Science and Technology of Nuclear Installations

Volume 2016, Article ID 3071686, 10 pages

http://dx.doi.org/10.1155/2016/3071686

## Analysis of Density Wave Oscillations in Helically Coiled Tube Once-Through Steam Generator

^{1}College of Energy, Xiamen University, Xiamen, China^{2}Institute of Nuclear and New Energy Technology, Tsinghua University, Beijing, China

Received 3 September 2016; Revised 1 November 2016; Accepted 6 November 2016

Academic Editor: Alejandro Clausse

Copyright © 2016 Junwei Hao 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

Helically coiled tube Once-Through Steam Generator (H-OTSG) is one of the key equipment types for small modular reactors. The flow instability of the secondary side of the H-OTSG is particularly serious, because the working condition is in the range of low and medium pressure. This paper presents research on density wave oscillations (DWO) in a typical countercurrent H-OTSG. Based on the steady-state calculation, the mathematical model of single-channel system was established, and the transfer function was derived. Using Nyquist stability criterion of the single variable, the stability cases were studied with an in-house computer program. According to the analyses, the impact law of the geometrical parameters to the system stability was obtained. RELAP5/MOD3.2 code was also used to simulate DWO in H-OTSG. The theoretical analyses of the in-house program were compared to the simulation results of RELAP5. A correction factor was introduced to reduce the error of RELAP5 when modeling helical geometry. The comparison results agreed well which showed that the correction is effective.

#### 1. Introduction

A steam generator is a type of heat exchanger specifically designed to transfer heat from a coolant into water, producing steam that can be utilized for power generation. Helically coiled tube steam generators are widely used in nuclear industry for their compactness, easy manufacture, and enhanced heat transfer efficiency [1]. They are widely adopted in different plants, such as HTGR, SMR, and IRIS. The most prominent characteristic of flow in helically coiled tubes is the secondary flow induced by centrifugal force due to the curvature of the pipe, thus resulting in significantly larger heat transfer and friction factors with respect to straight pipes.

In steam generators, extensive attention is attached to flow instabilities, as they can lead to mechanical vibrations, thermal fatigue, problems of system control, and heat transfer surface burnout issues [2]. Hence, it is imperative to avoid flow instabilities and determine the safe operating regions of steam generators through rational design and accurate definition of the threshold values of system parameters. DWO is the most representative instability encountered in boiling systems. It is well known that DWO is induced in boiling system by the interaction between the single-phase flow and two-phase flow pressure drops, the inlet mass flow rate, and the void fraction distribution [3].

Two-phase flow instabilities including DWO have been studied since the 1960s; many researchers contributed to understand the instability mechanisms, namely, Yadigaroglu and Bergles [4], Ishii [5], and Fukuda and Kobori [6]. Numerous theoretical and experimental works are collected in several excellent literature reviews [7, 8]. Previous and current researches on flow instabilities mainly focus on straight tubes, whereas the research on helically coiled tubes has received much less attention. Most helically coiled tube correlations are formed based on straight pipe correlations by introducing a correction factor to adapt to the new geometry. Zhou et al. [9] and Ju et al. [10] carried out experiments to study DWO in helically coiled tube steam generators. More recently, experimental and theoretical studies were performed by Papini et al. [3] to investigate DWO in single and two parallel helically coiled tubes. Frequency domain method was employed to evaluate DWO in HTR-10 in the study of Niu et al. [11]. Most studies with respect to flow instabilities have been limited to constant wall temperature or constant wall heat flux conditions, using electrically heated tubes to assure uniform power distribution. The simplification provides a more convenient way to study the influence of each parameter on flow instability phenomena. However, the power distribution in a practical steam generator is not uniform; the electrically heated conditions will bring in some differences.

The present work deals with a fluid to fluid helically coiled steam generator, where neither constant wall temperature nor constant wall heat flux conditions can be assumed. Therefore, the results are more applicable to engineering practice. The methods to model two-phase flow instabilities fall into two categories: time domain method and frequency domain method. The frequency domain method is inexpensive with respect to computer time and it is less susceptible to numerical stability problems, so it is chosen in this work to evaluate the stability of helically coiled tubes.

Small modular reactors are becoming the research focus of nuclear industry in China currently. H-OTSG is adopted in many small modular reactors, such as HTR-10 (THU), ACP100S (CNNC), and ACPR50S (CGN). The flow instability of the secondary side in H-OTSG is a common problem to be solved in all these reactors. This work deals with a typical H-OTSG, focusing on the investigation of the influence of geometrical parameters of helically tubes on instability occurrence comprehensively with an in-house code, which can offer effective guidance to the design of H-OTSG. The H-OTSG model was also built in RELAP5/MOD3.2 as a comparison to authenticate each other.

#### 2. Models and Correlations

##### 2.1. Description of the Code

A FORTRAN code, STFQX (STEAMFREQ-X), was developed by Chan [12] to predict DWO in liquid-sodium steam generators, using linear frequency domain methods. The stability predictions were in satisfactory agreement with the experimental data. The simulations in this work were performed on the basis of STFQX. In STFQX, sodium flows outside the pipe while water flows inside, representing the steam generator in countercurrent fashion. The secondary side is divided into five sections:(1)subcooled unheated region, which includes piping, pump, and channel inlet resistance,(2)heated subcooled region,(3)boiling region,(4)superheated region,(5)outlet resistance and adiabatic riser.

The analysis is versatile and allows any of the above parts that are absent in the system to be eliminated.

The STFQX code is applicable for three geometries: straight tubes, helical tubes, and serpentine tubes; however, correlations in the code are only valid for straight tubes. Helical tubes are represented by inclined straight tubes of the same length and inclination. The differences between helical tubes and straight tubes are ignored in this approximation, and it will bring in some deviations when modeling helically coiled configurations. In order to analyze DWO in helical tubes more precisely, heat transfer and pressure drop correlations in STFQX were modified. The modified STFQX code is named STFQH. New correlations dedicated to helical tubes are employed in STFQH, taking the effects of the centrifugal forces into account. The key geometrical parameters of helical tubes are the tube length, the tube inner diameter, the helix angle, the helix diameter, and wall thickness. Besides, the fluid properties in single-phase region are assumed to be constant in the original code, neglecting their variations with temperature. In STFQH, the fluid properties in subcooled region and superheated region, including density, heat capacity, viscosity, and thermal conductivity, are modified to be the function of temperature in the steady-state solution.

Assumptions are used as follows in the development of the model:(1)The homogenous flow model is assumed in boiling region.(2)One-dimensional model along the axis of tube is adopted.(3)The heat conduction in the axial direction is neglected.(4)The tube wall physical properties are assumed to be constant.(5)Fluid properties do not vary with pressure and enthalpy perturbations.(6)The flow and heat transfer parameter of every control unit are represented by the mean values.(7)Subcooled boiling is neglected.

##### 2.2. Correlations for H-OTSG

###### 2.2.1. Heat Transfer Correlations

Heat transfer correlations for H-OTSG are listed in Table 1, which are cited from Cao’s thesis [13]. The heat transfer coefficients in helically coiled pipes are modified on the basis of straight pipe correlations with correction factors. The heat transfer coefficients in pipes are closely related to the flow patterns. Laminar and turbulent flows are the two major forms of flow in straight tubes. In helical tubes, the flow conditions are affected by the centrifugal forces which separate the liquid and gas phases due to the density difference. De is the dimensionless Dean number, which accounts for the effects of secondary flow induced by centrifugal forces in helical tubes. Transition from laminar flow to turbulent flow is governed by the critical Reynolds number suggested by Cioncolini and Santini [14].