Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “convergence rate”

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 739 records · Page 41
All sourcesNASA NTRSDOE OSTI
NASA NTRS2000

Rainfall Morphology in Semi-Tropical Convergence Zones

Central Florida is the ideal test laboratory for studying convergence zone-induced convection. The region regularly experiences sea breeze fronts and rainfall-induced outflow boundaries. The focus of this study is the common yet poorly-studied convergence zone established by the interaction of the sea breeze front and an outflow boundary. Previous studies have investigated mechanisms primarily affecting storm initiation by such convergence zones. Few have focused on rainfall morphology yet these storms contribute a significant amount precipitation to the annual rainfall budget. Low-level convergence and mid-tropospheric moisture have both been shown to correlate with rainfall amounts in Florida. Using 2D and 3D numerical simulations, the roles of low-level convergence and mid-tropospheric moisture in rainfall evolution are examined. The results indicate that time-averaged, vertical moisture flux (VMF) at the sea breeze front/outflow convergence zone is directly and linearly proportional to initial condensation rates. This proportionality establishes a similar relationship between VMF and initial rainfall. Vertical moisture flux, which encompasses depth and magnitude of convergence, is better correlated to initial rainfall production than surface moisture convergence. This extends early observational studies which linked rainfall in Florida to surface moisture convergence. The amount and distribution of mid-tropospheric moisture determines how rainfall associated with secondary cells develop. Rainfall amount and efficiency varied significantly over an observable range of relative humidities in the 850- 500 mb layer even though rainfall evolution was similar during the initial or "first-cell" period. Rainfall variability was attributed to drier mid-tropospheric environments inhibiting secondary cell development through entrainment effects. Observationally, 850-500 mb moisture structure exhibits wider variability than lower level moisture, which is virtually always present in Florida. A likely consequence of the variability in 850-500 moisture is a stronger statistical correlation to rainfall, which observational studies have noted. The study indicates that vertical moisture flux forcing at convergence zones is critical in determining rainfall in the initial stage of development but plays a decreasing role in rainfall evolution as the system matures. The mid-tropospheric moisture (e.g. environment) plays an increasing role in rainfall evolution as the system matures. This suggests the need to improve measurements of magnitude/depth of convergence and mid-tropospheric moisture distribution. It also highlights the need for better parameterization of entrainment and vertical moisture distribution in larger-scale models.

Shepherd, J. Marshall↗
DOE OSTI2022

Scalable single-mode surface-emitting laser via open-Dirac singularities

Single-aperture cavities are a key component of lasers that are instrumental for the amplification and emission of a single light mode. However, the appearance of high-order transverse modes as the size of the cavities increases has frustrated efforts to scale-up cavities while preserving single-mode operation since the invention of the laser six decades ago. A suitable physical mechanism that allows single-mode lasing irrespective of the cavity size-a 'scale invariant' cavity or laser-has not been identified yet. Here we propose and demonstrate experimentally that open-Dirac electromagnetic cavities with linear dispersion-which in our devices are realized by a truncated photonic crystal arranged in a hexagonal pattern-exhibit unconventional scaling of losses in reciprocal space, leading to single-mode lasing that is maintained as the cavity is scaled up in size. The physical origin of this phenomenon lies in the convergence of the complex part of the free spectral range in open-Dirac cavities towards a constant governed by the loss rates of distinct Bloch bands, whereas for common cavities it converges to zero as the size grows, leading to inevitable multimode emission. An unconventional flat-envelope fundamental mode locks all unit cells in the cavity in phase, leading to single-mode lasing. We name such sources Berkeley surface-emitting lasers (BerkSELs) and demonstrate that their far-field corresponds to a topological singularity of charge two, in agreement with our theory. Open-Dirac cavities unlock avenues for light-matter interaction and cavity quantum electrodynamics.

