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NASA NTRS2006

An Initial Non-Equilibrium Porous-Media Model for CFD Simulation of Stirling Regenerators

The objective of this paper is to define empirical parameters (or closwre models) for an initial thermai non-equilibrium porous-media model for use in Computational Fluid Dynamics (CFD) codes for simulation of Stirling regenerators. The two CFD codes currently being used at Glenn Research Center (GRC) for Stirling engine modeling are Fluent and CFD-ACE. The porous-media models available in each of these codes are equilibrium models, which assmne that the solid matrix and the fluid are in thermal equilibrium at each spatial location within the porous medium. This is believed to be a poor assumption for the oscillating-flow environment within Stirling regenerators; Stirling 1-D regenerator models, used in Stirling design, we non-equilibrium regenerator models and suggest regenerator matrix and gas average temperatures can differ by several degrees at a given axial location end time during the cycle. A NASA regenerator research grant has been providing experimental and computational results to support definition of various empirical coefficients needed in defining a noa-equilibrium, macroscopic, porous-media model (i.e., to define "closure" relations). The grant effort is being led by Cleveland State University, with subcontractor assistance from the University of Minnesota, Gedeon Associates, and Sunpower, Inc. Friction-factor and heat-transfer correlations based on data taken with the NASAlSunpower oscillating-flow test rig also provide experimentally based correlations that are useful in defining parameters for the porous-media model; these correlations are documented in Gedeon Associates' Sage Stirling-Code Manuals. These sources of experimentally based information were used to define the following terms and parameters needed in the non-equilibrium porous-media model: hydrodynamic dispersion, permeability, inertial coefficient, fluid effective thermal conductivity (including themal dispersion and estimate of tortuosity effects}, and fluid-solid heat transfer coefficient. Solid effective thermal conductivity (including the effect of tortuosity) was also estimated. Determination of the porous-media model parameters was based on planned use in a CFD model of Infinia's Stirling Technology Demonstration Convertor (TDC), which uses a random-fiber regenerator matrix. The non-equilibrium porous-media model presented is considered to be an initial, or "draft," model for possible incorporation in commercial CFD codes, with the expectation that the empirical parameters will likely need to be updated once resulting Stirling CFD model regenerator and engine results have been analyzed. The emphasis of the paper is on use of available data to define empirical parameters (and closure models) needed in a thermal non-equilibrium porous-media model for Stirling regenerator simulation. Such a model has not yet been implemented by the authors or their associates. However, it is anticipated that a thermal non-equilibrium model such as that presented here, when iacorporated in the CFD codes, will improve our ability to accurately model Stirling regenerators with CFD relative to current thermal-equilibrium porous-media models.

Tew, Roy↗

NASA NTRS1991

Single and double point modeling of homogeneous turbulence

Investigations carried out for revisiting homogeneous turbulent flows in the presence of mean shear, rotation, or external compression are summarized. The simplest and most concise RDT (Rapid Distortion Theory) formulation, which includes a comprehensive linear stability analysis, is used for this purpose. Such a linear approach could be extended by a generalized EDQNM (Eddy Damped Quasi-Normal Markovian) to two point closure in order to model non-linear interactions, especially when pure Coriolis effects are present. The results are discussed in connection with databases obtained by DNS (Direct Numerical Simulations), including previous Center for Turbulence Research (CTR) results and new calculations in progress. The main goal is to contribute to and significantly improve on the rational one-point closure models in progress at the CTR and at Ecole Centrale de Lyon (ECL).

Cambon, C.↗

DOE OSTI2014

Predictive Engineering Tools for Injection-Molded Long-Carbon-Fiber Thermoplastic Composites - FY 2014 Fourth Quarterly Report

