Total Fluid Force Research Articles

Gravity effect on water entry during an early stage

Abstract

Flow-induced vibration of a near-wall circular cylinder with a small gap ratio at low Reynolds numbers

Numerical simulations of flow-induced vibration of a near-wall circular cylinder with a small gap (e) to diameter (D) ratio (e∕D=0.1) at low Reynolds numbers 55≤Re≤200 (based on the incoming velocity U∞ and the diameter D) are performed using a finite volume method by means of modified OpenFOAM codes. As the cylinder is very close to the wall, remeshing is regularly applied during the body oscillation to avoid over-distortion of the grid. A model to account for the collision of the cylinder with the wall is adopted, in which when the gap between the cylinder and the wall is smaller than a critical value, the direction of its velocity is reversed. Simulations are made for low mass ratio, relevant to the cases in hydrodynamics. The results show the anti-clockwise vortices in the wake are suppressed by the shear flow in the boundary layer near the wall and only one single vortex (“1S”) is periodically shed downstream. The unchanged vortex shedding mode indicates that the motion amplitude generally increases with the reduced velocity first and then decreases after reaching a peak, and there is no obvious hysteretic transition. As Re increases, the largest root-mean-square of the in-line displacements Xrms and the mean transverse amplitude AY increase, and the reduced velocity U∗ corresponding to the largest vibration amplitude decreases. The collision with the wall slightly increases the vibration frequency. In addition, potential and vortex force components in the total fluid force are computed and further investigated. The results indicate that the total fluid force is dominated by the vortex force component and that other harmonic modes of the vortex force coefficient CL,V (or the total fluid force coefficient CL,T) except the first one becomes more significant and their dominant mode will shift to the second harmonic mode as the dominant vibration frequency fY∗ becomes close to the natural frequency in still water fn∗ (or the natural frequency in vacuum fvac∗), the vibration displacement Y(t) is very much dominated by the first mode. Moreover, it is found that the wall has significant effect on the equivalent stiffness of the cylinder at e∕D=0.1. The largest vibration amplitudes appear at larger frequencies than the natural frequency at all Re. The equation for the equivalent stiffness proposed in the present study is able to rectify the ratio of the vibration frequency to the natural frequency at resonance.

Cavity formation on the surface of a body entering water with deceleration

The two-dimensional water entry of a rigid symmetric body with account for cavity formation on the body surface is studied. Initially the liquid is at rest and occupies the lower half plane. The rigid symmetric body touches the liquid free surface at a single point and then starts suddenly to penetrate the liquid vertically with a time-varying speed. We study the effect of the body deceleration on the pressure distribution in the flow region. It is shown that, in addition to the high pressures expected from the theory of impact, the pressure on the body surface can later decrease to sub-atmospheric levels. The creation of a cavity due to such low pressures is considered. The cavity starts at the lowest point of the body and spreads along the body surface forming a thin space between a new free surface and the body. Within the linearised hydrodynamic problem, the positions of the two turnover points at the periphery of the wetted area are determined by Wagner’s condition. The ends of the cavity’s free surface are modelled by the Brillouin–Villat condition. The pressure in the cavity is assumed to be a prescribed constant, which is a parameter of the model. The hydrodynamic problem is reduced to a system of integral and differential equations with respect to several functions of time. Results are presented for constant deceleration of two body shapes: a parabola and a wedge. The general formulation made also embraces conditions where the body is free to decelerate under the total fluid force. Contrasts are drawn between results from the present model and a simpler model in which the cavity formation is suppressed. It is shown that the expansion of the cavity can be significantly slower than the expansion of the corresponding zone of sub-atmospheric pressure in the simpler model. For forced motion and cavity pressure close to atmospheric, the cavity grows until almost complete detachment of the fluid from the body. In the problem of free motion of the body, cavitation with vapour pressure in the cavity is achievable only for extremely large impact velocities.

Non-linear hydrodynamics of thin laminae undergoing large harmonic oscillations in a viscous fluid

Smoothed Particle Hydrodynamics is implemented to study the motion of a thin rigid lamina undergoing large harmonic oscillations in a viscous fluid. Particularly, the flow physics in the proximity of the lamina is resolved and contours of non-dimensional velocity, vorticity and pressure are presented for selected oscillation regimes. The computation of the hydrodynamic load due to the fluid–structure interaction is carried out using Fourier decomposition to express the total fluid force in terms of a non-dimensional complex-valued hydrodynamic function, whose real and imaginary parts identify added mass and damping coefficients, respectively. For small oscillations, the hydrodynamic force reflects the harmonic nature of the displacement, whereas multiple harmonics are observed as both the amplitude and frequency of oscillation increase. We propose a novel formulation of hydrodynamic function that incorporates added mass and damping coefficients for a thin rigid lamina spanning large amplitudes in viscous fluids in a broad range of the oscillation frequencies. Results of the simulations are validated against numerical and experimental works available in the literature in addition to theoretical predictions for the limit case of zero-amplitude oscillations.

A Simplified Pump Tower Approach for Realistic CFD Simulation of Sloshing in LNG Tanks

The complexity of the sloshing analysis for liquefied natural gas carriers can be reduced by neglecting the pump tower. The validity of this assumption is examined by studying the effect of the pump tower, located near the aft bulkhead of a typical LNG tank on the sloshing flow evolution. Results are compared for surge-induced sloshing in a rectangular tank with pump tower to that without such an obstruction. A commercial flow solver is used to solve the unsteady Reynolds Averaged Navier Stokes equations for an inhomogeneous multiphase flow. Initial validation of the sloshing flow uses the experimental data of Hinatsu. It was found that a simplified pump tower consisting of a single vertical tube was suitable to capture the effect of the pump tower without the necessity of discretising the fine geometric detail of the pump tower structure. A suitable size for the simplified tower diameter was found using the total fluid force on a real pump tower in a steady flow for a similar range of Reynolds Number. This reduces the required mesh size by an order of magnitude. Although it is found that the effect of the pump tower on the overall force levels is small reductions of local impact pressures of up to 50% are observed and the sloshing flow develops a phase lag compared to the unobstructed tank.

