A computational model of aluminum melting is proposed which captures both the thermal fluid-solid phase transition and the mechanical effects of oxidation. The model hybridizes ideas from smoothed particle hydrodynamics and bonded particle models to simulate both hydrodynamic flows and solid elasticity. Oxidation is represented by dynamically adding and deleting spring-like bonds between surface fluid particles to represent the formation and rupture of the oxide skin. Various complex systems are simulated to demonstrate the adaptability of the method and to illustrate the significant impact of skin properties on material flow. As a result, initial comparison to experiments of a melting aluminum cantilever highlights that the computational model can reproduce key qualitative features of aluminum relocation.
Ultimately, our experiment measures two quantities on an aluminum bar: motion (which modeling must predict) and temperature (which sets thermal boundary conditions). For motion, stereo DIC is a technique to use imaging data to provide displacements relative to a reference image down to 1/100th of a pixel. We use a calibrated infrared imaging method for accurate temperature measurements. We will be capturing simultaneous data and then registering temperature data in space to the same coordinate system as the displacement data. While we will later show that our experiments are repeatable, indicating that separate experiments for motion and temperature would provide similar data, the simultaneous and registered data removes test to test variability as a source of uncertainty for model calibration and reduces the number of time-consuming tests that must be performed.
In order to impact physical mechanical system design decisions and realize the full promise of high-fidelity computational tools, simulation results must be integrated at the earliest stages of the design process. This is particularly challenging when dealing with uncertainty and optimizing for system-level performance metrics, as full-system models (often notoriously expensive and time-consuming to develop) are generally required to propagate uncertainties to system-level quantities of interest. Methods for propagating parameter and boundary condition uncertainty in networks of interconnected components hold promise for enabling design under uncertainty in real-world applications. These methods avoid the need for time consuming mesh generation of full-system geometries when changes are made to components or subassemblies. Additionally, they explicitly tie full-system model predictions to component/subassembly validation data which is valuable for qualification. These methods work by leveraging the fact that many engineered systems are inherently modular, being comprised of a hierarchy of components and subassemblies that are individually modified or replaced to define new system designs. By doing so, these methods enable rapid model development and the incorporation of uncertainty quantification earlier in the design process. The resulting formulation of the uncertainty propagation problem is iterative. We express the system model as a network of interconnected component models, which exchange solution information at component boundaries. We present a pair of approaches for propagating uncertainty in this type of decomposed system and provide implementations in the form of an open-source software library. We demonstrate these tools on a variety of applications and demonstrate the impact of problem-specific details on the performance and accuracy of the resulting UQ analysis. This work represents the most comprehensive investigation of these network uncertainty propagation methods to date.
This work summarizes the findings of a reduced order model (ROM) study performed using Sierra ROM module Pressio_Aria on Sandia National Laboratories' (SNL) Crash-Burn L2 milestone thermal model with pristine geometry. Comparisons are made to full order model (FOM) results for this same Crash-Burn model using Sierra multiphysics module Aria.
The design of thermal protection systems (TPS), including heat shields for reentry vehicles, rely more and more on computational simulation tools for design optimization and uncertainty quantification. Since high-fidelity simulations are computationally expensive for full vehicle geometries, analysts primarily use reduced-physics models instead. Recent work has shown that projection-based reduced-order models (ROMs) can provide accurate approximations of high-fidelity models at a lower computational cost. ROMs are preferable to alternative approximation approaches for high-consequence applications due to the presence of rigorous error bounds. The following paper extends our previous work on projection-based ROMs for ablative TPS by considering hyperreduction methods which yield further reductions in computational cost and demonstrating the approach for simulations of a three-dimensional flight vehicle. We compare the accuracy and potential performance of several different hyperreduction methods and mesh sampling strategies. This paper shows that with the correct implementation, hyperreduction can make ROMs up to 1-3 orders of magnitude faster than the full order model by evaluating the residual at only a small fraction of the mesh nodes.
