Numerical Simulations of Wave-Induced Flow Fields around Large-Diameter Surface-Piercing Vertical Circular Cylinder

Abstract

A computational analysis is performed on the diffraction of water waves induced by large-diameter, surface-piercing, vertical circular cylinder. With reference to linear-wave cases, the phenomenon is preliminarly considered in terms of velocity potential, a simplified theoretical framework in which both hypotheses of inviscid fluid and irrotational flow are incorporated. Then, and as a first-approximation analysis, the Euler equations in primitive variables are considered (a framework in which the fluid is still handled as inviscid, but the field can be rotational). Finally, the real-fluid behavior is analyzed, by numerically integrating the full Navier-Stokes equations (viscous fluid and rotational field) in their velocity-pressure formulation, by following the approach of the Direct Numerical Simulation (DNS, no models are used for the fluctuating portion of the velocity field). For further investigation of the flow fields, the swirling-strength criterion for flow-structure extraction, and the Karhunen-Loève (KL) decomposition technique for the extraction of the most energetic flow modes respectively, are applied to the computed fields. It is found that remarkable differences exist between the wave-induced fields, as derived within the different computing frameworks tested.

Recent Results from Analysis of Flow Structures and Energy Modes Induced by Viscous Wave around a Surface‐Piercing Cylinder

“…The process of code validation gave very satisfactory results, as related to both mean-flow quantities and high-order statistics of fluctuating velocities. Thus, we are now confident that high-energy modes and coherent structures of the flow, as computed in the present work, are correct (one can refer to Figures 4-8 of [21] for an extensive presentation of the benchmark-case results).…”

“…Table 4 of [21] reports (besides other relevant parameters) the partitions of the computing domain occupied by each block of grid points, and the grid-point distances Δ , Δ , Δ within each block. As for the computational grid, it can be noticed that (i) the grid point-distances Δ and Δ (along the -and -directions) are constant in the peripheral blocks 1, 2, 4, and 5, while, within the internal block 3, they are nonuniformly distributed according to a hyperbolic-tangent law, (ii) Δ (along the -direction) assumes a constant value through all blocks.…”

“…The Flow-3D solver has been validated in the case of the flow of a viscous fluid between two parallel plates at a moderate Reynolds-number value, against an accurate reference code, that is, the hybrid spectral-finite difference Navier-Stokes code, as originally developed by Alfonsi et al [35], and later tested by Passoni et al [36][37][38], and by Alfonsi and Primavera [39] (one can refer to Table 3 of [21] for an outlook of the computational parameters used in the numerical simulations of the benchmark case). The process of code validation gave very satisfactory results, as related to both mean-flow quantities and high-order statistics of fluctuating velocities.…”

“…The computational domain ( [21], Figure 3) has been discretized in a 5-block computational grid ( [21], Figure 9). Table 4 of [21] reports (besides other relevant parameters) the partitions of the computing domain occupied by each block of grid points, and the grid-point distances Δ , Δ , Δ within each block.…”

“…As for published works, in the numerical field, there exist a number of potential-flow studies [2][3][4][5] in which the good correspondence between potential flow fields and potential theory results is clearly demonstrated. In the experimental field, on the contrary, a number of authors [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] verified that linear diffraction actually strongly underestimates the run-ups (for a more extensive discussion about existing literature, one can refer to the review work [21]). In fact, under a computational viewpoint, the only correct approach to this problem is the integration of the system of the Navier-Stokes equations, a procedure still rarely used today.…”