florida, a hot and humid location. The profile developed from field location was compared with existing humidity test profiles in industrial and military standards to determine acceleration factors. Prior to the evaluation of the mission profiles, critical components in the PV inverter were identified based on vendor discussions along with failure modes of interest. The profiles considered in this study was demonstrated using a 4-kVA string inverter. The measurements from the devices were substituted in device manufacturer specified equation to determine the severity of each test. The severity of each test was compared against the severity of the 24-hour result to determine the acceleration factor of each test. The acceleration factors were determined to be over a range of 1.2-6 for the existing humidity tests from standards, when compared against the mission profile developed from field data. This optimal humidity/thermal profile will be passed to the IEC standards development for inverter qualification testing.

humidity models↗
DOE OSTI2019

Robust control of the current profile and plasma energy in EAST

Integrated control of the toroidal current density profile, or alternatively the q-profile, and plasma stored energy is essential to achieve advanced plasma scenarios characterized by high plasma confinement, magnetohydrodynamics stability, and noninductively driven plasma current. The q-profile evolution is closely related to the evolution of the poloidal magnetic flux profile, whose dynamics is modeled by a nonlinear partial differential equation (PDE) referred to as the magnetic-flux diffusion equation (MDE). The MDE prediction depends heavily on the chosen models for the electron temperature, plasma resistivity, and non-inductive current drives. To aid control synthesis, control-oriented models for these plasma quantities are necessary to make the problem tractable. However, a relatively large deviation between the predictions by these control-oriented models and experimental data is not uncommon. For this reason, the electron temperature, plasma resistivity, and non-inductive current drives are modeled for control synthesis in this work as the product of an “uncertain” reference profile and a nonlinear function of the different auxiliary heating and current-drive (H&CD) source powers and the total plasma current. The uncertainties are quantified in such a way that the family of models arising from the modeling process is able to capture the q-profile and plasma stored energy dynamics from a typical EAST shot. A control-oriented nonlinear PDE model is developed by combining the MDE with the “uncertain” models for the electron temperature, plasma resistivity, and non-inductive current drives. This model is then rewritten into a control framework to design a controller that is robust against the modeled uncertainties. The resulting controller utilizes EAST's H&CD powers and total plasma current to regulate the q profile and plasma stored energy even when mismatches between modeled and actual dynamics are present. The effectiveness of the controller is demonstrated through nonlinear simulations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2014

SU-E-T-220: Investigation of Intrafraction Changes to Photon Beam Profiles

Purpose: Treatment Planning Systems model beam profiles to be static and independent of gantry angle. This work investigates how beam profiles change over time, with varying gantry angle. Methods: 200 cGy was delivered to ICProfiler (Sun Nuclear) on 2 Elekta Synergys and 1 Varian 21EX linacs at 8 gantry angles and 1 clockwise arc. Measurements were recorded 8 times per second. To investigate the initial portion of the beams, single-shot and multi-control-point beams were measured. The differences in beam profiles were analyzed as well as the length of time for the beam to stabilize. Symmetry was calculated 5cm from the central axis at 100cm SSD. Field sizes ranged from 30×30 cm{sup 2} to 40×40 cm{sup 2}. Results: The beam profiles changed over time and were dependent on gantry angle. The composite profile for each beam met 1% tolerance described in TG-142. It took up to 14.7, 3.7 and 11.3 cGy for the two Elektas and Varian respectively to satisfy the tolerance. All linacs had the most flat, symmetric, and stable beam profile with the gantry at 0 degrees, where the symmetry was 100.5%±0.55, 101.0%±0.52 and 101.1%±0.44 respectively. The symmetry was 100.7%±1.06, 101.1%±1.05 and 101.2%±0.64 at the gantry angle with the biggest discrepancy (90, 180 and 180 degrees respectively). Symmetry was better in the X direction for the Elektas and the Y for the Varian. Fluctuations in beam profiles corresponded to changes in dose rate. Conclusion: Flatness and symmetry changed over time and with gantry angle. Because Treatment Planning Systems do not account for these changes, it may be necessary to limit certain beams from clinical use, for example, beams with low MU. It may also be necessary to add additional QA procedures beyond those suggested in TG-142 to account for these changes.

