Search NASA⌕ Search

SEARCH · Search NASA

Results for “Velocity Model”

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 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Joint Inversion of Body Wave Arrival Times, Surface Wave Dispersion Data and Receiver Functions: Method and Application to South China

In this work, we have developed a new joint inversion method that incorporates body wave arrival times, surface wave dispersion and receiver functions to simultaneously update earthquake locations and constrain three-dimensional P-wave (Vp) and S-wave velocity (Vs) models. Due to complementary sensitivities of the three types of data, the proposed joint inversion algorithm can reduce the intrinsic non-uniqueness of inversions using fewer types of data and better determine smooth velocity variations and velocity discontinuities. Synthetic tests demonstrate the advantages of this new joint inversion algorithm in resolving velocity structures, especially in constraining velocity gradients across the Moho interface. We have applied the proposed joint inversion algorithm to image the lithosphere velocity structure of south China. The inverted Vp and Vs models fit body wave arrival times, surface wave dispersion and receiver functions well. We further analyzed the distribution of Vs gradients across the Moho interface in detail, which helps us better understand tectonics in south China.

58 GEOSCIENCES↗
DOE OSTI2020

Comparison of Optimal Energy Management Strategies Using Dynamic Programming, Model Predictive Control, and Constant Velocity Prediction

Due to the recent advancements in autonomous vehicle technology, future vehicle velocity predictions are becoming more robust which allows fuel economy (FE) improvements in hybrid electric vehicles through optimal energy management strategies (EMS). A real- world highway drive cycle (DC) and a controls-oriented 2017 Toyota Prius Prime model are used to study potential FE improvements. We proposed three important metrics for comparison: (1) perfect full drive cycle prediction using dynamic programming, (2) 10-second prediction horizon model predictive control (MPC), and (3) 10-second constant velocity prediction. These different velocity predictions are put into an optimal EMS derivation algorithm to derive optimal engine torque and engine speed. The results show that the constant velocity prediction algorithm outperformed the baseline control strategy but underperformed the MPC strategy with an average 1.58% and 2.45% of FE improvement with highway and city-highway DC. Also, using a 10-second prediction window MPC strategy provided FE improvement results close to the full drive cycle prediction case. MPC has the potential to achieve 60%-65% and 70% - 80% of global FE improvement over highway and city-highway DC respectively.

Patel, Amol Arvind↗
DOE OSTI2021

Real-World Driving Features for Identifying Intelligent Driver Model Parameters

Driver behavior models play a significant role in representing different driving styles and the associated relationships with traffic patterns and vehicle energy consumption in simulation studies. The models often serve as a proxy for baseline human driving when assessing energy-saving strategies that alter vehicle velocity. Such models are especially important in connectivity-enabled energy-saving strategy research because they can easily adapt to changing driving conditions like posted speed limits or change in traffic light state. While numerous driver models exist, parametric driver models provide the flexibility required to represent variability in real-world driving through different combinations of model parameters. These model parameters must be informed by a representative set of parameter values for the driver model to adequately represent a real-world driver. It stands to reason that determining the parameter values from real-world driving data would serve the purpose of representing a real-world driver. Although the published literature is replete with techniques and consequences of using real-world driving data to determine parameter values for parametric driver models, none have explored them in the context of using shorter driving features where the parameter values may change over the course of a single trip for the same driver. In this study we consider the “intelligent driver model” (IDM) as our driver behavior model and use real-world driving data from the Transportation Secure Data Center (TSDC) maintained at the National Renewable Energy Laboratory (NREL). The TSDC includes real-world travel data from across the United States, from which NREL has created a wide range of driving routes consisting of road features such as speed limits, stop locations, and turn locations. The real-world driving data are categorized into different driving regimes and extracted into driving features. The driving features are then used to calibrate the parameter values for the IDM. The distribution of the parameters and the relationships among them are reported. The insights obtained from this study enable judicious usage of IDM or similar parametric driver models to represent baseline human driver behavior in simulations.

