KC Number Research Articles

Threshold of Keulegan–Carpenter instability within a 6 × 6 rod bundle

The literature is rich in fluid–structure interaction studies of a single rod in oscillating fluid (or the reciprocate), however, there is a dearth of experimental data for rod bundle oscillation, particularly if the bundle is in a confined environment. The presence of the fluid surrounding the moving solid is modeled with force coefficients such as inertial and drag. In case of small amplitudes oscillating flow, these force coefficients depend non-linearly on the Keulegan–Carpenter number KC. The dependence present different regimes, separated by threshold KC numbers. At different regimes correspond different fluid dynamics, hence different force coefficients. The aim of this paper is to experimentally investigate the fluid dynamic for a rod bundle oscillating in a stagnant fluid. The velocity fields have been measured with Particle Image Velocimetry (PIV). Both the rod bundle and the fluid have the same refractive index, which allow to measure the velocity fields within the rod bundle in an non intrusive manner. The bundle is hosted in a double tank, immersed in a refractive index matched solution and placed on an earthquake shake table. The shake table sets the bundle into motion along a single direction.Data enable the identification of a threshold effect in the fluid response to the oscillating assembly. This threshold effect is due to the formation of vortexes in the fluid. Data show a clear trend on how the development of turbulence occurs firstly inside the rod assembly and then in the bypass between the assembly and the tank wall. The experimental results indicate the presence of a viscous boundary layer developed along the rod, above the threshold KC. The results presented in this paper represent a step forward the comprehension of the damping effect induced by the fluid at different oscillating amplitudes and frequencies, due to different KC regimes.

Optimization Analysis of the Arrangement of the Submerged Floating Tunnel Subjected to Waves

The motion responses, mooring tensions, and submergence depth are the dominant factors for the arrangement of the Submerged Floating Tunnel (SFT) subjected to waves. Generally, the maximum values of motion responses, mooring tensions, and absolute submergence depth are mainly focused on. In the present study, experiments are implemented to measure the motion responses and mooring tensions of the SFT with different mooring patterns and submergence depths under waves with different characteristic wave heights and periods. In order to evaluate the arrangement of the SFT more effectively and comprehensively, besides the maximum values, several new characteristic parameters are introduced. Such parameters account for the motion responses in the frequency domain, the uniformity of the tension distribution, the length of time during which the cable reaches a relaxed condition during wave action, the KC number, the dimensionless period, the wave height, and the submergence depth. The results from the optimization analysis show the following: according to the characteristic values of motion responses and mooring tensions, the pattern of diagonal cables is better than that of diagonal cables + vertical cables; and within the range of the present experiments, there are optimal dimensionless parameters—the dimensionless submergence depth d0/LP ≥ 0.15, the KC number ≤ 0.8, or the dimensionless wave height Hs/d0 ≤ 0.10—for the condition of which the dynamic responses and mooring tensions vary slightly.

Tensioned flexible riser vibrations under wave excitation, an investigation on the scale effect

In order to study the scale effect in wave-structure interactions and the role that structure-related parameters (tension T or bending stiffness EI) plays, riser model tests under regular waves were conducted using the model with multiple geometric scales (1:15, 1:12 and 1:9) in a wave basin. The riser model used is a novel structural design combing the outer polyvinyl chloride pipe with the core steel rod which could be simplified as a cantilever beam. Different initial tension T acting on the riser are tested by adjusting the slotted weight. The results show that the amplitude varies in a cubic fashion with the distance from the fixed end. In addition, the influence of the wave period and top tension T on the amplitude are investigated, which ultimately leads to a dimensionless number π1 = KCd·TL2/EI where KC is the classical Keulegan–Carpenter number (KC), EI shows the bending stiffness of the riser model and L gives the pipe length. With the KC number revised to take the distance from the fixed end into the calculation, this parameter provides a good measure in estimating the amplitudes of the riser vibrations induced by the waves.

