Effect of flat wall length on decay and shock structure of a supersonic square wall jet

Experiments were conducted to find the effect of wall length on the decay behaviour and shock structure of a supersonic wall jet issuing from c-d nozzle of the square-shaped exit. A straight flat wall of width same as the side length of the square was attached to the lip of the nozzle such that the leading edge of the wall and the side of the square aligned properly which allowed the supersonic jet to graze past the flat wall. Experiments were conducted with five different wall lengths, that is, [Formula: see text] = 0.5, 1, 2, 4 and 8. Wall pressure measurements were made from leading edge to the trailing edge of the wall along its centreline. Schlieren flow visualization of the jet flow over the wall for the different wall lengths revealed the shock pattern and the effect of the wall length on the shock structure. The shock structure and jet deflection were significantly affected due to the presence of the wall. There was an upward jet deflection for [Formula: see text] up to [Formula: see text] whereas a downward jet deflection was observed for [Formula: see text]. Noticeable changes in the shock structure were observed for the wall lengths up to 2 D h. The wall length also significantly affected the jet decay characteristics and supersonic core length. Maximum enhancement in jet decay and maximum reduction in supersonic core length resulted when the wall length was [Formula: see text]. However, when the wall length was increased to [Formula: see text], there was a significant reduction in jet decay and a recovery of [Formula: see text]. Presence of wall always resulted a reduction in Lsc irrespective of wall length. The wall effect was to induce a more precipitous pressure drop closer to the nozzle exit, and a more gradual drop farther from it for [Formula: see text] > [Formula: see text].

Real-Time Detection of Long Lived Near Infrared luminescence from Colourless Cubic Zirconia by Time-Gated Imaging

Here, we report a long-lived ms time scale decay luminescing in the near infrared >800 nm present in productions of ‘white’ colourless, facetted yittrium stabilized cubic zirconia and observed using time-gated imaging. The spectrum of the strong luminescing feature also has characteristics of Neodymium (Nd3+) and has a multiexponential decay behaviour. Real-time detection of cubic zirconia mounted in diamond jewellery containing very small stones (≤0.01 ct) is made possible, where observation by loupe is more challenging or other conventional techniques impractical and or slow to implement. The near infrared observed can be excited using a low-cost and eye/skin safe-visible green LED light source and the time-gated imaging of the luminescence using a machine vision monochrome camera. The use of near infrared, time-gated detection in combination with other verification instruments increases the robustness of screening diamond parcels. Therefore, it is recommended that any stone exhibiting strong delayed luminescence in the near infrared be treated with caution, as this is not a typical feature found in this precious gemstone. In this case, the instrument developed was expanded to incorporate a white LED illumination ring as a viewfinder, in order to aid the inspection of loose and mounted configurations.

Degenerate equations in a diffusion–precipitation model for clogging porous media

In this article, we consider diffusive transport of a reactive substance in a saturated porous medium including variable porosity. Thereby, the evolution of the microstructure is caused by precipitation of the transported substance. We are particularly interested in analysing the model when the equations degenerate due to clogging. Introducing an appropriate weighted function space, we are able to handle the degeneracy and obtain analytical results for the transport equation. Also the decay behaviour of this solution with respect to the porosity is investigated. There a restriction on the decay order is assumed, that is, besides low initial concentration also dense precipitation leads to possible high decay. We obtain nonnegativity and boundedness for the weak solution to the transport equation. Moreover, we study an ordinary differential equation (ODE) describing the change of porosity. Thereby, the control of an appropriate weighted norm of the gradient of the porosity is crucial for the analysis of the transport equation. In order to obtain global in time solutions to the overall coupled system, we apply a fixed point argument. The problem is solved for substantially degenerating hydrodynamic parameters.

Some sharp results about the global existence and blowup of solutions to a class of pseudo-parabolic equations

In this paper we are interested in a sharp result about the global existence and blowup of solutions to a class of pseudo-parabolic equations. First, we represent a unique local weak solution in a new integral form that does not depend on any semigroup. Second, with the help of the Nehari manifold related to the stationary equation, we separate the whole space into two components S+ and S– via a new method, then a sufficient and necessary condition under which the weak solution blows up is established, that is, a weak solution blows up at a finite time if and only if the initial data belongs to S–. Furthermore, we study the decay behaviour of both the solution and the energy functional, and the decay ratios are given specifically.

Energy transfer and unusual decay behaviour of BaCa2Si3O9:Eu2+,Mn2+ phosphor

In this work the photoluminescence (PL) of BaCa2Si3O9:Eu2+, Mn2+ and the energy transfer between Eu2+ and Mn2+ were examined. Further, PL as well as luminescence lifetime measurements were performed at various temperatures.

