Hydrodynamic Systems Research Articles

An Investigation of Blood Flow through Parallel Plate Channel in the Presence of Inclined Magnetic Field with Heat and Mass Transfer

A Mathematical model for MHD flow of blood between a parallel plate channel with the effect of heat transfer and mass transfer has been investigated. An inclined magnetic field has been applied to the parallel plates filed with porous substance. The partial differential equations which are governing the flow field have been resolved numerically by applying non-dimensional parameters. The effect of inclination of magnetic field on the parallel plate channel has been analyzed, furthermore the effect of Prandtl number, thermal radiation, heat source parameter, chemical reaction parameter on the flow of blood has been studied in detail. The numerical results are analyzed and are represented graphically in the form of velocity profile, temperature profile and concentration profile. Moreover, the velocity of blood, temperature profile and concentration profile is adapting a wavy pattern as the various parameters vary.
 HIGHLIGHTS
 
 Heat and Mass transfer in hydro dynamical and biological systems is relevant in lots ofdiagnostic and coronary heart related issues that contains the changes in temperature hence this study can be of greater importance
 This study analyses the effect of Inclination of magetic field and heat source parameter on the flow of blood through parallel plate channel which can be utilised in the field of medical science
 Maximum emphasis is given on the blood flow with the impact of different parameters and how it behaves under the influence of these forces hence providing a pathway to deal with many deadly heart related diseases
 
 GRAPHICAL ABSTRACT

Dynamical spacetimes from nonlinear perturbations

Analog gravity describes fluctuations of hydrodynamic systems in terms of a massless scalar field propagating on curved spacetimes. This analogy between hydrodynamic and gravitational systems remains largely unexplored for nonlinear dynamical effects. In this paper, we provide the first description of dynamical analog spacetimes up to arbitrary order nonlinear perturbations constructed about stationary solutions. We find a high frequency response that exhibit known properties of perturbed black holes, as well as a low frequency regime for analog spacetimes with novel characteristics. Our framework more generally describes nonlinear perturbations of compressible hydrodynamic systems as analogs of nonlinear wave phenomena on black hole spacetimes.

A droplet‐based electricity generator with ultrahigh instantaneous output and short charging time

AbstractThe past several years have witnessed the rapid development in effectively transforming randomly distributed water kinetic energy into electrical energy, especially triggered by the emergence of droplet‐based electricity generators (DEG). Despite this, it still suffers from relatively low average power density, which is also achieved at the cost of long charging time, the time to reach stable and saturated surface charge density either through continuous droplet impingement or precharging. Although the harvested energy per droplet in DEG remains as the dominant metric, ultrahigh instantaneous output and short charging time are equally important in some specialized applications such as instantaneous luminescence. Here, we conduct systematical modeling and optimization to build the link between the hydrodynamic and electrical systems, which enables us to determine ultrahigh instantaneous output and short charging time by tailoring parameters such as dielectric layer thickness, droplet ion concentration, and external load. We envision that this strategy in achieving ultrahigh instantaneous output as well as shortening charging time would provide insights and design routes for water energy harvesting.

Modelling Nonlinear Supply Chains Using Methods of System Dynamics

This paper treats a three level nonlinear supply chain, which consists from a manufacturer, a distributor and a retailer as a dynamical system. The dynamic behavior of supply chain is modelled by using the continuous Lorenz-like model with disturbances. The Lorenz model is known from physics in the study of dissipative hydrodynamical systems with excitation and represents a paradigmatic example of the deterministic system, which is able to exhibit chaotic motions. Very complex supply chain relationships are modelled due to the information flow distortion at the distributor, caused by disturbances, which appear at the retailer. By using the proposed nonlinear supply chain model, the steady state, the saturation and the chaotic state of the supply chain are analyzed, respectively. The range of parameter values, which are characteristic for the appearance of such states are determined. In the paper, the meaning of the regular state in which the supply chain cannot keep due to the disturbances and the risk of the saturation state are explained. In the analysis of such states, the multistage homotopic perturbation method is used. The gained results are checked analyticaly or by the help of standard numerical integration, such as the Runge-Kutta method.

