Energy and velocity of a forming vortex ring

It is known that vortex rings formed by large stroke ratios (in a piston/cylinder arrangement) pinch off from their generating jets at a fairly constant universal time scale. In this paper we show that the hypothesis that at the pinch off the translational velocity of the ring equals the jet flow velocity near the ring is equivalent to the recently proposed idea based on a variational principle by Kelvin and Benjamin that the pinch off occurs when the apparatus is no longer able to deliver energy at a rate required for steady vortex ring existence. A formula for the propagation velocity of a thick vortex ring is also proposed and compared with available experimental data and empirical relations

Defocusing digital particle image velocimetry and the three-dimensional characterization of two-phase flows

Defocusing digital particle image velocimetry (DDPIV) is the natural extension of planar PIV techniques to the third spatial dimension. In this paper we give details of the defocusing optical concept by which scalar and vector information can be retrieved within large volumes. The optical model and computational procedures are presented with the specific purpose of mapping the number density, the size distribution, the associated local void fraction and the velocity of bubbles or particles in two-phase flows. Every particle or bubble is characterized in terms of size and of spatial coordinates, used to compute a true three-component velocity field by spatial three-dimensional cross-correlation. The spatial resolution and uncertainty limits are established through numerical simulations. The performance of the DDPIV technique is established in terms of number density and void fraction. Finally, the velocity evaluation methodology, using the spatial cross-correlation technique, is described and discussed in terms of velocity accuracy

Jamaan at the pass of Bi’rein. An Iron Age IIB-C Ammonite stronghold in central Jordan

In years 2015-2016 the Zarqa Directorate of the Department of Antiquities of the Hashemite Kingdom of Jordan carried out a rescue excavation at the site of Jamaan, an Iron Age IIB-C Ammonite stronghold 16 Km north of ‘Amman. The site survey and limited soundings allow to plot a plan of the structure, comprising an outer enclosure with a casemate wall, two cisterns, and a square podium tower, and to collect ceramic material dating from Iron Age IIB-C (c. 840-580 BC), as well as the head of a soft limestone statue, possibly depicting a local chief or an official. The latter adds to the relatively conspicuous number of statues from the Kingdom of Ammon, possibly illustrating the production of a non-royal commission

Structures in stratified plane mixing layers and the effects of cross-shear

A two-dimensional temporal mixing layer is generated in a stratified tilting tank similar to that used by Thorpe (1968). Extensive flow dynamics visualization is carried out using, for the top and bottom layers, fluids of different densities but of the same index of refraction. The two-dimensional density field is measured with the laser-induced fluorescence technique (LIF). The study examines further the classical problem of the two-dimensional mixing layer and explores the effects of cross-shear on a nominally two-dimensional mixing layer, a situation widespread in complex industrial and natural flows. Cross-shear is another component of shear, in plane with but perpendicular to the main shear of the base flow, generated by tilting the tank around a second axis

Flexibility effects on vortex formation of translating plates

Vortex structures made by impulsively translating low aspect-ratio plates are studied experimentally using defocusing digital particle image velocimetry. The investigation of translating plates with a 90° angle of attack is important since it is a fundamental model for a better understanding of drag-based propulsion systems. Rectangular flat rigid, flexible and curved-rigid thin plates with the same aspect ratio are studied in order to develop qualitative and quantitative understanding of their vortex structures and hydrodynamic forces. We find that the vortex formation processes of all three cases are drastically different from each other. The interaction of leading-edge vortices and tip flow near the tip region is an important mechanism to distinguish vortex patterns among these three cases. The drag trends of three cases are correlated closely with vortex structure and circulation. The initial peak of hydrodynamic force in the flexible plate case is not as large as the initial peak of the flat and curved rigid plate cases during the acceleration phase. However, after the initial peak, the flexible plate generates a large force comparable to that of the flat-rigid plate case in spite of its deformed shape, which results from the slow development of the vortex structure

