Hydrodynamic damping of an oscillating cylinder at small Keulegan–Carpenter numbers

Ren, Chengjiao; Lü, Lin; Cheng, Liang; Chen, Tingguo

doi:10.1017/jfm.2020.1159

Cited by 10 publications

(6 citation statements)

References 32 publications

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“…The KC number based on the diameter of the central main column, 6.5 m, is higher at 4.9. The cross members should experience significant flow separation with a KC number of approximately 20; however, the contribution to the global loads is likely limited because of their small diameter of just 1.6 m. The relatively low KC numbers, especially for the larger offset columns and heave plates, suggest that viscous drag associated with the wall boundary layer can potentially have nonnegligible contributions to the total surge damping [35]; therefore, it is important to resolve the shear layer on the floater surface properly with an adequately fine prism-layer mesh. Flow separation from the corners of the heave plates also contributes to the surge damping by exerting a transverse drag force on the thick heave plates.…”

Section: Computational Gridmentioning

confidence: 99%

“…It also suggests that the linear damping observed with the experiment and the CFD solutions is also caused by fluid viscosity. The linear viscous damping associated with the boundary layer on the surface of the structure typically becomes significant and comparable to the quadratic drag force for circular cylinders when the KC number is small (estimated to be 2.7 based on the diameter of the offset upper columns) and flow separation is weak; therefore, the original form of the Morison equation [29] without a linear drag term is fundamentally incorrect [35]. In this flow regime, potential-flow models with empirical drag forces need to either include an additional global linear damping matrix or use an alternative generalized form of the Morison equation with a linear drag term [35].…”

Section: Surge Dampingmentioning

confidence: 99%

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OC6 Phase Ia: CFD Simulations of the Free-Decay Motion of the DeepCwind Semisubmersible

et al. 2022

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Currently, the design of floating offshore wind systems is primarily based on mid-fidelity models with empirical drag forces. The tuning of the model coefficients requires data from either experiments or high-fidelity simulations. As part of the OC6 (Offshore Code Comparison Collaboration, Continued, with Correlation, and unCertainty (OC6) is a project under the International Energy Agency Wind Task 30 framework) project, the present investigation explores the latter option. A verification and validation study of computational fluid dynamics (CFD) models of the DeepCwind semisubmersible undergoing free-decay motion is performed. Several institutions provided CFD results for validation against the OC6 experimental campaign. The objective is to evaluate whether the CFD setups of the participants can provide valid estimates of the hydrodynamic damping coefficients needed by mid-fidelity models. The linear and quadratic damping coefficients and the equivalent damping ratio are chosen as metrics for validation. Large numerical uncertainties are estimated for the linear and quadratic damping coefficients; however, the equivalent damping ratios are more consistently predicted with lower uncertainty. Some difference is observed between the experimental and CFD surge-decay motion, which is caused by mechanical damping not considered in the simulations that likely originated from the mooring setup, including a Coulomb-friction-type force. Overall, the simulations and the experiment show reasonable agreement, thus demonstrating the feasibility of using CFD simulations to tune mid-fidelity models.

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Section: Computational Gridmentioning

confidence: 99%

Section: Surge Dampingmentioning

confidence: 99%

OC6 Phase Ia: CFD Simulations of the Free-Decay Motion of the DeepCwind Semisubmersible

et al. 2022

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“…(2006) and Ren et al. (2019, 2021). The height of the first macro-element next to the cylinder surface is approximately .…”

