SINOD—A Nonlinear Lumped-Parameter Model for Steady-State, Transient, and Stability Analysis of Two-Phase Flow in Natural Circulation Boiling-Water Loops

Abstract

The loop considered consists of an equivalent downcomer and a channel divided into a heated test section and an unheated riser. The preliminary structure of the lumped-parameter model is obtained by integrating partially, over the space coordinate, the system of nonlinear partial differential equations that state the mass, energy, and momentum conservation. The same formalism, however, should not be used for specifying the final structure of the model; it is shown that in this way it is not possible to represent adequately the basic mechanism of hydrodynamic instability, i.e., to define the interaction between the mass velocity and the void fraction, resulting from the friction in the boiling part of the heated test section. A procedure is proposed for specifying the final structure of the lumped-parameter model that can be adequately used instead of distributed parameter models in a wide range of system parameters and operating conditions. The model SINOD is formulated in terms of four nonlinear first-order ordinary differential equations and one time lag. Since the time lag can be neglected in most analyses, the model reduces to a system of only three nonlinear first-order ordinary differential equations. An important particularity of the model is that both the steady-state and the dynamic calculations can be performed by solving the same system of differential equations. The input data are the parameters specifying the geometry of the test loop, the physical parameters of the fluid, the channel inlet, and the riser outlet pressure drop coefficients. The two-phase friction multiplier and the slip ratio correlations are arbitrary. The validity of the proposed model is examined by comparing the results with the experimental data obtained on the test loops FRÖJA, FRIGG, SKÄLAVAN, and the Halden Loop, as well as with the results obtained using the distributed parameter models HYDRO and RAMONA.