Heat transfer from a totally blocked fuel subassembly of a liquid metal fast breeder reactor: II. Numerical simulation

Fast breeder nuclear reactors used for power generation, have fuel subassemblies in the form of rod bundles enclosed inside tall hexagonal cavities. Each subassembly can be considered as a porous medium with internal heat generation. A three-dimensional analysis is carried out here to estimate the heat transfer due to natural convection, in such an anisotropic, partially heat generating porous medium, which corresponds to the typical case of blocked flow in a fuel subassembly inside the reactor core. Using the finite volume technique, the temperatures at various locations inside hexagonal cavity are obtained. The simulations by the three-dimensional code developed are compared with the results of experiments [Suresh, Ch.S.Y., Sateesh, G., Das, Sarit K., Venkateshan, S.P., Rajan, M., 2004. Heat transfer from a totally blocked fuel subassembly of a liquid metalfast breeder reactor. Part 1: Experimental investigation. Nucl. Eng. Design, present issue] conducted using liquid sodium as the heat transfer fluid. Further, the code is used to predict the maximum temperature in typical liquid metal fast breeder reactors to find the power level where the liquid sodium starts boiling. It helps to decide the power level for initiation of monitoring the temperature for the purpose of reactor control.     

Sodium boiling experiments in a 19-pin bundle under loss-of-flow conditions

An experimental study was conducted on transient sodium boiling in a 19-pin electrically heated LMFBR fuel subassembly mockup under loss-of-flow conditions. In each run the inlet flow was reduced or stopped at constant heater power. There was no strong effect of temperature ramp rate on incipient-boiling (IB) wall superheat. The observed coolant voiding was initially limited to the center subchannel because of steep temperature gradient in the bundle. The bulk pressure rise registered upon initial vaporization was markedly lower than the vapor pressure corresponding to the IB wall superheat. The pressure pulse generated at vapor bubble collapse correlated reasonably well with the re-entrant liquid velocity, but the measured value was very much smaller than the calculation by sodium hammer analysis.     

Experimental research on heat transfer to liquid sodium and its incipient boiling wall superheat in an annulus

Liquid sodium is mainly used as a cooling fluid in the liquid metal fast breeder reactor （LMFBR）, whose heat transfer, whether convective heat transfer or boiling heat transfer, is different from that of water. So it is important for both normal and accidental operations of LMFBR to perform experimental research on heat transfer to liquid sodium and its boiling heat transfer. This study deals with heat transfer with high temperature （300-700℃） and low Pe number （20-70） and heat transfer with low temperature （250-270℃） and high Pe number （125-860）, and its incipient boiling wall superheat in an annulus. Research on heat transfer involves theoretical research and experiments on heat transfer to liquid sodium. It also focuses on the theoretical analysis and experimental research on its incipient boiling wall superheat at positive pressure in an annulus. Semiempirical correlations were obtained and they were well coincident with the experimental data.     

Natural Convection Sodium Boiling Experiments in 37-Pin Bundle Geometry

Decay heat removal capability under boiling condition was studied using an LMFBR fuel subassembly mockup loop. The sodium flow was driven by natural convection through the loop in which was installed a 37-pin bundle heated electrically over a length of 45 cm.

The heat flux furnished by the pins was increased stepwise, upon which the two-phase flow regime changed from bubble to slug flow and then to annular or annular mist flow. Dryout occurred even in slug flow regime, but only momentarily, and permanent dryout was not observed before establichment of annular flow. A suitable criterion for permanent dryout is considered to be 0.5 average exit sodium vapor quality. The results indicated that upon occurrence of sodium boiling, the coolability of fuel subassembly would be maintained by natural convection after reactor shutdown.     

Loss-of-flow experiment in a 37-pin bundle LMFBR fuel assembly simulator

An experimental study was conducted on transient sodium boiling in an LMFBR fuel subassembly mockup under loss-of-flow conditions. In the test section, an electrically heated 37-pin bundle was centered in a hexagonal tube. The measured maximum IB wall superheat was 36°C, and the effects of heat flux, temperature rise rate, and system pressure were unclear. Boiling was initiated at the end of the heated section, the bubble expanded mainly to the upstream central subchannels and to the downstream unheated section according to the expansion of the saturated temperature region. When the voided zone covered the whole flow cross-section, the void pattern changed to the one-dimensional slug ejection-type and the inlet flow decreased rapidly. Dryout occurred after the inception of flow reversal in the wide region of the bundle.     

