Numerical Study of the Amplitude and the Convection Speed of Periodic Large-Scale Vortices in a Square Array of Cylinders Subjected to Axial Flow

A square array of cylinders subjected to axial flow is commonly encountered in nuclear reactors and other heat exchangers. Large-scale vortices have been observed in the gaps between the cylinders, both experimentally and numerically. These periodic flow instabilities occur in tightly-spaced cylinder arrays and originate from the velocity difference between the gap and the subchannel regions. The pressure fluctuations caused by the coherent vortex structures are possibly a source of fretting and fatigue in the aforementioned applications. In order to quantify and comprehend this phenomenon, Large-Eddy Simulations are performed on an incompressible, Newtonian fluid flowing adiabatically through a numerical domain containing a single rigid cylinder with periodic boundary conditions, representative for a cylinder in an infinite square array. Subsequently, the temporal frequency spectrum of the wall pressure profile is calculated. The spatial autocorrelation function of this Fourier spectrum, the so-called Cross Spectral Density function, contains information regarding the amplitude and convection speed of the pressure fluctuations. It is shown that the flow instability is strongest for a pitch-over-diameter ratio of 1.03. Also, the simulations indicate that the convection speed is monotonously increasing with the pitch-over-diameter ratio. An updated model for this convection speed is proposed. Finally, it is shown that the single-cylinder approximation has its limitations, but provides valuable information with minimal computational cost.