A projection-based reduced order model (pROM) methodology has been developed for transient heat transfer problems involving coupled conduction and enclosure radiation. The approach was demonstrated on two test problems of varying complexity. The reduced order models demonstrated substantial speedups (up to 185×) relative to the full order model with good accuracy (less than 3% L∞ error). An attractive feature of pROMs is that there is a natural error indicator for the ROM solution: the final residual norm at each time-step of the converged ROM solution. Using example test cases, we discuss how to interpret this error indicator to assess the accuracy of the ROM solution. The approach shows promise for many-query applications, such as uncertainty quantification and optimization. The reduced computational cost of the ROM relative to the full-order model (FOM) can enable the analysis of larger and more complex systems as well as the exploration of larger parameter spaces.
This work aims to advance computational methods for projection-based reduced-order models (ROMs) of linear time-invariant (LTI) dynamical systems. For such systems, current practice relies on ROM formulations expressing the state as a rank-1 tensor (i.e., a vector), leading to computational kernels that are memory bandwidth bound and, therefore, ill-suited for scalable performance on modern architectures. This weakness can be particularly limiting when tackling many-query studies, where one needs to run a large number of simulations. This work introduces a reformulation, called rank-2 Galerkin, of the Galerkin ROM for LTI dynamical systems which converts the nature of the ROM problem from memory bandwidth to compute bound. We present the details of the formulation and its implementation, and demonstrate its utility through numerical experiments using, as a test case, the simulation of elastic seismic shear waves in an axisymmetric domain. We quantify and analyze performance and scaling results for varying numbers of threads and problem sizes. Finally, we present an end-to-end demonstration of using the rank-2 Galerkin ROM for a Monte Carlo sampling study. We show that the rank-2 Galerkin ROM is one order of magnitude more efficient than the rank-1 Galerkin ROM (the current practice) and about 970 times more efficient than the full-order model, while maintaining accuracy in both the mean and statistics of the field.
Melting and flowing of aluminum alloys is a challenging problem for computational codes. Unlike most common substances, the surface of an aluminum melt exhibits rapid oxidation and elemental migration, and like a bag filled with water can remain 2-dimensionally unruptured while the metal inside is flowing. Much of the historical work in this area focuses on friction welding and neglects the surface behavior due to the high stress of the application. We are concerned with low-stress melting applications, in which the bag behavior is more relevant. Adapting models and measurements from the literature, we have developed a formulation for the viscous behavior of the melt based on an abstraction of historical measurement, and a construct for the bag behavior. These models are implemented and demonstrated in a 3D level-set multi-phase solver package, SIERRA/Aria. A series of increasingly complex simulation scenarios are illustrated that help verify implementation of the models in conjunction with other required model components like convection, radiation, gravity, and surface interactions.
We propose a nonlinear manifold learning technique based on deep convolutional autoencoders that is appropriate for model order reduction of physical systems in complex geometries. Convolutional neural networks have proven to be highly advantageous for compressing data arising from systems demonstrating a slow-decaying Kolmogorov n-width. However, these networks are restricted to data on structured meshes. Unstructured meshes are often required for performing analyses of real systems with complex geometry. Our custom graph convolution operators based on the available differential operators for a given spatial discretization effectively extend the application space of deep convolutional autoencoders to systems with arbitrarily complex geometry that are typically discretized using unstructured meshes. We propose sets of convolution operators based on the spatial derivative operators for the underlying spatial discretization, making the method particularly well suited to data arising from the solution of partial differential equations. We demonstrate the method using examples from heat transfer and fluid mechanics and show better than an order of magnitude improvement in accuracy over linear methods.
