Variant Porosity Pebble Bed Reactor Core Thermal Hydraulic Simulation

This report documents the work completed on the X-PREX facility under NEUP Project 11- 3172. This project seeks to demonstrate the viability of pebble fuel handling and reactivity control for fluoride salt-cooled high-temperature reactors (FHRs). The research results also improve the understanding of pebble motion in helium-cooled reactors, as well as the general, fundamental understanding of low-velocity granular flows. Successful use of pebble fuels in with salt coolants would bring major benefits for high-temperature reactor technology. Pebble fuels enable on-line refueling and operation with low excess reactivity, and thus simpler reactivity control and improved fuel utilization. If fixed fuel designs are used, the power density of salt- cooled reactors is limited to 10 MW/m3 to obtain adequate duration between refueling, but pebble fuels allow power densities in the range of 20 to 30 MW/m3. This can be compared to the typical modular helium reactor power density of 5 MW/m3. Pebble fuels also permit radial zoning in annular cores and use of thorium or graphite pebble blankets to reduce neutron fluences to outer radial reflectors and increase total power production. Combined with high power conversion efficiency, compact low-pressure primary and containment systems, and unique safety characteristics including very large thermal margins (>500°C) to fuel damage during transients and accidents, salt-cooled pebble fuel cores offer the potential to meet the major goals of the Advanced Reactor Concepts Development program to provide electricity at lower cost than light water reactors with improved safety and system performance.This report presents the facility description, experimental results, and supporting simulation methods of the new X-Ray Pebble Recirculation Experiment (X-PREX), which is now operational and being used to collect data on the behavior of slow dense granular flows relevant to pebble bed reactor core designs. The X-PREX facility uses novel digital x-ray tomography methods to track both the translational and rotational motion of spherical pebbles, which provides unique experimental results that can be used to validate discrete element method (DEM) simulations of pebble motion. The validation effort supported by the X-PREX facility provides a means to build confidence in analysis of pebble bed configuration and residence time distributions that impact the neutronics, thermal hydraulics, and safety analysis of pebble bed reactor cores. Experimental and DEM simulation results are reported for silo drainage, a classical problem in the granular flow literature, at several hopper angles. These studies include conventional converging and novel diverging geometries that provide additional flexibility in the design of pebble bed reactor cores. Excellent agreement is found between the X-PREX experimental and DEM simulation results. This report also includes results for additional studies relevant to the design and analysis of pebble bed reactor cores including the study of forces on shut down blades inserted directly into a packed bed and pebble flow in a cylindrical hopper that is representative of a small test reactor.

A 6M digital twin for modeling and simulation in subsurface reservoirs

Pebble bed reactor with a once-through-then-out fuelling scheme has the advantage of simplifying the refueling system. However, the core upper-level power density is relatively higher than the bottom, producing an asymmetric core axial power distribution. Several burnable poison (BP) configurations are used to flatten the peak power density and improve power distribution while suppressing the excess core reactivity at the beginning of the burnup cycle. This study uses HTR-PM, China’s pebble bed reactor core, to simulate several burnable poison (BP) configurations. Serpent 2 coupled with Octave and a discrete element method simulation is used to model and simulate the pebble bed reactor core. It is found that erbium needs a large volumetric fraction in either QUADRISO or distributed BP to perform well. On the other hand, gadolinium and boron need a smaller volumetric fraction but perform worse in radial power distribution criteria in the fuel sphere. This study aims to verify the effect of BP added fuel pebbles on an OTTO refueling scheme HTR-PM core axial power distribution and excess reactivity.

​Preliminary steady state and transient thermal analysis of the new HCPB blanket for EU DEMO reactor