A two-dimensional boundary value problem for one overdetermined system

In the half-plane, we consider a stationary system of the two-velocity hydrodynamics with one pressure and homogeneous divergent and inhomogeneous boundary conditions for two velocities. This system is overdetermined. The solution of this system is reduced to the sequential solution of two boundary value problems: the Stokes problem for one velocity and pressure and the overdetermined system for the other velocity. With an appropriate choice of function spaces, the existence and uniqueness of a generalized solution with an appropriate stability estimate has been proved.

Preface

Due to recent pandemic, 2022 6th International Conference on Hydrodynamics, Energy and Electric Power System (HEEPS 2022) was held virtually online during March 25-27, 2022. The decision to hold the virtual conference was made in compliance with many restrictions and regulations that were imposed by countries around the globe. Such restrictions were made to minimize the risk of people contracting or spreading the COVID-19 through physical contact. There were 100 individuals who attended this online conference, represented many countries including China, India, Mexico, Australia and Italy.The conference is an international conference for the presentation of technological advances and research results in the fields of Hydrodynamics, Energy and Electric Power System. The conference brings together leading researchers, engineers and scientists in the domain of interest from around the world. We warmly welcome previous and prospected authors submit your new research papers to HEEPS 2022, and share the valuable experiences with the scientists and scholars around the world.During the conference, the conference model was divided into three sessions, including oral presentations, keynote speeches, and online Q&A discussion. In the first part, some scholars, whose submissions were selected as the excellent papers, were given about 5-10 minutes to perform their oral presentations one by one. Then in the second part, keynote speakers were each allocated 30-45 minutes to hold their speeches. In the second part, we invited four professors as our keynote speakers. Prof. Abdul Hasib Chowdhury, Bangladesh University of Engineering and Technology, Bangladeshi, performed a speech: Improving frequency resilience of power systems through dynamic-adaptive load shedding. And then we had Prof. Chuanchang Li, Changsha University of Science & Technology, China. He delivered a speech: Emerging composite phase change materials for thermal and cold energy storage. Prof. Zong Zhi, Dalian University of Technology, China. He shared a speech: Configuration Hydrodynamics of Trimaran ships. Lastly, we were glad to invite Assoc Prof. Pengcheng Lin, Guangdong University of Technology, China. He made a wonderful speech: Phase change gel: from organic to inorganic, from foundation to application. Their insightful speeches had triggered heated discussion in the third session of the conference. Every participant praised this conference for disseminating useful and insightful knowledge.List of Committee member is available in this pdf.

Ab initio method of calculating invariant measure for turbulent flow

We present a method of calculating the invariant measure (IM) of hydrodynamical systems describing incompressible viscous fluid flow in bounded 3D volume V. Using a basis { w I } of zero-divergence vector functions on V satisfying boundary conditions we transform the Navier–Stokes equations (NSE) for the velocity field v ( x , t) = ∑ I v I (t) w I ( x ) into a simple system of ordinary differential equations for v I (t). The fact that fluid consists of a finite number of molecules in thermal motion implies that the number N of variables v I is finite too and that the system of equations for v I (t) contains a white-noise term. We prove that all solutions of this system are global, the IM exists and is unique. Its density ψ(v) defined on the phase space satisfies an elliptic partial differential equation (PDE). Expanding into Hermite functions He μ (v) φ ε (v) (where φ ε is a Gaussian function on , He μ are Hermite polynomials orthonormal with the weight φ ε and are IM mean values of He μ ) we transform this PDE into an infinite system of linear algebraic equations for and suggest some methods for solving it numerically. From known first- and second-order we could easily calculate mean turbulent velocity and Reynolds stress at any point x . Cylindrical pipe flow is used to illustrate the method everywhere in the paper. All conclusions are derived from the mathematical model by rigorous mathematics, with no further assumptions. All approximations can be arbitrarily improved.

