Experimental investigation on bubble characteristics entrained by surface vortex

The cover gas entrainment at the free surface of sodium coolant becomes one of the significant issues according to the compact sizing of reactor vessel in the latest reactor design. In the present study, some basic experiments for the gas entrainment due to the surface vortex were performed in order to obtain the fundamental knowledge about the entrained bubble size. Distributions of entrained bubble diameters in several experimental conditions were obtained from bubble images using an image processing technique. Velocity fields around vortices and surface dimple shapes (gas cores) due to surface vortices were measured to grasp those influences on bubble shapes. The result showed that mean equivalent diameters of bubbles were varied from 1.3 to 2.1 mm in the range of present experimental conditions. The bubble sizes were influenced by the thickness of gas core.     

过冷水流经通道的闪蒸临界流模型研究

反应堆发生失水事故时,破口处的临界流量决定着冷却水系统的装量,影响着堆芯燃料元件温度分布,对事故后果起重要作用。为了更好理解临界流动中各项参数的变化规律及机理,提出了两流体六方程临界流动模型,用来计算初始滞止状态为过冷水通过通道的临界流量。模型中既考虑了两相之间的动力学不均匀,也考虑了相间热力学不平衡。模型中引入了合适的计算闪蒸起始点位置和过热度的公式,并将汽泡增长方程与基本方程联立求解,可比较准确地反映汽泡的增长规律。在较宽的压力和温度范围内、不同长径比情况下,模型预测结果与试验结果符合较好,表明该模型具有较强的通用性。     

Cross-comparison of fast reactor concepts with various coolants

Four fast reactor concepts using lead (LFR), liquid salt, NaCl-KCl-MgCl₂ (LSFR), sodium (SFR), and supercritical CO₂ (GFR) coolants are compared. Since economy of scale and power conversion system compactness are the same by virtue of the consistent 2400 MWt rating and use of the S-CO₂ power conversion system, the achievable plant thermal efficiency, core power density and core specific powers become the dominant factors. The potential to achieve the highest efficiency among the four reactor concepts can be ranked from highest to lowest as follows: (1) GFR, (2) LFR and LSFR, and (3) SFR. Both the lead- and salt-cooled designs achieve about 30% higher power density than the gas-cooled reactor, but attain power density 3 times smaller than that of the sodium-cooled reactor. Fuel cycle costs are favored for the sodium reactor by virtue of its high specific power of 65 kW/kgHM compared to the lead, salt and gas reactor values of 45, 35, and 21 kW/kgHM, respectively. In terms of safety, all concepts can be designed to accommodate the unprotected limiting accidents through passive means in a self-controllable manner. However, it does not seem to be a preferable option for the GFR where the active or semi-passive approach will likely result in a more economic and reliable plant. Lead coolant with its superior neutronic characteristics and the smallest coolant temperature reactivity coefficient is easiest to design for self-controllability, while the LSFR requires special reactivity devices to overcome its large positive coolant temperature coefficient. The GFR required a special core design using BeO diluent and a supercritical CO₂ reflector to achieve negative coolant void worth—one of the conditions necessary for inherent shutdown following large LOCA. Protected accidents need to be given special attention in the LSFR and LFR due to the small margin to freezing of their coolants, and to a lesser extent in the SFR.     

棒束定位格架两相CFD模拟方法研究

考虑气泡合并分裂,采用MUSIG模型,对3×3格架内空气-水两相分布进行计算流体力学(CFD)数值模拟研究发现,计算对入口两相分布预计不敏感,但对气泡直径大小敏感;在定位格架下游不远处,空泡份额分布由较小直径气泡起主导作用,格架下游较远处,空泡份额分布由较大直径气泡起主导作用。考虑空气-水两相流量、几何条件和压力对气泡直径的影响,本文提出针对棒束定位格架的数值模拟气泡最大直径设置关系式,并对模型选取和模拟方法给出建议。计算表明空泡份额分布曲线形状与峰值均和实验符合较好,该模拟方法能合理预测复杂通道两相数值分布。     

A study on reactivity insertion controlled LMR cores with metallic fuel

An inherently safe core concept with metallic fuel for sodium cooled fast reactor is proposed that has a negative void reactivity at the loss of coolant events without scram as well as a small excess reactivity during the operation cycle. The relationship of sodium void reactivities and burn-up reactivities to different core configurations has been studied quantitatively to clarify the core concept for large metallic fuel reactors. It has shown that the sodium void reactivity is greatly dependent on the core shapes while the excess reactivity is on the fuel compositions. It has also indicated that the core configuration that enables to enhance the neutron streaming through the region above the active core at coolant voiding is most effective to decrease sodium void reactivity.

