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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

A Conservative Finite-Volume Based Interface-Tracking Algorithm Using the Signed Distance Function

Methods for tracking an interface between two fluid phases are developed to ensure desired fluid properties, conservation, and stability are preserved in a finitevolume (FV) discretization. Here, the interface is tracked using a level set method where the signed distance function implicitly defines the interface. Marching methods are used to evaluate the value of the signed distance function, including a novel initialization method to initialize any implicit function to the signed distance function around sharp corners in the level set. Global conservation and consistency with a set of governing equations is enforced by a compression coefficient that measures the volumetric compression or expansion due to inaccuracies in the level set evaluation. A redistribution method is integrated into the volume correction to eliminate the small-cell instability while maintaining global conservation. This suite of methods is implemented and tested using static uniform velocity, and potential flow cases with multiple interface geometries. Results show these methods achieve up to second order accuracy, and are conservative. The application for these methods is intended to track the interface of a 3D printing filament in a finite-volume discretization of the all-speed Navier-Stokes equations.

42 ENGINEERING↗
NASA NTRS2003

Turbulent Mixing of Multiphase Flow

Thus we conduct numerical simulations of multiphase fluids stirred by two-dimensional turbulence to assess the possibility of self-similar drop size distribution in turbulence. In our turbulence simulations, we also explore the non-diffusive limit, where molecular mobility for the interface is vanishing. Special care is needed to transport the non-diffusive interface. Numerically, we use the particle level set method to evolve the interface. Instead of using the usual methods to calculate the surface tension force from the level set function, we reconstruct the interface based on phase- field modeling, and calculate the continuum surface tension forcing from the reconstructed interface.

Young, Y.-N.↗
DOE OSTI2025

Spectrally Stabilized Interface Capturing Formulation and Implementation in Nek5000/NekRS

This report documents the formulation of a novel level-set method for incompressible two-phase flows in the continuous Galerkin (CG) high order spectral element framework. The overall method hinges on a novel implementation of the spectral vanishing viscosity (SVV) operator for the stabilization of linear/non-linear hyperbolic problems. The multidimensional SVV convolution kernels, which in essence, have a similar effect as a high pass filter applied to the derivatives, are formulated by exploiting the tensor product form, analogous to the construction of the usual stiffness matrix system. The resulting kernels are directionally decoupled and ensure a linear, symmetric positive definite, elliptic matrix operator. The SVV formulation is demonstrated to provide a robust stabilizing mechanism through challenging linear and non-linear hyperbolic problems, including problems pertinent to the level-set formulation. The two-phase framework conceptualized herein is based on the conservative level-set (CLS) method which represents the interface between the fluids by the 0.5 iso-contour of the smoothed Heaviside function. The CLS method is augmented with a preconditioning procedure for interface normals using the signed distance function which precludes the manifestation of spurious oscillations in the vicinty of the interface. Further, the existing mixed explicit-implicit approach for the solution of Navier-Stokes equations in Nek5000, as described in Tomboulides et al, is augmented with a pressure coefficient splitting approach for the Poisson equation, which greatly accelerated the convergence of pressure solver for two-phase systems with large density ratio. The robustness and accuracy of the overall two-phase method is demonstrated through canonical challenging problems involving high density and viscosity ratios, with and without surface tension. The two-phase formulation is wholly implemented in Nek5000 and the SVV stabilization method is implemented in NekRS, which is the essential precursor to the two-phase framework, undergoing active development.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Pore Resolved Simulations of Joule Heating in Fibrous Media using an Embedded Boundary Method

