Hydrodynamic Force Coefficients Research Articles

Numerical analysis of an oscillating square and circular bluff body submerged in the wake of an identical static bluff body: A GPU Accelerated Immersed Boundary-Lattice Boltzmann Approach

Hydrodynamic forces acting on marine structures, tubes, and objects can trigger disruptive vibrations. This study is an effort to encapsulate the results of wake induced vibration among tandem bodies. Specifically, impact of a static upstream body on a downstream oscillating body at Reynolds number 100 and constant frequency ratio Fr=1.0. The effects of streamwise displacement are investigated in a tandem arrangement of 1.05≤Lx/D≤12.0. In this study an in-house developed code employed that combines an immersed boundary lattice Boltzmann method with a structural equation and is accelerated using a graphical processing unit. When comparing scenario 1 (both bodies oscillate) to scenario 2 (only the downstream body oscillates), the study finds that the upstream square body motion has little effect on the downstream square body oscillation. However, the upstream circular body motion significantly impacts the downstream body oscillation. In addition, the study observes that the maximum amplitude occurs after reaching the critical spacing in scenario 2, whereas it occurs at and after the critical spacing in scenario 1. The critical spacing ratio is similar in both scenarios but varies for square and circular bodies. Lastly, the study examines the flow physics and hydrodynamic force coefficients of the downstream oscillating body.

Forced surge motion of a floating bridge pontoon to evaluate the hydrodynamic damping properties

Dedicated model tests were carried out to investigate the hydrodynamic force coefficients in surge for a pontoon that is designed to support a floating bridge. The experiments were carried out by oscillating the pontoon at various Keulegan–Carpenter (KC) numbers and oscillation periods in forced motion. A pontoon designed for the floating bridge in Bjørnarfjorden, Norway, is investigated herein. Several numerical simulations are performed to supplement the experiments. The estimated damping coefficients in surge are of significant importance at the first horizontal resonant mode of the floating bridge, which may be excited due to swell sea in the fjord. The first horizontal resonant mode of the floating bridge is around 15–16 s. The model tests were conducted with and without turbulence triggers. A finding from the model tests were that turbulence triggers did not prove to be necessary to eliminate model scale effects in oscillatory flow.The KC-dependent added mass and damping coefficient in oscillatory flow is investigated. The added mass and damping coefficients are clearly KC-dependent. The wave radiation damping in surge is small at the tested oscillation periods, and the damping in surge is dominated by the damping due to flow separation.Numerical simulations using a hybrid potential flow-CFD solver with linear free-surface conditions, PVC3D, are carried out with both linear and nonlinear body-boundary conditions. The simulations with nonlinear body-boundary conditions predict the hydrodynamic force coefficients with reasonable accuracy, whilst the simulations with linear body-boundary conditions fail to predict the hydrodynamic coefficients with the desired accuracy — both used to investigate the viscous damping which arises due to flow separation along the pontoon body.

Numerical study flow-induced vibration of four two-degree-of-freedom circular cylinders in lozenge configuration using random vortex- boundary element scheme

Flow-induced vibration around industrial structures is a significant factor contributing to the mechanical degradation of these structures exposed to fluid flow. Numerical simulation of such flows is challenging with conventional simulation methods due to the displacement of the structural boundaries and the complexity of defining and satisfying boundary conditions. In this research, the development and combination of random vortex and boundary element methods have been employed to address the aforementioned challenges. Two-dimensional flow at Reynolds numbers of 100, 200, and 1000 around four two-degrees-of-freedom circular cylinders in two lozenge configurations with different diameter ratios (parallel and vertical diameter to the flow direction) has been simulated. In configuration 1, the diameter ratio is 1.5, the horizontal and vertical diameters are equal to 3 times and 2 times the cylinder diameter, respectively. In configuration 2, the diameter ratio is 1, and the diameter of the lozenge is equal to 4 times the cylinder diameter. The changes in hydrodynamic force coefficients, and streamlines are depicted for each scenario. The oscillation amplitude of the rear cylinders, which is affected by the vortex shedding from the front cylinders, increases. In certain instances, especially at higher Reynolds numbers like Reynolds 1000, increasing in oscillation amplitude may even result in collisions between the cylinders. For configuration 2, both the average drag coefficient and the range of variation for all four cylinders are greater than those for similar cylinders in configuration 1. The results indicate that an increase in the Reynolds number from 100 to 200 and 1000 results in approximately 1.4 and 11.5 times amplification in the oscillations of the drag coefficient, and the maximum value of lift coefficient increases nearly 2.2 and 80 times, respectively.

