Theoretical and experimental study on density wave oscillation of two-phase natural circulation of low equilibrium quality

doi:10.1016/S0029-5493(01)00456-3

Nuclear Engineering and Design

Volume 215, Issue 3, June 2002, Pages 187-198

https://doi.org/10.1016/S0029-5493(01)00456-3 Get rights and content

Abstract

A theoretical and experimental study of density wave oscillation (DWO) in natural circulation is presented in this paper. Experiments were performed on a natural circulation test facility. The influences of mass flow rate, pressure, inlet subcooling, heat flux and exit quality on DWO were analyzed. The marginal stability boundary (MSB) of DWO was obtained. A criterion of two-phase natural circulation, which predicts the stability thresholds, was developed by lumped parameter method. It is a function of non-dimensional parameters, such as phase change number N_pch, subcooling number N_sub, Froude number, Fr, geometry number N_l and friction number τ. The geometry number and friction number are first defined in this paper. A correlation of DWO period was also obtained, it is also a function of the above non-dimensional parameters. The results of the present criterion and period correlation were compared with those of the experimental data and references. It is shown that they agree very well.

Introduction

The flow instabilities and thermo-hydraulic oscillations have long been studied and many works have been performed by many researchers since flow excursion was first discovered by Ledinegg in 1938, Ledinegg (1938). These studies were prompted by potential harmfulness caused by instabilities in large-scale nuclear reactor systems. The 1979 accident at Three Mile Island (TMI) reactor proved the importance of the concept of inherent reactor safety. Passive residual heat removal systems (PRHRS) have been adopted such as in JPSR (Murao et al., 1995) and AP600 (Mcintyre and Beck, 1992) reactors. Natural circulation is used in some PRHRSs such as in AC600 (Su et al., 1994) provided by China. The natural circulation can also be used in the primary side of such reactors as the low temperature heating reactor (THR; Wang, 1993). Boiling natural circulation is the major cooling mechanism in the SBWR (Barbucci, 1995). Flow in natural circulation systems is induced by difference in fluid densities between the hot leg (riser) and the cold leg (downcomer). For a two-phase natural circulation loop, heat input and its removal induces a large volumetric change owing to phase changes-boiling and condensation-, thus the system easily becomes unstable. In such a two-phase natural circulation loop, various types of flow instabilities occur depending on the system geometry, fluid properties and the operating conditions etc. One of the most important phenomena in natural circulation loop is density wave oscillation (DWO) which can affect the operation and safety features of the system. That is, the self-sustained DWO may cause many undesired problems such as mechanical and thermal fatigue of components by mechanical vibration and thermal waves to require the system control considerations.

There are many studies dealing with two-phase oscillations. A large part of the studies is on forced circulations and relatively less works (Wissler et al., 1956, Chexal and Bergles, 1973, Ardron, 1984, Lee and Ishii, 1998, Balunov, 1990, Delmastro et al., 1991, Yun, 1994 etc.) have been done on natural circulation. Boure et al. (1973) made a clear classification of flow instabilities. But most of the instabilities mentioned by Boure concerned forced circulation. Fukuda and Kobori (1979) classified DWO into two types, namely, type I and II. Type I is the DWO occurring at low quality conditions, for which gravitational pressure drop in unheated riser plays a dominant role; and Type II is one occurring at high quality conditions, for which frictional pressure drop is dominant. Lee (1991) studied the flow instabilities in an open two-phase natural circulation loop and constructed typical instability map. Kyung and Lee (1994) investigated flow characteristics in an open two-phase natural circulation loop with Freon-113 as the working fluid and observed three basic circulation modes (periodic circulation A, continuous circulation and periodic circulation B) with variation of the heat flux and constant inlet subcooling. Further, Kim and Lee (2000) classified natural circulations into six different modes. Instability map in the plane of the heat flux and the heater-inlet subcooling was plotted. Rohatgi and Duffey (1998) presented critical subcooling number as a function of Froude number, Fr in natural circulation two-phase flow and showed the fundamental parametric dependencies on the loop loss coefficient and the ratio of the heated channel to downcomer heights. Inada et al., 1995, Inada et al., 1997, Inada et al., 2000 studied two-phase flow instability in a boiling natural circulation loop at relatively high system pressure and analyzed the inlet throttling effect on flow stability. Zhou, 1997, Jiang et al., 2000 studied stability structure of low quality DWO in a natural circulation system at heating reactor conditions by the frequency domain method. Su, 1997, Su et al., 2001 presented a non-linear dynamic model in time domain of two-phase natural circulation.

But unfortunately, there is not a perfect criterion to predict the stability of two-phase natural circulation, neither a period correlation to calculate DWO period. The main purpose of this paper is to derive the stability criterion and period correlation of two-phase natural circulation. Experimental study was also done to verify the criterion and correlation.

Section snippets

Test facility

The schematic diagram of the test system is shown in Fig. 1. Basically it consists of the primary loop, secondary loop (cooling loop), electrically heating system and measuring system. The primary loop is a two-phase natural circulation one, which consists of pre-heater, test section, riser, condenser, downcomer, pressurizer, throttle valve, and connection tubes. All of the components and tubes were made of stainless steel. Table 1 shows the main parameters of the natural circulation loop and

Stability criterion

The most different aspect of the natural circulation mode from the forced circulation one is that the mass flow rate is determined by the heated power. The bigger the mass flow rate is, the stronger the natural circulation ability is. Thus, a riser, which is also called a chimney, is always employed in a natural circulation as shown in Fig. 1 to increase the mass flow rate. So consider the boiling channel of the natural circulation loop, which is divided into three control volumes as shown in

Conclusions

DWO is quite an important phenomenon in natural circulation and it can be classified into two types. The type I DWO is experimentally studied in this paper. Experiments were performed on a natural circulation test facility.

•
The system will tend to be stable if the system pressure increases. The system pressure has no obvious influence on DWO period, but the DWO amplitude will decrease and the DWO period will increase a little if the system pressure increases. The critical exit equilibrium

Nomenclature

A	cross sectional area
g	gravitational acceleration
G	mass flow velocity
h	specific enthalpy
K	friction coefficient
L	heat length
P	pressure
q	heat flux
Q	heated power
t	time
V	velocity
W	mass flow rate
z	axial coordinate
α	void fraction
ρ	density
υ	specific volume

Subscripts
f	liquid
fg	transfer from liquid to vapor
g	vapor
in	inlet
out	outlet
o	steady-state
r	riser
s	saturated
sp	single-phase flow
tp	two-phase flow

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Theoretical and experimental study on density wave oscillation of two-phase natural circulation of low equilibrium quality

Abstract

Introduction

Section snippets

Test facility

Stability criterion

Conclusions

Nomenclature

Nucl. Eng. Des.

Nucl. Eng. Dec.

Nucl. Eng. Des.

Nucl. Eng. Des.

Nucl. Eng. Des.

Nucl. Eng. Des.

Nucl. Eng. Des.

Int. Comm. Heat Mass Transfer

Hydrodynamics stability of natural circulation loop operating with boiling water

Heat Transfer Soviet Res.

Simplified boiling water reactor thermal-hydraulic performance—a relap5/mod2 model simulation

Nucl. Technol.

Two phase instabilities in a low pressure natural circulation loop

AIChE Symp. Ser.

Classification of two-phase flow instability by density wave oscillation model

J. Nucl. Sci. Technol.

Theoretical study of natural circulation two-phase flow at low quality low pressure

Chin. J. Nucl. Power Eng.