A harmonic balance technique for the reduced-order computation of vortex-induced vibration

We present a harmonic balance (HB) method to model frequency lock-in effect during vortex-induced vibration (VIV) of elastically mounted circular cylinder and a flexible riser section in a freestream uniform flow. The fluid flow and structure are coupled by a fixed-point iteration process through a frequency updating algorithm. By minimizing the structural residual in the standard least-square norm, the convergence of HB-based fixedpoint algorithm is achieved for a range of reduced velocity. To begin with, the HB solver is first assessed for a periodic unsteady flow around a stationary circular cylinder. A freely vibrating circular cylinder is then adopted for the reduced-order computation of VIV at low Reynolds numbers of Re=100 and 180 with one- and two-degrees-of-freedom. The coupled VIV dynamics and the frequency lock-in phenomenon are accurately captured. The results show that the HB solver is able to predict the amplitude of vibration, frequency and forces comparable to its time domain counterpart, while providing a significant reduction with regard to overall computational cost. The proposed new scheme is then demonstrated for a fully-coupled three dimensional (3D) analysis of a linear-elastic riser section undergoing vortex-induced vibration in the lock-in range. The results reveal the 3D effects through isosurfaces of streamwise voracity blobs distributed over the span of flexible riser section. In comparison to time domain results, the 3D flow-structure interactions are accurately predicted while providing a similar speed up rate that of 2D simulations. This further corroborates that the HB solver can be extended to 3D flow structure dynamics without compromising efficiency and accuracy. (C) 2016 Elsevier Ltd. All rights reserved.