27 ARPA - Advanced Research Projects Agency-Energy↗
DOE OSTI2021

Real-World Driving Features for Identifying Intelligent Driver Model Parameters: Preprint

Driver behavior models play a significant role in representing different driving styles and the associated relationships with traffic patterns and vehicle energy consumption in simulation studies. The models often serve as a proxy for baseline human driving when assessing energy-saving strategies that alter vehicle velocity. Such models are especially important in connectivity-enabled energy-saving strategy research because they can easily adapt to changing driving conditions like posted speed limits or change in traffic light state. While numerous driver models exist, parametric driver models provide the flexibility required to represent variability in real-world driving through different combinations of model parameters. These model parameters must be informed by a representative set of parameter values for the driver model to adequately represent a real-world driver. It stands to reason that determining the parameter values from real-world driving data would serve the purpose of representing a real-world driver. While the published literature is replete with techniques and consequences of using real-world driving data to determine parameter values for parametric driver models, none have explored them in the context of using shorter driving features where the parameter values may change over the course of a single trip for the same driver. In this study we consider the “Intelligent Driver Model” (IDM) as the driver behavior model to explore and real-world driving data from the Transportation Secure Data Center (TSDC) maintained at the National Renewable Energy Laboratory (NREL). The TSDC includes real-world travel data from across the United States, from which NREL has created a wide range of driving routes consisting of road features such as speed limits, stop locations and turn locations. The real-world driving data are categorized into different driving regimes and extracted into driving features. The driving features are then used to calibrate the parameter values for the IDM. The distribution of the parameters and the relationships among them are reported. The insights obtained from this study enable judicious usage of IDM or similar parametric driver models to represent baseline human driver behavior in simulations.

27 ARPA - Advanced Research Projects Agency-Energy↗
DOE OSTI2025

Laser Measurements and Modeling of Shock Tunnel Freestream Velocity and Multispecies Thermal Nonequilibrium

Coherent anti-Stokes Raman scattering (CARS) and nitric oxide molecular tagging velocimetry (NO-MTV) were used to characterize the freestream in Sandia’s Hypersonic Shock Tunnel (HST) using a burst-mode laser operated at 100 kHz. Experiments were performed at nominal freestream velocities of 3 and 4 km/s using both air and N 2 test gas. The CARS diagnostic provides nonequilibrium characterization of the flow by measuring vibrational and rotational temperatures of N 2 and O 2 , which are compared to NO temperatures from separate laser absorption experiments. Simultaneous, collinear freestream velocities were measured using NO MTV along with pitot pressure measurements. Furthermore, this extensive freestream dataset is compared to nonequilibrium CFD that is capable of modeling species-specific, vibrational temperatures throughout the nozzle expansion. Significant nonequilibrium between vibrational and rotational temperatures was measured at each flow condition. N 2 exhibits the most nonequilibrium, followed by O 2 and NO. The CFD model captures this trend, although it consistently overpredicts N 2 and O 2 vibrational temperatures. At 3 km/s, the modeled NO nonequilibrium is underpredicted, whereas it is overpredicted at 4 km/s. Good agreement is seen between CFD and the velocity and rotational temperature measurements. Experiments with water added to the test gas yielded no discernable difference in vibrational relaxation.

Aerodynamics↗
DOE OSTI2024

Heterogeneous mantle effects on the behavior of SmKS waves and outermost core imaging

Seismic traveltime anomalies of waves that traverse the uppermost 100–200 km of the outer core have been interpreted as evidence of reduced seismic velocities (relative to radial reference models) just below the core–mantle boundary (CMB). These studies typically investigate differential traveltimes of SmKS waves, which propagate as P waves through the shallowest outer core and reflect from the underside of the CMB m times. The use of SmKS and S(m-1)KS differential traveltimes for core imaging are often assumed to suppress contributions from earthquake location errors and unknown and unmodelled seismic velocity heterogeneity in the mantle. The goal of this study is to understand the extent to which differential SmKS traveltimes are, in fact, affected by anomalous mantle structure, potentially including both velocity heterogeneity and anisotropy. Velocity variations affect not only a wave's traveltime, but also the path of a wave, which can be observed in deviations of the wave's incoming direction. Since radial velocity variations in the outer core will only minimally affect the wave path, in contrast to other potential effects, measuring the incoming direction of SmKS waves provides an additional diagnostic as to the origin of traveltime anomalies. Here we use arrays of seismometers to measure traveltime and direction anomalies of SmKS waves that sample the uppermost outer core. We form subarrays of EarthScope's regional Transportable Array stations, thus measuring local variations in traveltime and direction. We observe systematic lateral variations in both traveltime and incoming wave direction, which cannot be explained by changes to the radial seismic velocity profile of the outer core. Moreover, we find a correlation between incoming wave direction and traveltime anomaly, suggesting that observed traveltime anomalies may be caused, at least in part, by changes to the wave path and not solely by perturbations in outer core velocity. Modelling of 1-D ray and 3-D wave propagation in global 3-D tomographic models of mantle velocity anomalies match the trend of the observed traveltime anomalies. Overall, we demonstrate that observed SmKS traveltime anomalies may have a significant contribution from 3-D mantle structure, and not solely from outer core structure.