Joule heating has been regarded as an energy-efficient and sustainable method for heating materials and gases at large scales. The modeling of local temperature effects at pore-resolved scales for such systems, however, has been difficult to achieve due to challenges in coupling thermo-chemical processes in complex porous media and in large representative volume elements (RVEs). To this end, we developed an electro-thermal model at the pore scale to study Joule heating effects in large heterogeneous systems with different microstructures. This was achieved using the level set method to implicitly delineate distinct regions within the domain, and an embedded boundary method to facilitate heat exchange across the fluid-solid interface. Moreover, we applied this method to investigate unsteady non-linear electro-thermal effects in non-woven fibrous graphite conductors for RVEs with characteristic lengths of 2 mm, with different fiber orientations, porosity (80% – 90%) and fiber diameters (10 – 20µm). The coupled equations were solved numerically and they produced peak temperatures greater than 2000 K resulting in heating rates as high as 80,000 K/s. Moreover, the results depended strongly on the microstructure of the fiber skeleton and current density. Geometries with large fibers (∼ 20µm) had the highest average and peak temperatures with the mean temperature increasing by 3.9 % while the peak temperature increased by 9.9 %. Anisotropic domains on the other hand had the lowest mean and peak temperatures with peak and mean temperatures of 2293 K and 1437.7K respectively representing a corresponding 12.1% and 5.1% drop in the temperatures. An increase in porosity from 80% to 90%, however, led to an increase in the peak temperature by 5.1%.

Joule heating↗
DOE OSTI2022

Advanced Finite-Volume Numerics and Source Term Assumptions for Kernel and G-Equation Modelling of Propane/Air Flames

Here G-Equation models represent propagating flame fronts with an implicit two-dimensional surface representation (level-set). Level-set methods are fast, as transport source terms for the implicit surface can be solved with finite-volume operators on the finite-volume domain, without having to build the actual surface. However, they include approximations whose practical effects are not properly understood. In this study, we improved the numerics of the FRESCO CFD code’s G-Equation solver and developed a new method to simulate kernel growth using signed distance functions and the analytical sphere-mesh overlap. We analyzed their role for simulating propane/air flames, using three well-established constant-volume configurations: a one-dimensional, freely propagating laminar flame; a disc-shaped, constant-volume swirl combustor; and torch-jet flame development through an orifice from a two-chamber device. We tested the explicit (sub-cycled) vs. implicit formulation for the standard transport operators (advection, diffusion, compressibility). In addition to the accurate flame swept-volume method for chemistry and species source term, we developed a more accurate estimator for the burnt/unburnt split cell composition. Then, we developed a signed-distance-function (SDF) based method which provides a more stable reinitialization of the level-set field at every time-step. We found that simplifying assumptions common to several G-Equation implementations, for straightforward terms such as compressibility and advection, lead to large errors in predicting the propagation of even laminar flames, with deviations up to ~300% in simulated vs. formulated flame speed. Conversely, the enhanced numerics enabled through the SDF field reinitialization and improved chemistry source term improve simulation stability and smooth flame propagation even with significantly larger solver time-steps.

42 ENGINEERING↗
DOE OSTI2022

Stress Birth and Death: Disruptive Computational Mechanics and Novel Diagnostics for Fluid-to-Solid Transitions