On the importance of angle-dependent hydrodynamic coefficients in the equilibrium configuration analysis of synthetic fiber towing ropes

The underwater configuration analysis of a towing rope is crucial for estimating the rope tension and the state of the towed body. In the case where the rope inclination angle significantly increases, the partial hydrodynamic force coefficients of a rope segment should display apparent variations with the local inclination angle. However, constant drag coefficients ignoring the angle-dependent drag effect are widely used in numerical studies. To address the importance of the angle-dependent force coefficients for analyzing the underwater configuration of a towing rope, Large Eddy Simulations are carried out to obtain the drag forces of a cylindrical rope segment with varying inclination angles and Reynolds numbers. To model the rope deformation, a tensile experiment is also conducted to establish the nonlinear tension-strain relationship of the fibre rope. Parametric studies are performed to investigate the difference in the results calculated by both constant and angle-dependent hydrodynamic force coefficients. It was found that the application of constant drag coefficients leads to significant underestimation of the rope tension near the towed body, especially when the rope experiences large inclination angles. Therefore, the present study highlights the importance of using the angle-dependent hydrodynamic coefficients to predict the configuration and tension of towing ropes.

Experimental study of surface roughness effects on hydrodynamic characteristics of a submerged floating tunnel

Marine biofouling is a major concern in the operational performance of submerged floating tunnels (SFTs). The objective of this research is to investigate the effects of marine fouling (represented by surface roughness) on the hydrodynamic behavior of SFTs, including the hydrodynamic forces on the SFT subject to current-only, wave-only, and combined current-wave flow conditions. The effects of increased surface roughness induced by marine fouling on the dynamic response of an SFT are characterized by hydrodynamic force coefficients, including drag and inertia coefficients. At the Water Lab of Delft University of Technology (TU Delft), experiments have been performed in a wave-current flume to compare the SFTs’ behaviors as affected by different roughness characteristics. In addition, a parametric cross-section for an SFT is presented, and the hydrodynamic performance associated with surface roughness effects on the parametric shape and circular SFT cross-section shape are compared. The results show that the parametric shape can effectively reduce the drag coefficient (Cd) under current-only conditions and lower the inertia coefficient (Cm) when waves are present. As roughness height and coverage ratio increase, Cd generally increases while Cm decreases. However, small differences in Cd and Cm can be observed with regard to roughness parameters for wave-only conditions. The Morison coefficients adapted for a marine-fouled SFT measured in the experiments are compared to predictions from engineering standards and are recommended for engineering practice.

Contribution of debris and substructures to hydrodynamic forces on bridges

The frequency and intensity of recent flood events demonstrate the need for investigating the forces exerted on inundated bridges. The hydrodynamic force coefficients for bridge superstructures are well established in the literature, but they can be significantly affected by the accumulation of debris upstream and the presence of substructures (e.g., piers, bent caps). The aim of this study is to evaluate the effects of debris-damming and substructures on hydrodynamic forces exerted on bridge superstructures. For this purpose, a series of laboratory experiments on the small-scale bridge and debris models was performed, and the lift and drag forces and overturning moments on bridge decks with debris and substructures were measured and compared to the hydrodynamic forces generated by the flow on superstructures without blockages. The total streamwise and vertical forces and overturning moment were used to investigate the effects of debris and substructures on superstructure forces. Results are also presented on drag, lift, and moment coefficients, as they revealed a considerable change in the hydrodynamic force and moment coefficients because of the additional flow blockages created by debris and substructures. Maximum drag coefficients were observed for a flat plate debris model, combined bridge model (i.e., superstructure, debris, and superstructure), partially submerged model, and a substructure-superstructure model of a fully submerged bridge. Maximum lift and moment coefficients occurred for the substructure and wedge debris models, respectively.

