Fluid–structure interaction simulation of a flapping flag in a laminar jet

Abstract

The flapping flag is a classical and important Fluid–Structure Interaction (FSI) problem with many applications in nature, industry, and biological systems. However, the interaction between the flow field and the flag response is not fully understood due to the complex and nonlinear nature of the problem. Although theoretical models qualitatively predict the flapping frequency and the onset velocity, there are still quantitative discrepancies between the theoretical predictions and the experimental data. In this study, numerical FSI simulations of a standard flag in a viscous uniform laminar flow are performed to characterize the flow field around the flapping flag and correlate the flow field with the flag response for six Reynolds numbers (Re= 4.5 ×104, Re= 5.3 ×104, Re= 5.7 ×104, Re= 5.9 ×104, Re= 6.6 ×104, and Re= 7.5 ×104). Two-way coupled FSI simulations are conducted using commercial software ANSYS®. Rigorous solution verification is conducted first on three Re to ensure that solutions are independent of mesh and time-step refinement. Then validation is achieved by comparing the simulation predictions with experimental data. Overall, results showed a good agreement with an error range between 0.7%–4.7% for oscillation amplitude (Am), 1.3%–6.41% for drag coefficient (Cd), and 1.3%–5.3% for frequency (f). Moreover, a comparison between inviscid and viscous models is performed to evaluate the accuracy of using inviscid theoretical models for the same flow. It is observed that the inviscid model accurately predicted f but underpredicted Am and Cd, and overpredicted lift coefficient Cl. In the case of the viscous model, it is observed that a flow separation bubble and a thin flow circulation region exist on the suction side of the flag during the limit cycle oscillation (LCO). Finally, an instantaneous negative drag is observed for a short time during the LCO, suggesting that flag reconfiguration and flow separation significantly affects the drag. These observations suggest that viscous models may be needed to improve the theoretical predictions.