Self-limiting and regenerative dynamics of perturbation growth on a vortex column

We study the mechanisms of centrifugal instability and its eventual self-limitation, as well as regenerative instability on a vortex column with a circulation overshoot (potentially unstable) via direct numerical simulations of the incompressible Navier–Stokes equations. The perturbation vorticity (${\boldsymbol{\omega} }^{\prime } $) dynamics are analysed in cylindrical ($r, \theta , z$) coordinates in the computationally accessible vortex Reynolds number, $\mathit{Re}({\equiv }\mathrm{circulation/viscosity} )$, range of 500–12 500, mostly for the axisymmetric mode (azimuthal wavenumber $m= 0$). Mean strain generates azimuthally oriented vorticity filaments (i.e. filaments with azimuthal vorticity, ${ \omega }_{\theta }^{\prime } $), producing positive Reynolds stress necessary for energy growth. This ${ \omega }_{\theta }^{\prime } $ in turn tilts negative mean axial vorticity, $- {\Omega }_{z} $ (associated with the overshoot), to amplify the filament, thus causing instability. (The initial energy growth rate (${\sigma }_{r} $), peak energy (${G}_{\mathit{max}} $) and time of peak energy (${T}_{p} $) are found to vary algebraically with $\mathit{Re}$.) Limitation of vorticity growth, also energy production, occurs as the filament moves the overshoot outward, hence lessening and shifting $\vert {- }{\Omega }_{z} \vert $, while also transporting the core $+ {\Omega }_{z} $, to the location of the filament. We discover that a basic change in overshoot decay behaviour from viscous to inviscid occurs at $Re\sim 5000$. We also find that the overshoot decay time has an asymptotic limit of 45 turnover times with increasing $\mathit{Re}$. After the limitation, the filament generates negative Reynolds stress, concomitant energy decay and hence self-limitation of growth; these inviscid effects are enhanced further by viscosity. In addition, the filament transports angular momentum radially inward, which can produce a new circulation overshoot and renewed instability. Energy decays at the $\mathit{Re}$ studied, but, at higher $\mathit{Re}$, regenerative growth of energy is likely due to the renewed mean shearing. New generation of overshoot and Reynolds stress is examined using a helical ($m= 1$) perturbation. Regenerative energy growth, possibly resulting in even vortex breakup, can be triggered by this new overshoot at practical $\mathit{Re}$ (${\sim }1{0}^{6} $ for trailing vortices), which are currently beyond the computational capability.

The Self-Decay Characteristics of Chlorine Dioxide in Water

In order to learn the ClO2 decay behaviour in tap water, the kinetics of ClO2 decay in pure water was studied. Under the conditions of tap water treatment and keeping away from light, the effects of temperature and pH on ClO2 degradation were investigated. The results show that the ClO2 decay reaction in pure water is the first-order with respect to ClO2, the decay rate constants increase with increase in temperature or pH. At pH=6.87, the rate constants are 0.012h-1(15°C), 0.017h-1(25°C), 0.023h-1(35°C), and 0.029h-1(45°C), respectively. At 25°C, the rate constants are 0.0083h-1(pH=4.5), 0.0111h-1(pH=5.5), 0.0143h-1(pH=6.5), 0.0222h-1(pH=7.5), and 0.0351h-1(pH=8.5), respectively. The experimental data prove that ClO2 is more stable in acidic or lower temperature water than in neutral, alkalescent, or higher temperature water.

von Kármán self-preservation hypothesis for magnetohydrodynamic turbulence and its consequences for universality

We argue that the hypothesis of preservation of shape of dimensionless second- and third-order correlations during decay of incompressible homogeneous magnetohydrodynamic (MHD) turbulence requires, in general, at least two independent similarity length scales. These are associated with the two Elsässer energies. The existence of similarity solutions for the decay of turbulence with varying cross-helicity implies that these length scales cannot remain in proportion, opening the possibility for a wide variety of decay behaviour, in contrast to the simpler classic hydrodynamics case. Although the evolution equations for the second-order correlations lack explicit dependence on either the mean magnetic field or the magnetic helicity, there is inherent implicit dependence on these (and other) quantities through the third-order correlations. The self-similar inertial range, a subclass of the general similarity case, inherits this complexity so that a single universal energy spectral law cannot be anticipated, even though the same pair of third-order laws holds for arbitrary cross-helicity and magnetic helicity. The straightforward notion of universality associated with Kolmogorov theory in hydrodynamics therefore requires careful generalization and reformulation in MHD.