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At least 73 records · Page 4

Effect of deposition rate on microstructure and mechanical properties of 17-4 PH stainless steel fabricated by laser engineered net shaping

Laser engineered net shaping (LENS) is an additive manufacturing technique for fabricating and repairing metallic components. However, the relationships between its process parameters and the resulting mechanical properties of alloys such as 17-4 precipitation-hardening (PH) stainless steel require further investigation to enable reliable application. This study examines the specific effect of LENS deposition rate on the microstructure and mechanical properties of 17-4 PH stainless steel. Specimens were fabricated at two different deposition rates (8.47 and 9.31 mm s−1), subjected to subsequent solution and H900 aging treatment, and then evaluated via tensile testing, hardness measurements, and microscopy. A higher deposition rate results in a finer grain structure but increased porosity, leading to greater ultimate tensile strength (∼1294 MPa) yet lower ductility (strain at failure ∼5.8%) compared to the slower deposition rate (∼1266 MPa, ∼9.0% strain). Hardness follows the same trend as tensile strength. Tensile fracture surfaces for both conditions exhibited a mixed mode of ductile dimples and brittle quasi-cleavage regions, with chromium/silicon oxide particles identified within dimples. Complementary finite element modeling indicates that small void fractions primarily reduce ductility by enhancing localized plasticity, with only a marginal decrease in tensile strength. These integrated experimental and numerical results elucidate the mechanical properties linked to deposition rate, providing insight into tailoring LENS processes to achieve desired properties of 17-4 PH stainless steel.

17-4 PH stainlesssteel↗

Modeling Synergistic Fuel Cell Membrane Degradation with Mitigating Effects of Cerium

During operation, polymer-electrolyte-membrane (PEM) fuel cells undergo mechanical and chemical degradation mechanisms, which behave synergistically and lead to accelerated membrane degradation over time. This study builds upon previous modeling work on mechanical degradation as described by a pinhole in the membrane and the effects of cerium on chemical degradation.1 By combining these two models, analysis can be carried out on the coupled degradation methods and how the mitigation effects of cerium disrupt the degradation cycle. The mechanical model represents a pinhole in the membrane using an effective void fraction, which allows for increased gas crossover through the membrane and impacts the membrane transport and mechanical properties. A microkinetic model for the chemical degradation is included in the model, including attack of the membrane polymer by hydroxyl radicals as well as the mitigation reaction for quenching of hydroxyl radicals with cerium. A concentrated solution theory approach is used to model the transport of cerium ions throughout the cell.2 The model results show how the location of cerium in the cell can be used to prevent chemical degradation. In addition, the model shows how cerium slows down the rate of pinhole growth by reducing the gas crossover and membrane thinning rate. Finally, the model can be used to optimize the distribution of cerium in the membrane and catalyst layers by balancing trade-offs between lowering degradation rates and decreasing fuel cell performance.

25 ENERGY STORAGE↗

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

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

97 MATHEMATICS AND COMPUTING↗

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↗

Small-scale validation tests for MFIX-Exa CFD-DEM

This report describes several bench-scale fluidization experiments that can be used to validate the CFD-DEM method as encapsulated in the MFIX-Exa code. The five cases considered are the cold-flow fluidized beds of Müller et al., Link et al. (spout-fluid), and Goldschmidt et al. (bi-disperse), the hot fluidized bed of Patil et al., and the adsorbing fluidized bed of Li et al. and Janssen. In most cases, MFIX-Exa with “standard” or “typical” CFD-DEM settings, the Gidaspow drag model, and the Gunn heat transfer provide a relatively good prediction of the quantities considered: mean void fraction profiles, mean velocity profiles, fluctuating velocity profiles, mean particle temperature and segregation index. These results, with other verification and validation tests reported elsewhere, contribute to a body of work providing confidence and credibility in CFD predictions from the MFIX-Exa code.

