CFD investigation of vertical rod bundles of supercritical water-cooled nuclear reactor

The commercial CFD code STAR-CD v4.02 is used as the numerical simulation tool for the supercritical water-cooled nuclear reactor (SCWR). The numerical simulation is based on the real full 3D rod bundles’ geometry of the nuclear reactors. For satisfying the near-wall resolution of y⁺ ≤ 1, the structure mesh with the stretched fine mesh near wall is employed. The validation of the numerical simulation for mesh generation strategy and the turbulence model for the heat transfer of supercritical water is carried out to compare with 3D tube experiments. After the validation, the same mesh generation strategy and the turbulence model are employed to study three types of the geometry frame of the real rod bundles. Through the numerical investigations, it is found that the different arrangement of the rod bundles will induce the different temperature distribution at the rods’ walls. The wall temperature distributions are non-uniform along the wall and the values depend on the geometry frame. At the same flow conditions, downward flow gets higher wall temperature than upward flow. The hexagon geometry frame has the smallest wall temperature difference comparing with the others. The heat transfer is controlled by P/D ratio of the bundles.     

CFD in supercritical water-cooled nuclear reactor (SCWR) with horizontal tube bundles

The commercial CFD code STAR-CD 4.02 is used as a numerical simulation tool for flows in the supercritical water-cooled nuclear reactor (SCWR). The basic heat transfer element in the reactor core can be considered as round tubes and tube bundles. Reactors with vertical or horizontal flow in the core can be found. In a vertically oriented core, symmetric characters of flow and heat transfer can be found and two-dimensional analyses are often performed. However, in a horizontally oriented core the flow and heat transfer are fully three-dimensional due to the buoyancy effect. In this paper, horizontal tubes and tube bundles at SCWR conditions are studied. Special STAR-CD subroutines were developed by the authors to correctly represent the dramatic change in physical properties of the supercritical water with temperature. From the study of single round tubes, the Speziale quadratic non-linear high-Re k-? turbulence model with the two-layer model for near wall treatment is found to produce the best results in comparison with experimental data. In tube bundle simulations, it is found that the temperature is higher in the top half of the bundle and the highest tube wall temperature is located at the outside tubes where the flow rate is the lowest. The secondary flows across the bundle are highly complex. Their main effect is to even out the temperature over the area within each individual recirculation region. Similar analysis could be useful in design and safety studies to obtain optimum fuel rod arrangement in a SCWR.     

Thermo-mechanical analysis of supercritical pressure light water-cooled fast reactor fuel rod by FEMAXI-6 code

Thermo-mechanical behaviors of supercritical pressure light water cooled fast reactor (SWFR) fuel rod and cladding have been investigated by FEMAXI-6 (Ver.1) code with high enriched MOX fuel at elevated operating condition of high coolant system pressure (25 MPa) and high temperature (500 °C in core average outlet temperature). Fuel rod failure modes and associated fuel rod design criteria that is expected to be limiting in SWFR operating condition have been investigated in this fuel rod design study. Fuel centerline temperature is evaluated to be 1853 °C and fission gas release fraction is about 45% including helium production. Cumulative damage fraction is evaluated by linear life fraction rule with time-to-rupture correlation of advanced austenitic stainless steel. In a viewpoint of mechanical strength of fuel cladding against creep rupture and cladding collapse at high operation temperature, currently available stainless steels or being developed has a potential for application to SWFR. Admissible design range in terms of initial gas plenum pressure and its volume ratio are suggested for fuel rod design The stress ranges suggested by this study could be used as a preliminary target value of cladding material development for SWFR application.     

Numerical investigation of heat transfer in upward flows of supercritical water in circular tubes and tight fuel rod bundles

