Numerical study of Vortex-Induced Vibration of a Single Flexible Tube within a Non-uniform Tube Array*

Flow-induced vibration can lead to significant damage in heat exchangers. In small modular ‎reactors, helical coil steam generators (HCSGs) may potentially be susceptible to vortex-induced ‎vibrations due to single-phase flow on the shell side. This study examines vortex-induced ‎vibrations in a cross-section of HCSGs focusing on a non-uniform tube array. The non-uniform ‎tube array under consideration combines a normal square and a rotated triangle geometry with a ‎transverse spacing ratio (Xt) of 1.3 and a longitudinal spacing ratio (Xl) of 1.5. Through two-way coupling, the fluid force is transferred to the tube, and then the incremental displacement ‎of the tube is transferred back to the fluid domain at each time step. A validation case analysis ‎‎(Khalak & Williamson, 1996) was conducted prior to the real case study to demonstrate the ‎accuracy of the URANS model, specifically the turbulence model, k-ω SST. The Strouhal ‎number for the non-uniform tube array is different from those obtained for the two ‎fundamental tube patterns (i.e. Normal square and Rotated triangle). This particular Strouhal ‎number is close to the rotated triangle tube pattern Strouhal number. For the non-uniform tube ‎array, one flexible tube, which is free to vibrate in the transverse direction, is considered for ‎three different sections of the helical geometry. Simulations for three different flow velocities ‎were compared, and the onset of lock-in was observed. The results for the non-uniform array ‎show a slightly lower predicted frequency, but the margin for lock-in is reasonably accurate.  ‎The distinction between vortex-induced vibration and fluid-elastic instability is ‎intricately tied to the position of the flexible tubes. It has been determined that the section with the rotated triangle configuration within the non-uniform tube array predominantly influences the critical flow velocity and the lock-in region. A comparison was conducted between undamped tube vibration and vibration with low (structural) damping for one flexible tube to investigate the influence of damping on the flow periodicity lock-in dynamics in the tube array. Adding even small structural damping to the tubes significantly increases the critical flow velocity for the non-uniform tube array.