Many materials of interest to Sandia transition from fluid to solid or have regions of both phases coexisting simultaneously. Currently there are, unfortunately, no material models that can accurately predict this material response. This is relevant to applications that "birth stress" related to geoscience, nuclear safety, manufacturing, energy production and bioscience. Accurately capturing solidification and residual stress enables fully predictive simulations of the evolving front shape or final product. Accurately resolving flow of proppants or blood could reduce environmental impact or lead to better treatments for heart attacks, thrombosis, or aneurism. We will address a science question in this proposal: When does residual stress develop during the critical transition from liquid to solid and how does it affect material deformation? Our hypothesis is that these early phases of stress development are critical to predictive simulation of material performance, net shape, and aging. In this project, we use advanced constitutive models with yield stress to represent both fluid and solid behavior simultaneously. The report provides an abbreviated description of the results from our LDRD "Stress Birth and Death: Disruptive Computational Mechanics and Novel Diagnostics for Fluid-to-Solid Transitions," since we have written four papers that document the work in detail and which we reference. We give highlights of the work and describe the gravitationally driven flow visualization experiment on a model yield stress fluid, Carbopol, at various concentrations and flow rates. We were able to collapse the data on a single master curve by showing it was self-similar. We also describe the Carbopol rheology and the constitutive equations of interest including the Bingham-Carreau-Yasuda model, the Saramito model, and the HB-Saramito model including parameter estimation for the shear and oscillatory rheology. We present several computational models including the 3D moving mesh simulations of both the Saramito models and Bingham-Carreau-Yasuda (BCY) model. We also show results from the BCY model using a 3D level set method and two different ways of handling reduced order Hele-Shaw modeling for generalized Newtonian fluids. We present some first ever two-dimensional results for the modified Jeffries Kamani-Donley-Rogers constitutive equation developed during this project. We include some recent results with a successful Saramito-level set coupling that allows us to tackle problems with complex geometries like mold filling in a thin gap with an obstacle, without the need for remeshing or remapping. We report on some experiments for curing systems where fluorescent particles are used to track material flow. These experiments were carried out in an oven on Sylgard 184 as a model polymerizing system. We conclude the report with a summary of accomplishments and some thoughts on follow-on work.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Computational Fluid Dynamics (CFD) Simulations of Taylor Bubbles in Vertical and Inclined Pipes with Upward and Downward Liquid Flow

Summary Two-phase flow is a common occurrence in pipes of oil and gas developments. Current predictive tools are based on the mechanistic two-fluid model, which requires the use of closure relations to predict integral flow parameters such as liquid holdup (or void fraction) and pressure gradient. However, these closure relations carry the highest uncertainties in the model. In particular, significant discrepancies have been found between experimental data and closure relations for the Taylor bubble velocity in slug flow, which has been determined to strongly affect the mechanistic model predictions (Lizarraga-García 2016). In this work, we study the behavior of Taylor bubbles in vertical and inclined pipes with upward and downward flow using a validated 3D computational fluid dynamics (CFD) approach with level set method implemented in a commercial code. A total of 56 cases are simulated, covering a wide range of fluid properties, pipe diameters, and inclination angles: Eo ∈ [10, 700]; Mo ∈ [1×10–6, 5×103]; ReSL ∈ [–40, 10]; θ ∈ [5°, 90°]. For bubbles in vertical upward flows, the simulated distribution parameter, C0, is successfully compared with an existing model. However, the C0 values of downward and inclined slug flows where the bubble becomes asymmetric are shown to be significantly different from their respective vertical upward flow values, and no current model exists for the fluids simulated here. The main contributions of this work are (1) the relatively large 3D numerical database generated for this type of flow, (2) the study of the asymmetric nature of inclined and some vertical downward slug flows, and (3) the analysis of its impact on the distribution parameter, C0.

Engineering↗
DOE OSTI2024

MOSCATO Development and Integration in Fiscal Year 2024

MOSCATO (Molten Salt Chemistry and Transport) is a multiphysics code that provides high-fidelity, coupled simulations of fluid flow, heat transfer, mass transfer, chemistry, electrochemical phenomena, and alloy evolution for molten salt equipment. In FY24, significant developments were made to the code package, enhancing its capabilities in many aspects. The improvements and advancements can be summarized as follows: 1. Implementation of tritium transport capabilities and validation with experimental data: To enable modeling of tritium and other fission gases within MSRs, we implemented gas transport within MOSCATO via inclusion of couple mass transport equations within the salt and structural alloys. Comparisons to experimental data from literature showed good agreement with respect to tritium release rates. 2. Preliminary implementation of two-phase flow models in MOSCATO: To model tritium and other gases above their solubility limits, we implemented preliminary two-phase flow models within MOSCATO to account for bubble transport. The first model adopted was the Level-Set approach, which can handle the high void fraction regime, but with a requirement for high mesh resolution thus high computational expense. In this report, we present a verification of the Level-Set method using a simple benchmark case. We also performed a demonstration of the code as applied to an experimental case involving cover gas flow through salt in an experimental vessel. The second model adopted was the Eulerian-Eulerian dispersed flow model, which is computationally cheaper but limited to low void fraction regimes, such as bubbly flow. Validation and verification have not yet been performed for the Eulerian-Eulerian approach, but a preliminary implementation was completed. 3. Validation with static corrosion experiments: Static corrosion experimental data for stainless steel coupons within molten salts was used to further validate the corrosion model in MOSCATO. To do so, we leveraged the existing models in MOSCATO and simulated the sample mass loss and mass gain phenomena. Several ion species, including Cr 2+ , Fe 2+ and H + , were simulated in salt using the PNP solver, while Cr 0 and Fe 0 were simulated with a diffusion solver in stainless steel. The mass loss of the samples was compared with experimental data, and good agreement was achieved. These combined activities served to further expand the capabilities of MOSCATO and make it more generally applicable to the full range of phenomena that can control chemistry and corrosion in molten salt reactors.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS1996

