Transient friction and form loss factors in turbulent and laminar flow; a brief review

During pump coastdown steady state friction and form loss factors are currently used to calculate pressure drop. Both transient turbulent and laminar flow can exist in a typical LMFBR during the transition to natural convection and circulation. Existing transient friction and form loss data are very sparse. Nevertheless when existing deceleration rates in an LMFBR were compared with transient friction factor data it was concluded that use of steady state friction and form loss correlations is valid during pump coastdown.     

Transient flow analysis in reactor coolant pump systems during flow coastdown period

The rapid flow transient calculation in reactor coolant pump system is important in the safety analysis of a nuclear reactor. An accurate transient analysis of flow coastdown is also important and necessary for the design and manufacture of a reactor coolant pump. Only under the reliable work of a reactor coolant pump the safety of a nuclear power plant can be guaranteed. A mathematical model is developed for solving flow rate transient and pump speed transient during flow coastdown period. The detailed information of the centrifugal pump characteristics is not required. The flow rate and pump speed are solved analytically. The analytic solution of non-dimensional flow rate indicates that non-dimensional flow rate is determined by energy ratio β. The kinetic energy of the loop coolant fluid and the kinetic energy stored in the rotating parts are two important parameters in form of β. When the steady-state flow rate and pump speed are constant, the inertia of primary loop fluid and the pump moment of inertia are also two important parameters in flow transient analysis. For the condition all pump shafts are seized, the flow decay depends on the inertia of primary loop fluid. For the case that pump inertia is very large, the flow decay is determined by the pump inertia. The calculated non-dimensional flow rate and non-dimensional pump speed using the model are compared with published experimental data of two nuclear power plants and a reactor model test on flow coastdown transients. The comparison results show a good agreement. As the flow rate approaches to zero, the increase difference between experimental and calculated value is due to the effect of the mechanical friction loss.     

细长自然循环系统流动不稳定性实验研究

以水为工质,在常压下对拥有细长回路和较长水平段的自然循环系统进行可视化实验研究,并以典型的实验现象（ P =1.46 kW）为例分析该系统的瞬态运行特性和不稳定性机理。结果表明：阻力系数较大的细长自然循环回路难以产生有效的单相自然循环,只能通过间歇性沸腾和两相流动将热量导出。这是因当回路阻力较大时,过冷沸腾产生的驱动力无法驱动回路产生有效的自然循环,而只有当加热段内流体发生饱和沸腾时才能驱动系统产生循环流动。较大的回路阻力和沸腾过程中产生的系统降压闪蒸是细长自然循环系统难以维持稳定的流动驱动压头从而产生间歇性沸腾和强烈流动不稳定性的根本原因。     

LMFBR system analysis: Impact of heat transport system on core thermal-hydraulics

In discussing LMFBR thermal-hydraulic analysis, this paper focuses on the heat transport system and its impact on the predicted core behavior, particularly during off-normal or protected accident transients. Following a brief background of related work in the area of system simulation for both loop and pool-type LMFBR designs, modeling considerations for individual components such as reactor core, piping, pumps, heat exchangers and check valves, together with the overall integrated approach to system simulation, are discussed. The need for, and current approaches to, modeling pool stratification are also examined. The role of buoyancy forces in the system is clarified, with particular emphasis on its increasing influence during flow decay. Sample results are presented to illustrate the influence of system modeling details, and selection of component parameters and operational mode, on predicted core thermal-hydraulic response during protected loss-of-flow transients. From a systematic study of the effect of pump inertia for a flow coastdown to natural circulation event in a loop-type design, it is found that certain combinations of primary and secondary pump inertias can lead to core flow reversal for a sustained period, and eventual boiling in the hot fuel channel. This effect, based on its impact on core flow, is even more pronounced in pool-type designs.     

Transient Analysis for Design of Primary Coolant Pump Adopted to JAERI Passive Safety Reactor JPSR

In a course of a design study of the JAERI passive safety pressurized water reactor (JPSR), a complete loss-of-flow transient caused by a trip of all pumps was analyzed with the RETRAN code to determine an inertia of canned-motor pump utilized as the primary coolant pump and to confirm feasibility of the design condition. This transient was selected because the pump had a low inertia rotor inducing fast flow coastdown, and among the transients in which the pump had dominant effect on the departure from nucleate boiling (DNB), the analyzed transient was severest in view of the DNB occurrence. The DNB threshold was related, based on sensitivity calculations, with the coolant density reactivity coefficient and the pump inertia. From the calculations, it was concluded that the pump inertia higher than 250 kg·m² (8% of the ordinary PWRs) was necessary for preventing the DNB occurrence for the present design of JPSR, regardless of the actuation of the reactor scram. The DNB occurrence could be prevented only by the inherent nature of the reactor core which reduced the power by insertion of negative coolant density reactivity during the transient and this was one of major features of JPSR. It was shown by a rough estimation that the necessary condition could be practically realized by incorporation of a cylindrical-type flywheel.     