Hydrodynamic characteristics of coral nursery buoyancy system and prediction using machine learning methods under wave action

The buoyancy system is a critical structure that ensures the safety and stability of the floating coral nursery and reduces the rate of coral shedding. Firstly, experiments in a wave tank were conducted on the motion response characteristics of the buoyancy system with four different structural types and submerged states, using the buoyancy system as the experiment object. The experimental results showed that the submerged state of the floating sphere was an essential element in affecting the hydrodynamic characteristics of the buoyancy system. The variation trends of the maximum oscillating tension of mooring cable with increase in period, and of the floating sphere motion amplitude with increase in Kc number under different submerged states were significantly different. Subject to experiment conditions, it was hard to judge the change tendency of the floating sphere motion amplitude under the large Kc number. Machine learning models trained through experiment data samples can quickly and accurately predict physical phenomena over a broader parameter range. Secondly, the prediction results of various machine learning models were compared and analyzed. Then the traditional machine learning model was optimized based on the particle swarm algorithm, which can improve the accuracy by about 20%. Finally, the optimal PSO-RBF model was employed to predict the floating sphere motion amplitude under the large Kc number. The predicted results showed that Kc = 6 was the demarcation point where the motion amplitude of the floating sphere varies with the Kc number. In addition, the fully submerged single floating sphere of buoyancy system is the best choice for floating coral nurseries under the four experiment cases in this paper, which can effectively reduce the damage of extreme waves with large wave heights and periods to floating coral nurseries.

Scour around twin-piles under combined wave–current flows

The paper presents three dimensional simulations of scour around a pair of piles arranged side-by-side configurations under combined wave–current flow conditions using a computational fluid dynamics model. The Reynolds-averaged Navier–Stokes (RANS) equation is solved using the k-ω turbulence model in the present work. The Exner equation is used to measure the variations in bed elevation. The level-Set approach is used to capture the free surface realistically. The numerical model couples the hydrodynamic module with the morphological module to simulate the scour process. For accurate erosion and deposition calculations in the sediment bed, the morphological model employs a modified bed shear stress formula on a sloping bed in combination with a sand slide algorithm. In the present study, the simulations have been done in a truncated numerical wave tank with the Dirichlet boundary condition and active wave absorption method. The numerical model is validated with the experimental results of combined wave–current hydrodynamics and scour around a pair of piles. The validated numerical model is utilized to study the effect of the gap ratio and the effect of KC number in the various combined wave–current environment. In low KC conditions, normalized scour depth increments owing to waves alone, weak currents, and moderate currents are less, whereas the scour depth increases dramatically for waves with high currents. It is also found that the gap flow between the piles increases the depth of scour in a significant manner. For a given pile gap ratio, the scour depth is dependent on the KC number, which implies the larger the KC number, the larger scour depth. For a given KC number, the scour hole stretch in the flow direction reduces as the gap ratio increases, whereas the perpendicular stretch increases. It is also observed that the normalized scour depth decreases as the gap ratio increases for a fixed KC number and fixed Ucw. It is evident from the present research that the normalized scour depth increases with increase in KC number for a fixed wave–current parameter (Ucw).

Impacts of wave-induced seabed response on local scour around a pipeline: PORO–FSSI–SCOUR–FOAM

The problem of local scour around a submarine pipeline is vital for oil and gas projects. Conventional scour models around pipeline practically include the flow and sediment transport characteristics, but they ignore the interactions between flow and seabed soil in the scouring process. In this study, a new two-dimensional model for simulating the scouring process is established while considering the impact of the wave-induced soil response and the associated seepage. With the present model, the influence of seepage and soil response on the modified Shields number, repose angle and prediction of the local scour depth and profile are examined. The numerical results indicate that the influence of repose angle when modified by seepage in the whole scour process is small. Meanwhile, the wave-induced dynamic soil response promotes the development of the scour profile and eventually increases the maximum scour depth to some extent, regardless of the change in the soil characteristics. However, at smaller KC numbers, the variations in the maximum scour depth with seabed properties become more significant.

