Numerical Prediction of Secondary Flows in Complex Areas Using Concept of Local Turbulent Reynolds Number

A new model of turbulence is proposed for the estimation of Reynolds stresses in turbulent fully-developed flow in a wall-bounded straight channel of an arbitrary shape. Ensemble-averaged Navier-Stokes, or Reynolds, equations are considered to be sufficient and practical enough to describe the turbulent flow in complex geometry of rod bundle array. We suggest the turbulence is a process of developing of external perturbations due to wall roughness, inlet conditions and other factors. We also assume that real flows are always affected by perturbations of any possible scale lower than the size of the channel. Thus, turbulence can be modeled in the form of internal or “turbulent” viscosity. The main idea of a Multi-Scale Viscosity (MSV) model can be expressed in the following phenomenological rule: A local deformation of axial velocity can generate the turbulence with the intensity that keeps the value of the local turbulent Reynolds number below some critical one. Therefore, in MSV, the only empirical parameter is the critical Reynolds number. From analysis of dimensions, some physical explanations of Reynolds number are possible. We can define the local turbulent Reynolds number in two ways: i) simply as Re = ul/v, where u is a local velocity deformation within the local scale l and v is total accumulated molecular and turbulent viscosity of all scales lower then 1. ii) Re = K/W, where K is kinetic energy and W is work of friction/dissipation forces. Both definitions above have been implemented in the calculation of samples of basic fully-developed turbulent flows in straight channels such as a circular tube and annular channel. MSV has been also applied to prediction of turbulence-driven secondary flow in elementary cell of the infinitive hexagonal rod array. It is known that the nature of these turbulence-driven motions is originated in anisotropy of turbulence structure. Due to the lack of experimental data up to date, numerical analysis seems to be the only way to estimate intensity of the secondary flows in hexagonal fuel assemblies of fast breeder reactors (FBR). Since MSV can naturally predict turbulent viscosity anisotropy in directions normal and parallel to the wall, it is capable to calculate secondary flows in the cross-section of the rod bundle. Calculations have shown that maximal intensity of secondary flow is about 1% of the mean axial velocity for the low-Re flows (Re = 8170), while for higher Reynolds number (Re = 160,100) the intensity of secondary flow is as negligible as 0.2%.