Rod Heat Transfer Research Articles

Safety considerations related to boron redistribution during Loss-of-Coolant-Accident initiated beyond design basis events for the NuScale power module

The authors, as staff at the U.S. Nuclear Regulatory Commission (NRC), evaluated the potential consequences of boron dilution under beyond design basis conditions in the NuScale Power Module to inform NRC staff’s safety evaluation report for the NuScale design certification review. The authors identified the small break loss of coolant accident with coincident failure of control rods to insert as the scenario with the most adverse boron dilution and reactivity insertion consequences. The authors evaluated the sequence of events for the scenario to determine which conditions or phenomena could produce the potential for a core flow surge to yield core damage because of a super-prompt reactivity excursion. The authors screened the conditions and phenomena that could potentially cause a core flow surge based on the dynamic speed of the incursion compared to key reactivity feedback mechanisms: thermal–hydraulic coupling via rod heat transfer and convective mixing. Based on the screening process, the authors were able to identify two processes that could potentially lead to a power excursion. However, the authors’ analysis relies heavily on assumptions regarding convective mixing, making this an important phenomenon worth careful consideration in any evaluation of boron redistribution.

Improved multiphysics model of the High Temperature Engineering Test Reactor for the simulation of loss-of-forced-cooling experiments

We present a multiphysics model of the High Temperature Engineering Test Reactor for comparison with past and predict future loss-of-forced-cooling (LOFC) experiments. The approach selected combines (1) 3-D full-core superhomogenization-corrected neutronics, (2) 3-D full-core homogenized or semi-heterogeneous heat transfer (macroscale), (3) 2-D axisymmetric fuel rod heat transfer (pin-scale), and (4) 1-D thermal-hydraulics channels. Although large uncertainties remain, the time and magnitude of the first power peak after re-criticality is predicted within 1.5 h and 175 kW, respectively. The novelty of our work includes (1) a new macroscale/pin-scale heat transfer coupling approach relying on gap conductance to drastically speed up numerical convergence by two orders of magnitude, (2) determination of a radial effective thermal conductivity, reproducing the semi-heterogeneous re-criticality time within one hour using a homogenized macroscale model, and (3) a preliminary study of the reactor’s early behavior following a LOFC event, enabling further assessment of numerical models against fission power measurements.

Exergy, economic and environmental analysis of forced circulation flat plate solar collector using heat transfer enhancer in riser tube

This paper experimentally investigates the exergy of a riser tube with heat transfer enhancer in the flat plate collector. Two different internal heat transfer enhancers are used herein, namely, rod heat transfer enhancer and tube heat transfer enhancer. The environmental and sustainable assessment of the flat plate collector with and without heat transfer enhancer have been taken into consideration in the study. This is the first study performed on the exergy and economic analysis of a flat plate solar collector using this heat transfer enhancer, and the new findings on the exergy analysis using heat transfer enhancer of the flat plate collector have been reported. The improved exergy efficiency, useful exergy rate and exergy destruction for the flat plate collector are analyzed, and it is found that the rod heat transfer enhancer provides comparatively higher exergy efficiency than the tube heat transfer enhancer and plain tube flat plate collector. The maximum exergy efficiency is 11.3%, 10.9% and 8.3% for the rod, tube heat transfer enhancers, and plain tube respectively. The heat transfer enhanced collectors significantly reduce the total exergy destruction compared to plain tube collector. The increase in useful exergy rate is 1.29 and 1.25 times higher for the rod and tube heat transfer enhancers respectively, compared to the plain tube collector. The conclusion is that the rod heat transfer enhancer collector has the lowest energy payback time and a simple payback period.

