Resultant Hydrodynamic Forces Research Articles

Discrete element method–computational fluid dynamics analyses of flexible fibre fluidization

Abstract

Quantification of computational fluid dynamics simulation assists the evaluation of protection by Gypenosides in a zebrafish pain model

In recent years, due to its rapid reproduction rate and the similarity of its genetic structure to that of human, the zebrafish has been widely used as a pain model to study chemical influences on behavior. Swimming behaviors are mediated by motoneurons in the spinal cord that drive muscle contractions, therefore a knowledge of internal muscle mechanics can assist the understanding of the effects of drugs on swimming activity. To demonstrate that the technique used in our study can supplement biological observations by quantifying the contribution of muscle effects to altered swimming behaviours, we have evaluated the pain/damage caused by 0.1% acetic acid to the muscle of 5 dpf zebrafish larvae and the effect of protection from this pain/damage with the saponin Gypenosides (GYP) extracted from Gynostemma pentaphyllum. We have quantified the parameters related to muscle such as muscle power and the resultant hydrodynamic force, proving that GYP could alleviate the detrimental effect of acetic acid on zebrafish larvae, in the form of alleviation from swimming debility, and that the muscle status could be quantified to represent the degree of muscle damage due to the acetic acid and the recovery due to GYP. We have also linked the behavioral changes to alteration of antioxidant and inflammation gene expression. The above results provide novel insights into the reasons for pain-related behavioral changes in fish larvae, especially from an internal muscle perspective, and have quantified these changes to help understand the protection of swimming behaviors and internal muscle by GYP from acetic acid-induced damage.

Reorientation and propulsion in fast-starting zebrafish larvae: an inverse dynamics analysis.

Most fish species use fast starts to escape from predators. Zebrafish larvae perform effective fast starts immediately after hatching. They use a C-start, where the body curls into a C-shape, and then unfolds to accelerate. These escape responses need to fulfil a number of functional demands, under the constraints of the fluid environment and the larva's body shape. Primarily, the larvae need to generate sufficient escape speed in a wide range of possible directions, in a short-enough time. In this study, we examined how the larvae meet these demands. We filmed fast starts of zebrafish larvae with a unique five-camera setup with high spatiotemporal resolution. From these videos, we reconstructed the 3D swimming motion with an automated method and from these data calculated resultant hydrodynamic forces and, for the first time, 3D torques. We show that zebrafish larvae reorient mostly in the first stage of the start by producing a strong yaw torque, often without using the pectoral fins. This reorientation is expressed as the body angle, a measure that represents the rotation of the complete body, rather than the commonly used head angle. The fish accelerates its centre of mass mostly in stage 2 by generating a considerable force peak while the fish 'unfolds'. The escape direction of the fish correlates strongly with the amount of body curvature in stage 1, while the escape speed correlates strongly with the duration of the start. This may allow the fish to independently control the direction and speed of the escape.

Nonlinear Sloshing of Liquid in a Rigid Cylindrical Container with a Rigid Annular Baffle under Lateral Excitation

Nonlinear response of liquid partially filled in a rigid cylindrical container with a rigid annular baffle subjected to lateral excitation is studied. A semianalytical approach is presented to determine the natural frequencies and modes of the liquid sloshing. Introducing the generalized time‐dependent coordinates, the surface wave height and the velocity potential are expressed in terms of the natural modes of liquid sloshing. Based on the Bateman–Luke variational principle, the infinite‐dimensional modal system is given by the variational procedure. The infinite‐dimensional modal system is reduced by using the Moiseev asymptotic relations. The resultant hydrodynamic force and moment of the liquid pressure acting on the container mainly depend on the position vector of the mass center of the liquid. Expanding the integral about the weighted position coordinates into the Taylor series about the surface wave height at the unperturbed free surface gives the formula of the position vector of the mass center, which depends only on the generalized time‐dependent coordinates. Excellent agreements have been achieved by comparing the present results with those obtained from Gavrilyuk’s solution and SPH solution. Finally, the surface wave height, resultant hydrodynamic force, and hydrodynamic moment for a container subjected to harmonic lateral excitation are discussed in detail.

