Radial Void Distribution Research Articles

ON THE EFFECT OF FINE-SCALE RADIAL VOID DISTRIBUTIONS ON ASSEMBLY CRITICALITY AND PIN POWER DISTRIBUTION

The assumption that void fraction, and by extension coolant density, is uniform in the radial direction is a common approximation used in lattice physics simulations. In this study, models without uniform radial void fraction are used and lattice criticality and pin powers are investigated in two ways. One way uses hypothetical models that reflect extreme radial void distributions; modifications such as uniform radial pin enrichment and the removal of gadolinium rods are included in these models as well. Experimentally-determined boiling water reactor radial void distributions are also replicated in neutronics models using Serpent 2. It is found in the hypothetical models that the presence of gadolinium rods has a large effect on the interaction between lattice criticality and radial void distribution. It was also found that considering experimental radial void fraction distributions had the largest effect on the pin power of the rods containing gadolinium. Furthermore, it is observed that considering realistic radial void distributions, in general, decreased lattice criticality. The reason can be attributed that to the passive negative-feedback design of light water reactors. These are useful findings because calculation of more accurate peaking factors can lead to efficient and yet safer reactor operation.

A surrogate model based on sparse grid interpolation for boiling water reactor subchannel void distribution

Boiling water reactors are simulated using nodal diffusion core simulators which rely upon homogenized and condensed cross sections from a lattice physics code. In the lattice calculation, the void distribution is typically assumed to be uniform in the radial direction. To remove this assumption, a thermal hydraulic code can be coupled with a lattice physics code to include a radial void distribution in the cross sections. To minimize the additional computational costs, a surrogate model can be generated for the thermal hydraulic code. In this research, a surrogate model is generated for the thermal hydraulic code F-COBRA-TF using sparse grid interpolation. The surrogate model is tested on how well it can reproduce the F-COBRA-TF void distribution for various conditions on the ATRIUM 10 assembly. The surrogate model is found to be effective at reproducing the F-COBRA-TF void distribution and reducing the computational costs from the order of minutes to about a second. A coupling is created between the surrogate model and the lattice physics code APOLLO2-A. Including the void distribution in the lattice physics calculation is found to have a large effect on the gadolinium worth.

Neutronics modeling of bubbles in bubbly flow regime in boiling water reactors

Abstract This study mainly focused on the neutronics modeling of bubbles in bubbly flow in boiling water reactors. The bubble, ring and homogenous models were used for radial void fraction distribution. Effect of the bubble and ring models on the infinite multiplication factor and two-group flux distribution was investigated by comparing with the homogenous model. Square pitch unit cell geometry was used in the calculations. In the bubble model, spherical and non-spherical bubbles at random positions, sizes and shapes were produced by Monte Carlo method. The results show that there are significant differences among the proposed models from the viewpoint of physical interaction mechanism. For the fully-developed bubbly flow, k inf is overestimated in the ring model by about 720 ± 6 pcm with respect to homogeneous model whereas underestimated in the bubble model by about −65 ± 9 pcm with a standard deviation of 15 pcm. In addition, the ring model shows that the coolant must be separated into regions to properly represent the radial void distribution. Deviations in flux distributions principally occur in certain regions, such as corners. As a result, the bubble model in modeling the void fraction can be used in nuclear engineering calculations.

Assessment of the CUPID Code for Bubbly Flows in Horizontal Pipes

Two-phase flow in a horizontal pipe has a pronounced feature; that is, two-phase-flow parameters are highly nonsymmetric because gravity is perpendicular to the mean flow direction. Thus, three-dimensional analysis is necessary for the accurate prediction of two-phase flow in a horizontal pipe, such as the hot leg and cold leg of a pressurized water reactor and the pressure tubes in a CANDU reactor. In this study, we simulated bubbly flows in horizontal pipes using the CUPID code, which adopts a two-fluid, three-field model for two-phase flow. In the preliminary calculations, it was found that the particle-averaged two-fluid momentum equation, rather than the standard two-fluid momentum equation, predicts a physically reasonable slip ratio and nondrag forces, except turbulent dispersion forces have negligible effects on the radial void distribution when the particle-averaged two-fluid momentum equation is used. Based on the results, we selected the physical models and computational mesh for subsequent code assessment using various bubbly flow experiments in horizontal pipes. The turbulent dispersion force model was improved to take into account the large void fraction change at the top. The results of the code assessment show good predictions for the axial pressure drop, liquid velocity, and turbulent kinetic energy profile and predict reasonably well the effects of jl and jg on two-phase-flow parameters. However, additional studies are needed for more accurate prediction of the nonsymmetric distribution of gas velocity and turbulent kinetic energy.