58 GEOSCIENCES↗
DOE OSTI2024

Heterogeneous mantle effects on the behavior of SmKS waves and outermost core imaging

Seismic traveltime anomalies of waves that traverse the uppermost 100–200 km of the outer core have been interpreted as evidence of reduced seismic velocities (relative to radial reference models) just below the core–mantle boundary (CMB). These studies typically investigate differential traveltimes of SmKS waves, which propagate as P waves through the shallowest outer core and reflect from the underside of the CMB m times. The use of SmKS and S(m- 1)KS differential traveltimes for core imaging are often assumed to suppress contributions from earthquake location errors and unknown and unmodelled seismic velocity heterogeneity in the mantle. The goal of this study is to understand the extent to which differential SmKS traveltimes are, in fact, affected by anomalous mantle structure, potentially including both velocity heterogeneity and anisotropy. Velocity variations affect not only a wave’s traveltime, but also the path of a wave, which can be observed in deviations of the wave’s incoming direction. Since radial velocity variations in the outer core will only minimally affect the wave path, in contrast to other potential effects, measuring the incoming direction of SmKS waves provides an additional diagnostic as to the origin of traveltime anomalies. Here we use arrays of seismometers to measure traveltime and direction anomalies of SmKS waves that sample the uppermost outer core. We form subarrays of EarthScope’s regional Transportable Array stations, thus measuring local variations in traveltime and direction. We observe systematic lateral variations in both traveltime and incoming wave direction, which cannot be explained by changes to the radial seismic velocity profile of the outer core. Moreover, we find a correlation between incoming wave direction and traveltime anomaly, suggesting that observed traveltime anomalies may be caused, at least in part, by changes to the wave path and not solely by perturbations in outer core velocity. Modelling of 1-D ray and 3-D wave propagation in global 3-D tomographic models of mantle velocity anomalies match the trend of the observed traveltime anomalies. Overall, we demonstrate that observed SmKS traveltime anomalies may have a significant contribution from 3-D mantle structure, and not solely from outer core structure.

58 GEOSCIENCES↗
DOE OSTI2024

Assessment of Machine Learning for Ultrasonic Nondestructive Evaluation of Alkali–Silica Reaction in Concrete

Alkali–silica reaction (ASR) is a type of material degradation in concrete structures that leads to concrete cracking and rebar corrosion, thereby reducing the material’s structural integrity and the overall structure’s lifetime and raising safety concerns. Ultrasonic nondestructive evaluation (NDE) has been proven to be a valuable technique for assessing concrete properties and monitoring ASR progression in concrete. However, the deployment and analysis of ultrasonic NDE and its data requires specialized expertise, often relying on the engineer’s subjective interpretation. With the surge in computational power, artificial intelligence (AI) and machine learning (ML) algorithms have become popular in automating NDE data analysis. Various industrial sectors are increasingly adopting ML algorithms for NDE data analysis with a growing emphasis on AI–assisted automation. Regulatory agencies are also preparing for this technological shift, anticipating corresponding revisions in standards. Thus, there is an urgent need to identify the capabilities and limitations of current ML technologies for the evaluation of concrete material properties and damage status. Furthermore, the effects of various factors on ML model performance must be thoroughly investigated. The study summarized herein evaluated the effectiveness of two ML models (i.e., support vector regression (SVR) and deep neural network (DNN)) in predicting concrete material damage induced by ASR based on the long-term ultrasonic monitoring data. Four distinct concrete specimens were cast with artificially induced ASR, and over a period exceeding 500 days, ultrasonic signals and expansion data were continuously collected. For the SVR model, wave velocity and 12 other wave features were extracted from the ultrasonic signals, with 6 out of 13 features selected as input for the model. Different combinations of training and testing datasets were designed to explore factors influencing prediction performance, including the range of data within training and testing sets, in addition to various signal preprocessing methodologies. These findings suggest the importance of using a training dataset with a broader data range compared with testing datasets for improved model performance alongside consistent signal preprocessing across datasets.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Using Maximum Circular Velocity in Halo Occupation Distribution Models to Predict Galaxy Clustering