ИССЛЕДОВАНИЕ ОСТОЙЧИВОСТИ СУДНА В УСЛОВИЯХ ЗАХВАТА ВОЛНОЙ НОСОВОЙ ОКОНЕЧНОСТИ

Among all types of wrecking in the world shipping, stability loss stands out for the severity of its consequences, because it is often accompanied by the death of the crew. One of the reasons for the stability loss is wave run-up of the ship bow during the storm in a head sea. The article analyzes the level of danger of hydrodynamic loads acting on the deck at the bow in conditions of its wave run-up. Theoretical study has been undertaken on the transformation of the statiсal stability diagram during the wave run-up of the ship bow. It was found out that that the nature of change in the curves of the anti-tipping moment with the increase in the hydrodynamic load acting on the bow is dependent on the ship displacement. There has been investigated the effect of the initial transverse metacentric height on the value of critical load acting on the ship deck at the bow which causes its capsizing. It can be seen that displacement of the application point of the resultant hydrodynamic forces from the midship line leads to a significant decrease of the critical load. The results of the undertaken studies testify to the need to take into account ship behavior in the developed head sea at the stage of design and regulation of ship stability, as well as during ship operation.

A Nonlinear Computational Model of Tethered Underwater Kites for Power Generation

The dynamic motion of tethered undersea kites (TUSK) is studied using numerical simulations. TUSK systems consist of a rigid winged-shaped kite moving in an ocean current. The kite is connected by tethers to a platform on the ocean surface or anchored to the seabed. Hydrodynamic forces generated by the kite are transmitted through the tethers to a generator on the platform to produce electricity. TUSK systems are being considered as an alternative to marine turbines since the kite can move at a high-speed, thereby increasing power production compared to conventional marine turbines. The two-dimensional Navier–Stokes equations are solved on a regular structured grid to resolve the ocean current flow, and a fictitious domain-immersed boundary method is used for the rigid kite. A projection method along with open multiprocessing (OpenMP) is employed to solve the flow equations. The reel-out and reel-in velocities of the two tethers are adjusted to control the kite angle of attack and the resultant hydrodynamic forces. A baseline simulation, where a high net power output was achieved during successive kite power and retraction phases, is examined in detail. The effects of different key design parameters in TUSK systems, such as the ratio of tether to current velocity, kite weight, current velocity, and the tether to kite chord length ratio, are then further studied. System power output, vorticity flow fields, tether tensions, and hydrodynamic coefficients for the kite are determined. The power output results are shown to be in good agreement with the established theoretical results for a kite moving in two dimensions.

Coupled response of liquid in a rigid cylindrical container equipped with an elastic annular baffle

The coupled dynamic response of liquid partially filled in a rigid cylindrical container equipped with an elastic baffle under lateral excitation has been studied. Firstly, the liquid domain is divided into four simple sub-domains so that the non-convex liquid domain changes to four convex sub-domains. Therefore, the liquid velocity potential in each liquid sub-domain has continuous boundary conditions of class C1. Based on the superposition principle, the analytical solution of the liquid velocity potential corresponding to each liquid sub-domain is obtained by means of the method of separation of variables. Then, the wet mode of the elastic annular baffle is expressed in terms of the dry-modal functions. The free surface wave equation, the interface equations and the coupled liquid-baffle vibration equations are all expressed in terms of the Fourier series along the liquid height and the Bessel series in the radial direction, respectively. The orthogonality among the coupled modes of the system is demonstrated. Finally, the total velocity potential function under lateral excitation is taken as the sum of the container potential function and the liquid perturbed potential function. The coupled dynamic response equation of the liquid-baffle system is established by combining the free surface wave equation and the governing vibration equation of the baffle. The surface wave height, the hydrodynamic pressure distribution, the resultant hydrodynamic force and moment for a container subjected to lateral excitations are discussed in detail.

