Dense Suspension Flows: a Mathematical Model Consistent with Thermodynamics

We address the flows of dense suspensions of particles within the framework of two-velocity continuum. Thermodynamics of such a continuum is developed by the method suggested in the papers of L. D. Landau and I. M. Khalatnikov. As an application, we consider the convective settling problem. We capture the Boycott effect and prove that the enhanced sedimentation occurs in a 10 tilted vessel due to vortices. We do not call on additional interphase forces like the Stokes drag, the virtual mass force, the Archimedes force, the Basset-Boussinesq force and etc. Instead, we apply a generalized Fick's law for the particle mass concentration flux vector.

Trends in porosity сhanges of the unconsolidated part of ice ridge keel

An ice ridge is a special case of granular medium with a wide range of fractions. It represents a chaotic piling-up of blocks occurring under the action of gravity in the sail and due to the Archimedes force in the keel. An important characteristic of the internal structure of ice ridges is their porosity. Scientists from different countries have been dealing with this problem. First-year ice ridges are taken into consideration in Arctic and subarctic marine structural design, and the calculation of ice loads includes ridge porosity and strength, as well as other parameters. The aim of the present work is to discern the regularities of porosity distribution in the unconsolidated part of the keel with depth. Ice ridge porosity is identified by means of processing thermodrilling records. In this paper, porosity is interpreted as a step function equal to zero if there is ice at the point (x, y, z), and to one if there is no ice at the point (x, y, z). The author applies the model of compaction of the bulk medium under the influence of gravity, and, particularly for the keel, due to the Archimedes force. A zero depth corresponds to the lower surface of the keel, so each individual porosity distribution of the unconsolidated part of the keel at the drilling point must be shifted down until the maximum keel draft depth is reached in the region under consideration. After alignment, the step curves are averaged. The distance is measured up, starting from the depth of the maximum keel draft. The curve of the averaged porosity can be divided into segments reflecting the characteristic features of the distribution. According to the graphs, average porosity decreases exponentially. Ice ridges of several geographical regions are considered, and in each region is divided into groups by years of research. On the whole, 17 depth-wise distributions of the average porosity are obtained for seven regions. Each distribution was approximated according to the model, taking into account the average density of water and ice in the region. For each distribution, the values of compactibility and porosity at the zero depth, i. e. at the lower edge of the keel, were obtained; the second value only has mathematical sense. It is more convenient to consider the maximum value of the average porosity, which is taken as the initial porosity. With a probability of 90 %, the initial porosity is within the range of 0.450 ± 0.125. As the distance from the keel edge increases, the porosity curves converge to a fairly narrow range of values. At a distance of 12–14 m, this range is 0.07…0.12. The second parameter characterizing the porosity distribution in the unconsolidated part of the keel is compactibility. The steepness of the exponent approximating the average porosity curve depends on it, too. Compactibility is most affected by the strength of the ridged ice as well as the ice thickness. From the literature on the physical properties of ice it is known that as the temperature of ice increases, its strength decreases, and its plasticity increases. Thus, it can be concluded that compactibility is determined by the ice crystal structure as well the ice average temperature at the time of ridging — the warmer the ice, the higher the compactibility of the ice blocks in the keel.

New approach to injection of pressurizing gas into fuel tanks of power units

Purpose. Determination a rational way to injection of high-temperature pressurizing gas into fuel tanks of large elongation. Determination of longitudinal overload effect on the Archimedes force during the gas jet penetration in the tank. Reducing the need for pressurizing gas, the mass of the storage system. Methodology. A retrospective design analysis of devices for injecting the gas into tanks and taxonomy basics are used. With their help, it is possible to determine the causes of a wide variety of device designs for injecting gas into tanks and the common fundamental disadvantages of all known devices. Findings. As a result of the research carried out, a new method for supplying hot gas to the tanks has been found and substantiated. It is suitable for most conditions and provides a reduction in the need for pressurizing gas, does not reduce the operating fuel reserves, shows the trends for further research. Originality. The main reason for the differences between the results of ground tests and flight tests in terms of the gas parameters in the tank and the temperature of its upper bottom has been determined. This is overload effect on the increase in the buoyancy force on hot pressurizing gas jet, which is injected traditionally from the upper tank bottom to the side of the lower tank bottom. In this case, the buoyancy force acts against the dynamic component, reduces the jet range and presses the hot gas to the upper bottom. A new method for injecting the hot pressurizing gas, devoid of the indicated drawback, has been proposed and developed by using a theory of similarity. This makes it possible to mix the gas in the free volume of the tank as much as possible due to the action of the Archimedes force, to equalize gas temperature, reducing the maximum temperature at the upper bottom, and noticeable mass transfer processes in the tank are excluded. Practical value. The application of the proposed method permits defining correctly and accurately the gas flow rate for tank pressurization, using it with a temperature of up to ~1800 K. The drop in gas pressure disappears in the tank at the initial moment of operation of the pressurization system, caused by the injection of a hot gas jet into the fuel surface. Depending on the conditions, the pressurizing gas requirement can be reduced by up to 50%. In this case, the main fuel reserves in the tank are not reduced.

The Lifting Force of An Airplane Wing When Flying Horizontally at High Speeds.

In this paper, an explanation is given of the lift force of an airplane during horizontal flight. It is shown that during a flight, five vertical forces act on the airplane: gravity; pressure gradient with a minus sign; Archimedes force; potential force and the vortex force obtained from the action minimum. The first three forces were known before. The potential force was also known from the Bernoulli equation, but its effect on the airfoil from the air had not previously been taken into account. The vortex force obtained from the minimum action in the application to a continuous medium was not taken into account in aerodynamics. In horizontal flight the vortex force is directed upwards, it compensates for the gravity of the airplane at high speed commensurate with the speed of sound. The article provides an explanation of the vortex trail behind the airplane, mentioned in the CMI Millennium problem.

THE STUDY OF STUDENTS’ DIFFICULTIES IN MASTERING THE CONCEPT OF ARCHIMEDES’ PRINCIPLE

The focus of this study is to determine students' difficulties related to mastering the concept of Archimedes Principles topics. The study used descriptive quantitative method with the subject 35 XIth students. The research instrument was 10 multiple choice questions about Archimedes principle. Although there are improvements, but overall students do not fully understand the concept of the Archimedes principle. Difficulties among students are failing to understand that the buoyancy force is the resultant force by fluid pressure on the object and still considers the immersed object to have the Archimedes force affected by the depth of the object. When working on the application of the problem the students managed to answer correctly, but when completing the formulation questions the students were still get difficulties

Archimedes force on Casimir apparatus

This paper addresses a problem of Casimir apparatus in dense medium, put in weak gravitational field. The falling of the apparatus has to be governed by the equivalence principle with proper account for contributions to the weight of the apparatus from its material part and from distorted quantum fields. We discuss general expression for the corresponding force in metric with cylindrical symmetry. By way of example, we compute explicit expression for Archimedes force, acting on the Casimir apparatus of finite size, immersed into thermal bath of free scalar field. It is shown that besides universal term, proportional to the volume of the apparatus, there are non-universal quantum corrections, depending on the boundary conditions.