Science and Technology of Nuclear Installations

Volume 2018 (2018), Article ID 7862847, 11 pages

https://doi.org/10.1155/2018/7862847

## Study of Fast Transient Pressure Drop in VVER-1000 Nuclear Reactor Using Acoustic Phenomenon

^{1}Department of Nuclear Engineering, Science and Research Branch, Islamic Azad University, Tehran, Iran^{2}Department of Energy Engineering, Faculty of Engineering, Sharif University of Technology, Tehran, Iran

Correspondence should be addressed to Mohammad Rahgoshay

Received 10 June 2017; Revised 3 September 2017; Accepted 10 September 2017; Published 31 January 2018

Academic Editor: Eugenijus Ušpuras

Copyright © 2018 Soroush Heidari Sangestani et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This article aims to simulate the sudden and fast pressure drop of VVER-1000 reactor core coolant, regarding acoustic phenomenon. It is used to acquire a more accurate method in order to simulate the various accidents of reactor core. Neutronic equations should be solved concurrently by means of DRAGON 4 and DONJON 4 coupling codes. The results of the developed package are compared with WIMS/CITATION and final safety analysis report of Bushehr VVER-1000 reactor (FSAR). Afterwards, time dependent thermal-hydraulic equations are answered by employing Single Heated Channel by Sectionalized Compressible Fluid method. Then, the obtained results were validated by the same transient simulation in a pressurized water reactor core. Then, thermal-hydraulic and neutronic modules are coupled concurrently by use of producing group constants regarding the thermal feedback effect. Results were compared to the mentioned transient simulation in RELAP5 computer code, which show that mass flux drop is sensed at the end of channel in several milliseconds which causes heat flux drop too. The thermal feedback resulted in production of some perturbations in the changes of these parameters. The achieved results for this very fast pressure drop represent accurate calculations of thermoneutronic parameters fast changes.

#### 1. Introduction

One of the most important aspects in design of different safety systems with sufficient preparation is simulation and analysis of transient states in reactor core. For these kinds of analysis basic equations in neutronic and thermal-hydraulic modules have to be coupled. Coupling of neutronic and thermal-hydraulic modules is different from each other, considering numerical solution methods and time and body meshing size. Thus, written codes for different transient states are mostly used for study of fuel and coolant temperature changes, power peak level, coolant pressure, stability time, and other parameters. Computer coding submits models with different degree of accuracy and validity. Most codes are not able to analyze coupled conditions of very fast transient (FT) states in very short time. This deficiency is associated with neutronic and thermal-hydraulic calculations or both. Therefore designing a code which is capable of analyzing FT conditions is highly needed.

One of the efficient ways in analyzing FT is using waveform method. Chan (1991) studied asymptotic waveform evaluation in analysis of time-dependent calculations [1]. Ooi et al. (2003) studied the finite element method (FEM) in thermal analysis that usually produces a formulation in the space/time domain. However, the sizes of the equations in FEM usually are large, and thus the conventional algorithms involve considerable computational time. The conventional methods have to take a very small time step size to avoid undesirable numerically induced oscillations or numerical instabilities. Thus, a new solution algorithm, named the asymptotic waveform evaluation scheme, was introduced by them to solve transient problems [2]. Liu et al. (2006) studied fast thermal simulation when power density increases by fast spectrum in frequency domain for computing steady state response. It indicates that the resulting thermal analysis algorithms lead to 10x–100x speedup over the traditional integration-based transient analysis with small accuracy loss. The studied parameters minimum time order is 15 ms [3]. Ham and Bathe (2012) used FEM to solve time-dependent two-dimensional wave propagation problems [4]. Ranaa et al. (2014) presented the well condition asymptotic waveform evaluation to solve heat conduction problem in the frequency domain. The method is presented for time-dependent problems [5]. In addition, Ishii et al. (2009) investigated the effect of acoustic phenomenon in steam dryer (in a Boiling water reactor) which indicates the process of pressure pulsations caused by hydroacoustic resonance propagation along the steam dryer [6]. Proskuryakov (2017) studied the effect of acoustic vibrations in the nuclear power plant (NPP) coolant such as VVER-1000 reactor and created new scientific direction “diagnosis, prognosis and prevention of vibration - acoustic resonances in the NPP equipment” shows that the developed methods can be used to predict and prevent the occurrence of vibration-acoustic resonances in the NPP equipment [7].

Various kinds of thermal-hydraulic and neutronic calculating models are put to use in transient calculating code development studies. Reducing costs and runtime and achieving required accuracy are three main purposes of them. Leung et al. (1981) studied acoustic impact techniques for increasing the accuracy of FT states modeling in CODA code [8]. However, regarding its very small meshing, acoustic methods are time-consuming and are not used any more.