Dynamics of a BWR with inclusion of boiling nonlinearity, clad temperature and void-dependent core power removal: Stability and bifurcation characteristics of advanced heavy water reactor (AHWR)

We study the effect of including boiling nonlinearity, clad temperature and void-dependent power removal from the primary loop in the mathematical modeling of a boiling water reactor (BWR) on its dynamic characteristics. The advanced heavy water reactor (AHWR) is taken as a case study. Towards this end, we have analyzed two different simplified models with different handling of the clad temperature. Each of these models has the necessary modifications pertaining to boiling nonlinearity and power removal from the primary loop. These simplified models incorporate the neutronics and thermal–hydraulic coupling. The effect of successive changes in the modeling assumptions on the linear stability of the reactor has been studied and we find that incorporation of each of these complexities in the model increases the stable operating region of the reactor. Further, the method of multiple time scales (MMTS) is exploited to carry out the nonlinear analysis with a view to predict the bifurcation characteristics of the reactor. Both subcritical and supercritical Hopf bifurcations are present in each model depending on the choice of operating parameters. These analytical observations from MMTS have been verified against numerical simulations. A parametric study on the effect of changing the nominal reactor power on the regions in the parametric space of void coefficient of reactivity and fuel temperature coefficient of reactivity with sub- and super-critical Hopf bifurcations has been performed for all the models. We find that boiling nonlinearity and void-dependent power removal from the primary loop increases the supercritical region while inclusion of clad temperature to include fuel rod heat transfer increases the subcritical regime.

Experimental investigation on heat transfer and pumping power of forced circulation flat plate solar collector using heat transfer enhancer in absorber tube

This paper experimentally investigates the performance of an absorber tube with heat transfer enhancer in solar flat plate water heater. The objective of the work is to increase the convective heat transfer by reducing the cross sectional area between the absorbing fluid and inner wall of the tube. The heat transfer enhancers are frictionally engaged with the inner side of the tube wall, and it is kept in the axial flow direction of the fluid flow path. Two types of heat transfer enhancers, namely, rod heat transfer enhancer and tube heat transfer enhancer, are used herein and compared with each other. The efficiency, heat transfer coefficient and pumping power for flat plate solar collector were analyzed, and it was found that, the rod heat transfer enhancer provides higher heat transfer with a small increase in pumping power than tube heat transfer enhancer and plain tube flat plate solar collector. The maximum increase in pumping power is 1.081 and 1.044 times higher for rod and tube heat transfer enhancers respectively, compared to plain tube solar collector.

Preliminary study of parameter uncertainty influence on Pressurized Water Reactor core design

Sub-channel analysis can improve the accuracy of reactor core thermal design. However, the important initial parameters contain various uncertainties during reactor operation. In this work, the Sub-channel Analysis Code of Supercritical reactor (SACOS) code, which is also applicable for Pressurized Water Reactor (PWR), was used to study the coolant flow characteristic and fuel rod heat transfer characteristic of 1/8 assembly which has the maximum linear power density in 300 MWe PWR core firstly. Then the Wilks' method and Response Surface Method (RSM) were utilized to determine the influence of sub-channel input parameters uncertainties on the highest temperature of reactor core fuel rod and Minimum Departure from Nucleate Boiling Ratio (MDNBR). The results show that in the most conservative conditions, the maximum temperature of the fuel rod and MDNBR were 2167.4 °C and 1.08, respectively. Considering the uncertainties of assembly inlet flow rate, inlet coolant temperature and system pressure, the 95% probability values (with 95% confidence) of fuel rod maximum and MDNBR calculated using response surface methodology were 2144.0 °C and 1.6, while they were 2137 °C and 1.74 calculated by Wilks' approach. Results show that the uncertainty analysis methods can provide larger reactor design criteria margin to improve the economy of reactor. Furthermore, the code was developed to have the capacity to perform the uncertainty study of sub-channel calculation.