97 MATHEMATICS AND COMPUTING↗

MOSCATO Development and Integration in Fiscal Year 2025: Implementation of Multiphase, Multiphysics Modeling Capabilities for Molten Salt Systems

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 corrosion for molten salt systems. In FY25, significant developments were made to the code package, enhancing its capabilities for modeling all relevant phenomena within operating moltens salt reactors (MSRs). The developments and activities in FY25 included: 1. Implementation of Level-Set methods to enable modeling of single-bubble behavior in molten salts. In FY25, the Level-Set two-phase flow modeling implementation was improved to simulate single bubble behavior with molten salt media. The large density and viscosity ratios between typical gases and molten salt liquids present challenges for these types of numerical solvers. With enhancements to the pressure projection method, MOSCATO’s Level-Set solver was able to be successfully validated to experiments related to helium bubble rise in stagnant molten salt. The simulated bubble rising velocity showed reasonable good agreement with experimental measurements. The bubble shape and dynamics were also visually compared with experimental snapshots, demonstrating a good qualitative match. 2. Generation of mass transfer correlations for multiphase flow systems. To enable calculations of the tritium transport across the interface between gas bubbles and salt, we modeled high- Schmidt-number mass transfer around a sphere across a broad range of Reynolds numbers. The mesh near the sphere surface was highly refined to resolve steep concentration gradients caused by the low diffusion coefficient. Literature-based mass transfer correlations were compared with the numerical results, and modifications were proposed to improve agreement, particularly at higher Schmidt numbers. These mass transfer correlations were subsequently provided to other national laboratories to help enable high quality mass transfer simulations using lower-order solvers under development within the NEAMS program. 3. Preliminary implementation of a bubbly flow solver. To model bubbly flow in molten salt, we implemented a bubbly flow solver for void fractions less than 5%. To do so, an algebraic relative velocity model that assumes small bubbles with rapid momentum equilibration was added to MOSCATO to compute bubble velocities. Preliminary comparisons with experimental data showed reasonable agreement, and further improvements are underway. 4. Generation of mass transfer correlations for MSRE subchannel The Molten-Salt Reactor Experiment (MSRE) was a landmark historical project that demonstrated the feasibility of molten-salt reactor technology. The MSRE campaign also generated a significant body of experimental data and reports that continue to support molten-salt–related research. In this report, the MSRE core subchannel was used as the reference geometry for a mass transfer study performed with MOSCATO. The geometry and computational mesh were adapted from a previous study, providing adequate resolution for the relatively low Reynolds number in this case. Additional mesh refinement was applied to reach higher Schmidt numbers, enabling the derivation of a reliable mass-transfer correlation for the present scenario. 5. Simulations of oxygen ingressions into molten salt. In the previous fiscal year, we initiated a study to simulate oxygen ingression in stagnant salt. As oxygen enters the salt through its surface, it reacts with Ce 3+ to form solid CeO 2 and other reaction products. To more fully capture the complex diffusion-convection-reaction mechanisms, capabilities for modeling natural convection in the salt vessel were added. These were needed as the flow of the ingressed gas induced flow in the salt caused by surface shear and non-isothermal effects. With these updated physics in place, we were able to successfully reproduce the experimental results for the rate of change of CeCl 3 concentrations versus time. 6. Flow corrosion model validation. In FY24, MOSCATO’s corrosion model was validated against static corrosion experiments. In FY25, this work was extended to a flow corrosion experiment, where FLiNaK salt was driven by natural convection, with initial salt impurities to initiate corrosion. Despite uncertainties in parameters such as elemental diffusion coefficients in the alloy and unknown H + concentrations, the simulations achieved good agreement with experimental results, especially in predicting sample mass losses.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Measurement of Transport Properties of Woody Biomass Feedstock Particles Before and After Pyrolysis by Numerical Analysis of X-Ray Tomographic Reconstructions

Lignocellulosic biomass has a complex, species-specific microstructure that governs heat and mass transport during conversion processes. A quantitative understanding of the evolution of pore size and structure is critical to optimize conversion processes for biofuel and bio-based chemical production. Further, improving our understanding of the microstructure of biochar coproduct will accelerate development of its myriad applications. This work quantitatively compares the microstructural features and the anisotropic permeabilities of two woody feedstocks, red oak and Douglas fir, using X-ray computed tomography (XCT) before and after the feedstocks are subjected to pyrolysis. Quantitative analysis of the three-dimensional (3D) reconstructions allows for direct calculations of void fractions, pore size distributions and tortuosity factors. Next, 3D images are imported into an immersed boundary based finite volume solver to simulate gas flow through the porous structure and to directly calculate the principal permeabilities along longitudinal, radial, and tangential directions. The permeabilities of native biomass are seen to differ by three to four orders of magnitude in the different principal directions, but we find that this anisotropy is substantially reduced in the biochar formed during pyrolysis. The quantitative transport properties reported here enhance the ability of pyrolysis simulations to account for feedstock-specific effects and thereby provide a useful touchstone for the biorefining community.