In order to decrease complicated solving parameters in using compressible fluid method, geometry of every fuel assembly could be turned into a single heated channel (SHC). Four different methods are used to solve SHC transient equations. They are channel integral (CI), single mass velocity (SV), momentum integral (MI), and sectionalized compressible fluid (SC). SC model considers both sound impact and thermal expansion, while the other three models only consider thermal expansion [9]. The SHC method is used in costanza code (1967) in order to analyze the dynamics of liquid cooled nuclear reactor [10]. It is also used in DynCo code (2011) which is intended for complex neutron-physic and thermal-hydraulic dynamic calculation of the reactor core in 3D hex-Z geometry. DynCo code is designed to simulate the dynamic behavior of the Russian 3000-MWt pressurized water reactor (PWR) [11]. The coupling of CI and POWEX-K code (2011) simulates power excursion in reactor of Budapest University of Technology and Economics Reactor [12]. Hosseini et al. (2015) developed a coupled 3D neutronic with 1D thermal-hydraulic model in order to find reasonable power distribution. Neutronic module includes three-dimensional diffusion equation in two energy groups which was solved using analytic nodal method. Thermal-hydraulic module contains the conservation equations solved for 1D axial homogeneous downward flow through channel using SHC model (MI method). In conclusion, Xenon saturation transient analysis of a research reactor core was carried out [13].

The SHC compressible fluid method is one of the ways that make it possible to use wave propagation method and acoustic phenomenon. Shapiro (1953) considered the derivation and properties of the dynamics and thermodynamics of compressible fluid flow which is along with acoustic theory [14]. Meyer (1961) investigated that several approximations can be used to decouple the momentum and energy equations to facilitate solution of the transient problem. Additionally, the numerical solution of a transient problem would be particularly simplified if the compressibility of the fluid could be ignored [15]. Todreas and Kazimi (2001) investigated a rapid increase in the heat flux without change in the applied pressure drop in a PWR. The SC approach for a 10% heat flux step increase in the PWR channel shows that because the pressure begins to rise at internal channel points, a reduction in inlet flow rate and an accelerated exit flow rate occur [9].

The mechanism of compressible fluid method was published by Bar-Meir in 2007 [16]. Khola and Pandey (2013) studied the numerical simulation of transients in two-phase flow which is crucial to simulate accident-like conditions of nuclear reactors for safety analysis. In their work, a code for numerical computation of unsteady one-dimensional two-phase flow has been developed. The governing equations were obtained by the homogenous equilibrium mixture model and were decoupled and approximated using the SC and MI model [17].

Numerical considerations (i.e., the stability and/or accuracy) of the difference solution require that the time step of integration be less than the time interval for sonic wave propagation across the spatial grid points. Compared with the transport velocity, the fluid sonic velocity is large. It causes limitation of the time step in most numerical schemes to very small values. Acoustic phenomenon is used in accommodation of very short time and very small body meshing. This accommodation is determined by Courant’s criterion [8, 20]:

is time meshing period, is body meshing distance, is sound velocity in coolant, and is the mean transport velocity. The fluid sonic velocity is large comparing with the transport velocity. Therefore, limiting the time step in most numerical schemes to very small values leads to a computationally expensive solution of this problem. Regarding meshing size criterion, pressure wave propagation method mostly requires long-term computations for numeral stability. Therefore acoustic phenomenon features (despite the high accuracy) are not usually considered by researchers. However these features are very useful during core parameter vital changes.

FT pressure drop is a type of loss of coolant accident (LOCA). That is well known as the double ended guillotine break. When double ended guillotine break occurs (main coolant pipeline cold leg breaks at the reactor inlet), suddenly reactor coolant pressure decreases with leak coolant flow rate of 45000 Kg/s [18]. A pressure wave is also produced, while the large break LOCA occurs, which propagates across the channel. Therefore International Atomic Energy Agency (IAEA, 2003) studied the before-break vital moment (leak before break) [21].

The coolant fast pressure drop accident can lead the fluid to become two-phased and thermoneutronic parameters to change. Gonzalez-Santalo and Lahey Jr. (1972) investigated this matter by study of pressure drop transient in two-phase condition [22].

Calculation program of VVER-1000 reactor core FT pressure drop by means of SC method and acoustic phenomenon was developed in this investigation. In order to use the mentioned method every one of the 28 fuel assemblies should be considered as one SHC. Fuel assembly conversion into SHC and meshing method toward -axis are both shown in Figure 1.