PERFECTION OF FUNDAMENTALS OF MATHEMATICAL METHOD OF DESIGN OF HYDROSYSTEMS OF DRIVE OF TECHNICAL MACHINES

The vast majority of modern research on the study of hydromechanical systems is based on the use of the theory of automatic control and management. One of the main components of technical machines and cells are their drives. Hydraulic drives are often used as power. In general, its functional and operational characteristics have a decisive influence on the properties of hydrodynamic systems and general technical machines. In this regard, close attention is paid to the study of hydraulic power drives. However, the power hydraulic drive of technical machines and units in one form or another necessarily includes both electric and mechanical drives, which turns it into a system of various drive systems. The vast majority of modern research is devoted to the study of hydraulic drives, which are based on spool-type hydraulics, which limits the possibility of using new structural materials in the drive systems of technical machines. Many technical machines and installations, especially in agro-industrial complexes, work in harsh conditions, with high temperatures and dust, low quality of working fluid and other unfavorable characteristics that significantly reduce the reliability of drive systems equipped with hydraulic spool types and quality equipment. At current levels of working pressure in the hydraulic system, the forces and speeds of the working bodies of technical machines and units of the agro-industrial complex, the compressibility of the working fluid and the flexibility of the hydraulic elements of the drive system are determined, become noticeable, which requires further improvement of theory and methodology. The theoretical basis of the method of calculating the equipment drive system has been improved on the basis of the complex characteristics of the hydraulic system introduced by the author - the resulting volumetric stiffness is used to simplify the drive modeling process by increasing the accuracy of calculation and analysis of its results.

КРАЕВАЯ ЗАДАЧА ДЛЯ ОДНОЙ ПЕРЕОПРЕДЕЛЕННОЙ СИСТЕМЫ, ВОЗНИКАЮЩЕЙ В ДВУХСКОРОСТНОЙ ГИДРОДИНАМИКЕ

In the half-plane R2 , we consider a stationary system of two-velocity hydrodynamics with one pressure and homogeneous divergent and boundary conditions for two velocities. The system is overdetermined. The solution to this system is reduced to a consistent solution of the two boundary value problems: the Stokes problem for one velocity and pressure and the overdetermined system for a different velocity. For an appropriate choice of function spaces, the existence and uniqueness of the generalized solution with a corresponding stability estimate is proven.

Existence and stability of unidirectional flocks in hydrodynamic Euler alignment systems

In this note we reveal new classes of solutions to hydrodynamic Euler alignment systems governing collective behavior of flocks. The solutions describe unidirectional parallel motion of agents, and are globally well-posed in multi-dimensional settings subject to a threshold condition similar to the one dimensional case. We develop the flocking and stability theory of these solutions and show long time convergence to traveling wave with rapidly aligned velocity field. In the context of multi-scale models introduced in \cite{ST-multi} our solutions can be superimposed into Mikado formations -- clusters of unidirectional flocks pointing in various directions. Such formations exhibit multiscale alignment phenomena and resemble realistic behavior of interacting large flocks.

Propulsive performance of a pitching foil in a side-by-side arrangement with auxiliary pitching foil

A two-dimensional computational study is performed in the present work to simulate two NACA 0012 (National Advisory Committee for Aeronautics) airfoils pitching in a side-by-side configuration at Reynolds Number (Re) 12,000. An auxiliary airfoil with a smaller size is used to enhance the efficiency of the main airfoil. The thrust and lift coefficients of the main airfoil are quantified and compared with an isolated pitching airfoil for a range of reduced frequencies (k=1 to 8) and phase differences (Φ=0°to 180°) between the airfoils. The thrust force increases gradually with a maximum enhancement at an intermediate phase difference (Φ) between the airfoils and decreases further. The simulations cover three main flow regimes depending upon the vortex structure shed by the airfoils, i.e. (i) when both airfoil shed von Kármán (KV) vortex street (ii) auxiliary airfoil sheds von Kármán whereas main airfoil sheds reverse von Kármán (RKV) vortex street (iii) both airfoil sheds reverse von Kármán vortex street. The numerical results reveal that an auxiliary airfoil significantly changes the main airfoil’s hydrodynamic characteristics compared to an isolated airfoil. Maximum thrust enhancement of 23% and maximum efficiency enhancement of 49.2% are obtained compared to an isolated airfoil. The phase difference significantly impacts the propulsive efficiency of auxiliary foil, whereas its influence is marginal on the main foil. The interaction of different wake structures shed by the auxiliary, and the main airfoil leads to the formation of the deflected jet. The jet deflection and wake width are quantified to understand the influence of an auxiliary airfoil in a side-by-side configuration with the main airfoil. The finding of this study is expected to provide new insight for developing and enhancing the performance of hydrodynamic propulsive systems by adding an auxiliary airfoil.