Combined experimental and numerical investigation of multiphase flow during water entry of spheres with different densities

The objective of this work is to investigate the cavity dynamics during water entry of spheres with varied structural density by a combined experimental and numerical method. Similar to the observations of Aristoff et al. (2009), the cavity types are further classified considering the relationship between the splash and cavity, then a map of cavity types in a Froude number and density ratio (Fr-m*) plane is concluded. It is found that the critical velocity of each cavity type is reduced with increasing density ratio of the impact sphere, and the rebound phenomenon only forms in the case of low-density m*<1. The numerical results are in good agreement with the experimental measurements, and reveal details of cavity flow structures for different types, indicating that impact of sphere with higher density ratio generates faster air flow into the splash crown, greater impact pressure and closure pressure. According to the analysis of the measured trajectory, velocity, and acceleration, it is found that the lighter sphere is easier affected by forces, especially at pinch-off. The difference between the total hydrodynamic force coefficients and drag coefficients is found significantly related to the volume of the cavity attached to the immersion sphere.

The Development Study of the Drag Coefficient of Solid Cylinder on Inclined Plane in Water

The dynamic resistance of a fluid to a cylinder rolling on an inclined plane in water has been experimentally studied. This creates problems in the form of solid-liquid interactions, which include landslides on the seabed and debris flows on the seabed that cause Tsunamis. The development of flow around a rolling cylinder is described to highlight the implications on the nature of the hydrodynamic force coefficient acting on the cylinder as resistance. The coefficient of drag on the cylinder when rolling on an inclined plane in water is the coefficient of drag that prevents the cylinder from rolling. In addition, other external force coefficients (besides the drag coefficient) also impede the cylinder motion. The equation of motion of the cylinder is solved with experimental data which is used as the most suitable solution to get the drag coefficient value. The movement of the cylinder is also not perfectly linear because there is a force from the side of the track and the cylinder moves slightly zigzag in 1-D motion.&#x0D; HIGHLIGHTS&#x0D; &#x0D; In this study, we present the experimental results of cylindrical drag coefficients of various materials on inclined planes in water as modeling of broader scientific problems, especially the potential for hydrometeorological and sedimentation disasters&#x0D; Fluid dynamics of the cylinder drag force on an inclined plane in water were measured experimentally&#x0D; The motion of the cylinder on an inclined plane in water is recorded, then the recorded video is processed using Logger Pro to obtain experimental time, speed, and position data which is processed using the appropriate mathematical equations&#x0D; &#x0D; GRAPHICAL ABSTRACT

Experimental study to investigate the effects of bridge geometry and flow condition on hydrodynamic forces

Stream-crossing bridges are designed to pass the design flow while maintaining a minimum freeboard; however, flood events are reported as the most frequent cause of bridge failure in the U.S. and around the world. Floodwater exerts significant forces on bridges, shearing and overturning their decks, which may cause them to fail. When a bridge fails, it loses its total or partial serviceability, causing fatalities, delays in emergency transportation and evacuation efforts, and economic losses. An accurate estimation of hydrodynamic forces on a bridge superstructure, therefore, is vital to assess its vulnerability to flooding. The purpose of this study is to investigate the effects of bridge geometry and flow conditions on hydrodynamic forces. A series of experiments on bridge scale models were performed in a laboratory flume to analyze the response of the drag, lift and moment coefficients to bridge geometry (deck width, and girders height and shape) and flow conditions (inundation ratio, proximity ratio, blockage ratio, and Froude number). The experimental results showed that hydrodynamic force and moment coefficients are dependent on the extent of the bridge submergence, Froude number, and proximity of the bridge to the streambed. The relationship between bridge geometry and force coefficients indicated that the geometric features of bridges have a large influence on flow field as well as drag, lift, and moment coefficients.

Numerical study of vortex-induced vibrations of a circular cylinder at different incidence angles

The effects of four different incidence angles (α) on the vortex-induced vibration (VIV) response of a two degrees-of-freedom cylinder were studied using the two-dimensional unsteady Reynolds-averaged Navier-Stokes equation and shear stress transport k-ω model, combined with the fourth-order Runge-Kutta method. The VIV characteristics, including the structural vibration amplitude, vibration frequency, lock-in regime, the pattern of vortex shedding, Strouhal number, hydrodynamic coefficient, and power conversion efficiency were systematically researched. The numerical results showed that a change of the incidence angle made the VIV response of the cylinder display multifrequency characteristics. As the incidence angle increased, the amplitude in the y direction gradually decreased; comparatively, the amplitude in the x direction gradually increased. The VIV responses for different incidence angles all presented an obvious lock-in phenomenon; however, the width of lock-in region changed slightly with variation of the incidence angle. As the incidence angle increased, the root-mean-square value of the hydrodynamic force coefficient in the y direction and the mean value of the hydrodynamic force coefficient in the x direction both had a decreasing tendency.