Research on the Vortex-induced Vibration of A Cylinder Under Oscillatory Flow

Riser system is an indispensable structure connecting offshore platform and submarine wellhead, which is very common in offshore engineering. When the fluid flows through the riser system, the vortex falls off on both sides of the riser and stimulates the riser vibration, resulting in the fatigue damage of the riser. The vortex-induced vibration under oscillating flow is analyzed in this paper. The results show that the vortex-induced vibration of cylindrical structures in oscillating flow is more regular when the reduced velocity is low. The oscillating flow causes multi-mode vibration of the cylindrical structure, and the locking interval increases with the increase of KC number. The shed vortices will pass through the cylinder again after changing the flow direction, changing the fluid force on the cylinder structure.

Experimental and numerical study of the hydrodynamics of a flapping fin at zero speed

The flapping fins can be used as effective actuators of roll stabilizers at zero speed. They provide anti-roll torques to reduce the roll motion of ships in waves. The effects of roll amplitude, flapping frequency and aspect ratio on the hydrodynamic forces and moments at zero speed have been studied through experiments and numerical simulations. It is found that the forces and moments can be described using the added mass forces and damping forces respectively. Empirical formulas to calculate the forces and moments have been derived. The flapping frequency has no significant effects on the force coefficients and moment coefficients. The drag coefficients can be described by an exponential function of KC number, the added mass coefficients are the function of roll amplitude and aspect ratio due to the 3D flow separation.

Flow regime identification and flow instability analysis of oscillatory flows over twin circular cylinders

Oscillatory flows past two identical circular cylinders are investigated by two-dimensional direct numerical simulations in the parameter space of gap ratio (0.5 ≤ G ≤ 4.0), angle of flow incidence (0° ≤ α ≤ 90°) and Keulegan–Carpenter number (4 ≤ KC ≤ 12) with a constant Reynolds number Re = 150, where G = L/D, KC = UmT/D and Re = UmD/υ with D being the dimeter of the identical cylinders, L the shortest surface-to-surface distance between the two cylinders, Um and T being the velocity amplitude and period of the sinusoidal oscillatory flow, respectively, and α is defined as the angle between the flow direction to the line connecting the centers of the two cylinders. Comparing with the tandem or side-by-side arrangements of twin circular cylinders in oscillatory flows, the staggered twin cylinders (0° < α < 90°) involve more diverse flow regimes, including the periodic, quasi-periodic and chaotic flow states, due to the inherent asymmetric flow interference around the cylinder pair. In addition to introducing four flow regimes for the tandem and side-by-side arrangements, this study newly identifies 11 flow regimes for the staggered twin cylinders. The newly reported flow regimes in this work are collaboratively identified through the flow visualizations, steady streaming, frequency spectra of fluid forces and Lissajous phase diagrams, as well as the temporal-spatial symmetry features of the wake flows. Connecting with the previous work by Zhao and Cheng [“Two-dimensional numerical study of vortex shedding regimes of oscillatory flow past two circular cylinders in side-by-side and tandem arrangements at low Reynolds numbers,” J. Fluid Mech. 751, 1–37 (2014)], this study presents overall regime maps in the KC-α plane for varied gap ratios. It is found that the flow regimes previously and presently identified for the tandem and side-by-side arrangements may also appear for the staggered twin cylinders. The present numerical results suggest the sensitive dependence of the flow regimes on the parameters of KC, α, and G. It is also found that a specific flow regime with narrow parameter bands may appear within another flow regime, forming the abnormal regime hole in the regime map. To understand the profound influence of the control parameters on the flow regime transition, and the relevant temporal-spatial symmetry breaking, the linear Floquet stability analysis is conducted in this work. It was confirmed that the variation of the KC number may result in the Ky symmetry breaking over several periodic flow regimes, while the change of the angle of flow incidence may account for the H2 symmetry covering various periodic and quasi-periodic flow regimes. The stability analysis also explains the temporal flow transition and the abnormal occurrence of the regime holes within either quasi-periodic or chaotic flow regimes.

