Low Keulegan-Carpenter Numbers Research Articles

Non-Equilibrium Scour Evolution around an Emerged Structure Exposed to a Transient Wave

The present study evaluates the performance of two numerical approaches in estimating non-equilibrium scour patterns around a non-slender square structure subjected to a transient wave, by comparing numerical findings with experimental data. This study also investigates the impact of the structure’s positioning on bed evolution, analyzing configurations where the structure is either attached to the sidewall or positioned at the centerline of the wave flume. The first numerical method treats sediment particles as a distinct continuum phase, directly solving the continuity and momentum equations for both sediment and fluid phases. The second method estimates sediment transport using the quadratic law of bottom shear stress, yielding robust predictions of bed evolution through meticulous calibration and validation. The findings reveal that both methods underestimate vortex-induced near-bed vertical velocities. Deposits formed along vortex trajectories are overestimated by the first method, while the second method satisfactorily predicts the bed evolution beneath these paths. Scour holes caused by wave impingement tend to backfill as the flow intensity diminishes. The second method cannot sufficiently capture this backfilling, whereas the first method adequately reflects the phenomenon. Overall, this study highlights significant variations in the predictive capabilities of both methods in regard to the evolution of non-equilibrium scour at low Keulegan–Carpenter numbers.

Suppression of vortex shedding in the wake of a circular cylinder through high-frequency in-line oscillation

This paper presents a new flow control approach to suppress the vortex shedding in the wake of a circular cylinder through high-frequency oscillation. The circular cylinder is forced to oscillate in the streamwise direction at high-frequency and low amplitude, corresponding to a high Stokes number (β = 100–1000) and low Keulegan–Carpenter number (KC = 0.001–4). Two-dimensional (2-D) and three-dimensional (3-D) direct numerical simulations of an oscillating circular cylinder in steady current have been carried out in the parameter space of KC, Rec, and β. Our numerical results show that when the flow remains in the two-dimensional vortex shedding regime, the cylinder wake sequentially experiences transitions from the vortex shedding regime to the suppression of the vortex shedding regime and finally to the symmetry breaking regime, with increasing KC. Corresponding wake characteristics and variations of hydrodynamic forces over the three wake regimes are explored. Three quantities that represent shear-layer characteristics, including the length of separating shear layers, the circulation of shear layers and wake recirculation length, reach maxima at the onset of suppression. The physical mechanisms for the suppression of vortex shedding and occurrence of symmetry breaking are also explained. Once the flow becomes 3-D, vortex shedding from the cylinder cannot be suppressed, primarily because the outer shear layers induced by the steady approaching flow are enhanced in 3-D flows. The cylinder oscillation over the frequency range investigated in the present study delays wake transition to 3-D. The cylinder oscillation alters the 3-D vortical structure and its spanwise wavelength significantly.

Experimental and numerical investigations of solitary wave-induced non-equilibrium scour around structure of square cross-section on sandy berm

A series of laboratory experiments and high-fidelity numerical simulations were carried out to investigate the scour induced by a solitary wave around a non-slender, vertical structure of a square cross-section on a sandy berm. Various wave and water level combinations, structure layouts, and dimensions were studied. The flow separation at the sharp edges resulted in counterclockwise rotating out-of-plane vortices that extended from the free surface to the sandy berm. These energetic vortices were found to be the primary driving mechanism of the scouring through entraining, and entrapping the sand particles into their cores, keeping them in suspension, carrying them, and releasing them as the vortices propagate along a spiral trajectory. The analyses also showed that the flow blockage by the structure could result in flow field modulation and exacerbate the scour processes. The structure dimension appeared to be the most influential factor in the scouring process, drastically altering the characteristics of the non-equilibrium scour holes. Irrespective of the structure dimension or layout, the scour depth was greater around the seaside edge of the structure while the scour width was larger on the leeside edge. The uncertainties associated with the maximum non-equilibrium scour depth were quantified via Monte Carlo simulations which showed that the impact of the structure dimension on the maximum scour depth was almost twice more significant than that of the layout. The three-dimensional (3D) Eulerian two-phase flow numerical model, SedWaveFoam, was shown to be able to simulate sediment transport and scour around sharp-edged square structure at a low Keulegan-Carpenter ( K C ) number. • Interactions between a solitary wave and an impermeable structure placed on an erodible berm were studied experimentally. • Energetic vortices, formed at the corners of the structure, were found to be the primary driving mechanism of the scouring. • Structure dimension was the most influential factor in the scouring process. • Monte Carlo simulation was employed to assess the sensitivity of the maximum non-equilibrium scour depth to flow conditions. • SedWaveFoam model simulated scour around sharp-edged square structure at low Keulegan-Carpenter (KC) number.

