Hydrodynamic Coefficients Research Articles

Transport in cellular aggregates described by fluctuating hydrodynamics

Biological functionality of cellular aggregates is largely influenced by the activity and displacements of individual constituent cells. From a theoretical perspective this activity can be characterized by hydrodynamic transport coefficients of diffusivity and conductivity. Motivated by the clustering dynamics of bacterial microcolonies we propose a model of active multicellular aggregates and use recently developed macroscopic fluctuation theory to derive a fluctuating hydrodynamics for this model system. Both semianalytic theory and microscopic simulations show that the hydrodynamic transport coefficients are affected by nonequilibrium microscopic parameters and significantly decrease inside of the clusters. We further find that the Einstein relation connecting the transport coefficients and fluctuations breaks down in the parameter regime where the detailed balance is not satisfied. This study offers valuable tools for experimental investigation of hydrodynamic transport in other systems of cellular aggregates such as tumor spheroids and organoids. Published by the American Physical Society 2024

Empirical dependences of the hydrodynamic drag coefficient of cod-ends made of T0 and T90 netting

Empirical dependences of the hydrodynamic drag coefficient of cod-ends made of T0 and T90 netting

Incremental robust predictive control for anti-pitching in catamarans with appendage constraints

To solve the problem that high-speed catamarans have excessive amplitude of vertical motion in rough sea conditions, an anti-pitching method based on incremental robust predictive control of catamarans is proposed, which takes into account the model uncertainty and input rate of appendage requirements. Thus, a high-speed catamaran vertical control model is established with T-foils and flaps serving as anti-pitching appendages, and the hydrodynamic coefficient uncertainties is analyzed, which is converted into a state space model with norm-bounded uncertainty to facilitate control system design; moreover, transforming the norm-bounded uncertainty model of a high-speed catamaran into an incremental model, which can increase the integral action to improve the anti-pitching performance. On this basis, the hybrid H2/H∞ robust predictive control method is proposed to achieve wave disturbance resistance capability and robust stability of the catamaran system, taking the rate of input of the anti-pitching appendages as the input constraints, and the linear matrix inequality (LMI) receding-horizon optimization is used to solve the incremental control input of appendages. Ultimately, the effectiveness of the proposed algorithm is verified by digital simulation.

Investigation of hydrodynamic characteristics of an oyster reef under regular waves

Oyster reef living shorelines are popular solutions to mitigate coastal hazards while providing ecosystem services, and their hydrodynamic characteristics deserve further examination. This paper reports an experimental and numerical study of the hydrodynamic behavior of a bagged oyster shell (BOS) reef under regular waves. The dependence of the pore pressure within the reef and the hydrodynamic coefficients on the reef height, length, porosity, and wave parameters are investigated. The results show that the normalized maximum pore pressure ps_m∗ decreases from the seaside of the BOS reef to its leeside and decreases with increasing dimensionless reef length. With increasing wave steepness, ps_m∗ fluctuates with an overall increasing trend. With increasing BOS reef porosity, ps_m∗ decreases at seaside locations and increases at leeside locations; simultaneously, the wave reflection coefficient Kr and the wave dissipation coefficient Kd decrease, and the wave transmission coefficient Kt increases. With increasing wave steepness for a given wave period, Kr and Kt tend to increase, but Kd exhibits the opposite trend. As the dimensionless reef height and length increase, Kt decreases and Kd increases. Multivariate nonlinear regression and genetic programming-based symbolic regression methods are individually used to derive two formulas for predicting the wave transmission coefficient, with the formula from the latter method being found to give a higher prediction accuracy.

Layout Optimization of Wave Energy Park Based on Multi-Objective Optimization Algorithm

Abstract In this paper, both semi-analytical method and numerical simulation is applied to investigate the hydrodynamic behavior of large arrays of point-absorber wave energy converters (WECs). To analyze wave interactions among multiple WECs within an array, a semi-analytical model is developed based on the potential flow theory and the matched eigen-function expansions method. The fluid domain is divided into two kinds of regions: interior regions underneath the cylinders and an exterior region surrounding all the cylinders. The matched eigenfunction expansions method is employed to solve the radiation potential problem in each domain, and the hydrodynamic coefficients and motion response of the cylinders in the array are evaluated. To validate the accuracy of the semi-analytical method, WAMIT is adopted to simulate the wave energy park numerically and compared with the results by the semi-analytical model. The hydrodynamic characteristics and power absorption performance of the WECs within the wave energy park are analyzed. The power performance of a wave energy park is studied as functions of layout geometry, incident wave direction and separation distance between WECs respectively. Finally, MOPSO based on a surrogate model is used to optimize the layout of wave energy array.