Work carried out in the last decade or so suggests that the simulators for multiphase flow in porous media should include an additional term, namely a dynamic coefficient, as a measure of the dynamic effect associated with capillary pressure. In this work, we examine the dependence of the dynamic coefficient on temperature by carrying out quasi‐static and dynamic flow simulations for an immiscible perchloroethylene–water system. Simulations have been carried out using a two‐phase porous media flow simulator for a range of temperatures between 20 and 80°C. Simulation domains represent 3‐D cylindrical setups used by the authors for laboratory‐scale investigations of dynamic effects in two‐phase flow. Results are presented for two different porous domains, namely the coarse and fine sands, which are then interpreted by examining the correlations between dynamic coefficient(s) and temperature, time period(s) required for attaining irreducible water saturation, and the dynamic aqueous/nonaqueous phase saturation and capillary pressure plots. The simulations presented here maintain continuity from our previous work and address the uncertainties associated with the dependency of dynamic coefficient(s) on temperature, thereby complementing the existing database for the characterization of dynamic coefficients and subsequently enabling the users to carry out computationally economical and reliable modeling studies. © 2012 The Authors. AIChE Journal, published by Wiley on behalf of the AIChE. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. AIChE J, 58: 1951–1965, 2012

Synergistic effects in flows of mixtures of wormlike micelles and hydroxyethyl celluloses with or without hydrophobic modifications

COOLBALL is an IBM 650 machine program designed to calculate local gas and ball temperatures, gas flow, and pressure loss as induced by nonuniform power generation and voidage within an axial flow pebble-bed reactor core. This code was used extensively to study the thermal characteristics of pebble-bed reactor cores in support of a broad program for the development of the PBR concept. (auth)

Proper water management in Proton Exchange Membrane (PEM) fuel cell is important to achieve high performance. Understanding the percolation of the produced water at the cathode catalyst layer (CL) is critical for any robust water management technique. In this study, an ex-situ experimental setup is used to study percolation in the CL at different injection rates and relative humidity (RH) conditions. The results show that increasing the flow rate force the liquid to flow through the bulk of the pores due to the dominant viscous effect. On the other hand, at low injection rates, the capillary becomes dominant and liquid flow along the roughness of pores surfaces. At low flow rates, a big wetted area is captured, compared to high flow rates tests, but the liquid saturation is lower. Another set of testing were done at a fixed flow rate and a varied RH conditions, where permeability is calculated based on the steady percolation pressure. The Permeability of the CL for both gas and liquid decreases as RH increases, and that more likely related to ionomer swelling. A correlation between the permeability and water content (λ) is derived. A sharp decrease in the permeability is observed at low water content (λ < 3), beyond that there are no significant changes. Moreover, low and high RH conditions show significant effects on the structure of CL and flow regime. Static contact angle measurements at a range of RH also indicate possible morphological changes in the CL. In addition, fractional flow theory (FFT) model is adapted to study immiscible displacement of two-phase flow in a porous medium. The resulting model accurately predicts trapped saturation that occurs during imbibition and drainage of incompressible fluids for any capillary number. It also accurately predicts the fluid-fluid front displacement and critical capillary number at which trapped saturation begins to decrease. The unique aspect of this model is incorporation of a scaling factor, suggested by Médici and Allen (2016), that captures the propensity for gas or liquid holdup for any porous media and fluid pair.

Conventional Darcy's law for flow description in porous media was derived from a simple experiment carried out by Darcy in 1856 on a linear, homogeneous-and sourceless porous, medium. In this paper starting from basic Navier-Stokes momentum balance principle, a generalized Darcy's law has been derived that includes the effect of a source/sink term. Navier-Stokes momentum balance of similar nature was attempted by Casulli et al.(1), also in their studies on porous media flow even though many authors have objected to such analysis. Brinkman(2) and Hubbert(3) have also hinted at such .. application of Navier-Stokes equation to derive the traditional Darcy's law. In deriving the generalized Darcy's law, described in this paper, a similar to Casulli et al.(1), linear approximation of, the stress term has been used. A numerical investigation of the error resulting from not considering the source effect reveals that errors in pressure prediction may range to as high as 500 psi; This is a significant error and cannot be overlooked. Introduction Darcy's law that is widely used in petroleum engineering, hydrology and soil science mathematics has its origin in Darcy's(4) simple experiment on a linear, homogeneous, sourceless porous medium. To this date effect of a source term on Darcy velocity term has not been explored barring one work(5), In numerical reservoir simulation both source and heterogeneity are involved inthe input data, but not in the form of altered momentum expression such as a modified Darcy' s law. In this paper effect of source on Darcy flow velocity has been derived. It is opined that Navier-Stokes equation widely referred to in continuum fluid mechanics cannot exactly describe porous media flow, primarily because of the very structure of porous medium which offers a guided motion to permeating fluid. However, such analysis has been attempted by Casulli et al.(1), Brinkman(2) and Hubbert(3). There are possibly more references on such applications that have not come across this author's notice. In this paper a full Navier-Stokes type momentum balance has been considered as a starting equation and from this a generalized Darcy's law with source term has been derived. Before illustrating the derivation, it appears necessary to take note of Marle's(6) work which describes macroscopic averaging of microscopic (pore level) equations for representing porous media flow. From this standpoint it may appear that the current derivation in this paper or the starting Navier-Stokes equation is not valid. To this end, this author argues that the main motivation of averaging, which is avoiding of a meaningless concept of porosity at a point, is not important actually. In application phase such as in numerical simulation we consider a finite elemental volume with non-zero Δx, Δy, Δz of the elemental block and therefore a finite pore volume is considered and so meaningless point porosity situation is not encountered at all. Derivation of Generalized Darcy's Law Consider the elemental volume of size Δx, Δy, Δz. Then the accumulation term will be Δx Δy Δz(δ/ δt) (ρ φ&amp;gt; ux). The equation of motion in × direction will be:

