Vortex rings in radially confined domains

The dynamics of vortex rings generated within confined domains are relevant to important hydrodynamic processes such as flow past heart valves or severe arterial constrictions. However, despite their importance, these flows have not received much attention to date. This study examines the development and evolution of radially confined vortex rings. Time-resolved digital particle image velocimetry was used to investigate two levels of radial confinement and a range of vortex ring strengths. We found that for severely confined vortex rings, the formation time and peak circulation values were unaffected for L/D ₀?<?4 cases and slightly affected for larger L/D ₀ cases. After pinch-off, circulation decay was observed with an approximately constant normalized circulation decay rate. We found that with increasing circulation strength, the nondimensional time delay between the pinch-off and the onset of circulation decay reduced due to an increased vortex ring diameter within the confinement domain and a reduction in the necessary time for the surface induced and core vorticity regions to interact. This study uncovers the dynamics of radially confined vortex rings and show that the nondimensional rate of circulation decay is dependent on the vortex ring confinement ratio (ratio of the vortex ring orifice diameter to the diameter of the outer cylinder), and the time delay between the vortex pinch-off and the onset of circulation is dependent on the vortex ring circulation strength.     

A mechanism for mitigation of blade–vortex interaction using leading edge blowing flow control

The interaction of a vortical unsteady flow with structures is often encountered in engineering applications. Such flow structure interactions (FSI) can be responsible for generating significant loads and can have many detrimental structural and acoustic side effects, such as structural fatigue, radiated noise and even catastrophic results. Amongst the different types of FSI, the parallel blade–vortex interaction (BVI) is the most common, often encountered in helicopters and propulsors. In this work, we report on the implementation of leading edge blowing (LEB) active flow control for successfully minimizing the parallel BVI. Our results show reduction of the airfoil vibrations up to 38% based on the root-mean-square of the vibration velocity amplitude. This technique is based on displacing an incident vortex using a jet issued from the leading edge of a sharp airfoil effectively increasing the stand-off distance of the vortex from the body. The effectiveness of the method was experimentally analyzed using time-resolved digital particle image velocimetry (TRDPIV) recorded at an 800 Hz rate, which is sufficient to resolve the spatio-temporal dynamics of the flow field and it was combined with simultaneous accelerometer measurements of the airfoil, which was free to oscillate in a direction perpendicular to the freestream. Analysis of the flow field spectra and a Proper Orthogonal Decomposition (POD) of the TRDPIV data of the temporally resolved planar flow fields indicate that the LEB effectively modified the flow field surrounding the airfoil and increased the convecting vortices stand-off distance for over half of the airfoil chord length. It is shown that LEB also causes a redistribution of the flow field spectral energy over a larger range of frequencies.     

Synthesis of 4-acetylcolchicine

The synthesis of 4-acetylcolchicine ( 1 ) by Swern dehydrogenation of the corresponding mixture of 4-[(R)-1-hydroxyethyl]- and 4-[(S)-1-hydroxyethyl]colchicine ( 3a and 3b , respectively) is described (cf. Scheme). The X-ray analysis of 1 (cf. Fig.), crystallized from MeOH, showed the presence of MeOH in the crystals.     

Generalized sine equations,III

Summary We solve the equationf(x + y)f(x – y) = P(f(x), f(y)) under various conditions on the unknown functionsf, P.     

Generalized sine equations,II

In this paper we solve the equations

Low Level Lead Determination After Membrane Complexation and TXRF Analysis

New membranes containing a few micrograms of various complexing reagents in a Nafion^® matrix were produced on the surface of quartz glasses (reflectors). The reflectors were immersed in standard water solutions containing various, very low concentrations of lead salts (1–50ngmL^–1). The reflectors were left in 5–500mL solutions for many hours; when the equilibration stage was complete, they were cleaned with ultrapure water and left to dry. The stability (adhesion) of the membranes was tested. Analysis of the samples was performed by Total Reflection X-Ray Fluorescence and cross-evaluated by Atomic Absorption Spectrometry. A few ngmL^–1 of the lead were determined. The effect of various experimental parameters (complexing agent, membrane composition, equilibrium time, sample volume etc.) was examined.     

Mordell-Weil groups of the Jacobian of the 5-th Fermat curve

Let denote the Jacobian of the Fermat curve of exponent 5 and let . We compute the groups , , , where is the unique quadratic subfield of . As an application, we present a new proof that there are no -rational points on the 5-th Fermat curve, except the so called ``points at infinity".

     

The Hausdorff dimension of random walks and the correlation length critical exponent in Euclidean field theory

We study the random walk representation of the two-point function in statistical mechanics models near the critical point. Using standard scaling arguments, we show that the critical exponentv describing the vanishing of the physical mass at the critical point is equal tov /d_w, whered _w is the Hausdorff dimension of the walk, andv is the exponent describing the vanishing of the energy per unit length of the walk at the critical point. For the case ofO(N) models, we show thatv ₀=, where is the crossover exponent known in the context of field theory. This implies that the Hausdorff dimension of the walk is/v forO(N) models.