Search Results (7)

Explicit expressions for bubbly Taylor–Couette flow fields are rarely available in the literature. The present work aims to derive explicit expressions for bubble velocity fields in laminar gas–liquid Taylor–Couette flow between two rotating coaxial cylinders with the buoyancy effect on gas bubbles. It is assumed that the angular velocity of the rotating cylinder(s) is moderately low and the bubble radius is relatively small so that the Stokes number of bubbles is small enough and, consequently, the radial bubble migration is ignorable and the bubble volume fraction can be treated as being constant in a limited period of time. Explicit leading-order solutions are derived for the spiral rising bubble velocity field in the dilute limit. Unlike the heavy particles dominated by the Stokes drag, the added mass and lift forces are shown to be relevant for the bubbly flows. The radial bubble velocity field is discussed in detail for several cases of major interest under the condition that the added mass coefficient is equal to the lift force coefficient, as assumed by some authors in the literature. Our results show that the radial-to-azimuthal velocity ratio of bubbles is linearly proportional to the Stokes number of bubbles and can be controlled by the angular velocity of the rotating cylinder(s) and the bubble radius so that the assumption of ignorable radial bubble migration can be reasonably justified within a limited period of time (for example, in the first few tens of revolutions of the rotating cylinder(s)). Full article

The classic second-order Rayleigh equation governs the linear stability of single-phase inviscid plane flows, and its extension to two-phase inviscid plane flows with a crossflow of another fluid remains to be investigated. The present work studies the linear stability of steady uniform inviscid two-phase flow in a horizontal channel with gas bubbles injected from the lower wall and removed from the upper wall. An extended fourth-order Rayleigh equation with constant coefficients is derived for the linear stability of the two-phase uniform inviscid plane flow with the bubble crossflow injected at the bubble terminal velocity. Our analytical results show that the uniform inviscid plane flow driven by the bubble crossflow is linearly unstable with rapidly growing disturbances in the absence of the lift force. On the other hand, when the positive lift force coefficient is nearly equal to the added mass coefficient, the uniform inviscid plane flow driven by the bubble crossflow is linearly stable to the admissible disturbances consistent with the bubble-injection boundary conditions. These analytical results reveal the destabilizing effect of the bubble crossflow and confirm the stabilizing effect of the positive lift force on the inviscid plane flows, which could stimulate further research interest in the qualitatively different roles of the bubble crossflow and the lift force in the stability of inviscid plane flows as compared to viscous plane flows. Full article

The classical wake oscillator model is capable of predicting the vortex-induced vibration response of a cylinder at high mass-damping ratios, but it fails to perform satisfactorily at low mass-damping ratios. A modified wake oscillator model is presented in this paper. The modification method involves analyzing the variation law of the add mass coefficient of the cylinder versus reduced velocity and expressing the reference lift coefficient C_L0 as a function of the add mass coefficient. The modified wake oscillator model has been demonstrated to have better accuracy in capturing maximum amplitudes and flow velocity at low mass-damping ratios. However, the modified model at present form is unable to accurately predict the vortex-induced vibration response at high damping ratios. The purpose of this paper is to propose a new modification idea. In order to achieve better results when applying this modification idea to particular objects, it may be necessary to first understand the response law of these kinds of objects. Full article

To understand the nonlinear interaction between unsteady aerodynamic forces and the kinematics of structures, we theoretically and numerically investigated the characteristics of lift coefficients produced by a flapping thin flat plate controlled by the rotation axis position. The flat plate was placed in a 2-D incompressible flow at a very low Reynolds number (Re = 300). We showed that the behavior of the unsteady aerodynamic forces suggests the existence of a limit cycle. In this context, we developed a Reduced Order Model (ROM) by resolving the modified van der Pol oscillator using the Taylor development method and computational fluid dynamics (CFD) solutions. A numerical solution was obtained by integrating the differential equation of the modified van der Pol oscillator using the fourth-order Runge–Kutta method (RK4). The model was validated by comparing this solution with the reformulated equation of the added mass lift coefficient. Using CFD and ROM solutions, we analyzed the dependency of the unsteady lift coefficient generation on the kinematics of the flapping flat plate. We showed that the evolution of the lift coefficient is influenced by the importance of the rotation motion of the Leading Edge (LE) or Trailing Edge (TE), according to the position of the rotation axis. Indeed, when the rotation axis is moved towards the LE, the maximum and the minimum values of the lift coefficient are proportional to the downward and upward motions respectively of the TE and the rotation axis. However, when the rotation axis is moved towards the TE, the maximum and the minimum values of the lift coefficient are proportional to the downward and upward motions respectively of the LE and the rotation axis. Full article