Abstract Standard halo occupation distribution (HOD) models predict how galaxies occupy halos based on a single property, the virial mass, M vir . To incorporate galaxy assembly bias, we consider alternative halo mass proxies to use in the HOD. A promising replacement is maximum circular velocity, V max , which measures the halo’s potential well, and successfully predicts galaxy clustering in subhalo abundance matching models. We fit galaxy clustering measurements from SDSS DR7 with two modified HODs besides the standard M vir -based model: one where V max is used as the halo property that determines galaxy occupation, and the other adopting an adjustable combination of M vir and V max . Except for the reduced volume M r < − 20 threshold sample fit with V max alone, neither change improves the model performance in predicting the projected two-point correlation function, w p . We conclude that switching the primary variable to V max does not significantly improve the HOD model’s ability to fit galaxy clustering.

Mezini, Lorena↗
DOE OSTI2024

Advancing attenuation estimation through integration of the Hessian in multiparameter viscoacoustic full-waveform inversion

Accurate seismic attenuation models of subsurface structures not only enhance subsequent migration processes by improving fidelity, resolution, and facilitating amplitude-compliant angle gather generation but also provide valuable constraints on subsurface physical properties. Leveraging full-wavefield information, multiparameter viscoacoustic full-waveform inversion ( Q-FWI) simultaneously estimates seismic velocity and attenuation ( Q) models. However, a major challenge in Q-FWI is the contamination of crosstalk artifacts, where inaccuracies in the velocity model are mistakenly mapped to the inverted attenuation model. While incorporating the Hessian is expected to mitigate these artifacts, the explicit implementation is prohibitively expensive due to its formidable computational cost. In this study, we formulate and develop a Q-FWI algorithm via the Newton-conjugate gradient (CG) framework, where the search direction at each iteration is determined through an internal CG loop. In particular, the Hessian is integrated into each CG step in a matrix-free fashion using the second-order adjoint-state method. We find through synthetic experiments that our Newton-CG Q-FWI significantly mitigates crosstalk artifacts compared with the limited-memory Broyden-Fletcher-Goldfarb-Shanno method and the CG method, albeit with a notable computational cost. In the discussion of several key implementation details, we also determine the significance of the approximate Gauss-Newton Hessian, the second-order adjoint-state method, and the two-stage inversion strategy.

Geochemistry & Geophysics↗
DOE OSTI2020

Comparison of modular analytical wake models to the Lillgrund wind plant

Efficient and accurate wake models are required for wind plant performance modeling and the suite of engineering processes that support wind plant layout, control, and monitoring. Although many analytical and engineering wake models with low computational costs have been proposed, their ability to represent the power production of large wind plants in a wide range of atmospheric conditions is not completely understood. The following validation study reviews the underlying theory for analytical wake models, outlines quality control procedures for observational data, and compares model results with observational data from the Lillgrund Wind Plant. Lillgrund makes a valuable case study for wake modeling because of its regular arrangement and the relatively close spacing of constituent wind turbines, which lead to regular and significant wake interactions within the wind plant and the development of deep array flow conditions. Formulations for the velocity deficit, wake-added turbulence, and wake superposition methods are considered in a modular sense, yielding many possible configurations to represent wind turbine wakes, of which seven are examined in detail. Velocity deficit models that account for flow conditions in the near wake are better able to reproduce power production for wind turbines in the transitional region of the wind plant, where wind turbines experience as many as five wakes from upstream turbines. Finally, in the deep array, where power production reaches asymptotic values and wake statistics become quasi-periodic, wake superposition schemes become the largest driver in error reduction; using the linear or maximum wake superposition methods can reduce the relative root mean square error by as much as 40% in the deep array.

