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DOE OSTI2020

Simulated Precipitation Diurnal Variation With a Deep Convective Closure Subject to Shallow Convection in Community Atmosphere Model Version 5 Coupled With CLUBB

In order to improve the physical consistency between shallow and deep convection, we modify the deep convective closure in the Community Atmosphere Model version 5 (CAM5) coupled with a third-order turbulence closure parameterization (i.e., Cloud Layers Unified by Binormals; CLUBB). The revised closure reserves a portion of the total convective available potential energy for shallow convection via utilizing the heating and moistening profiles from CLUBB to distribute moisture and energy between shallow and deep convection. Simulations at two resolutions (i.e. 2° and 0.5°, respectively) are conducted to investigate the impacts of convective closure on the simulated precipitation diurnal variations. Results from low-resolution simulations show that the revised closure suppresses deep convection until the lower troposphere is sufficiently moistened by shallow convection, which improves the precipitation diurnal variation simulations compared to the default closure, with the precipitation diurnal peak over tropical lands delayed from 12LST to 19LST. The revised closure better simulates the diurnal variations for precipitation over the Asian monsoon region, such as the delayed precipitation onset, but still fails to well capture the nighttime peak for precipitation there. This deficiency is alleviated to some extent when applying the revised closure in highresolution simulations, but nighttime precipitation is still underestimated probably because key processes responsible for nighttime convection are missing. Altogether, our results indicate that establishing the consistency between shallow and deep convection is critical for the precipitation diurnal cycle simulations.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Variational multiscale reinforcement learning for discovering reduced order closure models of nonlinear spatiotemporal transport systems

Abstract A central challenge in the computational modeling and simulation of a multitude of science applications is to achieve robust and accurate closures for their coarse-grained representations due to underlying highly nonlinear multiscale interactions. These closure models are common in many nonlinear spatiotemporal systems to account for losses due to reduced order representations, including many transport phenomena in fluids. Previous data-driven closure modeling efforts have mostly focused on supervised learning approaches using high fidelity simulation data. On the other hand, reinforcement learning (RL) is a powerful yet relatively uncharted method in spatiotemporally extended systems. In this study, we put forth a modular dynamic closure modeling and discovery framework to stabilize the Galerkin projection based reduced order models that may arise in many nonlinear spatiotemporal dynamical systems with quadratic nonlinearity. However, a key element in creating a robust RL agent is to introduce a feasible reward function, which can be constituted of any difference metrics between the RL model and high fidelity simulation data. First, we introduce a multi-modal RL to discover mode-dependant closure policies that utilize the high fidelity data in rewarding our RL agent. We then formulate a variational multiscale RL (VMRL) approach to discover closure models without requiring access to the high fidelity data in designing the reward function. Specifically, our chief innovation is to leverage variational multiscale formalism to quantify the difference between modal interactions in Galerkin systems. Our results in simulating the viscous Burgers equation indicate that the proposed VMRL method leads to robust and accurate closure parameterizations, and it may potentially be used to discover scale-aware closure models for complex dynamical systems.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Deep learning surrogate model for kinetic Landau-fluid closure with collision

In this work, the kinetic Landau-fluid (LF) closure with collision and periodic boundary condition is used in the development of the deep learning (DL) surrogate model. A classical neural network, namely, feedforward neural network or sometimes termed multilayer perceptron, is constructed and trained to learn the kinetic LF closure in the static limit and arbitrary mean free path in configuration space. The preliminary relation between best hyperparameters and critical parameters for data generation is found. Compared with the numerical approach (non-Fourier method) of the LF closure, the deep learning surrogate model shows an order of magnitude of improvement in terms of accuracy. Perhaps most importantly, the surrogate model closure has been integrated for the first time with fluid simulations. Our DL-enabled fluid simulations, for the first time, give the correct Landau damping rate for a wide range of wave vectors, while the Hammett–Perkins closure cannot produce the correct damping rate. We correctly connect the collisionless Hammett–Perkins closure and collisional Braginskii closure to reproduce the intrinsic nonlocal feature of the heat flux with DL techniques. We address the most concerning error accumulation problem and find that simulations with the deep learning surrogate model are as good as, if not better than, simulations with the analytic closure in terms of long-term numerical stability in the linear Landau damping test.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Evaluation of thermodynamic closure models for partially reacted two-phase mixture of condensed phase explosives