42 ENGINEERING↗
DOE OSTI2024

Stress-hybrid virtual element method on six-noded triangular meshes for compressible and nearly-incompressible linear elasticity

In this paper, we present a first-order Stress-Hybrid Virtual Element Method (SH-VEM) on six-noded triangular meshes for linear plane elasticity. Here, we adopt the Hellinger–Reissner variational principle to construct a weak equilibrium condition and a stress based projection operator. In each element, the stress projection operator is expressed in terms of the nodal displacements, which leads to a displacement based formulation. This stress-hybrid approach assumes a globally continuous displacement field while the stress field is discontinuous across each element. The stress field is initially represented by divergence-free tensor polynomials based on Airy stress functions, but we also present a formulation that uses a penalty term to enforce the element equilibrium conditions, referred to as the Penalty Stress-Hybrid Virtual Element Method (PSH-VEM). Numerical results are presented for PSH-VEM and SH-VEM, and we compare their convergence to the composite triangle FEM and B-bar VEM on benchmark problems in linear elasticity. The SH-VEM converges optimally in the L 2 norm of the displacement, energy seminorm, and the L 2 norm of hydrostatic stress. Furthermore, the results reveal that PSH-VEM converges in most cases at a faster rate than the expected optimal rate, but it requires the selection of a suitably chosen penalty parameter.

42 ENGINEERING↗
DOE OSTI2025

Computational Fluid Dynamics-Based Modeling of Methane Flows Around Oil and Gas Equipment

Recent studies estimate that emissions from oil and gas production facilities contribute between 20 and 50% of the total methane ( CH 4 ) emitted in the US; therefore, quantifying and reducing these emissions are crucial for achieving climate goals. Methane quantification depends on both measuring methane concentrations and converting them to emissions through a modeling framework. Currently, simple atmospheric dispersion models are primarily used to quantify emissions and concentrations, but these estimates are highly uncertain when quantifying emissions from complex aerodynamic sources, such as oil and gas facilities. This investigation used a CFD modeling approach, which can account for aerodynamic complexity but has hitherto not been used to model methane concentrations downwind of a methane release of a known rate, and compared it against in situ measurements. High-time-resolution (1 Hz) methane concentration and meteorological data were measured during experiments conducted at the METEC on 21 March and 11 July 2024. The METEC site configuration, measured wind data, and controlled emission rates were used as input for the CONVERGE CFD model to model downwind CH 4 concentration. The modeling was carried out between 20 and 70 m, from two different points of release in two separate controlled-release experiments, one from a separator and another from a wellhead. In these experiments, we found that the CFD model could predict the CH 4 concentrations downwind of the release to a good degree. The model was evaluated on multiple metrics to assess its performance in estimating methane concentrations at typical fence line distances (∼30 m). These results help us to understand external flows and the ability of CFD models to predict downwind concentrations in aerodynamically complex environments.

03 NATURAL GAS↗
NASA NTRS1992

Gravity and the geoid in the Nepal Himalaya

Materials within the Himalaya are rising due to convergence between India and Asia. If the rate of erosion is comparable to the rate of uplift, the mean surface elevation will remain constant. Any slight imbalance in these two processes will lead to growth or attrition of the Himalaya. Although buried rocks, minerals and surface control points in the Himalaya are undoubtably rising, the growth or collapse or the Himalaya depends on the erosion rate which is invisible to geodetic measurements. A way to measure erosion rate is to measure the rate of change of gravity in a region of uplift. Essentially gravity should change precisely in accord with a change in elevation of the point in a free air gradient if erosion equals uplift rate. A measurement of absolute gravity was made simultaneously with measurements of GPS height within the Himalaya. Absolute gravity is estimated from the change in velocity per unit distance of a falling corner cube in a vacuum. Time is measured with an atomic clock and the unit distance corresponds to the wavelength of an iodine stabilized laser. An experiment undertaken in the Himalaya in 1991 provide a site description also with a instrument description.

Bilham, Roger↗
NASA NTRS1992

Gravity and the geoid in the Nepal Himalaya

Materials within the Himalaya are rising due to convergence between India and Asia. If the rate of erosion is comparable to the rate of uplift the mean surface elevation will remain constant. Any slight imbalance in these two processes will lead to growth or attrition of the Himalaya. The process of uplift of materials within the Himalaya coupled with surface erosion is similar to the advance of a glacier into a region of melting. If the melting rate exceeds the rate of downhill motion of the glacier then the terminus of the glacier will receed up-valley despite the downhill motion of the bulk of the glacier. Thus although buried rocks, minerals and surface control points in the Himalaya are undoubtably rising, the growth or collapse of the Himalaya depends on the erosion rate which is invisible to geodetic measurements. Erosion rates are currently estimated from suspended sediment loads in rivers in the Himalaya. These typically underestimate the real erosion rate since bed-load is not measured during times of heavy flood, and it is difficult to integrate widely varying suspended load measurements over many years. An alternative way to measure erosion rate is to measure the rate of change of gravity in a region of uplift. If a control point moves vertically it should be accompanied by a reduction in gravity as the point moves away from the Earth's center of mass. There is a difference in the change of gravity between uplift with and without erosion corresponding to the difference between the free-air gradient and the gradient in the acceleration due to gravity caused by a corresponding thickness of rock. Essentially gravity should change precisely in accord with a change in elevation of the point in a free-air gradient if erosion equals uplift rate. We were funded by NASA to undertake a measurement of absolute gravity simultaneously with measurements of GPS height within the Himalaya. Since both absolute gravity and time are known in an absolute sense to 1 part in 10(exp 10) it is possible to estimate gravity with a precision of 0.1 mu gal. Known systematic errors reduce the measurement to an absolute uncertainty of 6 mu gal. The free air gradient at the point of measurement is typically about 3 mu gals/cm. At Simikot where our experiment was conducted we determined a vertical gravity gradient of 4.4 mu gals/cm.

