Scaling of the steady state and stability behaviour of single and two-phase natural circulation systems

P. K. Vijayan, A. K. Nayak, M. H. Bade,

N. Kumar, D. Saha, R. K. Sinha

Bhabha Atomic Research Centre,

Mumbai, India

Abstract. Scaling methods for both single-phase and two-phase natural circulation systems have been presented. For single-phase systems, simulation of the steady state flow can be achieved by preserving just one nondimensional parameter. For uniform diameter two-phase systems also, it is possible to simulate the steady state behaviour with just one non-dimensional parameter. Simulation of the stability behaviour requires geometric similarity in addition to the similarity of the physical parameters appearing in the governing equations. The scaling laws proposed have been tested with experimental data in case of single-phase natural circulation.

1. INTRODUCTION

Natural circulation is being increasingly employed in many innovative designs of nuclear reactor cooling systems. The basic advantage of natural circulation systems is the enhanced safety due to its passive nature. One of the basic requirements, which arise prior to the incorporation of such systems in nuclear reactors, is the assessment of their performance. Generally, in the nuclear field the assessment is carried out by validated computer codes. Code validation is usually done with data obtained from scaled test facilities. The topic of the present paper is the scaling laws used for constructing such scaled facilities for simulating single and two-phase natural circulation. Such a scaled facility in nuclear parlance is also known as an integral test facility (ITF).

Scaling laws make possible the comparison of the performance of different natural circulation systems and to extrapolate the data from small scale to prototype systems. Scaling laws for nuclear reactor systems are arrived at using the governing conservation equations. Pioneering work in the field of scaling laws for nuclear reactor systems have been carried out by Nahavandi et al. (1979), Zuber (1980) and Heisler (1982). The scaling law proposed by Zuber is also known as the power-to-volume scaling philosophy and is widely used for the construction of scaled test facilities simulating nuclear reactor systems. Power to volume scaling can be applied to both forced and natural circulation systems. However, the power-to — volume scaling philosophy has certain inherent distortions (especially in downsized components), which can suppress certain natural circulation specific phenomena like the instability (Nayak et al. (1998)). Hence it is necessary to examine the scaling laws which are specific to natural circulation. In the present paper, the reported scaling laws for single — and two-phase natural circulation loops are reviewed with respect to their use for predicting the steady state and stability behaviour. Then scaling procedures for single and two-phase systems are presented and tested against the available data on the steady state and stability performance of natural circulation loops. This exercise has shown that the steady state behaviour of single-phase loops can be simulated by a single dimensionless parameter. This is also true for uniform diameter two-phase loops. The simulation of the stability behaviour requires simulation of at least three dimensionless parameters in addition to geometric scaling. For the stability behaviour, scaling of the characteristic equation (obtained by the linear stability analysis method) appears to be the appropriate method for achieving similarity.

2. REVIEW OF SCALING LAWS

Several scaling laws have already been proposed for the design of scaled loops simulating natural circulation phenomenon. Such scaling laws are available for both single — and two — phase natural circulation loops.