Showing papers on "Added mass published in 2015"

Force Balance Model for Bubble Rise, Impact, and Bounce from Solid Surfaces

Abstract: A force balance model for the rise and impact of air bubbles in a liquid against rigid horizontal surfaces that takes into account effects of buoyancy and hydrodynamic drag forces, bubble deformation, inertia of the fluid via an added mass force, and a film force between the bubble and the rigid surface is proposed. Numerical solution of the governing equations for the position and velocity of the center of mass of the bubbles is compared against experimental data taken with ultraclean water. The boundary condition at the air–water interface is taken to be stress free, which is consistent for bubbles in clean water systems. Features that are compared include bubble terminal velocity, bubbles accelerating from rest to terminal speed, and bubbles impacting and bouncing off different solid surfaces for bubbles that have already or are yet to attain terminal speed. Excellent agreement between theory and experiments indicates that the forces included in the model constitute the main physical ingredients to des...

Stabilized Lowest−Order Finite Element Approximation for Linear Three−Field Poroelasticity

Abstract: A stabilized conforming mixed finite element method for the three-field (displacement, fluid flux, and pressure) poroelasticity problem is developed and analyzed We use the lowest possible approximation order, namely piecewise constant approximation for the pressure and piecewise linear continuous elements for the displacements and fluid flux By applying a local pressure jump stabilization term to the mass conservation equation, we ensure stability and avoid pressure oscillations Importantly, the discretization leads to a symmetric linear system For the fully discretized problem we prove existence and uniqueness, an energy estimate, and an optimal a priori error estimate, including an error estimate for the divergence of the fluid flux Numerical experiments in two and three dimensions illustrate the convergence of the method, show its effectiveness in overcoming spurious pressure oscillations, and evaluate the added mass effect of the stabilization term

Radiation of waves by a cylinder submerged in water with ice floe or polynya

Abstract: The problems of radiation (sway, heave and roll) of surface and flexural-gravity waves by a submerged cylinder are investigated for two configurations, concerning; (i) a freely floating finite elastic plate modelling an ice floe, and (ii) two semi-infinite elastic plates separated by a region of open water (polynya). The fluid of finite depth is assumed to be inviscid, incompressible and homogeneous. The linear two-dimensional problems are formulated within the framework of potential-flow theory. The method of mass sources distributed along the body contour is applied. The corresponding Green’s function is obtained by using matched eigenfunction expansions. The radiation load (added mass and damping coefficients) and the amplitudes of vertical displacements of the free surface and elastic plates are calculated. Reciprocity relations which demonstrate both symmetry of the radiation load coefficients and the relation of damping coefficients with the far-field form of the radiation potentials are found. It is shown that wave motion essentially depends on the position of the submerged body relative to the elastic plate edges. The results of solving the radiation problem are compared with the solution of the diffraction problem. It is noted that resonant frequencies in the radiation problem correlate with those frequencies at which the reflection coefficient in the diffraction problem has a local minimum.

Numerical simulations of particle sedimentation using the immersed boundary method

Abstract: We study the settling of solid particles in a viscous incompressible fluid contained within a two-dimensional channel, where the mass density of the particles is greater than that of the fluid. The fluid-structure interaction problem is simulated numerically using the immersed boundary method, where the added mass is incorporated using a Boussinesq approximation. Simulations are performed with a single circular particle, and also with two particles in various initial configurations. The terminal particle settling velocity and drag coefficient correspond closely with other theoretical, experimental and numerical results, and the particle trajectories reproduce the expected behavior qualitatively. In particular, simulations of a pair of interacting particles similar drafting-kissing-tumbling dynamics to that observed in other experimental and numerical studies.

