A sensitivity study of BWR instability over global and regional modes at different exposures

Boiling water reactors have unique mechanisms coupling between neutronic and two-phase flow thermalhydraulic behaviors, and may exhibit in-phase (global mode) instability and out-of-phase (regional mode) instability. In some observation modes, the regional mode instability is associated with an increase in power in one half of the core and a simultaneous decrease in power in the other half, such that the average power remains essentially constant. Yet in practice, sometimes the real situation is hidden, the neutron flux may oscillate more vigorously than expected. To investigate the stability behavior at the stability boundary from BOC (beginning of cycle) to EOC (end of cycle), fractional changes of the decay ratio are used to evaluate the parametric sensitivity of the global mode and the regional mode at different exposures. Decay ratios for regional mode oscillations are much less than those under core-wide conditions. Current studies demonstrated that for some of the parameters under particular conditions, the variation in the regional mode decay ratio exceeded that in the global mode. In this work, the thermalhydraulic parameters (such as flow rate and system pressure) exhibit a more sensitive regional variation than global. Moreover, some parameters (density reactivity coefficient and delayed-neutron fraction, for example) depend on the shape of the axial power shape; for the bottom peak axial power shape, the regional mode decay ratio variation is more sensitive than global; for the top peak axial power shape, the opposite is true.     

Stability analysis of a liquid-metal reactor and its primary heat transport system

Part of the reactor design process is the assessment of the impact of different design changes on pre-defined performance criteria including stability of the reactor system under different conditions. This work focuses on the stability analysis of a combined liquid-metal reactor and primary heat transport system where system parameters are free to vary, with particular interest in low reactor power, low reactor coolant flow conditions. Such conditions might be encountered, for example, after a loss of flow without scram in some passively safe reactor designs. Linear-stability-analysis-based methods are developed to find the stability regions, stability boundary surface in system parameter space, and frequency of oscillation at oscillatory instability boundaries. Models are developed for the reactor, detailed thermal hydraulic reactivity feedback associated with coolant outlet and inlet temperatures, decay heat and primary system. The developed stability analysis tools are applied to the system model. The system parameters include integral reactivity parameters, decay heat, primary system mass, coolant flow and natural circulation flow. The resulting stability boundary surface and its associated frequency of oscillation surface in multidimensional system parameter space show the effect of system parameter changes. By adopting model parameters from liquid-metal reactor designs, a stability prediction procedure is illustrated.     

物理模型及边界条件对直流蒸发管两相流不稳定性边界影响研究

本文研究不同边界条件及物理模型对两相流不稳定性边界的影响。采用RELAP5程序模拟直流蒸发管内的两相流不稳定性实验工况,对计算程序和模型进行验证,分析恒定流量及恒定压降两种边界条件、并联管数量、轴向功率分布形式和传热管热容等不同边界条件和物理模型对不稳定性边界的影响。结果表明：恒定压降边界条件下,单根管、2根并联管和多根并联管的不稳定性边界差别小于5%;恒定流量边界条件下,多根并联管不稳定性边界和2根并联管相比差别小于5%,而与单根管不稳定性边界的差别则超过100%;并联管根数相同时,恒定流量边界条件的稳定性好于恒定压降边界条件;沿流动方向（轴向）功率递增分布时,系统稳定性好于沿流动方向功率均匀分布,沿流动方向功率均匀分布时,系统稳定性好于沿流动方向功率递减分布;当管壁厚度为0~20 mm时,管壁热容对不稳定性边界几乎没有影响。     