Statistical analysis of the hydrodynamic forces acting on pipe bends in gas–liquid slug flow and their relation to fatigue

In this paper, the resultant hydrodynamic force (FR, where FR=Fx2+Fy2) acting on pipe bends will be discussed. A hypothesis that the peak (resultant) forces, FR,peak acting on pipe bends can be described by the normal distribution function will be tested, with the purpose of predicting the mean of the FR,peak (FR,mean) and the standard deviations of the FR,peak (FR, standard deviation) generated. This in turn allows prediction of the probability of the largest forces that occasionally occur at various flow rates. This information is vital in designing an appropriate support for the piping system, to cater the maximum force over a long period of operation. Besides, this information is also important in selecting a pipe material or material for connections suitable to withstand fatigue failure, by reference to the S–N curves of materials. In many cases, large numbers of response cycles may accumulate over the life of the structure. By knowing the force distribution, ‘cumulative damage’ can also be determined; ‘cumulative damage’ is another phenomenon that can cause fatigue, apart from the reversal maximum force.

Influence of material selection on the structural behavior of a wave energy converter

In the last decades, the world energy demand has raised significantly. Concerning this fact, wave energy should be considered as a valid alternative for electricity production. Devices suitable to harness this kind of renewable energy source and convert it into electricity are not yet commercially competitive. This paper is focused on the selection and analysis of different types of elastic materials and their influence on the structural behavior of a wave energy converter (WEC). After a brief characterization of the device, a tridimensional computer aided design (3D CAD) numerical model was built and several finite element analyses (FEA) were performed through a commercial finite element code. The main components of the WEC, namely the buoy, supporting cables and hydraulic cylinder were simulated assuming different materials. The software used needs, among other parameters, the magnitude of the resultant hydrodynamic forces acting upon the floating buoy obtained from a WEC time domain simulator (TDS) which was built based on the WEC dynamic model previously developed. The Von Mises stress gradients and displacement fields determined by the FEA demonstrated that, regardless of the WEC component, the materials with low Young's modulus seems to be unsuitable for this kind of application. The same is valid for the material yield strength since materials with a higher yield strength lead to a better structural behavior of WEC components because lower stress and displacement values were obtained. The developed 3D CAD numerical model showed to be suitable to analyze different combinations of structural conditions. They could depend of different combinations of buoy position and resultant hydrodynamic forces acting upon the buoy, function of the specific sea wave parameters found on the deployment site.

Sloshing of liquid in rigid cylindrical container with multiple rigid annular baffles: Lateral excitations

Sloshing response of liquid in a rigid cylindrical container with multiple annual rigid baffles subjected to lateral excitations has been studied. Firstly, the liquid domain is divided into several simple sub-domains so that the liquid velocity potential in each liquid sub-domain has continuous boundary conditions of class C1. Based on the superposition principle, the analytical solutions of the liquid velocity potential corresponding to each liquid sub-domain are obtained by means of the method of separation of variables. The total velocity potential function under lateral excitation is taken as the sum of the container potential function and the liquid perturbed potential function. The orthogonality among the modes of liquid velocity potential is demonstrated. The dynamic response equation of liquid is established by substituting the liquid potential functions into the free surface wave equation. Finally, the surface wave height, hydrodynamic pressure distribution, resultant hydrodynamic force and moment for a container subjected to harmonic and seismic lateral excitations are discussed in detail.

Sloshing of Liquid in Rigid Cylindrical Container with a Rigid Annular Baffle. Part II: Lateral Excitation

Sloshing response of liquid in a rigid cylindrical container with a rigid annual baffle subjected to lateral excitation has been studied. The complicated liquid domain is separated into several simple sub-domains by introducing the artificial interfaces. The analytical solutions of potential function corresponding to every sub-domain are obtained by using the method of separation of variables and the superposition principle. The total potential function under lateral excitation is taken as the sum of the container potential function and the liquid perturbed function. The expression of the liquid perturbed function is obtained by introducing the generalized coordinates. On the base of the natural frequencies and modes having been obtained by the sub-domain method, the orthogonality among the sloshing modes has been demonstrated. Substituting the potential functions into the free surface wave equation establishes the dynamic response equation of liquid. Then, the generalized coordinates are solved. The sloshing surface displacement, the hydrodynamic pressure distribution, the resultant hydrodynamic force and moment are discussed for the containers subjected to harmonic and seismic lateral excitation, respectively.