Investigation into the effects of a coastdown flow on the characteristics of early stage cooling of the reactor pool in KALIMER-600

A numerical investigation into the effect of a coastdown flow on the early stage cooling of the reactor pool in Korea Advanced Liquid Metal Reactor (KALIMER)-600 during a loss of normal heat sink accident has been carried out. Based on the design values of KALIMER-600, thermal-hydraulic calculations for steady and transient states have been done using the COMMIX-1AR/P code. Coastdown flow effect was evaluated based on a transient analysis of reactors employing various flywheels, which had coastdown flow time (CDT) values ranging from 0 (without a flywheel) to 300 s. The transient analysis has been done from a reactor trip to the onset of an overflow into the DHX support barrel. It was found that the coastdown flow range could be divided into three zones, based on its effect. Among them an excessive core coolant peak temperature and a reversed flow at the core region were observed for a medium coastdown flow range. The medium ranged coastdown flow induces the development of a high density layer near the core exit. This layer contributes to the development of an adverse effect in the core coolant flow, and finally results in increasing the core peak temperature. It was also found that the initiation of heat removal by DHX could be accelerated by the increase of the CDT, although it needs a large flywheel. From this analysis the best CDT is determined to be 25 s.     

Thermo-hydraulics during start-up in natural circulation boiling water reactors

The transient behavior of natural circulation for boiling two-phase flow was investigated by simulating normal and abnormal start-up conditions to research the feasibility of natural circulation BWRs such as the SBWR. It was found that the instabilities, which are out-of-phase geysering, in-phase natural circulation oscillation and out-of-phase density wave instability, may occur during the start-up when the vapor generation rate is insufficient. In this paper, the mechanism of in-phase natural circulation oscillation induced by hydrostatic head fluctuation in steam separators, which has never been understood well enough, is experimentally clarified. Next, the effect of system pressure on the occurrences of the geysering and the natural circulation oscillation are investigated. Finally, from the results, a recommendation is provided to establish the rational start-up procedure and reactor configuration for natural circulation BWRs.     

The effect of primary pump coastdown characteristics on loss-of-flow transients without scram in EBR-II

A series of loss-of-flow (LOF) tests without scram (unprotected) is planned for the Experimental Breeder Reactor II (EBR-II) to demonstrate the inherent shutdown capability of the reactor during an LOF event. The purpose of this paper is to discuss in detail the unprotected LOF transient analysis, the validation of the EBR-II reactivity feedback modeling, and the significance of pump coastdown characteristics on peak reactor temperatures. The tests as designed are limited by the fuel-cladding eutectic temperature of the fuel elements, and in order to meet the required temperature limit, the initial power and flow of all the tests are 16.7 and 20% of their rated values, respectively. To further reduce peak temperature, the primary tank temperature is to be decreased to 338°C from the nominal 371°C. The results show that primary flow coastdown rate and the capacity of the auxiliary pump have dramatic effects on the reactor temperatures. The impact of secondary flow depends somewhat on test conditions. When the auxiliary pump is in operation, the effect of secondary flow behavior on the reactor temperature becomes less significant during an unprotected LOF event.     

反应堆冷却剂泵惯量设计影响因素研究

主泵惯量设计应考虑主泵本身和回路特性的综合影响。本文建立了基于四象限特性的主泵惰转数值计算模型,评估主泵本身和回路特性对主泵惰转的影响。结果表明,转动惯量、摩擦损失等主泵因素,沿程阻力、局部阻力等回路因素均影响主泵惰转流量特性,但惰转转速下降主要与主泵本身因素相关,与回路因素关系不大。采用初始动能比ε表征主泵惯性和回路流体惯性的综合影响,流量下降相对转速下降的滞后程度与ε线性相关。对于ε较大的回路,应充分考虑惰转流量的滞后影响,避免主泵转动惯量设计采用过大的裕量,造成机组效率下降和设计难度提高。     

自然循环流动不稳定条件下的传热特性实验研究

为探究流动不稳定性机理,在低压自然循环系统中开展了一系列相关实验,分析了不同流量振荡模式下自然循环的沸腾传热机制及局部传热特性。实验表明：中、低热流密度下出现的较规则的周期性振荡由加热段内流动沸腾诱发,壁面过热度不会随流量振荡而大幅度变化;高热流密度下自然循环系统出现的周期性不规则振荡现象中,流动沸腾类型间的相互转变不是流量波动的唯一原因。大幅度的流量脉动可能在高热流密度下导致沸腾临界的发生,出口壁面出现间歇性干涸,局部传热系数下降的同时伴随壁温的短暂飞跃。随着热流密度的提高,自然循环系统可能出现持续性干涸。     

