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DOE OSTI2019

Modeling curved interfaces without element‐partitioning in the extended finite element method

Summary In this paper, we model holes and material interfaces (weak discontinuities) in two‐dimensional linear elastic continua using the extended finite element method on higher‐order (spectral) finite element meshes. Arbitrary parametric curves such as rational Bézier curves and cubic Hermite curves are adopted in conjunction with the level set method to represent curved interfaces. Efficient computation of weak form integrals with polynomial integrands is realized via the homogeneous numerical integration scheme—a method that uses Euler's homogeneous function theorem and Stokes' theorem to reduce integration to the boundary of the domain. Numerical integration on cut elements requires the evaluation of a one‐dimensional integral over a parametric curve, and hence, the need to partition curved elements is eliminated. To improve stiffness matrix conditioning, ghost penalty stabilization and the Jacobi preconditioner are used. For material interface problems, we develop an enrichment function that captures weak discontinuities on spectral meshes. Taken together, we show through numerical experiments that these advances deliver optimal algebraic rates of convergence with h ‐refinement ( p =1,2,…,5) and exponential rates of convergence with p ‐refinement ( p =1,2,…,7) for elastostatic problems with holes and material inclusions on Cartesian p th‐order spectral finite element meshes.

Chin, Eric B.↗

DOE OSTI2015

A Kinetic Approach to Modeling the Manufacture of High Density Polyurethane Structural Foam: Foaming and Polymerization

This report details the study of PMDI structural foam and the development of a computational model to represent it. This polyurethane has a fast catalyst, such that foaming and polymerization occur simultaneously. The foam is over-packed to twice or more of its free rise density to reach the density of interest. Our approach is to combine model development closely with experiments to discover underlying physical phenomena, to parameterize models, and to validate the models once they have been developed. The model must be able to represent the expansion, filling of molds, curing, and final foam properties. PMDI is a chemically blown foam, where carbon dioxide is produced via the reaction of water and isocyanate. The isocyanate also reacts with polyol in a competing reaction, which produces the polymer. A new kinetic model is developed and implemented, which follows a simplified mathematical formalism that decouples these two reactions. The model predicts the polymerization reaction via condensation chemistry, where vitrification and glass transition temperature evolution must be included to correctly predict the temperature dependence of the kinetics. The foam gas generation kinetics are determined by tracking the molar concentration of both water and carbon dioxide. Understanding the thermal history and loads on the foam due to exothermicity and oven curing is very important to the results, since the kinetics and material properties are all sensitive to temperature. The conservation equations, including the equations of motion, an energy balance, and three rate equations are solved via a stabilized finite element method. We assume generalized-Newtonian rheology that is dependent on the extent of cure, gas fraction, and temperature. The conservation equations are combined with a level set method to determine the location of the free surface over time. Results from the model are compared to experimental flow visualization data and post-test X-ray computed tomography (CT) data for the density. Several geometries are investigated including a mock encapsulation part, two configurations of a mock structural part, and a bar geometry to specifically test the density model. We have found that the model predicts both average density and filling profiles well. However, it under predicts density gradients, especially in the gravity direction. Further model improvements are also discussed.

36 MATERIALS SCIENCE↗

DOE OSTI2015

A two-stage method for microcalcification cluster segmentation in mammography by deformable models

