SEARCH · Engineering Papers

Results for “Closure correlations”

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.

SourceResearch connectionFrom yearThrough year

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

At least 163 records · Page 9

All sources NASA NTRS DOE OSTI

DOE OSTI2024

Improving the modeling of near-wall interphase heat transfer in porous media models of Pebble Bed Reactors

Here, this work aims to improve capabilities for modeling localized effects in porous media models of Pebble Bed Reactors. The wall-channeling effect is the primary local phenomenon of interest in a PBR, where the presence of the reflector wall disrupts the pebble packing, causing the pebbles near the wall to pack less efficiently and creating large void regions. Accurate modeling of the near-wall region is important as it will affect core bypass flow and temperature predictions. Porous media models are commonly used for design scoping and plant-level simulations of PBRs. Although these models have some capabilities to model the near-wall region, the correlations that are available in porous media codes are often inaccurate when a multi-region model is used to discretize the near-wall region. This work employs a high-to-low analysis to study the accuracy of available interphase heat transfer closures. NekRS, a spectral element computational fluid dynamics code, is used to perform Large Eddy Simulations. These LES simulation results are compared to porous media model results from the Pronghorn porous media code. The friction term of the KTA drag closure is first improved, reducing the error in the prediction of the near-wall velocity from over 50% to less than 5%. This is combined with improvements to the form term from previous works to produce a drag closure that is capable of accurately modeling the wall-channeling effect across a variety of flow conditions. The Nusselt number predictions of several heat transfer correlations are compared to the high-fidelity results where it is found that the KTA heat transfer correlation is capable of accurately predicting the local Nusselt numbers that were determined in the high-fidelity simulation. Comparison of the radial solid temperature profiles, however, reveal discrepancies between NekRS and Pronghorn. It is discovered that the implementation of the interphase heat transfer coefficient that exists in many current porous media codes is not valid when local porosities are modeled. Instead, it is suggested that the interphase heat transfer coefficient should be dependent on the local porosity, the Nusselt number, and the local solid surface-to-volume ratio. Implementation of this change produces improvement in the agreement between the results obtained by NekRS and Pronghorn while using the KTA heat transfer correlation.

interphase heat transfer↗

NASA NTRS1992

Effects of constraint on crack growth under aircraft spectrum loading

The objective is to study the effects of constraint on fatigue crack growth under aircraft spectrum loading. A plasticity-induced crack-closure model that accounts for constraint variations during the transition from flat-to-slant crack growth was used to correlate crack-growth rate data under constant-amplitude loading and to calculate crack growth under simulated aircraft spectrum loading. The model was applied to several thin-sheet aluminum alloy materials. Under laboratory air conditions, the transition was shown to be related to the size of the cyclic plastic zone based on the effective stress-intensity factor range for several sheet materials and thicknesses. Results from three-dimensional, elastic-plastic, finite-element analyses of a flat, straight-through crack in a thin-sheet aluminum alloy specimen showed a constraint loss similar to that assumed in the model. Using test data and the closure model, the location of the constraint-loss regime in terms of growth rate and the value of the constraint factor at these rates were determined by trial and error. The model was then used to calculate crack growth under the TWIST spectrum. The calculated results agreed reasonably well with test data. In general, the model predicted shorter crack-growth lives than tests under the TWIST spectrum by about 40 percent. For the TWIST spectrum clipped at Level 3, the calculated lives were within about 20 percent. The results demonstrated that constraint variations, especially for thin-sheet alloys, should be accounted for to predict crack growth under typical aircraft spectra.

Newman, J. C., Jr.↗

DOE OSTI2020

Reynolds-Averaged Turbulence Modeling Using Deep Learning with Local Flow Features: An Empirical Approach

Reynolds-Averaged Navier-Stoke (RANS) models offer an alternative avenue in predicting flow characteristics when the corresponding experiments are difficult to achieve due to geometry complexity, limited budget, or knowledge. RANS models require the knowledge of subgrid scale physics to solve conservation equations for mass, energy, and momentum. Mechanistic turbulence models, such as k-epsilon, are generally evaluated and calibrated for specific flow conditions with various degrees of uncertainty. These models have limited capability to assimilate a substantial amount of data due to model form constraints. Meanwhile, deep learning (DL) has been proven to be universal approximators with the potential to assimilate available, relevant, and adequately evaluated data. Moreover, deep neural networks (DNNs) can create surrogate models without knowing function forms. Such a data-driven approach can be used in updating fluid models based on observations as opposed to hard-wiring models with precalibrated correlations. The paper presents progress in applying DNNs to model Reynolds stress using two machine learning (ML) frameworks. A novel flow feature coverage mapping is proposed to quantify the physics coverage of DL-based closures. It can be used to examine the sufficiency of training data and input flow features for data-driven turbulence models. The case of a backward-facing step is formulated to demonstrate that not only can DNNs discover underlying correlation behind fluid data but also they can be implemented in RANS to predict flow characteristics without numerical stability issues. Finally, the presented research is a crucial stepping-stone toward the data-driven turbulence modeling, which potentially benefits the design of data-driven experiments that can be used to validate fluid models with ML-based fluid closures.

