Twin Cavities Research Articles

Numerical prediction of the hydrodynamic performance of a centrifugal pump in cavitating flows

AbstractA computational modelling for the prediction of the hydrodynamic performance of a centrifugal pump in cavitating flows is presented in this paper. The cavitation model is implemented in a viscous Reynolds‐averaged Navier–Stokes solver. The cavity interface and shape are determined using an iterative procedure matching the cavity surface to a constant pressure boundary. The pressure distribution, as well as its gradient on the wall, is taken into account in updating the cavity shape iteratively. Numerical validation of the present cavitation model and algorithms is performed on different headform/cylinder bodies for a range of cavitation numbers through comparing with the experimental data. Flow characteristics trends associated with off‐design flow and twin cavities in the blade channel are observed using the presented cavitation prediction. The rapid drop in head coefficient at low cavitation number is captured for two different flow coefficients. Local flow field solution illustrates the principle physical mechanisms associated with the onset of breakdown. Copyright © 2006 John Wiley & Sons, Ltd.

The Placenta

The human placenta is a discoid organ that has a hemochorial relationship with the mother. That is to say, the trophoblast that covers the villi is in direct contact with the maternal blood. Transfer of substances has to traverse the syncytiotrophoblast, cytotrophoblast, villous basement membrane, fetal capillary bed, and its endothelium. Although the placenta is the most available tissue, it is the least thoroughly investigated organ, and many aspects of its control still are unknown. Especially deficient is our knowledge of the genetic control of its many functions. The placenta also has a different imprinting pattern (paternal imprinting) from that of the embryo. The prevailing sentiment is that once delivery has occurred, it is a superfluous tissue that only needs to be discarded. There are many reasons, however, that knowledge of placental pathology can aid materially in a better understanding of newborns who have anomalies or neonatal problems. Further, a detailed examination of the placenta at birth can provide a better insight into prenatal life and its possible disturbances than is possible from notes in the history of the patient. The shape of the placenta is extremely variable (Fig. 1), probably due to placental location, its interaction with the endometrium, and uterine shape. The placenta implants anywhere in the uterus, but most commonly, it is in an anterior or posterior location. Much less often it is on the fundus. The shape often can be understood best by considering the history of its implantation. The reason for a specific shape can be derived further from the frequently aberrant shapes of twin placentas where competition for space in the uterus, a phenomenon that has been termed “trophotropism,” can be inferred to have existed. This term was used initially in attempts to explain the placental features in the uncommon event of a placenta …

Comparative Supramolecular Chemistry of Coronene, Hexahelicene, and [18]Crown-6: Hydrated and Solvated Molecular Complexes of [18]Crown-6 with 5-Hydroxyisophthalic Acid and Related Di- and Tricarboxylic Acids