Mass flow rate sensitivity and uncertainty analysis in natural circulation boiling water reactor core from Monte Carlo simulations

Our aim was to evaluate the sensitivity and uncertainty of mass flow rate in the core on the performance of natural circulation boiling water reactor (NCBWR). This analysis was carried out through Monte Carlo simulations of sizes up to 40,000, and the size, i.e., repetition of 25,000 was considered as valid for routine applications. A simplified boiling water reactor (SBWR) was used as an application example of Monte Carlo method. The numerical code to simulate the SBWR performance considers a one-dimensional thermo-hydraulics model along with non-equilibrium thermodynamics and non-homogeneous flow approximation, one-dimensional fuel rod heat transfer. The neutron processes were simulated with a point reactor kinetics model with six groups of delayed neutrons. The sensitivity was evaluated in terms of 99% confidence intervals of the mean to understand the range of mean values that may represent the entire statistical population of performance variables. The regression analysis with mass flow rate as the predictor variable showed statistically valid linear correlations for both neutron flux and fuel temperature and quadratic relationship for the void fraction. No statistically valid correlation was observed for the total heat flux as a function of the mass flow rate although heat flux at individual nodes was positively correlated with this variable. These correlations are useful for the study, analysis and design of any NCBWR. The uncertainties were propagated as follows: for 10% change in the mass flow rate in the core, the responses for neutron power, total heat flux, average fuel temperature and average void fraction changed by 8.74%, 7.77%, 2.74% and 0.58%, respectively.

Fuel rod model based on Non-Fourier heat conduction equation

In this paper we explore the applicability of a fuel rod mathematical model based on Non-Fourier transient heat conduction as constitutive law for the Light Water Reactors transient analysis (LWRs). In the classical theory of diffusion, Fourier law of heat conduction is used to describe the relation between the heat flux vector and the temperature gradient assuming that the heat propagation speeds are infinite. The motivation for this research was to eliminate the paradox of an infinite thermal wave speed. The time-dependent heat sources were considered in the fuel rod heat transfer model. The close of the Main Steam Isolated Valves (MSIV) transient in a Boiling Water Reactor (BWR) was analyzed by different relaxation times. The results show that for long-times the heat fluxes on the clad surface under Non-Fourier approach can be important, while for short-times and from the engineering point of view the changes are very small. Some results from transient calculations are examined.

A Cleanup Machine Using Reverse Osmosis Method to Remove Silica from Boric Acid Tank at Maanshan Nuclear Power Station

Silica concentration in the primary coolant of a reactor coolant system of a pressurized water nuclear plant is a considerable operational issue. It also becomes a safety issue if the crud is very significant. To keep its amount to a minimum is the basic requirement for the purpose of zinc injection in the primary system and protection against its deposition on the fuel rod and poor heat transfer on the primary system and piping. A boric acid cleanup machine has been developed, designed, and installed on the base floor at the auxiliary building of the Maanshan power station of Taiwan Power Company. It is located above the boric acid tank (BAT). This machine with reverse osmosis method was used to clean up boric acid of ~62 m3 stored in the BAT. The results show that its performance has excellent efficiency and capability. The silica concentration was reduced to ~0.605 ppm from the original value of ~3.150 ppm. The resulting waste contained ~2.52 wt% of boron depending on the original boron amounts in the BAT. After the cleanup is finished, the concentration of boron in the BAT still maintains its operable and safe operating range of 7000 to 7700 ppm. Finally, the written procedure has been completed in order that the machine will be applied as a routine cleanup system.

A Linear Stability Analysis of Supercritical Water Reactors, (II)

A mathematical model is developed to study the coupled neuronic thermal-hydraulic stability for a high-temperature reactor cooled and moderated by supercritical-pressure light water (SCLWR-H). The present model incorporates coolant and fuel dynamics as well as reactor neutronics. One-dimensional single-channel single-phase conservation equations are used in the thermal-hydraulics model and point-kinetics approximation is used in the reactor neutronics model. One-dimensional heat conduction equations are used in heat transfer model. The water rod thermal-hydraulic model and heat transfer model are included to study the effects of water rods on reactor stability. The stability of SCLWR-H for full-power and partial-power normal operation is investigated by frequency domain linear stability analysis. The decay ratio for coupled neutronic thermal-hydraulic stability of SCLWR-H is considerable due to the time delay of the heat transfer to the water rod. The stability criterion can be satisfied at normal operation. The sensitivity of the coupled neutronic thermal-hydraulic stability to various operating conditions and design parameters is also studied.