42 ENGINEERING↗

NASA NTRS1991

Second-order closure models for supersonic turbulent flows

Recent work on the development of a second-order closure model for high-speed compressible flows is reviewed. This turbulent closure is based on the solution of modeled transport equations for the Favre-averaged Reynolds stress tensor and the solenoidal part of the turbulent dissipation rate. A new model for the compressible dissipation is used along with traditional gradient transport models for the Reynolds heat flux and mass flux terms. Consistent with simple asymptotic analyses, the deviatoric part of the remaining higher-order correlations in the Reynolds stress transport equations are modeled by a variable density extension of the newest incompressible models. The resulting second-order closure model is tested in a variety of compressible turbulent flows which include the decay of isotropic turbulence, homogeneous shear flow, the supersonic mixing layer, and the supersonic flat-plate turbulent boundary layer. Comparisons between the model predictions and the results of physical and numerical experiments are quite encouraging.

Speziale, Charles G.↗

NASA NTRS1991

Second-order closure models for supersonic turbulent flows

Recent work by the authors on the development of a second-order closure model for high-speed compressible flows is reviewed. This turbulence closure is based on the solution of modeled transport equations for the Favre-averaged Reynolds stress tensor and the solenoidal part of the turbulent dissipation rate. A new model for the compressible dissipation is used along with traditional gradient transport models for the Reynolds heat flux and mass flux terms. Consistent with simple asymptotic analyses, the deviatoric part of the remaining higher-order correlations in the Reynolds stress transport equation are modeled by a variable density extension of the newest incompressible models. The resulting second-order closure model is tested in a variety of compressible turbulent flows which include the decay of isotropic turbulence, homogeneous shear flow, the supersonic mixing layer, and the supersonic flat-plate turbulent boundary layer. Comparisons between the model predictions and the results of physical and numerical experiments are quite encouraging.

Speziale, Charles G.↗

DOE OSTI2014

Theory and Implementation of Nuclear Safety System Codes - Part II: System Code Closure Relations, Validation, and Limitations

This is Part II of two articles describing the details of thermal-hydraulic sys- tem codes. In this second part of the article series, the system code closure relationships (used to model thermal and mechanical non-equilibrium and the coupling of the phases) for the governing equations are discussed and evaluated. These include several thermal and hydraulic models, such as heat transfer coefficients for various flow regimes, two phase pressure correlations, two phase friction correlations, drag coefficients and interfacial models be- tween the fields. These models are often developed from experimental data. The experiment conditions should be understood to evaluate the efficacy of the closure models. Code verification and validation, including Separate Effects Tests (SETs) and Integral effects tests (IETs) is also assessed. It can be shown from the assessments that the test cases cover a significant section of the system code capabilities, but some of the more advanced reactor designs will push the limits of validation for the codes. Lastly, the limitations of the codes are discussed by considering next generation power plants, such as Small Modular Reactors (SMRs), analyz- ing not only existing nuclear power plants, but also next generation nuclear power plants. The nuclear industry is developing new, innovative reactor designs, such as Small Modular Reactors (SMRs), High-Temperature Gas-cooled Reactors (HTGRs) and others. Sub-types of these reactor designs utilize pebbles, prismatic graphite moderators, helical steam generators, in- novative fuel types, and many other design features that may not be fully analyzed by current system codes. This second part completes the series on the comparison and evaluation of the selected reactor system codes by discussing the closure relations, val- idation and limitations. These two articles indicate areas where the models can be improved to adequately address issues with new reactor design and development.

