Hydrodynamic Problem Research Articles

Исследование однородности распределения накачки в активном элементе в виде стержня мощных квантронов с диодной накачкой

Experimental investigations and calculations of various optical schemes of high-power DPSS and solid-state lasers with cylindrical active elements and transverse pumping by laser diode arrays are presented. Numerical simulations were used to solve hydrodynamic problems and problems of geometric optics for DPSS with rod active elements pumping by quasi-continuous laser diode arrays. The dependencies of the uniformity of active element illumination on the geometry of the optical scheme were studied, as well as the influence of the uniformity of coolant flows over different pump arms on the uniformity of the luminescence distribution pro-file from the end of the active element. An optical pumping scheme for active element of a high-power DPSS with an optimal geometry is proposed and implemented.

SPHydro: Promoting smoothed particle hydrodynamics method toward extensive applications in ocean engineering

This paper aims at presenting a general-purpose-oriented and fully parallelized meshless framework to simulate complex Fluid–Structure Interaction (FSI) problems in ocean engineering. In this framework, a Weakly Compressible Smoothed Particle Hydrodynamics (WCSPH) solver is combined with several advanced pre- and post-processing techniques. Based on the framework, we have been developing our in-house WCSPH-FSI package named SPHydro for solving hydrodynamic problems involving complex FSI processes in an accurate, efficient, and convenient manner. Three benchmarks are performed to qualitatively and quantitatively validate the accuracy and convergence of SPHydro. In addition, several practical applications are also provided to further highlight the generality and applicability of SPHydro in ocean engineering simulations. It is demonstrated that SPHydro holds satisfactory performance in solving complex FSI problems in ocean engineering and that the present framework can be further developed to tackle more complex FSI problems for general engineering applications due to its high flexibility and extensibility.

Простые волны и малоамплитудные возмущения в радиационной газодинамике

The paper analyses one-dimensional simple waves and small-amplitude disturbances in radiating and scattering grey gas. The governing equation of radiation acoustics describing the dynamics of simple waves is derived. Radiation-thermal dissipation conditions and radiation resistance force are introduced into this equation to describe the propagation and attenuation of various radiation perturbation waves. To study non-equilibrium wave phenomena in a radiating medium, the phenomenological Whitham method is used. This method is an effective way to analyse fundamental modes when more than one velocity appears in the governing equation. The use of this method is demonstrated in the paper by considering the evolution of one-dimensional harmonic waves caused by a short-wave initial perturbation of the equilibrium state of the radiating and scattering medium. For all wave modes, analytical solutions have been obtained, which allow us to understand their physical significance. These solutions can be, in particular, an additional test for radiative hydrodynamic codes operating in the radiative acoustics regime. The general approach can be useful in the development of higher-order Godunov numerical schemes for radiation hydrodynamics problems.

Can probability theory really help tame problems in mathematical hydrodynamics?

Article Can probability theory really help tame problems in mathematical hydrodynamics? was published on December 30, 2022 in the journal Mitteilungen der Deutschen Mathematiker-Vereinigung (volume 30, issue 4).

Analytical solution to wave diffraction by a hemisphere in infinite water depth using the multipole expansion method

Linear water wave diffraction by a hemisphere in infinite water depth is investigated using the multipole expansion method in this paper. In the spherical coordinate system, the diffraction potential is expressed in the form of multipole wave potentials and the wave-free potential, as derived by Hulme (1982) for radiation potentials. The issues associated with the high-order multipole expansion are solved in this paper. The new method can calculate the multipole wave potentials at arbitrary orders and thus successfully calculate the diffraction potentials on the body surface and free surface around a hemisphere. The wave exciting forces acting on hemispheres are calculated using the near-field and far-field methods, which utilizes the radiation potential computed by Hulme's (1982) method to verify the accuracy of the analytical solution in this paper. Compared with the far-field method, the analytical solution in this paper converges more quickly as the truncation term N increases, especially when the wavenumber Ka is large. In this paper, the theory of applying the multipole expansion method to solve hydrodynamic problems with a hemisphere on the free surface is completed, which makes the multipole expansion method no longer limited to low-order expansion calculations and can be applied to more fields.