Numerical and experimental modelling of wave interaction with fixed and floating porous cylinders

We consider wave forces on fixed porous cylinders with and without a solid inner cylinder and wave-induced motions of floating cylinder with and without a porous outer cylinder. Comparisons between experimental measurements and numerical predictions from an iterative boundary element method (BEM) model are presented. The BEM model assumes that pressure drop across porous surface is proportional to the square of the velocity through the surface. It is shown that the BEM model is able to accurately predict the nonlinear variation of the forces with wave amplitude or motion amplitude. It is demonstrated that adding a porous outer cylinder to a solid vertical cylinder leads to increased excitation force on the combined structure. For floating cylinders adding a porous outer cylinder also leads to a corresponding increase in excitation force. However, the porous outer cylinder provides a larger increase in the damping, resulting in reduced motion response. Further numerical simulations indicate that placing the porous cylinder lower in the water column can lead to increased damping without the corresponding increase in excitation forces. It is shown that for low Keulegan Carpenter numbers, the damping coefficient for a porous cylinder is significantly higher than the viscous damping on a solid cylinder. The results suggest that porous materials could be beneficial for motion damping of floating structures.

Three-dimensional Computational Fluid Dynamics modelling of scour around a single pile due to combined action of the waves and current using Level-Set method

This paper presents three dimensional (3D) numerical modeling of local scour around a single pile under the combined action of waves and currents. A semi-coupled hydrodynamic and morphological model (REEF3D) is used in this study which solves the Reynolds-averaged Navier–Stokes (RANS) equation with k-ω turbulence model closure. The Exner equation is used to calculate the changes in bed elevation. The use of the Level-Set method is done to capture the changes in the free surface. Realistic scour and deposition calculations are aided with the use of modified critical bed shear stress reduction formulation on a sloping bed supplemented with the use of Sand Slide algorithm in the morphological model. The scouring process is modeled in this study using a reduced-length numerical wave tank with wave generation and wave absorption implemented using active wave absorption method. The model is validated for the numerical modeling of local scour around a single pile in steady current, waves alone, and combined wave–current environment. The validated model is used to analyze the effect of Keulegan–Carpenter (KC) number and combined wave–current parameter (Ucw) on normalized equilibrium scour depth. It is found that the normalized equilibrium scour depth for scour under waves alone, waves combined with weak currents, and waves combined with mild current do not significantly differ for flow developed in a low KC number environment. However for waves combined with strong currents the normalized equilibrium scour depth increases significantly. For large KC numbers, the normalized equilibrium scour depth is found to have increased with an increase in KC number as well as combined wave–current parameter (Ucw).