In order to impact design decisions and realize the full promise of high-fidelity computational tools, simulation results must be integrated at the earliest stages in the design process. This is particularly challenging when dealing with uncertainty and optimizing for system-level performance metrics as full-system models (often notoriously expensive and time-consuming to develop) are generally required to propagate uncertainties to system-level quantities of interest. Methods for propagating parameter and boundary condition uncertainty in networks of interconnected components hold promise for enabling design under uncertainty in real-world applications. These methods preclude the need for time consuming mesh generation of full-system geometries when changes are made to components or subassemblies. Additionally, they explicitly tie full-system model predictions to component/subassembly validation data which is valuable for qualification. This is accomplished by taking advantage of the fact that many engineered systems are inherently modular, being comprised of a hierarchy of components and subassemblies which are individually modified or replaced to define new system designs. We leverage this hierarchical structure to enable rapid model development and the incorporation of uncertainty quantification and rigorous sensitivity analysis earlier in the design process. The resulting formulation of the uncertainty propagation problem is iterative. We express the system model as a network of interconnected component models which exchange stochastic solution information at component boundaries. We utilize Jacobi iteration with Anderson acceleration to converge stochastic representations of system level quantities of interest through successive evaluations of component or subassembly forward problems. We publish our open-source tools for uncertainty propagation in networks remarking that these tools are extensible and can be used with any simulation tool (including arbitrary surrogate modeling tools) through the construction of a simple Python interface class. Additional interface classes for a variety of simulation tools are currently under active development. The performance of the uncertainty quantification method is determined by the number of iterations needed to achieve a desired level of accuracy. Performance of these networks for simple canonical systems from both a heat transfer and solid mechanics perspective are investigated; the models are examined with thermal and mechanical Dirichlet and Neumann type boundary conditions separately imposed and the impact of varying governing equations and boundary condition type on the performance of the networks is analyzed. The form of the boundary conditions is observed to have a large impact on the convergence rate with Neumann-type boundary conditions corresponding to significant performance degradation compared to the Dirichlet boundary conditions. Nonmonotonicity is observed in the solution convergence in some cases.
In this work, we revisit the classic problem of site percolation on a regular square lattice. In particular, we investigate the effect of quantization bias errors on percolation threshold predictions for large probability gradients and propose a mitigation strategy. We demonstrate through extensive computational experiments that the assumption of a linear relationship between probability gradient and percolation threshold used in previous investigations is invalid. Moreover, we demonstrate that, due to skewness in the distribution of occupation probabilities visited the average does not converge monotonically to the true percolation threshold. We identify several alternative metrics which do exhibit monotonic (albeit not linear) convergence and document their observed convergence rates.
Thermal protection system designers rely heavily on computational simulation tools for design optimization and uncertainty quantification. Because high-fidelity analysis tools are computationally expensive, analysts primarily use low-fidelity or surrogate models instead. In this work, we explore an alternative approach wherein projection-based reduced-order models (ROMs) are used to approximate the computationally infeasible high-fidelity model. ROMs are preferable to alternative approximation approaches for high-consequence applications due to the presence of rigorous error bounds. This work presents the first application of ROMs to ablation systems. In particular, we present results for Galerkin and least-squares Petrov-Galerkin ROMs of 1D and 2D ablation system models.
Melting and flowing of aluminum alloys is a challenging problem for computational codes. Unlike most common substances, the surface of an aluminum melt exhibits rapid oxidation and elemental migration, and like a bag filled with water can remain 2-dimensionally unruptured while the metal inside is flowing. Much of the historical work in this area focuses on friction welding and neglects the surface behavior due to the high stress of the application. We are concerned with low-stress melting applications, in which the bag behavior is more relevant. Adapting models and measurements from the literature, we have developed a formulation for the viscous behavior of the melt based on an abstraction of historical measurement, and a construct for the bag behavior. These models are implemented and demonstrated in a 3D level-set multi-phase solver package, SIERRA/Aria. A series of increasingly complex simulation scenarios are illustrated that help verify implementation of the models in conjunction with other required model components like convection, radiation, gravity, and surface interactions.
We present a novel graph convolutional layer that is conceptually simple, fast, and provides high accuracy with reduced overfitting. Based on pseudo-differential operators, our layer operates on graphs with relative position information available for each pair of connected nodes. Our layer represents a generalization of parameterized differential operators (previously shown effective for shape correspondence, image segmentation, and dimensionality reduction tasks) to a larger class of graphs. We evaluate our method on a variety of supervised learning tasks, including 2D graph classification using the MNIST and CIFAR-100 datasets and 3D node correspondence using the FAUST dataset. We also introduce a superpixel graph version of the lesion classification task using the ISIC 2016 challenge dataset and evaluate our layer versus other state-of-the-art graph convolutional network architectures.The new layer outperforms multiple recent architectures on graph classification tasks using the MNIST and CIFAR-100 superpixel datasets. For the ISIC dataset, we outperform all other graph neural networks examined as well as all of the submissions to the original ISIC challenge despite the best of those models having more than 200 times as many parameters as our model.
