基于逆动态法的ADS次临界度在线监测方法数值验证

加速器驱动次临界系统(ADS)的次临界度在线监测是ADS运行和安全的核心问题,目前次临界度的测量方法主要有:外推-周期法,跳源法,脉冲中子源法等。本文研究了基于逆动态法的ADS次临界度在线测量方法,并对该法进行初步数值模拟验证。基于临界堆反应性逆动态测量方法,增加外源项的特殊考虑:采用次临界稳态中子通量密度(或功率)及初始次临界度以确定外源,实现适用于次临界堆反应性计算的逆动态求解算法。本文使用欧洲小型加速器驱动的次临界系统PDS-XADS进行数值验证,与动力学程序NTC-2D的计算结果进行对比。结果表明:该方法可有效实现次临界堆的次临界度在线监测。     

铍反射层光激缓发中子对物理启动特性的影响

给出铍的光激缓发中子组常数、停堆倒换料期间和向临界过渡前堆内中子源强值。全部采用解析函数模型,给出不同反应性引入速率下物理启动到临界状态时的中子源强值及到达周期保护的时间;给出阶跃引入反应性下堆芯发生超临界缓发瞬变、瞬发瞬变时堆功率的变化结果和释放的总能量等。     

溶液堆气泡效应测量

在次临界堆（如ADS次临界堆）物理实验中,反应堆动态参数的测量很重要,通常测量瞬发中子动态参数伍的值。反应堆在各种不同次临界装载下的α值可反映堆的次临界深度及相关的中子动力学特征。自主开发的费曼方差平均比方法测量系统是基于计算机数据采集和处理分析的系统,为建设数字化反应堆物理实验室起到一定的促进作用。     

内生脉冲中子源方法测量固态零功率堆的某些动态参数

用内生脉冲中子源方法测量固态零功率堆的瞬发中子衰减常数，从而得到不同装载下的反应堆次临界度，还给出了测量瞬发中子衰减常数所用的一些参量。     

跳源法在启明星1#次临界装置中的应用

简要介绍了跳源法在启明星1#次临界装置上测量次临界度的原理、外源驱动的次临界中子学实验装置、堆芯布置及中子源驱动系统。主要研究了中子源在堆芯轴向中心位置、不同装载情况下的反应性变化,并给出不同的有效倍增系数keff。实验测量结果与理论计算结果进行了比较,结果符合较好。     

一种测量快堆α_c的方法研究

在超瞬发临界状态下,直接测量脉冲前沿的功率上升,得到瞬发中子增殖常数(α)。在超缓发临界,刻度调节棒的反应性当量,累加调节棒的反应性当量得出爆发脉冲的预加反应性。由超瞬发临界实验数据外推得到了CFBR-II堆缓发临界瞬发中子衰减常数(αc)和反应性定向差。测量得到的αc与Rossi-α方法测量得到的结果一致。     

大阶跃反应性下考虑燃料温度反馈时的中子倍增公式

用有燃料温度反馈的中子倍增公式对输入大阶跃反应性的反应堆超瞬发临界变化过程进行研究。通过与经典中子动力学数值解法进行对比,计算结果基本一致;求得不同初始功率下反应性和功率的变化规律,并进行分析讨论,得出中子数与反应性在反应性大于缓发中子总份额时呈二次函数关系,其结论可作为弹棒事故等大阶跃反应性引入的反应堆安全分析的理论依据。     

非平衡态的中子增殖统一公式

导出了反应堆处于非平衡状态条件下的反应性阶跃变化时,反应堆从深度次临界到瞬发超临界整个区间通用的中子增殖统一的计算公式.通过对单组模型的修正,该公式还可以用于计算六组缓发中子的点堆中子动力学方程组.计算结果表明:利用修正后的单组解析方法计算阶跃反应性输入的中子密度响应问题,其计算结果与六组缓发中子的点堆中子动力学方程接近,精度满足工程计算要求.     