This paper presents the calculation of the hydrodynamic forces exerted on an oscillating circular cylinder when it moves perpendicular to its axis in infinitely deep water covered by compressed ice. The cylinder can oscillate both horizontally and vertically in the course of its translational motion. In the linear approximation, a solution is found for the steady wave motion generated by the cylinder within the hydrodynamic set of equations for the incompressible ideal fluid. It is shown that, depending on the rate of ice compression, both normal and anomalous dispersion can occur in the system. In the latter case, the group velocity can be opposite to the phase velocity in a certain range of wavenumbers. The dependences of the hydrodynamic loads exerted on the cylinder (the added mass, damping coefficients, wave resistance and lift force) on the translational velocity and frequency of oscillation were studied. It was shown that there is a possibility of the appearance of negative values for the damping coefficients at the relatively big cylinder velocity; then, the wave resistance decreases with the increase in cylinder velocity. The theoretical results were underpinned by the numerical calculations for the real parameters of ice and cylinder motion. Full article

This work experimentally investigated the performance of hydrodynamic forces on a semi-submerged cylinder under an oscillatory flow. To generate the equivalent oscillatory flow, the semi-submerged cylinder is forced to oscillate in several combinations of different periods and amplitudes. The mean downward lift force was observed to be significant and the fluctuating lift forces show dominant frequency is twice that of oscillatory flow and amplitude that is the same as the mean lift force. Based on this main hydrodynamic feature, a novel empirical prediction formula for the lift forces on semi-submerged cylinder under oscillatory flow is proposed where the lift forces expression is proportional to the square of oscillatory flow velocity. This novel empirical formula directly assigns the fluctuating lift force with frequency twice of oscillatory flow and the amplitude that is the same as the mean lift force. This assignment of empirical lift force formula reduces parameters required to determine a dynamic lift force but is demonstrated to well predict the fluctuating lift force. The lift coefficient can reach 1.5, which is larger than the typical value 1.2 of the drag coefficient for a fully submerged cylinder with infinite depth. Moreover, relationships among hydrodynamic coefficients, Keulegan-Carpenter (KC) number, Stokes number and Froude number are studied. With the increase of KC number, the Froude number has a more significant influence on the distribution of hydrodynamic coefficients. As Froude number is increasing, the drag coefficient shows a nonlinear decay (KC < 20) but a linear increase (KC > 20), while the added mass coefficients show a nonlinear (KC < 20) and a linear (KC > 20) increase trend. The present work can provide useful references for design of the relevant marine structures and serve as the useful guideline for future research. Full article

Laboratory tests were carried out to investigate the cross-flow (CF) dynamic responses and hydrodynamic forces of a flexible pipe that subjected to vortex-induced vibration (VIV). The pipe had a critical mass ratio of 0.54 and an aspect ratio of 181.8. The uniform flow environment was realized by towing the pipe along a towing tank. The towing velocity ranged from 0.1–1.0 m/s with an interval of 0.05 m/s. Two axial pre-tension cases (200 N and 300 N) were enforced. The structural strains were measured at seven positions evenly distributed along the pipe. Then a modal analysis method was applied to reconstruct the displacement responses. It is revealed that the maximum CF displacement amplitude reached up to 2.18 pipe diameter and the strain response exhibited higher harmonic components. The CF dominant frequency gradually rises with the increase of reduced velocity and up to a three-order vibration mode can be observed. In addition, mean drag coefficient, lift force coefficient and added mass coefficient were also calculated to further investigate the fluid force feature of a low mass flexible pipe undergoing VIV. Full article