Bilham, Roger↗
NASA NTRS1978

Release of dissolved nitrogen from water during depressurization

Experiments were run to study depressurization of water containing various concentrations of dissolved nitrogen gas, the primary case being room temperature water saturated with nitrogen at 4 MPa. In a static depressurization experiment, water with very high nitrogen content was depressurized at rates from 0.09 to 0.50 MPa per second and photographed with high speed movies. The pictures showed that the bubble population at a given pressure increased strongly with decreasing depressurization rate. Flow experiments were performed in an axisymmetric converging-diverging nozzle and in a two-dimensional converging nozzle with glass sidewalls. Depressurization gradients were roughly 500 to 1200 MPa per second. Both nozzles exhibited choked flow behavior even at nitrogen concentration levels as low as 4 percent of saturated. The flow rates were independent of concentration level and could be computed as incompressible water flow based on the difference between stagnation and throat pressures; however, the throat pressures were significantly different between the two nozzles.

Simoneau, R. J.↗
NASA NTRS1956

The Compressible Laminar Boundary Layer with Heat Transfer and Arbitrary Pressure Gradient

An approximate method for the calculation of the compressible laminar boundary layer with heat transfer and arbitrary pressure gradient, based on Thwaites' correlation concept, is presented. With the definition of dimensionless shear and heat-transfer parameters and an assumed correlation of these parameters in terms of a momentum parameter, a complete system of relations for calculating skin friction and heat transfer results. Knowledge of velocity or temperature profiles is not necessary in using this calculation method. When the method is applied to a convergent-divergent, axially symmetric rocket nozzle, it shows that high rates of heat transfer are obtained at the initial stagnation point and at the throat of the nozzle. Also indicated are negative displacement thicknesses in the convergent portion of the nozzle; these occur because of the high density within the lower portions of the cooled boundary layer. (author)

Cohen, Clarence B↗
NASA NTRS1979

Phase change in liquid face seals. II - Isothermal and adiabatic bounds with real fluids

Analytical studies of phase change effects in parallel and tapered liquid face seals are presented. An isothermal and adiabatic model of low Reynolds number flow are considered by numerical integration of the descriptive equations for a real fluid, and its thermodynamic properties are calculated for each step, using a computer program for the steam tables or fluid thermodynamic properties. It was shown that for low leakage rate the isothermal model is more accurate and for high leakage rates the adiabatic model is more accurate; that both models yield the same conclusions regarding stability; and that the transient of collapse is described by the adiabatic model which predicts a catastrophic collapse and then either failure or explosive return to a larger film thickness value. Finally, it is shown that converging seals may become unstable and the mass leakage rate is reduced significantly below the all liquid value when boiling occurs.

Hughes, W. F.↗
DOE OSTI2023

Impacts of Permeability Heterogeneity and Background Flow on Supercritical CO 2 Dissolution in the Deep Subsurface