This milestone campaign was focused on coupling Sandia physics codes SIERRA low Mach module Fuego and RAMSES Boltzmann transport code Sceptre(Scefire). Fuego enables simulation of low Mach, turbulent, reacting, particle laden flows on unstructured meshes using CVFEM for abnormal thermal environments throughout SNL and the larger national security community. Sceptre provides simulation for photon, neutron, and charged particle transport on unstructured meshes using Discontinuous Galerkin for radiation effects calculations at SNL and elsewhere. Coupling these ”best of breed” codes enables efficient modeling of thermal/fluid environments with radiation transport, including fires (pool, propellant, composite) as well as those with directed radiant fluxes. We seek to improve the experience of Fuego users who require radiation transport capabilities in two ways. The first is performance. We achieve this through leveraging additional computational resources for Scefire, reducing calculation times while leaving unaffected resources for fluid physics. This approach is new to Fuego, which previously utilized the same resources for both fluid and radiation solutions. The second improvement enables new radiation capabilities, including spectral (banded) radiation, beam boundary sources, and alternate radiation solvers (i.e. Pn). This summary provides an overview of these achievements.
The goal of this milestone is to demonstrate effective coupling between the Sierra low-Mach module Fuego and the RAMSES Boltzmann transport (particle and radiation) code Sceptre.
Radiation heat transfer is an important phenomenon in many physical systems of practical interest. When participating media is important, the radiative transfer equation (RTE) must be solved for the radiative intensity as a function of location, time, direction, and wavelength. In many heat-transfer applications, a quasi-steady assumption is valid, thereby removing time dependence. The dependence on wavelength is often treated through a weighted sum of gray gases (WSGG) approach. The discrete ordinates method (DOM) is one of the most common methods for approximating the angular (i.e., directional) dependence. The DOM exactly solves for the radiative intensity for a finite number of discrete ordinate directions and computes approximations to integrals over the angular space using a quadrature rule; the chosen ordinate directions correspond to the nodes of this quadrature rule. This paper applies a projection-based model-reduction approach to make high-order quadrature computationally feasible for the DOM for purely absorbing applications. First, the proposed approach constructs a reduced basis from (high-fidelity) solutions of the radiative intensity computed at a relatively small number of ordinate directions. Then, the method computes inexpensive approximations of the radiative intensity at the (remaining) quadrature points of a high-order quadrature using a reduced-order model constructed from the reduced basis. Finally, this results in a much more accurate solution than might have been achieved using only the ordinate directions used to compute the reduced basis. One- and three-dimensional test problems highlight the efficiency of the proposed method.
Concurrent sound associated with very bright meteors manifests as popping, hissing, and faint rustling sounds occurring simultaneously with the arrival of light from meteors. Numerous instances have been documented with â '11 to â '13 brightness. These sounds cannot be attributed to direct acoustic propagation from the upper atmosphere for which travel time would be several minutes. Concurrent sounds must be associated with some form of electromagnetic energy generated by the meteor, propagated to the vicinity of the observer, and transduced into acoustic waves. Previously, energy propagated from meteors was assumed to be RF emissions. This has not been well validated experimentally. Herein we describe experimental results and numerical models in support of photoacoustic coupling as the mechanism. Recent photometric measurements of fireballs reveal strong millisecond flares and significant brightness oscillations at frequencies ≥40 Hz. Strongly modulated light at these frequencies with sufficient intensity can create concurrent sounds through radiative heating of common dielectric materials like hair, clothing, and leaves. This heating produces small pressure oscillations in the air contacting the absorbers. Calculations show that â '12 brightness meteors can generate audible sound at ∼25 dB SPL. The photoacoustic hypothesis provides an alternative explanation for this longstanding mystery about generation of concurrent sounds by fireballs.