Hydrodynamic force coefficients for spherical triangle shell fragments: Dependence on the aspect ratio and flatness

Euler–Lagrange simulations of particle-laden flow require hydrodynamic models of drag and lift forces for individual particles. Our goal is to develop models that can prescribe these forces for arbitrarily orientated shell objects. Here, we use computational fluid dynamics simulations of steady bottom-boundary layer flow over a series of spherical triangle shell fragments to calculate the hydrodynamic forces. The simulations explicitly resolve the wall boundary layers using grid resolution on the order of y+=1 at the shell fragment surface and use the SST k-omega turbulence closure model. These fragments cover a range of aspect ratio and flatness characteristics. The shell fragments are generated as triangular selections of a spherical shell with azimuthal and longitudinal angles proscribed based on elongation and flatness parameters (varying between 1 to 5, and 0.02 to 0.2 respectively), while characteristic length of the fragment is held constant to define the overall fragment size. Fragment orientations are considered with independently varying pitch, roll, and yaw each ranging from 0 to 180 degrees. The numerical estimates for the forces from all simulations were used to develop robust parameterizations of the drag and lift as a function of aspect ratio and flatness characteristics, as well as orientation of the shell fragments.

A frequency domain analysis method for the dynamic response of a submerged floating tunnel under wave action

To investigate the dynamic response of a submerged floating tunnel (SFT) under the action of waves, a modal superposition method in the frequency domain was established, and the amplitudes of the modals were determined using the generalized wave loads and hydrodynamic coefficients of the structural modals. In this model, the SFT was simplified as a constant-cross-section Euler–Bernoulli beam with multiple anchor cables, and its structural modals were resolved using the finite element method (FEM). The generalized wave loads and generalized hydrodynamic coefficients were obtained using the Fourier expansion strategy of the modal function, by which the hydrodynamic problem can be converted into 2D problems with the modified Helmholtz controlling equation and solved using the matched higher-order boundary element method (HOBEM) and eigenfunction expansion. The effects of the diameter of the anchor cables and length of the SFT on the stiffness of the structure and the dynamic response of an SFT with anchor cables under wave action were investigated. Furthermore, the effects of different added mass calculation methods on the structural response were studied. In addition, the wave exciting forces were calculated using potential flow theory or linearized Morison equations according to the wave scale. Finally, the effects of the incident wave frequencies and incident angles were investigated in detail to reveal the combined resonance mechanism.

Modeling and performance estimation for L-shaped OWC wave energy converters with a theoretical correction for spring-like air compressibility

The investigation of Oscillating Water Columns (OWC) has gained significant attention in recent years thanks to their resilient structural design, allowing them to withstand harsh environmental conditions. This study focuses on the L-shaped OWC (L-OWC) due to its excellent energy capture efficiency. It should be noted that air compressibility plays a significant role in the plenum chamber of the OWC, especially at full scale. The present paper proposes a scaling-rematched approach, facilitating the evaluation of hydrodynamic coefficients and the performance estimation with a theoretical correction for the unmatched scaling problem of spring-like air compressibility. The methodology is applied successfully to a model-scale L-OWC design, employing three-dimensional, incompressible-flow simulations combined with an impeller model. The present study reveals the hydrodynamic characteristics (advantages) of the L-OWC: small fluid damping coefficient and large added mass, and hence the possibility that the spring-like air compressibility can be used to raise the efficiency of power capturing. Furthermore, there exists an interval where the air compressibility has a positive effect on the performance, not only having a significantly longer span than that of the conventional OWC but also much more directly matching the period range of high energy potential found in the wave climate of Northeastern Taiwan waters.

Coupled Motion Response Analysis for Dynamic Target Salvage under Wave Action

The strategic recovery of buoys is a critical task in executing deep-sea research missions, as nations extend their exploration of marine territories. This study primarily investigates the dynamics of remotely operated vehicle (ROV)-assisted salvage operations for floating bodies during the recovery of dynamic maritime targets. It focuses on the hydrodynamic coefficients of dual floating bodies in this salvage process. The interaction dynamics of the twin floats are examined using parameters such as the kinematic response amplitude operator (RAO), added mass, damping coefficient, and mean drift force. During the “berthing stage”, when the double floats are at Fr = 0.15–0.18, their roll and yaw Response Amplitude Operators are diminished, resulting in smoother motion. Thus, the optimal berthing speed range for this stage is Fr = 0.15–0.18. During the “side-by-side phase”, the spacing between the ROV and FLOAT under wave action should be approximately 0.4 L to 0.5 L. The coupled motion of twin floating bodies under the influence of following waves can further enhance their stability. The ideal towing speed during the “towing phase” is Fr = 0.2. This research aims to analyze the mutual influence between two floating bodies under wave action. By simulating the coupled motion of dual dynamic targets, we more precisely assess the risks and challenges inherent in salvage operations, thus providing a scientific basis for the design and optimization of salvage strategies.