07 ISOTOPE AND RADIATION SOURCES↗
DOE OSTI2026

A Physical Model Enhanced Data Driven Method for High-Resolution Residential Load Profile Generation

Residential buildings account for significant energy consumption, creating opportunities to offer grid services. As electric utilities seek to implement effective system operation strategies, understanding residential energy consumption patterns becomes essential; However, the time intervals of load profiles measured by utilities' smart meters are typically from 15 minutes to 60 minutes. The low-resolution data make it hard to extract appliance-level load information, which is critical for providing grid services. This paper presents a load profile generator designed to produce synthetic load profiles for residential buildings that emphasizes the importance of accurate representations of realistic energy consumption patterns. The generator takes realistic low-resolution residential load measurements and weather data as inputs, producing 1-minute interval profiles that match the characteristics of the original profiles. Further, this generator can be used to populate load profiles in areas where actual measurements are limited to improve the ability of utilities to analyze their distribution systems. By providing more high-resolution residential building load profiles, this tool supports electric utilities to enhance their residential building load control strategies and improve overall grid stability.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2022

Data-driven analysis of neutron diffraction line profiles: application to plastically deformed Ta

Abstract Non-destructive evaluation of plastically deformed metals, particularly diffraction line profile analysis (DLPA), is valuable both to estimate dislocation densities and arrangements and to validate microstructure-aware constitutive models. To date, the interpretation of whole line diffraction profiles relies on the use of semi-analytical models such as the extended convolutional multiple whole profile (eCMWP) method. This study introduces and validates two data-driven DLPA models to extract dislocation densities from experimentally gathered whole line diffraction profiles. Using two distinct virtual diffraction models accounting for both strain and instrument induced broadening, a database of virtual diffraction whole line profiles of Ta single crystals is generated using discrete dislocation dynamics. The databases are mined to create Gaussian process regression-based surrogate models, allowing dislocation densities to be extracted from experimental profiles. The method is validated against 11 experimentally gathered whole line diffraction profiles from plastically deformed Ta polycrystals. The newly proposed model predicts dislocation densities consistent with estimates from eCMWP. Advantageously, this data driven LPA model can distinguish broadening originating from the instrument and from the dislocation content even at low dislocation densities. Finally, the data-driven model is used to explore the effect of heterogeneous dislocation densities in microstructures containing grains, which may lead to more accurate data-driven predictions of dislocation density in plastically deformed polycrystals.

36 MATERIALS SCIENCE↗
DOE OSTI2020

TDCOSMO - IV. Hierarchical time-delay cosmography – joint inference of the Hubble constant and galaxy density profiles

The H0LiCOW collaboration inferred via strong gravitational lensing time delays a Hubble constant value of H0 = 73.3−1.8+1.7 km s−1 Mpc−1, describing deflector mass density profiles by either a power-law or stars (constant mass-to-light ratio) plus standard dark matter halos. The mass-sheet transform (MST) that leaves the lensing observables unchanged is considered the dominant source of residual uncertainty in H0. We quantify any potential effect of the MST with a flexible family of mass models, which directly encodes it, and they are hence maximally degenerate with H0. Our calculation is based on a new hierarchical Bayesian approach in which the MST is only constrained by stellar kinematics. The approach is validated on mock lenses, which are generated from hydrodynamic simulations. We first applied the inference to the TDCOSMO sample of seven lenses, six of which are from H0LiCOW, and measured H0 = 74.5−6.1+5.6 km s−1 Mpc−1. Secondly, in order to further constrain the deflector mass density profiles, we added imaging and spectroscopy for a set of 33 strong gravitational lenses from the Sloan Lens ACS (SLACS) sample. For nine of the 33 SLAC lenses, we used resolved kinematics to constrain the stellar anisotropy. From the joint hierarchical analysis of the TDCOSMO+SLACS sample, we measured H0 = 67.4−3.2+4.1 km s−1 Mpc−1. This measurement assumes that the TDCOSMO and SLACS galaxies are drawn from the same parent population. The blind H0LiCOW, TDCOSMO-only and TDCOSMO+SLACS analyses are in mutual statistical agreement. The TDCOSMO+SLACS analysis prefers marginally shallower mass profiles than H0LiCOW or TDCOSMO-only. Without relying on the form of the mass density profile used by H0LiCOW, we achieve a ∼5% measurement of H0. While our new hierarchical analysis does not statistically invalidate the mass profile assumptions by H0LiCOW – and thus the H0 measurement relying on them – it demonstrates the importance of understanding the mass density profile of elliptical galaxies. The uncertainties on H0 derived in this paper can be reduced by physical or observational priors on the form of the mass profile, or by additional data.Key words: gravitational lensing: strong / galaxies: general / galaxies: kinematics and dynamics / distance scale / cosmological parameters / cosmology: observations⋆ The full analysis is available at https://github.com/TDCOSMO/hierarchy_analysis_2020_public.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2014