One of the key fundamental issues that is crucial in the continuum modeling of reactive flow phenomena is the thermodynamically consistent description of reaction mixture properties. To define the mixture properties, thermodynamic closure rules that relate the properties of the individual reaction components to the mixture properties are required. In the context of reactive two-phase modeling approaches, various strategies to define the thermodynamic closures have been adopted such as pressure temperature (PT) equilibrium between the individual reaction components, pressure (specific) volume (PV) equilibrium, etc. The choice of closure rules determines the relative distribution of specific volume and energy across the reaction components that comprise the mixture. Therefore, depending on the choice of the closure, the mixture thermodynamic behavior can vary. The present work examines the effect of different closure approaches on the thermodynamic properties of the reaction mixture. The analysis is performed for a condensed phase HMX (octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine) based plastic bonded explosive (PBX) 9501 explosive using four different thermodynamic closures, viz., PT equilibrium, PV equilibrium, volume temperature (VT) equilibrium, and pressure (P) equilibrium with reactants on an isentrope. Furthermore, the relative variations in the thermodynamic properties of the mixture are analyzed and compared under both compression and expansion loading regimes. It is shown that out of the four closure models, only PT equilibrium and P equilibrium closures lead to a thermodynamically accurate description of the mixture under both compression and expansion.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2017

Uncertainty Quantification of Multi-Phase Closures

In the ensemble-averaged dispersed phase formulation used for CFD of multiphase ows in nuclear reactor thermohydraulics, closures of interphase transfer of mass, momentum, and energy constitute, by far, the biggest source of error and uncertainty. Reliable estimators of this source of error and uncertainty are currently non-existent. Here, we report on how modern Validation and Uncertainty Quanti cation (VUQ) techniques can be leveraged to not only quantify such errors and uncertainties, but also to uncover (unintended) interactions between closures of di erent phenomena. As such this approach serves as a valuable aide in the research and development of multiphase closures. The joint modeling of lift, drag, wall lubrication, and turbulent dispersion|forces that lead to tranfer of momentum between the liquid and gas phases|is examined in the frame- work of validation of the adiabatic but turbulent experiments of Liu and Banko , 1993. An extensive calibration study is undertaken with a popular combination of closure relations and the popular k-ϵ turbulence model in a Bayesian framework. When a wide range of super cial liquid and gas velocities and void fractions is considered, it is found that this set of closures can be validated against the experimental data only by allowing large variations in the coe cients associated with the closures. We argue that such an extent of variation is a measure of uncertainty induced by the chosen set of closures. We also nd that while mean uid velocity and void fraction pro les are properly t, uctuating uid velocity may or may not be properly t. This aspect needs to be investigated further. The popular set of closures considered contains ad-hoc components and are undesirable from a predictive modeling point of view. Consequently, we next consider improvements that are being developed by the MIT group under CASL and which remove the ad-hoc elements. We use non-intrusive methodologies for sensitivity analysis and calibration (using Dakota) to study sensitivities of the CFD representation (STARCCM+) of uid velocity pro les and void fraction pro les in the context of Shaver and Podowski, 2015 correction to lift, and the Lubchenko et al., 2017 formulation of wall lubrication.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

A status review on DNB prediction using CASL baseline boiling model and possible suggestions regarding wall boiling closures