The Hydrodynamic Similarity between Different Power Levels and a Dynamic Analysis of Ocean Current Energy Converter–Platform Systems with a Novel Pulley–Traction Rope Design for Irregular Typhoon Waves and Currents

In the future, the power of a commercial ocean current energy convertor will be able to reach the MW class, and its corresponding mooring rope tension will be very good. However, the power of convertors currently being researched is still at the KW class, which can bear less rope tension. The main mooring rope usually has a single cable and a single foundation. To investigate the dynamic response and rope tension of an MW-class ocean current generator mooring system, here, a similarity rule is proposed for (1) coefficients without any fluid–structure interaction (FSI) using the Buckingham theorem and (2) ones with FSI. The overall hydrodynamic drag and moment including the hydrodynamic coefficients in these two situations are represented in a Taylor series. Assuming similarity between the commercial MW-class and KW-class ocean current convertors, all hydrodynamic parameters of the MW-class system are estimated based on the known KW-class parameters and based on the similarity formula. In order to overcome the extreme tension of the MW-class system and to provide good stability, in this paper, we propose a pulley–rope design to replace the traditional single-traction-rope design. The static and dynamic mathematical models of this mooring system subjected to the impact of typhoon waves and currents are proposed, and analytical solutions are obtained. We find that the pulley–rope design can significantly reduce the dynamic rope tensions of the mooring system. The effect of the length ratio of the main traction rope, rope A, to the seabed depth on the dynamic tension of stabilizing converter rope D is significant. The length ratio is within a safe range, and the maximum rope dynamic tension is less than the fracture strength. In addition, if the rope length ratio is over the critical value, the larger the ratio, the higher the safety factor of the rope. In summary, the pulley–rope design can be safely used in an MW-level ocean current generator system.

Locomotion of Bacillus subtilis SL-44 mediated by root exudate and carrier in Cr(OH)3-modified porous media

Plant growth promoting rhizobacteria (PGPR) have a remediation effect on Cr-contaminated soil; however, the remediation scope is only within a small area around the bacteria. Hence, the remediation effect depends on the migration ability of bacteria in the soil. Root exudates enhance the chemotaxis and locomotion of Bacillus subtilis SL-44 by reducing its adhesion coefficient katt and hydrodynamic dispersion coefficient D. The locomotion capacity was enhanced by 7.84%–20.00%. Among the root exudates, proline and sucrose remarkably improved the motility of SL44. Biochar and bentonite increased the katt and D of SL-44, inhibited bacterial locomotion, and improved the retention rate on the carrier surface. Bacterial locomotion was reduced by biochar and bentonite by 57.99% and 50.42%, respectively. These reductions were caused by macropore. SL-44 locomotion was positively correlated with the concentration of environmental root exudate (R2 = 0.88−0.92). The results of the simulated soil study were validated in actual agricultural Cr-contaminated soils through qPCR.

Wave excited motion of a body floating on water confined between a semi-infinite ice sheet and a side wall

In this paper, we investigate the diffraction and radiation coupling problem of a floating body confined between a fixed wall and a semi-infinite ice sheet under the action of incident waves. Based on the linear water wave theory and Kirchhoff Love elastic thin plate assumption, the ice sheet is considered as an elastic beam, and the boundary conditions of fluid boundaries covered by the ice sheet are obtained. Dividing flow domains with different upper surfaces, the eigenfunction expansion method was used to obtain the velocity potential expansion equations for each sub-domain. Then, through the matching conditions at the interface of sub-domains, a system of equations was constructed to solve the unknown coefficients of the expansion equations. The influence of the existence of the ice sheet on the diffraction and radiation motion of the floating body is analyzed. The effects of changes in the draft and open water width of the floating body on the wave excitation force and hydrodynamic coefficient of the floating body are discussed. The influence of the reflection effect of the ice sheet on the added mass and damping coefficient of the floating body has been discovered, especially the changes and oscillation rules of their extreme points. This research achievement provides theoretical support for the safety design of floating structures in frozen harbors.