Heat transfer in upward flows of supercritical water in circular tubes and in tight fuel rod bundles is numerically investigated by using the commercial CFD code STAR-CD 3.24. The objective is to have more understandings about the phenomena happening in supercritical water and for designs of supercritical water cooled reactors. Some turbulence models are selected to carry out numerical simulations and the results are compared with experimental data and other correlations to find suitable models to predict heat transfer in supercritical water. The comparisons are not only in the low bulk temperature region, but also in the high bulk temperature region. The two-layer model (Hassid and Poreh) gives a better prediction to the heat transfer than other models, and the standard k– high Re model with the standard wall function also shows an acceptable predicting capability. Three-dimensional simulations are carried out in sub-channels of tight square lattice and triangular lattice fuel rod bundles at supercritical pressure. Results show that there is a strong non-uniformity of the circumferential distribution of the cladding surface temperature, in the square lattice bundle with a small pitch-to-diameter ratio (P/D). However, it does not occur in the triangular lattice bundle with a small P/D. It is found that this phenomenon is caused by the large non-uniformity of the flow area in the cross-section of sub-channels. Some improved designs are numerically studied and proved to be effective to avoid the large circumferential temperature gradient at the cladding surface.     

Subchannel analysis of supercritical light water-cooled fast reactor assembly

Subchannel analyses have been carried out for supercritical water-cooled fast reactor fuel assembly. Peak cladding surface temperature difference arising from subchannel heterogeneities have been calculated by using the improved subchannel analysis code STARS and was evaluated to be about 18.5 °C. Several suggestions have been also made for reducing the PCST difference arising from channel heterogeneity. Influences of local power peaking on deflection of cladding surface temperature are explained with pin power distribution taken from core depletion calculation in this paper. Maximum cladding surface temperature at nominal condition is evaluated to be 645.3 °C over the cycle. Statistical thermal design uncertainty associated with PCST calculation is evaluated by Monte-Carlo sampling technique combined with subchannel analysis code. Maximum statistical design uncertainty of PCST is calculated to be 31 °C and is in a good agreement with that from RTDP method. Influence of downward flow in seed region on system sensitivity is investigated by improved Monte-Carlo thermal design procedure. Limiting thermal condition of MCST is 681 °C (650 °C of nominal + 31 °C) within 95/95 limit for SWFR.     

Control system design for a pressure-tube-type supercritical water-cooled nuclear reactor via a higher order sliding mode method

Nuclear power plants exhibit non-linear and time-variable dynamics. Therefore, designing a control system that sets the reactor power and forces it to follow the desired load is complicated. A supercritical water reactor(SCWR) is a fourthgeneration conceptual reactor. In an SCWR, the non-linear dynamics of the reactor require a controller capable of controlling the nonlinearities. In this study, a pressure-tube-type SCWR was controlled during reactor power maneuvering with a higher order sliding...     

Design of a supercritical water-cooled reactor with a three-pass core arrangement

The Supercritical Water-cooled Reactor (SCWR) is one of the six concepts of the Generation IV International Forum. In Europe, investigations have been integrated into a joint research project, called High Performance Light Water Reactor (HPLWR). Due to the higher heat up within the core and a higher outlet temperature, a significant increase in turbine power and thermal efficiency of the plant can be expected.Besides the higher pressure and higher steam temperature, the design concept of this type of reactor differs significantly from a conventional LWR by a different core concept. In order to achieve the high outlet temperature of over 500 °C, a core with a three-step heat up and intermediate mixing is proposed to keep local cladding temperatures within today's material limits. A design for the reactor pressure vessel (RPV) and the internals has been worked out to incorporate a core arrangement with three passes. All components have been dimensioned following the safety standards of the nuclear safety standards commission in Germany. Additionally, a fuel assembly cluster with head and foot piece has been developed to facilitate the complex flow path for the multi-pass concept. The design of the internals and of the RPV is verified using mechanical or, in the case of large thermal deformations, combined mechanical and thermal stress analyses. Furthermore, the reactor design ensures that the total coolant flow path remains closed against leakage of colder moderator water even in case of large thermal expansions of the components. The design of the RPV and internals is now available for detailed analyses of the core and the reactor.     

Safety analysis of a supercritical-pressure water-cooled fast reactor under supercritical pressure

The supercritical-pressure water-cooled fast reactor (SWFR) is a fast spectrum supercritical water-cooled reactor (SCWR) studied by the University of Tokyo. The SWFR is designed as a two-pass core with an outlet temperature 500 °C. The SWFR has fuel channels cooled by downward flow, higher power density, and smaller coolant density reactivity feedback compared with Super LWR. This paper describes the safety analyses of abnormal events for the SWFR. SPRAT-F code is used for the safety analysis at supercritical pressure considering the downward flow cooled seed fuel channel. This code is based on a 1-D node junction model with point kinetics and decay heat calculations. Flow redistribution among parallel paths is calculated by pressure-loss balance and momentum conservation. The initiating events are selected from those of LWRs. For the safety analysis, nine abnormal transients and four accidents are selected with considering types of abnormality. By the numerical analyses, it was found that the loss of flow events can be mitigated by the “water source” effect of the downward flow blanket channels in the abnormal transients and accidents. All the abnormal events satisfy the criteria with margin.     