A viscosity equivalent reduced-order method and its application to ship roll prediction

The prediction of ship roll response in waves is still a major issue. The widely used potential flow theory can provide the results in a short time. However, its accuracy is highly dependent on the correction of fluid-viscosity. Viscous-flow theory can simulate the fluid viscosity directly, but it is accompanied by high computational costs. This study proposes a viscosity equivalent reduced-order method (VEROM) for predicting ship roll motion to achieve a balance between computational efficiency and prediction accuracy. To shorten the simulation time, the method neglects the fluid viscosity, solves the Euler equation, and uses large-size compatible meshes. To improve the prediction accuracy, the viscous effect is corrected in the time domain based on the principle of viscosity equivalence. A new type of forced roll motion with gradually increasing roll amplitude was introduced to obtain the nonlinear roll damping property for different KC numbers. The effectiveness of the VEROM model was examined by comparing the predicted roll responses with the experimental measurements. It was found that the maximum prediction error was less than 11%. Concerning the simulation time, the VEROM model is 20 times faster than the traditional viscous-flow model. The reduce-order method is effective for the seakeeping performance assessment.

Experimental investigation on the hydrodynamic effects of heave plates used in floating offshore wind turbines

Due to the abundant wind energy in deep water, floating offshore wind turbines (FWTs), especially for the semisubmersible FWTs, have attracted more attention these years. To reduce the heave motion of FWTs, heave plates are often attached at the bottom of the column. In this paper, experimental investigations of the hydrodynamic performance of the heave plates via the forced oscillation method are conducted. The impacts of the KC number (KC = 0.1–1.1), oscillation frequency (f = 0.4–1.43 Hz), diameter ratio-Dd/Dc (Dd and Dc are the diameter of the heave plate and column), thickness ratio-td/Dd (td is the thickness of the heave plate), shapes of the heave plates, on the added mass, and damping coefficients are investigated. The results show that the added mass and damping coefficients are independent of oscillation frequencies, while the KC number influences significantly the hydrodynamic coefficients. Increase in the diameter ratios will decrease the added mass and damping coefficients. The thinner heave plates obtain larger damping coefficients. Comparison between the different shapes of the heave plates shows that the octagonal heave plate displays similar added mass and damping coefficients to the circular heave plate. However, square one obtains lower added mass coefficients compared to the other three shapes. And the hexagonal plate seems to have the highest damping force for different KC numbers.

Experimental study of flow field and sediment suspension in the gap area of tandem piles under oscillatory flows

This study experimentally investigates the local scour mechanism around tandem piles in oscillatory flows with emphasis on the flow characteristics and sediment suspension during the scouring process. The instantaneous flow field is measured by the particle image velocimetry (PIV) technology meanwhile the sediment transport is measured by an image processing method. A preprocessing technique for the same PIV particle image is employed to identify the water particle and sediment particle, thereby realizing the simultaneous measurement of flow field and sediment movement. It shows that with the temporal development of scour, the scour profiles tend to be symmetrical, and the equilibrium scour depth is expected increased with the increase of KC number. Suspended sediment is observed significant in the gap area of the piles with large magnitude of suspended sediment concentration, which contributes most to the bed scour. From the instantaneous flow field, a noticeable upward flow is occurred in the gap area, which is identified as the primary driving force lifting the sediment. From the time-averaged flow field, a vortex is formed, inducing a strong rising flow with high velocity magnitude below it, which is responsible for the suspension of sediment. It is found that there exists a linear correlation between flow velocity and sediment motion velocity.

Experimental study on dynamic responses of a tensioned flexible vertical cylinder under waves and combined current and waves

The two degree-of-freedom (2DOF) dynamic responses of a flexible vertical cylinder under waves only and combined current and waves in a finite water depth were experimentally studied. The cylinder has multi-frequency response in both in-line (IL) and crossflow (CF) directions under waves. The response frequencies in the IL direction are multiples of wave frequency. The CF response frequencies include the multiples of wave frequency and the natural frequency of the cylinder, indicating that the CF response is controlled by both the wave actions and the vortex shedding. When the natural frequency of the cylinder is a multiple of the wave frequency, the CF vibration has the largest amplitude. A top tension can suppress the CF response more than the IL response amplitude, and the suppression effect increases with the increase of the top tension. With the decrease of the water depth, the response amplitudes in both directions decrease. Under combined current and waves, the IL response amplitude increases with the increase of KC number and the primary frequency of IL response is still the wave frequency. For a current velocity where VIV occurs, the superimposition of waves on current reduces the CF response amplitude because the vortex shedding frequency moves away from the natural frequency. The multi-frequencies of CF response are related to both the natural frequency of the cylinder and the wave frequency. The trajectories of the cylinder are mainly dependent on the ratio of the natural frequency to the wave frequency under waves or combined current and waves. There can be 2–6 cycles in the CF direction for each IL cycle with different wave frequencies and the top tension.

