Flow around cylinders is widespread in marine engineering projects such as marine risers, marine pipelines, and tension leg. To understand the wake characteristics of the circular cylinder with different roughness, at a Reynolds number of 7400, a circulation water tunnel is used for experimental PIV measurements to compare the wake characteristics among the smooth cylinder, the original grooved cylinder, and the secondary grooved cylinder. The results revealed that the secondary grooved reduced the recirculation region, the flow-direction velocity gradient, the Reynolds shear stresses, and turbulent kinetic energy. Both small-scale and large-scale vortices are present in the wake vortex shedding. The instantaneous large-scale vortices behind the grooved cylinders are dispersed into several relatively small-scale vortices. Furthermore, the spike of the secondary grooved cylinder is a vortex generator, and directly impacts the generation of small eddies and the dissipation of large vortices.

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The objective of the paper is to propose the empirical formulas of the entrained water effect based on numerical method to estimate the virtual mass and the virtual moment of inertia for tandem propellers. The fluid-solid interaction of combined propellers in the flow field has been taken into consideration in the calculation. The axial added mass and the added moment of inertia of the entrained water are calculated for a single propeller using the finite element method and the existing empirical formulas to verify the feasibility and accuracy of numerical method. Consequently, the numerical calculation of tandem propellers is conducted to obtain the novel empirical formulas of entrained water properties, which are available to evaluate the influence of the blade diameter, the expanded area ratio and the pitch/diameter ratio. The corresponding correction coefficients in the empirical formulas considering the entrained water effect of tandem propellers are given. The empirical formulas are beneficial to relevant practical engineering calculation of entrained water properties for combined propellers.