300#反应堆瞬发中子衰减常数测量

利用反应堆噪声分析技术测量300^#池式研究堆缓发临界下的瞬发中子衰减常数。堆芯采用低富集度U燃料装载，燃料元件带一定燃耗。利用紧靠堆芯布置的两个中子探测器，信号经测量系统和相关软件得到互谱密度，用非线性最小二乘法拟合得到瞬发中子衰减常数。在4kW功率水平测得缓发临界下的瞬发中子衰减常数α_c=(83.4±0.7)s^.-1。     

次临界系统中瞬发中子衰减常数与反应性的关系

一、引言中子增殖系统的物理参数测量中,经常通过瞬发中子衰减常数α的测定,来得到系统的反应性ρ或中子有效增殖因子k。瞬发中子衰减常数可以用多种方法测定,如脉冲中子法,频域和时域的相关分析法等。α对系统的次临界度或反应性很敏感,即使系统的次临界度很深,α仍然可以以很高的准确度测得。可是两者之间,特别当次临界度较深时,没有一个令人满意的关系式。本文将就这个问题作一探讨。     

Sub-critical reactor kinetics analysis using incomplete gamma functions and binomial expansions

Point reactor kinetics equations with one group of delayed neutrons are solved analytically to determine the neutron population as a function of time for any ramp reactivity insertion in the presence of external neutron source using prompt jump approximation. With the time dependent neutron population the other important kinetic parameters such as the reactor period also can be derived. Analytical solutions are available in the literatures for any ramp reactivity insertion into a critical reactor without considering the source term. Analytical solutions available in the literature by considering the source term also to study sub-critical reactor kinetics. But such a solutions either uses constant source approximation which under predicts the solution, or the available solution is not useful for all kind of sub-critical reactivity and external ramp reactivity insertion combination due to the computer precision incompatibility. In the present work, analyses are carried out to determine the reactivity boundary to which the existing results can converge to a true solution, beyond where the precision incompatibility arises. A new series solution is recommended in the region where existing solution converges to false solution due to precision incompatibility.     

Inhomogeneous point kinetics equations and the source contribution

Inhomogeneous point reactor kinetics equations with one-group of delayed neutrons are solved analytically for linear reactivity insertion as well as for step reactivity insertion in the presence of external neutron source using the prompt jump approximation. The solution is obtained as an infinite series. The methodology is found to be a promising tool for analyzing nuclear reactor kinetics with positive or negative ramp reactivity insertion on a sub-critical or a zero power delayed critical reactor, where the temperature reactivity feedback is negligibly small. To check the consistency and the accuracy of the analytical solution, the results are compared with the numerical solution for different sub-critical and delayed critical states. The comparison is found to be good for all kinds of positive and negative step and ramp reactivity insertions. The analytical solution is arranged into two terms, one as a function of source contribution the other without that. Using the newly rearranged solution, the importance of the source term and the contribution to the error while neglecting source term to the reactor kinetics analysis, can be realized. Contribution to the error is small (less than 0.1%) when the equilibrium power is more than about one megawatt for a medium sized LMFBR. Similarly, the importance of source contribution to the total reactor period as a function of initial equilibrium power is also realized with the newly rearranged analytical solution. The total reactor period is over predicted (larger period in place of smaller period) which is not conservative, if the source contribution is not considered, for considerably small initial equilibrium power. The percentage of error in not considering the source term in period calculation varies as a function of net reactivity and ramp rate. The percentage of error in period determination without considering the source is comparatively high for small ramp rates.     

Reactivity monitoring in ADS, application to the MYRRHA ADS project

Monitoring of reactivity in an ADS should be performed on-line with a simple, accurate and robust technique. Within the range of experimental reactor techniques, no single technique can be selected which meet these requirements. Therefore a combination of different techniques has to be chosen in a way that various off-line techniques serve as a calibration method for the on-line measurement technique. As an on-line measurement technique, the current-to-flux reactivity indicator is the most simple and robust solution. The current-to-flux reactivity indicator is based on the fact that in a sub-critical multiplying medium with a driving source the flux level is proportional to the driving source intensity, hence the beam current, and the reactivity level. However, since the proportionality constant depends on a number of core-dependent parameters and detector characteristics, this current-to-flux indicator has to be calibrated on a regular basis. For this calibration, one could benefit from the occurrence of accelerator beam trips to determine the reactivity level in dollars by means of a prompt jump analysis of the flux level change. Hence, the prompt jump reactivity indicator could act as a first calibration tool of the current-to-flux indicator. Since the prompt jump indicator still relies on the value for the effective delayed neutron fraction to determine reactivity level, complementary techniques have to be used to obtain a more accurate determination of the reactivity. Techniques based on reactor noise methods such as the RAPJA-technique which is a combination of the Rossi-Alpha method and a Prompt Jump Analysis can be used in this respect. In the future the bi-spectral ratio from the Cf-source driven noise analysis could be used for this purpose.     