The main goal of FY18 THM’s focus task is to evaluate where the current CASL boiling model stands for DNB predictive performance, to identify which components should be improved or calibrated to enhance DNB performance. Over the past three year’s validation tests, Gen1A boiling model has presented an under-predictive behavior for DNB at the high pressure of interest for PWR application. With this in mind, this year’s task is to focus on 1) best practice guidelines on DNB detection criteria, 2) interfacial momentum transfer closure tests, and 3) wall boiling closure sensitivity on DNB. Best practice guidelines on DNB detection criteria are demonstrated by the following three monitoring variables: 1) max wall temperature, 2) K-value and 3) energy balance. Interfacial momentum transfer closure govern the bubble distribution, especially in lateral direction, as well as bubble mean diameter. A clear correlation between interfacial momentum closure and DNB prediction is not observed in the current tests. However, void distributions are changed with different interfacial momentum closure tests which requires further validation with corresponding experimental measurement. From a variety of wall boiling closure tests, bubble departure diameter seems the most sensitive for DNB performance while fulfilling numerical robustness in DNB simulation. Tolubinski’s bubble departure diameter model was calibrated to see if any improvement is observed in DNB performance. Notable DNB improvement was observed as the bubble departure diameter is reduced. However, reduced bubble departure diameter by calibrated Tolubinski’s model seemed to lead to relatively high wall superheat temperature prediction which requires further validation with associated experimental measurement It should be noted that lack of experimental measurement close to DNB condition hampers this boiling closure sensitivity study significantly. This situation directly reflects some of limitations of the CASL boiling model development. With this in mind, the implementation of improved boiling closure on 5x5 NMVG and MVG tests will be pursued in FY19, the associated DNB best practice guidelines and possible limitations will be addressed for industry DNB application.

42 ENGINEERING↗

DOE OSTI2022

Post-closure Nuclear Criticality Safety Evaluations for Disposition of Criticality Control Overpacks at the Waste Isolation Pilot Plant

The Waste Isolation Pilot Plant (WIPP) is a geological repository in southern New Mexico that provides for disposal of transuranic (TRU) wastes from atomic energy defense activities. The Sandia National Laboratories (Sandia) Report, Consideration of Nuclear Criticality When Disposing of Transuranic Waste at the Waste Isolation Pilot Plant, addresses nuclear criticality safety based on the projected inventory characteristics for the initial compliance certification application of WIPP in 1996. As the inventory, waste forms, and disposal package designs change, revised or new analyses are necessary to demonstrate acceptability for these configurations within the WIPP safety basis and compliance with 10,000-year post-closure standards of the US Environmental Protection Agency (EPA). Saylor and Scaglione evaluated criticality control overpacks (CCOs) in 2017 based on conservative assumptions for post-closure repository structural conditions with resulting effects on containers and container spacing, The Saylor and Scaglione evaluation of CCOs addressed a single waste configuration that represents the Surplus Plutonium Disposition Program’s dilute and dispose waste form and composition. This initial CCO study demonstrated that 50 grams of boron carbide (B 4 C) per CCO is sufficient to ensure post-closure criticality safety based on a well-mixed waste composition, and Oak Ridge National Laboratory (ORNL) subsequently determined that this amount of B 4 C does not require constraints on moisture or plastic present as moderator. The Saylor and Scaglione analysis conservatively assumes repository room closure that eliminates all space between fissile gram equivalent (FGE) 239 Pu masses. The close-packed array was selected based on limited availability of repository salt creep modeling results at that time. In 2019, Brickner provided additional evaluations for pipe overpack containers (POCs), building on the conservative basis provided by Saylor and Scaglione. Brickner’s 2019 analysis made use of new geomechanical data for post-closure spacing that rely on advances in repository modeling as documented in the work by Reedlunn and Bean. This current CCO evaluation for generic waste materials expands on earlier work performed at ORNL and includes evaluation of CCOs across a much broader range of possible waste compositions and geometries. This evaluation is intended to provide input for the required feature, event and process (FEP) screening to determine if post-closure criticality must be included as an event in the 10,000-year regulatory evaluation. As such, the approach to modeling post-closure criticality presented in this report has been coordinated with the Sandia team responsible for FEP screening. The resulting analysis supports disposition of fissile materials in the CCO containing up to 380 FGE 239 Pu and expands conditions acceptable for disposal of fissile material in CCOs. This evaluation builds on the methodology of Saylor and Scaglione and Brickner, using the most recently available geomechanical data for CCO spacing under salt creep compaction scenarios provided by Reedlunn and Bean. The broad range of fissile material configurations analyzed in this report are intended to account for configurations that may occur during the post-closure disposal time period, and it also includes waste configurations that are not physically possible to support analysis of conditions that influence neutron fluence.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2022

