Mathematical description of the cavitation process in the jet apparatus

The problem of mathematical description of non-steady processes in hydrodynamic systems is currently relevant and requires early resolution. The description of cavitation as a non-steady process is one of the most important issues of hydrodynamics. In this paper, as a result of the analysis and generalization of a priori information, plus transformation of the basic equations describing cavitation processes, a number of expressions are obtained that reflect the behavior of the incompressible fluid main flow in a jet apparatus, taking into account the conduct of hydrodynamic cavitation in it. To create a cavitation process mathematical description, it is proposed to apply an empirical formula for determining the ejected flow pressure. The newly developed mathematical dependencies can be used in the design of jet devices (ejectors, cavitators, ejectors-cavitators) for various purposes in both marine and stationary coastal technological systems for processing fluid media. In particular, it is advisable to use them in the preparation and conditioning of drinking and industrial water, wastewater and oily water purification, etc.

Effect of Fluid Chemistry on the Consolidation and Hydraulic Conductivity of Sand-Clay Liners

The clay swelling potential of sand-clay liners exposed to saline water or specific chemicals can influence their hydraulic conductivity and other consolidation properties. The effect of saline water or chemicals on the sand-clay liners was thus studied and evaluated. The consolidation characteristics of the sand-clay liner can be different when tested under different fluid media. Bentonite and cement grouts are chemicals that have a significant effect on the sand-clay liners. Cement and bentonite can be used to seal off the openings within the liner to repair a defect or a malfunction. In this study, Al-Qatif clay was used to form a sand-clay liner when mixed with fine-grained sand (clay is 20% by dry weight). Soil samples extracted from this liner were exposed to inorganic chemical solutions. NaCl and CaCl2 solutions with concentration ranges of 0.1%, 0.5%, and 1.5% were used. Acidic water with pH values of 4, 5, and 6 was similarly used as fluid media. The effects of NaCl, CaCl2, and water with different acidity on the consolidation characteristics and hydraulic conductivity were obtained and compared to those of the distilled water. The effects of grout materials containing bentonite (1%, 2%, and 3% by weight) and cement (2.5%, 5%, and 7.5% by weight) were also investigated. The addition of bentonite grout to the liner surface was found to improve its hydraulic conductivity. The cement effect on the compressibility was found to be very significant. The findings of this study can serve as a guide for selecting parameters in the design and assessment of sand-clay liners in semi-arid regions and coastal zones.

Low Reynolds Number Swimming Near Interfaces in Multi-Fluid Media

Microorganisms often swim within heterogeneous fluid media composed of multiple materials with very different properties. The swimming speed is greatly affected by the composition and rheology of the fluidic environment. In addition, biological locomotions are also strongly influenced by the presence of phase boundaries and free interfaces, across which physical properties of the fluid media may vary significantly. Using a two-fluid immersed boundary method, we investigate the classical Taylor’s swimming sheet problem near interfaces within multi-fluid media. The accuracy of the methodology is illustrated through comparisons with analytical solutions. Our simulation results indicate that the interface dynamics and phase separation in the multi-fluid mixture are closely coupled with the movement of the swimmer. Depending on the interface location, the frictional coefficient, and the multi-fluid composition, the swimmer can move faster or slower than that in a single phase fluid.

A simple justification of effective models for conducting or fluid media with dilute spherical inclusions

We present a gentle approach to the justification of effective media approximations, for PDE’s set outside the union of n ≫ 1 spheres with low volume fraction. To illustrate our approach, we consider three classical examples: the derivation of the so-called strange term, made popular by Cioranescu and Murat, the derivation of the Brinkman term in the Stokes equation, and a scalar analogue of the effective viscosity problem. Under some separation assumption on the spheres, valid for periodic and random distributions of the centers, we recover effective models as n → + ∞ by simple arguments.

Heat-mass transfer simulation of fluid media in the magma channel

<p>The paper presents a non-stationary model of heat-mass transfer of heterophase media in application to the study of the intrusion processes of magmatic melts in permeable zones of the lithospheric mantle and crust. Special emphasis is given to the study of the change in rheological properties of the fluido-magmatic mixture in the process of magmatic channel formation. The increased compressibility of the fluid phase is taken into account in the model by setting the Van der Waals equation of state. The calculated values of thermodynamic parameters of the fluid-magmatic system such as pressure, temperature, volumetric phase content, are the basis for the analysis of metasomatic changes in mantle matter. The Numerical model is based on the Runge-Kutta-TVD method. Verification of the numerical model on standard tests shows good accuracy of the program code and the possibility of using it for investigations of the currents of fluid-magmatic flows. The study of variation in interphase interaction parameters during melt movement in permeable zone, including change in interphase viscous friction, demonstrates a significant change in temperature distribution in the section of fluid-magmatic system. The work was financially supported by the Russian Foundation for Basic Research, grants No. 19-05-00788.</p>

Procedure and Installation for Determining the Filtering Capacity

The paper presents a method and an installation for determining the filtration capacity of filters made of composite materials with ceramic matrices. Applicable to fluid media (liquid, gaseous) the process is based on generating a pressure gradient in the filter area. The pressure difference between the two sides of the filter determines the passage of the fluid through the filter and its retention of the suspended particles. The process allows the testing of filters with a great diversity regarding the nature of the materials from which they are made, respectively their geometry and dimensions. In the present experiment, filters made of ceramic composite materials based on bentonite reinforced with SiC type ceramic powders and Al type metal powders were tested. From these materials were made cylindrical filters (diameters of 16 mm and length of 15 mm), which, after sintering at a temperature of 1250°C, were tested on the installation, for filtering rainwater samples. The determinations made highlighted a good ability of the filter to retain suspended particles in the water.