Effects of superficial gas velocity and static bed height on gas-solid flow characteristics in a 60-meter-high transparent CFB riser

A 60-meter-high transparent circulating fluidized bed (CFB) cold experimental apparatus was constructed to experimentally study the axial/radial voidage distribution, and the axial/radial particle diameter distribution in the upper riser. The experiments indicated that the variation of the average voidage in the upper riser with superficial gas velocity could be divided into four successive stages. A modifiedcorrelation was proposed to predict the voidage in the upper riser more accurately. For the current 60m riser, there existed an optimal static bed height of 500mm which enabled the gas to exactly reach its saturation carrying capacity Gs∗ of 6.0kg/(m2s). The radial voidage distribution, which was verified to be in accord with dimensionless distribution (when the cross-sectional average voidage was larger than 0.9900), was influenced by the superficial gas velocity and static bed height. In the upper riser, the mean particle diameter varied little along the radial direction while decreased along the axial direction. In addition, it was verified that the current experimental data coincided well with the operational results of the Baima 600MW supercritical CFB (SCCFB) boiler. Implications of the experimental results for the design and operation of SCCFB boilers were discussed.

An integrated workflow for resolved-particle packed bed models with complex particle shapes

A promising workflow for computational generation and meshing of resolved-particle randomly packed beds of arbitrary-shaped particles is described. The workflow is based on an automated package that is developed for the Bullet Physics Library for packed bed generation, and on the shrink-wrap method for handling the meshing challenges of the particle contact areas. Packed bed properties such as radial voidage and particle angle distributions are validated against existing experimental data and theoretical methods in the literature. Furthermore, the accuracy of the generated mesh using the shrink-wrap technique is evaluated by calculating the bulk and radial voidage distribution, the pressure drop, and by velocity profile and heat transfer analysis using computational fluid dynamics (CFD) simulations. It is shown that the proposed workflow can speed up the process of the geometry and mesh generation while it maintains the structural features of the bed. Finally, applications of such geometries to fixed bed reaction engineering problems are presented to illustrate simulations that can be achieved using the new workflow.

Quantifying cluster dynamics to improve EMMS drag law and radial heterogeneity description in coupling with gas-solid two-fluid method

Quantification of multiscale heterogeneity is the key to the simulation of gas-solid two-phase flow. The energy-minimization multiscale (EMMS) model can be used at different scales to describe local and global heterogeneities as well as steady-state fluid dynamics of gas-solid fluidization. However, the same cluster diameter correlation based on energy dissipation was used in all cases, which may give a smaller cluster diameter than single particle diameter at low solids fluxes. In this paper, a description of the solids mass transfer between the dilute and dense phases in heterogeneous gas-solid flow is proposed to replace the correlation of cluster diameter to avoid some problems associated with the empirical calculation of the cluster diameter. This cluster description can facilitate the prediction of the drag coefficient at the scale of numerical cells in computational fluid dynamics (CFD) at extremely low solids fluxes and the radial heterogeneity in large-scale circulating fluidized bed (CFB) risers with downward particle velocities near the wall. It is integrated with two-fluid model (TFM) to simulate the fluid dynamics in an industrial-scale CFB riser accurately, which is also accelerated significantly by using the predicted radial voidage distribution as the initial condition of CFD.

CFD simulation of hydrodynamics and heat transfer for scale-up of the jetting fluidized beds

This paper presents a CFD modelling of hydrodynamics and heat transfer for scaling up the gas-solid jetting fluidized beds. Through coupling with energy conservation equation, a simple hydrodynamic model (Brandani and Zhang, 2006) is extended to predict the heat transfer between the gas and particle phases in a fluidized bed. A similitude method is established by nondimensionalizing the governing equations involved in the CFD model for fluidized beds. Numerical simulations are conducted in the platform of CFX 4.4, a commercial CFD code, together with user-defined FORTRAN subroutines. The controlling equations are verified in the fluidized bed with a pulse jet by using the penetration theory (Kuipers et al., 1992). The effect of jet on heat transfer is examined by introducing a continuous jet. The computational results show that local time-averaged heat transfer coefficient increases with an increase in solid thermal conductivity or with a decrease in jet gas velocity, particle size and nozzle size. Reasonable similarities of jet evolution, time-averaged radial voidage distribution and dimensionless heat transfer coefficient can be obtained in the standard, two-sized and five-sized fluidized beds when dimensionless parameters are matched.