Determination of Force Coefficients for a Submerged Rigid Breakwater under the Action of Solitary Waves

We present an analysis related to the evaluation of Morison and transverse force coefficients in the case of a submerged square barrier subject to the action of solitary waves. To this purpose, two-dimensional experimental research was undertaken in the wave flume of the University of Calabria, in which a rigid square barrier was provided by a discrete battery of pressure sensors to determine the horizontal and vertical hydrodynamic forces. A total set of 18 laboratory tests was carried out by varying the motion law of a piston-type paddle. Owing to the low Keulegan–Carpenter numbers of the tests, the force regime of the physical tests was defined by the dominance of the inertia loads in the horizontal direction and of the lift loads in the vertical one. Through the use of the time series of wave forces and the undisturbed kinematics, drag, horizontal inertia, lift, and vertical inertia coefficients in the Morison and transverse semi-empirical schemes were calculated using time-domain approaches, adopting the WLS1 method for the minimization of the difference between the maximum forces and the linked phase shifts by comparing laboratory and calculated wave loads. Practical equations to calculate these coefficients as a function of the wave non-linearity were introduced. The obtained results highlighted the prevalence of the horizontal forces in comparison with the vertical ones which, however, prove to be fundamental for stability purposes of the barrier. An overall good agreement between the experimental forces and those calculated by the calibrated semi-empirical schemes was found, particularly for the positive horizontal and vertical loads. The analysis of the hydrodynamic coefficients showed a decreasing trend for the drag, horizontal inertia, and lift coefficients as a function of the wave non-linearity, while the vertical inertia coefficient underlined an initial increasing trend and a successive slight decreasing trend.

Large Scale Experimental Study of the Scour Protection Damage Around a Monopile Foundation Under Combined Wave and Current Conditions

This paper presents a series of large-scale wave flume experiments on the scour protection damage around a monopile under combined waves and current conditions with model scales of 1:16.67 and 1:8.33. The main objective is to compare the damage data obtained from these large-scale models with existing monopile scour protection design approaches, which were proposed based on small scale wave flume experiments, and to study the applicability of the existing approaches. The static stability (onset of motion and bed shear stress) and the dynamic stability (three-dimensional damage numbers) of the scour protection are investigated. Both results show that the existing design approaches can be conservative when applied to large scale models, which highlights the need of further investigations on scale and model effects. In addition, this paper also analyses the scour protection damage depth. It is observed that damage depths of the scour protection layer under low Keulegan–Carpenter number (KC) conditions are smaller than predictions. The study provides valuable large scale experimental data for future research on the monopile scour protection design.

Vortex elongation in outer streaming flows

We study the secondary time-averaged flow (streaming) generated by an oscillating cylinder immersed within a fluid, under high amplitude forcing so that inertial effects are significant. This streaming is decomposed into a viscous boundary layer flow where vorticity is created, and an outer flow of larger size. We operate under conditions of relatively low viscosity, so that the boundary layer is smaller than the object diameter. While for low Keulegan-Carpenter (KC) number (small enough amplitude), the size of the outer flow is typically that of the object, here we show that at large enough forcing, the outer flow stretches along the direction of the vibration by up to 8 times, while the flow still keeps its axial symmetry. We quantify the elongation through PIV measurements under an unprecedented range of frequency and amplitude, so that the streaming Reynolds number reaches values much larger than unity. The absence of significant unsteady component of vorticity outside the viscous boundary layer - and the fact that the length of elongation scales well with the streaming Reynolds number - suggest that the stretching should be due to the convection of stationary vorticity by the streaming flow itself.

On the wavy flow past a weakly submerged horizontal circular cylinder at low Keulegan–Carpenter numbers

The interaction of regular waves with a weakly submerged horizontal circular cylinder at Keulegan–Carpenter KC numbers up to 2.5 is studied by means of numerical simulations, solving the two-phase flow Navier–Stokes equations with the Finite Volume method and the Volume of Fluid interface capturing method. Experimental data from laboratory tests conducted in the past by one of the authors are used as reference data. The study is focused on the surface wave transformation, on the flow field in the near region and on the loads on the cylinder. The interest is driven on the spectral content of the transmitted waves at higher order frequencies and on the non-linear features of the wave reflected by the cylinder. The flow field in the near-body region is analyzed in terms of vortex onset, development and detachment, and correlating pressure pulses with the vorticity field at the cylinder surface. Inviscid flow simulations are carried out too, to evince the origin of higher order terms either from the free surface or from the viscous terms in the momentum equations. The steady streaming around the cylinder is analyzed, including its variability along the cylinder surface and its relationship with the vortex cores generated at the body surface.

