Control rod drop analysis by finite element method using fluid–structure interaction for a pressurized water reactor power plant

doi:10.1016/j.nucengdes.2009.05.023

Nuclear Engineering and Design

Volume 239, Issue 10, October 2009, Pages 1857-1861

https://doi.org/10.1016/j.nucengdes.2009.05.023 Get rights and content

Abstract

The control rod drop analysis is very important for safety analysis. For seismic and loss of coolant accident event, the control rod assemblies shall be capable of traveling from a fully withdrawn position to 90% insertion without any blockage and within specified time and displacement limits. The analysis has been executed by analytical method using in-house code. In this method, several field data are needed. These data are obtained from nuclear, thermal–hydraulic and mechanical design groups, peculiar codes, those work groups need to cooperate together.

Following the enhancement of a computer and development of the multi-physics analysis code, a new method for the control rod drop analysis is proposed by finite element method. This analysis model incorporates the structure and fluid parts, termed as a fluid and structure interaction (FSI). Because a control rod is submerged inside a guide tube of a fuel assembly, the FSI boundary condition is applied. In this model, it is assumed that the fluid is incompressible laminar flow. The structures are modeled with the solid elements because there is no deformation due to the fluid flow. The analysis two-dimensional plane model is created in the analysis with considering an axi-symmetric geometry. Therefore, the proposed analysis model will be very simple and the design data from other fields will be unnecessary.

The analysis results are compared with those of the in-house code, which have been used for a commercial design. After validation, it is found that the present analysis gives a useful tool in the design of the control rod and fuel assembly.

Introduction

The fuel system consists of guide tubes (or thimbles); fuel rods with fuel pellets, claddings, springs; top and bottom end pieces; spacer grids and springs; assembly end fittings; and the reactivity control assembly. In the case of the control rods, the reactivity control elements extend from the coupling interface of the control rod drive mechanism (CEDM) as in Chang (1993). The control rod contains poison material over the entire active fuel length and have, as a principal function, major reactivity control including reactor shutdown. The mechanical design description of the fuel system should include the following aspects: (1) mechanical design limits such as those for allowable stresses, a deflection, a cycling, and fatigue, (2) capacity for a fuel fission gas inventory and pressure, (3) a list of material properties, and (4) considerations for radiation damage, cladding collapse time, materials cross-section, and a normal operational vibration. In this document, in-house code for the control rod drop analysis was validated with experimental measurement.

Fluid–structure interaction (FSI) have been made for resolving the problem of a blood flow in carotid arteries with stenoses (Tang et al., 1999, Tang et al., 2004a, Tang et al., 2004b), the fluid–structure interaction problem of a reactor vessel (Andersson and Andersson, 1997, Andersson et al., 2003), and the thermo-fluid analysis of a fusion reactor (Kurihara, 2002). All of these works were executed using the FSI code, ADINA (Zhang et al., 2003).

In the structural components of a fuel assembly for a pressurized water reactor power plant, guide tubes serve as the main lateral and axial load carrying members of a fuel assembly. And they provide a guide path for the control element assembly (CEA), neutron sources and in-core instrumentation. Among the guide tubes, the outer guide tubes comprise four units that are fabricated from tube material of zirconium-based alloy. On the other hand, the control rod is made from the Inconel 625. These guide tubes form a basic structural member of a fuel assembly by supporting the spacer grids and by their direct attachment to the lower and upper end fittings. Fig. 1 is a schematic drawing showing the expanded region of a guide tube and its corresponding interfaces as in Yoon (1996).

For the reactivity control or safe shutdown of a core, the control rod assembly has to be inserted into the guide tubes. In the case of the safe shutdown, it is dropped into the guide tube by its own weight. Under conditions I and II of the design criteria the drop time is limited to be 3.5 s from a safety aspect. In a conventional analysis for this, the Navier–Stokes equation has to be solved under actual core conditions. The present analysis model and procedure developed by using the FSI algorithm are simple because the previous methods (i.e. in-house code analysis) need various data such as the fuel mechanical, thermal/hydraulic and nuclear design data. It is very difficult to conduct a control rod drop analysis and some error is likely to arise (Khan et al., 1996).