Characteristics of Local Scour Around the Double Pile in Waves

Scour in a flow field affected by waves, such as river estuaries or shallow waters, is more difficult to predict than scour in a currents. The main issue in predicting the scour around circular files, such as undersea bridges, is the maximum scour depth and the point of occurrence. In the case of two or more adjacent circular piles, the location and depth of maximum scour according to the spacing between piles and the arrangement method show a lot of difference compared to the case of a single pile. In this paper, the KC number are calculated as dimensionless variables representing the strength of the flow. And the correlation between pile gap size and relative scour depth was analyzed.

Surge slow drift viscous drag damping of an advanced spar: A numerical–experimental method for variable damping rates

In order to economically, efficiently and reliably deploy offshore moored structures, the calculation of slow drift motions is crucial. Although there has been a great deal of research into this topic in recent years, the predicted accuracy of simulations is still poor. In parallel, the deployments of novel structures such as floating wind turbines on a diverse range of platform types and designs is increasing rapidly, necessitating the greater understanding of these motions.The viscous damping effects are crucial to the slow drift motion predictions, but are also one of the most difficult parameters in a model to quantify. In this work, a novel experimental numerical method for calculating nonconstant drag coefficients is introduced and applied to a moored advanced spar. The method involving a combined potential flow and Morison’s equation model is used to calculate the drag coefficients and added mass from decay tests in still water, monochromatic sinusoidal waves and in current flows. An inverse KC number drag coefficient relationship was observed for both still water and wave cases. With increasing current flow velocity the KC number drag coefficient tendency decays to a constant value equal to the steady state drag coefficient. A similar inverse KC number drag coefficient relationship is shown from the full scale Fukushima FORWARD’s floating substation. Discussions on the flow behaviour and recommendations on simulation techniques are given.

Peak force coefficients on small-diameter spanning pipelines under waves

This paper reports an experimental investigation undertaken to measure the peak force coefficients for small-diameter pipelines (cables and umbilicals) spanning over rocky, uneven seabed under regular wave conditions. The free spans formed by the uneven bed are investigated by modelling multiple regularly spaced free spans (referred to as multi-span) in a flume. Approximately 600 physical tests were conducted to quantify the effects of gap height to pipeline diameter ratio G and the span length to pipeline diameter ratio S on the peak force coefficients. The Keulegan–Carpenter number KC and Reynolds number Re p tested were in the range 20 ≤ KC ≤ 2000 and 5 × 10 3 ≤ Re p ≤ 10 5 , respectively. The ratios between the peak force coefficients for the multi-span configuration and a uniform-span configuration ( S → ∞) are demonstrated to be a function of S /[( S + C ) G ], where C is the contact ratio, defined as the distance between two adjacent free spans divided by the pipeline diameter. Combined with the peak force coefficients under uniform-span conditions obtained from the present experiments, this finding enables the peak force coefficients under a multi-span condition to be reasonably estimated. • Peak force coefficients for fully spanning small-diameter pipelines subject to waves are provided based on a number of physical tests with KC up to 2000. • Quantification method for the peak force coefficients under the effect of multiple free spans is proposed. • The scattered seabed roughness and the multiple free spans lead to significant reductions in the peak force coefficients.

