A two-dimensional hydrodynamic analysis of three equilaterally arranged cylinders under combined steady and oscillatory flow

The two-dimensional hydrodynamics of an equilateral three-cylinder array (gap ratio 𝐺 = 3) are investigated computationally under combined steady and oscillatory flow conditions. With the parameter space oscillatory Reynolds number fixed at 𝑅𝑒𝑚 = 100, the Keulegan–Carpenter number, 𝐾𝐶 ∈ Z4,12, velocity ratio (steady to oscillatory component), 𝑚 ∈ R0,1.0, and relative flow incidence angle 𝛼 varied from 0◦ to 60◦ in steps of 15◦, are systematically varied. Recurrence Quantification Analysis (RQA), alongside a modified Keulegan–Carpenter number, 𝐾𝐶𝑝, is employed to evaluate intra-cycle repeatability and classify the flow. It is found that specific combinations of the steady flow component and incidence angle can restore spatial symmetry, yielding highly organised synchronous or quasi-periodic states with negligible lift, while other regions remain highly chaotic. The array orientation either facilitates vortex merging or provides geometric spacing that promotes smooth vortex advection. Finally, the applicability of Morison’s equation in respect of global hydrodynamic loading is critically assessed: demonstrating that a 3-term model significantly outperforms the traditional 2-term one in capturing the forces associated with the complex mixed-flow regimes encountered.