Small field campaign: aerosol – ice formation closure pilot study. Final Report

Prediction of atmospheric ice formation from aerosol particles by heterogeneous nucleation represents one of the grand challenges in atmospheric science. Our insufficient predictive understanding of primary ice formation is the reason that climate models typically do not include heterogeneous ice nucleation with subsequent effects on climate uncertainty. Mixed-phase clouds, where supercooled water droplets and ice crystals coexist play globally an important role regulating climate. This is especially the case for the Arctic region that experiences the greatest warming due to climate change compared to other regions in the world. Immersion freezing initiated by ice-nucleating particles (INPs) in supercooled water droplets is recognized as the dominant primary ice formation pathway in mixed-phase cloud regimes. For this reason, it is crucial to evaluate our capability to predict immersion freezing for a given ambient aerosol population. The goal of this project is conducting a field-based pilot study at the U.S. DOE Atmospheric Radiation Measurement (ARM) user facility at Southern Great Plains (SGP) to evaluate our capability to predict the number concentration of aerosol particles that serve as INPs in the immersion freezing mode. Successful prediction of INP number concentrations is also termed “closure”. This field-observational approach represents a first-of-its kind attempt of an aerosol–ice formation closure study (AEROICESTUDY). Very few closure studies related to INPs have been conducted, and to our knowledge, none using robust size-resolved ambient aerosol composition measurements as a starting point. Achievement of aerosol–ice formation closure relies on our ability to characterize the ambient aerosol population with respect to particles size and composition and to determine INP number concentrations for specified freezing temperatures. This requires numerous online and offline instrumentation resulting in this pilot field campaign being a multi-institutional and community-collaborative effort. We chose the ARM SGP megasite for this first aerosol-ice formation closure pilot study due to its significant measurement capabilities available to obtain detailed physical characterization of the local aerosol population including size distribution, mass loading, and chemical composition of non-refractory aerosol particles. The overall objective of this project is to identify ice nucleation parameterizations that produce the most robust predictions of INP numbers and thus are best suited to be included in cloud and climate models. This objective includes the following goals for this field and laboratory-based project: i) What are the crucial aerosol physicochemical property measurements needed to accurately guide ice nucleation representations in models and long-term INP measurements? ii) What level of parameter details needs to be known to achieve aerosol–ice formation closure? iii) What are the leading causes for climate model bias in INP predictions? We found that the advances in our understanding of immersion freezing garnered over the last 20 years allowed us to yield partial and full closures of atmospheric immersion freezing from ambient aerosol particles. When the aerosol population is physicochemically complex and parameterizations for representative INP types are not yet available, we still struggle to accurately predict INP number concentrations. This project clearly demonstrates that with more laboratory and field measurements that are accompanied by particle composition analysis, the necessary datasets to achieve aerosol–ice formation closure for various locations will emerge, thus providing a robust foundation for guiding the representation of INPs in cloud and climate models.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1994

A statistical analysis of the dependency of closure assumptions in cumulus parameterization on the horizontal resolution

Simulated data from the UCLA cumulus ensemble model are used to investigate the quasi-universal validity of closure assumptions used in existing cumulus parameterizations. A closure assumption is quasi-universally valid if it is sensitive neither to convective cloud regimes nor to horizontal resolutions of large-scale/mesoscale models. The dependency of three types of closure assumptions, as classified by Arakawa and Chen, on the horizontal resolution is addressed in this study. Type I is the constraint on the coupling of the time tendencies of large-scale temperature and water vapor mixing ratio. Type II is the constraint on the coupling of cumulus heating and cumulus drying. Type III is a direct constraint on the intensity of a cumulus ensemble. The macroscopic behavior of simulated cumulus convection is first compared with the observed behavior in view of Type I and Type II closure assumptions using 'quick-look' and canonical correlation analyses. It is found that they are statistically similar to each other. The three types of closure assumptions are further examined with simulated data averaged over selected subdomain sizes ranging from 64 to 512 km. It is found that the dependency of Type I and Type II closure assumptions on the horizontal resolution is very weak and that Type III closure assumption is somewhat dependent upon the horizontal resolution. The influences of convective and mesoscale processes on the closure assumptions are also addressed by comparing the structures of canonical components with the corresponding vertical profiles in the convective and stratiform regions of cumulus ensembles analyzed directly from simulated data. The implication of these results for cumulus parameterization is discussed.

