The effective convectivity model for simulation of melt pool heat transfer in a light water reactor pressure vessel lower head. Part II: Model assessment and application

The paper reports detailed assessments and representative application of the effective convectivity model (ECM) developed and described in the companion paper (Tran and Dinh, submitted for publication). The ECM capability to accurately predict energy splitting and heat flux profiles in volumetrically heated liquid pools of different geometries over a range of conditions related to accident progression is examined and benchmarked against both experimental data and CFD results. Augmented with models for phase changes in binary mixture, the resulting PECM (phase-change ECM) is validated against a non-eutectic heat transfer experiment. The PECM tool is then applied to predict thermal loads imposed on the reactor vessel wall and Control Rod Guide Tubes (CRGTs) during core debris heatup and melting in the BWR lower plenum. The reactor-scale simulations demonstrate the PECM's high computational performance, particularly needed to analyze processes during long transients of severe accidents. The analysis provides additional arguments to support an outstanding potential of using the CRGT cooling as a severe accident management measure to delay the vessel failure and increase the likelihood of in-vessel core melt retention in the BWR.     

Modelling of heat and mass transfer processes during core melt discharge from a reactor pressure vessel

The objective of this paper is to study the heat and mass trasnfer processes related to core melt discharge from a reactor vessel in a light water reactor severe accident. The phenomenology modelled includes the convection in, and heat transfer from, the melt pool in contact with the vessel lower head wall, the fluid dynamics and heat transfer of the melt flow in the growing discharge hole and multi-dimensional heat conduction in the ablating lower head wall. A research programme is underway at the Royal Institute of Technology (Kungliga Tekniska Högskolan, KTH) to (1) identify the dominant heat and mass transfer processes determining the characteristics of the lower head ablation process: (2) develop and validate efficient analytical/computational models for these processes; (3) apply models to assess the character of the melt discharge process in a reactor-scale situation; (4) determine the sensitivity of the melt discharge to structural differences and variations in the in-vessel melt progression scenarios. The paper also presents a comparison with recent results of vessel hole ablation experiments conducted at KTH with a melt simulant.     

熔融物压力容器内滞留瞬态传热特性分析

基于SCDAP/RELAP5程序建立了用于熔融物压力容器内滞留（IVR）瞬态分析的系统简化模型,通过对模块式小型堆IVR过程的瞬态计算与分析,初步探索了IVR策略实施过程中压力容器下封头的瞬态热负荷特性。SCDAP/RELAP5程序的计算结果表明,利用外部冷却实施IVR策略的瞬态传热特性可分为熔融物注入之初的激烈传热阶段和熔融物硬壳形成之后的准稳态传热阶段。模块式小型堆的IVR瞬态分析表明,瞬态过程中的热流密度峰值不会达到临界热流密度,最终形成的稳定熔融池传热具有很大的安全裕量。研究同时发现SCDAP/RELAP5程序用于IVR分析时在模型上存在一定的不足。     

Analysis of likelihood of lower head failure and ex-vessel fuel coolant interaction energetics for AP1000

A one-dimensional model is formulated to assess the thermal response of the Westinghouse Advanced Plant (AP1000) lower head based on two bounding melt configurations. Melt Configuration I involves a stratified light metallic layer on top of a molten ceramic pool, and melt Configuration II represents the conditions that an additional heavy metal layer forms below the ceramic pool. The approach consists of the specification of initial conditions; determination of the mode, the size and the location of lower head failure based on heat transfer analyses; computer simulation of the fuel coolant interaction processes; and finally, an examination of the impact of the uncertainties in the initial conditions and the model parameters on the fuel coolant interaction energetics through a series of sensitivity calculations. The results of the calculations for melt Configuration I show that the heat flux remains below critical heat flux (CHF) in the molten oxide pool, but the heat flux in the light metal layer could exceed CHF because of the focusing effect associated with presence of the thin metallic layers. The thin metallic layers are associated with smaller quantities of the molten oxide in the lower plenum following the initial relocation into the lower head. The calculations show that the lower head failure probability due to the focusing effect of the stratified metal layer ranges from 0.04 to 0.30. On the other hand, the thermal failure of the lower head at the bottom location for melt Configuration II is assessed to be highly unlikely. Based on the in-vessel retention analysis, the base case for the ex-vessel fuel coolant interaction (FCI) is assumed to involve a side failure of the vessel involving a metallic pour into the cavity water. The FCI sensitivity calculations intended to assess the implications of the uncertainties in initial conditions and the FCI modeling parameters show that the FCI loads range from a few MPa to upward of 1000 MPa (maximum pool pressure) with corresponding impulse loads ranging from a few kPa s to a few hundred kPa s.     