We investigate the Moreau-Yosida regularization and the associated proximal map in the context of discrete gradient flow for the 2-Wasserstein metric. Our main results are a stepwise contraction property for the proximal map and an above the tangent line inequality for the regularization. Using the latter, we prove a Talagrand inequality and an HWI inequality for the regularization, under appropriate hypotheses. In the final section, the results are applied to study the discrete gradient flow for Renyi entropies. As Otto showed, the gradient flow for these entropies in the 2 Wasserstein metric is a porous medium flow or a fast diffusion flow, depending on the exponent of the entropy. We show that a striking number of the remarkable features of the porous medium and fast diffusion flows are present in the discrete gradient flow and do not simply emerge in the limit as the time-step goes to zero.

High-temperature gas-cooled reactors (HTGRs), renowned for their safety features and capacity to provide high-temperature heat, are anticipated to find widespread applications. The HTR-10 serves to demonstrate the intrinsic safety characteristics of modular HTGRs. Different refueling schemes result in varied pebble bed flows, with the Once-Through Then Out (OTTO) scheme causing fuel pebbles to remain in the core for longer periods. This increased residency in the core exposes the pebbles to more intense operating conditions, especially those pebbles that traverse the core’s center. In this work, the VSOP code coupled with THERMIX is used to calculate the pebble bed power distribution and radius-wised graphite temperature while tracing the flow of representative pebble and TRISO. Obtained data are fed to a 1-D OFFBEAT TRISO model to simulate the temperature distribution and variation, as well as the deformation of each layer of the particle. By this method, the fuel temperature, mechanistic properties, and fission gas release during the OTTO cycle can be estimated. The results show that in the core center, the fuel temperature reaches over 1100K while at the edge of the core is about 1050K, well below the criteria of 1473K. Mechanical analyses show that the maximum equivalent stress of TRISO particles in the core is about 350 MPa with an FGR of about 17.5%. This work offers a foundation for further analysis of fuel failure probability and fission product diffusion and release under normal operating conditions. This work established a method to analyze the fuel behavior of HTR TRISO fuel using legacy code and high-fidelity solver and play as a foundation for further fuel failure and fission products diffusion analyses.