Xu, Kuan-Man↗

DOE OSTI2023

Sodium Components Maintenance Shop (SCMS) Carbonation Vessel – Partial HWMA/RCRA Closure Certification Report

This report documents the Hazardous Waste Management Act (HWMA)/ Resource Conservation and Recovery Act (RCRA) Partial Closure Certification of the Sodium Components Maintenance Shop (SCMS) Carbonation Vessel. The HWMA/RCRA Closure followed the multi step review and evaluation closure process identified in the Idaho National Laboratory (INL) Materials and Fuels Complex (MFC) HWMA/RCRA Partial Permit Closure Plan, October 1, 2015. This closure certification report documents that the SCMS Carbonation Vessel was removed from the SCMS, packaged as hazardous waste and stored for future treatment and disposal, and therefore has met the closure performance standards in accordance with the Department of Energy Idaho National Laboratory Materials and Fuels Complex HWMA/RCRA Partial Permit Closure Plan (EPA No. ID4890008952, October 1, 2015).

99 GENERAL AND MISCELLANEOUS↗

DOE OSTI2026

A careful examination of closure models in Euler–Lagrange Simulations of compressible multiphase flow in a planar shock particle curtain problem

In this work we present a comprehensive investigation of state-of-the-art closure models employed to represent interphase momentum, thermal, and work exchange between the gas and particulate phases for Euler–Lagrange (EL) simulations in shock-driven flows. A complete list of closures for the force, torque, heat transfer, and work exchange models is provided. In particular, the present work includes a stochastic closure for the particle-to-particle variation in the quasi-steady force and a deterministic closure for particle-to-particle variation in the added mass force in an EL framework. These variations arise due to the presence of neighboring particles and particle–particle interactions. To investigate the importance of each closure term, we carry out fully three-dimensional simulations for a planar shock propagating over a random bed of inert particles. The primary goal is to evaluate the role of each closure term on the gas dynamic features (such as transmitted and reflected shock locations) and particle curtain features (such as upstream and downstream curtain locations). To this end, thirteen cases are considered, with each case progressively including a closure model with the goal to identify and quantify its contribution to the simulated dynamics. We show that the volume fraction dependence of the mean force models plays an important role in generating wave-like instabilities that lead to concentration bands. In addition, fluctuations in quasi-steady and added mass forces primarily decrease the internal instabilities that tend to enhance local volume fraction variations. Particle rotation is primarily due to inter-particle collisions, is generally weak, and does not play an important role in the translational dynamics for the present configuration. Inter-phase heat transfer has a strong effect on gas phase temperature, slows down the transmitted and reflected shocks, and decreases the width of the curtain. Furthermore, the absence of a work-coupling model fails to conserve the total energy, greatly under-predicts the gas temperature which in turn affects the particle dynamics.

Compressible flow↗

DOE OSTI2022

Evaluating and Improving Scale–Awareness of a Convective Parameterization Closure Using Cloud–Resolving Model Simulations of Convection

This study aims to evaluate a revised closure of the Zhang-McFarlane (ZM) scheme for deep convection and to further improve its scale awareness. Output from two cloud-resolving model (CRM) simulations of both midlatitude organized (MC3E) and tropical unorganized (TWP-ICE) convection are used for the evaluation. By averaging the CRM output over different subdomain sizes from 64 km to 4 km, convection-associated fields are obtained to represent the fields at different horizontal resolutions of global climate models (GCMs). The convection parameterization closure is then tested using these fields. Results show that the cloud base mass flux M b determined from the closure has a relatively good relationship with CRM-simulated convection at coarse resolutions for both MC3E and TWP-ICE, but their correlation degrades at higher resolutions, especially when approaching the gray zone scale under 10 km. The fluctuation of CAPE consumption rate per unit cloud base mass flux for different convective events is found to be an important factor affecting the correlation. When averaged over the base domain, the cloud base mass flux determined by the closure is found to increase with decreasing subdomain size, implying that the closure is not scale-aware. To improve its scale-awareness, a modified closure is designed to alleviate the overprediction of convection at high GCM resolutions. Furthermore, results show that the modified closure has the scale-aware ability to suppress the overprediction problem at high GCM resolutions for both MC3E and TWP-ICE.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2017