Purpose: Segmentation of microcalcification (MC) clusters in x-ray mammography is a difficult task for radiologists. Accurate segmentation is prerequisite for quantitative image analysis of MC clusters and subsequent feature extraction and classification in computer-aided diagnosis schemes. Methods: In this study, a two-stage semiautomated segmentation method of MC clusters is investigated. The first stage is targeted to accurate and time efficient segmentation of the majority of the particles of a MC cluster, by means of a level set method. The second stage is targeted to shape refinement of selected individual MCs, by means of an active contour model. Both methods are applied in the framework of a rich scale-space representation, provided by the wavelet transform at integer scales. Segmentation reliability of the proposed method in terms of inter and intraobserver agreements was evaluated in a case sample of 80 MC clusters originating from the digital database for screening mammography, corresponding to 4 morphology types (punctate: 22, fine linear branching: 16, pleomorphic: 18, and amorphous: 24) of MC clusters, assessing radiologists’ segmentations quantitatively by two distance metrics (Hausdorff distance—HDIST{sub cluster}, average of minimum distance—AMINDIST{sub cluster}) and the area overlap measure (AOM{sub cluster}). The effect of the proposed segmentation method on MC cluster characterization accuracy was evaluated in a case sample of 162 pleomorphic MC clusters (72 malignant and 90 benign). Ten MC cluster features, targeted to capture morphologic properties of individual MCs in a cluster (area, major length, perimeter, compactness, and spread), were extracted and a correlation-based feature selection method yielded a feature subset to feed in a support vector machine classifier. Classification performance of the MC cluster features was estimated by means of the area under receiver operating characteristic curve (Az ± Standard Error) utilizing tenfold cross-validation methodology. A previously developed B-spline active rays segmentation method was also considered for comparison purposes. Results: Interobserver and intraobserver segmentation agreements (median and [25%, 75%] quartile range) were substantial with respect to the distance metrics HDIST{sub cluster} (2.3 [1.8, 2.9] and 2.5 [2.1, 3.2] pixels) and AMINDIST{sub cluster} (0.8 [0.6, 1.0] and 1.0 [0.8, 1.2] pixels), while moderate with respect to AOM{sub cluster} (0.64 [0.55, 0.71] and 0.59 [0.52, 0.66]). The proposed segmentation method outperformed (0.80 ± 0.04) statistically significantly (Mann-Whitney U-test, p < 0.05) the B-spline active rays segmentation method (0.69 ± 0.04), suggesting the significance of the proposed semiautomated method. Conclusions: Results indicate a reliable semiautomated segmentation method for MC clusters offered by deformable models, which could be utilized in MC cluster quantitative image analysis.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2015

Virtual Flow Simulator

Virtual Flow Simulator (VFS) is a state-of-the-art computational fluid mechanics (CFD) package that is capable of simulating multi-physics/multi-phase flows with the most advanced turbulence models (RANS, LES) over complex terrains. The flow solver is based on the Curvilinear Immersed Boundary (CURVIB) method to handle geometrically complex and moving domains. Different modules of the VFS package can provide different simulation capabilities for specific applications ranging from the fluid-structure interaction (FSI) of solid and deformable bodies, the two-phase free surface flow solver based on the level set method for ocean waves, sediment transport models in rivers and the large-scale models of wind farms based on actuator lines and surfaces. All numerical features of VFS package have been validated with known analytical and experimental data as reported in the related journal articles. VFS package is suitable for a broad range of engineering applications within different industries. VFS has been used in different projects with applications in wind and hydrokinetic energy, offshore and near-shore ocean studies, cardiovascular and biological flows, and natural streams and river morphodynamics. Over the last decade, the development of VFS has been supported and assisted with the help of various United States companies and federal agencies that are listed in the sponsor lists. In this version, VFS-Wind contains all the necessary modeling tools for wind energy applications, including land-based and offshore wind farms. VFS is highly scalable to run on either desktop computers or high performance clusters (up to 16,000 CPUs). This released version comes with a detailed user’s manual and a set of case studies designed to facilitate the learning of the various aspects of the code in a comprehensive manner. The included documentation and support material has been elaborated in a collaboration effort with Sandia National Labs under the contract DE-EE0005482. The VFS-Wind source code is distributed under the GNU General Public License (GPL 2.0), offering to the community the flexibility to use and expand the capabilities of the package. We note that future publications including academic journals that result from the use of VFS must be cited appropriately under the GPL v.2 license agreement.