熔融池相变传热特性的大涡模拟数值研究

研究反应堆熔融池内部的流动与传热特性对保证熔融物堆内滞留具有重要意义。本文基于开源软件OpenFOAM平台,结合大涡模拟湍流方法和熔融池相变过程建立熔融池传热模型,针对典型熔融池传热实验LIVE工况开展数值计算,得到了熔融池内速度场和温度场以及下封头内壁面硬壳厚度和热流密度分布情况。结果表明,熔融池内速度、温度和热流密度随高度或径向角度的增大而增大;硬壳厚度随径向角度的增大而减小;下封头壁面上的热负荷在顶部聚集。传热参数计算结果与实验数据整体符合较好,可以有效反映出熔融池内自然对流与相变过程,验证了计算模型的可靠性,可为进一步研究熔融池相变传热特性提供参考。      

压水堆堆芯熔融物的运动及传热数值分析

针对HPR1000堆型堆芯熔融坍塌问题建立了精确的三维堆芯模型,使用时间推进方法通过求解熔融物的瞬态运动、传热微分方程,确定熔融物在堆芯中的瞬态位置和瞬时温度,以模拟堆芯升温及堆芯熔融进程。研究结果表明：停堆后约2 400 s开始出现熔融现象,熔融物在堆芯活性区域内下落且发生多重相变过程;在4 900 s后,熔融物在堆芯底部形成约1.5 m高的稳定熔池;由于外围组件与低温围栏装置换热,最外围的组件不会发生熔融。本文建立的堆芯熔融物运动与传热分析模型及相关计算结果,可为事故缓解和处理提供技术参考。     

严重事故下大功率先进压水堆IVR-ERVC有效性分析

通过压力容器外部冷却(ERVC)以实现堆内熔融物滞留(IVR)作为反应堆严重事故缓解管理的一项重要举措一直以来广泛受到关注和研究。本文使用严重事故分析程序MELCOR,从瞬态角度对大型先进压水堆进行了IVR-ERVC相关研究。过程中重点关注了堆芯熔毁和重新定位,熔池形成、生长及其传热过程,并且对压力容器外部流动传热进行了分析。MELCOR计算所得下封头热流密度分布的瞬态结果与临界热流密度(CHF)比较和分析表明,1700 MWe大功率压水堆发生严重事故后在IVRERVC条件下能够保证压力容器的完整性,即,IVR-ERVC能够有效带出下封头熔融物的衰变热量,缓解严重事故后果。     

熔融物堆芯冷却滞留特性研究

以模块式小型堆ACP100为分析对象,建立MELCOR程序严重事故分析模型,分析了堆芯衰变热依次经过吊篮、压力容器壁面然后进入堆腔注水系统(CIS)的传热行为。采用燃料棒失效模型评价燃料组件坍塌行为,并通过ANSYS程序蠕变断裂模型评价堆芯下板失效行为。分析结果表明,严重事故后堆芯中心燃料组件坍塌形成堆芯熔融池,堆芯周围燃料组件保持完整结构状态,堆芯下板支撑堆芯熔融池和未坍塌的燃料组件且未发生蠕变断裂失效;CIS冷却压力容器外壁面并导出堆芯衰变热,最终实现熔融物堆芯滞留,避免下封头内形成熔融池。     

熔融物堆芯冷却滞留特性研究

The severe accident analysis model of the small modular reactor ACP100 is built using MELCOR code, and the core heat removed process through the barrel and wall of reactor pressure vessel (RPV) is analyzed by the cavity injection system (CIS). The collapse behavior of the fuel assemblies is estimated by the fuel rod degradation model, and the failure behavior of the lower core plate is estimated by ANSYS program. The results show that the fuel assemblies in the core center melt and collapse to form the core melting pool, while the structure of the fuel assemblies surrounding the core melting pool remains intact, and the core lower plate supports the core melting pool and un-collapsed fuel assemblies all the time, and no creep rupture phenomenon occurs; the core heat can be removed by CIS and the debris in-vessel retention successfully avoids the formation of molten pool in the lower head.     