Analytic closures for M1 neutrino transport

Carefully accounting for neutrino transport is an essential component of many astrophysical studies. Solving the full transport equation is too expensive for most realistic applications, especially those involving multiple spatial dimensions. For such cases, resorting to approximations is often the only viable option for obtaining solutions. One such approximation, which recently became popular, is the M1 method. It utilizes the system of the lowest two moments of the transport equation and closes the system with an ad hoc closure relation. The accuracy of the M1 solution depends on the quality of the closure. Several closures have been proposed in the literature and have been used in various studies. We carry out an extensive study of these closures by comparing the results of M1 calculations with precise Monte Carlo calculations of the radiation field around spherically symmetric protoneutron star models. We find that no closure performs consistently better or worse than others in all cases. The level of accuracy that a given closure yields depends on the matter configuration, neutrino type and neutrino energy. As a result, given this limitation, the maximum entropy closure by Minerbo on average yields relatively accurate results in the broadest set of cases considered in this work.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Aerosol–Ice Formation Closure: A Southern Great Plains Field Campaign

Prediction of ice formation in clouds presents one of the grand challenges in the atmospheric sciences. Immersion freezing initiated by ice-nucleating particles (INPs) is the dominant pathway of primary ice crystal formation in mixed-phase clouds, where supercooled water droplets and ice crystals coexist, with important implications for the hydrological cycle and climate. However, derivation of INP number concentrations from an ambient aerosol population in cloud-resolving and climate models remains highly uncertain. We conducted an aerosol–ice formation closure pilot study using a field-observational approach to evaluate the predictive capability of immersion freezing INPs. The closure study relies on collocated measurements of the ambient size-resolved and single-particle composition and INP number concentrations. The acquired particle data serve as input in several immersion freezing parameterizations, which are employed in cloud-resolving and climate models, for prediction of INP number concentrations. We discuss in detail one closure case study in which a front passed through the measurement site, resulting in a change of ambient particle and INP populations. We achieved closure in some circumstances within uncertainties, but we emphasize the need for freezing parameterization of potentially missing INP types and evaluation of the choice of parameterization to be employed. Overall, this closure pilot study aims to assess the level of parameter details and measurement strategies needed to achieve aerosol–ice formation closure. Furthermore, the closure approach is designed to accurately guide immersion freezing schemes in models, and ultimately identify the leading causes for climate model bias in INP predictions.

58 GEOSCIENCES↗

DOE OSTI2020

Probing interfacial momentum closures in two-phase bubbly flow with machine learning-aided methods

Computational fluid dynamics (CFD) approach has already reached a high level of maturity for single-phase flows, however the development of closure models for two-phase flow requires additional attention. Multiphase CFD (M-CFD) methods resolve the conservation equations for mass, momentum and energy while differing in the approaches and strategies adopted in the physical closure models. The most widely adopted framework for M-CFD is the Eulerian-Eulerian two-fluid approach which assumes that all phases are co-existing inside each computational cell. For each fluid, the full set of conservation equations is solved; therefore, each fluid has a different velocity field. For adiabatic two-phase flow, the mechanisms of the interfacial momentum transfer are modeled by the interfacial forces representing different physical mechanisms. One of the crucial issues in the development and application of two-fluid model is the understanding of the interfacial momentum closures which determines the bubble distribution and migration behaviors. Dedicated experiments are performed to support the physical understanding and drive the closures’ development. However, limitations exist due to the uncertainties in the experimental measurement and the simplified analytical assumptions which have difficulties on representing the complex non-linear flow fields. In this paper, a data-driven approach, Feature Similarity Measurement (FSM), is developed and proposed to resolve the challenges of modeling the interfacial forces closures. Case study is performed with two-phase flow scenarios where the high-fidelity experimental data is available. Within the Eulerian-Eulerian two-fluid framework, only momentum equations for gas and liquid phases are solved and reduced-order interfacial momentum closures are aided with FSM. Predictions of void fraction and velocity fields are analyzed and demonstrate the potential of machine learning-driven interfacial forces closures.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1977

A study of fatigue crack closure using electric potential and compliance techniques

The objective of this study was to compare closure data obtained on the same specimen with crack tip compliance gage and electric potential techniques. Equivalent results on closure using the two techniques were obtained on 7075-T651 aluminum center cracked panels. The results also indicated that closure was a function of stress ratio, specimen thickness and maximum applied stress intensity. Maximum stress intensity had a particularly strong effect on closure in the range of applied stresses used. This observed dependence of closure on specimen thickness and maximum stress intensity should account for many of the discrepancies in closure behavior found in the literature. Observations on potential system behavior during closure measurements are also reported.