The outer rim of C-H bonds of coronene (COR) and hexahelicene (HEL) is similar to that of the crown conformation of [18]crown-6 (CRO), which is exploited for crystal engineering of molecular complexes of CRO. However, although CRO does form the adduct (TMA)2 x CRO x (H2O)2 (TMA = trimesic acid = 1,3,5-benzenetricarboxylic acid), its structure does not correspond to the H-bonded, three-connected honeycomb sheet architectures of (TMA)2 x COR and (TMA)2 x HEL. Instead, porous, but noninterpenetrating, H-bonded four-connected sheets are observed, with the dihydrated, crown-shaped CRO molecules functioning as spacers rather than molecular guests. In the adduct (CHTA)2 x CRO x (H2O)5 (CHTA = cis,cis-1,3,5-cyclohexanetricarboxylic acid), the tetrahydrated CRO molecules again take up the crown conformation and act as spacers, this time within porous, noninterpenetrating H-bonded three-connected sheets. The engineering goal of CRO-filled H-bonded, hexagonal honeycomb cavities similar to the COR- and HEL-filled TMA honeycomb pores in (TMA)2 x COR and (TMA)2 x HEL was met in the adduct (HIPA)6 x CRO x (H2O)10 (HIPA = 5-hydroxyisophthalic acid), crystallized from aqueous EtOH. The crystal structure of this complex is on the one hand built up of isolated hexagonal honeycomb cavities established by six HIPA molecules cyclically linked through pairwise intercarboxylic H bonds. These cavities accommodate the crown-shaped CRO molecules, oriented such that maximally straight C-H...O contacts are enabled between its 12 equatorial H atoms and the surrounding 12 carboxylic groups of HIPA, in complete analogy to the situation prevailing in (TMA)2 x HEL and (probably) (TMA)2 xCOR. The second building block of (HIPA)6 x CRO x (H2O)10 is represented by a centrosymmetric decameric water cluster, which has the connectivity of the carbon skeleton of a bishomocubane with opposite methylene bridges, in agreement with vibrational spectroscopic evidence on gaseous (H2O)10. The crystal architecture of the adduct as a whole may either be likened to a severely distorted NaCl-type lattice, with the (HIPA)6 x CRO units replacing, for example, the Na+ ions, and the water clusters substituting the Cl- ions, or else to a system of stacked host sheets set up by C-H...O bonded (HIPA)6 macrorings, which give rise to perpendicular channels taking up guest columns of alternating, H-bonded CRO and (H2O)10 units. Crystals of another, solvated HIPA-CRO adduct of the composition (HIPA)4 x CRO x (EtOH)2 were obtained from aqueous EtOH. Their crystal structure is related to those of (TMA)2 x HEL and (TMA)2 x COR inasmuch distorted HIPA honeycomb sheets are adopted, which may be developed from the hexagonal TMA sheets by replacing one third of the pairwise intercarboxylic linkages by single interphenolic H bonds. The cavities in the HIPA sheets are thus smaller than those of the TMA honeycomb sheets and elliptically shaped. The HIPA sheets associate in pairs yielding twin cavities which take up one CRO and two EtOH molecules. The CRO molecules are suspended in the twin HIPA cages through H bonds extended from the phenolic OH groups and relayed by interposed EtOH "bridges". In keeping with the elliptic shape of the pores in (HIPA)4 x CRO x (EtOH)2, the CRO molecules are not crown-shaped, but rather adopt the more rectangular form as observed in crystalline CRO itself. The crystal structure of a dihydrate of HIPA itself was analysed, too, which assembles in a complex three-dimensional H-bonded network. It is finally concluded that hydrated CRO appears to be an avid H-bond acceptor, in particular towards carboxylic acids functioning as H-bond donors.

Three‐Dimensional Dynamic Response of Twin Cavities due to Traveling Loads

An analytical procedure is proposed to determine the three-dimensional response of a multiple-cylindrical-cavity system deeply buried in a viscoelastic medium subjected to moving or seismic loading. The tunnels are treated in the local coordinate systems. The interaction between the tunnels is taken into account by a coordinate system transform. The accuracy of the coordinate transform has been investigated. A numerical study describes the dynamic through-soil interaction between a main tunnel and a service tunnel when the main tunnel is subjected to vehicles moving with constant velocity and applying pressure over rectangular areas. The effects of the Mach number of the traveling load, the space between the tunnels, and the vibration frequency of the traveling load are examined. The numerical results show that the through-soil interaction is important for the service tunnel when it is close to the main tunnel where vehicles travel at high speed.

Torsional Stress Interference in Transverse Isotropy

An unbounded homogeneous transversely isotropic body of revolution containing two twin spheroidal cavities is subjected to a torsional loading at infinity. The axis of twist coincides with the axis of elastic symmetry of the material and the axis of revolution of the body. The linear elasticity solution is obtained in series form by employing the Lekhnitskii stress function approach, and numerical results are presented for the case of two spherical cavities perturbing the Saint‐Venant torsion field for a circular cylinder. Of particular interest is the influence of cavity spacing and material constants on the degree of stress interference between the two perturbations.

Stress Interference in a Transversely Isotropic Body under Axisymmetric Loading

An unbounded homogeneous transversely isotropic body of revolution containing two twin spheroidal cavities is subjected to an axisymmetric loading. The axis of loading symmetry coincides with the axis of elastic symmetry of the material and the axis of revolution of the body. The elasticity solution is obtained in series form utilizing the displacement potential representation for the equilibrium of transversely isotropic solids, and numerical results are presented for the cases of two spherical cavities perturbing uniaxial and hydrostatic tension fields in certain hexagonal crystals and in isotropic materials. Of primary interest is the influence of cavity spacing and material type on the degree of stress interference between the two perturbations.