09 BIOMASS FUELS↗

Methods of forming fuel rods comprising porous fuel materials

A method of forming a fuel rod for a nuclear reactor comprises disposing a powder comprising particles of a fuel material on a substrate, exposing the powder to energy from an energy source to form a first layer of a nuclear fuel, the first layer comprising inter-granular bonds between the particles of the fuel material, disposing additional powder comprising particles of the fuel material over the first layer of the nuclear fuel, and exposing the additional powder to energy from the energy source to form a second layer of the nuclear fuel and to form the nuclear fuel to have a void fraction greater than about 0.20, the second layer comprising inter-granular bonds between the additional powder and the first layer of the nuclear fuel. Related nuclear fuels comprising a porous structure, fuel rods, nuclear reactors, and methods are disclosed.

O'Brien, Robert C.↗

DEMONSTRATION OF A DATA-DRIVEN PHYSICS-BASED APPROACH FOR COMPUTATIONALLY EFFICIENT CFD PREDICTION OF TWO-PHASE BUBBLY FLOW

To realize efficient computational fluid dynamics (CFD) prediction of two-phase flow, a multi-scale physics-guided data-driven approach, Feature Similarity Measurement (FSM) technique was developed for error estimation in two-phase flow simulation using coarse-mesh CFD, to achieve a comparable accuracy as fine-mesh simulations with fast-running feature. By defining physics-guided parameters and variable gradients as physical features, FSM has the capability to capture the underlying local patterns in the coarse-mesh CFD simulation. Massive low-fidelity data and respective high-fidelity data are used to explore the underlying information relevant to the main simulation errors and the effects of phenomenological scaling. By learning from previous simulation data, a surrogate model using deep feedforward neural network (DFNN) can be developed and trained to estimate the simulation error of coarse-mesh CFD. In a demonstration case of two-phase bubbly flow, the DFNN model well captured and corrected the unphysical “peaks” in the velocity and void fraction profiles near the wall in the coarse-mesh configuration, even for extrapolative predictions. The research documented supports the feasibility of the physics-guided deep learning methods for coarse mesh CFD simulations which has a potential for the efficient industrial design.

42 ENGINEERING↗

The Modified Void Nucleation and Growth Model (MNAG) for Damage Evolution in BCC Ta

A void coalescence term was proposed as an addition to the original void nucleation and growth (NAG) model to accurately describe void evolution under dynamic loading. The new model, termed as modified void nucleation and growth model (MNAG model), incorporated analytic equations to explicitly account for the evolution of the void number density and the void volume fraction (damage) during void nucleation, growth, as well as the coalescence stage. The parameters in the MNAG model were fitted to molecular dynamics (MD) shock data for single-crystal and nanocrystalline Ta, and the corresponding nucleation, growth, and coalescence rates were extracted. The results suggested that void nucleation, growth, and coalescence rates were dependent on the orientation as well as grain size. Compared to other models, such as NAG, Cocks–Ashby, Tepla, and Tonks, which were only able to reproduce early or later stage damage evolution, the MNAG model was able to reproduce all stages associated with nucleation, growth, and coalescence. The MNAG model could provide the basis for hydrodynamic simulations to improve the fidelity of the damage nucleation and evolution in 3-D microstructures.

36 MATERIALS SCIENCE↗

Woven ceramic matrix composite surrogate model based on physics-informed recurrent neural network

A recurrent neural network (RNN) based surrogate model is developed to emulate the nonlinear constitutive behavior of woven ceramic matrix composites (CMCs) driven by matrix damage at multiple length scales. Physics-informed constraints are introduced into the surrogate model through regularization to ground the prediction in physics and improve its predictive capabilities. Training data is generated using the multiscale generalized method of cells (MSGMC) approach coupled with a matrix damage model. This coupling permits simulating the nonlinear behavior of woven CMCs based on constituent response at the micro-, meso-, and macroscales. The multiscale repeating unit cell is loaded under non-monotonic conditions including multiple load / unload cycles and tension / compression. The fiber volume fraction as well as the intra- and intertow void volume fractions are also varied in the generation of training data. Therefore, the RNN-based surrogate model is tasked with predicting, as a function of variable input strain sequence and fiber and void volume fractions, the resulting stress versus strain response while satisfying physical constraints such as positive semi-definiteness of the tangent stiffness matrix and linear elastic unloading. Further, the trained surrogate model effectively matches the stress versus strain response and successfully predicts the tangent modulus throughout the loading regime. Neural network based surrogate models can offer efficient alternatives to running computationally intensive multiscale material models to simulate the nonlinear response of large structural models. Therefore the presented work provides evidence towards the feasibility of developing, training, and running such models for CMCs with complex architectures, nonlinear multiaxial material response, and under non-monotonic loading conditions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Equivalent Properties of Interfacial Void Defects at the CFRTP-adhesive Interface and Their Detrimental Effects on the Bonding Performance of Metal-CFRTP Dissimilar Joints