Numerical studies of nuclear traveling waves in a supercritical water cooled fast reactor

An axial fuel shuffling strategy is proposed based on the mechanism of the nuclear fission traveling wave and implemented numerically in the calculation for a supercritical water cooled fast reactor (SCWFR). The ERANOS code is adopted to perform the neutronics and burn-up calculations, and the calculation scheme for axial fuel shuffling and coolant density coupling are set up. The parametric studies of a typical PWR with Th-U and U-Pu (²³⁵U instead of ²³⁹Pu) conversions by burn-up and k_eff calculations indicate that the breeding effects only exist in configurations with very low water content and the conversion or breeding becomes worse as the initial enrichment is increasing. The shuffling calculations for the 1-D SCWFR model described in this paper brought about some interesting results for a certain range of water content. The results indicate that the non-enriched fresh fuel is not possible for both Th-U and U-Pu conversions. As could be expected due to the η-values of the main fissile isotopes ²³³U and (²³⁵U, ²³⁹Pu), respectively, the Th-U conversion needs a lower enrichment, and results in a slightly higher burn-up than the U-Pu conversion. The asymptotic power density distribution of the Th-U conversion is broader and lower than that of the U-Pu conversion. By reducing the water volume fraction, an increased burn-up can be achieved with correspondingly reduced fuel shuffling speed and reduced initial enrichment. Furthermore, the steady state calculations for the asymptotic state show that the Th-U conversion is superior to the U-Pu one concerning SCWFR safety aspects, where the absolute value of the Doppler constant is larger and the coolant feedback is negative for the Th-U conversion, while the coolant feedback is positive for the U-Pu one.     

Natural convection heat transfer from horizontal rod bundles in liquid sodium. Part 2: Correlations for horizontal rod bundles based on theoretical results

Natural convection heat transfer from horizontal rod bundles in N_xm × N_ym arrays (N_xm, N_ym = 5–9) in liquid sodium was numerically analyzed for three types of the bundle geometry (in-line rows, staggered rows I and II). The unsteady laminar two-dimensional basic equations for natural convection heat transfer caused by a step heat flux were numerically solved until the solution reaches a steady state. The PHOENICS code was used for the calculation considering the temperature dependence of thermophysical properties concerned. The surface heat fluxes for each cylinder were equally given for a modified Rayleigh number, R_f, ranging from 0.0637 to 63.1 (q = 1×10⁴ to 7×10⁶ W/m²). S_x/D and S_y/D for the rod bundle, which are the ratios of the distance between center axes on the abscissa and the ordinate to the rod diameter, respectively, were ranged from 1.6 to 2.5 on each bundle geometry. The spatial distribution of Nusselt numbers, Nu, on horizontal rods of a bundle was clarified. The average value of Nusselt number, Nu_av, for three types of bundle geometry with various values of S_x/D and S_y/D were calculated to examine the effect of the array size, S/D and R_f on heat transfer. The bundle geometry for the higher Nu_av value under the condition of S_x/D×S_y/D = 4 was examined by changing the ratio of S_x/S_y. A correlation for Nu_av for the three types of bundle geometry above mentioned including the effects of S_x/D and S_y/D was developed. The correlation can describe the theoretical values of Nu_av for the three types of bundle geometry in N_xm × N_ym arrays (N_xm, N_ym = 5–9) for S_x/D and S_y/D ranging from 1.6 to 2.5 within 10% difference.     