Dynamic analysis of the closed-loop transfer function in the miniature neutron source reactor (MNSR)

The closed-loop transfer function of Syrian miniature neutron source reactor (MNSR) has been measured experimentally using the prompt jump approximation technique. Analysing the reactor stability behaviour, a physical model has been formulated based on the open-loop (neutronics) transfer function employing the lumped parameter concept to describe the reactor thermohydraulic characteristics. The reactor kinetics is described by the point kinetic model for one-group of delayed neutrons. Inherent internal feedback effect is considered as a single reactivity feedback that represents the coolant temperature effect. Comparison of the analytically derived transfer-function with the experimental one shows good agreement. Stability analysis of the closed-loop transfer function has been made using the Nyquist criterion and Bode diagram. Routh–Hurwitz criterion has been applied to estimate the stability limit of the MNSR closed-loop. The Nyquist and Bode criteria have shown that the MNSR closed-loop transfer function is indeed stable. The Routh–Hurwitz criterion enabled the estimation of the upper limit of temperature feedback coefficient of reactivity. Results indicate that MNSR has high inherently safety features. Various relationships that govern relation amongst reactor variables such as the isothermal reactivity coefficient of moderator temperature, temperature difference across the core and coolant flow rate of the natural circulation and mean time for heat transfer to the coolant have been concluded.     

跳源法测量ADS启明星Ⅱ号的次临界度及动态特性

本文主要利用²⁵²Cf外中子源驱动的ADS启明星Ⅱ号次临界装置来验证理论计算的次临界度及不同次临界度下的断束动态特性。简要介绍了利用跳源法在ADS启明星Ⅱ号上测量次临界度的原理、实验装置、测量系统、堆芯布置及实验结果等。实验通过变化堆芯燃料棒的装载来模拟3个次临界状态,即k_eff分别为0.99、0.98和0.97。实验结果与理论计算结果符合较好,验证了理论计算的正确性。经过实验验证的理论计算程序和核数据,为将来的中国科学院战略性先导科技专项--未来先进核裂变能ADS嬗变系统的次临界反应堆设计提供参考价值。     

Transient of a Pulse Reactor

Power and temperature transients following a prompt critical pulse applied to an experimental reactor has been studied by prompt jump approximation in two-dimensional phase space. The phenomena are classified into several types characterized by the amount of inserted reactivity and the value of cooling time constant. The temperature is shown to exceed in no case a level twice as high as the equilibrium value.     

A neutronics–thermalhydraulics model for preliminary studies on TRADE dynamics

In the last few years the possible role of accelerator driver systems (ADS) for effective transmutation strategies with fully closed cycles has received increased attention due to their potential to improve the flexibility and safety characteristics of transmutation systems. The substantial difference between the neutron kinetics and dynamic behavior of ADS and conventional critical reactors has given rise to a wide international consensus on the need of an experimental program to improve their knowledge and to validate calculation methods. To this end the international cooperation TRADE proposed a sub-critical experiment based on the coupling of a TRIGA reactor in sub-critical core configuration with a proton accelerator (cyclotron) by means of a neutron spallation target. The experiment was initially conceived in the RC1-TRIGA reactor located at the ENEA Center of CASACCIA (Rome, Italy) to demonstrate the feasibility of the accelerator driven system (ADS) concept at a representative power. This article presents a preliminary study performed with the RELAP5/PARCS code on the dynamic behavior of such a system in order to demonstrate the code capability to support the design of the experiment and the safety analysis. The specific code version used joins the well known capability of RELAP5 to treat light water reactors with the potentiality of PARCS modified by ENEA to simulate the three-dimensional neutronics of sub-critical systems, i.e. to treat external neutron sources. PARCS modifications are preliminary assessed against a simple analytical solution of the sub-critical neutronics of the experiment based on the kinetics pseudo-potentials method. A quite detailed model for the coupled code is developed in order to realistically evaluate both the thermal feedback effects, the control rod action and the external source strength changes. A wide range of operational and accidental transients of the sub-critical reactor are simulated with the coupled model in order to obtain a first system response to a number of reactor elementary events at different subcriticality levels. The calculation results show a high qualitative agreement with the sub-critical system physical theory underlining how the numerical model developed could be a useful tool for the definition of the operational procedures and the investigation of accidental conditions; moreover the accidental transient trends highlight the inherent safety behavior of the TRIGA research reactors that makes them extremely suitable for the coupling of the different components with a quite simple licensing procedures.     