Large eddy simulation of flow past an inclined finite cylinder

This paper presents the numerical analysis of the hydrodynamic characteristics and wake structures of an inclined finite cylinder with large eddy simulation (LES). The Reynolds number (Re) is fixed at 3,900 and the inclination angle θ is varied over the range 0°≤θ≤45° with an increment Δθ=7.5°. The numerical method applied in the present study is first validated for the case of an upright finite cylinder (θ = 0°), which shows reasonably good agreement with the literature. According to the results, the hydrodynamic force coefficients and Strouhal number of the inclined cylinder do not comply with the independent principle (IP), despite they remain constant in the range 15°≤θ≤30°. In this range, the magnitude of these parameters is considerably smaller than that of the upright case, which is favorable to the structural stability. The wake structures in the lee of the cylinder are visualized quantitatively, which are shown to be dependent of the inclination angle. Intermittent switching in vortex mode from parallel to the cylinder axis (Mode I) to re-orientation towards downstream (Mode II) at small inclination angle, and from the vortex diminished zone (Mode VD) to that with vortex tubes (VDT) at large inclination angle, are captured. Moreover, the breakup mechanism of the corrugated shear layer (CSL) can be elaborated in two forms, one associated with strong downward flow and the other with helical upward flow in the wake of the inclined finite cylinder.

Evaluation of Hydrodynamic Force Coefficients in Presence of Biofouling on Marine/Offshore Structures, a Review and New Approach

Novel attempts to optimize the design and requalification of offshore structures draws attention to the importance of updating information about the environmental forces. One of the important steps to design or re-assess offshore structures is the re-evaluation/evaluation of bio-colonization’s effects. This paper presents a review of studies that considered biofouling in marine/offshore structures. Most of the previous researchers conducted the effects of biofouling as a surface roughness; however, some others proved that despite the surface roughness, other marine fouling components such as surface coverage ratio, biofouling species, and aggregation, may significantly influence hydrodynamic force coefficients, particularly at higher Reynolds numbers (Re). In addition, a new approach is proposed in this paper to estimate the drag coefficient of circular members covered by biofouling. The new approach relies on a multiple parameter equation and builds on the existing measurement of the drag force coefficient. Two relationships between biofouling parameters and drag coefficient are given for hard biofouling at the post-critical Re regime.

Computational analysis of naturally oscillating tandem square and circular bluff bodies: a GPU based immersed boundary – lattice Boltzmann approach

ABSTRACT In this study, a fluid-structure interaction solver is employed to explore the flow physics of tandem oscillating square bluff bodies by varying the corner radius. Based on previous research, dynamic behavior, and fluid forces only square and circular bluff bodies are chosen for a supplementary investigation. This study investigates the effects of the streamwise displacement, , of two elastically mounted square and circular bluff bodies in a tandem arrangement. Fluid flows at a Reynolds number of 100 and a fixed mass ratio are used for the upstream and downstream bluff bodies. As the most complex oscillations and wake flows occur adjacent to the approximate natural frequency ratio, thus a constant natural frequency of is defined. To achieve excellent parallel performance, an immersed boundary lattice Boltzmann method code coupled with a structural equation is developed and accelerated using a graphical processing unit. The results for flow-induced vibrations suggest that the flow response characteristics of the tandem oscillating bluff bodies are strong functions of the streamwise displacement. Four different flow regimes of the bluff body arrangements are identified on the basis of response amplitude. Both the square and circular downstream bluff bodies exhibit two peak transverse amplitudes in the existing scrutinized spacing ratios. In addition, the critical spacing ratio values are dissimilar for the two bluff bodies. Moreover, at the end of the spacing ratio (), the wake effects for the downstream square body are amplified, and it oscillates near a single oscillating circular bluff body. Finally, the flow physics, as well as the hydrodynamic force coefficients of the tandem oscillating bluff bodies are also reviewed.