Motivated by CO 2 capture and sequestration (CCS) design considerations, we consider the coupled effects of permeability heterogeneity and background flow on the dissolution of a supercritical CO 2 lens into an underlying deep, confined aquifer. We present the results of a large-scale Monte Carlo simulation study examining the interaction of background flow rate and three parameters describing multi-Gaussian log-permeability fields: mean, variance, and correlation length. Hundreds of high-resolution simulations were performed using the PFLOTRAN finite volume software to model CO 2 dissolution in a kilometer-scale aquifer over 1,000 years. Predictive dimensionless scaling relationships relating CO 2 dissolution rate to heterogeneity statistics, Rayleigh (Ra) and Péclet (Pe) numbers were developed for both gravitationally dominated free convection to background flow-dominated forced convection regimes. An empirical criterion, Pe = Ra 3/4 , was discovered for regime transition. All simulations converged quickly to a quasi-steady, approximately linear dissolution rate. However, this rate displayed profound variability between permeability field realizations sharing the same heterogeneity statistics, even under mild permeability heterogeneity. In general, increased heterogeneity was associated with a lower mean and higher variance of dissolution rate, undesirable from a CCS design perspective. The relationship between dissolution rate and background flow was found to be complex and nonlinear. Dimensionless scaling relationships were uncovered for a number of special cases. Results call into question the validity of the Boussinesq approximation in the context of modest-to-high background flow rates and the general applicability of numerical simulations without background flow.

42 ENGINEERING↗
NASA NTRS1993

The characteristics of sprays produced by coaxial airblast atomisers

Measurements of droplet size, velocity, liquid flux and concentration were made in sprays produced by a coaxial airblast atomizer using a phase Doppler anemometer. The atomizer comprised a liquid jet with exit diameter varied between 1.1 and 2.3 mm positioned in the center of a gaseous annular stream. The characteristics of the preburner sprays of the main engine of the space shuttle were simulated by using water and air respectively replacing liquid oxygen and hydrogen. Reduction of the diameter of the liquid tube was found to improve the atomization and reduce the rate of spread of sprays with similar gas-to-liquid velocity ratio. The presence of a converging nozzle at the exit of the gaseous jet improved the atomization and increased the rate of spread of sprays with gas-to-liquid velocity ratio up to around 45, but had no effect for higher velocity ratios.

Hardalupas, Y.↗
DOE OSTI2025

Convergence analysis for a nonlocal gradient descent method via directional Gaussian smoothing

We analyze the convergence of a nonlocal gradient descent method for minimizing a class of high-dimensional non-convex functions, where a directional Gaussian smoothing (DGS) is proposed to define the nonlocal gradient (also referred to as the DGS gradient). The method was first proposed in [Zhang et al., Enabling long-range exploration in minimization of multimodal functions, UAI 2021], in which multiple numerical experiments showed that replacing the traditional local gradient with the DGS gradient can help the optimizers escape local minima more easily and significantly improve their performance. However, a rigorous theory for the efficiency of the method on nonconvex landscape is lacking. In this work, we investigate the scenario where the objective function is composed of a convex function, perturbed by deterministic oscillating noise. We provide a convergence theory under which the iterates exponentially converge to a tightened neighborhood of the solution, whose size is characterized by the noise wavelength. Here, we also establish a correlation between the optimal values of the Gaussian smoothing radius and the noise wavelength, thus justifying the advantage of using moderate or large smoothing radii with the method. Furthermore, if the noise level decays to zero when approaching the global minimum, we prove that DGS-based optimization converges to the exact global minimum with linear rates, similarly to standard gradient-based methods in optimizing convex functions. Several numerical experiments are provided to confirm our theory and illustrate the superiority of the approach over those based on the local gradient.

Tran, Hoang [Oak Ridge National Laboratory (ORNL),↗
DOE OSTI2020

Construction of a Code Verification Matrix for Heat Conduction With Finite Element Code Applications

When establishing the pedigree of a simulation tool, code verification is used to ensure that the implemented numerical algorithm is a faithful representation of its underlying mathematical model. During this process, numerical results on various meshes are systematically compared to a reference analytic solution. The selection of analytic solutions can be a laborious process, as it is difficult to establish adequate code confidence without performing redundant work. In this report we address this issue by applying a physics-based process that establishes a set of reference problems. In this process, code simulation options are categorized and systematically tested, which ensures that gaps in testing are easily identified and addressed. The resulting problems are primarily intended for code verification analysis but may also be useful for comparison to other simulation codes, troubleshooting activities, or training exercises. The process is used to select fifteen code verification problems relevant for the one-dimensional steady-state heat conduction equation. These problems are applicable to a wide variety of simulation tools, but, in this work, a demonstration is performed using the finite element-based nuclear fuel performance code BISON. Convergence to the analytic solution at the theoretical rate is quantified for a selection of the problems, which establishes a baseline pedigree for the code. Not only can this standard set of conduction solutions be used for verification of other codes, but also the physics-based process for selecting problems can be utilized to quantify and expand testing for any simulation tool.