Bifurcation-based micro-/nanoelectromechanical mass detection

Abstract: This paper investigates an alternative mass-sensing technique based on nonlinear micro-/nanoelectromechanical resonant sensors. The proposed approach takes advantage of multi-stability and bifurcations of the hysteretic frequency responses of the electrostatically actuated resonator. For this purpose, a reduced-order model is considered. Numerical results show that sudden jumps in amplitude make the detection of a very small mass possible. Moreover, the limit of detection can be set with the value of the operating frequency. However, when operating at fixed frequency, the study of basins of attraction indicates that this bifurcation-based mass detection does not exhibit the expected robustness. A possible improvement is proposed, based on the reinitialization of the system by a forced jump down on the hysteretic response curve. Using a frequency sweep which varies slowly in sinusoidal form solves the reinitialization problem and enables automatic real-time detection. Finally, the added mass is located on the beam by using the resonance at the first two natural frequencies.

Frequency response of rectangular plate structures in contact with fluid subjected to harmonic point excitation force

Abstract: Numerical procedure for the forced vibration analysis of bottom and vertical rectangular plate structures in contact with fluid, subjected to internal point harmonic excitation force is developed. The procedure is based on the assumed mode method for free vibration calculation and mode superposition method for forced vibration analysis. Structural model covers Mindlin rectangular plates and stiffened panels. Lagrange's equation of motion is utilized to formulate the eigenvalue problem taking into account potential and kinetic energies of a plate and reinforcements, and fluid kinetic energy which is calculated according to potential flow theory, respectively. From the boundary conditions for the fluid and structure the fluid velocity potential is derived and it is utilized for the calculation of added mass using the assumed modes. The developed theoretical model and in-house code are verified with extensive numerical examples related to forced vibration of bare plates and stiffened panels in contact with different fluid domains. Comparisons of the results with those obtained by a general purpose finite element (FE) software confirmed high accuracy of the presented numerical procedure.

Numerical modeling of a spar platform tethered by a mooring cable

Abstract: Virtual simulation is an economical and efficient method in mechanical system design. Numerical modeling of a spar platform, tethered by a mooring cable with a spherical joint is developed for the dynamic simulation of the floating structure in ocean. The geometry modeling of the spar is created using finite element methods. The submerged part of the spar bears the buoyancy, hydrodynamic drag force, and effect of the added mass and Froude-Krylov force. Strip theory is used to sum up the forces acting on the elements. The geometry modeling of the cable is established based on the lumped-mass-and-spring modeling through which the cable is divided into 10 elements. A new element-fixed local frame is used, which is created by the element orientation vector and relative velocity of the fluid, to express the loads acting on the cable. The bottom of the cable is fixed on the seabed by spring forces, while the top of the cable is connected to the bottom of the spar platform by a modified spherical joint. This system suffers the propagating wave and current in the X-direction and the linear wave theory is applied for setting of the propagating wave. Based on the numerical modeling, the displacement-load relationships are analyzed, and the simulation results of the numerical modeling are compared with those by the commercial simulation code, ProteusDS. The comparison indicates that the numerical modeling of the spar platform tethered by a mooring cable is well developed, which provides an instruction for the optimization of a floating structure tethered by a mooring cable system.

Abrupt reduction of the critical temperature difference of a thermoacoustic engine by adding water

Abstract: The critical temperature difference (ΔTcri) that causes a thermoacoustic spontaneous oscillation is reduced by the presence of water in the working fluid of a thermoacoustic engine. This letter introduces the effects of two design parameters on the reduction of ΔTcri: one is the mass of water added as the working fluid and the other is the characteristic length of the stack, which is the heart of a thermoacoustic engine. The experimental results show that when the mass of added water exceeds the threshold value, ΔTcri decreases abruptly; however, the decreased ΔTcri changes slightly with further increase in the added mass. Moreover, the characteristic length of the stack was found to have little effect on ΔTcri when water is added. These results provide a design guide for a thermoacoustic engine that includes water as the working fluid.

Generalized Langevin equation with hydrodynamic backflow: Equilibrium properties

Abstract: a b s t r a c t We review equilibrium properties for the dynamics of a single particle evolving in a visco- elastic medium under the effect of hydrodynamic backflow which includes added mass and Basset force. Arbitrary equilibrium forces acting upon the particle are also included. We discuss the derivation of the explicit expression for the thermal noise correlation function that is consistent with the fluctuation-dissipation theorem. We rely on general time- reversal arguments that apply irrespective of the external potential acting on the particle, but also allow one to retrieve existing results derived for free particles and particles in a harmonic trap. Some consequences for the analysis and interpretation of single-particle tracking experiments are briefly discussed.