Assessment of the Prony's method for BWR stability analysis

It is known that Boiling Water Reactors are susceptible to present power oscillations in regions of high power and low coolant flow, in the power-flow operational map. It is possible to fall in one of such instability regions during reactor startup, since both power and coolant flow are being increased but not proportionally. One other possibility for falling into those areas is the occurrence of a trip of recirculation pumps. Stability monitoring in such cases can be difficult, because the amount or quality of power signal data required for calculation of the stability key parameters may not be enough to provide reliable results in an adequate time range. In this work, the Prony's Method is presented as one complementary alternative to determine the degree of stability of a BWR, through time series data. This analysis method can provide information about decay ratio and oscillation frequency from power signals obtained during transient events. However, so far not many applications in Boiling Water Reactors operation have been reported and supported to establish the scope of using such analysis for actual transient events. This work presents first a comparison of decay ratio and frequency oscillation results obtained by Prony's method and those results obtained by the participants of the Forsmark 1 & 2 Boiling Water Reactor Stability Benchmark using diverse techniques. Then, a comparison of decay ratio and frequency oscillation results is performed for four real BWR transient event data, using Prony's method and two other techniques based on an autoregressive modeling. The four different transient signals correspond to BWR conditions from quasi-steady to power oscillations. Power signals from such transients present a challenge for stability analysis, either because of the low number of data points or need of much iteration, and thus reducing their capability for real time analysis. The results show that Prony's method can be a complementary reliable tool in determining BWR's stability degree.     

基于频域法超临界水冷堆CSR1000流动不稳定性研究

基于频域法研究了超临界水冷堆CSR1000的流动不稳定性。建立了CSR1000的堆芯数学模型,并利用开发的程序FREDO-CSR1000分析了堆芯平均通道和热通道在额定功率和流量范围内的流动不稳定性,得到衰减率、合适的进口阻力系数及超临界水堆的稳定运行区域。计算结果表明：在堆芯额定功率和流量范围内,第1流程的衰减率是单调变化的,第2流程因受进口温度的影响会出现急剧上升和急剧下降的趋势。     

两相自然循环系统的静态漂移特性及输热能力限分析

基于分岔理论及其ＤＥＲＰＡＲ数值方法,运用最简单的均相模型计算出典型两相自然循环系统的静态分岔解图,详细讨论了由浮力和阻力随加热功率（含汽率）的非线性变化特性引起的静态分岔机理;导出对应于强迫循环系统的Ｌｅｄｉｎｅｇｇ不稳定性现象及其判断准则;定义稳定性裕度、自然循环系统输热能力限、静态分岔迟滞现象;讨论了系统压力、欠热度、阻力、几何构型等参数对运行稳定性及输热能力限的影响;强调指出了简单理论预测     

混合能谱超临界水冷堆快谱区流动稳定性研究

在混合能谱超临界水冷堆中,冷却剂通过堆芯过程中跨拟临界点引起的密度等参数的剧烈变化易导致系统产生密度波振荡而不稳定,因此混合能谱超临界水冷堆的稳定性对系统的安全性至关重要。本文利用频域法研究快谱区的流动稳定性,给出在不同状态下的稳定性边界,同时对冷却剂入口流量、进出口压差和通道划分等对稳定性的影响进行了分析。结果表明：大的入口流量有利于系统的稳定;高的进出口压差对系统稳定性有利;轴向功率均匀分布较非均匀分布系统的稳定性差,可提供保守结果;热通道的功率密度越大,对系统的稳定越不利。研究结果对超临界水冷堆设计和优化有一定指导价值。     

非均匀加热蒸发管内两相流动不稳定性数值分析

针对蒸发管非均匀加热工况,采用包含水平、倾斜上升、垂直上升和垂直下降流动的优化内螺纹管,建立了基于均相流模型的蒸发管数学模型,采用时域法模拟了蒸发管内两相流动不稳定性。计算了不稳定发生时,进口流量在各时间点的数值,并与Siemens公司的计算结果进行了对比,结果符合良好,表明本文采用的数学模型和数值方法在模拟两相流动不稳定性上具有一定的可靠性。分析了系统参数对两相流动不稳定性的影响,并与均匀加热工况进行了比较。结果表明:非均匀加热工况系统参数影响规律与均匀加热工况具有相似性,增加进口压力或进口流量系统的稳定性提高;减小进口阻力系数或增大出口阻力系数系统的稳定性降低。     