The dispersion and connectivity of particles with a high degree of polydispersity is relevant to problems involving composite material properties and reaction decomposition prediction and has been the subject of much study in the literature. This work utilizes Monte Carlo models to predict percolation thresholds for a two-dimensional systems containing disks of two different radii. Monte Carlo simulations and spanning probability are used to extend prior models into regions of higher polydispersity than those previously considered. A correlation to predict the percolation threshold for binary disk systems is proposed based on the extended dataset presented in this work and compared to previously published correlations. A set of boundary conditions necessary for a good fit is presented, and a condition for maximizing percolation threshold for binary disk systems is suggested.
The discrete ordinates method is a popular and versatile technique for solving the radiative transport equation, a major drawback of which is the presence of ray effects. Mitigation of ray effects can yield significantly more accurate results and enhanced numerical stability for combined mode codes. When ray effects are present, the solution is seen to be highly dependent upon the relative orientation of the geometry and the global reference frame. This is an undesirable property. A novel ray effect mitigation technique of averaging the computed solution for various reference frame orientations is proposed.
Participating media radiation (PMR) in weapon safety calculations for abnormal thermal environments are too costly to do routinely. This cost may be s ubstantially reduced by applying reduced order modeling (ROM) techniques. The application of ROM to PMR is a new and unique approach for this class of problems. This approach was investigated by the authors and shown to provide significant reductions in the computational expense associated with typical PMR simulations. Once this technology is migrated into production heat transfer analysis codes this capability will enable the routine use of PMR heat transfer in higher - fidelity simulations of weapon resp onse in fire environments.
The common methods for finding the local radiative flux divergence in participating media through solution of the radiative transfer equation are outlined. The pros and cons of each method are discussed in terms of their speed, ability to handle spectral properties and scattering phenomena, as well as their accuracy in different ranges of media transport properties. The suitability of each method for inclusion in the energy equation to efficiently solve multi-mode thermal transfer problems is discussed. Finally, remaining topics needing research are outlined.
ASME 2016 Heat Transfer Summer Conference, HT 2016, collocated with the ASME 2016 Fluids Engineering Division Summer Meeting and the ASME 2016 14th International Conference on Nanochannels, Microchannels, and Minichannels
Radiation heat transfer is an important phenomenon in many physical systems of practical interest. When participating media is important, the radiative transfer equation (RTE) must be solved for the radiative intensity as a function of location, time, direction, and wavelength. In many heat transfer applications, a quasi-steady assumption is valid. The dependence on wavelength is often treated through a weighted sum of gray gases type approach. The discrete ordinates method is the most common method for approximating the angular dependence. In the discrete ordinates method, the intensity is solved exactly for a finite number of discrete directions, and integrals over the angular space are accomplished through a quadrature rule. In this work, a projection-based model reduction approach is applied to the discrete ordinates method. A small number or ordinate directions are used to construct the reduced basis. The reduced model is then queried at the quadrature points for a high order quadrature in order to inexpensively approximate this highly accurate solution. This results in a much more accurate solution than can be achieved by the low-order quadrature alone. One-, two-, and three-dimensional test problems are presented.
High-speed photometric observations of meteor fireballs have shown that they often produce high-amplitude light oscillations with frequency components in the kHz range, and in some cases exhibit strong millisecond flares. We built a light source with similar characteristics and illuminated various materials in the laboratory, generating audible sounds. Models suggest that light oscillations and pulses can radiatively heat dielectric materials, which in turn conductively heats the surrounding air on millisecond timescales. The sound waves can be heard if the illuminated material is sufficiently close to the observer’s ears. The mechanism described herein may explain many reports of meteors that appear to be audible while they are concurrently visible in the sky and too far away for sound to have propagated to the observer. This photoacoustic (PA) explanation provides an alternative to electrophonic (EP) sounds hypothesized to arise from electromagnetic coupling of plasma oscillation in the meteor wake to natural antennas in the vicinity of an observer.