A subchannel and CFD analysis of void distribution for the BWR fuel bundle test benchmark

The subchannel grade and microscopic void distributions in the NUPEC (Nuclear Power Engineering Corporation) BFBT (BWR Full-Size Fine-Mesh Bundle Tests) facility have been evaluated with a subchannel analysis code MATRA, a system code MARS and a CFD code CFX-10. Sixteen test series from five different test bundles were selected for the analysis of the steady-state subchannel void distributions. Four test cases for a high burn-up 8×8 fuel bundle with a single water rod were simulated using CFX-10 for the microscopic void distribution benchmark. Two transient cases, a turbine trip without a bypass as a typical power transient and a re-circulation pump trip as a flow transient, were also chosen for this analysis. It was found that the steady-state void distributions calculated by both the MATRA and MARS codes coincided well with the measured data in the range of thermodynamic qualities from 5 to 25%. The results of the transient calculations were also similar to each other and very reasonable. The CFD simulation reproduced the overall radial void distribution trend which produces less vapor in the central part of the bundle and more vapor in the periphery. However, the predicted variation of the void distribution inside the subchannels is small, while the measured one is large showing a very high concentration in the center of the subchannels. The variations of the void distribution between the center of the subchannels and the subchannel gap are estimated to be about 5–10% for the CFD prediction and more than 20% for the experiment.

Radial voidage variation in fixed beds of fuel wood pellets

Fixed beds of fuel wood are commonly found in numerous processes: storage and transportation, drying and thermal conversion such as combustion or gasification. Pellets in particular are mostly used as fuel for domestic heating boilers. The characterization of spatial voidage distribution is of great importance for flow and reactor modelling. The present study focuses on the radial porosity variations of cylindrical beds of commercially available wood pellets. The experimental procedure is based on the classical technique of consolidating packed beds with a resin. The radial voidage distribution of three different cylindrical beds is determined by image analysis of sections of the solidified packing. The results are discussed and summarized in a mathematical expression correlating the radial voidage distribution depending on packing core porosity and dimensionless distance from the tube wall.

Transition of Bubbly Flow in Vertical Tubes: Effect of Bubble Size and Tube Diameter

In a companion paper (“Modelling Bubbly Flow by Population Balance Technique Part I: Axial Flow Development and Its Transitions,” ASME J. Fluids Eng), a two fluid model along with a multiclass population balance technique has been used to find out comprehensive criteria for the transition from bubbly to slug flow, primarily through a study of axial flow development. Using the same basic model the transition mechanism has been investigated in the present paper covering a wide range of process parameters. Though the dominating rate of bubble coalescence during the axial development of the flow acts as the main cause for the transition to slug flow, the simultaneous transformation of the radial voidage pattern cannot be overlooked. Appearance of core, intermediate, wall, and two peaks are observed in the radial voidage distribution depending on the phase superficial velocities. A map has been developed indicating the boundaries of the above subregimes. It has been observed that not only the size of the bubbles entering the inlet plane but also the size distribution (monodispersion or bidispersion) changes the voidage peak and shifts the transition boundary. It is interesting to note that the bubbly flow only with a core peak void distribution transforms into slug flow with a change in the operating parameters. Transition boundary is also observed to shift with a change in the tube diameter. The simulation results have been compared with experimental data taken from different sources and very good agreements have been noted.

