Simulations of turbulent fluid flow around long cylindrical structures are computationally expensive because of the vast range of length scales, requiring simplifications such as dimensional reduction. Current dimensionality reduction techniques such as strip-theory and depth-averaged methods do not take into account the natural flow dissipation mechanism inherent in the small-scale three-dimensional (3-D) vortical structures. We propose a novel flow decomposition based on a local spanwise average of the flow, yielding the spanwise-averaged Navier–Stokes (SANS) equations. The SANS equations include closure terms accounting for the 3-D effects otherwise not considered in 2-D formulations. A supervised machine-learning (ML) model based on a deep convolutional neural network provides closure to the SANS system. A-priori results show up to 92% correlation between target and predicted closure terms; more than an order of magnitude better than the eddy viscosity model correlation. The trained ML model is also assessed for different Reynolds regimes and body shapes to the training case where, despite some discrepancies in the shear-layer region, high correlation values are still observed. The new SANS equations and ML closure model are also used for a-posteriori prediction. While we find evidence of known stability issues with long time ML predictions for dynamical systems, the closed SANS simulations are still capable of predicting wake metrics and induced forces with errors from 1-10%. This results in approximately an order of magnitude improvement over standard 2-D simulations while reducing the computational cost of 3-D simulations by 99.5%.

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A machine-learning based closure is explored for the prediction of the turbulent wake of flow past a circular cylinder at a high Reynolds number. We show that classic turbulence closures based on the turbulent-viscosity hypothesis are not capable of modelling the non-linear relationship between the mean quantities and the target turbulent fields. Instead, different multiple-input multiple-output auto-encoder convolutional neural networks are explored in this work to develop a data-driven closure. A detailed hyper-parameter study is completed including network architecture, loss functions and input sets, among others. A-priori results show 80% to 90% correlation coefficients between target and predicted turbulent fields of previously unseen data. High correlation coefficients are rapidly achieved by networks with a large number of trainable parameters, whereas smaller networks require more training epochs. The integration of the model in live simulations is theoretically discussed from its stability standpoint as well as preliminary physics-based constraints ideas to provide more stable data-driven closures.@en

Turbulent flow evolution and energy cascades are significantly different in two-dimensional (2-D) and three-dimensional (3-D) flows. Studies have investigated these differences in obstacle-free turbulent flows, but solid boundaries have an important impact on the cross-over from 3-D to 2-D turbulence dynamics. In this work, we investigate the span effect on the turbulence nature of flow past a circular cylinder at . It is found that even for highly anisotropic geometries, 3-D small-scale structures detach from the walls. Additionally, the natural large-scale rotation of the Kármán vortices rapidly two-dimensionalise those structures if the span is 50Â % of the diameter or less. We show this is linked to the span being shorter than the Mode B instability wavelength. The conflicting 3-D small-scale structures and 2-D Kármán vortices result in 2-D and 3-D turbulence dynamics which can coexist at certain locations of the wake depending on the domain geometric anisotropy.

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Vortex-induced vibration (VIV) of elastic structures with a square-shaped prismatic column exposed to flow has a significant impact on many aspects of structural design and stability. The main aim of the present numerical study is to investigate an alternative design of square column for minimizing the impact of VIV on the elastic structures. The numerical study is carried out at moderate Reynolds numbers (1000 ≤ Re ≤ 22000). For both stationary and freely vibrating square cylinders, a systematic validation of the numerical results is performed with the available experimental data. In particular, various turbulence models are explored to assess their effectiveness to capture the separated wake flow dynamics behind the square cylinder. The simulation results via k−ω SST-SAS (Scale Adaptive Simulation) model are found closer to the reported measurements for both stationary and vibrating cases. After establishing the validity of our numerical methodology, the VIV simulations of twisted square cylinders with different twisted angles are performed at the moderate Reynolds numbers. In comparison to the square cylinder counterpart, the results of the twisted square cylinder demonstrate good controlling effect on the VIV response at two oncoming flow directions (0° and 45°). The twisted surface of the cylinder causes the variation of separation or vortex shedding points as well as the frequency of vortex shedding, which in turn affect the distributions of hydrodynamic forces along the cylinder. The power spectral analysis of hydrodynamic forces of twisted square cylinder indicates that the twisted surface has a significant influence on the frequencies of both drag and lift forces. Finally, comparisons of the detailed flow patterns, the 3D vortex structures and the vortex-shedding modes between square and twisted cylinders are presented in detail.@en