The complexity of transient processes during travelling-wave propagation in extra high voltage overhead lines is deter-mined by the fact that many frequency components are presented in the electromagnetic wave front. For the correct analysis of the aforementioned transient processes and for further development of travelling-wave-based relay protec-tion and fault location devices, it is necessary to take into account the parameters of the environment where electromagnetic wave propagation occurs. For the transmission line, these parameters are longitudinal inductance, longitudinal resistance, shunt capacitance and shunt resistive conductance. It is worth mentioning that for a variety of reasons unit-area longitudinal inductance and resistance are the parameters which depend on frequency, thus travelling wave velocity is different for different frequency components of the electromagnetic wave front. The popular researches which address this problem either fail to consider the dependence of overhead line inductance and resistance on frequency or this dependence is considered approximately for the high-frequency range, which can cause significant errors in the transient processes analysis during travelling wave propagation. In view of this, the development of the approach to overhead transmission lines simulation, which will allow both determining the line parameters in a wide frequency range and evaluating steady-state behaviour and transient processes in long-distance transmission lines, arrears relevant. The main research method to establish extra-high voltage transmission line parameters employs the simulation study in COMSOL Multiphysics. A number of assumptions were made in the simulation process: homogeneous soil layer, entire transmission line section and absence of transmission line conductor sag. The usage of finite elements method (FEM) for differential equation solution in the above-mentioned software is also seen as an assumption. The approach to extra-high voltage transmission lines simulation has been offered. This approach consists of the usage of Maxwell’s equations in combination with numerical integration with finite elements method (FEM). Frequency response for transmission line parameters and travelling-wave propagation velocity rate for different frequency components have been obtained. The results obtained can be used in updating of electrical power system models for further research in the relay protection field. The suggested approach will allow evaluating line parameters of other voltage types and obtaining more accurate values of transmission line parameters and travelling wave propagation speed along transmission lines for high-frequency range. The use of these transmission line models will enable to formulate approaches to improve the existing algorithms of travelling-wave-based relay protection and fault location devices.

This book contains lecture notes of current development in multiscale modeling, computations and applications. It covers fundamental mathematical theory, numerical algorithms as well as practical computational advice for analysing single and multiphysics models containing a variety of scales in time and space. Complex fluids, porous media flow and oscillatory dynamical systems are treated in some extra depth, as well as tools like analytical and numerical homogenization, fast multipole methods and wavelets. The text includes well designed exercises and project reports on different applications such as astrophysics, computational chemistry, porous media flow and climate change.

The present study investigates various effects of MEMS-based microfluidic fuel cell on the performance of direct formic acid microfluidic fuel cells that breathe air as an oxidant. A miniaturized fuel cell of the structure and design of a typical T-shaped air- breathing Direct Formic Acid Fuel Cell with micro channel is 1.5 mm x 25 mm in width multiply length. Both anode and cathode electrode having a width and length of 0.6 mm and 20 mm, respectively, with an electrode spacing of 0.3 mm. An air-breathing microfluidic fuel cell having a 0.6 mm in width and 20 mm in length that is placed on cathode GDE down-side. In such systems for the fluid delivery, both formic acid (0.5 M) as a fuel solution mixing sulfuric acid (0.5 M) at a node channel side and as an electrolyte used sulfuric acid (0.5 M) place take on the cathode channel side are injected together into the end of the channel outlet by two syringe pumps. Firstly, a three-dimensional microfluidic fuel cell model was established using Computational Fluids Dynamics to simulate the fuel cell performance. Further, both V-I curves obtained from simulation and published experimental data under similar operating condition were compared to assure the validity of the simulation. Modelling the transport and electrochemical phenomena were described with hydrodynamic equations, the porous media flow, mass transport, electrochemical reaction and charge equation. The porous media flow in the gas diffusion layer was described by Brinkman equation. The Butler-Volmer equations were applied to get the V-I-P curves. An anode electrode surface performance, respectively, is presented.

HypothesisThe emulsification of water and crude oil is typically examined and optimized in test tubes by optical means, that is, mixed under turbulent conditions and detected outside the porous medium in equilibrium. In this study, we investigate the rather complex case of crude oil emulsification by alkaline solutions to assess whether the classical phase behavior experiments are representative of the emulsification under laminar flow conditions in porous media. ExperimentsWe characterized the phase equilibrium in the test tubes through X-ray attenuation in micro-X-ray computed tomography (μCT). Moreover, we showed that for these systems, the conventional qualitative optical inspection leads to considerable misinterpretation. X-ray attenuation ensures a quantitative analysis directly comparable to results from μCT-based core-flood experiments, where phase mixing occurs in porous media flow. The study was complemented with microfluidic experiments providing additional high-resolution information on emulsion phases. FindingsWe conclusively show that in the complex in situ saponification of crude oil by alkaline flooding, (a) the emulsifications in test tubes and in porous media flow are comparable, considering the displacement process in the latter; (b) a minimum emulsion volume with balanced compositions leads to optimal oil recovery in μCT-based and conventional core flooding and in microfluidics.