Section: Tablementioning

confidence: 95%

Bistabilities in two parallel Kármán wakes

et al. 2021

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Bistabilities of two equilibrium states discovered in the coupled side-by-side Kármán wakes are investigated through Floquet analysis and direct numerical simulation (DNS) with different initial conditions over a range of gap-to-diameter ratio ( $g^*= 0.2\text {--}3.5$ ) and Reynolds number ( $Re = 47\text {--}100$ ). Two bistabilities are found in the transitional $g^*-Re$ regions from in-phase (IP) to anti-phase (AP) vortex shedding states. By initialising the flow in DNS with zero initial conditions, the flow in the first bistable region (i.e. bistable IP/FF $_C$ at $g^*= 1.4 \text {--} 2.0$ , where FF $_C$ denotes the conditional flip-flop flow) attains flip-flop (FF) flow, it settles into the IP state by initialising the flow with an IP flow. The second bistability is observed between cylinder-scale IP and AP states at large $g^*$ ( $=$ 2.0–3.5). The transition from the FF $_C$ to IP is dependent on initial conditions and irreversible over the parameter space, meaning that the flow cannot revert back to the FF $_C$ state once it jumps to the IP state irrespective of the direction of $Re$ variations. Its counterpart for the bistable IP/AP state is reversible. We also found that the FF $_C$ flow in the first bistable region is primarily bifurcated from synchronised AP with cluster-scale features, possibly because the cluster-scale AP flow is inherently unstable to FF flow instabilities. It is demonstrated that the irreversible bistability exists in other interacting wakes around multiple cylinders. A good understanding of flow bistabilities is pivotal to flow control applications and the interpretation of desynchronised flow features observed at high $Re$ values.

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“…The spatial domain is discretised into quadrilateral finite elements and within each element both the geometry and fluid quantities are represented by N p th polynomial expansions. A second-order time integration method, a velocity correction scheme and a Galerkin formulation are employed for all 2-D base flow simulations, which have been widely used and validated in the similar studies (Barkley & Henderson 1996;Carmo et al 2008;Ren et al 2019Ren et al , 2021b.…”

Section: Two-dimensional Dnsmentioning

confidence: 99%

Three-dimensional wake transitions of steady flow past two side-by-side cylinders

Ren,

Liu,

Cheng

et al. 2023

J. Fluid Mech.

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Three-dimensional (3-D) wake transitions of a steady flow past two side-by-side circular cylinders are investigated through Floquet analysis and direct numerical simulations (DNS) over the gap-to-diameter ratio $g^*$ up to 3.5 and Reynolds number ${\textit {Re}}$ up to 400. When the flows behind two cylinders form in-phase and anti-phase wakes at large $g^*$ , the wake transition is similar to the isolated cylinder counterpart, with the critical ${\textit {Re}}$ for the onset of 3-D transition ( ${\textit {Re}}_{cr-1}$ ) happens at around 180. At small $g^*$ , 3-D transition becomes interestingly complex due to the distinct characteristics formed in base flows. The ${\textit {Re}}_{cr-1}$ suddenly drops to around 60–100 and forms distinct variation trends with $g^*$ . Precisely, the ${\textit {Re}}_{cr-1}$ of the single symmetric wake (SS, $g^*\lessapprox 0.25$ ) is more than half of the isolated cylinder counterpart due to the large length scale of the SS wake. Only mode A is detected in SS. In the asymmetric single wake (ASS, $g^* \approx 0.25\unicode{x2013}0.6$ ) and flip-flop wake (FF, $g^* \approx 0.6\unicode{x2013}1.8$ ), the 3-D transition develops at ${\textit {Re}} \approx 103\unicode{x2013}60$ and 75–60, respectively. The decrease in ${\textit {Re}}_{cr-1}$ with increasing $g^*$ is because of the increased level of wake asymmetry in ASS and irregular vortex shedding in FF. Floquet analysis predicts two new unstable modes, namely mode A $'$ and subharmonic mode C $'$ , of ASS. Both modes are transient features in 3-D DNS and the flow eventually saturates into a new 3-D mode, mode ASS. The gap flow of mode ASS is distinctly characterised by its time-independent spanwise waviness structure that is deflected towards different transverse directions with a long wavelength of about $14$ cylinder diameters. The 3-D mode of the FF is irregular both temporally and spatially. Variations of ${\textit {Re}}_{cr-1}$ with $g^*$ , the characteristics and the physical mechanisms of each 3-D mode are discussed in this study.

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Hydrodynamic damping of an oscillating cylinder at small Keulegan–Carpenter numbers

Abstract: Abstract

Cited by 10 publications

References 32 publications

OC6 Phase Ia: CFD Simulations of the Free-Decay Motion of the DeepCwind Semisubmersible

OC6 Phase Ia: CFD Simulations of the Free-Decay Motion of the DeepCwind Semisubmersible

Bistabilities in two parallel Kármán wakes

Three-dimensional wake transitions of steady flow past two side-by-side cylinders

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