Effect of long-term infiltration on porosity-permeability evolution in carbonate rocks: An online NMR coupling penetration test

Investigating the porosity–permeability evolution in carbonate rocks during long-term infiltration is a challenging hydrodynamic problem in rock engineering (hydroelectric engineering, CO2 geological storage, and oil/gas development). In general, we consider the evolution of porosity and permeability to be positively correlated. However, the complex pore structures in carbonate rocks include multiscale pore-fracture structures, such as intergranular pores, dissolution pores, and even fractures. Although the permeability levels of carbonate rocks are similar, the evolution of the pore structure is highly variable. Here, we use the “rock seepage coupled nuclear magnetic resonance (NMR) online analysis and imaging system” platform to conduct a long-term penetration test in carbonate rocks under the coupling of stress and reactive fluid. The variation in the multiscale pore volume was quantitatively characterized by the inversion of the T2 spectrum. Subsequently, in combination with permeability measurement, the permeability-porosity evolution during long-term infiltration can be roughly divided into three stages. The experimental results show that the evolution of permeability exhibits noticeable stress sensitivity at the initial stage of the test (0–156 h). Since the compression of the pore volume is the dominant mechanism, the permeability decreases with porosity at this stage. A negative correlation between the evolution of porosity and permeability was observed during the subsequent stage of the test (156–400 h). This phenomenon may be attributed to mineral dissolution at this stage, causing the cementation to be exfoliated from the pore surface and to re-precipitate at the pore throat, locally blocking the seepage channels. As the test continued (400–720 h), mineral dissolution transitioned from micropores to mesopores and macropores, with a synergistic increase in porosity and permeability. These results revealed the competing mechanism of stress compression and mineral dissolution during long-term infiltration, providing an accurate prediction of the seepage properties in carbonate rocks.

Research and Development of Criterial Correlations for the Optimal Grid Element Size Used for RANS Flow Simulation in Single and Compound Channels

At present, software products for numerical simulation of fluid dynamics problems (ANSYS Fluent, Ansys CFX, Star CCM, Comsol, etc.) problems are widely used. These software products are mainly based on the numerical solution of the Navier–Stokes equations, the most common and computationally easy method of solving, which is Reynolds averaging (RANS), and further closing the system using semi-empirical turbulence models. Currently, there are many modeling methods and turbulence models; however, there are no generalized recommendations for setting up grid models for modeling flows, while for practical use both the correct mathematical models and the setting of the computational grid are important. In particular, there are no generalized recommendations on the choice of scale of global elements of grid models for typical single channels. This work is devoted to the development and study of relations for a priori estimation of the parameters of a grid model in relation to solving hydrodynamic problems with fluid flow in channels. The paper proposes the introduction of a generalized grid convergence criterion for single channels at high Reynolds numbers. As single channels, a channel with a sudden expansion, a channel with a sudden contraction, and diffuser channels with different opening angles are considered. Based on the results of variant calculations of typical single channels at various Reynolds numbers and various geometric parameters, generalized criterion correlations were obtained to find dimensionless linear scales of grid elements relative to the hydrodynamic characteristics of the flow in the channel. Variant calculations of the compound channel were investigated, which showed the adequacy of correlations proposed.

THERMOPHYSICAL PROPERTIES OF MULTICOMPONENT OZONE-SAFE REFRIGERANTS

The paper presents the results of the analysis of the use of multi-component working bodies in throttle cooling systems of an open or closed cycle using the Joule-Thompson effect (cryocoolers). The use of multicomponent refrigerants makes it possible to obtain the required thermodynamic efficiency of the cooling cycle at low throttling pressure values of 1.5...2.0 MPa. This effect becomes possible due to the introduction of components with a higher boiling point into the composition of the working fluid. In order to obtain higher operational characteristics, irreversible losses in J-T cryocoolers must be analyzed and ways of their reduction determined. The thermodynamic analysis of the installation cycle and subsequent design of the heat exchange equipment of cryocoolers formulates the conclusion that in order to optimize the design of the heat exchange equipment of the installation, which consists in solving hydrodynamic and thermal problems, a careful determination of the thermophysical properties of mixed working bodies is necessary. It should be taken into account that the principle of additivity is not always possible to apply for different compositions. By choosing certain components of the working body and changing their mass composition, it is possible to obtain the necessary properties. On the basis of experimental studies conducted at Ltd «DNIPRO MTV», the main components of the refrigerant were determined. When using mixed refrigerants, their thermophysical and calorific properties are determined taking into account the polarity of the molecules and the mass amount of the components of the mixture. Methods for determining thermophysical properties were analyzed, proposed by generalizing dependencies for determining the caloric properties of mixed refrigerants. the main components of the refrigerant are determined, namely: methane CH4, ethylene С2Н4, propane С3Н8 and isobutane С4Н10. The peculiarity of these substances is that they belong to hydrocarbons of the alkane series and are characterized by different values of thermophysical parameters. When calculating the parameters of the throttling and heat exchange processes, it is necessary to determine not only the integral characteristics, but also their values ​​at certain parameters at the characteristic points of the process on the cycle diagram. Therefore, there is a need for obtained generalized dependencies both for individual components and for the mixture as a whole. With a significant number of options for parameters and components of the mixture, when determining the thermophysical properties of refrigerants, it is advisable to use empirical dependencies, where the values ​​of the coefficients are obtained by processing experimental data. Bibl. 15, Fig. 1, Tab. 1.