Conceptual design of compact supercritical water-cooled fast reactor with thermal hydraulic coupling

Fuel rod design for high power density supercritical water-cooled fast reactor was conducted with mixed-oxide (MOX) fuel and stainless steel (SUS304) cladding under the limiting cladding surface temperature of 650 °C. Fuel and cladding integrities, and flow-induced vibration were taken into account as design criteria. Designed fuel rod has the diameter of 7.6 mm and is arranged in the fuel assembly with pitch-to-diameter ratio of 1.14. New core arrangement for negative void reactivity is proposed by three-dimensional tri-z core calculation fully coupled with thermal hydraulic calculation, where ZrH layer concept is used for negative void reactivity. The core has high power density of 156 W/cm³ and its equivalent diameter is only 2.7 m for 1000 MWe class reactor core. High average core outlet temperature of 500 °C is achieved by introducing radial fuel enrichment zoning and downward flow in seed assembly. Small pressure vessel size and simplified direct steam cycle with higher thermal efficiency give an economical potential in aspect of capital and operating cost.     

混合能谱超临界水堆堆芯设计分析

提出了一种新型的超临界水堆概念设计:混合能谱超临界水堆,它包括慢谱区和快谱区两部分.其慢谱区燃料组件采用双排燃料组件,快谱区采用简单的正方形栅元燃料组件.慢谱区与快谱区的燃料组件都采用同向流动方式来简化堆芯设计.慢谱区的冷却剂出口温度远低于整个堆芯的出口温度,这大大降低了慢谱区包壳的温度峰值.此外,由于快谱区冷却剂密度很小,流速很高,故可采用较大的栅元结构,这有效地降低了包壳周向局部传热不均匀性.所以混合堆在充分继承慢谱、快谱堆芯优点的基础上,弥补两者的不足.     

Possibility of using tube shell tables for calculating the heat-transfer crisis in rod bundles of water-cooled reactors

Conclusions The results of the comparison of the procedure of [2] to the experimental data on the crisis of heat transfer in bundles rod fuel elements from the domestic and foreign databases show the following: The formula of the Russian Scientific Center "Kurchatovskii institut" has much better statistical characteristics than Groeneveld's method in generalizing arrays of points on which the basis of the experimental generalization of the thermotechnical safety of domestic VVéR reactors is based. The use of a shell table for a tube (AECL-86 variant) at low pressure (2–5 MPa) results in overestimation ofq _calc/q _exp by up to a hundred of percent. At pressures above 12 MPa, however, the calculation is on the average 1.5 times lower than the experimental value. For simulators modeling the conditions for the appearance of a heat-transfer crisis in PWR and BWR cores, the method of [2] describes well an array of 11,000 points in the Columbia University database. In the case of a triangular arrangement of rods, however, there is a large discrepancy (by up to 40%) between the calculation and experiment. The additional correction [3] of the constantK ₂ for bundles did not compensate the systematic underestimation by the calculation (by 37%) for a triangular arrangement of the simulators in the presence of axial nonuniformity of energy release. Experience in operating domestic power reactors over a period of many years shows that the modern database and accurate empirical correlation make it possible to perform a reliable calculation of the admissible thermal power of rod bundles in a wide range of geometric and operating parameters, spacing methods, and energy-release fields without using the additional procedure of making the transition from a pipe to a bundle. Institute of Nuclear Reactors, Russian Scientific Center "Kurchatovskii Institut." Translated from Atomnaya énergiya, Vol. 77, No. 2, pp. 108–111, August, 1994.     

Accident analysis on supercritical water-cooled reactor during design basis and beyond design-basis condition

Supercritical water-cooled reactor (SCWR) is the only water-cooled reactor among six Generation IV reactor concepts. Safety analysis is one of the most important tasks for SCWR design. A typical thermal spectrum SCWR with passive safety system during design-basis accident (DBA) and beyond design-basis accident (BDBA) is performed. For DBA, reactor system is modeled based on a revised code ATHLET-SC. Loss of coolant accident is chosen to perform safety analysis and sensitive analysis. The results achieved demonstrate the feasibility of proposed passive cooling system to provide sufficient cooling. However, it should be noted that if one of safety systems fails to actuate during loss of coolant accident, although the likelihood is fairly low, there is potential risk of cladding failure. Consequently, the DBA will develop into the BDBA. For BDBA, a postulated severe accident is analyzed after melt pool is formed in the lower plenum. Heat transfer behavior in the melt pool as well as two-dimensional heat transfer effect in the lower head wall is discussed. Then, key parameters are chosen to perform parametric analysis. Results show that the safety margin to critical heat flux is significant. After considering two-dimensional heat conduction effect in the lower head, the safety margin could be further increased.     