Dynamical Modeling of Surface Tension

In a recent review it is said that free-surface flows 'represent some of the difficult remaining challenges in computational fluid dynamics'. There has been progress with the development of new approaches to treating interfaces, such as the level-set method and the improvement of older methods such as the VOF method. A common theme of many of the new developments has been the regularization of discontinuities at the interface. One example of this approach is the continuum surface force (CSF) formulation for surface tension, which replaces the surface stress given by Laplace's equation by an equivalent volume force. Here, we describe how CSF formulation might be made more useful. Specifically, we consider a derivation of the CSF equations from a minimization of surface energy as outlined by Jacqmin (1996). This reformulation suggests that if one eliminates the computation of curvature in terms of a unit normal vector, parasitic currents may be eliminated. For this reformulation to work, it is necessary that transition region thickness be controlled. Various means for this, in addition to the one discussed by Jacqmin (1996), are discussed.

Brackbill, Jeremiah U.↗
NASA NTRS2000

Marangoni Effects on Near-Bubble Microscale Transport During Boiling of Binary Fluid Mixtures

In earlier investigations, Marangoni effects were observed to be the dominant mechanism of boiling transport in 2-propanol/water mixtures under reduced gravity conditions. In this investigation we have examined the mechanisms of binary mixture boiling by exploring the transport near a single bubble generated in a binary mixture between a heated surface and cold surface. The temperature field created in the liquid around the bubble produces vaporization over the portion of its interface near the heated surface and condensation over portions of its interface near the cold surface. Experiments were conducted using different mixtures of water and 2-propanol under 1g conditions and under reduced gravity conditions aboard the KC135 aircraft. Since 2-propanol is more volatile than water, there is a lower concentration of 2-propanol near the hot surface and a higher concentration of 2-propanol near the cold plate relative to the bulk quantity. This difference in interface concentration gives rise to strong Marangoni effects that move liquid toward the hot plate in the near bubble region for 2-propanol and water mixtures. In the experiments in this study, the pressure of the test system was maintained at about 5 kPa to achieve the full spectrum of boiling behavior (nucleate boiling, critical heat flux and film boiling) at low temperature and heat flux levels. Heat transfer data and visual documentation of the bubble shape were extracted from the experimental results. In the 1-g experiments at moderate to high heat flux levels, the bubble was observed to grow into a mushroom shape with a larger top portion near the cold plate due to the buoyancy effect. The shape of the bubble was somewhat affected by the cold plate subcooling and the superheat of the heated surface. At low superheat levels for the heated surface, several active nucleation sites were observed, and the vapor stems from them merged to form a larger bubble. The generation rate of vapor is moderate in this regime and the bubble shape is cylindrical in appearance. In some instances, the bubble interface appeared to oscillate. At higher applied heat flux levels, the top of the bubble became larger, apparently to provide more condensing interface area adjacent to the cold plate. Increasing the applied heat flux ultimately led to dry-out of the heated surface, with conditions just prior to dryout corresponding to the maximum heat flux (CHF). A more stable bubble was observed when the system attained the minimum heat flux (for film boiling). In this regime, most of the surface under the bottom of the bubble was dry with nucleate boiling sometimes occuring around the contact perimeter of the bubble at heated surface. Different variations (e.g. gap between two plates, molar concentration of the liquid mixture) of the experiments were examined to determine parametric effects on the boiling process and to determine the best conditions for the KC135 reduced gravity tests. Variation of the gap was found to have a minor impact on the CHF. However, reducing the gap between the hot and cold surface was observed to significantly reduce the minimum heat flux for fixed molar concentration of 2-propanol. In the reduced gravity experiments aboard the KC135 aircraft, the bubble formed in the 6.4 mm gap was generally cylindrical or barrel shaped and it increased its extent laterally as the surface superheat increased. In reduced gravity experiments, dryout of the heated surface under the bubble was observed to occur at a lower superheated temperature than for 1g conditions. Observed features of the boiling process and heat transfer data under reduced gravity will be discussed in detail. The results of the reduced gravity experiments will also be compared to those obtained in comparable 1g experiments. In tandem with the experiments we are also developing a computational model of the transport in the liquid surrounding the bubble during the boiling process. The computational model uses a level set method to model motion of the interface. It will incorporate a macroscale treatment of the transport in the liquid gap between the surfaces and a microscale treatment of transport in the regions between the bubble interface and the solid surfaces. The features of the model will be described in detail. Future research directions suggested by the results to date will also be discussed.

