For two-phase natural circulation, scaling laws are provided by Ishii-Kataoka (1984) which is widely applied. The PUMA facility simulating the SBWR has been designed based on this philosophy. The power to volume scaling philosophy proposed by Zuber (1980) is also applicable for two-phase systems. The integral test facility being set-up to simulate the Advanced Heavy Water Reactor (AHWR) has been designed based on this philosophy. Prior studies by Nayak et al. (1998) has shown that this philosophy is well-suited for pressure-tube — type reactors where it is possible to use full-size components for most parts of the loop. It requires 1:1 scaling for elevation, pressure, temperature and velocity with the same fluid used in the prototype and the model. Such constraints do not exist for the scaling philosophy proposed by Ishii and Kataoka. [3]

(1) (2)

A 2 і Ai

FIG. 1. Schematic of non-unform diameter natural circulation loop.

The above equations can be non-dimensionalised using the following substitutions.

A A.
z H	D D.
W a a =—- ; в W
ai	and di
; S	т ■

Where tr, Ar and Dr are respectively the reference values of time, flow rate and hydraulic diameter defined as

Vtp.
(6)
r
W

It is easy to see that the reference time is nothing but the loop circulation time. Dr and Ar are respectively the length average hydraulic diameter and flow area of the loop and the total circulation length, Lt=ELi. In case of negligible local pressure losses, X(Leff)i becomes equal to the total circulation length, Lt of the loop. The non-dimensional equations can be expressed as:

	Grm Re3
(7)
дв a дв = Vt dT+ah dS=V
heater
(8a) (8b) (8c)
дв + a дв = stPcLt в дт ac ds Ac
cooler
дв + a дв = 0 дт ap дs
pipes

Where T=ESi/ai, (leff)i=(Leff)i/Lt, Grm=DI3pI2PgATr/p2, and St=Nu/RessPr. Assuming fully developed forced flow correlations are valid, the friction factor, fi can be expressed as

_ p _ pa = Rif = Re (d / a )

Where p=64 and b=1 for laminar flow and assuming Blassius correlation to be valid for turbulent flow p and b are respectively 0.316 and 0.25. In a non-uniform diameter loop, it is possible that some pipe sections are in turbulent flow (Re>4000) and some in laminar flow (Re<2000) and still others in transition flow (2000<Re<4000). However, if we assume the entire length of the loop to be under either laminar or turbulent flow conditions, then equation (7) can be expressed as

(10)

(11)