Particle Transport Monte Carlo Method for Heat Conduction Problems

The very high temperature gas-cooled reactor (VHTR) is envisioned as a single- or dual-purpose reactor for electricity and hydrogen generation. The concept has average coolant temperatures above 1173 K (900°C) and operational fuel temperatures above 1523 K (1250°C). The concept provides the potential for increased energy conversion efficiency and for high-temperature process heat application in addition to power generation. While all the high-temperature gas-cooled reactor concepts have sufficiently high temperatures to support process heat applications, such as hydrogen production, tar sands, oil shale, desalination, or cogenerative processes, the VHTR’s higher temperatures can be detrimental to safety if a loss-of-coolant accident occurs and causes the mechanical strength degradation of the supporting graphite in the lower plenum. Following the loss of coolant through the break and coolant depressurization, air will enter the core through the break by molecular diffusion or density-gradient–driven stratified flow phenomena and ultimately by natural convection, leading to oxidation of the in-core graphite structure and fuel. The oxidation will accelerate heatup of the reactor core and the release of toxic gases (CO and CO2) and fission products. Thus, without any effective countermeasures, a pipe break may lead to significant fuel damage and fission product release. Therefore, there was a need to develop a computer code that can be used for VHTR air ingress-related graphite oxidation analyses. Prior to the start of the Republic of Korea/United States International Nuclear Energy Research Initiative collaboration, no computer codes were available that had been sufficiently developed and validated to reliably simulate an air ingress phenomenon in the VHTR. Therefore, we have worked for the past 3 yr on developing and validating advanced computational methods for simulating air ingress in the VHTR. The Idaho National Laboratory is developing a system integration model of VHTR and hydrogen production plant. GAMMA code is being considered to be an integrated computer tool to analyze the thermal hydraulics of the coupled plant. Computer models for a high-temperature steam electrolysis (HTSE) process were developed and were implemented in an overall system process optimization code, HYSYS. The HTSE model will be implemented into GAMMA code as the integrated computer tool.This paper describes the governing equations and numerical methods used in GAMMA code and presents a portion of verification of the GAMMA code along with turbomachinery models and HTSE models that will be linked to GAMMA code.

Numerical experiments using hierarchical finite element method for nonlinear heat conduction in plates

The Very High Temperature Gas-Cooled Reactor (VHTR) coupled to the High Temperature Steam Electrolysis (HTSE) process is one of two reference integrated systems being investigated by the U.S. Department of Energy and Idaho National Laboratory for the production of hydrogen. In this concept the VHTR outlet temperature of 900 °C provides thermal energy and high efficiency electricity for the electrolysis of steam in the HTSE process. In the second reference system the Sulfur Iodine (SI) process is coupled to the VHTR to produce hydrogen thermochemically. In the HyPEP project we are investigating and characterizing these two reference systems with respect to production, operability, and safety performance criteria. Under production, plant configuration and working fluids are being studied for their effect on efficiency. Under operability, control strategies are being developed with the goal of maintaining equipment within operating limits while meeting changes in demand. Safety studies are to investigate plant response for equipment failures. Specific objectives in FY07 were (1) to develop HyPEP Beta and verification and validation (V&V) plan, (2) to perform steady state system integration, (3) to perform parametric studies with various working fluids and power conversion unit (PCU) configurations, (4) the study of design options such as pressure, temperature, etc. (5) to develop a control strategy and (6) to perform transient analyses for plant upsets, control strategy, etc for hydrogen plant with PCU. This report describes the progress made in FY07 in each of the above areas. (1) The HyPEP code numeric scheme and Graphic User Interface have been tested and refined since the release of the alpha version a year ago. (2) The optimal size and design condition for the intermediate heat exchanger, one of the most important components for integration of the VHTR and HTSE plants, was estimated. (3) Efficiency calculations were performed for a variety of working fluids for this reference design. (4) Efficiency improvements over the reference VHTR/HTSE plant were investigated for an alternative design that directly couples a High Temperature Steam Rankin Cycle (HTRC) to the HTSE process. Integration of the VHTR with SI process plants was begun. (5) Plant control studies showed that inventory control in the VHTR plant and flow control in the HTSE plant is effective in maintaining hot-side temperatures near constant during load change. (6) Dynamic calculations showed that thermal transients arising in the chemical plant are strongly damped at the reactor resulting in a stable combined plant.