Present analysis method simulates a fluid–structure interaction phenomenon during a control rod insertion into the guide tubes: the solid structural part is in contact with the fluid inside the guide tubes, an interaction between a control rod assembly (the solid structural part) and the fluid inside the guide tubes is inserted into a guide tube, it push out the coolant to the outside of the guide tube. The contact surfaces between the outer surfaces of a control rod and the fluid surfaces are defined as the fluid–structure interfaces. So, the displacements of the fluids and structures are exactly the same during the full analysis time domain. Simultaneously, a fluid–structure interaction takes place between the coolant and a control rod in a guide tube. Therefore, the displacement and traction at every increment time have to be the same at the boundary of the control rod and coolant. The aim of this paper is to propose an analysis model for a control rod drop analysis. The fluid–structure interaction problem is solved by using a commercial finite element program, ADINA (2007).

This paper deals with two topics: a simplified analysis method is studied for a control rod drop analysis. Both the previous and the present methods are compared to check on the validity of the simulation. The discrepancies between the two methods will be discussed. Second, a finite element analysis is carried out to verify the simulation capability of the FSI problem. In the finite element analysis, a half region of the guide tube in the axial direction are identified and modeled. This approach is found to be a useful tool for investigating the behavior of a control rod in actual core conditions.

Section snippets

Theoretical description

A fluid–structure interaction analysis of one single program is necessary for a solution to the problems where fluids are fully coupled to general structures that undergo a highly nonlinear response due to large deformations, an in-elasticity, a contact and a temperature-dependency. A fully coupled fluid–structure interaction means that the response of the solid is strongly affected by the response of the fluid, and vice versa.

From a fluid's point of view, the Navier–Stokes flow can be

FEM model

The finite element model should be accurately created as an actual fuel configuration. A control rod is dropped into a guide tube by gravity. The retarding forces against the gravity fall of the CEA include the hydraulic pressure forces resulting from forcing the coolant out of the fuel assembly guide tubes, the hydraulic suction effects as the coolant rushes into the CEDM hydraulic shear and the drag forces on various components, as well as the mechanical friction and external forces resulting

The analysis results

The drop time of a control rod was obtained by the FSI analysis. And the analysis results were compared with those of the in-house code, a licensed in-house code. Unfortunately, the analysis results could not be compared with the experimental results. However, the previous method using the in-house code was validated by the comparing with the experimental results (Chang, 1993). All data for this study were nearly the same of that test loop.

The results are summarized in Table 3. The difference

Concluding remarks

A control rod drop analysis was executed with the commercial FE code, ADINA. An analysis model for simulating the drop behavior of a control rod assembly was studied with the aim of satisfying the design criterion of drop time. It was found that the present method can simulate the fluid–structure interaction between the control rod and the fluid by using a fluid–structure coupled algorithm under the core conditions at an operating temperature. The results showed a good agreement with those of

Acknowledgement

This work was supported by Nuclear Research & Development Program of the Korea Science and Engineering Foundation (KOSEF) grant funded by the Korean government (MEST) (grant code: M20706020005-08M0602-00510).

References (11)

L. Andersson et al.
On the validation and application of fluid–structure interaction analysis of reactor vessel internals at loss of coolants accidents
Computers & Structures
(2003)
L. Andersson et al.
Some experiences in the use of ADINA in the Swedish nuclear industry
Computers & Structures
(1997)
R. Kurihara
Thermo-fluid analysis of free surface liquid divertor in Tokamak fusion reactor
Fusion Engineering and Design
(2002)
D.L. Tang et al.
Wall stress and strain analysis using a three-dimensional thick-wall model with fluid–structure interactions for blood flow in carotid arteries with stenoses
Computers & Structures
(1999)
H. Zhang et al.
Recent development of fluid–structure interaction capabilities in the ADINA system
Computers & Structures
(2003)

There are more references available in the full text version of this article.