Local Sodium Boiling behind Local Flow Blockage in Simulated LMFBR Fuel Subassembly

This paper deals with local sodium boiling in the downstream of a six-subchannel blockage in an electrically heated LMFBR fuel subassembly mock-up.

The first series of experiments were conducted to measure temperature distributions in the downstream of the blockage under non-boiling conditions. The measured temperature rise due to the blockage agreed fairly well with the calculation by the LOCK code.

The second series of experiments were performed to investigate local boiling phenomena. In the local boiling region, no flow instability was observed since the sub-channels near the wrapper wall were still filled with sub-cooled liquid. In the nearly bulk boiling region, however, considerable upstream voiding occurred and then the inlet flow decreased, leading to final dryout.

The boiling caused a considerable increase in acoustic noise intensity. The root-mean-square (RMS) noise level of approximately 20 mbar obtained in the present local boiling experiments with sodium was much higher than that (approximately 0.5 mbar) in the ordinary nucleate boiling experiments with water. The peak observed in the hertz ranges was due to the repetition of bubble formation and collapse. In the kilohertz ranges, however, resonance peaks were superposed on a smooth curve with a broad peak at approximately 7 kHz.

The frequency (2.9 and 20.2 sec^?1) of bubble formation decreased with the increase of the bubble size at its point of maximum development. The product of the bubble frequency and the equivalent diameter was found to be constant.     

Sodium boiling experiments in a seven-pin bundle: Flow patterns and two-phase pressure drop

Two series of quasi-steady state sodium boiling experiments have been carried out in an electrically heated seven-pin bundle. The power levels (130–170 and 30–40 W/cm²) and other test conditions were selected to correspond to the core and radial breeder zones of a typical LMFBR. The test procedure involved the gradual reduction of mass flow rate through the bundle in a simulation of the consequences of a slowly growing blockage in the lower part of a reactor subassembly. By this means it was possible to study the development of quasi-steady state boiling up to the onset of permanent dryout. The results obtained provide information on flow regimes in the two-phase region, vapour qualities and flow rates at which cooling of the bundle can be effectively maintained, and the ultimate incidence of dryout. A relation for the two-phase pressure drop multiplier obtained from adiabatic pressure drop measurements in this geometry is given and compared with earlier results from single-channel geometry tests.     

钠冷快堆中熔融池模型的建立与验证

快堆在超设计基准事故下运行时,会导致钠沸腾和干涸,如果不能及时停堆,接着就会产生燃料元件的熔化坍塌,在组件盒下部形成熔融池.为了对熔融池给出合理的安全分析,采用机理建模的方法,建立了完整的熔融池模型,并在法国的SCARABEE系列实验中的BF1三种功率的实验上进行了验证,和实验吻合较好,通过和所验证过的GEYSER及BF2等实验模型进行比较,得出了有关熔融池机理的相关结论.通过排热和温升等相关数据的比较,对熔融池向外的排热形式给出了合理分析,并得出了相关结论.     

Analysis of low-heat-flux sodium boiling test in a 37-pin bundle by the two-fluid model computer code SABENA

This paper summarizes the development of a new detailed multi-dimensional multi-field computer code SABENA and its application to an out-of-pile low-heat-flux sodium boiling test in a 37-pin bundle. The semi-implicit numerical method employed in the two-fluid six-equation two-phase flow model has proved in solving a wide spectrum of sodium boiling transients in a rod bundle under low pressure conditions. The code is capable of predicting the spatial incoherency of the boiling, dryout on fuel cladding surfaces and fuel pin heat transfer. Essential to the successful application of such a mechanistic model computer code are validational efforts aimed at the LMFBR accident phenomenology analyses. Through the simulation of the natural circulation boiling conditions, this study provides a consistent analytical interpretation of the experimental data. The important influences of such parameters as the inlet flow restriction and bundle geometry have been examined through interpretations of two-phase flow analysis including considerations of the flow instability induced dryout mechanism.     

