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.

Visualization of hydrodynamic and physico-chemical processes in rotating and vibrating containers

Variable inertial fields are an efficient way to control the behaviour of hydrodynamic systems. Forces of inertia can be used, for example, to stabilize or destabilize systems with an interface or density gradient, to mix multiphase or non-isothermal fluids. The implementation of this approach means that liquids fill the periodically moving containers. In this paper, the situations are considered when the containers perform either rotation or translational vibrations. Methods for measuring the density and velocity fields of convective flows in reacting hydrodynamic systems are described. Interferometry is used to visualize the density distribution. Particle image velocimetry (PIV) is used to study the structure and velocity of the flows. Optical instruments are installed stationary in the laboratory system. For video recording, a camera shutter is synchronized with the motion of a container, and thus the images are captured in a fixed phase of oscillations or rotation. Constructions of the containers make it possible to illuminate the working volume through transparent walls at different angles or in different planes. They also provide a compensation for the centrifugal pressure and allow interference cells to be used in overload conditions. The successful application of the methods in experimental studies of chemo-hydrodynamic processes is demonstrated.

Electrospun Polycaprolactone Nanofibers: Current Research and Applications in Biomedical Application

Unique mechanical properties, miscibility potency, and biodegradability are the three prominent features of Polycaprolactone (PCL), making it an attractive biomaterial which commonly applied in regenerative medicine and biomedical engineering. Different strategies developed for fabricating nanofibrous construct, electrospinning is a practical, simple, and efficient technique based on electro-hydrodynamic systems that use an electrified viscous fluid jet drawn by the air toward a collector at a changing electric potential. PCL electrospun-based nanofibrous composites as proper scaffolds are employed in stem cell-related research, particularly in tissue engineering, wound dressing, and systems designed for sending drugs. A compilation of mechanochemical properties and most common biological performance on PCL-based electrospun fibrous structures in biomedical application are included in this study. Therefore, electrospun PCL nanofiber applying has been presented, and after that, current progress and prospects have been discussed. Literature reviews revealed that electrospun PCL nanofibrous composites had gained significant attention in regenerative medicine, and these structures have shown notable development in mechanobiological properties. This evidence is a crucial success for biomedical strategies, especially in regenerative medicine.

Definition and Validation of Cavitating Rocket Turbopump Transmission Matrices for Modular Multi Actuator Disk Approach

Cavitation induced instabilities are a critical issue to face in the design process of rocket turbopumps, and reduced-order linear methods still represent a powerful tool to evaluate their onset. The modular multi actuator disk approach is a successful method developed to study the dynamic behavior of compressors. Recently, it has also been proposed for the assessment of the dynamics of cavitating turbopumps. In this paper, the modular multi actuator disk approach was used as the mathematical framework to implement and validate a well-established model of a cavitating inducer developed in the 90s for the assessment of azimuthal instabilities with a particular focus on rotating cavitation. The matching between the obtained results and the available data in the open literature for a tapered inducer validated the dynamic model of the cavitating inducer implemented in the new mathematical framework. The flexibility introduced by the new modular approach represents a step toward the study of complex hydrodynamic systems that are not limited to the simplified configuration studied by the actuator disk model proposed in the 90s.

Probabilistic Characterization of the Vegetated Hydrodynamic System Using Non-Parametric Bayesian Networks

The increasing risk of flooding requires obtaining generalized knowledge for the implementation of distinct and innovative intervention strategies, such as nature-based solutions. Inclusion of ecosystems in flood risk management has proven to be an adaptive strategy that achieves multiple benefits. However, obtaining generalizable quantitative information to increase the reliability of such interventions through experiments or numerical models can be expensive, laborious, or computationally demanding. This paper presents a probabilistic model that represents interconnected elements of vegetated hydrodynamic systems using a nonparametric Bayesian network (NPBN) for seagrasses, salt marshes, and mangroves. NPBNs allow for a system-level probabilistic description of vegetated hydrodynamic systems, generate physically realistic varied boundary conditions for physical or numerical modeling, provide missing information in data-scarce environments, and reduce the amount of numerical simulations required to obtain generalized results—all of which are critically useful to pave the way for successful implementation of nature-based solutions.

THEORETICAL PRINCIPLES OF SAVING GROUNDWATER USE INFOGEOFRAMES IN HYDROGEOLOGY

Theoretical bases of information support of geological prospecting researches and works on use and protection of underground waters are considered. The methodology of information support is based on the principles of target infogeological structuring of the geological environment on the basis of traditional methods of formational analysis taking into account hydrogeological (hydrodynamic and hydrochemical) components. Prospects for the introduction of a system of frame organization of the geological environment in infogeological modeling are discussed. In the applied sense, research focuses on that part of the underground hydrosphere that is now or in the future able to meet the needs of mankind in drinking, mineral, technical, industrial, thermal waters. The principles of management of groundwater resources based on the ratio of renewable natural (dynamic resources, which make up the majority of open hydrodynamic systems in the zone of intensive water exchange), renewable manmade (artificial or disturbed resources) and non-renewable components (capacitive reserves and semi-closed structures). Accordingly, during the operation of deposits, not only the calculated value of the allowable level reduction but also the "allowable balance" of groundwater should be observed. It is also proposed to define and agree on the boundaries of deposits and boundary conditions. The latter should be responsible not only for the water intake production, but also to demonstrate the degree of hydrodynamic, hydrochemical, geological protection and the risk of quantitative and qualitative depletion. Groundwater extraction must be balanced by restoring their reserves, which can be achieved by combined alternate water use of surface and groundwater sources, the creation of infiltration basins and more. On this conceptual basis, a system of information support for research and work on the use and protection of groundwater is proposed, which in the long run should be as close as possible to world standards.

Convective differential rotation in stars and planets – I. Theory

ABSTRACT We derive the scaling of differential rotation in both slowly and rapidly rotating convection zones using order of magnitude methods. Our calculations apply across stars and fluid planets and all rotation rates, as well as to both magnetized and purely hydrodynamic systems. We find shear |R∇Ω| of order the angular frequency Ω for slowly rotating systems with Ω ≪ |N|, where N is the Brünt–Väisälä frequency, and find that it declines as a power law in Ω for rapidly rotating systems with Ω ≫ |N|. We further calculate the meridional circulation rate and baroclinicity and examine the magnetic field strength in the rapidly rotating limit. Our results are in general agreement with simulations and observations and we perform a detailed comparison with those in a companion paper.

On the Integrable Chaplygin Type Hydrodynamic Systems and Their Geometric Structure

A class of spatially one-dimensional completely integrable Chaplygin hydrodynamic systems was studied within framework of Lie-algebraic approach. The Chaplygin hydrodynamic systems were considered as differential systems on the torus. It has been shown that the geometric structure of the systems under analysis has strong relationship with diffeomorphism group orbits on them. It has allowed to find a new infinite hierarchy of integrable Chaplygin like hydrodynamic systems.