SCWR single channel stability analysis using a response matrix method

A system response matrix method, which directly solves the linearized differential equations in the matrix form without Laplace transformation, is introduced for the supercritical fluids flow instability analysis. The model is developed and applied to the single channel or parallel channel type instability analyses of a typical proposed Supercritical Water Reactor (SCWR) design. A uniform axial heat flux is assumed, and the dynamics of the fuel rods and water rods are not considered in this paper. The sensitivity of the decay ratio (DR) to the axial mesh size is analyzed and found that the DR is not sensitive to mesh size once sufficient number of axial nodes is applied. The sensitivity of the stability to inlet orifice coefficient is conducted for the hot channel and found that a higher inlet orifice coefficient will make the system more stable. The susceptibility of stability to operating parameters such as mass flow rate, power and system pressure is also performed. It is found that the SCWR stability sensitivity feature can be improved by carefully choosing the inlet orifice coefficients and operating parameters. The stability feature of the average channel is also analyzed with an equivalent inlet orifice coefficient. Finally, the manufacturing feasibility of the inlet orifices for both the hot channel and average channel is studied and found to be favorable.     

并联通道内超临界水流动不稳定性的数值模拟研究

超临界水的流动不稳定性特征研究是超临界水冷堆热工水力设计的重点,为进一步获得超临界水流动不稳定性发生的内部机理,采用系统分析程序RELAP5对已有实验本体进行建模,并基于已有超临界水不稳定性实验数据开展了计算方法的验证;系统研究了并联通道内超临界水的流动不稳定性规律,并对比研究了超临界水与亚临界水的不稳定边界。结果表明,超临界水的流动不稳定界限功率随入口温度的增加存在变化拐点;相同入口温度下,随压力上升,不稳定界限功率增加,超临界水相比亚临界气-液两相流具有更好的稳定性;无量纲准则数在超临界条件下具有适用性,超临界水不稳定性变化规律与亚临界水具有相似性。     

直流沸腾系统不稳定性分析

根据直流沸腾系统的特点．采用了以集中参数和可移动边界为特征的简化动态模型．推导出了两相流反馈系统。利用自动控制中的频域理论以及MATLAB软件的不稳定性分析语句和Tool Box中的Simulink工具,对其进行了分析和仿真．并得出了几种主要因素影响下的稳定性边界曲线：     

Numerical research on oscillation of two-phase flow in multichannels under rolling motion

Two-phase flow instability and dynamics of a parallel multichannels system has been theoretically studied under periodic excitation induced by rolling motion in the present research. Based on the homogeneous flow model considering the rolling motion, the parallel multichannels model and system control equations are established by using the control volume integrating method. Gear method is used to solve the system control equations. The influences of the inlet, upward sections, heating power and rolling amplitudes on the flow instability under rolling motion have been analyzed. The marginal stability boundary (MSB) under the rolling motion condition is obtained. The unstable regions occur in both low and high equilibrium quality and inlet subcooling regions. The multiplied period phenomenon occurs in the high equilibrium quality region and the chaos phenomenon appears on the right of MSB. The concept of stability space is presented.     

两相自然循环密度波不稳定性的实验研究

在自然循环水回路上进行了两相流密度波不稳定性的实验研究，得到了不同工况下的实时脉动曲线。分析了系统压力、质量流密度、进口欠热度对系统稳定边界的影响。得出了用无量纲量相变数Ｎｐｃｈ、欠热度数Ｎｓｕｂ、弗劳德数Ｆｒ表示的系统稳定边界图及稳定性判别准则式。     

Stability analysis of parallel-channel systems with forced flows under supercritical pressure

The flow in the core of supercritical water reactors (SCWRs) experiences drastic change in its thermodynamic properties and transport properties near the pseudo-critical temperature, thus the core flow may be susceptible to density wave oscillation instability, which is a challenge to the system safety and must be studied carefully. This paper studies the dynamic stability characteristics of the fast-spectrum zone of a newly designed mixed-spectrum SCWR (SCWR-M), which is characterized as a parallel-channel system. A frequency-domain model has been developed for linear stability analysis, and marginal stability boundaries under several conditions for the parallel-channel system are generated, which indicate that the system normal operational condition is in the stable region. The stability of parallel-channel systems is dominated by the hottest channel. The higher the power density of the hottest channel is, the less stable the system will be. Increasing mass flow is beneficial for the system stability. Systems with uniformly axial power distribution are less stable than those with cosine-shaped or stair-shaped axial power distributions. In the time-domain, a single-phase one-dimensional model has been developed for non-linear analysis, and several perturbation transients are calculated. The results of analysis show a good agreement with that of the frequency-domain analyses, and the existence of transitional stable region has been verified.     