Yang, Xiaolei↗

DOE OSTI2015

Virtual Flow Simulator

Calderer, Antoni↗

DOE OSTI2017

An immersed boundary method for fluid–structure interaction with compressible multiphase flows

This paper presents a two-dimensional immersed boundary method for fluid–structure interaction with compressible multiphase flows involving large structure deformations. This method involves three important parts: flow solver, structure solver and fluid–structure interaction coupling. In the flow solver, the compressible multiphase Navier–Stokes equations for ideal gases are solved by a finite difference method based on a staggered Cartesian mesh, where a fifth-order accuracy Weighted Essentially Non-Oscillation (WENO) scheme is used to handle spatial discretization of the convective term, a fourth-order central difference scheme is employed to discretize the viscous term, the third-order TVD Runge–Kutta scheme is used to discretize the temporal term, and the level-set method is adopted to capture the multi-material interface. In this work, the structure considered is a geometrically non-linear beam which is solved by using a finite element method based on the absolute nodal coordinate formulation (ANCF). The fluid dynamics and the structure motion are coupled in a partitioned iterative manner with a feedback penalty immersed boundary method where the flow dynamics is defined on a fixed Lagrangian grid and the structure dynamics is described on a global coordinate. We perform several validation cases (including fluid over a cylinder, structure dynamics, flow induced vibration of a flexible plate, deformation of a flexible panel induced by shock waves in a shock tube, an inclined flexible plate in a hypersonic flow, and shock-induced collapse of a cylindrical helium cavity in the air), and compare the results with experimental and other numerical data. The present results agree well with the published data and the current experiment. Finally, we further demonstrate the versatility of the present method by applying it to a flexible plate interacting with multiphase flows.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2015

TU-CD-304-05: 4Ï€ Non-Coplanar Radiotherapy: From Mathematical Modeling to Clinical Implementation

Purpose: To develop and clinically implement 4π radiotherapy, an inverse optimization platform that maximally utilizes non-coplanar intensity modulated radiotherapy (IMRT) beams to significantly improve critical organ sparing. Methods: A 3D scanner was used to digitize the human and phantom subject surfaces, which were positioned in the computer assisted design (CAD) model of a TrueBeam machine to create a virtual geometrical model, based on which, the feasible beam space was calculated for different tumor locations. Beamlets were computed for all feasible beams using convolution/superposition. A column generation algorithm was employed to optimize patient specific beam orientations and fluence maps. Optimal routing through all selected beams were calculated by a level set method. The resultant plans were converted to XML files and delivered to phantoms in the TrueBeam developer mode. Finally, 4π plans were recomputed in Eclipse and manually delivered to recurrent GBM patients. Results: Compared to IMRT utilizing manually selected beams and volumetric modulated arc therapy plans, markedly improved dosimetry was observed using 4π for the brain, head and neck, liver, lung, and prostate patients. The improvements were due to significantly improved conformality and reduced high dose spillage to organs mediolateral to the PTV. The virtual geometrical model was experimentally validated. Safety margins with 99.9% confidence in collision avoidance were included to the model based model accuracy estimates determined via 300 physical machine to phantom distance measurements. Automated delivery in the developer mode was completed in 10 minutes and collision free. Manual 4 π treatment on the GBM cases resulted in significant brainstem sparing and took 35–45 minutes including multiple images, which showed submillimeter cranial intrafractional motion. Conclusion: The mathematical modeling utilized in 4π is accurate to create and guide highly complex non-coplanar IMRT treatments that consistently and significantly outperform human-operator-created plans. Deliverability of such plans is clinically demonstrated. This work is funded by Varian Medical Systems and the NSF Graduate Research Fellowship DGE-1144087.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2017

A sharp interface method for compressible liquid–vapor flow with phase transition and surface tension

The numerical approximation of non-isothermal liquid–vapor flow within the compressible regime is a difficult task because complex physical effects at the phase interfaces can govern the global flow behavior. We present a sharp interface approach which treats the interface as a shock-wave like discontinuity. Any mixing of fluid phases is avoided by using the flow solver in the bulk regions only, and a ghost-fluid approach close to the interface. The coupling states for the numerical solution in the bulk regions are determined by the solution of local two-phase Riemann problems across the interface. The Riemann solution accounts for the relevant physics by enforcing appropriate jump conditions at the phase boundary. A wide variety of interface effects can be handled in a thermodynamically consistent way. This includes surface tension or mass/energy transfer by phase transition. Moreover, the local normal speed of the interface, which is needed to calculate the time evolution of the interface, is given by the Riemann solution. The interface tracking itself is based on a level-set method. The focus in this paper is the description of the two-phase Riemann solver and its usage within the sharp interface approach. One-dimensional problems are selected to validate the approach. Finally, the three-dimensional simulation of a wobbling droplet and a shock droplet interaction in two dimensions are shown. In both problems phase transition and surface tension determine the global bulk behavior.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017