99 GENERAL AND MISCELLANEOUS↗

DOE OSTI2018

Two-point spectral model for variable-density homogeneous turbulence

We present a study of buoyancy-driven variable-density homogeneous turbulence, using a two-point spectral closure model. We compute the time-evolution of the spectral distribution in wave number $k$ of the correlation of density and specific volume $b$($k$), the velocity associated with the turbulent mass flux $a$($k$) , and the turbulent kinetic energy $E$($k$) , using a set of coupled equations. Under the modeling assumptions, each dynamical variable has two coefficients governing spectral transfer among modes. In addition, the velocity $a$($k$) has two coefficients governing the drag between the two fluids. Using a prescribed initial condition for $b$($k$) and starting from a quiescent flow, we first evaluate the relative importance of the different coefficients used to model this system and their impact on the statistical quantities. We next assess the accuracy of the model, relative to direct numerical simulation of the complete hydrodynamical equations, using $b$, $a$, and $E$ as metrics. We show that the model is able to capture the spectral distribution and global means of all three statistical quantities at both low and high Atwood number for a set of optimized coefficients. The optimization procedure also permits us to discern a minimal set of four coefficients which are sufficient to yield reasonable results while pointing to the mechanisms that dominate the mixing process in this problem.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

THM: the MOOSE thermal hydraulics module

The MOOSE Thermal Hydraulics Module (THM) is designed to facilitate the development of thermal hydraulic system models. It provides the capability to assemble networks of coupled components such as pipes, junctions, valves, turbomachinery, and heat exchangers. Its library of components supports a single-phase, compressible flow model based on a variable-area formulation of the Euler equations of gas dynamics and discretized using a finite volume scheme. THM offers a flexible system for specifying closures such as friction factors or heat transfer coefficients, allowing the user to choose from built-in correlations or define their own in the input file. A control logic system can be used to control input parameters, necessary for implementing transient scenarios and mirroring real control systems in thermal hydraulic systems. THM can be coupled with other MOOSE-based applications for multiphysics calculations. This talk will give an introduction to the capabilities of THM and provide some examples of its usage and validation.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

MOOSE Thermal-Hydraulics Module - MOOSE workshop

The MOOSE Thermal Hydraulics Module (THM) is designed to facilitate the development of thermal hydraulic system models. It provides the capability to assemble networks of coupled components such as pipes, junctions, valves, turbomachinery, and heat exchangers. Its library of components supports a single-phase, compressible flow model based on a variable-area formulation of the Euler equations of gas dynamics and discretized using a finite volume scheme. THM offers a flexible system for specifying closures such as friction factors or heat transfer coefficients, allowing the user to choose from built-in correlations or define their own in the input file. A control logic system can be used to control input parameters, necessary for implementing transient scenarios and mirroring real control systems in thermal hydraulic systems. THM can be coupled with other MOOSE-based applications for multiphysics calculations. This training will give an introduction to the capabilities of THM and provide some examples of its usage and validation.

97 - MATHEMATICS AND COMPUTING↗

DOE OSTI2016

A NEW SIMPLE DYNAMO MODEL FOR STELLAR ACTIVITY CYCLE

A new simple dynamo model for stellar activity cycle is proposed. By considering an inhomogeneous flow effect on turbulence, it is shown that turbulent cross helicity (velocity–magnetic-field correlation) enters the expression of turbulent electromotive force as the coupling coefficient for the mean absolute vorticity. This makes the present model different from the current α –Ω-type models in two main ways. First, in addition to the usual helicity ( α ) and turbulent magnetic diffusivity ( β ) effects, we consider the cross-helicity effect as a key ingredient of the dynamo process. Second, the spatiotemporal evolution of cross helicity is solved simultaneously with the mean magnetic fields. The basic scenario is as follows. In the presence of turbulent cross helicity, the toroidal field is induced by the toroidal rotation. Then, as in usual models, the α effect generates the poloidal field from the toroidal one. This induced poloidal field produces a turbulent cross helicity whose sign is opposite to the original one (negative production). With this cross helicity of the reversed sign, a reversal in field configuration starts. Eigenvalue analyses of the simplest possible model give a butterfly diagram, which confirms the above scenario and the equatorward migrations, the phase relationship between the cross helicity and magnetic fields. These results suggest that the oscillation of the turbulent cross helicity is a key for the activity cycle. The reversal of the cross helicity is not the result of the magnetic-field reversal, but the cause of the latter. This new model is expected to open up the possibility of the mean-field or turbulence closure dynamo approaches.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Space–time structure of weak magnetohydrodynamic turbulence