Cited by (33)

UA-CRD, a computational framework for uncertainty analysis of control rod drop with time-variant epistemic uncertain parameters
2024, Annals of Nuclear Energy
Due to the influence of multiple factors, the control rod drop involves some uncertain parameters. The mechanical friction on the control rod is a time-variant uncertain parameter and is related to the position of the control rod. For the first time, this paper adopts the interval process model, which accurately describes the uncertainty parameters by using small-scale samples, to describe the uncertain mechanical friction on the control rod. The numerical experimental results demonstrate that the interval process model can describe the mechanical friction with high accuracy, even when employing small-scale samples. Furthermore, it is found that the uncertainty analysis can be considered as solving the extremal problem of a black-box model. Based on it, we propose a novel and general calculation framework for uncertainty analysis of control rod drop, UA-CRD. Through the analysis of numerical examples, it is verified that UA-CRD can accurately and efficiently conduct the uncertainty analysis of control rod drop.
Eccentric drop of a control rod in the guide tube with annular gap flow
2023, Nuclear Engineering and Design
The drop time of control rod is essential for safety analysis of nuclear power plant. The motion of control rod can be characterized by an annular gap flow with large blockage ratio. In this study, we studied the effects of the eccentricity between the control rod and the guide tube on the annular gap flow, and further on the drop time. By considering the added mass and the upward flow of fluid in the annular gap, we developed a theoretical model for computing the drop time of eccentric rod. In the proposed model, particularly, the annular gap flow velocity was obtained from full-scale computational fluid simulations with respect to blockage ratio and eccentricity. The simulation and experiment results agree well on the drop time, the histories of velocity and acceleration, and the hydrodynamic characteristics. Results show that the drop time increases drastically when blockage ratio α increases from 0.83 to 0.91, and the eccentricity effect on drop time is negligible when the blockage ratio is small (e.g., α < 0.83). Nevertheless, for large blockage ratio (α ≥ 0.83), the drop time increases significantly for eccentric rod drop, especially for a lighter control rod. The present study provides a general method for analysis of control rod drop, which is critical for the nuclear reactor design.
Uncertainty analysis of the control rod drop based on the adaptive collocation stochastic perturbation method
2023, Annals of Nuclear Energy
There are many uncertain factors to affect the control rod drop from its design and manufacture to the chain reaction in the reactor. They have to be considered in the simulation to realistically predict the dynamic behavior of control rod drop. Different from the previous method by using the nominal and extreme values of the uncertain factors, a statistical method is applied in this paper to analyze them in the process of the control rod drop. The uncertain factors obey uniform distribution, based on which a fifth-order adaptive collocation stochastic perturbation (ACSP) method is established in this paper, which is featured with simple format, high precision, and high calculation efficiency. The mean and standard deviation of the responses (such as the final time of the control rod drop) in two different types of reactors are calculated by using the ACSP method. On this basis, the response intervals and corresponding probabilities of the control rod drop are obtained. Besides, influences of each random variable on the responses are analyzed by the sensitivity analysis. In addition, the linear correlation degree and correlation between the two are discussed through the correlation coefficient of random variables and the responses. The uncertainty analysis of control rod drop in this paper not only provides a relatively strong theoretical support for scientifically dealing with uncertain factors, but also offers specific help for the optimal design of control rod assembly.
Nonlinear state equation and adaptive symplectic algorithm for the control rod drop
2022, Annals of Nuclear Energy
Citation Excerpt :
In Bulín et al. (2021), an original combination of the absolute nodal coordinate formulation and the classical finite element method is used to analyze the influence of guide thimbles vibration on the control rod drop. Rabiee and Atf (2016) and Yoon et al. (2009) conducted the control rod drop analysis by the CFD commercial software ADINA and FLUENT. Scholars have also researched the control rod drop in fourth-generation nuclear reactors such as sodium-cooled fast reactors.