A 3000 MWt core composed of the flat inner core and annular outer core where the fuel volume fraction is relatively high and the sodium plenum is placed just above the active core region has been selected as a candidate core.

The maximum excess reactivity of the candidate core at UTOP is about 0.4 $ and it can be reduced to approximately zero by power or inlet temperature adjustment during the operation cycle, meanwhile the sodium void reactivity is as low as -1.3 $ in negative that is enough to prevent ULOF sequences.     

Characterization of a sodium-cooled fast reactor in an MHR–SFR synergy for TRU transmutation

In the task of destroying the light water reactor (LWR) transuranics (TRUs), we consider the concept of a synergistic combination of a deep-burn (DB) gas-cooled reactor followed by a sodium-cooled fast reactor (SFR), as an alternative way to the direct feeding of the LWR TRUs to the SFR. In the synergy concept, TRUs from LWR are first deeply incinerated in a graphite-moderated DB-MHR (modular helium reactor) and then the spent fuels of DB-MHR are recycled into the closed-cycle SFR. The DB-MHR core is 100% TRU-loaded and a deep-burning (50–65%) is achieved in a safe manner (as discussed in our previous work). In this analysis, the SFR fuel cycle is closed with a pyro-processing technology to minimize the waste stream to a final repository. Neutronic characteristics of the SFR core in the MHR–SFR synergy have been evaluated from the core physics point of view. Also, we have compared core characteristics of the synergy SFR with those of a stand-alone SFR transuranic burner. For a consistent comparison, the two SFRs are designed to have the same TRU consumption rate of ∼250 kg/GW EFPY that corresponds to the TRU discharge rate from three 600 MW DB-MHRs. The results of our work show that the synergy SFR, fed with TRUs from DB-MHR, has a much smaller burnup reactivity swing, a slightly greater delayed neutron fraction (both positive features) but also a higher sodium void worth and a less negative Doppler coefficients than the conventional SFR, fed with TRUs directly from the LWRs. In addition, several design measures have been considered to reduce the sodium void worth in the synergy SFR core.     

Comparison of JSFR design with EDF requirements for future SFR

A comparison of the Japan sodium-cooled fast reactor (JSFR) design with the future French sodium-cooled fast reactor (SFR) concept has been done based on the requirements of Electricité de France (EDF), the investor-operator of the future French SFR, and the French safety baseline, under the framework of an EDF and Japan Atomic Energy Agency (JAEA) bilateral agreement of research and development cooperation in future SFRs..     

Analytical evaluation on dynamical response characteristics of reduced-moderation water reactor with tight-lattice core under natural circulation core cooling

The time-domain analyses with TRAC-BF1 code were performed for clarifying the dynamical response characteristics of the reduced-moderation water reactor (RMWR) with tight-lattice core configuration. The response characteristics were evaluated based on the step response basically utilized for dynamical system evaluation. As for the most fundamental dynamical characteristics, the channel flow response characteristics of single fuel assembly were evaluated. In the evaluation, the appropriate single-phase pressure drop setting at the inlet orifice was determined in terms of response stability from the design viewpoint. In addition, from the investigation on the relation of the response and transit time of coolant, it is confirmed that the channel flow response of RMWR is dominated by the transit time of vapor phase resulting from a high void fraction operation condition. As for a natural circulation flow response, it is clarified that the response is strongly influenced by the effect of two-phase pressure loss owing to a high void fraction condition. The reactor power response with reactivity feedback shows quite stable response characteristics on account of the small absolute value of void reactivity coefficient.     