The two-time energy spectrum of weak magnetohydrodynamic turbulence is found by applying a wave-turbulence closure to the cumulant hierarchy constructed from the dynamical equations. Solutions are facilitated via asymptotic expansions in terms of the small parameter $\varepsilon$ , describing the ratio of time scales corresponding to Alfvénic propagation and nonlinear interactions between counter-propagating Alfvén waves. The strength of nonlinearity at a given spatial scale is further quantified by an integration over all possible delta-correlated modes compliant in a given set of three-wave interactions that are associated with energy flux through the said scale. The wave-turbulence closure for the two-time spectrum uncovers a secularity occurring on a time scale of order $\varepsilon ^{-2}$ , and the asymptotic expansion for the spectrum is reordered in a manner comparable to the one-time case. It is shown that for the regime of stationary turbulence, the two-time energy spectrum exponentially decays on a lagged time scale $(\varepsilon ^2 \gamma _k^s)^{-1}$ in proportion to the strength of the associated three-wave interactions, characterized by nonlinear decorrelation frequency $\gamma _k^s$ . The scaling of the form $k_{\perp } v_0 \chi _0$ exhibited by this frequency is reminiscent of random sweeping by the outer scale with characteristic fluctuation velocity $v_0$ that is modified due to competition with Alfvénic propagation (characterized by $\chi _0$ ) at the said scale. A brief calculation of frequency broadening of the power spectrum due to nonlinear interactions is also presented.

Physics↗

DOE OSTI2022

Development of machine learning framework for interface force closures based on bubble tracking data

Interfacial force closures in the two-fluid model play a critical role for the predictive capabilities of void fraction distribution. However, the practices of interfacial force modeling have long been challenged by the inherent physical complexity of the two-phase flows. The rapidly expanding computational capabilities in the recent years have made high-fidelity data from the interface-captured direct numerical simulation become more available, and hence potential for data-driven interfacial force modeling has prevailed. In this work, we established a data-driven modeling framework integrated to the HZDR multiphase Eulerian-Eulerian framework for computational fluid dynamics simulations. The data-driven framework is verified in a benchmark problem, where a feedforward neural network managed to capture the non-linear mapping between bubble Reynolds number and drag coefficient and reproduce the void distribution resulting from the baseline model in the test case. The second focus is on utilizing the bubble tracking data set to form a closure for the bubble drag in the turbulent bubbly flow, in which the drag coefficient is set to be correlated with the bubble Reynolds number and the Eötvös number. Pseudo-steady state filtering in the Frenet Frame was carried out to obtain the drag coefficient from the turbulent bubbly flow data. The performance of the data-driven drag model is also examined through a case study, where improvement of model’s prediction near-wall is regarded necessary. In conclusion, discussion and further plans of investigation are provided.

42 ENGINEERING↗

NASA NTRS1993

Discrete ordinates solutions of nongray radiative transfer with diffusely reflecting walls

Nongray gas radiation in a plane parallel slab bounded by gray, diffusely reflecting walls is studied using the discrete ordinates method. The spectral equation of transfer is averaged over a narrow wavenumber interval preserving the spectral correlation effect. The governing equations are derived by considering the history of multiple reflections between two reflecting wails. A closure approximation is applied so that only a finite number of reflections have to be explicitly included. The closure solutions express the physics of the problem to a very high degree and show relatively little error. Numerical solutions are obtained by applying a statistical narrow-band model for gas properties and a discrete ordinates code. The net radiative wail heat fluxes and the radiative source distributions are obtained for different temperature profiles. A zeroth-degree formulation, where no wall reflection is handled explicitly, is sufficient to predict the radiative transfer accurately for most cases considered, when compared with increasingly accurate solutions based on explicitly tracing a larger number of wail reflections without any closure approximation applied.

Menart, J. A.↗

NASA NTRS1990

Fatigue crack growth in unidirectional metal matrix composite

The weight function method was used to determine the effective stress intensity factor and the crack opening profile for a fatigue tested composite which exhibited fiber bridging. The bridging mechanism was modeled using two approaches; the crack closure approach and the shear lag approach. The numerically determined stress intensity factor values from both methods were compared and correlated with the experimentally obtained crack growth rates for SiC/Ti-15-3 (0)(sub 8) oriented composites. The near crack tip opening profile was also determined for both methods and compared with the experimentally obtained measurements.