During the last quarter of FY 2014, the following technical progress has been made toward project milestones: 1) Autodesk, Inc. (Autodesk) has implemented a new fiber length distribution (FLD) model based on an unbreakable length assumption with Reduced Order Modeling (ROM) by the Proper Orthogonal Decomposition (POD) approach in the mid-plane, dual-domain and 3D solvers. 2) Autodesk improved the ASMI 3D solver for fiber orientation prediction using the anisotropic rotary diffusion (ARD) – reduced strain closure (RSC) model. 3) Autodesk received consultant services from Prof. C.L. Tucker at the University of Illinois on numerical simulation of fiber orientation and fiber length. 4) PlastiComp, Inc. (PlastiComp) suggested to Purdue University a procedure for fiber separation using an inert-gas atmosphere in the burn-off furnace. 5) Purdue University (Purdue) hosted a face-to-face project review meeting at Purdue University on August 6-7, 2014. 6) Purdue conducted fiber orientation measurements for 3 PlastiComp plaques: fast-fill 30wt% LCF/PP edged-gated, slow-fill 50wt% LCF/PP edge-gated, and slow-fill 50wt% LCF/PP center-gated plaques, and delivered the orientation data for these plaques at the selected locations (named A, B, and C) to PNNL. 7) PNNL conducted ASMI mid-plane analyses for the above PlastiComp plaques and compared the predicted fiber orientations with the measured data provided by Purdue at Locations A, B, and C on these plaques. 8) PNNL planned the project review meeting (August 6-7, 2014) with Purdue. 9) PNNL performed ASMI analyses for the Toyota complex parts with and without ribs, having different wall thicknesses, and using the PlastiComp 50wt% LCF/PP, 50wt% LCF/PA66, 30wt% LCF/PP, and 30wt% LCF/PA66 materials to provide guidance for tool design and modifications needed for molding these parts. 10) Magna Exteriors and Interiors Corp. (Magna) molded plaques from the 50% LCF/PP and 50% LCF/PA66 materials received from Plasticomp in order to extract machine purgings (purge materials) from Magna’s 200-Ton Injection Molding machine targeted to mold the complex part. 11) Toyota and Magna discussed with PNNL tool modification for molding the complex part.

36 MATERIALS SCIENCE↗

DOE OSTI2015

Nevada National Security Site (NNSS) Environmental Remediation Using EPA's Model Evaluation Guidance to Move to Closure - 15588

The National Nuclear Security Administration Nevada Field Office (NNSA/NFO) has adapted the Environmental Protection Agency's guidance on environmental model evaluation as a framework for evaluating corrective action investigation models. Model evaluation is an important confidence building activity, which is needed to support closure of the Nevada National Security Site (NNSS) Corrective Action Units (CAUs) associated with underground nuclear testing. Through this process, site-investigation models of groundwater flow and contaminant transport are reviewed and compared to new site-specific data to determine if the results can be used to support regulatory decisions required for closure and to achieve NNSA/NFO site management objectives. The regulatory decisions include identifying and establishing CAU regulatory boundaries; identifying institutional controls, including use-restriction boundaries; and developing a long-term closure monitoring program. A successful case study from Frenchman Flat, Nevada is used to illustrate the model evaluation process. Groundwater flow and transport from two of the 10 underground nuclear tests in Frenchman Flat had the largest potential for contaminating groundwater, and were selected for evaluation. Wells were drilled, logged, hydraulically tested, sampled, and analyzed for radionuclides and the data was evaluated with respect to previous site conceptualization and numerical model results. The approach and results of this process as applied to the PIN STRIPE test and how it helped build confidence to close the Frenchman Flat CAU is described in this case study. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

NASA NTRS1988

Simulations using a 3D-moment turbulence closure in a two-dimensional cloud model - Comparisons with observations

A method for deep cumulus cloud simulations is presented, in which the plumes or clouds are simulated using a two-dimensional axisymmetric numerical cloud model with third-moment turbulence closure. This method is based on the assumption that the only uncertainty in the turbulence closure is in the turbulent length scale specification. Therefore, the length scale is varied, and, using different length scales, the simulated plumes are compared to the observed ones, making it possible to optimize the length scale prescription.

Krueger, Steven K.↗

DOE OSTI2012

Cloud Droplet Number Closure Study based on ISDAC Observational Data

Aerosol-cloud droplet closure analysis was conducted for five cases from the Indirect and Semi-Direct Aerosol Campaign (ISDAC). All cases corresponded to clouds dominated by liquid droplets, with two in relatively clean conditions, and the remaining three in more polluted conditions. This analysis entailed adiabatic cloud parcel model simulations to link the observed properties of aerosols, cloud droplets, and atmospheric dynamics with theoretical predictions. The extent of agreement between observed and modelled droplet number concentrations allowed for the assessment of representations of the physical and chemical properties of aerosols and of the vertical velocity involved in cloud droplet formation. Finally the list of journal publications and conferences are given which corresponds to the research for this DOE grant.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS1988

Reynold stress closure in jet flows using wave models

Research program efforts have continued to concentrate on the development of the numerical methods that will form the computational part of the turbulence closure scheme. Studies have continued on the wave model for the two dimensional shear layer. This configuration is being used as a test case for the closure schemes. Several numerical schemes for the solution of the non-separable Rayleigh equation were developed. This solution is required for the closure scheme in more complex geometries. The most efficient method found is a Hybrid scheme that combines both pseudospectral and finite difference techniques. In addition, conformal transformation techniques were developed to transform the arbitrary geometry of the jet to a simple computational domain. The study of the shock structure in arbitrary geometry jets and multiple jets. These developments are described briefly.