Control rod drop is the key part of ensuring the safety of nuclear reactor shutdown. Aiming at the control rod drop problem, we established a physical model of the control rod drive line. The proposed model considers the influence of the absorbing rod’s position and hence evaluates the resultant force accurately on the control rod during the whole dropping process. Based on the physical model, a unified coupling state equation on the control rod drop and fluid flow is developed by integrating the motion variables of the control rod and the fluid into a state vector. A time step adaptive symplectic (TSAS) algorithm is proposed to solve the proposed state equation. The TSAS algorithm efficiently and stably predicts the motion states of the control rod and the fluid synchronously and accurately captures the sudden change of flow state. Numerical examples confirm the correctness of the proposed model and the TSAS algorithm. Sensitivity analysis is also conducted to discuss the effects of different parameters on the control rod drop, which provides reference and help for the design and manufacturing of the control rod drive line.
Cylinder-lamina system fluid–structure interaction problem solved with an original OpenFOAM code
2021, Journal of Computational Science
Citation Excerpt :
In this paper, a further solver improvement in terms of coupling nature is presented. In fact, in the present work ModsFsiFoam solver outputs are compared with a system the results of which are known for both fluid-dynamics and structural fields, in terms of characteristic time-dependent quantities and corresponding plots [15–18]. The FSI system is made of a flow able, in the laminar regime, to deform the elastic compressible polypropylene structure.
In numerical simulations, the partitioned approach allows treating a multi-physics phenomenon as two different computational fields, which are solved separately with their respective mesh discretisation and algorithms. This is of particular interest to fluid–structure interaction (FSI) problems for their complex resolution. In this respect, through the partitioned approach, ModsFsiFoam (MODalSuperpositionFsiFoam) solver has been developed. It allows the application of two different methods for fluid and solid solutions. In particular, it is based on a theoretical approach, the modal superposition principle, for the structural solution; this method provides a certain result for the linear structural field. The FVM (Finite VolumeMethod), by far the most widely used method for fluid-dynamics and gas-dynamics problems, has been used instead to solve the Navier–Stokes equations for an incompressible laminar flow of Newtonian fluid. The interfacial conditions have been used to pass information between the domains through a coupling algorithm. Implemented in OpenFOAM, a development environment consisting of libraries and applications for Linux distributions, written in the C++ source code, ModsFsiFoam solver has been already applied with satisfactory results to a typical fluid–structure interaction case found in literature, i.e. a system composed by an inverted flag treated as a flexible lamina, clamped to a wind tunnel wall, in which airflow is introduced in the axial direction. In this work, ModsFsiFoam solver outputs are compared with a system, the results of which are known for both fluid-dynamics and structural fields. The configuration consists of a laminar incompressible channel flow around a solid structure with an elastic part.
Experimental and numerical study on the critical working condition of control rod in liquid-suspended shutdown device
2021, Annals of Nuclear Energy
The purpose of this work was to guide the design of the suspended control rod in a sodium-cooled fast reactor. Retaining the dimensions and main flow characteristics of the prototype device, a hydraulic model of the passive shutdown device was designed. An experiment was carried out on the critical flow of the upper working position and the lower position (accident condition). The critical flow rate maintaining a stable suspension in the upper working position and hydraulic self-tightening in the lower working position was determined. The study found that the critical flow of the control rod in the lower working position was obviously affected by the circumferential angle; the force that causes the control rod to incline was inevitable and the key position that affects critical working conditions was pointed out. The study also found that the working fluid temperature had little impact on the critical working conditions.

View all citing articles on Scopus

View full text

Control rod drop analysis by finite element method using fluid–structure interaction for a pressurized water reactor power plant

Abstract

Introduction

Section snippets

Theoretical description

FEM model

The analysis results

Concluding remarks

Acknowledgement

Computers & Structures

Computers & Structures

Fusion Engineering and Design

Computers & Structures

Computers & Structures