Geophysical fluid dynamics at deep levels in the lithosphere in the Ciscaucasia

The geophysical fluid dynamics at deep levels in the Ciscaucasia lithosphere is analyzed. The analysis shows that this structurally complex region lacks geological ability to ensure spatially extended hydraulic communication between all closely spaced geoblocks. Given zero meteoric water flows and deficient connate water, the phenomena observed in all basins are reflective of major vertical downward flows of fluids between geological formations along high-amplitude faults and discontinuities, and point at the dominating nature of a cardinally new type of hydrodynamic systems – the upper and lower hydrogeological levels. The regional and local oil and gas contents in any geological environment is a complex function of various factors and different-scale multi-vector fluid dynamics mechanisms and processes, such as generation of hydrocarbons, their primary and secondary migration, formation and spatial arrangement of reservoirs, conservation and dissipation of oil and gas accumulations. This is an integral effect of interrelation of geodynamic and geophysical fluid dynamic processes, which conditions dependence of oil and gas content on the geophysical fluid dynamics in a region – hydrogeochemical, groundwater dynamics, thermobaric conditions, etc. These dependences can be used as the reliable qualitative and quantitative criteria for hydrocarbon exploration at minimized risk and maximized efficiency of geological exploration.The study was carried out under the state contract with the Ministry of Science and Higher Education of the Russian Federation, Project No. 075-00069-20-02 dated 10 September 2020, Topic No. AAAA-A20-120092590017-4.

Колебания системы твёрдых тел, частично заполненных вязкими жидкостями, под действием упругодемпфирующего устройства

In this paper, we investigate the linearized two-dimensional problem on small motions of a system of rigid bodies partially filled with viscous incompressible fluids and connected in series by springs. The first and last bodies are attached by springs to two supports with a given law of motion. The trajectory of the system is perpendicular to the direction of gravity, and the damping forces acting on the hydrodynamical system are generated by the friction of bodies against a stationary horizontal support. For the described system, the law of total energy balance is formulated. Using the orthogonal projection method and a number of auxiliary boundary problems, the original initial-boundary value problem is reduced to the Cauchy problem for a first-order differential-operator equation in the orthogonal sum of some Hilbert spaces. The properties of operator matrices, which are coefficients of the obtained differential equation, are investigated. A theorem on the unique solvability of the resulting Cauchy problem on the positive semi-axis is proved. On the basis of the proved theorem, sufficient conditions for the existence of a strong with respect to time solution of an initial-boundary value problem describing the evolution of a hydrodynamical system, are found. From a mathematical point of view, the system under consideration is a finite-dimensional perturbation of the well-known S.G. Krein’s problem on small motions of a viscous fluid in an open vessel.

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.

Special Conditions for the Formation of Large Exogenic Epigenetic Uranium Deposits

—For uranium deposits to form from oxidizing waters of surface origin, it is necessary to combine several conditions and processes of different ranks that make up a specific mineral system. Analysis of exogenic deposits of different scales and ore quality from different regions of the world showed that, among all the critical processes necessary for the formation of large deposits and vast provinces, global tectonic movements play a particular role. A geodynamic regime with moderate vertical differentiation of crustal blocks is most favorable for development of a hydrodynamic infiltration ore-forming system under near-surface conditions. An infiltration artesian system is capable of functioning for millions and tens of millions of years, which makes it possible to accumulate large uranium reserves at the geochemical reduction barrier. The required regime is typical of regions with a certain geotectonic position. For example, the peripheral regions of orogenic belts along tectonic plate boundaries, as well as the frames of some long-lived intraplate deep faults. In the same regions, the proximity of infiltration and expulsion hydrodynamic systems is possible. In local areas where groundwater of various origin and composition interact, conditions occur for particularly efficient uranium concentration in ores. Limitations on the productivity of a hydrodynamic infiltration ore-forming system are imposed by historical factors that predetermine the formation of the uranium source and lithological conditions for ore localization, as well as the climatic conditions of the time in which the system functioned and postore conditions determining the preservation of mineralization accumulated in the system. The revealed patterns be used to predict ancient provinces of exogenic uranium deposits.