Viscous effects on the hydrodynamic performance of a two-body wave energy converter with a damping plate

In this study, the hydrodynamic forces and power absorption performance of an autonomous underwater vehicle (AUV)-based two-body wave energy converter (2BWEC) are investigated. A theoretical model is developed within the framework of linear potential flow to solve for added mass, radiation damping, and wave excitation force using the matched eigenfunction expansion method (MEEM). A computational fluid dynamics (CFD) model is employed to account for vortex-shedding effects of the floater and inner cylinder with a damping plate under various excitation conditions. Empirical formulas for supplementary added mass and drag coefficients caused by flow separation are proposed based on curve-fitting the differences between CFD results and MEEM calculations. These formulas are integrated into motion equations to enhance accuracy in evaluating the power absorption of the 2BWEC. It has been found that in the context of viscous flow, both the added mass and damping coefficients are increased, particularly for the inner cylinder with a damping plate. In addition, the viscous hydrodynamic coefficients exhibit strong dependence on the Keulegan–Carpenter number, while showing insensitivity to changes in the frequency parameter β. The supplementary (viscous) added mass provides additional inertia for the AUV with a limited mass itself, which is advantageous for the power absorption of the AUV-based 2BWEC. Conversely, the presence of viscous damping from the damping plate impedes wave energy capture.

Hydrodynamic features specific to the dynamic movements of an underwater glider

The purpose of this study was to show the influence of the underwater glider's motion on its hydrodynamic coefficients. The proposed drone was based on a scaled-down geometry of the DARPA suboff bare hull model that was equipped with wings and fins. A series of Computer Fluid Dynamics simulations were performed using the ANSYS Fluent software. It was shown that with the increase of the drone's rotational velocity, the detachment of flow on the wings was delayed, and thus, the overall lift was increased. The hysteresis present in the characteristics of hydrodynamic properties during pitching movement had higher amplitude with increased pitching frequency. It was concluded that the parameters of the underwater glider's motion can have a significant influence on its hydrodynamic properties.

Analytical gradients of first-order diffraction and radiation forces for design optimization of floating structures

Gradient-based design optimization of floating structures with many design variables requires efficient and accurate computation of hydrodynamic coefficients including wave excitation forces and their derivatives with respect to design variables. For large-volume structures or structures with many component members, the only practical method to determine diffraction and radiation forces is to apply a boundary element method solver. This work presents the first known boundary element method solver with implicit analytic derivatives, allowing for total derivative computation alongside force evaluation. Two case studies are presented: a single floating circular column and a structure with multiple square columns attached to a horizontal pontoon. Force results from both case studies agree well with reference data, while derivative results agree with the best comparisons available. Computational requirements limit the applicability of this method and suggest further work is required to refine this approach.

Evaluation of hydrodynamic coefficients and sensitivity analysis of a work-class remotely operated vehicle using planar motion mechanism tests

This paper presents a comprehensive analysis of the hydrodynamic forces and moments relating to the drag on an open-frame work-class remotely operated vehicle (ROV) AUTO-1000. We describe the results of planar motion mechanism experiments conducted with the aim of modeling and simplifying the mathematical maneuverability model for such an ROV. The scale of the model is 1:4. Various experiments are performed in a nonlinear wave channel. The flow speeds in the static drag tests range from ±0.2–±0.5 m/s and the angle in the drift tests is less than 10°. The motion frequencies of the dynamic tests range from 0.25 to 3.14 rad/s. The amplitude of the translation motions is 0.03 m and the largest angular amplitude in the rolling tests is 5°. The viscous and inertial hydrodynamic coefficients are estimated. Normalized sensitivity coefficients are used to investigate the sensitivity of both the viscous and inertial hydrodynamic coefficients considering the multi-degree-of-freedom motion and velocity effect. The drag, drift, and stationary random motions are used to examine the sensitivity. A comparison of the motion simulation results given by simplified and complete models shows that a threshold normalized sensitivity coefficient value of 0.01 is suitable for filtering the ROV coefficients.

Insights into the scale effects on ship motions and wave loads considering hydroelasticity

To investigate the scale effects on ship seakeeping and wave loads, ship motions and wave loads considering hydroelasticity responses of a 310-m-long ship are calculated in four different scales, i.e., model scale 1:100, 1:50, 1:25 and full-scale 1:1 by using a partitioned CFD-FEM two-way coupled method. The simulation results of the 1:50 scaled model are also compared with tank experimental data of a segmented model with a same scale and configuration for validation. Then the hydrodynamic coefficients, incident waves, heave and pitch motions, vertical bending moment, vertical shearing force and whipping loads obtained by different scaled simulations are compared and the associated scale effects are systematically analyzed. This paper also investigates the influence of segment scheme and backbone configuration on ship modal characteristics, which sheds some light on the design of segmented models with backbone for hydroelasticity experiments.