Detection of local boiling in an LMFBR subassembly by temperature fluctuations analysis at the outlet

The aim of the experiments is to detect boiling in a sodium cooled subassembly by measuring fluctuations behind the bundle outlet. The measurements were carried out on an electrically heated 28-rod bundle with a partially blocked section. Fast responding thermocouples were installed downstream of the bundle outlet and downstream of a flow mixing system. Statistical parameters were investigated such as root mean square (RMS) and power spectrum density (PSD). The boiling conditions were generated by reducing the system pressure or flow velocity reduction. The experiments have shown that statistical analysis of temperature fluctuations can produce significant results in the detection of boiling behavior at both the outlet of a subassembly, and behind a flow mixing system.     

Boiling and dryout behind local blockages in sodium cooled rod bundles

Much attention has been given in LMFBR safety analysis to cooling disturbances caused by local blockages within a fuel subassembly. Such blockages are generally considered to be more probable in gridded fuel pin clusters which present the possibility for solid particles in the coolant to be trapped at grids to form a radially extending flow obstruction. The temperature distribution produced in the region of impaired cooling has been studied in water and sodium experiments in pin bundles of various sizes. The experimental work at KfK on local cooling disturbances culminated in two local blockage experiments in the KNS sodium loop simulating LMFBR fuel elements with a 49% central and a 21% corner blockage. In the frame of this work pin cooling in the wake of the blockage was investigated in single-phase conditions, in boiling conditions up to dryout and in conditions simulating gas release from failed pins. The general aims of the studies were to demonstrate that the consequences of a local blockage do not lead to rapid propagation of damage within a pin bundle and to obtain data for validation of theoretical models.     

Experimental study of whole core thermal-hydraulic phenomena in EBR-II

In the analysis of core-wide temperature distributions in a liquid-metal-cooled fast breeder reactor (LMFBR) under both normal and abnormal operating conditions, it is commonly assumed that there is little, if any, thermal interaction between adjacent subassemblies. Since intersubassembly heat transfer tends to reduce the transverse temperature gradients in a reactor, thereby ameliorating the effects of local overheating, this assumption is conservative. In order to assess the importance of this effect as well as of flow redistribution in a reactor core, an experimental study was conducted in EBR-II covering a wide range of operating power and flow conditions, including both forced and natural convection. The results of this study indicate that radial heat transfer and flow redistribution are important mechanisms in the thermal-hydraulics of LMFBR cores, especially at low flow rates.     

冷却剂丧失条件下钠冷快堆棒束传热的三维蒙特卡罗模拟方法

采用蒙特卡罗方法分析钠冷快堆在假想冷却剂丧失条件下燃料棒束的钠两相流传热问题。以分子运动理论的基本定律为基础，开发出替代宏观经验模型来分析反应堆棒束中的钠蒸发率和冷凝率的微观模型，且采用三维蒙特卡罗方法模拟分子的运动轨迹，分子间的碰撞率以及分子与棒束、分子与棒束组件盒壁的碰撞率。对包壳干涸区的再浸润现象用动力膜模型描述，并计算了通过液膜的液体速度分布和平均液膜速度，对于从冷凝液膜蒸发的钠分子则被重新记为蒙特卡罗计算的源项。用微观和宏观模型相结合的方法数字模拟了德国卡斯鲁尔研究中心的堆外钠沸腾实验。     

Characterization of heat transfer and temperature distributions in an electrically heated model of an LMFBR blanket assembly