Numerical study of scour below vibrating pipelines under waves and currents

Local scour of the seabed near a submarine pipeline is a major factor in pipeline damage and failure. Previous studies on local scour of submarine pipelines mainly focused on fluid flow and sediment transport, ignoring the influence of vibration on the local scour process. In this study, a two-dimensional scour model based on the time-averaged N–S equation was established to analyze the local scour and vortex-induced vibration of the pipeline. The clear-water and live-bed scours beneath submerged horizontal pipelines are presented under current-wave coupling conditions. The study shows that when the submarine pipeline is partially suspended, the vibration of the submarine pipeline is gradually intensified under the action of waves and currents and then affects the scour process near the pipeline, especially for KC numbers larger than 0.8. In addition, thresholds of embedment depth e/D = 0.4 and relative water depth h/D = 6.7 were found, that is, the influence of bed and free surface on the scouring process are greatly reduced once these thresholds are met.

Experimental investigation on vortex-induced force of a flexible pipe under oscillatory flow

In this paper, vortex-induced force (VIF) characteristics of a flexible pipe under oscillatory flow are experimentally investigated with different KC numbers ranging from 10 to 178, and reduced velocities from 4 to 7.9. The strain information caused by vortex-induced vibration (VIV) at different cross-sections on the flexible cylinder is measured in the model test. Combined with the modal superposition method and inverse analysis method for hydrodynamic force, the hydrodynamic forces on the flexible cylinder are inverted, including the excitation force in phase with velocity and added mass force in phase with acceleration. Then, through a least square method with forgetting factors, the excitation coefficients and added mass coefficients at each time step are identified. The results show that the VIV excitation coefficient of a flexible pipe under oscillatory flow has a significant “acceleration and deceleration” effect, that is, the excitation coefficients are mostly positive at the acceleration section of the oscillatory flow and negative at the deceleration section. This “acceleration and deceleration” effect also explains the response amplitude modulation feature of VIV under oscillatory flow. And this effect can be represented by the dimensionless acceleration parameter γ of the flow field, and the range of γ corresponding to the positive excitation coefficient is affected by the KC number and the maximum reduced velocity. In addition, the added mass coefficients present different time-varying features under oscillatory flow with different maximum reduced velocity. When the maximum reduced velocity is larger than 6.5, the time-varying trend of the added mass coefficient is opposite to that of the flow velocity. While when the maximum reduced velocity is smaller than 6.5, the added mass coefficient is maintained around 2.0 in VIV excitation region; and it is around 1.0 in the non-excited region which is close to the added mass coefficient of a cylinder in still water.

Local scour characteristics of monopile foundation and scour protection of cement-improved soil in marine environment - Laboratory and site investigation

Monopile foundations are the most common foundation type for offshore wind turbines. Local scour and scour protection around piles in the marine environment are major concerns for the engineering community. Physical simulations of local scour around monopiles without scour protection and edge scour around monopiles with cement-improved soil protection under the combined action of wave and current were performed using a flume. The effects of Ucw, the KC number and (θ/θcr)0.5 on the local scour were investigated. The empirical expressions of the relative scour depth S/D based on the average-velocity based Froude number (Fra) and modified Ursell number Urp’ under the combined wave and current conditions were proposed. Moreover, the scour protection performance of cement-improved soil was revealed, and the optimal protection range was 7D and 5D for small- and large-diameter piles, respectively. The effects of the ratio of protection range to pile diameter (Ds/D) and aspect ratio Ar on edge scour were investigated. Finally, the feasibility and effectiveness of the new scour protection method for cement-improved soil were verified by site testing.

Functional kupffer cells migrate to the liver from the intraperitoneal cavity

We established a method of KC transplantation by intraperitoneal (i.p.) injection using EGFP-expressing cells (EGFP-KCs) and normal KCs. The novel method is easier and less invasive than conventional methods so that it is not only technically advantageous but also ethically preferable for experiments using animals. We demonstrated that KCs migrated to the liver following i.p. Injection. Engraftment in the liver was not observed for peritoneal macrophages (pMPs). This suggests that KCs migrate to the liver via a sorting mechanism. KC injection decreased the KC number at 24 h and then recovered the KCs at 10 days to a normal level. Additionally, recovery to the normal level by KC injection was observed in mice with KC depletion induced by GdCl3. These results suggest that a regulatory mechanism exists for controlling the number of KCs.