Ghosn, Louis J.↗

NASA NTRS1990

Fatigue crack growth in unidirectional metal matrix composite

The weight function method was used to determine the effective stress intensity factor and the crack opening profile for a fatigue tested composite which exhibited fiber bridging. The bridging mechanism was modeled using two approaches; the crack closure approach and the shear lag approach. The numerically determined stress intensity factor values from both methods were compared and correlated with the experimentally obtained crack growth rates for SiC/Ti-15-3 (0) (sub 8) oriented composites. The near crack tip opening profile was also determined for both methods and compared with the experimentally obtained measurements.

Ghosn, L. J.↗

NASA NTRS2001

Modeling and Test Data Analysis of a Tank Rapid Chill and Fill System for the Advanced Shuttle Upper Stage (ASUS) Concept

The Advanced Shuttle Upper Stage (ASUS) concept addresses safety concerns associated .with cryogenic stages by launching empty, and filling on ascent. The ASUS employs a rapid chill and fill concept. A spray bar is used to completely chill the tank before fill, allowing the vent valve to be closed during the fill process. The first tests of this concept, using a flight size (not flight weight) tank. were conducted at Marshall Space Flight Center (MSFC) during the summer of 2000. The objectives of the testing were to: 1) demonstrate that a flight size tank could be filled in roughly 5 minutes to accommodate the shuttle ascent window, and 2) demonstrate a no-vent fill of the tank. A total of 12 tests were conducted. Models of the test facility fill and vent systems, as well as the tank, were constructed. The objective of achieving tank fill in 5 minutes was met during the test series. However, liquid began to accumulate in the tank before it was chilled. Since the tank was not chilled until the end of each test, vent valve closure during fill was not possible. Even though the chill and fill process did not occur as expected, reasonable model correlation with the test data was achieved.

Flachbart, Robin↗

DOE OSTI2013

Dynamic Stochastic Superresolution of sparsely observed turbulent systems

Real-time capture of the relevant features of the unresolved turbulent dynamics of complex natural systems from sparse noisy observations and imperfect models is a notoriously difficult problem. The resulting lack of observational resolution and statistical accuracy in estimating the important turbulent processes, which intermittently send significant energy to the large-scale fluctuations, hinders efficient parameterization and real-time prediction using discretized PDE models. This issue is particularly subtle and important when dealing with turbulent geophysical systems with an vast range of interacting spatio-temporal scales and rough energy spectra near the mesh scale of numerical models. Here, we introduce and study a suite of general Dynamic Stochastic Superresolution (DSS) algorithms and show that, by appropriately filtering sparse regular observations with the help of cheap stochastic exactly solvable models, one can derive stochastically ‘superresolved’ velocity fields and gain insight into the important characteristics of the unresolved dynamics, including the detection of the so-called black swans. The DSS algorithms operate in Fourier domain and exploit the fact that the coarse observation network aliases high-wavenumber information into the resolved waveband. It is shown that these cheap algorithms are robust and have significant skill on a test bed of turbulent solutions from realistic nonlinear turbulent spatially extended systems in the presence of a significant model error. In particular, the DSS algorithms are capable of successfully capturing time-localized extreme events in the unresolved modes, and they provide good and robust skill for recovery of the unresolved processes in terms of pattern correlation. Moreover, we show that DSS improves the skill for recovering the primary modes associated with the sparse observation mesh which is equally important in applications. The skill of the various DSS algorithms depends on the energy spectrum of the turbulent signal and the observation time relative to the decorrelation time of the turbulence at a given spatial scale in a fashion elucidated here. The DSS technique exploiting a simple Gaussian closure of the nonlinear stochastic forecast model emerges as the most suitable trade-off between the superresolution skill and computational complexity associated with estimating the cross-correlations between the aliasing modes of the sparsely observed turbulent signal. Such techniques offer a promising and efficient approach to constraining unresolved turbulent fluxes through stochastic superparameterization and a subsequent improvement in coarse-grained filtering and prediction of the next generation atmosphere–ocean system (AOS) models.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1992

The present state and future direction of second order closure models for compressible flows

The topics are presented in viewgraph form and include: (1) Reynolds stress closure models; (2) Favre averages and governing equations; (3) the model for the deviatoric part of the pressure-strain rate correlation; (4) the SSG pressure-strain correlation model; (5) a compressible turbulent dissipation rate model; (6) variable viscosity effects; (7) near-wall stiffness problems; (8) models of the Reynolds mass and heat flux; and (9) a numerical solution of the compressible turbulent transport equation.

Gatski, Thomas B.↗