This paper describes results of an experimental program to reduce uncertainties associated with the thermal-hydraulic design and analysis of LMFBR blanket assemblies. These assemblies differ significantly from fuel assemblies in design detail and operating conditions. In blanket assemblies, heat transfer occurs over a wide range of complex operating conditions. The range and complexity of conditions are the result of flux and power gradients which are an inherent feature of the blanket region and the power generation level in an assembly which can vary from 20 kW to 2 MW. To provide effective cooling of all assemblies and economical operation, coolant is metered to groups of assemblies in proportion to their ultimate power level. As a result, the assembly flow can be in the laminar, transition or turbulent range. Because of the wide range of heat generation rates and the range of coolant flow velocities, heat transfer from rods to coolant may take place in the forced, natural or mixed convection mode. Under low flow conditions, buoyancy affects the flow pattern in the bundle, and thus, alters the temperature distribution. The complexities are further compounded since, in addition to temperature gradients within an assembly, there are also significant temperature differences between adjacent assemblies. This results in heat transfer by conduction between adjacent assemblies, which tends to further distort flow and temperature patterns.Since these effects cannot be accurately predicted analytically, full-size radial blanket assembly heat transfer tests are being conducted using electrically heated fuel rod simulators in flowing sodium. A 61-rod electrically heated radial blanket assembly mockup of prototypic dimensions was designed, constructed and installed in a 200 gpm (45 m³/hr) sodium test loop.Heat transfer tests are being conducted over a wide range of power and sodium flow rates with this full-scale, vertical, electrical-resistance-heated rod bundle. The rod bundle is extensively instrumented by thermocouples located at six distinct elevations in the wire wrap and inside the heater cladding. Tests were conducted covering the flow range from fully turbulent to fully laminar with approximately constant power-to-flow ratio. The power input patterns included across bundle gradients of 2.8 to 1 and 2.0 to 1 maximum to minimum, uniform power input to all rods and a dished distribution with low power in the central row and high power in the two rows of rods adjacent to the duct walls.The test program provided experimentally measured axial and transverse temperature profiles for the test model over a range of anticipated plant operating conditions. The data were used to (a) determine the effect of Reynolds Number, power gradients and power-to-flow ratio on transverse and axial temperature profiles and particularly on peak and peripheral channel temperatures; (b) determine the effect of inter-assembly heat transfer on peak temperatures and temperature distributions; and (c) determine the effect of buoyancy on temperature profiles.     

Turbulent flow simulation in a wire-wrap rod bundle of an LMFBR

The pressure drop and heat transfer characteristics of wire-wrapped 19-pin rod bundles in a nuclear reactor subassembly of liquid metal cooled fast breeder reactor (LMFBR) have been investigated through three-dimensional turbulent flow simulations. The predicted results of eddy viscosity based turbulence models (k-?, k-ω) and the Reynolds stress model are compared with those of experimental correlations for friction factor and Nusselt number. The Re is varied between 50,000 and 150,000 and the ratio of helical pitch of wire wrap to the rod diameter is varied from 15 to 45. All the three turbulence models considered yield similar results. The friction factor increases with reduction in the wire-wrap pitch while the heat transfer coefficient remains almost unaltered. However, reduction in the wire-wrap pitch also enhances the transverse flow velocity in the cross-sectional plane as well as the local turbulence intensity, thereby improving the thermal mixing of coolant. Consequently, the presence of wire wrap reduces temperature variation within each section of the subassembly. The associated reduction in differential thermal expansion of rods is expected to improve the structural integrity of the fuel subassembly.     

Phenomenological investigation of sodium boiling in a SFR core during a postulated ULOF transient with CATHARE 2 system code: a stabilized boiling case

In the framework of the research and development on GEN IV sodium fast reactors (SFRs), the phenomenology of sodium boiling during a postulated unprotected loss of flow (ULOF) transient has been investigated with the CATHARE 2 system code. This study focuses on a stabilized boiling case: in such a regime, no flow redistribution occurs from the subassemblies which have reached the saturation temperature to those that are still single-phase. In this paper, for a subassembly design featuring no restrictive structures above the fuel bundle, a quasi-static approach is first developed to get an upper bound of the reactor core power at boiling onset that would be compatible with the well-known Ledinegg criteria for diphasic flow static equilibrium. Then, dynamics results achieved through simulation with the CATHARE 2 code for a postulated ULOF are presented: boiling is shown to remain stable during the transient for such a core power at boiling onset. Another important outcome of the simulation is the calculation of a dynamic instability, in the form of a two-phase hydrodynamic chugging phenomenon. The predicted phenomenology of this stabilized boiling case should be studied further in order to consider its dependency on the underlying closure laws and to eliminate the possibility of a numerical instability.     