The optimum design of tight lattice reactor core with thin rod bundles

The fuel height, rod diameter, pitch, and the loading pattern are all important parameters in the reactor core design process. Based on the analysis of the core performance, optimization calculation is performed on the three objective functions of ABV-6M reactor, i.e., power density, coolant temperature difference between the inlet and outlet, and flow-induced vibration are proposed for optimization calculation. Then a multi-objective problem (MOP) model is applied and computed optimally by non-dominated sorting genetic algorithm (NSGA-II) with the aim of maximizing power density and temperature difference as well as minimizing the flow-induced vibration. The results of optimal designs called ‘Pareto-optimal solutions’ are a set of multiple optimum solutions, from which the final optimization can be chosen after sensitivity analysis is performed. On the basis of lattice parameters optimization, the radial one-dimensional fuel loading pattern was optimized for achieving the optimum fuel utilization. The typical optimum design considered to be safe in a verification check showed that tight lattice effectively improved the reactor performances and saved the fuel consumption.     

Experimental investigation of turbulent flow through spacer grids in fuel rod bundles

This paper contains experimental data of pressure, velocity and turbulence intensity in a 24-rod fuel bundle with spacer grids. Detailed pressure measurements inside the spacer grid have been obtained by use of a sliding pressure-sensing rod. Laser Doppler Velocimetry technique was used to measure the local axial velocity and its fluctuating component upstream and downstream of the spacer grid in sub-channels with different blockage ratios. The measurements show a changing pattern in function of radial position in the cross-section of the fuel bundle. For sub-channels close to the box wall, the turbulence intensity suddenly increases just downstream of the spacer and then gradually decays. In inner sub-channels, however, the turbulence intensity downstream of the spacer decreases below its upstream value and then gradually increases until it reaches the maximum value at approximately two spacer heights. The present study reveals that spacer effects, such as local pressure distribution and turbulence intensity enhancement, not only depend exclusively on the local geometry details, but also on the location in the cross-section of the rod bundle.     

Experiment and numerical simulation of bubbly two-phase flow across horizontal and inclined rod bundles

Experimental and numerical analyses were carried out on vertically upward air-water bubbly two-phase flow behavior in both horizontal and inclined rod bundles with either in-line or staggered array. The inclination angle of the rod bundle varied from 0 to 60° with respect to the horizontal. The measured phase distributions indicated non-uniform characteristics, particularly in the direction of the rod axis when the rods were inclined. The mechanisms for this non-uniform phase distribution is supposed to be due to: (1) Bubble segregation phenomenon which depends on the bubble size and shape; (2) bubble entrainment by the large scale secondary flow induced by the pressure gradient in the horizontal direction which crosses the rod bundle; (3) effects of bubble entrapment by vortices generated in the wake behind the rods which travel upward along the rod axis; and (4) effect of bubble entrainment by local flows sliding up along the front surface of the rods. The liquid velocity and turbulence distributions were also measured and discussed. In these speculations, the mechanisms for bubble bouncing at the curved rod surface and turbulence production induced by a bubble were discussed, based on visual observations. Finally, the bubble behaviors in vertically upward bubbly two-phase flow across horizontal rod bundle were analyzed based on a particle tracking method (one-way coupling). The predicted bubble trajectories clearly indicated the bubble entrapment by vortices in the wake region.     

Cladding response to uniform radial compaction of clinch river breeder reactor blanket rod bundles

Neutron radiation induced growth can lead to compaction of fast reactor fuel and blanket rod bundles within their duct assemblies, resulting in local cladding stresses and coolant channel closure. The stiffness of the Clinch River Breeder Reactor (CRBRP) blanket rod bundle during uniform radial compaction was measured experimentally, and was compared to theoretical predictions which assumed no relative rod-rod motion within the bundle during compaction. The basic agreement between the measured and theoretical compaction stiffness values permitted an assessment to be made of cladding stresses and coolant channel closures in CRBRP blanket rod bundles due to rod bundle-duct differential growth.