A formulation for fluid–structure interaction problems with immersed flexible solids: Application to splitters subjected to flow past cylinders with different cross-sections

In the finite element method framework, a fluid–structure formulation is developed by coupling an Eulerian fixed-mesh fluid approach with a Lagrangian deforming-mesh description for a flexible solid. The coupled formulation is solved using a staggered scheme during time. For the fluid solution stage, the solid walls are considered as a time-variable internal boundary. The velocity and pressure fields are obtained by solving the weak form of the fluid dynamic equations in which the solid velocity is imposed on the internal boundary via a penalization term. For the solid solution stage, the displacement field is obtained by solving the discrete solid dynamic equations which consider traction forces computed by integrating pressures and viscous stresses on the nodes belonging to the solid walls. This novel technique is firstly applied to analyze a flexible splitter under the shedding of a flow past square cylinder due to this problem is considered as a benchmark in the literature. The present solutions agree with those computed using body-fitted techniques, thus validating the proposal. Secondly, flexible splitter motions under the shedding of flow past cylinders with different cross-sections and splitter lengths are comprehensively studied. Overall, the computed results confirmed that the hydrodynamic coefficients on the cylinders were reduced because of the presence of the splitter.

Numerical investigation on the suppression of vortex-induced vibration system by assembling different rotors based on quasi-active control method

Combining the innovative concept of quasi-active control method, a numerical simulation is conducted to investigate the vortex-induced vibration (VIV) responses. The objects of this study include a main cylinder (MC) and a cylindrical system outfitted with a pair of rotors of different types (with Banki rotors, Darrieus rotors, and Savonius rotors, denoted as WBR, WDR, and WSR), and the VIV responses are analyzed within the Reynolds number range of 0.8 × 103≤Re ≤ 5.6 × 103. The findings indicate that all three kinds of rotors show excellent vibration suppression effect in downstream and cross-flow directions by adjusting the VIV response (amplitude, frequency, hydrodynamic coefficient) and vortex pattern (vortex mode, wake shape). The maximum amplitude suppression rate can reach 99% for the Banki and Savonius cases at high reduced velocity. Within the whole velocity range, the maximum amplitudes of WBR, WDR, and WSR cases in the downstream and cross-flow directions were 0.32 and 0.45 times, 0.73 and 0.65 times, and 0.28 and 0.33 times, respectively, compared to the maximum amplitude of MC. The time-averaged drag coefficient of the controlled cylinder in the WBR case was minimized to about 0.015. The Banki rotor and Savonius rotor significantly reduced the vibration frequency of the VIV system compared to the Darrieus rotor. Especially, the Banki rotor could keep the VIV system vibration frequency within a narrow range at different reduced velocity. Moreover, the vorticity contour of the VIV system with assembled rotors was significantly improved, with a narrower flow wake width and more regular vortex shedding at high reduced velocity. Considering both amplitude suppression and drag coefficient, Banki rotors were recommended.

Design, hydrodynamics analysis, and control of an underwater glider with controllable wing mechanism

Due to the effect of biofouling and different mission sensors that may be onboard, hydrodynamic coefficients of underwater glider (UG) may experience gradual or obvious changes, which increases the energy consumption and reduces the glide range. This paper proposes a controllable wing mechanism (CWM) for UG, which enables it adjust the hydrodynamic coefficients and kinematic performance without changing the net buoyancy. Only by two degrees of freedom (DoF), that CWM can realize the control of wingspan, sweep back angle and chord width. To apply the hydrodynamics controlled with CWM in glide model, the fitting precision of hydrodynamics function is improved based on backpropagation artificial neural network (BPANN). A nonlinear state observer based on finite impulse response (FIR) filter is employed for state estimation and random noise interference filtering to realize measurements and evaluation of velocity and reduce the attitude angle measurement error for UG. Then, the FIR-based fuzzy PID (FFPID) controller is established for a steady-state gliding motion control, which suppresses the unknown interference to stablize the system quickly. Finally, the effectiveness of the FFPID closed-loop controller and observer is verified through the simulation in matlab and the experimental test of the UG with CWMs in a water tank.