17 WIND ENERGY↗
DOE OSTI2023

Ion emission from warm dense matter produced by irradiation with a soft x-ray free-electron laser

Here we report on an experiment performed at the FLASH2 free-electron laser (FEL) aimed at producing warm dense matter via soft x-ray isochoric heating. In the experiment, we focus on study of the ions emitted during the soft x-ray ablation process using time-of-flight electron multipliers and a shifted Maxwell–Boltzmann velocity distribution model. We find that most emitted ions are thermal, but that some impurities chemisorbed on the target surface, such as protons, are accelerated by the electrostatic field created in the plasma by escaped electrons. The morphology of the complex crater structure indicates the presence of several ion groups with varying temperatures. We find that the ion sound velocity is controlled by the ion temperature and show how the ion yield depends on the FEL radiation attenuation length in different materials.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Multi-scale model based design of membrane reactor/separator processes for intensified hydrogen production through the water gas shift reaction

This paper aims to first quantify the impact of various diffusion models (Maxwell-Stefan, Wilke, Dusty-Gas) on the predictions of a multi-scale membrane reactor/separator mathematical model, and to then demonstrate this model's use for the design and process intensification of membrane reactor/separator systems for hydrogen production. This multi-scale model captures velocity, temperature and species' concentration profiles along the catalyst pellet's radial direction, and along the reactor's axial direction, by solving the momentum, energy, and species transport equations, accounting for convection, conduction, reaction, and diffusion mechanisms. In the first part of work, the effect of pellet-scale design parameters (mean pore diameter, volumetric porosity, tortuosity factor, etc.) and various species' flux models on the model predictions is studied. In the second part, the study focuses on the comparison, in terms of their process intensification characteristics, of various hydrogen production processes. These include a conventional high-temperature shift reactor (HTSR)/low-temperature shift reactor (LTSR) sequence, a novel HTSR/membrane separator (MS)/LTSR/MS sequence, and a process that involves low-temperature shift membrane reactors-LTSMR in a series.

08 HYDROGEN↗
DOE OSTI2021

Development and Evaluation of Velocity Predictive Optimal Energy Management Strategies in Intelligent and Connected Hybrid Electric Vehicles

In this study, a thorough and definitive evaluation of Predictive Optimal Energy Management Strategy (POEMS) applications in connected vehicles using 10 to 20 s predicted velocity is conducted for a Hybrid Electric Vehicle (HEV). The presented methodology includes synchronous datasets gathered in Fort Collins, Colorado using a test vehicle equipped with sensors to measure ego vehicle position and motion and that of surrounding objects as well as receive Infrastructure to Vehicle (I2V) information. These datasets are utilized to compare the effect of different signal categories on prediction fidelity for different prediction horizons within a POEMS framework. Multiple artificial intelligence (AI) and machine learning (ML) algorithms use the collected data to output future vehicle velocity prediction models. The effects of different combinations of signals and different models on prediction fidelity in various prediction windows are explored. All of these combinations are ultimately addressed where the rubber meets the road: fuel economy (FE) enabled from POEMS. FE optimization is performed using Model Predictive Control (MPC) with a Dynamic Programming (DP) optimizer. FE improvements from MPC control at various prediction time horizons are compared to that of full-cycle DP. All FE results are determined using high-fidelity simulations of an Autonomie 2010 Toyota Prius model. The full-cycle DP POEMS provides the theoretical upper limit on fuel economy (FE) improvement achievable with POEMS but is not currently practical for real-world implementation. Perfect prediction MPC (PP-MPC) represents the upper limit of FE improvement practically achievable with POEMS. Real-Prediction MPC (RP-MPC) can provide nearly equivalent FE improvement when used with high-fidelity predictions. Constant-Velocity MPC (CV-MPC) uses a constant speed prediction and serves as a “null” POEMS. Results showed that RP-MPC, enabled by high-fidelity ego future speed prediction, led to significant FE improvement over baseline nearly matching that of PP-MPC.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2020