Effect of Subchannel Void Fraction Distribution on Lattice Physics Parameters for Boiling Water Reactor Fuel Bundles

In boiling water reactor (BWR) cores, the radial void distribution in fuel bundles is thought to deviate from uniform distribution. The effect of heterogeneity in the subchannel void fraction distribution, caused by the presence of Gd-poisoned and cold surfaces as well as control blades on BWR lattice physics parameters, has been evaluated. The cross-sectional void distributions in each axial plane of a fuel bundle are calculated using the subchannel thermal hydraulics code COBRAG. The rod power distributions to be fed to COBRAG are calculated using either the Monte Carlo code MCNP4C or the fuel lattice code TGBLA. Iterative methods consisting of COBRAG and MCNP4C (or TGBLA) are established. A set of test cases was generated for a typical BWR 8 × 8 fuel bundle. The results of the coupled MCNP4C and COBRAG method reveal that both Gd rods and control blade increase in worth due to the void heterogeneity, showing a maximum decrease in K∞ of ∼0.7%Δk/K∞ and ∞1.5%Δk/K∞, respectively, at moderator density conditions equivalent to ∼40% void fraction. With the capability of the coupled TGBLA and COBRAG method to deplete fuel bundles, the acceleration of Gd depletion was evaluated. The impacts on the burnup characteristics of K∞ reached ±0.6%ΔK∞ at maximum.

Near-wall porosity characteristics of fixed beds packed with wood chips

Packed beds of fuel wood chips are commonly found in thermal conversion processes such as combustion or gasification. Wood chips in particular are mostly used as fuel for small-scale domestic heating boilers but also for commercial-scale combustion units. The characterization of spatial voidage distribution inside the wood chip beds is of great importance for flow and reactor modelling. This study focuses on the radial porosity variations of cylindrical beds of three different types of commercially available wood chips including chips classified as G30 size class. The conventional technique of consolidating packed beds with a resin was chosen as the experimental procedure. The radial voidage distribution in different cylindrical beds is determined by image analysis of sections of the solidified packings. Additionally, a packing of monosized spheres was investigated in order to assess the selected procedure in comparison with widely available literature data for spheres. The results are discussed and summarized in a mathematical expression correlating the radial voidage distribution depending on average wood chip size, packing core porosity and dimensionless distance from the tube wall.

Effect of Subchannel Void Fraction Distribution on Lattice Physics Parameters for Boiling Water Reactor Fuel Bundles

In boiling water reactor (BWR) cores, the radial void distribution in fuel bundles is thought to deviate from uniform distribution. The effect of heterogeneity in the subchannel void fraction distribution, caused by the presence of Gd-poisoned and cold surfaces as well as control blades on BWR lattice physics parameters, has been evaluated. The cross-sectional void distributions in each axial plane of a fuel bundle are calculated using the subchannel thermal hydraulics code COBRAG. The rod power distributions to be fed to COBRAG are calculated using either the Monte Carlo code MCNP4C or the fuel lattice code TGBLA. Iterative methods consisting of COBRAG and MCNP4C (or TGBLA) are established. A set of test cases was generated for a typical BWR 8 × 8 fuel bundle. The results of the coupled MCNP4C and COBRAG method reveal that both Gd rods and control blade increase in worth due to the void heterogeneity, showing a maximum decrease in K∞ of ∼0.7%Δk/K∞ and ∞1.5%Δk/K∞, respectively, at moderator density conditions equivalent to ∼40% void fraction. With the capability of the coupled TGBLA and COBRAG method to deplete fuel bundles, the acceleration of Gd depletion was evaluated. The impacts on the burnup characteristics of K∞ reached ±0.6%ΔK∞ at maximum.

The effect of vibration on bed voidage behaviors in fluidized beds with large particles

The effects of vibration parameters, operating conditions and material properties on bed voidage were investigated using an optical fiber probe approach in a vibrating fluidized bed with a diameter of 148 mm. Variables studied included frequency (0-282 s-1), amplitude (0 mm-1 mm), bed height (0.1 m-0.4 m) as well as four kinds of particles (belonging to Geldart's B and D groups). The axial and radial voidage distribution with vibration is compared with that without vibration, which shows vibration can aid in the fluidization behaviors of particles. For a larger vibration amplitude, the vibration seriously affects bed voidage. The vibration energy can damp out for particle layers with increasing the bed height. According to analysis of experimental data, an empirical correlation for predicting bed voidage, giving good agreement with the experimental data and a deviation within ±15%, was proposed.