Two of the most popular deterministic radiation transport methods for treating the angular dependence of the radiative intensity for heat transfer: The discrete ordinates and simplified spherical harmonics approximations are compared. A problem with discontinuous boundary conditions is included to evaluate ray effects for discrete ordinates solutions. Mesh resolution studies are included to ensure adequate convergence and evaluate the effects of the contribution of false scattering. All solutions are generated using finite element spatial discretization. Where applicable, any stabilization used is included in the description of the approximation method or the statement of the governing equations. A previous paper by the author presented results for a set of 2D benchmark problems for the discrete ordinates method using the PN-TN quadrature of orders 4, 6, and 8 as well as the P1, M1, and SP3 approximations. This paper expands that work to include the Lathrop-Carlson level symmetric quadrature of order up to 20 as well as the Lebedev quadrature of order up to 76 and simplified spherical harmonics of odd orders from 1 to 15. Two 3D benchmark problems are considered here. The first is a canonical problem of a cube with a single hot wall. This case is used primarily to demonstrate the potentially unintuitive interaction between mesh resolution, quadrature order, and solution error. The second case is meant to be representative of a pool fire. The temperature and absorption coefficient distributions are defined analytically. In both cases, the relative error in the radiative flux or the radiative flux divergence within a volume is considered as the quantity of interest as these are the terms that enter into the energy equation. The spectral dependence of the optical properties and the intensity is neglected.
The simplified spherical harmonics (SPn) approximation to the radiative transport equation (RTE) is a computationally efficient deterministic solution method that may be derived either as an asymptotic correction to the diffusion approximation or as a 3D analog to the 1D spherical harmonics (Pn) or discrete ordinates (Sn) approximations. It is used to approximate the effects of participating media radiation. In order to trust the output of a given implementation for a high consequence application, code verification activities must be undertaken to build confidence in the results generated. The method of manufactured solutions is a widely accepted code verification technique in which a solution is assumed and arbitrary source terms are derived such that the code should converge to the prescribed solution. This convergence rate is then confirmed. In this paper we consider the set of coupled PDEs representative of radiation/conduction problems. The RTE is approximated using the “canonical” SPn equations with Mark boundary conditions. All boundaries are diffuse and emissivities range from 0 to 1. A set of manufactured solutions are presented for 1D-planar, 2D-planar, 2D-axisymmetric, and 3D-radially symmetric geometries. These manufactured solutions are used to verify the convergence rate of the conduction and simplified spherical harmonics approximations implemented in Sierra Aria, a highly scalable thermal analysis code.
Thermal analysts address a wide variety of applications requiring the simulation of radiation heat transfer phenomena. There are gaps in the currently available modeling capabilities. Addressing these gaps would allow for the consideration of additional physics and increase confidence in simulation predictions. This document outlines a five year plan to address the current and future needs of the analyst community with regards to modeling radiation heat transfer processes. This plan represents a significant multi-year effort that must be supported on an ongoing basis.
The discrete ordinates method is a popular and versatile technique for deterministically solving the radiative transport which governs the exchange of radiant energy within a fluid or gas mixture. It is the most common 'high fidelity' technique used to approximate the radiative contribution in combined-mode heat transfer applications. A major drawback of the discrete ordinates method is that the solution of the discretized equations may involve nonphysical oscillations due to the nature of the discretization in the angular space. These ray effects occur in a wide range of problems including those with steep temperature gradients either at the boundary or within the medium, discontinuities in the boundary emissivity due to the use of multiple materials or coatings, internal edges or corners in non-convex geometries, and many others. Mitigation of these ray effects either by increasing the number of ordinate directions or by filtering or smoothing the solution can yield significantly more accurate results and enhanced numerical stability for combined mode codes. When ray effects are present, the solution is seen to be highly dependent upon the relative orientation of the geometry and the global reference frame. This is an undesirable property. A novel ray effect mitigation technique is proposed. By averaging the computed solution for various orientations, the number of ordinate directions may be artificially increased in a trivially parallelizable way. This increases the frequency and decreases the amplitude of the ray effect oscillations. As the number of considered orientations increases a rotationally invariant solution is approached which is quite accurate. How accurate this solution is and how rapidly it is approached is problem dependent. Uncertainty in the smooth solution achieved after considering a relatively small number of orientations relative to the rotationally invariant solution may be quantified.