V. Carey↗
NASA NTRS1997

Computational Modeling as a Design Tool in Microelectronics Manufacturing

Plans to introduce pilot lines or fabs for 300 mm processing are in progress. The IC technology is simultaneously moving towards 0.25/0.18 micron. The convergence of these two trends places unprecedented stringent demands on processes and equipments. More than ever, computational modeling is called upon to play a complementary role in equipment and process design. The pace in hardware/process development needs a matching pace in software development: an aggressive move towards developing "virtual reactors" is desirable and essential to reduce design cycle and costs. This goal has three elements: reactor scale model, feature level model, and database of physical/chemical properties. With these elements coupled, the complete model should function as a design aid in a CAD environment. This talk would aim at the description of various elements. At the reactor level, continuum, DSMC(or particle) and hybrid models will be discussed and compared using examples of plasma and thermal process simulations. In microtopography evolution, approaches such as level set methods compete with conventional geometric models. Regardless of the approach, the reliance on empricism is to be eliminated through coupling to reactor model and computational surface science. This coupling poses challenging issues of orders of magnitude variation in length and time scales. Finally, database development has fallen behind; current situation is rapidly aggravated by the ever newer chemistries emerging to meet process metrics. The virtual reactor would be a useless concept without an accompanying reliable database that consists of: thermal reaction pathways and rate constants, electron-molecule cross sections, thermochemical properties, transport properties, and finally, surface data on the interaction of radicals, atoms and ions with various surfaces. Large scale computational chemistry efforts are critical as experiments alone cannot meet database needs due to the difficulties associated with such controlled experiments and costs.

Meyyappan, Meyya↗
NASA NTRS2002

A geometric deformable model for echocardiographic image segmentation

Gradient vector flow (GVF), an elegant external force for parametric deformable models, can capture object boundaries from both sides. A new geometric deformable model is proposed that combines GVF and the geodesic active contour model. The level set method is used as the numerical method of this model. The model is applied for echocardiographic image segmentation.

NASA Program Biomedical Research and Countermeasur↗
NASA NTRS2013

Robust Maneuvering Envelope Estimation Based on Reachability Analysis in an Optimal Control Formulation

This paper discusses an algorithm for estimating the safe maneuvering envelope of damaged aircraft. The algorithm performs a robust reachability analysis through an optimal control formulation while making use of time scale separation and taking into account uncertainties in the aerodynamic derivatives. Starting with an optimal control formulation, the optimization problem can be rewritten as a Hamilton- Jacobi-Bellman equation. This equation can be solved by level set methods. This approach has been applied on an aircraft example involving structural airframe damage. Monte Carlo validation tests have confirmed that this approach is successful in estimating the safe maneuvering envelope for damaged aircraft.