Sloshing of Liquid in Rigid Cylindrical Container with a Rigid Annular Baffle. Part II: Lateral Excitation

Sloshing response of liquid in a rigid cylindrical container with a rigid annual baffle subjected to lateral excitation has been studied. The complicated liquid domain is separated into several simple sub-domains by introducing the artificial interfaces. The analytical solutions of potential function corresponding to every sub-domain are obtained by using the method of separation of variables and the superposition principle. The total potential function under lateral excitation is taken as the sum of the container potential function and the liquid perturbed function. The expression of the liquid perturbed function is obtained by introducing the generalized coordinates. On the base of the natural frequencies and modes having been obtained by the sub-domain method, the orthogonality among the sloshing modes has been demonstrated. Substituting the potential functions into the free surface wave equation establishes the dynamic response equation of liquid. Then, the generalized coordinates are solved. The sloshing surface displacement, the hydrodynamic pressure distribution, the resultant hydrodynamic force and moment are discussed for the containers subjected to harmonic and seismic lateral excitation, respectively.

A non‐invasive dolphin telemetry tag: Computer design and numerical flow simulation

AbstractThe impact of devices attached to animals remains a challenge in telemetry studies of dolphins. It was hypothesized that the hydrodynamic design of a tag could provide stable attachment to the dorsal fin by means of resultant hydrodynamic force appearing when a dolphin is swimming. To verify this hypothesis the computer fluid dynamics (CFD) study of tag performance was carried out. A virtual model presenting authentic geometry of a dolphin with tag attached to the dorsal fin was constructed. The same model without tag was used as a reference object to calculate tag impact as regards drag, lift, and moments coefficients. Flow around the models was simulated for the range of velocities as well as the ranges of pitch and yaw angles. It was shown that in 33 of 35 CFD scenarios the streamlined shape of a tag generates the lift force that facilitates keeping a tag attached to the fin. Throughout the set of calculations the tag‐associated drag coefficient does not exceed 4%, which indicates low impact. Data obtained present a baseline for the further development of non‐invasive dolphin telemetry tags.

Time-Domain Hydrodynamic Forces on Rigid Dams with Reservoir Bottom Absorption of Energy

In this investigation, a two-dimensional time-domain closed-form mathematical model for the hydrodynamic forces on the upstream vertical face of a given rigid dam subjected to a specified horizontal ground motion accelerogram was developed. The model includes the absorption of energy at the elastic reservoir bottom, characterized by the impedance ratio of the sub-bottom materials with respect to water (α) . The formulated boundary-value problem is solved in Laplace’s domain and subsequently transformed back to the time domain. Response spectra for the hydrodynamic base shear force and overturning moment are constructed for extreme values of the parameter α . It is found that, frequently, including the solid-foundation elasticity in the reservoir model attenuates the resultant hydrodynamic forces on a rigid barrier, as compared to the results for the case of a rigid reservoir foundation. In this case, the elasticity of the sub-bottom materials constitutes an effective energy dissipating mechanism (radiatio...