This paper revealed the detrimental effects of micro-scale air interfacial voids on the debonding at the interface of carbon-fiber-reinforced polyphthalamide (CFRPPA) and thermoset adhesive, representing a weak adherend-adhesive interface, within a dissimilar joint made of an aluminum alloy and a CFRPPA. The reduced lap shear strength of the joint, due to different void area fractions at the CFRPPA-adhesive interface, can be computationally described by using equivalent interfacial properties in the modeling to avoid the explicit modeling of the micro-scale interfacial voids. Such equivalent interfacial properties (e.g., interfacial normal strength, etc.) was found to have a non-linear relationship with respect to interfacial void area fraction as well as lap shear strength. This work has practical applications by utilizing equivalent interfacial properties for the analytical and/or computational design(s) of adhesively bonded joints.

Qiao, Yao↗

A fusion relevant data-driven engineering void swelling model for 9Cr tempered martensitic steels

The UCSB database on cavity evolution in 9-12Cr tempered martensitic steels (TMS), includes the results for both dual heavy and helium ion (DII), and High Flux Isotope Reactor (HFIR) in situ helium injection (ISHI) neutron irradiations at 500°C. These results were combined with literature single ion and fission neutron irradiation data to derive a model for the void volume fraction, f v , as a function of displacements per atom (dpa) and transmutant helium concentrations in atomic parts per million (appm). The scientific foundation for the paper is described in a companion paper entitled “Cavity Evolution and Void Swelling in Dual Ion Irradiated Tempered Martensitic Steels”. Here, in this study, we show that f v (dpa, He/dpa) is described by the incubation dose, dpa i , for the onset of void growth, and the post-incubation growth rate, f v ’(%/dpa). Both dpa i and f v ’ decrease with increasing He/dpa at > ~ 5. The dpa i is also lower for the ISHI neutron irradiations at the same He/dpa. Single heavy ion and fission reactor neutron irradiations, with low He/dpa ratios, have a much larger dpa i . Based on a combined analysis of DII, single ion, ISHI and fission neutron data, we further show that the post-incubation f v data analyzed here have a common empirical curve shape, with f v ’ reaching up to ~ 0.2%/dpa at very high dpa. We also show that f v ’ can be predicted based on a physical model of defect partitioning between evolving sinks. At 500°C and fusion relevant He/dpa ≈ 10, the best-fit model predicts nominal swelling, S = f v /(1-f v ), of ~ 1.1, 4.9 and 16% at 50, 100 and 200 dpa, respectively. The physically motivated, data-driven model includes estimated uncertainties for both dpa i and f v ’.

36 MATERIALS SCIENCE↗

Carbide Particle Redistribution in U-10Mo Alloy during Hot and Cold Rolling Processes: Synthetic Microstructure-Based Finite-Element Approach

The influence of initial carbide particle distribution features on particle fracture and the evolution of stringer distribution within an alloy of uranium with 10 weight percent molybdenum during cold rolling was investigated in this study. This work will provide guidance to casting optimization work and identify actionable process changes to eliminate the surface features directly attributed to carbides. In a previous study, various synthetic microstructure-based finite-element (FE) models were generated with consideration of different parameters (i.e., particle shape, particle volume fraction, and particle distribution), and used to examine the effects of hot rolling on the microstructure evolution. In this study, microstructures after ~80% hot rolling were used as the initial microstructures for the subsequent cold rolling simulation. Plane-strain compression loading was employed in the FE models to simulate cold rolling with reductions from ~80% to ~94%. Stringer analyses with the consideration of particle fracture were then performed with the simulated cold rolling results. The results of void evolution analyses show that microstructures with elliptical particles incorporate a much larger (almost double) void volume fraction than those with circular particles, indicating that the elliptical particles are fractured more easily than the circular ones. The results from the fracture mode analyses show that, under the adopted simple compression loading assumption, almost all the particles (i.e., >99%) were fractured by tensile separation. The results of stringer analyses show that, during cold rolling, the stringer volume fractions increase substantially due to the particle fracture, especially for the microstructures with the elliptical particles, and that the stringer volume fractions from stringers comprising many particles tend to increase faster. The maximum stringer lengths for the microstructures with circular particles tend to remain constant or decrease during cold rolling, whereas those for elliptical particles tend to slightly increase after a slight decrease. The number of particles at the surface increases very rapidly due to particle fracture during cold rolling.