Safety Strategy of JSFR Eliminating Severe Recriticality Events and Establishing In-Vessel Retention in the Core Disruptive Accident

In the Japan Sodium Cooled Fast Reactor (JSFR) design, elimination of severe power burst events in the Core Disruptive Accident (CDA) is intended as an effective measure to ensure retention of the core materials within the reactor vessel. The design strategy is to control the potential of excessive void reactivity insertion in the initiating phase by selecting appropriate design parameters such as maximum void reactivity on one hand, and to exclude core-wide molten-fuel-pool formation, which has been the main issue of CDA, by introducing an inner duct on the other hand. The effectiveness of these measures is evaluated based on existing experimental data and computer simulation with validated analytical tools. It is judged that the present JSFR design can exclude severe power burst events. Phenomenological consideration of general characteristics and preliminary evaluations for the long-term material relocation and cooling phases gave the perspective that in-vessel retention would be attained with appropriate design measures.     

A unified model considering force balances for departing vapour bubbles and population balance in subcooled boiling flow

Population balance equations combined with a three-dimensional two-fluid model are employed to predict subcooled boiling flow at low pressure in a vertical annular channel. The MUltiple-SIze-Group (MUSIG) model implemented in CFX4.4 is extended to account for the wall nucleation and condensation in the subcooled boiling regime. A model considering the forces acting on departing bubbles at the heated surface is formulated. This model provides the capacity of complex analyses on the bubble growth and departure for a wide range of wall heat fluxes and flow conditions.Comparison of model predictions against local measurements is made for the void fraction, bubble Sauter mean diameter and gas and liquid velocities covering a range of different mass and heat fluxes and inlet subcoolings. Good agreement is achieved with the local radial void fraction, bubble Sauter mean diameter and liquid velocity profiles against measurements. However, significant weakness of the model is evidenced in the prediction of the vapour velocity. Work is in progress to circumvent the deficiency of the MUSIG boiling model by the consideration of additional momentum equations to better represent the momentum forces acting on the range of bubble sizes in the bulk subcooled liquid.     

Full-scale modelling of the MNSR reactor to simulate normal operation, transients and reactivity insertion accidents under natural circulation conditions using the thermal hydraulic code ATHLET

A full-scale ATHLET system model for the Syrian miniature neutron source reactor (MNSR) has been developed. The model represents all reactor components of primary and secondary loops with the corresponding neutronics and thermal hydraulic characteristics. Under the MNSR operation conditions of natural circulation, normal operation, step reactivity transients and reactivity insertion accidents have been simulated. The analyses indicate the capability of ATHLET to simulate MNSR dynamic and thermal hydraulic behaviour and particularly to calculate the core coolant velocity of prevailing natural circulation in presence of the strong negative reactivity feed back of coolant temperature. The predicted time distribution of reactor power, core inlet and outlet coolant temperature follow closely the measured data for the quasi steady and transient states. However, sensitivity analyses indicate the influence of pressure form loss coefficients at core inlet and outlet on the results. The analysis of reactivity accidents represented by the insertion of large reactivity, demonstrates the high inherent safety features of MNSR. Even in case of insertion of total available cold excess reactivity without scram, the high negative reactivity feedback of moderator temperature limits power excursion and avoids consequently the escalation of clad temperature to the level of onset of sub-cooled void formation. The calculated peak power in this case agrees well with the data reported in the safety analysis report. The ATHLET code had not previously been assessed under these conditions. The results of this comprehensive analysis ensure the ability of the code to test some conceptual design modifications of MNSR's cooling system aiming the improvement of core cooling conditions to increase the maximum continuous reactor operation time allowing more effective use of MNSR for irradiation purposes.     