Experimental investigation of water entry of dimpled spheres

This study presents the experimental results of the vertical water entry of dimpled spheres. The role of the number and arrangement of the surface dimples under different impact velocities in the air cavity formation/evolution/collapse is mainly considered. The diameter of all the spheres is fixed, and they all enter into a tank filled with tap water. Hence, in all experiments, the Bond number and Capillary length are the same, but the Reynolds, Weber, Capillary, and Froude numbers will vary concerning the difference in impact velocities. A PcoDimax-S high-speed camera visualizes dimpled spheres' trajectory at a frame rate of 1 to 2kfps. In addition to the cavity dynamics, the motion kinetics of the spheres (comprising trajectory, velocity, acceleration, and hydrodynamic force coefficient) is also studied. One important outcome is that dimples are crucial in air entrainment cavity formation, even if the spheres impact the water at low velocities. Also, the results show that at a given impact velocity, increasing the number of dimples can change the pinch-off regime from shallow-seal to deep-seal. In addition, surface dimples improve the descent velocity and acceleration and reduce the hydrodynamic force coefficient.

Experimental study on the entry of solid spheres into Newtonian and non-Newtonian fluids

This study experimentally investigates the entry of hydrophobic/hydrophilic spheres into Newtonian and Boger fluids. By considering solution of 82% glycerin and 18% water and solution of 80% glycerin, 20% water and 100 ppm polyacrylamide, Newtonian and Boger fluids are made, respectively. It has been tried that liquids' surface tension, density, and viscosity are almost the same. Thus, all dimensionless numbers are approximately the same at a similar impact velocity except for the elasticity number. A PcoDimaxS highspeed camera captures the spheres' trajectory from the impact to the end of the path. Regarding the range of released height (0.5–100 cm), the impact velocities are approximately in the range of 0.31–4.43 ms−1. The role of fluid elasticity in combination with the sphere surface wettability on the air cavity formation/evolution/collapse is mainly studied. Also, the kinetics of the sphere motion (velocity, acceleration, and hydrodynamic force coefficient) is studied. The results show that air drawn due to the sphere's impact with the Newtonian liquid is more, and the pinch-off takes place later. Also, shedding bubbles are cusped-shaped in the Boger fluid, while in the Newtonian fluid, they are elliptical. In addition, the most significant impact of surface wettability is observed in the Newtonian fluid. Finally, the results reveal that the sphere in the Newtonian fluid can move faster and travel a longer distance in a specific time interval. The differences observed are closely related to the viscoelastic fluid's elasticity property and extensional viscosity.

Modelling Open Ocean Aquaculture Structures Using CFD and a Simulation-Based Screen Force Model

The numerical framework of the open source CFD solver REEF3D is utilised to study the fluid–structure interaction of an open ocean aquaculture system and waves. The presence of the net is considered in the momentum equations of the fluid using a forcing term based on Lagrangian–Eulerian coupling and the hydrodynamic loads on the net. They are defined semi-empirically using a screen force model. Here, the hydrodynamic force coefficients are calculated from the net geometry and fluid velocity. The necessary force coefficients are predicted from a new simulation-based screen force model. Here, CFD simulations are performed to obtain the hydrodynamic loads on net panels for varying net geometries, angles of attack and velocities. Then, a Kriging metamodel is applied to fit a polynomial to the data. The proposed net model is validated against measurements for waves and current through rigid net panels and applied to simulate the dynamics of an open ocean aquaculture cage in waves. In current, the model predicts the drag forces and velocity reduction within a 10% error band, whereas it tends to under-predict the lift forces by up to 20%. In waves, the model tends to over-predict the crests with increasing wave height, but the deviations are also within a 10% error band.