Stability and Nonlinear Vibrations of Closed Cylindrical Shells Interacting with a Fluid Flow (Review)

Abstract: Results of systematic study of the stability and nonlinear vibrations of thin cylindrical shells interacting with a fluid flow are presented. The main patterns of dynamical deformation of shells during divergence and flutter are considered. The effect of different structural features (initial geometrical imperfections, added concentrated masses, boundary conditions, longitudinal and transverse static loads) on the critical (divergence and flutter) velocities is analyzed. The amplitude–frequency response of shells to external periodic radial loads and internal periodic pressure caused by small pulsations of the fluid velocity is determined. A method is proposed to solve nonlinear problems describing nonstationary processes of passing resonance zones by shells interacting with the fluid flow

Effects of Dynamic Fluid-Structure Interaction on Seismic Response of Multi-Span Deep Water Bridges Using Fragility Function Method

Abstract: This paper employs the fragility function method to study the effects of dynamic fluid-structure interaction on seismic response of multi-span deep water bridges. Currently, two approaches are widely used to study the dynamic fluid-structure interaction effect of structures: the analytical ‘added mass’ method and full-scale two- or three dimensional finite element modeling. This paper offers a computationally economical yet adequate procedure. In this procedure, Morrison equation is employed to calculate the added mass for piles and columns, and a water-foundation coupling system is modeled to calculate the added mass for pile cap. In this water-foundation coupling system, a pile beam-element was adopted to avoid the thorough water domain modeling. A typical multi-span continuous composite girder bridge in China lying in deep water environment is used as a case study. The uncertainty of modeling parameters is considered using an experimental design method. The limit state functions are derived through a s...

Resonant frequency of mass-loaded membranes for vibration energy harvesting applications

Abstract: Vibration based energy harvesting has been widely investigated to target ambient vibration sources as a means to generate small amounts of electrical energy. While cantilever-based geometries have been pursued frequently in the literature, here membrane-based geometries for the energy harvesting device is considered, with the effects of an added mass and tension on the effective resonant frequency of the membranes studied. An analytical model is developed to describe the vibration response for a circular membrane with added mass structure, with the results closely agreeing with finite element simulation in ANSYS. A complementary study of square membranes loaded with a central mass shows analogous behavior. The analytical model is then used to interpret the experimentally observed shift in resonance frequency of a circular membrane with a proof mass. The impact of membrane tension and central proof mass on the resonant frequency of the membrane suggests that this approach may be used as a tuning method to optimize the response of membrane-based designs for maximum power output for vibration energy harvesting applications.

Mesoscale Flow Structures and Fluid–Particle Interactions

Abstract: During the last two decades, the insight has gradually grown—thanks to advances in both experimental techniques and computational simulation tools—that many dispersed two-phase flows are dominated by dynamic mesoscale coherent structures in which particles, bubbles, or drops organize themselves. Evidence from experiments, hydrodynamic analyses, and computational simulations on the presence and dynamics of such structures, strands, and clusters is presented. Their origin being less well understood, the general consensus is that fluid–particle interaction forces play a dominant role in bringing and keeping the dispersed-phase particles together. This chapter then revisits the topic of the fluid–particle interaction in all of its aspects and constituents such as single-particle steady-state drag, added mass, Basset force, lift, and particle rotation, while also the effects of particle and fluid acceleration and carrier phase turbulence are reviewed. The common practice of linearly adding the various correlations obtained for very specific canonical cases is to be rejected for other flow conditions than just creeping flow. Particular attention is paid to the way the pertinent fluid–particle interaction correlations are utilized in computational simulations of both the Euler–Lagrange (point-particle tracking) and Euler–Euler (two-fluid) type, where a distinction is made between Reynolds-averaged Navier–Stokes-based simulations and large-eddy simulations. Tracking a particle immersed in a 3D turbulent fluid in the presence of other particles by means of the steady-state drag force is a dubious approach. Undoubtedly, the best representation of the fluid–particle interaction can be obtained from periodic-box direct numerical simulations.