Morris, P. J.↗

DOE OSTI2017

High-to-Low Activities across VVI, AMA and PHI

This milestone report documents work performed in CASL that was broadly focused on the use of validated high-fidelity simulation codes to inform, improve and calibrate low-fidelity codes to facilitate multiphysics coupling, design, performance analysis, and risk assessment. This high-to-low (Hi2Lo) initiative has the following objectives: employ physics encapsulated in high-fidelity codes to improve the functionality of low-fidelity codes, quantify biases in low-fidelity codes, develop and calibrate physical models and closure relations so that low-fidelity codes more accurately incorporate requisite physics, and develop low-fidelity codes that can be effectively coupled to simulate multiphysics behavior. In combination, these efforts are designed to impact both CIPS and DNB. For example, the development and experimental design-based Bayesian calibration of dynamic gas conductance models in CTFFuel will provide the capability to better model crud-induced power shifts. Whereas the present emphasis has focused on the high-fidelity codes STAR-CCM+ and BISON and low-fidelity codes CTF and CTFFuel, future emphasis will be expanded to include MAMBA. During the reporting period, Hi2Lo efforts focused on two broad components: demonstration of the experimental design-based Bayesian calibration framework to calibrate CTF using both STAR-generated synthetic data and experimental data, and the use of STAR to inform and improve the turbulence modeling and grid heat transfer modeling capabilities in CTF. A complementary milestone focused on the implementation and verification of fuel models in CTFFuel, for which we demonstrated initial calibration results. Future Hi2Lo work will focus on the use of the experimental design-based Bayesian calibration framework, demonstrated this year for STAR and CTF, to calibrate parameters in the fuel swelling, fuel irradiation-induced densification, and fuel relocation models in CTFFuel using both experimental and BISON-generated data. A second component will focus on the continued use of STAR to improve grid modeling capabilities in CTF.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2015

A Two-length Scale Turbulence Model for Single-phase Multi-fluid Mixing

A two-length scale, second moment turbulence model (Reynolds averaged Navier-Stokes, RANS) is proposed to capture a wide variety of single-phase flows, spanning from incompressible flows with single fluids and mixtures of different density fluids (variable density flows) to flows over shock waves. The two-length scale model was developed to address an inconsistency present in the single-length scale models, e.g. the inability to match both variable density homogeneous Rayleigh-Taylor turbulence and Rayleigh-Taylor induced turbulence, as well as the inability to match both homogeneous shear and free shear flows. The two-length scale model focuses on separating the decay and transport length scales, as the two physical processes are generally different in inhomogeneous turbulence. This allows reasonable comparisons with statistics and spreading rates over such a wide range of turbulent flows using a common set of model coefficients. The specific canonical flows considered for calibrating the model include homogeneous shear, single-phase incompressible shear driven turbulence, variable density homogeneous Rayleigh-Taylor turbulence, Rayleigh-Taylor induced turbulence, and shocked isotropic turbulence. The second moment model shows to compare reasonably well with direct numerical simulations (DNS), experiments, and theory in most cases. The model was then applied to variable density shear layer and shock tube data and shows to be in reasonable agreement with DNS and experiments. Additionally, the importance of using DNS to calibrate and assess RANS type turbulence models is highlighted.

04 OIL SHALES AND TAR SANDS↗

DOE OSTI2024

A Variable Eddington Factor Model for Thermal Radiative Transfer with Closure Based on Data-Driven Shape Function

Here, a new variable Eddington factor (VEF) model is presented for nonlinear problems of thermal radiative transfer (TRT). The VEF model is data-driven and acts on known (a-priori) radiation-diffusion solutions for material temperatures in the TRT problem. A linear auxiliary problem is constructed for the radiative transfer equation (RTE) whose emission source and opacities are evaluated at these known material temperatures. The solution to this RTE approximates the specific intensity distribution in phase-space and time. It is applied as a shape function to define the Eddington tensor for the presented VEF model. The shape function computed via the auxiliary RTE problem will capture some degree of transport effects within the TRT problem. The VEF moment equations closed with this approximate Eddington tensor will thus carry with them these captured transport effects. In this study, the temperature data comes from multigroup P 1 , P 1/3 , and flux-limited diffusion radiative transfer models. The proposed VEF model can be interpreted as a transport-corrected diffusion reduced-order model. Numerical results are presented on the Fleck-Cummings test problem which models a supersonic wavefront of radiation. The VEF model is shown to improve accuracy by 1–2 orders of magnitude compared to the considered radiation-diffusion model solutions to the TRT problem.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