Flow-induced vibration analysis of two unequal-diameter flexible cylinders in staggered configuration from a hydrodynamic force perspective

This paper presents an experimental study on the hydrodynamic features of two unequal-diameter flexible cylinders in staggered arrangement subject to flow-induced vibration (FIV). Five position angles (α = 15°, 30°, 45°, 60°, and 75°) are defined between the tandem (α = 0°) and side-by-side (α = 90°) cases with the centre-to-centre spacing being fixed at P = 6.0d, where d is the diameter of the small cylinder. The time-varying strains obtained from the experimental tests are converted into displacements, and then the hydrodynamic force coefficients of the two cylinders are derived using an inverse analysis method. It is found that the variation trends of the cross-flow (CF) hydrodynamic coefficients with the reduced velocity do not demonstrate qualitative differences from those of their isolated counterparts except in the mode transition regions. The downstream cylinder experiences stronger influence from the upstream cylinder on its CF hydrodynamic characteristics especially at small α. The more frequent mode transitions in the in-line (IL) direction lead to the multi-frequency responses associated with changes in the IL hydrodynamic coefficients. The typical wake-induced flutter (WIF) phenomenon is observed when Vrs = 5.01, 8.77 and 16.28–25.05 for the downstream small cylinder in Case I and α = 75°. The influence of the characteristics of the WIF phenomenon on the hydrodynamic force is evident because of the nonexistence of the high-frequency components in the oscillations.

A Method for Measuring Hydrodynamic Force Coefficients Applied to an Articulated Concrete Mattress

A physical model testing method to determine the hydrodynamic force coefficients of an object is proposed and applied to an articulated concrete mattress placed on a flat surface under steady current condition. The test setup, which comprises of a pulley system that is able to pull the concrete mattress in either direction relative to the flow (e.g., with the flow direction or against the flow direction) and one load cell to measure the force required to pull the mattress, is simple and straightforward. Writing the equations of load balance for two different pulling directions allows the force coefficients to be deduced. The novelty and advantages of the method are that it completely removes the difficulties associated with measuring forces on individual concrete blocks and isolating the mattresses from contacting the solid surface, which were common in conventional test methods for measuring hydrodynamic forces on structures founded on a solid surface. A series of flume tests have been conducted to demonstrate the validity of the proposed method. It is expected that the proposed testing method is applicable to a wide range of structures, bed surfaces and flow conditions.

On the behavior of nonlinear hydrodynamic coefficients of a submerged cylinder beneath the water surface

This study aims at numerically exploring the behavior of flow fields and nonlinear hydrodynamic coefficients of a horizontal cylinder beneath the free surface flow considering the effects of nonlinear surface waves and various cylinder shapes. The computational model is based on two-dimensional incompressible Navier-Stokes solvers along with the treatment of the free surface flow using the volume of fluid method. The effect of the turbulent flow is also considered by using the shear stress transport turbulence model. The simulation result of a benchmark case study of the submerged cylinder is first validated with available experiment data, where a mesh convergence analysis is also performed. Afterward, the flow fields and hydrodynamic force coefficients around the cylinder surface are analyzed, and the influences of various cylinder shapes and Reynolds numbers on the hydrodynamic coefficients are investigated. A state diagram representing the hydrodynamic behavior including stable and unstable stages is finally proposed; this is an important criterion for the practice design of submerged civil structures under the free surface flow.

Tsunami-like flow induced forces on the structure: Dependence of the hydrodynamic force coefficients on Froude number and flow channel width in quasi-steady flow phase

During the tsunami landfall, the structures near the coast perform like a wall of certain obstruction, b/W (b = structure width, W = available flow channel width) to the incoming flow due to abutting adjacent structures. In the previous paper (Harish et al., 2021), the generalized semi-analytical equation for the horizontal forces using the free flow parameter during the quasi-steady flow is provided. The emphasis was on understanding flow characteristics at the structure front. However, the quantitative dependence of the hydrodynamic drag force coefficient (Cd) on the influence of b/W and Froude number (Fr) are not investigated in detail. In the present paper, from the experimental analysis, in addition to show Cd as a function of b/W and Fr, the influence of Fr in Cd variation for various b/W is brought out. Based on this, a generalized empirical equation for Cd is proposed. The experimental analysis on the vertical force shows that the hydrodynamic uplift force (Fu) can be explicitly estimated based on the average water depth at the structure front and backside from the buoyancy force equation (Fub). Further, Fu/Fub is found to be independent of Fr and b/W, unlike the horizontal force. From the practical design perspective, these two explicit expressions are essential, and the physical process involved in obtaining this expression has been discussed in this paper.