椭球形与球形下封头压力容器内熔融物滞留传热特性分析

严重事故下堆芯熔融物再分布于压力容器下封头,在衰变热作用下高温堆芯熔融物对压力容器壁面施加较大的热负荷,可能导致压力容器失效。针对压力容器内熔融物滞留下的传热过程,基于Fortran90语言开发了椭球形下封头压力容器内熔融物堆内滞留（IVR）分析程序IVRASA-ELLIP,计算具有椭球形下封头的压力容器在严重事故下稳态熔池的传热过程及IVR特性。利用IVRASA-ELLIP程序计算了VVER-1000压力容器内熔池的传热,分析具有椭球形下封头的压力容器各处的壁面热流密度、氧化物硬壳厚度和压力容器壁厚,并与运用IVRASA程序计算的AP1000稳态熔池传热结果进行对比分析。研究结果表明,在相同初始参数下椭球形下封头内的壁面热流密度较球形下封头内的小,与热流密度的变化趋势相对应,椭球形下封头内压力容器壁的消融量较球形下封头内的小,椭球形下封头内形成的氧化物硬壳厚度较球形下封头内的厚。     

A simple novel and fast computational model for the LIVE-L4

The LIVE-L4 test was conducted to investigate the transient and steady state behavior of the molten pool and the crust influenced by different heat generation rates. The main purpose of this work is to develop a simple novel model of the LIVE code to calculate the entire process of the LIVE-L4 test after the melt of KNO₃–NaNO₃ poured into the test vessel. The LIVE code is a transient code and can be used as a fast computational program to calculate the LIVE tests. Natural convection heat transfer in the melt pool, crust behavior, heat conduction in the vessel wall, and radiative heat transfer were all considered in the model of the LIVE code.In the LIVE code, Asfia–Dhir correlations were used to calculate average and local heat transfer coefficients in the melt pool. With the assumption of no considering the composition change of local melt at melt/crust interface, many important parameters, including the melt pool temperature, heat flux distribution along the vessel wall, the thickness of the crust in steady state, and crust growth rate during the test, were calculated and compared with the LIVE-L4 experimental data.The melt pool Nu calculated by the LIVE code is larger than experimental data due to the use of Asfia–Dhir correlation in the LIVE code, which caused the average heat flux through the vessel wall larger than experiment data except the heating phase of 5 kW. It is attributed that the temperature difference between the melt pool temperature and the interface temperature at melt/crust measured in the test is larger than that calculated by the LIVE code due to the constant interface temperature at melt/crust of 284 °C used in the LIVE code. Crust growth rate calculated by the LIVE code was consistent well with the experiment data. Calculation results indicated that the LIVE code could generally predict the main parameters of the melt and crust well during the LIVE-L4 test.     

Analysis of safety margin of in-vessel retention for AP1000

In-vessel retention (IVR) of core melt is a key severe accident management strategy adopted by most operating nuclear power plants and advanced light water reactors (ALWRs), AP600, AP1000, etc. External reactor vessel cooling (ERVC) is a novel severe accident management for IVR analysis. In present study, IVR analysis code in severe accident (IVRASA) has been developed to evaluate the safety margin of IVR in AP1000 with anticipative depressurization and reactor cavity flooding in severe accident. For, IVRASA, the point estimate procedure has been developed for modeling the steady-state endpoint of two core melt configurations: Configuration I and Configuration II. The results of benchmark calculations of AP600 by IVRASA were consistent with those of the UCSB and INEEL. Then, IVRASA is used to calculate the heat transfer process caused by two core melt configurations of AP1000. The results of calculations of Configuration I indicate that the heat flux remains below the critical heat flux (CHF), however, the sensitivity calculations show that the heat flux in the metallic layer could exceed the CHF because of the focusing effect due to the thin metallic layer. On the other hand, the results of calculations of Configuration II suggest that the thermal failure of the lower head at the bottom location is highly unlikely, but the heat flux in light metallic layer could be higher than that of base case due to the portion of metal partitioning into the lower head. This work also investigated the effect of the uncertainties of the CHF correlations on the analysis of IVR.     