42 ENGINEERING↗
DOE OSTI2024

Algorithm 1049: The Delaunay Density Diagnostic

Accurate approximation of a real-valued function depends on two aspects of the available data: the density of inputs within the domain of interest and the variation of the outputs over that domain. There are few methods for assessing whether the density of inputs is sufficient to identify the relevant variations in outputs—i.e., the “geometric scale” of the function—despite the fact that sampling density is closely tied to the success or failure of an approximation method. In this article, we introduce a general purpose, computational approach to detecting the geometric scale of real-valued functions over a fixed domain using a deterministic interpolation technique from computational geometry. The algorithm is intended to work on scalar data in moderate dimensions (2–10). Our algorithm is based on the observation that a sequence of piecewise linear interpolants will converge to a continuous function at a quadratic rate (in L 2 norm) if and only if the data are sampled densely enough to distinguish the feature from noise (assuming sufficiently regular sampling). We present numerical experiments demonstrating how our method can identify feature scale, estimate uncertainty in feature scale, and assess the sampling density for fixed (i.e., static) datasets of input–output pairs. Finally, we include analytical results in support of our numerical findings and have released lightweight code that can be adapted for use in a variety of data science settings.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1982

Statistics of cold cumulonimbus anvils based on enhanced infrared photographs

Infrared photographs from the Atlantic Geosynchronous Satellite, enhanced to resolve cold anvil temperatures of tropical clouds, are analyzed statistically to determine their spatial-temporal variability during the NASA-U2 Flight Experiment of 1980. Diurnal dependence varies regionally, indicating topographic control via low level convergence and release of convective instability. Anvil growth rates, area covered and duration are discussed for individual and merging anvil systems. Gradients of anvil temperatures implied by infrared photographs are shown to be caused, in part, by radial decrease in anvil depth, i.e., to emissivities less than 1. An error in cloud top temperature of 10C is caused by 10% reduction in emissivity. Errors are near zero in dense, actively growing portions of the anvil.

Danielsen, E. F.↗
NASA NTRS1987

Performance improvement of robots using a learning control scheme

Many applications of robots require that the same task be repeated a number of times. In such applications, the errors associated with one cycle are also repeated every cycle of the operation. An off-line learning control scheme is used here to modify the command function which would result in smaller errors in the next operation. The learning scheme is based on a knowledge of the errors and error rates associated with each cycle. Necessary conditions for the iterative scheme to converge to zero errors are derived analytically considering a second order servosystem model. Computer simulations show that the errors are reduced at a faster rate if the error rate is included in the iteration scheme. The results also indicate that the scheme may increase the magnitude of errors if the rate information is not included in the iteration scheme. Modification of the command input using a phase and gain adjustment is also proposed to reduce the errors with one attempt. The scheme is then applied to a computer model of a robot system similar to PUMA 560. Improved performance of the robot is shown by considering various cases of trajectory tracing. The scheme can be successfully used to improve the performance of actual robots within the limitations of the repeatability and noise characteristics of the robot.

Krishna, Ramuhalli↗
NASA NTRS1991

Modern CFD applications for the design of a reacting shear layer facility

The RPLUS2D code, capable of calculating high speed reacting flows, was adopted to design a compressible shear layer facility. In order to create reacting shear layers at high convective Mach numbers, hot air streams at supersonic speeds, rendered by converging-diverging nozzles, must be provided. A finite rate chemistry model is used to simulate the nozzle flows. Results are compared with one-dimensional solutions at chemical equilibrium. Additionally, a two equation turbulence model with compressibility effects was successfully incorporated with the RPLUS code. The model was applied to simulate a supersonic shear layer. Preliminary results show favorable comparisons with the experimental data.

Yu, S. T.↗
NASA NTRS1991

Modern CFD applications for the design of a reacting shear layer facility

The RPLUS2D code, capable of calculating high speed reacting flows, has been adopted to design a compressible shear layer facility. In order to create reacting shear layers at high convective Mach numbers, hot air streams at supersonic speeds, render by converging-diverging nozzles, must be provided. A finite rate chemistry model is used to simulate the nozzle flows. Results are compared with one-dimensional, chemically equilibrium solutions. Additionally, a two equation turbulence model with compressibility effects has been successfully incorporated with the RPLUS code. The model has been applied to simulate a supersonic shear layer. Preliminary results show favorable comparisons with the experimental data.

Yu, S. T.↗