Level set topology optimization of structural problems with interface cohesion

Summary This paper presents a finite element topology optimization framework for the design of two‐phase structural systems considering contact and cohesion phenomena along the interface. The geometry of the material interface is described by an explicit level set method, and the structural response is predicted by the extended finite element method. In this work, the interface condition is described by a bilinear cohesive zone model on the basis of the traction‐separation constitutive relation. The non‐penetration condition in the presence of compressive interface forces is enforced by a stabilized Lagrange multiplier method. The mechanical model assumes a linear elastic isotropic material, infinitesimal strain theory, and a quasi‐static response. The optimization problem is solved by a nonlinear programming method, and the design sensitivities are computed by the adjoint method. The performance of the presented method is evaluated by 2D and 3D numerical examples. The results obtained from topology optimization reveal distinct design characteristics for the various interface phenomena considered. In addition, 3D examples demonstrate optimal geometries that cannot be fully captured by reduced dimensionality. The optimization framework presented is limited to two‐phase structural systems where the material interface is coincident in the undeformed configuration, and to structural responses that remain valid considering small strain kinematics. Copyright © 2017 John Wiley & Sons, Ltd.

Behrou, Reza↗

DOE OSTI2017

Numerical comparison of bubbling in a waste glass melter

Radioactive tank waste is scheduled for vitrification at the Hanford Tank Waste Treatment and Immobilization Plant, also known as the Vit Plant, being constructed at the Hanford Site. Testing of the pilot-scale, joule-heated DuraMelter 1200 at the Vitreous State Laboratory has shown that bubbling increases the melt rate, and as a result, melter throughput. Computational fluid dynamics (CFD) models of this pilot-scale waste glass melter were developed to improve our understanding of the processes that occur within the melter to aid in process optimization and troubleshooting of the Vit Plant melters. Unfortunately, model validation is complicated by the difficulty of obtaining suitable experimental data for operational melters attributed to the large-scale, radioactivity and high temperatures at which these melters are operated. This study focuses on confirming the fidelity of the CFD models to accurately reproduce the bubbling behavior. Because of the paucity of experimental data at the resolution required for CFD validation, a code-to-code comparison was used to evaluate two common approaches for simulating flows of immiscible fluids on numerical grids and resolving multiphase interfaces. Here, the volume of fluid and level set methods are used to track the dynamically evolving interfaces between the molten glass and the air bubbles. To aid in the verification of the results of these codes, a comparison of the bubble behavior, growth, and frequency of bubble generation are presented and a grid convergence study is performed for the two approaches. In addition to comparing the numerical results to available experimental data and observations from pilot-scale testing, the results are evaluated in relation to laboratory experiments with bubbles injected into viscous fluids, empirical correlations obtained from the published literature, and the basic laws of fluid dynamics. Furthermore, the results of this work can assist in validating waste glass melter models and provide a better understanding of the flow patterns within the WTP melters.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗

DOE OSTI2017

A broadly-applicable unified closure relation for Taylor bubble rise velocity in pipes with stagnant liquid

Taylor bubble velocity in slug flow is a closure relation which significantly affects the prediction of liquid holdup (or void fraction) and pressure gradient in mechanistic models of slug flow for oil and gas pipe applications. In this work, we use a validated Computational Fluid Dynamics (CFD) approach to simulate the motion of Taylor bubbles in pipes; the interface is tracked with a Level-Set method implemented in a commercial code. A large numerical database is generated covering the most ample range of fluid properties and pipe inclination angles explored to date (Eo ∊ [10, 700],Mo ∊ [1 x 10 -6 , 5 x 10 3 , and θ ∊ [0°, 90°]). A unified Taylor bubble rise velocity correlation is extracted from that database. The new correlation predicts the numerical database with 8.6% absolute average relative error and a coefficient of determination R 2 = 0.97 and other available experimental data with 13.0% absolute average relative error and R 2 = 0.84 outperforming existing correlations and models.