인공어초 주변의 흐름장에 관한 수치해석

This study investigated the fluid force acting on an artificial reef and the scour pattern at the bottom of the artificial reef in a steady-flow field using the finite difference method (Flow-3D). The structure was tetragonal in shape, like similar objects found in nature. The numerical analysis showed that the hydrodynamic characteristics and incipient scouring pattern matched natural phenomena. The velocity distribution around the tetragon was symmetric and wake occurred inside the tetragon and behind the bottom of the tetragon. The length of the recirculation flow behind the tetragon for each velocity was about 4-5 cm and the magnitude of the recirculation flow inside the tetragon generally increased with the Reynolds' number, although it decreased slightly for Reynolds' numbers from 11,000 to 12,000. In addition, the total fluid force acting on the tetragon increased with the inflow velocity, although the increment was smaller when the velocity exceed 18 cm/sec. The incipient pattern for the scouring of sediment matched the natural phenomenon.

Fluid Force Acting on a Particle Falling toward a Wall

A direct simulation of the falling motion of an immersed solid particle toward a wall is performed to investigate the mechanics of hydrodynamic collision of particles. The time-dependent boundary-fitted coordinate system is applied to the calculation of fluid flow around solid bodies. The fluid force acting on the particle is calculated by integrating the surface stress without any models. The obtained particle motion is compared with the corresponding experiment and theoretical analysis. The results of the numerical simulation, the experiment and the analysis using theoretical models agree quantitatively with respect to the falling motion of the particle. When the particle falls toward the wall, fluid force due to the squeeze of fluid in the gap is increased and prevents the particle from approaching the wall. As a result, the particle is decelerated and the fluid force caused by the unsteady motion of the particle is significantly increased. The numerical results reveal that the total fluid force acting on the particle can be explained by the sum of steady and unsteady fluid forces.

Experimental Behavior of a Short Cylindrical Squeeze Film Damper Executing Circular Centered Orbits

The experimentally determined behavior of a short radial squeeze-film damper with no end seals, executing circular centered orbits, is discussed. Accurate circular orbits were achieved, for ε values in the range 0.1 and 0.8, by using digitally generated signals to drive two electromagnetic shakers. Radial and tangential dynamic fluid force coefficients were estimated from measurements of the applied forces and the orbit radii, using a simple algebraic method. Cavitation was found to occur when ε exceeded 0.5, at large orbit frequencies, and was the cause of an observed jump-up phenomenon. The magnitude of an oil stiffness effect, previously reported by the authors and confirmed by the present results, was found to depend significantly on the oil supply pressure. Its contribution to the total fluid force was of the same order as that from fluid inertia, in the case of small orbits (ε ≪ 1).

Forces and Moments Due to Combined Motion of Conical and Cylindrical Whirls for a Long Seal

The mutual interaction effects of cylindrical and conical whirl on the dynamic fluid forces and moments, which act on a long annular seal, were studied experimentally. A whirling motion composed of cylindrical and conical whirls is actuated by intentionally giving the phase difference between the seal exit and inlet whirling movements. This whirling motion is believed to generate during actual pump running. The experiment was conducted by changing the phase difference, at various rotor speeds and with a pressure difference between the seal inlet and exit. The result of this study revealed that fluid forces and moments are greatly dependent on the phase difference of the whirl, namely the long seal has a significant coupling between displacements and rotations. Furthermore, dynamic fluid forces and moments were derived theoretically, assuming that total fluid force acting on the rotor could be determined by superposing fluid forces due to conical and cylindrical whirling movements. It was confirmed that the experimental results moderately agree with the theoretical values, if the rotor and seal are set in concentric alignment, the principle of superposition becomes applicable.

Experimental study of the dynamic characteristics of a long annular seal. Fluid force due to conical and cylindrical whirl.

This paper describes a study of dynamic fluid forces acting on a long seal where the rotating motions of a rotor were composed of conical and cylindrical whirl. Theoretical fluid forces were determined using a bulk-flow model to obtain the rotor-dynamic coefficients of the long seal. The experiment was conducted under changing phase difference between the seal inlet and outlet whirling movements. The tangential and restitutional forces were obtained from the measured dynamical fluid forces at various rotor speeds, whirling amplitude and with different pressure drops across the long seal. Then these measured values were compared with the theoretical finite-length solution and were found to be compatible. As a result, the dynamic fluid forces are largely affected by the whirling phase difference between the seal inlet and outlet. It was confirmed that the total fluid force acting on the rotor is given by the sum of two fluid forces due to the cylindrical whirl and due to the conical whirl, when the rotor and the outer cylinder are set in concentric alignment.

Influence of wave-current interactions on fluid force

Influence of wave-current interactions on fluid force on a single cylinder and on two cylinders in tandem is examined. Quantities obtained are spectra of fluid force on elements, total fluid force and its statical moment. Comparisons are made of the cases in which wave-current interactions are considered and ignored. It is shown that interactions affect spectra of element force and statical moment more than do total force spectrum. For two cylinders in tandem, for cylinder spacings, current conditions and frequency range of practical interest, the effect of interactions is slightly reduced.