NASA NTRS2019

A New Approach to Model Delamination Growth in Fatigue Using the Virtual Crack Closure Technique Without Re-Meshing

A modeling approach is proposed to simulate delamination propagation in fatigue that combines the Virtual Crack Closure Technique (VCCT) with a progressive nodal release strategy. The progressive nodal release alleviates the artificial stress concentrations found when using the VCCT with instantaneous release to model 3D delamination without re-meshing. This enables crack shapes that do not conform to the underlying mesh to be readily simulated. The progressive release is formulated such that no artificial growth or healing occurs as a result of a change in loading conditions. Furthermore, expressions for calculating energy release rates at partially released nodes are proposed and applied to arbitrarily shaped delamination fronts. The shape of the delamination front is considered explicitly in the energy release rate calculations, and is determined by considering the normalized crack positions associated with the partial nodal release. Contrary to previous implementations, the local delamination propagation direction is not assumed to follow mesh lines, but instead is computed as part of the iterative procedure proposed to determine the maximum energy release along the crack front. The results obtained suggest the approach can accurately simulate Mode I, Mixed Mode I/II and Mode II fatigue delamination growth and be used to simulate growth of arbitrarily shaped cracks that do not conform to the underlying mesh.

N V De Carvalho↗

DOE OSTI2017

Numerical Uncertainties vs. Model Uncertainties in Two-phase Flow Simulations

In recent years, verification, validation and uncertainty quantification (VVUQ) have become a common practice in thermal-hydraulics analysis. In general, these activities deal with propagations of uncertainties in computer code simulations, e.g., through system analysis codes. However, most existing such activities in thermal-hydraulics analysis have been primarily focused on model uncertainties, while numerical uncertainties were largely overlooked. Numerical uncertainties (or numerical errors) can appear in many different forms, e.g., round-off error, statistical sampling error, and discretization error. As pointed out by Oberkampf and Roy, discretization error is usually the largest however the most difficult type of error to estimate reliably. In thermal-hydraulics analysis, especially two-phase flow simulations commonly encountered in reactor safety analysis, the lack of consideration on discretization error is mainly due to the difficulty in estimating them. Accurate estimations on discretization error require continuous mesh refinement and/or implementation of high-order numerical schemes in system analysis code, both of which are unfortunately difficult to achieve for existing codes. At first, it should be emphasized that mesh refinement (or mesh sensitivity study) is a well-understood concept in the thermal-hydraulics field. However, it is not commonly practiced for many reasons, e.g., lack of understanding on numerical errors by code users, consideration on computational cost, deteriorated numerical stability performance with refined meshes, and etc. Secondly, high-order (e.g., second-order) numerical schemes are simply unavailable in almost any existing system analysis code. Implementation of high-order numerical schemes in these codes is difficult, if not impossible, given the complexity of these codes. On the other hand, people tend to argue that numerical uncertainties (or discretization error as we have emphasized) are not as important as the commonly large uncertainties in two-phase flow models, e.g., closure correlations. As a result, nodalization is sometimes played unintentionally, or maybe intentionally, to match experimental data, which is referred as 'user effects' or 'compensating errors' in thermal-hydraulics community. Such a practice is highly criticized by Levy. In this work, we will at first build a computer code that incorporates both first-order and second-order numerical methods to solve the two-phase flow problems. The first-order method resembles the one used in many existing system analysis codes; and the second-order method works as the reference to estimate numerical errors. Numerical verifications on spatial discretization schemes will be presented in the form of mesh convergence study. It will also be demonstrated that, in practical scenarios, discretization errors can be as large as, or even larger than, model uncertainties via case studies.

42 ENGINEERING↗

DOE OSTI2016

Arbitrary Lagrangian–Eulerian methods for modeling high-speed compressible multimaterial flows

This paper reviews recent developments in Arbitrary Lagrangian Eulerian (ALE) methods for modeling high speed compressible multimaterial flows in complex geometry on general polygonal meshes. We only consider the indirect ALE approach which consists of three key stages: a Lagrangian stage, in which the solution and the computational mesh are updated; a rezoning stage, in which the nodes of the computational mesh are moved to improve grid quality; and a remapping stage, in which the Lagrangian solution is transferred to the rezoned mesh.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