36 MATERIALS SCIENCE↗

A mechanistic damage model for solid oxide fuel cell ceramic materials - Part I: Constitutive modeling

A multiscale mechanistic damage model for solid oxide fuel cell (SOFC) ceramics that combines micromechanics of stiffness reduction due to material porosity change and microcracking with a continuum damage mechanics (CDM) description for the evolution of microcracks up to fracture is developed in this work. The model also accounts for volumetric swelling of the anode due to redox cycling. Porosity change and swelling during redox combined with normal operating thermomechanical loads could increase the stress, strain and damage distributions in SOFC stacks leading them to failure. The proposed model involves three governing parameters: (i) the porosity in terms of the pore or void volume fraction, (ii) material swelling magnitude prescribed at a given loading step, and (iii) the damage variable that describes microcracking caused by thermomechanical loads and swelling. Pores and microcracks in the ceramics are modeled as randomly distributed ellipsoidal inclusions with negligible stiffness by an Eshelby-Mori-Tanaka formulation combined with an inclusion orientation distribution method. Microcracking damage evolution is described by a CDM formulation. Volumetric swelling is treated in a similar way to thermal expansion in the constitutive relations. After validation and numerical checks, the damage model is used to analyze a simplified SOFC positive-electrode/electrolyte/negative-electrode (PEN) structure subjected a redox cycle in addition to thermomechanical loads experienced during normal operation of a SOFC stack.

30 DIRECT ENERGY CONVERSION↗

Effects of MOF linker rotation and functionalization on methane uptake and diffusion

The flexible degrees of freedom in metal–organic frameworks (MOFs) can have significant effects on guest molecule behavior. However, in the majority of studies applying molecular simulations to MOFs, the framework is assumed to be rigid in order to minimize computational cost. Here, in this work, we assess the significance of this assumption on a representative example of methane uptake and diffusion in UiO-66. We introduce an open-source code to modify MOFs through functionalization and linker rotation and we perform Grand Canonical Monte Carlo and molecular dynamics simulations of methane in each of the functionalized and linker-rotated derivatives of UiO-66. We find that linker rotation moderately influences methane uptake and significantly influences methane diffusion. Our assessment provides ranges of property values that serve as measures of uncertainty of these two properties associated with linker rotation. We further determine that void volume fraction and minimum pore size are the features that govern methane uptake and diffusion, respectively. These findings illustrate the impact of linker rotation on MOFs and provide design principles to guide future investigations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Fully Recyclable CFRP Particles (CRADA 519)

The proposed resin-enhanced materials, which utilize fully recycled CFRP (carbon-fiber-reinforced polymer) particles, are enabled by PARC's proprietary Chemically Linked Particles Networks (13 granted patents and patent applications). PNNL and PARC have collaborated to develop manufacturing methods, such as vacuum-assisted wet compression molding and filament winding, for fabricating fiber-reinforced composites with the PARC matrix. PNNL has conducted various mechanical, physical, and thermal characterizations to compare their differences between the composites with baseline and PARC matrices. Those characterizations include density, void volume fraction, optical micrography, uniaxial tension, four-point bending/flexure, interlaminar shear, coefficient of thermal expansion, glass transition temperature, and curing kinetics.

36 MATERIALS SCIENCE↗

Updated Void Catalogs of the SDSS DR7 Main Sample

Abstract We produce several public void catalogs using a volume-limited subsample of the Sloan Digital Sky Survey Data Release 7 (SDSS DR7). Using new implementations of three different void-finding algorithms, VoidFinder and two ZOBOV-based algorithms (VIDE and REVOLVER), we identify 1163, 531, and 518 cosmic voids with radii >10 h −1 Mpc, respectively, out to a redshift of z = 0.114 assuming a Planck 2018 cosmology, and 1184, 535, and 519 cosmic voids assuming a WMAP5 cosmology. We compute effective radii and centers for all voids and find none with an effective radius >54 h −1 Mpc. The median void effective radius is 15–19 h −1 Mpc for all three algorithms. We extract and discuss several properties of the void populations, including radial density profiles, the volume fraction of the catalog contained within voids, and the fraction of galaxies contained within voids. Using 64 mock galaxy catalogs created from the Horizon Run 4 N -body simulation, we compare simulated and observed void properties and find good agreement between the SDSS DR7 and mock catalog results.

79 ASTRONOMY AND ASTROPHYSICS↗