Modelling multiphase gases in cosmological simulations using compressible multifluid hydrodynamics

ABSTRACT The diffuse medium in and around galaxies can exist in a multiphase state: small, cold gas clouds contributing significantly to the total mass embedded in pressure equilibrium with a hotter, more diffuse volume-filling component. Modelling this multiphase state in cosmological simulations poses a significant challenge due to the requirements to spatially resolve the clouds and consequently the interactions between the phases. In this paper, we present a novel method to model this gas state in cosmological hydrodynamical simulations. We solve the compressible two-fluid hydrodynamic equations using a moving-mesh finite-volume method and define mass, momentum, and energy exchange terms between the phases as operator-split source terms. Using a stratified flow model, our implementation is able to maintain volume fraction discontinuities in pressure equilibrium to machine precision, allowing for the treatment of both resolved and unresolved multiphase fluids. The solver remains second order accurate on smooth hydrodynamics problems. We use the source and sink terms of an existing two-phase model for the interstellar medium to demonstrate the value of this type of approach in simulations of galaxy formation, compare it to its effective equation of state implementation, and discuss its advantages in future large-scale simulations of galaxy formation.

In uence of numerical diffusion on the growth rate of viscous ngers in the numerical implementation of the Peaceman model by the finite volume method

A numerical model of oil displacement by a mixture of water and polymer based on the Peaceman model is considered. Numerical experiments were carried out using the DuMux package, which is a software library designed for modeling nonstationary hydrodynamic problems in porous media. The software package uses the vertex-centered variant of finite volume method. The effect of diffusion on the growth rate of ''viscous fingers'' has been studied. The dependencies of the leading front velocity on the value of model diffusion are obtained for three viscosity models. It is shown that the effect of numerical diffusion on the growth rate of ''viscous fingers'' imposes limitations on calculations for small values of model diffusion.

Viability of circle and sphere theorems in potential theory and hydrodynamics via Maxwell's conjecture

AbstractIn A Treatise on Electricity and Magnetism, Maxwell determines the angles of intersection for which one may use Kelvin's inversion method to obtain the perturbed electric potential upon placing intersecting spherical conductors into a region with a known potential. There are numerous modern applications utilizing this geometric construction in potential theory and hydrodynamics, and generalized circle and sphere theorems play a foundational role in this area of mathematical physics. In his work, Maxwell gives an intuitive argument for obtaining the perturbed potential based on intersecting planar conductors and a spherical inversion, and in this paper we extend his ideas to a full proof using rotational transformations and reflections. In the process, we disprove results in [Proc Lond Math Soc., 1966:3(16)] and [Stud Appl Math., 2001:106(4); Z. Angew. Math. Mech., 2001:81(8)] on boundary value problems in hydrodynamics involving intersecting circles and spheres, and we detail the angles of intersection for which these theorems are viable. Moreover, our proof recovers a special case overlooked by Maxwell for which Kelvin's inversion method may be utilized to obtain full solutions.

Field Theory Approaches to Relativistic Hydrodynamics.

Just as non-relativistic fluids, oftentimes we find relativistic fluids in situations where random fluctuations cannot be ignored, with thermal and turbulent fluctuations being the most relevant examples. Because of the theory's inherent nonlinearity, fluctuations induce deep and complex changes in the dynamics of the system. The Martin-Siggia-Rose technique is a powerful tool that allows us to translate the original hydrodynamic problem into a quantum field theory one, thus taking advantage of the progress in the treatment of quantum fields out of equilibrium. To demonstrate this technique, we shall consider the thermal fluctuations of the spin two modes of a relativistic fluid, in a theory where hydrodynamics is derived by taking moments of the Boltzmann equation under the relaxation time approximation.