Performance and data analysis aspects of the new DIII-D monostatic profile reflectometer system

A new frequency-modulated profile reflectometer system, featuring a monostatic antenna geometry (using one microwave antenna for both launch and receive), has been installed on the DIII-D tokamak, providing a first experimental test of this measurement approach for profile reflectometry. Significant features of the new system are briefly described in this paper, including the new monostatic arrangement, use of overmoded, broadband transmission waveguide, and dual-polarization combination/demultiplexing. Updated data processing and analysis, and in-service performance aspects of the new monostatic profile reflectometer system are also presented. By using a raytracing code (GENRAY) to determine the approximate trajectory of the probe beam, the electron density (n{sub e}) profile can be successfully reconstructed with L-mode plasmas vertically shifted by more than 10 cm off the vessel midplane. Specifically, it is demonstrated that the new system has a capability to measure n{sub e} profiles with plasma vertical offsets of up to ±17 cm. Examples are also presented of accurate, high time and spatial resolution density profile measurements made over a wide range of DIII-D conditions, e.g., the measured temporal evolution of the density profile across a L-H transition.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2017

Understanding and predicting profile structure and parametric scaling of intrinsic rotation

This study reports on a recent advance in developing physical understanding and a first-principles-based model for predicting intrinsic rotation profiles in magnetic fusion experiments. It is shown for the first time that turbulent fluctuation-driven residual stress (a non-diffusive component of momentum flux) along with diffusive momentum flux can account for both the shape and magnitude of the observed intrinsic toroidal rotation profile. Both the turbulence intensity gradient and zonal flow E×B shear are identified as major contributors to the generation of the k ∥ -asymmetry needed for the residual stress generation. The model predictions of core rotation based on global gyrokinetic simulations agree well with the experimental measurements of main ion toroidal rotation for a set of DIII-D ECH discharges. The validated model is further used to investigate the characteristic dependence of residual stress and intrinsic rotation profile structure on the multi-dimensional parametric space covering the turbulence type, q-profile structure, and up-down asymmetry in magnetic geometry with the goal of developing the physics understanding needed for rotation profile control and optimization. It is shown that in the flat-q profile regime, intrinsic rotations driven by ITG and TEM turbulence are in the opposite direction (i.e., intrinsic rotation reverses). The predictive model also produces reversed intrinsic rotation for plasmas with weak and normal shear q-profiles.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Probing nonlinear velocity profiles of shear-thinning, nematic platelet dispersions in Couette flow using x-ray photon correlation spectroscopy

In this study, we report experiments employing x-ray photon correlation spectroscopy (XPCS) to characterize the velocity profiles of complex fluids in Couette flow. The approach involves modeling the XPCS correlation functions obtained with the incident x-ray beam passing tangentially through the Couette cell gap at various distances from the inner wall. We first demonstrate the technique with measurements on a dilute colloidal dispersion in the Newtonian liquid glycerol, where the expected linear velocity profiles are recovered. We then employ the technique to map the shear-rate-dependent velocity profiles of a shear-thinning dispersion of nematically ordered Gibbsite platelets. The nonlinear velocity profiles of the Gibbsite dispersion include a narrow slip region adjacent to the outer wall and a band with a small velocity gradient in the interior of the gap that evolves into a region increasingly resembling plug flow with increasing shear rate. Variations in the velocity profile along the vorticity direction indicate an instability in the interface between this region of small velocity gradient and a region of high velocity gradient near the inner wall. The analysis of the small-angle scattering patterns provides information about the spatial and temporal variations in the nematic order of the Gibbsite dispersion and their coupling to the velocity profile. Additional potential applications of this XPCS-based technique and comparisons with established methods for characterizing velocity profiles are discussed.