In Korea, the Very High Temperature Gas-Cooled Reactor (VHTR) PMR200 is being developed in the Nuclear Hydrogen Development and Demonstration project. Its core consists of hexagonal prism-shaped graphite blocks for the fuel and reflector, and each hexagonal fuel block contains 108 cylindrical coolant holes and 210 fuel compacts. Because of these holes and fuels, the heat transfer in lateral directions in the fuel blocks becomes very complicated. Especially in accident situations when forced convection is lost, the majority of the afterheat flows in the radial direction by conduction across the large number of coolant holes. Moreover, radiation heat transfer is supposed to be added to the radial heat transfer modes owing to the high temperature of the VHTR core. Because of these complexities in radial heat transfer, reliable modeling for effective thermal conductivity (ETC) is required in order to analyze the reactor core thermal behavior using lumped-parameter codes, which are often used to evaluate the integrity of nuclear fuel embedded in the graphite block. In this study, the ETC model adopted in the GAMMA+ code was introduced, and the adequacy of the model was assessed by the commercial computational fluid dynamics (CFD) code CFX-13. The results of the CFD analysis were consistent with the ETC model in general even if a slight disagreement was shown for the case of high temperature. From these analyses, it could be concluded that the ETC model adopted in the GAMMA+ code is an adequate model for the analysis of the PMR200 reactor core. Moreover, it was found that the effect of fuel gap can cause an overprediction of the ETC if the fuel compact thermal conductivity is larger than the applicable range of the model.

The Department of Energy envisions the next generation very high temperature gas-cooled reactor (VHTR) as a single-purpose or dual-purpose facility that produces hydrogen and electricity. The Ministry of Science and Technology (MOST) of the Republic of Korea also selected VHTR for the Nuclear Hydrogen Development and Demonstration (NHDD) Project. The report will address the evaluation of hydrogen and electricity production cycle efficiencies for such systems as the VHTR and NHDD, and the optimization of system configurations. Optimization of such complex systems as VHTR and NHDD will require a large number of calculations involving a large number of operating parameter variations and many different system configurations. The research will produce (a) the HyPEP which is specifically designed to be an easy-to-use and fast running tool for the hydrogen and electricity production evaluation with flexible system layout, (b) thermal hydraulic calculations using reference design, (c) verification and validation of numerical tools used in this study, (d) transient analyses during start-up operation and off-normal operation. This project will also produce preliminary cost estimates of the major components.

The Monte Carlo method was used in modelling steady state heat conduction problems. The method uses the fixed and the floating random walks to determine temperature in the domain of the definition of the heat conduction equation, at a single point directly. A heat conduction problem with an irregular shaped geometry and prescribed boundary temperatures was analyzed. Computer programs for the analysis were coded using VAX FORTRAN on a VAX 4.4 mainframe. The fixed random walk and the floating random walk methods gave comparable results of 507.260K and 506.980K respectively for temperature at a point. The Monte Carlo method also gave a result of 50.580C , similar to that of 50.000C for a particular node, with the Finite Difference method (using Gauss- Seidel iteration) for a 2-dimensional regular shaped heat conduction problem. Keywords: Monte Carlo Method, Fixed Random Walk, Floating Random Walk, Modelling, Steady-State Heat Conduction African Research Review Vol. 2 (4) 2008: pp. 31-53

The fully ceramic microencapsulated (FCM) fuel, one of the accident tolerant fuel (ATF) concepts, consists of TRISO particles randomly dispersed in SiC matrix. This high heterogeneity in compositions leads to difficulty in explicit thermal calculation of such a fuel. For thermal analysis of a fuel element in very high temperature reactors (VHTRs) which has a similar configuration to the FCM fuel, a two-temperature homogenized model was proposed by the authors. The model was developed using particle transport Monte Carlo method for heat conduction problems. It gives more realistic temperature profiles and provides the fuel-kernel and graphite temperatures separately. In this paper, we apply the two-temperature homogenized model to single-channel thermal analysis of the FCM fuel element for steady- and transient-states using 2-D FEM/1-D FDM hybrid method. The results of analyses are compared to those of conventional UO2 fuel having the same geometric dimension and operating conditions.