The Adjoint Petrov–Galerkin method for non-linear model reduction

Here, we formulate a new projection-based reduced-order modeling technique for non-linear dynamical systems. The proposed technique, which we refer to as the Adjoint Petrov–Galerkin (APG) method, is derived by decomposing the generalized coordinates of a dynamical system into a resolved coarse-scale set and an unresolved fine-scale set. A Markovian finite memory assumption within the Mori–Zwanzig formalism is then used to develop a reduced-order representation of the coarse scales. This procedure leads to a closed reduced-order model that displays commonalities with the adjoint stabilization method used in finite elements. The formulation is shown to be equivalent to a Petrov–Galerkin method with a non-linear, time-varying test basis, thus sharing some similarities with the Least-Squares Petrov–Galerkin method. Theoretical analysis examining a priori error bounds and computational cost is presented. Numerical experiments on the compressible Navier–Stokes equations demonstrate that the proposed method can lead to improvements in numerical accuracy, robustness, and computational efficiency over the Galerkin method on problems of practical interest. Improvements in numerical accuracy and computational efficiency over the Least-Squares Petrov–Galerkin method are observed in most cases.

42 ENGINEERING↗

NASA NTRS1990

Analytical methods for the development of Reynolds stress closures in turbulence

Analytical methods for the development of Reynolds stress models in turbulence are reviewed in detail. Zero, one and two equation models are discussed along with second-order closures. A strong case is made for the superior predictive capabilities of second-order closure models in comparison to the simpler models. The central points are illustrated by examples from both homogeneous and inhomogeneous turbulence. A discussion of the author's views concerning the progress made in Reynolds stress modeling is also provided along with a brief history of the subject.

Speziale, Charles G.↗

NASA NTRS2015

Cloud Feedbacks on Greenhouse Warming in a Multi-Scale Modeling Framework with a Higher-Order Turbulence Closure

Five-year simulation experiments with a multi-scale modeling Framework (MMF) with a advanced intermediately prognostic higher-order turbulence closure (IPHOC) in its cloud resolving model (CRM) component, also known as SPCAM-IPHOC (super parameterized Community Atmospheric Model), are performed to understand the fast tropical (30S-30N) cloud response to an instantaneous doubling of CO2 concentration with SST held fixed at present-day values. SPCAM-IPHOC has substantially improved the low-level representation compared with SPCAM. It is expected that the cloud responses to greenhouse warming in SPCAM-IPHOC is more realistic. The change of rising motion, surface precipitation, cloud cover, and shortwave and longwave cloud radiative forcing in SPCAM-IPHOC from the greenhouse warming will be presented in the presentation.

Cheng, Anning↗

DOE OSTI2025

Online learning of quadratic manifolds from streaming data for nonlinear dimensionality reduction and nonlinear model reduction

Here, this work introduces an online greedy method for constructing quadratic manifolds from streaming data, designed to enable in situ analysis of numerical simulation data on the Petabyte scale. Unlike traditional batch methods, which require all data to be available upfront and take multiple passes over the data, the proposed online greedy method incrementally updates quadratic manifolds in one pass as data points are received, eliminating the need for expensive disk input/output operations as well as storing and loading data points once they have been processed. A range of numerical examples demonstrate that the online greedy method learns accurate quadratic manifold embeddings while being capable of processing data that far exceed common disk input/output capabilities and volumes as well as main-memory sizes.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2015

Decadal Prediction and Stochastic Simulation of Hydroclimate Over Monsoonal Asia

We developed further our advanced methods of time series analysis and empirical model reduction (EMR) and applied them to climatic time series relevant to hydroclimate over Monsoonal Asia. The EMR methodology was both generalized further and laid on a rigorous mathematical basis via multilayered stochastic models (MSMs). We identified easily testable conditions that imply the existence of a global random attractor for MSMs and allow for non-polynomial predictors. This existence, in turn, guarantees the numerical stability of the MSMs so obtained. We showed that, in the presence of low-frequency variability (LFV), EMR prediction can be improved further by including information from selected times in the system’s past. This prediction method, dubbed Past-Noise Forecasting (PNF), was successfully applied to the Madden-Julian Oscillation (MJO). Our time series analysis and forecasting methods, based on singular-spectrum analysis (SSA) and its enhancements, were applied to several multi-centennial proxy records provided by the Lamont team. These included the Palmer Drought Severity Index (PDSI) for 1300–2005 from the Monsoonal Asia Drought Atlas (MADA), and a 300-member ensemble of pseudo-reconstructions of Indus River discharge for 1702–2005. The latter was shown to exhibit a robust 27-yr low-frequency mode, which helped multi-decadal retroactive forecasts with no look-ahead over this 300-year interval.

54 ENVIRONMENTAL SCIENCES↗