42 ENGINEERING↗
DOE OSTI2022

Equilibrium reconstruction of DIII-D plasmas using predictive modeling of the pressure profile

New workflows have been developed for predictive modeling of magnetohydrodynamic (MHD) equilibrium in tokamak plasmas. The goal of this work is to predict the MHD equilibrium in tokamak discharges without having measurements of the kinetic profiles. The workflows include a cold start tool, which constructs all the profiles and power flows needed by transport codes; a Grad–Shafranov equilibrium solver; and various codes for the sources and sinks. For validation purposes, a database of DIII-D tokamak discharges has been constructed that is comprised of scans in the plasma current, toroidal magnetic field, and triangularity. Initial efforts focused on developing a workflow utilizing an empirically derived pressure model tuned to DIII-D discharges with monotonic safety factor profiles. This workflow shows good agreement with experimental kinetic equilibrium calculations, but is limited in that it is a single fluid (equal ion and electron temperatures) model and lacks H-mode pedestal predictions. The best agreement with the H-mode database is obtained using a theory-based workflow utilizing pressure profile predictions from a coupled TGLF turbulent transport and EPED pedestal models together with external magnetics and Motional Stark Effect (MSE) data to construct the equilibrium. Here, we obtain an average root mean square error of 5.1% in the safety factor profile when comparing the predicted and experimental kinetic equilibrium. We also find good agreement with the plasma stored energy, internal inductance, and pressure profiles. Including MSE data in the theory-based workflow results in noticeably improved agreement with the q-profiles in high triangularity discharges in comparison with the results obtained with magnetic data only. The predictive equilibrium workflow is expected to have wide applications in experimental planning, between-shot analysis, and reactor studies.

Kinsey, J. E. (ORCID:0000000193347473)↗
DOE OSTI2014

Galaxy halo formation in the absence of violent relaxation and a universal density profile of the halo center

While N-body simulations testify to a cuspy profile of the central region of dark matter halos, observations favor a shallow, cored density profile of the central region of at least some spiral galaxies and dwarf spheroidals. We show that a central profile, very close to the observed one, inevitably forms in the center of dark matter halos if we make a supposition about a moderate energy relaxation of the system during the halo formation. If we assume the energy exchange between dark matter particles during the halo collapse is not too intensive, the profile is universal: it depends almost not at all on the properties of the initial perturbation and is very akin, but not identical, to the Einasto profile with a small Einasto index n ∼ 0.5. We estimate the size of the 'central core' of the distribution, i.e., the extent of the very central region with a respectively gentle profile, and show that the cusp formation is unlikely, even if the dark matter is cold. The obtained profile is in good agreement with observational data for at least some types of galaxies but clearly disagrees with N-body simulations.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

A dynamically driven, universal thermal profile of galaxy groups and clusters

Large scale structures such as groups and clusters of galaxies show a universal, nearly linear entropy radial profile K(r). Using deprojected 16 clusters and 12 groups from the literature, we find that K∝r{sup 0.96±0.01}, consistent with the mean power-law index (0.9–1.1) of previous studies. A similarly good fit is given by a τ∝r{sup 0.72±0.01} ratio between cooling and free-fall times. Both profiles slightly flatten at small radii, as τ becomes of order unity. The entropy profile is usually attributed to self-similar shock accretion (shown to be inconsistent with the data), to non-standard heat conduction, or to turbulent heating. We argue that a dynamical mechanism is needed to sustain such a universal profile, oblivious to the temperature peak at the edge of the core and to the virial shock at the outskirts, and robust to the presence of ongoing cooling, merger, and active galactic nucleus activity. In particular, we show that such a profile can be naturally obtained in a spiral flow, which is likely to underlie most galaxy aggregates according to the ubiquitous spiral patterns and cold fronts observed. Generalizing a two-phase spiral flow model out to the virial radius surprisingly reproduces the thermal profile. A generalized Schwarzschild criterion indicates that observed spiral patterns must involve a convective layer, which may regulate the thermal profile.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2015