Experimental studies on the thermal and hydraulic performance of the fuel stack of the VHTR: Part II. HENDEL multi-channel test rig with twelve fuel rods

The tritium concentration in the hydrogen product in Japan's future very high temperature gas-cooled reactor (VHTR) system coupled with a thermochemical water-splitting iodine-sulfur (IS) process (VHTRIS system), named GTHTR300C, was estimated by numerical analysis. The tritium concentration in the hydrogen product significantly depended on undetermined parameters, i.e., the permeabilities of a SO3 decomposer and a H2SO4vaporizer made of SiC. Thus, the estimated tritium concentration in the hydrogen product for the conservative analytical condition ranged from 3.4 × 10−3 Bq/cm3 at STP (38 Bq/g-H2) to 0.18 Bq/cm3 at STP (2,000 Bq/g-H2). By considering the tritium retained by core graphite and the reduction in permeation rate by an oxide film on the heat transfer tube of the IHX and the HI decomposer, the tritium concentration in the hydrogen product decreased to the range from 3.3 × 10−5 Bq/cm3 at STP (0.36 Bq/g-H2) to 5.6 × 10−3 Bq/cm3 at STP (63 Bq/g-H2), which were smaller than those for the conservative analytical condition by factors of about 3.2 × 10−2 and 9.6 × 10−3, respectively. The effectof the helium flow rate in the helium purification system on the tritium concentration in the hydrogen product was also evaluated.

Scaling and design analyses of a scaled-down, high-temperature test facility for experimental investigation of the initial stages of a VHTR air-ingress accident

This work is concerning a methodology of Ni-base superalloy development for a very high temperature gas-cooled reactor(VHTR) using design of experiments(DOE) and thermodynamic calculations. Total 32 sets of the Ni-base superalloys with various chemical compositions were formulated based on a fractional factorial design of DOE, and the thermodynamic stability of topologically close-packed(TCP) phases of those alloys was calculated by using the THERMO-CALC software. From the statistical evaluation of the effect of the chemical composition on the formation of TCP phase up to a temperature of 950 oC, which should be suppressed for prolonged service life when it used as the structural components of VHTR, 16 sets were selected for further calculation of the mechanical properties. Considering the yield and ultimate tensile strengths of the selected alloys estimated by using the JMATPRO software, the optimized chemical composition of the alloys for VHTR application, especially intermediate heat exchanger, was proposed for a succeeding experimental study.

Air-ingress events caused by large pipe breaks are important accidents considered in the design of Very High Temperature Gas-Cooled Reactors (VHTRs). A main safety concern for this type of event is the possibility of core collapse following the failure of the graphite support column, which can be oxidized by ingressed air. In this study, the main target is to predict the strength of the oxidized graphite support column. Through compression tests for fresh and oxidized graphite columns, the compressive strength of IG-110 was obtained. The buckling strength of the IG-110 column is expressed using the following empirical straight-line formula: σ cr,buckling = 91.34—1.01 (L/r). Graphite oxidation in Zone 1 is volume reaction and that in Zone 3 is surface reaction. We notice that the ultimate strength of the graphite column oxidized in Zones 1 and 3 only depends on the slenderness ratio and bulk density. Its strength degradation oxidized in Zone 1 is expressed in the following nondimensional form: σ/σ0 = exp(—kd), k = 0.114. We found that the strength degradation of a graphite column, oxidized in Zone 3, follows the above buckling empirical formula as the slenderness of the column changes.

Thermo-economic analysis and optimization of the very high temperature gas-cooled reactor-based nuclear hydrogen production system using copper-chlorine cycle

Pebble bed very high temperature reactor (VHTR) has been identified as one of six Generation-IV (Gen-IV) types of reactor which could operate at a high thermal power. The calculation of the temperature in the fuel pebble is a key part of VHTR thermal hydraulics numerical simulation. However, due to the special structure of the VHTR fuel pebble, the temperature calculation involves a multiscale problem. The multiscale heat conduction model includes mesoscale temperature of fuel pebble and microscale temperature of TRISO fuel particles calculation. To deal with the particularity of temperature calculation of the fuel pebble, this paper presents a multiscale heat conduction model based on an open source CFD package OpenFOAM. Firstly, the quasi steady state heat conduction method (QSSHC) and homogeneous layers method (HL) was verified by a simple multiscale model. The results show that the QSSHC method has a good ability of multiscale temperature prediction. Secondly, the mesoscale temperature distribution and the maximum temperature in the microscale of VHTR fuel pebbled are calculated with QSSHC method based on OpenFOAM. This multiscale solver will be couple with other solvers of OpenFOAM, to provide a new perspective of VHTR simulation.

Parametric study of effective thermal conductivity for VHTR fuel pebbles based on a neutronic and thermal coupling method