Kuosheng BWR/6 stability analysis with LAPUR5 code

Unstable power/flow oscillation of a nuclear power reactor core is one of the main reasons that cause minor core damage. Stability analysis to determine system’s decay ratio needs to be performed at each core reload design to prevent core instability events from happening. Making use of LAPUR5 and SIMULATE-3 codes, we have established a methodology to conduct such analysis. Comparisons made with vendor’s STAIF results indicated close agreements, within acceptable ±0.2 in decay ratios, for Kuosheng NPP Unit2 Cycle 17 reloads design. Sensitivity studies have shown that density reactivity coefficient, delayed-neutron fractions (β) and decay constants (λ), total core flow, and core power axial shape are the most important parameters that might affect the accuracy of decay ratios. We have also found that core conditions at EOC result in larger decay ratios than those at BOC.     

重力注水过程流动不稳定现象关键影响因素研究

重力驱动注水过程中由于流量较小以及蒸汽的积聚可能导致流动不稳定现象的发生,对核反应堆安全运行具有重要的影响。通过实验研究的方法,搭建了重力注水模拟实验装置,研究了不同蒸汽出口形阻、高位储水箱水位和加热棒初始温度下流动不稳定现象的变化规律。结果表明,重力驱动注水过程流动不稳定现象包含冷却水初次注入阶段、注入水逐出阶段和冷却水再注入阶段等。在一定冷却水初始温度、冷却水入口形阻以及系统压力下,蒸汽排出速度以及实验本体内筒顶部的聚集情况取决于蒸汽出口形阻,减小蒸汽出口形阻可加快蒸汽排放速度,压力峰峰值降低、振荡周期变长,有利于系统稳定;提高高位储水箱水位加快了冷却水注入速率,增加了加热棒被淹没率,降低了流动不稳定现象的发生次数和持续时间;随加热棒初始温度的升高,冷却水流量出现了波动向停滞的转变,流动不稳定现象发生的次数增加且持续时间加长。     

横摇条件下九通道系统两相流动不稳定性研究

对横摇条件下并联多通道系统的两相流动不稳定性进行了理论研究。基于横摇条件的均匀流模型,通过控制容积积分法建立了并联九通道系统的分析模型。用吉尔方法对系统控制方程组进行了求解。分析了在横摇条件下并联九通道系统入口段和上升段及加热功率对管间脉动不稳定性的影响,得到了相应的不稳定性边界。在低含汽率、高含汽率及低过冷度数区域,系统均不稳定。同时,在高含汽率区域会出现倍增周期现象及混沌现象。     

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。     

Density Wave Instability in Once-Through Boiling Flow System, (I)

Density wave instability in a once-through boiling flow system was systematically observed using a uniformly joule-heated water loop operated at system pressures ranging from 20 to 43 ata. The test section consisted of two heated tubes connected in parallel and further paralleled by an unheated by-pass. The oscillatory behavior is analyzed as well as the effects brought on the threshold of instability by changes in the operating variables—mass velocity, system pressure, inlet resistance, inlet subcooling, by-pass ratio and exit quality. The experimental data are also presented in form convenient for verifying various analytical methods devised to predict the stability boundary.     

基于RELAP5的运动条件下并联双通道流动不稳定性研究

随着船用核动力装置的广泛应用,运动条件引起的热工水力现象逐渐受到重视。反应堆堆芯内存在大量并联通道,通过在RELAP5程序的动量方程源项中添加运动条件引起的附加力,开展了倾斜、起伏及摇摆等典型单一运动条件及其耦合运动条件下的并联双通道在强迫循环下的流动不稳定性研究。对比了静止条件及不同运动条件下的不稳定性边界曲线,结果表明,强迫循环下运动条件对并联通道流动不稳定性的影响较小。相同过冷度数下,运动条件与静止条件的相变数差别在2%以下。