This research concerns the scattering of electromagnetic waves by thin dielectric impediments in 2D geometry. Dielectric and geometric properties of the impediments are modeled by varying the ...inhomogeneous component of the refractive index. It is assumed that the impediments have arbitrary finite lengths, and their widths are much lesser in comparison with the incident wavelength. In contrast to the previous approaches the proposed one enables us to solve the scattering problem simultaneously on several objects in the case where the impediments structure is not a regular one. A system of integral equations to provide a solution to the problem is derived. A unique solvability of the obtained system is discussed.
We propose an approach for controlling the weighted average price of a manufacturers sales on commodity exchanges. This problem is highly relevant due to the need for the manufacturer to hedge their ...profits in case of a sharp drop in market prices. We consider applications of the proposed control to executing trading operations on real commodity exchanges in order to demonstrate its efficiency.
In this research, we study the scattering of electromagnetic waves by a dielectric impediment in 2D geometry. The impediment is determined by an inhomogeneous component of the refractive index in the ...Helmholtz equation. It is assumed that the characteristic gauge of one of the two impediment sizes is much lesser than the length of waves generated by a monochromatic point source. Nevertheless, the structure of the impediment is taken into consideration in the process of calculating the scattered field. The scattered field is defined by a derived model integral equation the unique solvability of which is proved.
An attempt is made to experimentally study some of the effects observed during the gravitational deposition of drops on a model with a hemispherical end. By a frame-by-frame analysis of video ...recordings, the features of the interaction of the drops with the surface of the model are analyzed. Data are obtained on the velocities and sizes of both small (secondary drops) and large (fragments) drops in the case of a high (close to the dynamic Leidenfrost temperature) temperature of the model. The effect of the formation of drops with near-zero velocities near the surface of the model as a result of the coagulation and momentum exchange of incident and reflected drops is revealed. Data are obtained on the decrease in the velocity recovery coefficient with an increase in the inertia of drops in the case of their interaction with curved surfaces. The effect of the noncoincidence of the points of contact and rebound (detachment) of drops from the surface, which increases with increasing drop size, is found.
The present study examines the molten NaCl explosive fragmentation in subcooled distilled water. It is noted that the explosion occurred in all experiments performed. However, such a good ...reproducibility was not observed at a two-phase cooling of the molten metal. This fact can be explained by the lower value of the liquid salt viscosity in comparison with liquid metals viscosity. In addition, a description of explosion propagation in a group of melt drops is given.
With the use of high-speed video filming, the effect of the appearance of droplets with near-zero velocities in gas–droplet flows past bodies was discovered for the first time. The formation of ...levitating droplets occurred as a result of the coalescence of droplets falling and reflected from the model. It has been suggested that the main mechanism for the appearance of drops with near-zero velocities is momentum exchange as a result of the collision of droplets with opposite directions and values of velocity close in magnitude. The effect of an increase in the size of large levitating drops due to the coalescence of falling droplets with them due to multiple collisions has been detected.
The paper presents a number of provisions that develop the phenomenological Snyder–Bergles model, which allows the most plausible description of the boiling of a liquid subcooled to the saturation ...temperature (one of the most effective ways to remove large heat fluxes). As a result of studies of the dynamics of single vapor bubbles carried out using high-speed video recording (with a frame rate of up to 150 kHz), it has been shown that this phenomenon is determined by such repeating processes as the explosive boiling up of each new bubble, the evaporation of the microlayer formed at the root of the bubble, and removal of the heat of condensation of vapor from the dome of the bubble into the bulk of the cold liquid by nonstationary thermal conduction. From experiments performed on two liquids with very different thermophysical properties (water and freon R-113), it follows that the shape of bubbles at the growth stage strongly depends on the value of the reduced pressure of the boiling liquid
p
red
= p
/
p
cr
(here
p
is a pressure in the liquid;
p
cr
is its critical pressure). At low pressures (
p
red
≤ 0.005), the bubble, as a rule, acquires a shape close to a hemisphere, which, with increasing
p
red
tends to be spherical. The shape of the bubble affects the size of the zone of maximum evaporation intensity (microlayer dimension). It is shown that a high level of heat transfer during boiling of the subcooled liquid is achieved as a result of an increased intensity of both processes: evaporation in the zone of the triple line and removal of condensation heat by nonstationary heat conduction into a “semi-infinite” layer of a cold liquid with a moving boundary when the boundary conditions of the first kind is realized. Estimates show that the main part of the heat accumulated by the heat-releasing surface is transferred to the surrounding liquid at the initial phase of the inertial stage of bubble growth.
Abstract
An experimental study of the characteristics of single (solitary) bubbles obtained by means of focused laser heating of the surface during the boiling of two subcooled liquids with ...significantly different properties: water and refrigerant R113 has been carried out. To obtain the most complete detailed information, the technique of synchronized high-speed video filming of the process in two mutually perpendicular planes with a frame rate of up to 150 kHz was used. It is shown that during the boiling of a subcooled liquid, the main mechanism of heat removal from the bubble dome into the surrounding liquid is an unsteady heat conductance. Differences in the behavior of solitary vapor bubbles in the case of boiling of two liquids (water and refrigerant R113) are shown.
An experimental study on the explosive fragmentation of strongly heated lead melt inside a steel cup in distilled subcooled has been conducted. Analysis of high-speed video recordings of the process ...showed that an explosion can be initiated both with complete and partial hardening of the upper lead melt layer. The observed phenomena are described. The results may be useful for the determination of causes of the initiation of a steam explosion when the melt contacts with a solid surface or is partially crystallized.
In this work, we studied the explosive fragmentation of a molten drop of sodium chloride NaCl in distilled water subcooled to saturation temperature and in water saturated with carbon dioxide in the ...absence of external triggering (process initiation). Explosive split of a droplet of NaCl into fragments occurred in all experiments performed with water with a temperature of 20 to 70°C, which was not saturated with gas. This phenomenon was not observed upon contact with water droplets of molten metals (lead, Rose and Wood alloys, etc.) when the explosive fragmentation was of a random nature. This fact can be explained by the lower viscosity of the salt melt in comparison with the viscosity of liquid metals as well as by its solubility in water. The saturation of water with carbon dioxide prevented the occurrence of a vapor explosion even when the NaCl melt droplets were in contact with water at a temperature of 15–20°C. It is assumed that the presence of a large amount of dissolved carbon dioxide in water leads to its intense release upon contact of water with the surface of an NaCl droplet, shields it from water, and prevents the development of fragmentation according to any of the most probable process models (thermoacoustic, liquid capture, destruction of the solidified crust under the action of thermoelastic forces). Based on the analysis of high-speed video filming of the process, a preliminary conclusion was made about the actual merging of the stages of triggering, fine fragmentation, and the vapor explosion itself upon contact of a molten NaCl drop with water at a temperature of 20–70°C and about the absence of a vapor explosion on drops of NaCl melt at a water temperature above 80°C.
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