Assessments of the kinetic and dynamic transient behavior of sub-critical systems (ADS) in comparison to critical reactor systems

The neutron kinetic and the reactor dynamic behavior of Accelerator Driven Systems (ADS) is significantly different from those of conventional power reactor systems currently in use for the production of power. It is the objective of this study to examine and to demonstrate the intrinsic differences of the kinetic and dynamic behavior of accelerator driven systems to typical plant transient initiators in comparison to the known, kinetic and dynamic behavior of critical thermal and fast reactor systems. It will be shown that in sub-critical assemblies, changes in reactivity or in the external neutron source strength lead to an asymptotic power level essentially described by the instantaneous power change (i.e. prompt jump). Shutdown of ADS operating at high levels of sub-criticality, (i.e. k_eff 0.99), without the support of reactivity control systems (such as control or safety rods), may be problematic in case the ability of cooling of the core should be impaired (i.e. loss of coolant flow). In addition, the dynamic behavior of sub-critical systems to typical plant transients such as protected or unprotected loss of flow (LOF) or heat sink (LOH) transients are not necessarily substantially different from the plant dynamic behavior of critical systems if the reactivity feedback coefficients of the ADS design are unfavorable. As expected, the state of sub-criticality and the temperature feedback coefficients, such as Doppler and coolant temperature coefficient, play dominant roles in determining the course and direction of plant transients. Should the combination of these safety coefficients be very unfavorable, not much additional margin in safety may be gained by making a critical system only sub-critical (i.e. k_eff0.95). A careful optimization procedure between the selected operating level of sub-criticality, the safety reactivity coefficients and the possible need for additional reactivity control systems seems, therefore, advisable during the early design phase of any ADS systems in order to assure a benign transient response of the particular ADS design under investigation to typical plant transient initiators.     

反应性阶跃方法测量次临界反应性

反应性阶跃法和落棒法相似,均通过快速改变控制棒的位置快速改变反应堆反应性,但在实验条件上存在较大差异。本文以6群缓发中子点堆方程为基础,反应性阶跃假定为条件,得到了反应性阶跃法所适用的反应性方程,并采用CFBR-Ⅱ堆实验数据验证了该方法。     

Determination of neutron generation time in miniature neutron source reactor by measurement of neutronics transfer function

The prompt neutron generation time Λ and the total effective fraction of delayed neutrons (including the effect of photoneutrons) β have been experimentally determined for the miniature neutron source reactor (MNSR) of Syria. The neutron generation time was found by taking measurements of the reactor open-loop transfer function using newly devised reactivity-step- ejection method by the reactor pneumatic rabbit system. Small reactivity perturbations i.e. step changes of reactivity starting from steady state, were introduced into the reactor during operation at low power level i.e. zero-power. Relative neutron flux and reactivity versus time were obtained. Using transfer function analysis as well as least square fitting techniques and measuring the delayed neutrons fraction, the neutron generation time was determined to be 74.6±1.57 μs. Using the prompt jump approximation of neutron flux, the total effective fraction of delayed neutrons was measured and found to be 0.00783±0.00017. Measured values of Λ and β were found to be very consistent with calculated ones reported in the Safety Analysis Report.