Temperature influence on elastic-hydrodynamic interaction of rolling bodies in roller bearing

The lubricating layer located between the rolling bodies plays a crucial role in ensuring the service life of the bearings. Calculating the contact of rolling bodies with each other taking into account their compliance and lubrication parameters is a complex elastic-hydrodynamic problem, for the solution of which complex computer programs are usually used. The paper proposes a hybrid approach based on a separate solution of elastic and hydrodynamic problems with subsequent coordination of the complete solution. The semi-analytical approach of the created method allows solving a large range of problems, and was used in this work to assess the effect of temperature on the stress state of rolling bodies in a roller bearing. The results of calculations show the operability of the procedure and made it possible to establish the dependence of contact stresses on oil viscosity and temperature. The proposed approach is applicable for solving elastic-hydrodynamic problems for any bearings.

TRANSFER PHENOMENA IN ECOLOGICAL SYSTEMS

The phenomenon of transfer finds great application in the problems of hydromechanics of heat and mass transfer associated with structural features and rheological properties of liquid media. A wide distribution of problem solving on the use of ideas about the phenomena of transfer was found in the physicochemical processes of biological media, the processes of transfer of mechanical media, phenomena associated with systems. The article considers cases of solving hydrodynamic problems using the analysis of transport processes for different types of channel flows described by non-stabilized pulsating flow equations, as well as open channel flows that find their place in practice.

A simple Eulerian–Lagrangian weakly compressible smoothed particle hydrodynamics method for fluid flow and heat transfer

AbstractIn this article, we propose a simple, consistent, and robust Eulerian–Lagrangian weakly compressible smoothed particle hydrodynamics (EL‐WCSPH) for the simulation of hydrodynamics and convection heat transfer problems. First, the basic governing equation is formulated using the ALE‐SPH framework. The universal formulation is similar to the standard WCSPH, but the degree of Eulerian and Lagrangian schemes can be controlled by inserting a pre‐defined arbitrary parameter . To alleviate potential numerical errors and inconsistency, particle mass correction is proposed along with particle disorder correction. Then, an algorithm is introduced, in which only a slight modification is necessary compared to the standard WCSPH. Finally, extensive benchmark simulations are conducted to validate the proposed method. As a result, the proposed method is found to perform well in hydrodynamics problems with various flow conditions (pipe flow, lid‐driven problem, Taylor–Green vortex, vortex shedding problem, and water sloshing) and thermal‐hydraulics problems (natural convection in a square cavity).

CENTRIFUGAL PUMP DESIGN USING AXSTREAM® SOFTWARE

The work uses AxSTREAM® software and documentation from SoftInWay (USA) for the design of turbomachines. National Technical University "KhPI" (Kharkov) received the right to use licensed software and documentation of the AxSTREAM® trademark in the educational process. The results of computer modeling and numerical studies were obtained in the process of preparing masters under the program "Industrial Mechanical Engineering". The work uses a modern approach to the design of flow parts of hydraulic machines. It is based on the joint solution of direct and inverse problems of hydrodynamics. The operation of the interface of the AxSTREAM® environment was tested to solve the problems of designing, calculating and optimizing the flow parts of hydraulic machines. The preliminary design module in the AxSTREAM® system is considered. The features of designing and numerical simulation of the flow of a viscous incompressible fluid of a centrifugal pump are considered. In the work, a design of a centrifugal pump for the given technical conditions was obtained. The energy parameters of the centrifugal pump have been calculated. A study was made of the influence of impeller turning on the energy characteristics of the pump. The calculation of the spatial flow in the flow part of the impeller of the pump NK 65/35-70 was performed. Comparison of the results of calculations by both methods with experiment is presented. The expediency of using semi-empirical models to obtain preliminary approximations on the optimization of the flow path has been confirmed. A review of modern packages of computational fluid dynamics is carried out.