Reactor core thermohydraulic transients with thermohydrodynamic coupling

A study of the reactor core thermohydraulics in an LMFBR has been performed for the strongly coupled thermo-hydrodynamic transients. A numerical method to solve the coupled energy-momentum equations among multichannels in a core is presented and the computer code ORIFS-TRANSIENT has been developed.The results of sample calculations for a flow coastdown transient to natural circulation following a reactor scram in a typical loop-type LMFBR are as follows: (1) the inter-subassembly coolant flow redistribution due to buoyancy forces is significant under the low flow condition, such as natural circulation; (2) the maximum coolant temperature was decreased by about 80°C (corresponding to about 22% in terms of hot channel factor) due to the flow redistribution; (3) due to thermohydrodynamic coupling between upper plenum and other regions, the maximum coolant temperature was decreased by about 9°C; (4) due to inter-subassembly heat redistribution, the maximum coolant temperature was increased by about 7°C.     

Capability of the RELAP5 code to simulate natural circulation behavior in test facilities

Many advanced reactor designs incorporate passive systems mainly to enhance the operational safety and possible elimination of severe accident condition. Some reactors are even designed to remove the nominal fission heat passively by natural circulation without using mechanical pumps e.g. ESBWR, AHWR, CHTR, CAREM, etc. while in most other new reactor concepts, the decay heat is removed passively by natural circulation following the pump trip conditions. The design and safety analysis of these reactors are carried out using the best estimate codes such as RELAP5, TRAC and CATHARE, etc. These best estimate codes have been developed for pumped circulation systems and it is not proven about their adequacy or applicability for natural circulation systems wherein the driving mechanism is completely different. Some of the key phenomena which are difficult to model but are significantly important to assess the natural circulation system performances are – low flow natural circulation mainly because the flow is not fully developed and can be multi-dimensional in nature; flow instabilities; critical heat flux under oscillatory condition; flow stratification particularly in large diameter vessel; thermal stratification in large pools; effect of non-condensable gases on condensation, etc. Though, these best estimate codes use a six equation two-fluid model formulation for the thermal-hydraulic calculation which is considered to be the best representative of two-phase flows, but their accuracies depend on the accuracies of the models for interfacial relationships for mass, energy and momentum transfer which are semi-empirical in nature. The other problem with two-fluid models is the effect of ill-posedness which may cause numerical instability. Besides, the numerical diffusion associated due to truncation of higher order terms can affect the prediction of flow instabilities. All these effects may lead to inability to capture the important physical instability in natural circulation systems and instability characteristics i.e. amplitude and frequency of flow oscillation. In view of this, it is essential to test the capability of these codes to simulate natural circulation behavior under single and two-phase flow conditions before applying them to the future reactor concepts.In the present study, one of the extensively used best estimate code RELAP5 has been used for simulation of steady state, transient and stability behavior of natural circulation based experimental facilities, such as the High-Pressure Natural Circulation Loop (HPNCL) and the Parallel Channel Loop (PCL) installed and operating at BARC. The test data have been generated for a range of pressure, power and subcooling conditions. The computer code RELAP5/MOD3.2 was applied to predict the transient natural circulation characteristics under single-phase and two-phase conditions, thresholds of flow instability, amplitude and frequency of flow oscillations for different operating conditions of the loops. This paper presents the effect of nodalisation in prediction of natural circulation behavior in test facilities and a comparison of experimental data in with that of code predictions. The errors associated with the predictions are also characterized.     

Ultimate heat sink for PHWRs—evaluation of existing methods and alternative proposals

Two methods are proposed for removal of decay heat after a reactor trip under loss of class IV power. One is based on natural circulation (thermosyphon) cooling while the other depends on the direct introduction of the standby cooling system (SCS) heat exchanger after the main pump coast-down. The present analysis shows that under bottled condition thermosyphon cooling is adequate to remove up to 10% full power without boiling and up to 12% power with boiling in the primary coolant channels. However, the direct introduction of the SCS obviates the uncertainties of thermosyphon and ensures positive flow driven by a pump available on class III power supply. This flow is so chosen that there is no boiling on the secondary side of SCS within the operable pressure range. The analysis shows that such an operation does not induce undue stresses in the equipment.     