Three-dimensional features of void morphology in resin transfer molded composites

Detailed analyses of shape, size, and spatial variations of void morphology are presented for a disk-shaped, resin transfer molded (RTM), E-glass/epoxy composite. The disk is molded at constant injection rate and contains 17.5% E-glass random fiber mats. Voids throughout the composite are evaluated by microscopic image analysis of through-the-thickness and planar surfaces obtained from adjacent radial samples. The void content of 2.15% is obtained from the analysis of through-the-thickness images and believed to be representative of the actual void content in the studied part. Relatively large cylindrical voids are observed in cigar shapes in the planar surfaces, whereas these voids only appear as small irregular or elliptical voids on through-the-thickness surfaces. Along the radial direction, combined effects of void formation by mechanical entrapment and void mobility are shown to yield a complex radial void distribution. It is shown that fewer voids are trapped mechanically with increasing distance from the inlet and most of the medium and small voids that are mobile migrate towards the exit during resin injection. These findings are believed to be applicable not only to RTM, but generally to liquid composite molding processes with varying fluid front velocities.

Effect of Radial Void Distribution within Fuel Assembly on Assembly Neutronic Characteristics

The effect of radial subchannel-wise void distribution in a fuel assembly on assembly neutronic characteristics has been investigated using the assembly calculation code SRAC95 and the subchannel analysis code THERMIT2. With the iterative calculation of assembly calculation and the subchannel analysis (Method 1), subchannel-wise void fraction distribution, pin-power distribution and the infinite multiplication factor of the assembly are calculated. The results are compared with the result of the assembly calculation using uniform void distribution as input (Method 2). The calculation is performed for two assembly configurations in the present study: one is a fuel assembly that does not include a water rod (Case 1) and the other is the assembly that includes a water rod (Case 2). The differences in the infinite multiplication factor and pin-power peaking factor between the two methods are small in both cases. In typical BWR fuel assemblies that are investigated in the present study, the method that does not consider the radial subchannel-wise void fraction distribution within a fuel assembly (Method 2) is accurate enough for practical applications.

Effect of Radial Void Distribution within Fuel Assembly on Assembly Neutronic Characteristics.

Effect of Radial Void Distribution within Fuel Assembly on Assembly Neutronic Characteristics.

The Effect of Bubble Size on the Radial Distribution of Void Fraction in Two-Phase Flow in a Circular Tube

SIMMER-IV, a three-dimensional version of SIMMER-III, has been developed at JNC to study the safety of fast reactors mechanistically. SIMMER-IV was applied to the experimental analysis of bubbly flow to verify the models. The results of an experiment performed by Valukina et al. showed that the radial distribution of void fraction changes suddenly as the bubble size changes. In the present work, the analysis focuses on reproducing the change of the radial void distribution. The diffusion term, “lateral lift force,” and “wall force” were introduced in sequence into its momentum conservation equation. Naturally, the diffusion term improved the radial distribution of vertical velocity but did not explain the change of the radial void distribution in the experiment. Subsequent introduction of the lateral lift force increased the void fraction along the wall, but it did not change the radial void distribution as the bubble size changed. Finally, the wall force was introduced and, in accordance with the experimental results, the dependence of radial void distribution on the bubble size was proved. The behavior of a molten pool that is bubbly with steel steam plays an important role in the evaluation of LMFR severe accidents. This study is expected to improve the evaluation.

Analysis of the Void Distribution in a Circular Tube with the Two-Fluid Particle Interacthion Method

A particle interaction method called MPS (Moving Particle Semi-Implicit) has been developed in recent years, which formulates the differential operators in Navier-Stokes' equation as interactions between particles characterized by a kernel function and adopts a mesh-free algorithm. This method is suitable especially for treating fluid breakup. We have extended this method to a two-fluid (liquid-liquid and gas-liquid) system and introduced a potential-type surface tension to calculate the two-phase flow without experimental correlation. With this extended method, a several number of two-phase flow experiments were analyzed successfully as reported in our previous paper. Herein, as one of the verification studies, the experiment by Valukina et al. was analyzed to show that our method could reproduce the bubble size effect on the radial void distribution in a circular tube. The experiment showed that the radial void distribution changes drastically as the bubble size changes. Our previous work with SIMMER-IV code which has a general solver for multi-phase flows revealed that the “lateral lift force” and “wall force” should be introduced into the momentum conservation equation to reproduce the bubble size effect. We evaluated these forces using the velocities of particles calculated by our particle method and compared with the SIMMER-IV results.