Numerical study on the heat transfer characteristics of LIVE-L4 melt pool with a partial solidification process

Using the source-based SIMPLE algorithm based on a fixed grid method, a two-dimensional numerical model for a convection-diffusion controlled mushy region phase-change problem was developed to investigate the heat transfer characteristics of LIVE L4 melt pool subjected to a partial solidification process in a Pressurized Water Reactor (PWR) lower plenum during a hypothetical severe accident. For the binary non-eutectic mixtures of L4 melt, a linear liquid fraction temperature relationship was implemented on the calculations of the velocity and enthalpy in the mushy zone. The effect of fluid flow in the melt pool was analyzed, and numerical results for the cases with and without phase change model were calculated to investigate the effects of solidification on the heat transfer characteristics of L4 melt pool. Numerical results indicated that the phase-change model could well predict the main parameters of melt pool, e.g. the melt pool temperatures, heat flux through the melt pool, and the crust thickness. Results also indicated that the predicted Nu number without solidification was overestimated by about 12%, compared with that with solidification.     

Late-phase melt conditions affecting the potential for in-vessel retention in high power reactors

If cooling is inadequate during a reactor accident, a significant amount of core material could become molten and relocate to the lower head of the reactor vessel, as happened in the Three Mile Island Unit 2 accident. In such a case, concerns about containment failure and associated risks can be eliminated if it is possible to ensure that the lower head remains intact so that relocated core materials are retained within the vessel. Accordingly, in-vessel retention (IVR) of core melt as a key severe accident management strategy has been adopted by some operating nuclear power plants and planned for some advanced light water reactors. However, it is not clear that currently proposed external reactor vessel cooling (ERVC) without additional enhancements can provide sufficient heat removal to assure IVR for high power reactors (i.e., reactors with power levels up to 1500 MWe). Consequently, a joint United States/Korean International Nuclear Energy Research Initiative (I-NERI) has been launched to develop recommendations to improve the margin of success for in-vessel retention in high power reactors. This program is initially focussed on the Korean Advanced Power Reactor—1400 MWe (APR1400) design. However, recommendations will be developed that can be applied to a wide range of existing and advanced reactor designs. The recommendations will focus on modifications to enhance ERVC and modifications to enhance in-vessel debris coolability. In this paper, late-phase melt conditions affecting the potential for IVR of core melt in the APR1400 were established as a basis for developing the I-NERI recommendations. The selection of ‘bounding’ reactor accidents, simulation of those accidents using the SCDAP/RELAP5-3D^© code, and resulting late-phase melt conditions are presented. Results from this effort indicate that bounding late-phase melt conditions could include large melt masses (>120,000 kg) relocating at high temperatures (3400 K). Estimated lower head heat fluxes associated with this melt could exceed the maximum critical heat flux, indicating additional measures such as the use of a core catcher and/or modifications to enhance external reactor vessel cooling may be necessary to ensure in-vessel retention of core melt.     

DVI 管线中小破口叠加 IRWST 失效引发严重事故的 ERVC 研究

以AP1000核电厂为参考对象,采用SCDAP/RELAP5/MOD3.4程序,用确定论方法计算直接注入(DVI)管线中、小破口初因叠加内置换料水箱(IRWST)失效严重事故和采取压力容器外部冷却(ERVC)后的效果,重点分析了主要非能动注入系统的响应,熔池和下封头行为。计算结果表明,DVI管线发生破口导致堆芯熔化比热段同等尺寸破口要早,ERVC可以有效防止下封头熔穿。     

Simulation of scaled vessel failure experiments and investigation of a possible vessel support against failure

Scaled coupled melt pool convection and vessel creep failure experiments are being performed in the FOREVER program at the Royal Institute of Technology, Stockholm. These experiments are simulating the lower head of a pressurized reactor vessel under the thermal load of a melt pool with internal heat sources and a specified internal pressure. Due to the multi-axial creep deformation of the three-dimensional vessel with a prototypic non-uniform temperature field these experiments offer an excellent opportunity to validate numerical creep models. A Finite Element Model is developed and using the Computational Fluid Dynamic module, the melt pool convection is simulated and the temperature field within the vessel wall is evaluated. The transient structural mechanical calculations are then performed applying a new creep modeling procedure. Additionally, the material damage is evaluated considering the creep deformation as well as the prompt plastic deformation.After post-test calculations for the FOREVER-C2 experiment, pre-test calculations for the forthcoming experiments are performed. Taking into account both—experimental and numerical results—gives a good opportunity to improve the simulation and understanding of real accident scenarios. After analyzing the results of the calculations, it seems to be advantageous to provide a vessel support, which can unburden the vessel from a part of the mechanical load and, therefore, avoid the vessel failure or at least prolong the time to failure. This can be a possible accident mitigation strategy. Additionally, it may be advantageous to install a passive automatic control device to initiate the flooding of the reactor pit to ensure external vessel cooling in the event of a core melt down.     

