Extended five-term nonlinear drag model for a wide range of cylinder wakes

Abstract The unsteady variations in the near wake of a moving cylinder induce lift and drag forces on it, which are customarily normalized and expressed in terms of nondimensional lift and drag coefficients. While there are already several wake oscillator models for either a fixed or moving cylinder, special attention was given to modeling the lift coefficient for the case of a fixed cylinder or the case of a cylinder with one-degree-of-freedom motion in the cross-stream direction. When the drag coefficient is molded for a fixed or two-degree-of-freedom moving cylinder, a two-to-one frequency relationship (or quadratic coupling) between the drag and lift coefficients was assumed in the literature. However, we report situations of the excited wake of a vibrating cylinder, where such a modeling assumption fails to reproduce the actual pattern of the drag coefficient. We excite the wake of the cylinder by vibrating it harmonically in straight lines, and we then investigate the effect of this mechanical harmonic excitation on the lift-drag coupling using three tools for nonlinear dynamics analysis, namely, (1) time domain, (2) projection of the limit cycle, and (3) power spectra. We perform this analysis under different motion cases with manifested lift-drag coupling types that call on an extended universal drag model that accommodates such cases. Based on this, we propose a new reduced-order drag model with both linear and quadratic coupling terms to the lift as well as a mean component (thus, the proposed model consists of five terms). We verified the accuracy of the proposed reduced-order drag model by testing its ability to reproduce the time-dependent drag coefficient signals at a low Reynolds number of 300. These drag coefficient signals were obtained by applying direct numerical simulation (DNS) to integrate the two-dimensional incompressible Navier–Stokes equations governing the near wake fluid flow, with the aid of the finite difference method (FDM). The proposed drag model helps in extending the wake oscillators to more general cases of fluid–structure interaction (FSI) or vortex-induced vibration (VIV).