Improved profile fitting and quantification of uncertainty in experimental measurements of impurity transport coefficients using Gaussian process regression

The need to fit smooth temperature and density profiles to discrete observations is ubiquitous in plasma physics, yet the prevailing techniques for this have many shortcomings that cast doubt on the statistical validity of the results. This issue is amplified in the context of validation of gyrokinetic transport models (Holland et al 2009 Phys. Plasmas 16 052301), where the strong sensitivity of the code outputs to input gradients means that inadequacies in the profile fitting technique can easily lead to an incorrect assessment of the degree of agreement with experimental measurements. In order to rectify the shortcomings of standard approaches to profile fitting, we have applied Gaussian process regression (GPR), a powerful non-parametric regression technique, to analyse an Alcator C-Mod L-mode discharge used for past gyrokinetic validation work (Howard et al 2012 Nucl. Fusion 52 063002). We demonstrate that the GPR techniques can reproduce the previous results while delivering more statistically rigorous fits and uncertainty estimates for both the value and the gradient of plasma profiles with an improved level of automation. Moreover, we discuss how the use of GPR can allow for dramatic increases in the rate of convergence of uncertainty propagation for any code that takes experimental profiles as inputs. The new GPR techniques for profile fitting and uncertainty propagation are quite useful and general, and we describe the steps to implementation in detail in this paper. These techniques have the potential to substantially improve the quality of uncertainty estimates on profile fits and the rate of convergence of uncertainty propagation, making them of great interest for wider use in fusion experiments and modelling efforts.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2016

CLASH-VLT: testing the nature of gravity with galaxy cluster mass profiles

We use high-precision kinematic and lensing measurements of the total mass profile of the dynamically relaxed galaxy cluster MACS J1206.2-0847 at z=0.44 to estimate the value of the ratio η=Ψ/Φ between the two scalar potentials in the linear perturbed Friedmann-Lemaitre-Robertson-Walker metric. An accurate measurement of this ratio, called anisotropic stress, could show possible, interesting deviations from the predictions of the theory of General Relativity, according to which Ψ should be equal to Φ. Complementary kinematic and lensing mass profiles were derived from exhaustive analyses using the data from the Cluster Lensing And Supernova survey with Hubble (CLASH) and the spectroscopic follow-up with the Very Large Telescope (CLASH-VLT). Whereas the kinematic mass profile tracks only the time-time part of the perturbed metric (i.e. only Φ), the lensing mass profile reflects the contribution of both time-time and space-space components (i.e. the sum Φ+Ψ). We thus express η as a function of the mass profiles and perform our analysis over the radial range 0.5 Mpc≤ r≤ r{sub 200}=1.96 Mpc. Using a spherical Navarro-Frenk-White mass profile, which well fits the data, we obtain η(r{sub 200})=1.01 {sub −0.28}{sup +0.31} at the 68% C.L. We discuss the effect of assuming different functional forms for mass profiles and of the orbit anisotropy in the kinematic reconstruction. Interpreting this result within the well-studied f(R) modified gravity model, the constraint on η translates into an upper bound to the interaction length (inverse of the scalaron mass) smaller than 2 Mpc. This tight constraint on the f(R) interaction range is however substantially relaxed when systematic uncertainties in the analysis are considered. Our analysis highlights the potential of this method to detect deviations from general relativity, while calling for the need of further high-quality data on the total mass distribution of clusters and improved control on systematic effects.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2025

Reconstruction of current profiles from external magnetic and MSE measurements on DIII-D