Mechanics↗

DOE OSTI2015

Maximum probability domains for the analysis of the microscopic structure of liquids

We introduce the concept of maximum probability domains (MPDs), developed in the context of the analysis of electronic densities, in the study of the microscopic spatial structures of liquids. The idea of locating a particle in a three dimensional region, by determining the domain where the probability of finding that, and only that, particle is maximum, gives an interesting characterization of the local structure of the liquid. The optimization procedure, required for the search of the domain of maximum probability, is carried out by the implementation of the level set method. Results for a couple of case studies are presented, to illustrate the structure of liquid water at ambient conditions and upon increasing pressure from the point of view of MPDs and to compare the information encoded in the solvation shells of sodium in water with, once again, that extracted from the MPDs.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2014

TH-E-17A-11: Tracking Tumor’s Boundary in MV Image Sequences for Image-Guided Radiation Therapy

Purpose: To develop a level set method (LSM)-based algorithm to track the tumor’s boundary in MV image sequences for image-guided radiation therapy (IGRT). Method: Four MV image sequences, each of which consists of 100 frames at frame rate of 7.5 Hz, are acquired by using the electronic portal imaging device (EPID) (Varian Medical Systems, Pal Alto, USA) during the treatment of lung cancer. In the first frame of each sequence, we roughly delineate an initial contour of the target tumor by hand. Using a LSM-based algorithm, the initial contour can automatically shape itself to fit the tumor, and eventually detect the tumor’s boundary. We then employ the tumor’s boundary obtained from the previous frame as the initial contour in the subsequent frame, so that the LSM-based method can drive this initial contour to the tumor’s boundary quickly and fulfill a tracking task. Results: The proposed method has been evaluated on four MV image sequences. The mean tracking errors were 0.23, 0.29, 0.37, and 1.18 mm, and their corresponding standard deviations were 0.97, 0.75, 1.2 and 1.48 mm, respectively. Conclusion: Compared with conventional tumor tracking techniques, the proposed system is capable not only of tracking the tumor’s position, but also of detecting the tumor’s boundary varying with the respiration during the treatment. Considering current radiation therapy technique, for example, dynamical multi-leaf collimator (DMLC) has been widely applied in clinical treatment, this study indicates the potential for significant accuracy improvement in radiation therapy. This work was partially supported by a research grant from Varian Medical Systems (Palo Alto, California)

60 APPLIED LIFE SCIENCES↗

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 OSTI2013

HERMES Model Modifications and Applications 2012

HERMES was developed to meet requirements for a model to describe explosive response to impacts that do not produce prompt detonation, but can include delayed detonations such as DDT and XDT. Such response is termed High Explosive Violent Response (HEVR). The HERMES model includes a constitutive description of strength as a function of pressure, strain-rate, strain, and ambient temperature; the development of damage including fragmentation and porosity; the conditions leading to ignition; the propagation of a burning reaction through the volume of damaged explosive; the burn-up of the damaged and undamaged explosive; and the development of detonation using the Computational Reaction Evolution dependent on Entropy (S) and Time (CREST) detonation model. CREST can distinguish gradual pressure increases from shock waves, and also predict the increase in shock sensitivity to detonation that results from increased porosity. This year HERMES has been implemented as a User Defined Function in ALE 3D. As a result, modifications to the model can be implemented in a timely fashion asynchronously from the ALE 3D distribution process. There are differences between the implementation of HERMES in ALE 3D and the implementation in LS DYNA. The major difference is the propagation of an ignition front from an element that has started to burn. In LS DYNA, the time at which an element begins to burn is based on the minimum line-of-sight distance between the element and any previously ignited element. In ALE 3D the time to burn is based on a level-set method that propagates the ignition front from all elements that were previously ignited. The ALE 3D implementation modifies the time of ignition when element deformation changes the distance from the element to the source. The LS DYNA implementation does not. There are also differences in the implementation of artificial viscosity, which is important for CREST since the artificial viscosity increases the element entropy in a shock. In general, however, the differences have proven minor. In collaboration with the Atomic Weapons Establishment, UK (AWE), we have characterized two additional explosives – PETN and Composition B, a mixture of 60% RDX and 40% TNT by weight. Applications of HERMES to these explosives are described below.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

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↗