Void distribution and bubble motion in bubbly flows in a 4×4 rod bundle. Part I: Experiments

Lack of local void fraction data in a rod bundle makes it difficult to validate a numerical method for predicting gas–liquid two-phase flow in the bundle. Distributions of local void fraction and bubble velocity in each subchannel in a 4×4 rod bundle were, therefore, measured using a double-sensor conductivity probe. Liquid velocity in the subchannel was also measured using laser Doppler velocimetry (LDV) to obtain relative velocity between bubbles and the liquid phase. The size and pitch of rods were 10 and 12.5 mm, respectively. Air and water at atmospheric pressure and room temperature were used for the gas and liquid phases, respectively. The volume fluxes of gas and liquid phases ranged from 0.06 to 0.15 m/s and from 0.9 to 1.5 m/s, respectively. Experimental results showed that the distributions of void fraction in inner and side subchannels depend not only on lift force acting on bubbles but also on geometrical constraints on bubble dynamics, i.e. the effects of rod walls on bubble shape and rise velocity. The relative velocity between bubbles and the liquid phase in the subchannel forms a non-uniform distribution over the cross-section, and the relative velocity becomes smaller as bubbles approach the wall due to the wall effects.     

Effect of Gas Entrainment on Thermal-Hydraulic Performance of Sodium Cooled Reactor Core

With the view to determining whether or not gas entrained in the sodium coolant could cause overheating of a fast reactor core, the following items were studied:

1. The effect of gas entrainment on the coolant flow rate and on coolant temperature rise.

2. The effect of gas entrainment on the coolant heat transfer coefficient and film temperature drop.

Equations were derived to serve in estimating the thermal-hydraulic effect of the gas entrainment, and calculations performed therewith to obtain information on conditions corresponding to the Core A under operation in the Fermi Reactor.

The results of the present examination reveal that in the Fermi Reactor an amount of gas almost inconceivable as a practical possibility must be entrained before the coolant or the fuel surface would be heated to the boiling point of sodium.     

摇摆条件下小型反应堆堆芯入口流量分配特性数值分析

为研究摇摆条件下小型反应堆强迫循环时堆芯入口处冷却剂的流量分配特性,采用数值计算的方法,使用计算流体力学（CFD）软件STAR-CCM+建立小型反应堆模型,完成模型验证,开展摇摆条件下反应堆堆芯入口流量分配特性研究。结果表明,堆芯入口位置距摇摆轴的距离越大,摇摆幅度越大,堆芯入口冷却剂流量波动越大;长周期摇摆对流量影响较小,但随着摇摆周期减小,冷却剂流量会发生跃变。堆芯入口冷却剂分布不均匀程度随摇摆幅度的增加而增加,但对摇摆周期变化并不敏感。     

Improvement of Gas Entrainment Prediction Method—Introduction of Surface Tension Effect—

A gas entrainment (GE) prediction method has been developed to establish design criteria for the largescale sodium-cooled fast reactor (JSFR) systems. The prototype of the GE prediction method was already confirmed to give reasonable gas core lengths by simple calculation procedures. However, for simplification, the surface tension effects were neglected. In this paper, the evaluation accuracy of gas core lengths is improved by introducing the surface tension effects into the prototype GE prediction method. First, the mechanical balance between gravitational, centrifugal, and surface tension forces is considered. Then, the shape of a gas core tip is approximated by a quadratic function. Finally, using the approximated gas core shape, the authors determine the gas core length satisfying the mechanical balance. This improved GE prediction method is validated by analyzing the gas core lengths observed in simple experiments. Results show that the analytical gas core lengths calculated by the improved GE prediction method become shorter in comparison to the prototype GE prediction method, and are in good agreement with the experimental data. In addition, the experimental data under different temperature and surfactant concentration conditions are reproduced by the improved GE prediction method.     

Reactor core design optimization of the 200 MWt Pb–Bi cooled fast reactor for hydrogen production

In this study reactor core geometrical optimization of 200 MWt Pb–Bi cooled long life fast reactor for hydrogen production has been conducted. The reactor life time is 20 years and the fuel type is UN-PuN. Geometrical core configurations considered in this study are balance, pancake and tall cylindrical cores. For the hydrogen production unit we adopt steam membrane reforming hydrogen gas production. The optimum operating temperature for the catalytic reaction is 540 °C. Fast reactor design optimization calculation was run by using FI-ITB-CHI software package. The design criteria were restricted by the multiplication factor that should be less than 1.002, the average outlet coolant temperature 550 °C and the maximum coolant outlet temperature less than 700 °C. By taking into account of the hydrogen production as well as corrosion resulting from Pb–Bi, the balance cylindrical geometrical core design with diameter and height of the active core of 157 cm each, the inlet coolant temperature of 350 °C and the coolant flow rate of 7000 kg/s were preferred as the best design parameters.     