The wake behind a bluff body constitutes an intrinsically three-dimensional flow and it is known that two-dimensional simulations yield to an unphysical prediction of the body forces because of the nature of the two-dimensional Navier-Stokes equations. However, three-dimensional simulations are too computationally expensive for cases such as marine risers, which have very large aspect ratios and are exposed to a high Reynolds number flow. A quantitative and qualitative study has been performed to investigate the fundamental differences on the wake of two-dimensional and three-dimensional fixed spanwise periodic cylinders for a Reynolds number of 10⁴. A very fine unifrom grid (503M points) has been used for the near and mid wake range, and it is shown that the wake presents very different vortical structures when the spanwise dimensionality is omitted. In this case, forces such as lift and drag are overpredicted. The kinetic energy spectra of the flow is also investigated to further discuss the physics inherent of each case together and it is found that the contribution of the spanwise velocity on the large wavenumbers is significantly smaller than the other velocity components.

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Bluff body structures exposed to ocean current can undergo vortex-induced motion (VIM) for certain geometric and physical conditions. Recently, the study of VIM has been gaining attention for many engineering applications, in particular offshore structures such as buoys, FPSOs, semi-submersibles, Spars and TLPs. The present work is a part of a systematic effort to investigate the VIM response of multi-columns floating platform. In real sea condition, floating platforms are in high Reynolds numbers region and flow patterns around structures are turbulent in nature. For the purpose of investigating and simulating accurately the nonlinear dynamic processes of vortex shedding, transport and wake interactions with the bluff body, the fundamental study of VIM around a square column at moderate Reynolds numbers (1500 ≤ Re ≤ 14000) is firstly investigated. In the present work, the transient flow pattern around a free vibrating square cylinder at moderate Reynolds numbers is numerically investigated by an open source CFD toolbox, OpenFOAM. Good consistency and agreement are found between the present numerical findings and that of experiments. The cylinder, with a blockage area of 4.2%, is mounted on an elastic support for free vibration in the transverse direction. Hybrid RANS-LES turbulence models are considered here for accurate prediction of massively separated turbulent wake flow while maintaining the reasonable computational cost. Three hybrid turbulence models, the DDES (Delayed Detached Eddy Simulation, the k-ω SST-DES (Detached Eddy Simulation), and the k-ω SST-SAS (Scale Adaptive Simulation), are studied and their results are compared with the reported experimental measurements. It is shown that the result of simulation with the k-ω SST-SAS model is closer to the reported literature than the other two and therefore, subsequently adopted for all the simulations of our study in this paper. The scaling effect of cylinder length in the spanwise direction is also studied with the objective to reduce the computational cost. From the comparison with the recent experimental measurements, the discrepancy between the present simulations of reducing cylinder length and the experiment increases only when Re ≥ 4000. This might stem from the increase in wavelength of some vortex shedding modes and turbulence intensity variation in the spanwise direction near the cylinder as Re ≥ 4000. The detailed flow patterns, 3D vortex structures (based on Q-criterion) and vortex-shedding modes are presented in this work as well.@en

Vortex induced motion (VIM) can occur on any bluff body (such as buoys, FPSOs, semi-submersibles, Spars and TLPs) exposed to current. VIM is well-acknowledged to have a strong impact on the fatigue life of mooring and riser systems and must be quantified and sometimes mitigated. As part of the effort to numerically investigate VIM response of multi-columns floating platform, we start with the fundamental study of VIM around a square column at low Reynolds numbers (Re), seeking to investigate and accurately simulate the dynamic processes of vortex shedding, transportation and wake interactions with the bluff body and its motion in response. OpenFOAM, an open source CFD toolbox, is used to solve the transient flow pattern around a stationary and free moving square cylinder. A rigorous benchmark of the present simulation against experiments and numerical simulations is demonstrated for both stationary and free moving square cylinders at 60 ≤ Re ≤ 200. The cylinder, with a blockage area of 5%, is mounted on elastic supports for free vibration in both in-line and transverse directions. The effects of grid types and resolutions on the key features of vortex dynamics, vortex induced motion, and the stability of dynamic mesh solver in OpenFOAM are explored. It is found that hybrid unstructured grid has better performance and stability than structured-O grid in OpenFOAM dynamic solver. The effects of mass ratio, spring stiffness and damping on the motion of square cylinder are discussed. It is observed that the phase angle difference between lift coefficient and transverse motion of the cylinder is correlated with mass ratio, spring damping and Reynolds number. An abrupt jump of phase angle difference between lift coefficient and transverse amplitude occurs at Re=76 with mass ratio of 25. The damping effect plays a significant role in the phase angle difference between lift coefficient and transverse amplitude of the cylinder.@en