Hybrid three-dimensional finite-difference and finite-element analysis of seismic wave induced fluid–structure interaction of a vertical cylinder

The two-dimensional finite-difference scheme has been extended to three dimensions to solve nonlinear hydrodynamic pressures and structural responses of a deformable, vertical and circular surface-piercing offshore cylinder during earthquakes. A complete three-dimensional analysis has been made with both the three-dimensional equations of motion and the simultaneous action of three components of ground acceleration included in the analysis. Not only the magnitude but also the direction of the acting ground motion can be varied with time. The dynamic response of a cylinder is approximated by the displacements in the fundamental modes of vibration. A comparison of the dynamic displacement of the cylinder with and without surrounding sea water has been made. The flexibility of the offshore cylinder can significantly increase the hydrodynamic pressures acting on cylinder faces, that is, the fluid–structure interaction is necessary in offshore cylinder analysis. Although the hydrodynamic pressure induced by the vertical ground acceleration of the El Centro 1979 earthquake is significant, the calculated structural dynamic response of a cylinder is very small and the corresponding resultant hydrodynamic force is almost nil. The hydrodynamic force induced by two-horizontal ground acceleration is about the same as that by three simultaneous components of ground acceleration. For a solid and stubbier circular cylinder, the vertical component of ground acceleration may be neglected.

Effects of Fin and Jet Vortex Generators on the Crossflow

The effect of fin and jet vortex generators on the crossflow separation of a submersible vehicle in a sideslip was studied. The sideslip orientation simulates the dominant features of a turning maneuver. The vortex generators are located on the top and bottom centerline of the body to improve turning performance by changing the crossflow separation and the resultant hydrodynamic forces. Oil-flow visualization and force and moment measurements are used as the primary diagnostics. The fins are found to be very effective in delaying crossflow separation, while the jets were not. In addition, the oil flows revealed the importance of locating vortex generators near the bow and the critical role a forward-mounted, low-aspect-ratio appendage plays in the near-body fluid dynamics. Overall the fins were found to be viable as a concept for flow control, while the jets employed were not. The concept of using vortex generators to control flow separation and thus forces and moments applies equally well to all bodies of revolution, including aircraft fuselages and missiles

Application of the Unsteady-Lifting-Surface Theory to the Study of Propeller-Rudder Interaction

The propeller-rudder interaction problem is studied by means of the unsteady-lifting- surface theory. Both surfaces of arbitrary geometry are immersed in a non-uniform flow- field (i.e., hull wake) of an ideal incompressible fluid. The boundary-value problem yields a pair of surface integral equations, the inversion of which is achieved by the so- called "generalized lift operator" technique, a new approach developed by the authors, in conjunction with the presently used "mode-collocation" method. The analysis demonstrates the mechanism of the interaction phenomenon by exhibiting the filtering effects of the propeller on the harmonic constituents of the wake which allow the rudder to be exposed only to the blade harmonic and multiples thereof. A numerical procedure adaptable to the CDC 6600 computer has been developed which furnishes information about (i) the steady and time-dependent pressure distribution on both lifting surfaces, and (ii) the resultant hydrodynamic forces and moments. A limited number of calculations exhibit the importance of some parameters such as axial clearance, number of blades, and harmonic components of the hull wake.

Comment on "Numerical Lifting Surface Theory-Problems and Progress"

N a recent paper, Landahl and Stark1 present a progress report on the status of numerical approaches to nonsteady lifting-surface theory for planar and nonplanar configurations as applied to the linearized thin-wing problem, with particular stress on the subsonic case. Over the past few years, in the course of studies adapting unsteady lifting-surface theory to marine propellers,24 Davidson Laboratory has developed a new method for the solution of the downwash surface integral equation. By proper expansion of the kernel function and introduction of the so-called lift operator/7 the chordwise integration is performed analytically with the additional advantage that the numerical solution is greatly simplified. These studies indicate that use of the generalized lift operator, which is in fact dictated by the nature of the integral equation itself, is a more accurate and rapid procedure than the usual numerical approaches for evaluating the steady and unsteady pressure distributions on lifting surfaces and resultant hydrodynamic forces. This technique has been used in Ref. 5, where the lifting surfaces are the blades of a marine propeller operating in nonuniform inflow, and in Ref. 6 for the case of a deeply submerged, flat, rectangular hydrofoil in steady flow. In Ref. 7, this new approach has been applied to several two-dimensional, unsteady airfoil problems and has yielded results identical to the known explicit solutions.