Development of ATR Type Steam Separator Performance Analysis Code and Its Validation, (I)

The purpose of the study is to develop a method for predicting steam carryunder which is one of the important characteristics of a steam separator. Bubbles returning to the liquid surface and trapped by the re-circulating flow are calculated by tracking the behavior of bubbles moving in liquid bulk where velocity and temperature distributions have been calculated beforehand in conjunction with the Monte-Carlo method. Regarding the statistics of bubbles, a survey of references and visual tests have been conducted. To validate this method, several tests to measure bubble behavior under air/water conditions at atmospheric pressure and high temperature and pressure ranging 3~7 MPa have been conducted with a full-scale steam separator.

As a result, the developed method predicted with good precision the carryunder ratio obtained by the full-scale tests under the condition that carried-under void fraction was less than 20%, but underestimated carryunder ratio in the ATR “Fugen” reactor in which steam drum water level was shallow and average void fraction in water bulk was high. This method has a characteristic that carryunder ratio is underestimated in the case that void fraction is more than 20%.     

Flow structure and bubble characteristics of steam–water two-phase flow in a large-diameter pipe

The flow structure and bubble characteristics of steam–water two-phase upward flow were observed in a vertical pipe 155 mm in inner diameter. Experiments were conducted under volumetric flux conditions of J_G<0.25 m s⁻¹ and J_L<0.6 m s⁻¹, and three different inlet boundary conditions to investigate the developing state of the flow. The radial distributions of flow structure, such as void fraction, bubble chord length and gas velocity, were obtained by horizontally traversing optical dual void probes through the pipe. The spectra of bubble chord length and gas velocity were also obtained to study the characteristics of bubbles in detail. Overall, an empirical database of the multi-dimensional flow structure of two-phase flow in a large-diameter pipe was obtained. The void profiles converged to a so-called core-shaped distribution and the flow reached a quasi-developed state within a relatively short height-to-diameter aspect ratio of about H/D=4 compared to a small-diameter pipe flow. The PDF histogram profiles of bubble chord length and gas velocity could be approximated fairly well by a model function using a gamma distribution and log–normal distribution, respectively. Finally, the correlation of Sauter mean bubble diameter was derived as a function of local void fraction, pressure, surface tension and density. With this correlation, cross sectional averaged bubble diameter was predicted with high accuracy compared to the existing constitutive equation mainly being used in best-estimate codes.     

大型MOX燃料快堆钠空泡反应性微扰理论研究

钠空泡反应性效应是钠冷快堆核设计和安全分析的重要内容。本文基于多群节块扩散法,采用微扰理论推导出钠空泡反应性的计算方法,对1 000 MWe钠冷快堆MOX燃料堆芯的总钠空泡反应性、空间分布、物理分项进行了计算。结果表明,钠空泡反应性主要来源于中子泄漏的增加和能谱的硬化,两者一正一负,且空间分布规律相反,导致钠空泡反应性具有强烈的空间依赖性;对于所计算的MOX燃料堆芯钠空泡反应性高达3 $左右。计算和分析结果阐明了钠空泡反应性的产生机理和分布规律,可为低钠空泡的设计提供参考。     

The behavior of reactor power and flux resulting from changes in core-coolant temperature for a miniature neutron source reactor

In this work, measurements were performed to verify the theoretical predictions of reactor power and flux parameters that result from changes in core inlet temperature (T_in) and the temperature difference between the coolant inlet and outlet (ΔT) in the Nigeria Research Reactor-1 (NIRR-1), which is a Miniature Neutron Source Reactor (MNSR). The measured data shows that there is a strong dependence of the reactor power on coolant temperature in agreement with the design of MNSR. The experimental parameters were found to be in good agreement with data obtained using a semi-empirical relationship between the reactor power, flux parameters, core inlet temperature, and the coolant temperature rise. The relationship was therefore used to predict the power level of NIRR-1 from its neutron flux parameters to which it has been found to be proportional. The variation of T_in and ΔT with the reactor power and flux was also investigated and the results obtained are hereby discussed.