A numerical study of flow in the Thermal-Hydraulic Out-of-Reactor Safety facility expansion tank

A new, fast-running, two-dimensional computer code was developed to model the flow and temperature patterns in the expansion tank of the Thermal-Hydraulic Out-of-Reactor Safety (THORS) facility. The THORS facility, located at the Oak Ridge National Laboratory (ORNL), is an engineering-scale sodium loop used for thermal-hydraulic testing of simulated Liquid Metal Fast Breeder Reactor (LMFBR) subassemblies. In the computer model, the fluid is considered Boussinesq and a simple turbulence model is provided so that a wide range of inlet conditions can be studied. A vorticity-stream function formulation is used on a uniform finite difference grid. The model also includes the thermal response of the tank wall. The results of simulated experiments for natural circulation and forced flow conditions are compared. Inflow boundary conditions were adjusted to simulate boiling in the THORS test section upstream of the expansion tank during some runs made with the code. Streamline and isotherm plots of the results are presented. All cases studied reached thermally stratified conditions in the tank, and regions of buoyancy and convection-dominated flow are observed.     

Investigation of Effect of Gas Release on Coolability of Locally Blocked LMFBR Fuel Subassemblies

The objective of the present study is to evaluate the temperature rise due to gas release behind local blockage in LMFBR fuel subassemblies.

The experiments were conducted using six sets of electrically heated 37-, 61-and 91-pin bundles. The central or edge subchannels of each test section were blocked by a non-heat generating blockage of stainless steel plate. The effect of operational and geometrical conditions on the coolability of the blocked bundle were investigated from the test results. The examined factors are gas release rate, sodium flow rate, spacer type and blockage location.

The high coolant flow more than 2m/s in the velocity at the blocked plane, forced the released gas to be accumulated within the recirculation region resulting in marked temperature increase. The dependency of the temperature rise on the gas release rate was classified into two stages; (1) the temperature increases with the gas release rate, (2) after reaching a peak value, the temperature gradually decreases with the gas release rate. From these conclusions empirical correlations were derived to estimate the temperature rise under the condition of blockage with gas release. It was deduced that fission gas release in an LMFBR fuel subassembly with a local blockage has a potential to cause a limited pin-to-pin failure propagation in the recirculation region.     

快堆中熔融物在相邻组件中传播的数学模型

快堆发生堆芯熔融事故,会形成熔融池和沸腾池,熔融物在向相邻组件中传播时,是否造成相邻组件径向方向的全堵是事故进一步发展的关键.为了弄清熔融物在相邻组件中传播的机理,本文基于英国sMPR系列实验中的管排型实验装置,分别建立了导热冻结和整体冻结的数学模型,并用英国SMPR系列实验中的A2、A3实验数据进行了验证.结果表明,导热冻结和整体冻结都会使熔融物停止传播;在固化壳生长机理和熔融物温降等相关因素的共同作用下,压差越小,越偏向于导热冻结;导热冻结数学模型预测的固体结构温度及固化壳生长更符合实验结果.     

Numerical Simulation on Subcooled Boiling Heat Transfer Characteristics of Water-Cooled W/Cu Divertors

In order to realize safe and stable operation of a water-cooled W/Cu divertor under high heating condition,the exact knowledge of its subcooled boiling heat transfer characteristics under different design parameters is crucial.In this paper,subcooled boiling heat transfer in a water-cooled W/Cu divertor was numerically investigated based on computational fluid dynamic(CFD).The boiling heat transfer was simulated based on the Euler homogeneous phase model,and local differences of liquid physical properties were considered under one-sided high heating conditions.The calculated wall temperature was in good agreement with experimental results,with the maximum error of 5%only.On this basis,the void fraction distribution,flow field and heat transfer coefficient(HTC)distribution were obtained.The effects of heat flux,inlet velocity and inlet temperature on temperature distribution and pressure drop of a water-cooled W/Cu divertor were also investigated.These results provide a valuable reference for the thermal-hydraulic design of a water-cooled W/Cu divertor.