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.     

Characterization of heat transfer processes in a melt pool convection and vessel-creep experiment

The results of an integral experiment on melt pool convection and vessel-creep deformation are presented and analyzed. The experiment is performed on a test facility, named Failure Of REactor VEssel Retention (FOREVER). The facility employs a 1/10-scaled 15Mo3-(German)-steel vessel of 400-mm diameter, 15-mm wall thickness and 750-mm height. A high-temperature (1300 °C) oxide melt is prepared in a SiC-crucible placed in a 50 kW induction furnace and is, then, poured into the 1/10th scale vessel. A MoSi₂ 50 kW electric heater is employed in the melt pool to heat and maintain its temperature at 1200 °C. The vessel is pressurized with argon at the desired pressure. In the FOREVER/C1 experiment, the vessel wall, maintained at about 900 °C and pressurized to 26 bars, was subjected to creep deformation in a 24-h non-stop test. The FOREVER/C1 test is the first integral experiment, in which a decay-heated oxidic naturally-convecting melt pool was maintained in long-term contact with the hemispherical lower head of a pressurized, creeping, steel vessel. A sizeable database was obtained on melt pool temperatures, melt pool energy split, heat transfer rates, heat flux distribution on the melt (crust)–vessel contact surface, vessel temperatures and, in particular the vessel wall creep rate as a function of time. The paper provides information on the FOREVER/C1 measured thermal characteristics and analysis of the observed thermal behavior. The coupled nature of thermal and mechanical processes, as well as the effect of other system conditions (such as depressurization) on the melt pool and vessel temperature responses are analyzed.     

三维MORN试验能量分配比和安全裕量研究

MORN试验对三维氧化物层的熔池传热进行了试验研究,试验工质为水和硝酸盐。结果表明,不同下冷却边界会影响熔池温度和能量分配比。水冷条件下,熔池壁面热流密度分布差异很大,最大值为最小值的6.5～7.9倍。当熔池上下冷却边界相同时,向上/向下的能量分配比近似为100%。能量分配比不仅取决于上下冷却边界的种类,可能还取决于上下冷却边界是否进行了充分冷却,即能量分配比并不一定总为100%。将MORN-Nitrate的壁面热流密度分布经验关系式运用到AP1000压力容器下封头壁面热流密度计算中,结果表明,AP1000在出现堆芯融毁事故时,下封头不会失效,IVR有效。     

IVR-ERVC下压水堆压力容器下封头传热及应力/应变分析

以某1000?MW压水堆为例,利用二维极坐标热模型分析RPV壁面与双层堆芯熔池和外部冷却水堆腔之间的传热,计算下封头壁面瞬态二维温度场分布和烧蚀情况,同时通过有限元分析程序计算下封头壁面的各瞬态温度场和烧蚀引起的热应力/应变情况,分析压水堆RPV下封头在压力容器内熔融物滞留-压力容器外冷却（IVR-ERVC）下的结构完整性。计算结果表明:①芯熔融坍塌后200?s下封头壁面开始熔融,最薄厚度直线下降;3000?s后熔融区沿下封头内壁呈一片柳叶形状分布;②下封头内表面的吸热热流大于外表面的散热热流,在两层熔池界面处内外表面热流密度达到最大值;③RPV下封头热应力在0~400?s时集中于下封头内壁面;在400 s后,下封头内壁面热应力逐渐减小,形变量逐渐增大,下封头完整性可以得到保证;④2000?s以后,RPV下封头烧蚀损伤处内外壁面均产生应力集中,下封头烧蚀处内外壁应力值均大于许用应力,在2000?s后有可能发生断裂,在烧蚀损伤边缘处可能出现破口。