optimal control↗
NASA NTRS2015

Level-Set Topology Optimization with Aeroelastic Constraints

Level-set topology optimization is used to design a wing considering skin buckling under static aeroelastic trim loading, as well as dynamic aeroelastic stability (flutter). The level-set function is defined over the entire 3D volume of a transport aircraft wing box. Therefore, the approach is not limited by any predefined structure and can explore novel configurations. The Sequential Linear Programming (SLP) level-set method is used to solve the constrained optimization problems. The proposed method is demonstrated using three problems with mass, linear buckling and flutter objective and/or constraints. A constraint aggregation method is used to handle multiple buckling constraints in the wing skins. A continuous flutter constraint formulation is used to handle difficulties arising from discontinuities in the design space caused by a switching of the critical flutter mode.

Dunning, Peter D.↗
NASA NTRS2019

Level Set Topology Optimization of Load Carrying Heat Dissipation Devices

In this paper, we introduce a level set method topology optimization method of structures subjected to coupled mechanical and thermal loads. Different examples considering compliance minimization and stress minimization under temperature and volume constraints, and mass minimization under stress and temperature constraints, are presented. The p-norm of the stress field and temperature field is used to approximate the maximum stress and temperature, respectively. The developed method is applied in the design of an L-bracket and a battery package. The results show that designs obtained by ignoring the thermal or structural constraints can result in high values of temperature or stress, respectively.

Kambampati, Sandilya↗
NASA NTRSDate not supplied

TPSAS-NF1676L-18502-DND

1. Aeroelastic tailoring with tow-steered composites 2. Aeroelastic tailoring with functionally-graded metals 3. Wing box topology optimization - Curvilinear rib/spar/stiffener placement - Cellular-based stringer topologies - Optimal topology of lightening holes within ribs/spars - 3D level set methods

Stanley R Cole↗
NASA NTRS2021

Analysis of Arc Welding Process in Space

This work is motivated by NASA plans to conduct welding experiments on the ISS. It is expected that deployment of welding and additive manufacturing technologies in the space environment has the potential to revolutionise how orbiting platforms are designed, manufactured, and assembled. However, the structure, composition and quality of a weld is extremely dependent on the environment and can be difficult to control in space. Shielding gases would also be tough to manage as gases behave differently in zero gravity and airless environments. Additional points of concern are related to the spatter and sparks dynamics in space. Therefore, there is a need for a more basic understanding of welding processes by computational modelling. To provide such an insight we developed state of art models of the ARC torch, droplet detachment and transfer, and the melt pool build up using magnetohydrodynamics approximation and level set method for two-phase liquid metal/-gas flow modelling. Two finite element models were built using 2D axisymmetric geometry in COMSOL Multiphysics®: (i) stationary model of the ARC torch and (ii) dynamical model of droplet detachment and transfer. Both models demonstrate reasonable agreement with earlier experimental observations and high sensitivity to the temperature dependence of the thermophysical parameters on the system materials. The models were used to provide physical insight into ARC welding in various environments and geometries. It was shown, in particular, that there is a significant probability of gas bubbles trapping in the meltpool and a possibility of unbounded wondering of sparks in the welding chamber in zero gravity. In addition, we estimated metal evaporation rate that may be hazardous in the confined environment of the ISS. These issues raise concern of quality of the weld and safety for ISS applications.

ARC welding↗
NASA NTRS2005

Method for implementation of recursive hierarchical segmentation on parallel computers

A method, computer readable storage, and apparatus for implementing a recursive hierarchical segmentation algorithm on a parallel computing platform. The method includes setting a bottom level of recursion that defines where a recursive division of an image into sections stops dividing, and setting an intermediate level of recursion where the recursive division changes from a parallel implementation into a serial implementation. The segmentation algorithm is implemented according to the set levels. The method can also include setting a convergence check level of recursion with which the first level of recursion communicates with when performing a convergence check.

Tilton, James C.↗