Investigation on mechanism of critical cavitating flow in liquid jet pumps under operating limits

The critical cavitating flow in liquid jet pumps under operating limits is investigated in this paper. Measurements on the axial pressure distribution along the wall of jet pumps indicate that two-phase critical flow occurs in the throat pipe under operating limits. The entrained flow rate and the distribution of the wall pressure upstream lowest pressure section does not change when the outlet pressure is lower than a critical value. A liquid-vapor mixing shockwave is also observed under operating limits. The wave front moves back and forth in low frequency around the position of the lowest pressure. With the measured axial wall pressures, the Mach number of the two-phase cavitating flow is calculated. It's found that the maximum Mach number is very close to I under operating limits. Further analysis infers a cross-section where Mach number approaches to I near the wave front. Thus, the liquid-vapor mixture velocity should reach the local sound velocity and resulting in the occurrence of operating limits.

Nonlinear Dynamic Responses of Tension Leg Platform with Slack-Taut Tether

The slack-taut state of tether is a particular Averse circumstance, which may influence the normal operation stale of tension leg platform (TLP). The dynamic responses of TLP with slack-taut tether are studied with consideration of several nonlinear factors introduced by large amplitude motions. The time histories of stresses of tethers of a typical TLP in slack-taut state are given. In addition, the sensitivities of slack to stiffness and mass are investigated by varying file stiffness of tether and mass of TLP. It is found that slack is sensitive to the mass of TLP. The critical culled surfaces (over which indicates the slack) for the increase of mass are obtained.

Some modified bifurcation problems with application to imperfection sensitivity in buckling

The branching theory of solutions of certain nonlinear elliptic partial differential equations is developed, when the nonlinear term is perturbed from unforced to forced. We find families of branching points and the associated nonisolated solutions which emanate from a bifurcation point of the unforced problem. Nontrivial solution branches are constructed which contain the nonisolated solutions, and the branching is exhibited. An iteration procedure is used to establish the existence of these solutions, and a formal perturbation theory is shown to give asymptotically valid results. The stability of the solutions is examined and certain solution branches are shown to consist of minimal positive solutions. Other solution branches which do not contain branching points are also found in a neighborhood of the bifurcation point.

The qualitative features of branching points and their associated nonisolated solutions are used to obtain useful information about buckling of columns and arches. Global stability characteristics for the buckled equilibrium states of imperfect columns and arches are discussed. Asymptotic expansions for the imperfection sensitive buckling load of a column on a nonlinearly elastic foundation are found and rigorously justified.