Large Eddy Simulation of Unidirectional and Wave Flows through Vegetation

AbstractMassively parallel large eddy simulation (LES) experiments were conducted to study the flow fields developed by unidirectional flow over submerged vegetation and wave flow-through emergent vegetation. For the submerged vegetation, vertical profiles of mean and turbulent horizontal and vertical velocities were found to be in good agreement with laboratory experiments. Canopy-averaged bulk drag coefficient calculated from the depth-integrated forces on the cylinders compares well with empirical measurements. For the emergent vegetation, wave-induced drag forces were calculated, and the inertia and pressure-drag coefficients were compared with laboratory experiments, which were found to be in good agreement. Vertical variation of forces and moments about the stem base are presented and compared with a single stem case under a variety of wave conditions and Keulegan-Carpenter (KC) numbers. It is seen that at low KC numbers the effect of the inertia force is significant. The vertical variation of the v...

Numerical simulations of 2-D steady and unsteady breaking waves

In this work we analyze by means of numerical simulations the features of breaking of two dimensional free surface waves induced by a body or a sloping bottom. The sample cases selected for the simulations characterize different aspects of wave breaking, thus they are supposed to represent rather widely a problem of large interest for ship hydrodynamics and ocean engineering applications. The simulations considered are: wave breaking induced by a fully submerged hydrofoil towed in calm water at constant speed; shallow water waves breaking on a sloping beach in spilling and plunging mode; regular intermediate depth waves breaking gently over a weakly submerged horizontal circular cylinder at a low Keulegan–Carpenter number. Each simulated case is supported by detailed comparisons with experimental data in time and frequency domain. The results presented have been obtained adopting a standard RANS approach. They show a generally good reproduction of the wave breaking characteristics even though it is rather clear that there is a case dependent potential loss of accuracy in the presence of pronounced foamy flow.

Evaluating wave forces on groups of three and nine cylinders using a 3D numerical wave tank

The evaluation of the complex wave regime due to wave interaction with a large group of cylinders placed in proximity requires an efficient and accurate numerical model. This paper presents the application of a two-phase Computational Fluid Dynamics (CFD) model to carry out a detailed investigation of wave forces and flow around vertical circular cylinders placed in groups of different configurations at low Keulegan-Carpenter (KC) numbers. The 3D numerical wave tank is validated by comparing the numerical results with experimental data. Further, the hydrodynamic effects associated with three cylinders placed in tandem, side by side and in a 3 × 3 square array of nine cylinders are investigated. Wave forces are seen to reduce along the row in a tandem array. In a side-by-side arrangement, the central cylinder experiences the highest force. A combination of these effects is seen in the 3 × 3 square array. The variation of the wave forces on the cylinders in the array for different center-to-center distances and incident wavelengths is evaluated and the results show that the wave forces are the highest on the cylinders when the center-to-center distance is slightly less than half the incident wavelength.

Combined action of uniform flow and oscillating flow around marine riser at low Keulegan-Carpenter number

With the increase of petroleum and gas production in deep ocean, marine risers of circular cylinder shape are widely used in the offshore oil and gas platform. In order to research the hydrodynamic performance of marine risers, the dynamic mesh technique and User-Defined Function (UDF) are used to simulate the circular cylinder motion. The motion of a transversely oscillating circular cylinder in combination of uniform flow and oscillating flow is simulated. The uniform flow and oscillating flow both are in x direction. SIMPLE algorithm is used to solve the Navier-Stokes equations. The User-Defined Function is used to control the cylinder transverse vibration and the inlet flow. The lift and drag coefficient changing with time and the map of vorticity isolines at different phase angle are obtained. Force time histories are shown for uniform flow at Reynolds number (Re) of 200 and for the combination of uniform and oscillating flows. With the increase of amplitude of oscillating flow in combined flow, the change of lift amplitude is not sensitive to the the change of cylinder oscillating frequency. Lift amplitude increases with the increase of oscillating flow amplitude in the combined flow, but there is no definite periodicity of the lift coefficient. The drag and inertia force coefficients change when the maximum velocity of the oscillating flow increases in the combined flow. The vortex shedding near the circular cylinder shows different characteristics.

