# Helical Coil Thermal Hydraulic Model

Helical coil pipes have been widely used in the past in many industrial applications such as thermal process plants or power plants for the steam generation. In nuclear industry, helical coil steam generators (SG) and intermediate heat exchangers (IHX) have been installed in the fast reactors like Monju (Japan) [1] and Super-Phénix (France). These components are still considered for the future reactors projects such as the small modular reactors (SMR), like IRIS [2], and the fourth generation reactors like the Russian project BREST.

Coiled geometries are of particular interest because they allow to obtain high values of the inner heat transfer coefficients and guarantee an efficient power removal with a very high degree of compactness. Secondary motions in the velocity field are due to the centrifugal forces induced by the pipe curvature: these forces produce a shift of the fluid towards the outer part of the pipe, reducing the boundary layer and increasing the heat transfer. Centrifugal forces induce also a displacement of the maximum values of temperature and velocity from the centre of the axis to the outer side.

Helical coil fluid dynamics has been studied by several authors as regards both the laminar to turbulent transition [3] and the heat transfer and pressure drops in single-phase flow. Many reviews related to the fluid dynamics and heat transfer of curved tubes are available in literature, also recently (Naphon and Wongwises [4] and Vashisth [5]). Most of the work already done considers single-phase heat transfer with constant wall temperature or fixed heat flux boundary conditions, concentrating the efforts on the inner side of the helix. In order to characterize efficiently the heat transfer in steam generators is also important to develop models of heat transfer between fluids, characterized by their own temperature profile, with variable heat flux and wall temperature distribution in space. Escha et al. [6] studied a helical coil steam generator for a gas cooled reactor with the system code TRACE and the results obtained with different heat transfer coefficient correlations were compared with experimental data. In the present study a model has been implemented in Matlab environment with the aim to evaluate temperature and pressure profiles, heat transfer, pressure drops and two-phase flow dynamic considering an helical coil and shell steam generator. The semiempirical correlations for the evaluation of the heat transfer coefficients and the friction factors have been taken from literature. The model has been applied to the steam generator configuration of the SMR IRIS and the profiles of temperature, pressure and heat transfer coefficients have been compared with the ones obtained with the commercial code RELAP5/Mod.3.3.