Showing papers on "Added mass published in 1997"

The collision rate of particles in turbulent flow

Abstract: A review of previous derivations of particle collision rates in turbulent fluid flow shows that these are applicable only to limited cases. A more general derivation is given, taking into account the effects of the inertia of the particles and the difference in densities of the fluid and the particles. A universal solution for the relative velocity of two particles due to turbulent accelerations in a gaseous or liquid system is presented. In gaseous systems the acceleration mechanism becomes predominant at particle sizes far below the Kolmogorov microscale of turbulence. In liquid systems, the particle inertial and added mass effects become important above the Kolmogorov microscale. Here the particle collision rate cannot be estimated from the fluid turbulent velocity fluctuations only.

Vibration type measuring instrument

Abstract: A vibration type measuring instrument measures at least one of density and mass flow rate of a fluid in a straight measurement pipe by vibrating the pipe. The vibration type measuring instrument comprises the pipe; a sensor for detecting the vibration of the pipe; and a signal processing circuit for obtaining the resonant angular frequency ω and axial force T based on the detection signal of the sensor, and obtaining the density ρw of the fluid flowing through the pipe using the obtained resonant angular frequency ω and axial force T. The density ρw is obtained by the following equation (E1). ##EQU1## (E: the Young's modulus of the pipe, I: a cross-sectional secondary moment of the pipe, Si: a cross-sectional area of the hollow portion of the pipe, ρt: a density of the pipe, St: the actual cross-sectional area of the pipe, L: the length in the axial direction of the pipe, x: a position in the axial direction of the pipe, y: a vibration amplitude of the pipe at position x, n: a number of masses added to the pipe, mk: a mass of a k-th added mass, and yk: a vibration amplitude of the k-th added mass).

Dynamic Modeling and Optimal Control of Rotating Euler-Bernoulli Beams

Abstract: The nonlinear integro-differential equations, describing the transverse and rotational motions of a nonuniform Euler-Bernoulli beam with end mass attached to a rigid hub, are derived. The effects of both the linear and nonlinear elastic rotational couplings are investigated. The linear couplings are exactly accounted for in a decoupled Euler-Bernoulli beam model and their effects on the eigensolutions and response are significant for a small ratio of hub-to-beam inertia. The nonlinear couplings with a resultant stiffening effect are negligible for small angular velocities. A discretized model, suitable for the study of large angle, high speed rotation of a nonuniform beam, is presented. The optimal control moment for simultaneous vibration suppression of the beam at the end of a prescribed rotation is determined. Influences of the nonlinearity, nonuniformity, maneuver time, and inertia ratio on the optimal control moment and system response are discussed.

Flexural Vibration of Cylindrical Shells Partially Coupled With External and Internal Fluids

Abstract: In this paper, the free flexural vibrations of a partially fluid-loaded simply supported circular cylindrical shell are studied; the fluid is assumed to be inviscid and to present a free-surface parallel to the shell axis. The presence of external and internal fluids are both studied and the problem for incompressible and compressible fluid are both discussed by using the added virtual mass approach. Circumferential dependence of displacement is extended in a Fourier series. The maximum potential energy of the cylinder is evaluated using a sum of reference kinetic energies of the shell vibrating in vacuum; this fact allows the proposed method to be independent from the theory of shells used. Then, the Rayleigh quotient for fluid-shell coupled vibration is formulated and minimized to obtain the Galerkin equation whose solution gives the natural frequencies and mode shapes. Numerical computations are performed to obtain the modal characteristics as functions of the level of water in contact with the shell in the range of good accuracy of the theory, that is around the half-wet shell level. Results for both a shell partially surrounded and filled with water are obtained and compared.

Dynamic deflection of a cracked beam with moving mass

Abstract: An analytical method along with the experimental verification have been utilized to investigate the vibrational behaviour of a cracked beam with a moving mass. The local stiffness matrix is taken into account when analysing the cracked beam. The Runge—Kutta method has been used to solve the differential equations involved in analysing the dynamic deflection of a cantilever beam.

An analysis of particle saltation dynamics

Abstract: A two-dimensional particle saltation model for unidirectional flow is applied to simulate the motion of single particles. The equations of motion include added mass, gravity, drag, shear lift, Basset history, and Magnus or spin lift forces. A sensitivity analysis is performed on the forces, initial lift-off speeds and angles, and for different size particles. The Magnus lift force is found to have a significant effect on a particle's trajectory for coarse sand sized and larger particles. The shear lift and Basset history forces cause particles to saltate farther. Most of the forces vary with particle size. The model predictions compare favorably to observations if appropriate initial conditions are assumed.

Added mass of a disc accelerating within a pipe

Abstract: The flow of inviscid fluid around a disc in a pipe is computed, and the results are used to determine the added mass of the accelerating disc in the frame in which the mixture velocity is zero. The added mass of an array of discs spaced at regular intervals along the pipe is then computed, and is related to the pressure gradient along the pipe. Some flow profiles are also presented. The results show that the added mass per particle increases as the pipe diameter is reduced relative to the particle size. The added mass per particle decreases as the number density of particles increases, but the added mass per unit length of the pipe nevertheless increases. Thus an increase of either the particle size or number density leads to a tighter coupling between the liquid and the particles; this result should hold for other particle shapes and configurations. Results are also presented for the drift, i.e., the displacement of fluid particles caused by the motion of an isolated disc along the axis of the pipe. If the diameter of the pipe is sufficiently small, the added mass of the disc is modified from that in unbounded fluid, and the background drift at the walls of the pipe can no longer be estimated from the added mass of the disc.