Crustal Structure of the Mesopotamian Plain, East of Iraq

The crustal structure of Iraq was investigated through analyzing teleseismic data from 12 new seismic stations. Three seismic stations are located within the Zagros Fold-Thrust Belt, and nine are within the Mesopotamian Plain. Joint inversion of P wave receiver function and Rayleigh wave dispersion data were employed to resolve S wave velocity structure models beneath each station. Combining these models with available Moho depths within and around the study area reveals that the Moho depth is smoothly increasing from the Arabian platform toward the Zagros Mountains. Further, an exceptional deeper root is observed near the eastern edge of the Mesopotamian Plain where sedimentary pile is the thickest. This root was interpreted as a structure inherited from the successive Mesozoic rifting of the NE Arabian platform enhanced by sedimentary loading and progressive subsidence. A low-velocity uppermost mantle was observed beneath the Arabian Foredeep attesting the existence of a low-strength lithospheric mantle beneath the region southwest from the Zagros deformation front. The weak rheology of the uppermost mantle may have allowed local sinking of the crust and deepening of the Moho boundary due to vertical loading and the Late Miocene lateral contraction.

58 GEOSCIENCES↗
DOE OSTI2026

Computational Thermal Hydraulics of a High-Performance Low-Enriched-Uranium Annular Target for HFIR Irradiation

Molybdenum-99 has historically been generated via isolation from fissioned highly enriched uranium (HEU) targets. Here, this isotope is in high demand due to its daily use across the world in radiopharmaceutical medical procedures. The primary objective of this work was to design and analyze an experimental target assembly containing one low-enriched-uranium (LEU) annular target for irradiation at the High Flux Isotope Reactor (HFIR). Efforts included incorporating spatially dependent energy sources from neutron and gamma interactions, quantifying thermal contact conductance at material interfaces, performing grid-independent studies, comparing turbulence models, and simulating various steady-state and transient scenarios relevant for irradiation qualification and eventual insertion. These models provide velocity, pressure, and temperature distributions in both space and time. Such results enable the selection of an appropriate irradiation location, fission rate density, and flow-limiting orifice size and demonstrate compliance with HFIR safety requirements such that insertion into the reactor can be approved. This analysis shows that across all scenarios, wetted surface temperatures remain below the coolant saturation temperature with no net vapor formation in the coolant. In every scenario, all components stay below 30% of the aluminum 6061 melting temperature. Computational fluid dynamics and system-level models predict peak target temperatures that agree within 4%, though the predicted axial location of the peak differs by about 10% of the heated length due to differences in flow development length. These results de-risk the irradiation of LEU (annular targets) and strengthen a domestic, HEU-independent 99 Mo supply by providing important fuel performance data to form the foundation for a robust licensing basis.

Molybdenum-99↗
DOE OSTI2021

Slope-Aspect Induced Climate Differences Influence How Water Is Exchanged Between the Land and Atmosphere

Cross-slope climate differences in the midlatitudes are ecologically important, and impact vegetation-mediated water balance between the earth surface and the atmosphere. We made high-resolution in situ observations of air temperature, relative humidity, soil moisture, insolation, and sap velocity observations on 14 Pacific madrone trees (Arbutus menziesii) spanning adjacent north and south slopes at the University of California's Angelo Coast Range Reserve. To understand the cross-slope response of sap velocity, a proxy for transpiration, to microclimate, we modeled the sap velocity on each slope using a transpiration model driven by ambient environment and parameterized with a Markov Chain Monte Carlo parameter estimation process. The results show that trees on opposing slopes do not follow a shared pattern of physiological response to transpiration drivers. This means that the observed sap velocity differences are not due entirely to observed microclimate differences, but also due to population-level physiological differences, which indicates acclimation to inhabited microclimate. While our present data set and analytical tools do not identify mechanisms of acclimation, we speculate that differing proportions of sun-adapted and shade-adapted leaves, differences in stomatal regulation, and cross-slope root zone moisture differences could explain some of the observed and modeled differences.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Attached and Attaching Three-Dimensional Jets from Circular Nozzles: Analytical Model

Here we evaluate velocity profiles of three dimensional attached jets emerging from circular nozzles. 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 industrial importance of attached jets, simple, complete, and quantitative expressions for their velocity profiles remain elusive. Here we present a quantitative analytical model of the three dimensional velocity profiles of attached jets inclusive of a local skin coefficient of friction. We compare these expressions to experimental velocity profiles at moderate and high nozzle Reynolds numbers to find reasonable quantitative agreement.

Jet, attached jet, offset jet, reattaching offset ↗