A model for vortex ring formation in a starting buoyant plume

Vortex ring formation in a starting axisymmetric buoyant plume is considered. A model describing the process is proposed and a physical explanation based on the Kelvin–Benjamin variational principle for steady vortex rings is provided. It is shown that Lundgren et al.'s (1992) time scale, the ratio of the velocity of a buoyant plume after it has travelled one diameter to its diameter, is equivalent to the time scale (formation time) proposed by Gharib et al. (1998) for uniform-density vortex rings generated with a piston/cylinder arrangement. It is also shown that, similarly to piston-generated vortex rings (Gharib et al. 1998), the buoyant vortex ring pinches off from the plume when the latter can no longer provide the energy required for steady vortex ring existence. The dimensionless time of the pinch-off (the formation number) can be reasonably well predicted by assuming that at pinch-of the vortex ring propagation velocity exceeds the plume velocity. The predictions of the model are compared with available experimental results

Vector bundles on toric varieties

CORRECTION. One of the main results in this paper contains a fatal error. We cannot conclude the existence of nontrivial vector bundles on X from the nontriviality of its K-group. The K-group that is computed here is the Grothendieck group of perfect complexes and not vector bundles. Since the varieties are not quasi-projective, existence of nontrivial perfect complexes says nothing about the existence of nontrivial vector bundles. We thank Sam Payne for drawing our attention to the error and Christian Haesemeyer for explanations about the K-theory. Abstract: Following Sam Payne's work, we study the existence problem of nontrivial vector bundles on toric varieties. The first result we prove is that every complete fan admits a nontrivial conewise linear multivalued function. Such functions could potentially be the Chern classes of toric vector bundles. Then we use the results of Corti\~nas, Haesemeyer, Walker and Weibel to show that the (non-equivariant) Grothendieck group of the toric 3-fold studied by Payne is large, so the variety has a nontrivial vector bundle. Using the same computation, we show that every toric 3-fold X either has a nontrivial line bundle, or there is a finite surjective toric morphism from Y to X, such that Y has a large Grothendieck group.Comment: There is an error in one of the main conclusions of the paper. Please see the abstract for more detail

A method for three-dimensional particle sizing in two-phase flows

A method is devised for true three-dimensional (3D) particle sizing in two-phase systems. Based on a ray-optics approximation of the Mie scattering theory for spherical particles, and under given assumptions, the principle is applicable to intensity data from scatterers within arbitrary interrogation volumes. It requires knowledge of the particle 3D location and intensity, and of the spatial distribution of the incident light intensity throughout the measurement volume. The new methodology is particularly suited for Lagrangian measurements: we demonstrate its use with the defocusing digital particle image velocimetry technique, a 3D measurement technique that provides the location, intensity and velocity of particles in large volume domains. We provide a method to characterize the volumetric distribution of the incident illumination and we assess experimentally the size measurement uncertainty

Computational studies of resonance wave pumping in compliant tubes

The valveless impedance pump is a simple design that allows the producion or amplification of a flow without the requirement for valves or impellers. It is based on fluid-filled flexible tubing, connected to tubing of different impedances. Pumping is achieved by a periodic excitation at an off-centre position relative to the tube ends. This paper presents a comprehensive study of the fluid and structural dynamics in an impedance pump model using numerical simulations. An axisymmetric finite-element model of both the fluid and solid domains is used with direct coupling at the interface. By examining a wide range of parameters, the pump's resonance nature is described and the concept of resonance wave pumping is discussed. The main driving mechanism of the flow in the tube is the reflection of waves at the tube boundary and the wave dynamics in the passive tube. This concept is supported by three different analyses: (i) time-dependent pressure and flow wave dynamics along the tube, (ii) calculations of pressure–flow loop areas along the passive tube for a description of energy conversion, and (iii) an integral description of total work done by the pump on the fluid. It is shown that at some frequencies, the energy given to the system by the excitation is converted by the elastic tube to kinetic energy at the tube outlet, resulting in an efficient pumping mechanism and thus significantly higher flow rate. It is also shown that pumping can be achieved with any impedance mismatch at one boundary and that the outlet configuration does not necessarily need to be a tube