欠热沸腾诱发自然循环不稳定性的研究

以最佳估算程序RELAP5为基本分析工具,对自然循环系统进行数值分析,得出了不同条件下系统的不稳定性边界。研究发现自然循环对过冷沸腾有一定的承受能力,不稳定性一般发生在低欠热沸腾区,气泡脱离壁面和凝结时的扰动可能是自然循环系统不稳定性的诱因,系统驱动力、阻力和流量之间的相位差使振荡得以维持和发展。     

Analysis of two-phase flow characteristics in a natural circulation loop using the drift-flux model taking flow pattern change and subcooled boiling into consideration

This study investigated the steady-state characteristics of a two-phase natural circulation loop based on the drift flux model, taking flow pattern change and subcooled boiling into consideration. Transcendental equations of non-dimensional loop mass flow rate under various conditions were also derived. The model proposed herein was verified by comparing our results with experimental data found in literature. In addition, various steady-state characteristics of a natural circulation loop were analyzed and discussed; these characteristics include the one-third-power dependence of the single phase mass flow rate on heating power, the incipient power of two-phase flow, the maximum mass flow rate, and the existence of multiple solutions under certain conditions. This study also examined the effects of changing important parameters.     

喷射泵对自然循环过渡特性影响分析

分析了喷射泵在压水堆－回路自然循环过渡过程中的作用以及在不同流动条件下的阻力特性。分析结果表明：选择结构合理的喷射泵，可以改善压水堆一回路的过渡特性和自然循环能力；强迫循环条件下；压水堆一回路主循环泵有效压的损失随喷射泵阻力系数的增加而增加；自然循环条件下，喷射泵流动阻力系数影响压水堆一回路过度过程时间及自然循环流量的大小。为了改善压水堆一回路过度特性和提高一回路自然循环能力，可以采用无扩散段形式     

自然循环棒束形通道流动不稳定性起始点研究

针对自然循环条件下3×3棒束形通道内流动不稳定性起始点（OFI）进行了实验和RELAP5数值模拟研究。通过对实验数据进行处理,得出了计算自然循环条件下棒束形通道内OFI对应的热流密度的经验关系式,计算的最大相对误差为20.10%。运用驱动力方法分析了OFI的产生原因,计算结果表明：棒束形通道加热段出口处因过冷沸腾产生气泡,使得自然循环冷热段密度差大幅增大,进而使总驱动力增大,最终促使了OFI的产生。RELAP5对于低压自然循环OFI计算适用性好,其对OFI的计算结果较实验结果更不保守。     

带喷射泵系统中自然循环过渡特性实验研究

将喷射泵引入与反应堆一回路系统相似的自然循环系统中，进行了实验研究，研究结果表明：安装喷射泵不仅可以提高系统自然循环能力。而且还可以改善系统自然循环过渡特性，系统初始流量和喷射泵的带流比对过渡过程的初期影响较大，加热段加热功率对整个过渡过程的影响都很显著，但加热段入门温度的影响并不明显。     

Flow transients performance in an MTR-type research reactor

During a flow coastdown event leading to slowing down coolant flow, the rate of heat removal from the fuel element must be sufficiently high to prevent meltdown. It is essential to estimate the flow rate change and the decay heat removal capability. In many studies complete pump operating characteristics are used in analytical solutions of the problem. Under the coastdown phenomenon, retarding torque replaces motor torque. In order to determine this torque, all the induction motor losses during the event are identified and where possible these loss parameters are measured. Stator and rotor core losses, stator and rotor stray load losses and magnetizing saturation and rotor conductor skin effects are taken into account. The basics equations for coolant flow and for the rotating parts of the centrifugal pump are subsequently derived for an MTR-type research reactor such Tehran Research Reactor (TRR). Then the equation of flow motion is solved with another one which predicts the pump speed during the coastdown transient. The results of the present work are validated by comparison with experimental and analytical studies of the similar work. The model shows good agreement with the present literature.     

Experimental investigations on steady state natural circulation behavior of multiple parallel boiling channel system

In some industrial applications, including nuclear power plants, natural circulation flow is often employed as a reliable heat transport method. A common characteristic of many industrial two-phase natural circulation systems is the presence of a large number of parallel boiling channels. Sensitivity of the steady state behavior of such a two-phase natural circulation system to different system parameters has many implications vis-à-vis performance of the system as per the design intent under various operating conditions. This article reports the results of experimental studies carried out on the characteristics of a low pressure two-phase natural circulation system with parallel boiling channels having their individual heat sources. The work covers the study of dependence of system behavior on operational history, down-comer resistance and channel power. In view of its particular significance in nuclear industry, a special system condition with zero power in one of the parallel channels was also studied. An experimental setup consisting of 10 transparent parallel channels was designed and constructed for conducting these experimental investigations.