Experimental study of the flow field induced by a resonating piezoelectric flapping wing

Flexible plate structures with integrated piezoelectric patches offer interesting possibilities when considered as actuation mechanisms for energy harvesting devices, cooling devices and propulsion devices of micro-aerial vehicles. Most of the studies reported in literature are based on the assumption of a 2D aerodynamic flow. However, the flow behind a finite span wing is significantly more complex than that of an infinite span wing. In order to corroborate this statement, the present experimental study contains high-speed particle image velocimetry measurements performed on a piezoelectric finite span wing oscillating in air, at 84.8 Hz. The paper focuses on the situation of low Keulegan–Carpenter numbers (KC < 3). The dimensionless KC number describes the relative importance of the drag forces over inertia forces for objects that oscillate in a fluid flow at rest. The evolution of the unsteady vortex structures near the plate is characterized for different conditions. This allows a better understanding of the unsteady aerodynamics of flapping flight. The accomplished experimental data analysis has shown that the flow phenomena are strongly dependent on the KC values.

An immersed boundary method with an approximate projection on nonstaggered grids to solve unsteady fluid flow with a submerged moving rigid object

An immersed boundary method is presented, which uses an approximate projection method on nonstaggered grids for computing flows with submerged and moving boundaries. The incompressible Navier–Stokes equations are discretized using a second-order accurate finite difference technique on a nonstaggered grid system, and the new immersed boundary method is proposed based on an approximate projection method with two pressure correction techniques, the Armfield method and the geometrical grid Reynolds modified method on nonstaggered grids. By using this method, the results obtained from (1) flow past a rigid cylinder in two dimensions with different Reynold numbers and (2) flow around an oscillatory circular cylinder in flow at low Keulegan–Carpenter numbers are in agreement with the reported experimental and numerical data, demonstrating that this convenient method of constraining the interface is a reliable and robust numerical approach for solving unsteady fluid flow with a submerged moving rigid object. This method has the advantage of using significantly less computation time and lower computation sources than the traditional immersed boundary methods.

Numerical study of flow around an oscillating diamond prism and circular cylinder at low Keulegan-Carpenter number

In order to identify the influence of shape corners on the instantaneous forces in the case of oscillating bodies, the simulated flow field is compared for two kinds of cross sections: diamond prism and circular cylinder. For these two flow configurations, the same Reynolds number and a Keulegan-Carpenter are considered. To compute the dynamic flow field surrounding the body, the Navier-Stokes transport equations in a non-inertial reference frame attached to the body are considered. Hence, a source term is added locally to the momentum equation to take into account the body acceleration. The proposed model is solved using the PHOENICS code. For the oscillating circular cylinder, the simulated results are in good agreement with the experimental data available in the litterature. After validation of this proposed model, flow field for diamond prism is determined. For both bodies, the process of the vortex formation is similar, with the formation of a recirculation zone in the near-wake containing a symmetric pair of vortices of equal strength and opposite rotation. The length of recirculation zone varies approximately linearly with time. However, the in-line force coefficient of the oscillating diamond prism is found to be greatest, since the recirculation zone is longer compared with that of the oscillating circular cylinder.

Physical model studies and system identification of hydrodynamics around a vertical square-section cylinder in irregular sea waves

In the present study, the results obtained from a series of experiments conducted in a wave flume were investigated to assess the hydrodynamic characteristics and pressure distribution around a vertical square-section cylinder in irregular waves. Experimental measurements were taken at moderately high Reynolds numbers and low Keulegan-Carpenter numbers with the cylinder at different rotation angles. The ARMAX (Auto Regressive Moving Average with exogenous input) parametric model was proposed as a numerical approach to model the variation of the hydrodynamic pressure on the cylinder over time based on the concept of system identification. The validation results demonstrated that the ARMAX model was able to simulate the signals of the wave pressure on the front side of the cylinder but failed for most of the points located after the separation points. The results obtained using the principal component approach and the concept of subspace angle implied that the efficiency of the proposed model depended on the onset of nonlinear behavior in the measured data. It was due to the non-linearity induced by the flow patterns after the separation points.