MODERN SOFTWARE FOR THE NUMERICAL STUDY OF FLOW IN HYDRAULIC MACHINES

In the past few decades, the field of developing computer software systems has been actively developing, which in turn leads to competition in the software market. Qualified engineers working in the hydroturbine industry must be able to use a computer not only at the user level, but also at the programmer level in order to program modules for their own needs based on existing software systems. Recently, numerical simulation has become applicable to an ever wider class of flows, replacing experimental research methods. Certain numerical models are characterized by different areas of applicability and expenditures of computational resources. The paper provides an analytical review of modern CFD software systems. The advantages and disadvantages of these programs are analyzed in terms of building a three-dimensional model of the object of study, creating a computational grid, setting boundary conditions and visualizing the calculation results. The analysis and comparison of existing mathematical models that used to calculate the spatial flow in the flow path of hydraulic machines has been carried out. There are many different programs for solving hydrodynamic problems, some of the advanced commercial software systems are Ansys, SolidWorks Flow Simulation, Autodesk CFD. There are also open source software products. These automatic design systems make it possible not only to perform high-quality modeling of systems of various physical nature, but also to study the response of these systems to external influences in the form of distributions of pressures, temperatures, and velocities. The calculation algorithms in the programs are similar; the distinctive features of the programs can be evaluated according to the following criteria: grid generation, accuracy, reliability (convergence), calculation speed, model physics, system flexibility. The use of modern software packages for studying the hydrodynamic characteristics of the flow in hydraulic machines significantly reduces the time and material resources in comparison with physical modeling.

Hydrodynamic performance and energy absorption of multiple spherical absorbers along a straight coast

The development and utilization of wave energy have great potentiality to alleviate the urgent problem of global energy shortage. Spherical bodies can be used as point absorbers to extract wave energy, and much attention has been paid to the performance of spherical absorbers in an open water domain. This study focuses on the hydrodynamic performance and energy absorption of multiple spherical absorbers in front of a straight coast. The coast is assumed to be a fully reflecting vertical wall, and all the absorbers are restricted to only heave motion. An analytical solution based on linear potential flow theory is developed for the problem of wave diffraction and radiation by multiple absorbers. In the solution procedure, the hydrodynamic problem is transformed into an equivalent problem in an open water domain by applying the image principle. The velocity potential of the fluid motion is solved using the method of multipole expansions combined with the shift of local spherical coordinate systems. Then, the wave excitation force, added mass coefficient, radiation damping coefficient, and energy extraction performance of the absorbers are calculated. Case studies are presented to analyze the effects of the coastal reflection and hydrodynamic interaction among absorbers on the energy extraction performance of the wave energy converter (WEC) system. The effects of wave frequency, incident angle, spacing between the absorber and coast, submergence depth, absorber number, and plane layout are also clarified. The results suggest that the energy extraction performance of an isolated absorber is significantly improved when the motions of the waves and absorber are in resonance, and the coastal reflection can enhance the overall energy extraction performance for a WEC system with multiple absorbers. In addition, when the number of absorbers increases, the effects of the coastal reflection and hydrodynamic interaction become more complicated.

Numerical Assessment of Symmetric Wedge Water-entry Impact Using OpenFOAM

The hydrodynamic problem of a two-dimensional symmetric wedge vertically entering the water, initially flat, with a deadrise angle of 30° is considered. This numerical study assesses turbulence, gravity, viscosity, and surface tension during the early stage of penetration. The OpenFOAM software package has been used to simulate the water entry of the wedge at a constant speed of 3 m/s. The governing equations have been numerically built in the solver called overInterDyMFoam. The method has also been used to model the turbulence effect. The effects of turbulent and laminar flow assumptions and for the laminar flow, viscosity, gravity, and surface tension influence on pressure distributions along the wedge's walls have been investigated. It is illustrated that turbulence, viscosity, and surface tension have negligible effects on the pressure distribution in the primary water entry process. However, the pressure distribution is found to be significantly influenced by gravity.

Physical mechanisms of conduction-to-keyhole transition in laser welding and additive manufacturing processes

Thermo-hydrodynamic phenomena which take place during laser welding or additive manufacturing processes as laser powder bed fusion, have been investigated for years, but recent advances in X-ray images and in situ analysis have highlighted new findings that are still under debate. Conduction-to-keyhole transition, and more broadly, keyhole dynamics, are typical cases, where complex coupling between hydrodynamic and optical problems are involved. In this paper, a keyhole and melt pool model is developed with the software COMSOL Multiphysics®, where laser energy deposition is computed self-consistently thanks to a ray tracing algorithm. The model successfully reproduces experimental findings published in the literature and helps to analyze accurately the role played by the beam trapping phenomenon during the conduction-to-keyhole transition, in both spot welding (i.e., stationary laser illumination) and welding configurations (i.e., with scanning speed). In particular, it is shown that depending on the welding speed, multiple reflections might be either a stabilizing or a destabilizing factor. Understanding these mechanisms is thus a prerequisite for controlling the stability of the melt pools during the joining or the additive manufacturing processes.