Автоматизированная генерация каскадных моделей турбулентности методами компьютерной алгебры

Описана разработанная методика генерации уравнений каскадных моделей турбулентности с помощью систем компьютерной алгебры. Методика позволяет варьировать размер масштабной нелокальности модели, вид квадратичных законов сохранения и спектральных законов, знаменатель геометрической прогрессии масштабов. Ее использование позволяет быстро и безошибочно генерировать целые классы моделей. Может использоваться для разработки каскадных моделей гидродинамических, магнитогидродинамических и конвективных турбулентных систем. There is a great variety of shell turbulence models. Such models reproduce certain characteristics of turbulence. A model that could reproduce all turbulence regimes does not exist at the moment. Information about a particular model is contained in a set of persistent quantities, which are some quadratic forms of turbulent fields. These quadratic forms should be formal analogs of the exact conserved quantities. It is important to note that the main idea of Shell models presupposes a refusal to describe the geometric structure of movements. At the same time, it is well known that turbulent processes in spaces of two and three dimensions behave differently. Therefore, the provision of certain combinations of conserved quantities allows indirect introducing into the shell model the information about the dimension of the physical space in which the turbulent process develops. Purpose. The aim of this work was to create software tools that would quickly generate classes of models that satisfy one or another set of conservation laws. The choice of a specific model within these classes can then be specified using additional physical considerations, for example, the existence of a given probability distribution for the interaction of certain shells. Methods. The developed technique for generating equations of shell turbulence models is carried out using symbolic computation systems (computer algebra systems - CAS). Note that symbolic packages are used not for studying ready-made shell models, but for the automated generation of the equations of these models themselves. The technique allows varying the value of the scale nonlocality of the model, the form of the quadratic conservation laws and spectral laws, the denominator of the geometric progression of scales. It allows quickly and accurately generating the entire set of classes of the models. It can be used to develop shell models of hydrodynamic, magnetohydrodynamic and convective turbulent systems. Findings. It seems that the proposed technique will be useful for studying the properties of turbulence in the framework of cascade models

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.

Soliton gas in integrable dispersive hydrodynamics

We review the spectral theory of soliton gases in integrable dispersive hydrodynamic systems. We first present a phenomenological approach based on the consideration of phase shifts in pairwise soliton collisions and leading to the kinetic equation for a non-equilibrium soliton gas. Then, a more detailed theory is presented in which soliton gas dynamics are modelled by a thermodynamic type limit of modulated finite-gap spectral solutions of the Korteweg–de Vries and the focusing nonlinear Schrödinger (NLS) equations. For the focusing NLS equation the notions of soliton condensate and breather gas are introduced that are related to the phenomena of spontaneous modulational instability and the rogue wave formation. The integrability properties of the kinetic equation for soliton gas are discussed and some physically relevant solutions are presented and compared with direct numerical simulations of dispersive hydrodynamic systems.

Complete Integrability of a New Class of Hamiltonian Hydrodynamic Type Systems

In this paper we consider a new class of Hamiltonian hydrodynamic type systems, whose conservation laws are polynomial with respect to one of field variables.

Theoretical analysis and justification of the process of interaction of hydrodynamic oscillatory systems under technological influence on grain and leguminous crops

The article presents the results of a theoretical analysis of the regularities of mass transfer occurring during the technological impact on soybean grain in a liquid environment during the inactivation of anti-nutrient substances. Based on the classic hydrodynamic patterns occurring during mass transfer in biological material, it is established that processing of soybean without further intensifying the process influences not rational from the perspective of productivity and quality of manufactured products. To this end, the article considers the issues of controlling the mass transfer process by influencing the driving forces and, accordingly, the diffusion coefficient of additional means that intensify the process.