A numerical modeling of the vortex-induced vibration of cascade in turbomachinery using immersed boundary method

Based on the immersed boundary method, a fast simulation for solving unsteady, incompressible, viscous flow associated with the oscillating cascade is established on a quasi-three-dimensional coordinate system. The numerical method is applied to the simulation of the flow passing an oscillating circular cylinder which is forced to move in X direction under prescribed motions in water at rest at low Keulegan-Carpenter numbers. Then vortex-induced vibration of a cylinder with two degrees of freedom which oscillates in in-line direction and transverse direction is simulated using this method. The results are in good agreement with the previous research. Then the method is extended to the oscillating cascade simulation of making various comparisons. It is found that the IBPA (inter blade phase angle) will change as the time goes on, because of the non-uniformity of the flow in the circumferential direction, until the oscillating cascade goes to a stable situation. The reduced velocity and the number of blades are chosen to investigate the effects of them on IBPA. The results indicate that both the reduced velocity and the number of blades are the main factors which influence IBPA. It is worth noting that the coupling process is not necessary to generate any body-fitting grids, which makes it much faster in computational process for such a complicated fluid-structure interaction problem.

Three-dimensional vortex dynamics in oscillatory flow separation

The dynamics of coherent columnar vortices and their interactions in an oscillatory flow past an obstacle are examined experimentally. The main focus is on the low Keulegan–Carpenter number range (0.2 &lt; KC &lt; 2), where KC is the ratio between the fluid particle excursion during half an oscillation cycle and the obstacle size, and for moderate Reynolds numbers (700 &lt; Rev &lt; 7500). For this parameter range, a periodic unidirectional vortex pair ejection regime is observed, in which the direction of vortex propagation is set by the initial conditions of the oscillations. These vortex pairs provide a direct mechanism for the transfer of momentum and enstrophy to the outer region of rough oscillating boundary layers. Vortices are observed to be short-lived relative to the oscillation time scale, which limits their propagation distance from the boundary. The instability mechanisms leading to vortex decay are elucidated via flow visualizations and digital particle image velocimetry (DPIV). Dye visualizations reveal complex three-dimensional vortex interactions resulting in rapid vortex destruction. These visualizations suggest that one of the instabilities affecting the spanwise vortices is an elliptical instability of the strained vortex cores. This is supported by DPIV measurements which identify the spatial structure of the perturbations associated with the elliptical instability in the divergence field. We also identify regions in the periphery of the vortex cores which are unstable to the centrifugal instability. Vortex longevity is quantified via a vortex decay time scale, and the results indicate that vortex pair lifetimes are of the order of an oscillation period T.

Direct numerical simulation of oscillatory flow around a circular cylinder at low Keulegan–Carpenter number

The Honji instability is studied using direct numerical simulations of sinusoidal oscillatory flow around a circular cylinder. The three-dimensional Navier–Stokes equations are solved by a finite element method at a relatively small value of the Keulegan–Carpenter numberKC. The generation and subsequent development of Honji vortices are discussed over a range of frequency parameters by means of flow visualization. It is found that the spacing between Honji vortices is only weakly dependent on the frequency of oscillation, but is strongly correlated toKCbecause it is the terms within the governing equation containingKCthat dominate the three-dimensional features of the flow. An empirical relationship betweenKCand the spacing between neighbouring vortices is proposed. The three-dimensional steady streaming structure within the vortices is identified and it is found that at high frequencies the steady streaming is two-dimensional although the instantaneous flow structure is itself fully three-dimensional.