Clarke, C. K.↗

NASA NTRS1995

Working toward a three-dimensional fatigue closure model for surface cracks

The first reliable elastic fracture mechanics solutions for a surface crack in a plate were obtained by Newman and Raju. The authors, both from the Mechanics of Materials Branch at NASA-Langley, used a highly detailed finite element solution requiring substantial computational resources. Computers have since become more powerful and available; however, many important related problems remain computationally expensive. The problem of three-dimensional fatigue crack growth taking into account plasticity-induced crack closure is one such problem. It is the goal of this research to provide an efficient method to account for three-dimensional crack closure in fatigue. Newman developed a two-dimensional plasticity-induced crack closure model for center cracked specimens. This model requires iterations to determine both the contact solution at each growth step and the extent of the plastic zone at the crack tip. A three-dimensional version of this model would require obtaining these nonlinear variables all along the crack front. This model must be efficient so that repeated calculations can be performed during crack growth simulations. The highly versatile line spring model (LSM) with contact, fatigue, and plasticity will form the basis of the closure model. There are several required additions to past work to address the three-dimensional crack closure problem. Initially, these additions will include (1) an improved LSM to more accurately obtain the crack opening displacement, stress intensity factors, and elastic T-stress near the ends of the surface crack; (2) a method to determine the extent of the plastic zone all along the crack front; (3) a method to determine the contact zone given a perfectly plastic layer of material on the crack surfaces; (4) a method to determine the magnitude of the compressive contact stress; and (5) a way to implement the degree of constraint along the curved crack front. During the summer ASEE program an enhanced LSM was developed. A method similar to that of 'strip synthesis' first introduced by Fujimoto was used. Briefly, the crack opening displacements of 'slices' of the surface crack in a direction parallel to the plate surface are considered in addition to the standard LSM approach that makes use of springs obtained from slices perpendicular to the plate surface. This enhancement is necessary so that an accurate three-dimensional representation of quantities such as contact zone size, plastic zone size, stress intensity factors, T-stress, and crack opening displacement can be determined. By combining results of previous investigations with the LSM, the problem of three-dimensional crack closure will be addressed. In addition to a closure model, the enhanced LSM can be used for many other problems including interacting surface cracks and fatigue crack growth of a through crack with a curved crack front.

Joseph, Paul F.↗

NASA NTRS2021

Aerosol–Ice Formation Closure: A Southern Great Plains Field Campaign

Prediction of ice formation in clouds presents one of the grand challenges in the atmospheric sciences. Immersion freezing initiated by ice-nucleating particles (INPs) is the dominant pathway of primary ice crystal formation in mixed-phase clouds, where supercooled water droplets and ice crystals coexist, with important implications for the hydrological cycle and climate. However, derivation of INP number concentrations from an ambient aerosol population in cloud-resolving and climate models remains highly uncertain. We conducted an aerosol-ice formation closure pilot study using a field-observational approach to evaluate the predictive capability of immersion freezing INPs. The closure study relies on co-located measurements of the ambient size-resolved and single-particle composition and INP number concentrations. The acquired particle data serve as input in several immersion freezing parameterizations, that are employed in cloud-resolving and climate models, for prediction of INP number concentrations. We discuss in detail one closure case study in which a front passed through the measurement site, resulting in a change of ambient particle and INP populations. We achieved closure in some circumstances within uncertainties, but we emphasize the need for freezing parameterization of potentially missing INP types and evaluation of the choice of parameterization to be employed. Overall, this closure pilot study aims to assess the level of parameter details and measurement strategies needed to achieve aerosol-ice formation closure. The closure approach is designed to accurately guide immersion freezing schemes in models, and ultimately identify the leading causes for climate model bias in INP predictions.

ice formation↗