Study of the thermal plasma etching at atmospheric pressure on silica rods

Etching of SiO2 rods has been obtained with a dc torch with argon as the process gas in an air environment at atmospheric pressure; the high temperature of the plasma jet causes vaporization of the exposed area. The apparatus and torch operative parameters have been set up to obtain a depth etch rate of up to 0.6 mm min−1 corresponding to 0.826 g min−1.An enthalpy probe has been employed to monitor the plasma conditions before the thermal plasma etching process and from the experimental etch rate a surface rod temperature of Tsur = 2057 K has been derived. Etching has been obtained with uniformity over the entire exposed area with peak to peak differences below 1%.The plasma to rod heat transfer has been simulated using a commercial CFD code Fluent©. The model consists of a non-steady two-dimensional simulation for a compressible turbulent fluid, with an adapted grid calculation. Boundary conditions have been set out using the enthalpy probe plasma jet map. In particular for the flow, the continuity equation for chemical species, the species transport equations (Fick's Law), the momentum conservation equations, the energy equation and the turbulent kinetic energy have been solved. In the solid regions the convective energy transfer due to the rotational motion of the rod, the conduction and radiation energies have been considered. The heat transfer between the fluid and the silica walls (continuity temperature between the fluid and the solid) accounts for the energy loss due to surface radiation (qr) and vaporization (qv) obtained from experimental data.A rod surface temperature of 2057 K obtained from experimental etch rate data agrees well with the calculated temperature obtained using Fluent© (Tsim = 2010 K).

Post DNB Heat Transfer Experiments for PWR Fuel Assemblies

Nuclear Power Engineering Corporation (NUPEC) and Mitsubishi performed heat transfer experiments on post DNB (departure from nucleate boiling) for the pressurized water reactor (PWR) fuel assemblies under the sponsorship of the Japanese Ministry of Economy, Trade and Industry (METI) as one of a series of fuel assembly verification tests. Based on the obtained experimental data, a new evaluation model for the fuel rod heat transfer behavior after DNB was developed. A large safety margin, which had remained in the present thermal-hydraulic design that did not allow DNB, was confirmed by applying the developed model to the PWR plant safety analysis.

Determination of Transient Radial-Azimuthal Temperature Distributions in Fuel Bundles Under Loss-of-Coolant-Accident Conditions

A methodology is presented to determine the transient temperature distributions in fuel bundles under loss-of-coolant accident (LOCA) conditions using a recently developed variational technique for the solution of radial-azimuthal heat conduction in the fuel rods and the modified view factor concept proposed by Uchida and Nakamure to model the radiative heat transfer between the rods. The variational technique is based on the Lebron-Labermont restricted variational principle and represents the temperature distribution in the rods at a given time during the LOCA via parabolic and circular trial functions in the radial and azimuthal directions, respectively. The methodology is implemented to a 4 x 4 boiling water reactor fuel bundle under typical LOCA conditions to investigate the effects of changes in rod heat transfer characteristics and simplifying modeling assumptions on predicted rod temperature distributions. The results show that these effects depend on the rod location in the assembly and LOCA phase under consideration and indicate that same degree of modelling detail may not be necessary for all the rods in the bundle at all times during the LOCA.

Post-dryout heat transfer of high-pressure steam-water two-phase flow in single rod channel and multi rod bundle

Low flow rate post-dryout heat transfer experiments of steam-water two-phase flow were conducted at the Japan Atomic Energy Research Institute using single rod and 25 rod heat transfer test facilities. The experiments covered mass flow rates from 20 to 800 kg/m 2s, qualities from 0.0 to 1.0 and pressures from 3 to 12 MPa. New correlations for the post-dryout heat transfer coefficient have been proposed by improving the Groeneveld correlation. The proposed correlations can account for the dependence of the heat transfer on the heat transfer surface temperature which the original Groeneveld correlation cannot do explicitly. The agreement between the predicted and measured values is satisfactory.

The Effect of Variable Thermal Conductivity in Thermal-Hydraulic Calculations

Many thermal-hydraulic computer codes employ a fuel rod heat transfer model to couple the fuel rod temperatures with the hydraulic driving forces. Frequently, these models utilize uniform thermal c...