This work introduces a new current model into the EFIT code for plasma current profile reconstruction. Using this model, edge-localized current density profiles are reconstructed solely from external magnetic measurements. Quantitative comparisons show that edge current profiles obtained with the new current model align closely with those from kinetic equilibrium reconstruction. The new model enables current density reconstruction with fewer diagnostics than kinetic equilibrium reconstruction (Lao et al 1990 Nucl. Fusion 30 1035–49), demonstrating that edge-localized current density information can be obtained from external magnetic measurements only, without the help of kinetic profiles and internal diagnostics, and without using the bootstrap current model. Furthermore, with the constraints of external magnetic and MSE measurements, current profiles in full radius obtained from the new model are in good agreement with the results of kinetic equilibrium reconstruction, which not only improves the efficiency of current reconstruction but also helps avoid possible errors caused by different kinds of diagnoses. Possible applications are also discussed, and a brief analysis of the evolution of the full-radius current density is performed. Noticeable decreases in both the magnitude and gradient of the edge current around the time of ELM bursts are observed. Moreover, analysis of the full radius current density profiles ( ρ N = 0 − 1.0, ρN denotes to square root of the normalized toroidal flux) reveals that as the edge current changes, the inner current also changes following a sinusoidal-like pattern at almost all time slices during four type-I ELMs in discharge 161493. The current evolution in the inner region ( ρ N = 0.2 − 0.6) is synchronized with the boundary region ( ρ N = 0.89 − 1.0), while the intermediate region ( ρ N = 0.6 − 0.89) shows opposite behavior. This sinusoidal-like variations in full-radius current density profile indicates strong core-pedestal coupling, suggesting ELMs significantly affect core plasmas, though current changes manifest differently across radial regions.

EFIT↗
DOE OSTI2016

New figuring model based on surface slope profile for grazing-incidence reflective optics

Surface slope profile is widely used in the metrology of grazing-incidence reflective optics instead of surface height profile. Nevertheless, the theoretical and experimental model currently used in deterministic optical figuring processes is based on surface height, not on surface slope. This means that the raw slope profile data from metrology need to be converted to height profile to perform the current height-based figuring processes. The inevitable measurement noise in the raw slope data will introduce significant cumulative error in the resultant height profiles. As a consequence, this conversion will degrade the determinism of the figuring processes, and will have an impact on the ultimate surface figuring results. To overcome this problem, an innovative figuring model is proposed, which directly uses the raw slope profile data instead of the usual height data as input for the deterministic process. In this article, first the influence of the measurement noise on the resultant height profile is analyzed, and then a new model is presented; finally a demonstration experiment is carried out using a one-dimensional ion beam figuring process to demonstrate the validity of our approach.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Attached Jet Velocity Profiles in Mixing Tanks

Free jets have been studied in detail over much of the last century, but the theory for offset and attached jets remains incomplete. Attached jets differ from free jets in that they lose momentum to nearby surfaces, attenuating their velocities. The velocity profiles of free circular jets are nearly Gaussian, with quantitative mathematical descriptions derived from first principles by Goertler and Tollmien (Rajaratnam, 1976). In contrast, mathematical descriptions of three-dimensional attached jets from circular nozzles remain much less mature. Agelin-Chaab and Tachie (2011) used particle imaging velocimetry of a three-dimensional attached jet to show that the scaled velocity decays with scaled distance from the nozzle with a power law exponent between -1.15 and -1.21, which is larger in magnitude than that of a free jet. However, quantitative analytical expressions for the velocity profiles of attached jets similar to those of free jets remain elusive. This paper addresses this critical gap. Here we evaluate the velocity profiles of three-dimensional offset jets emerging from circular nozzles that that become attached jets. These jets lose momentum due to interactions with nearby surfaces and are important to evaluating flows in mixing vessels and to suspending solids and trapped gases in radioactive waste tanks. Despite the importance of attached jets, prior insight has been purely experimental, limited to overly simplistic analytical models, or restricted to computationally expensive computational fluid dynamics case studies. We compare the expression of Verhoff (1963) to experimental results to find reasonable quantitative agreement. As stated by Agelin-Chaab and Tachie (2011), “detailed velocity measurements of 3D offset jets are rare.” Such remains the case. This study adds to the literature by providing information at two additional Reynolds numbers (1.43 106 and 1.87 106) and evaluating simple but accurate expressions for velocity profiles. These Reynolds numbers are an order of magnitude higher than prior reports. The semi-empirical stream wise velocity profile perpendicular to the surface proposed by Verhoff (1963) is in approximate agreement with these velocity profiles, which is surprising because these attached jets are three-dimensional instead of two-dimensional as evaluated by Verhoff. However, additional work is necessary to fully describe these profiles quantitatively.

jet, attached jet, offset jet↗