Ideal Incompressible Liquid Research Articles

Wave resistance of slender body in unsteady motion under an ice sheet

The paper is devoted to the theoretical study of the rectilinear unsteady movement of a slender body in a liquid near the free surface and an ice sheet. Water is an ideal incompressible liquid, and the motion of the liquid is potential. The ice cover is modeled by a floating viscoelastic plate. The viscoelastic properties of ice are described using the Kelvin–Voigt model. A slender body of a given shape in the liquid flow is modeled by the flow of the source-sink system. Various modes of body movement are considered: acceleration, deceleration, movement at a given speed. The effect of the ice sheet, acceleration and deceleration of the body on its wave resistance is analyzed. It is obtained that unsteady modes of motion (acceleration and deceleration) significantly affect the wave resistance of a slender body. Motion with low initial acceleration makes it possible to reduce amplitude of the first-time hump of wave resistance. During body deceleration to a full stop, the curve of wave resistance has an oscillations. Reduction of deceleration coefficient results in decrease of oscillation amplitude of wave resistance curve. The presence of the ice cover smoothes the hump of wave resistance during acceleration and reduces the number of oscillations and their amplitude during deceleration.

Generalised Isentropic Relations in Thermodynamics

Isentropic processes in thermodynamics are fundamental to our understanding of numerous physical phenomena across different scientific and engineering fields. They provide a theoretical reference case for the evaluation of real thermodynamic processes and observations. Yet, as analytical relations for isentropic transformations in gas dynamics are limited to ideal gases, the inability to analytically describe isentropic processes for non-ideal gases is a fundamental shortcoming. This work presents generalised isentropic relations in thermodynamics based on the work by Kouremenos et al., where three isentropic exponents γPv, γTv and γPT are introduced to replace the ideal gas isentropic exponent γ to incorporate the departure from the non-ideal gas behaviour. The general applicability of the generalised isentropic relations is presented by exploring its connections to existing isentropic models for ideal gases and incompressible liquids. Generalised formulations for the speed of sound, the Bernoulli equation, compressible isentropic flow transformations, and isentropic work are presented thereafter, connecting previously disjoint theories for gases and liquids. Lastly, the generalised expressions are demonstrated for practical engineering examples, and their accuracy is discussed.

ACOUSTIC RADIATION OF CHARGED DROPLETS OSCILLATING IN THE SUPERPOSITION OF GRAVITATIONAL AND ELECTROSTATIC FIELDS

The intensity of acoustic radiation and the characteristic widths (depending on the radii and charges of the drops) of the frequency ranges in which the radiation falls have been calculated for charged droplets of convective clouds and near-ground fogs, which are immobile in the superposition of gravitational and electric fields. The calculations have been carried out using the methods of classical mathematical physics taking into account two small parameters: the dimensionless oscillation amplitude and the equilibrium spheroidal deformation of a charged droplet in an external electrostatic field. All calculations have been performed using the model of an ideal incompressible electroconducting liquid. It has turned out that the acoustic radiation from clouds and fogs occurs in the ultrasonic frequency range, while the acoustic radiation of large rain-drops is in the acoustic range audible to the human ear. The boundary between the ultrasonic and sonic radiations is determined by droplet sizes, electric field strengths (in a small vicinity of the droplets), and the values of interfacial tension coefficient.

Control of flow in the side outflow channel

The article discusses the task of regulating the flow in the channel with a lateral outflow. A form of retraction channel is recommended to ensure a smooth flow. Solving the issues with water distribution along the channel route and determining the shape of these channels, providing non-cavitation and non-water current, comes down to the problem of the flow of the ideal incompressible liquid in the channels with a side drain.

On the Instability with Probability One of Equilibrium of Ideal Incompressible Liquid Situated in a Vertical Cylinder under Its Random Coaxial Vibration

On the Instability with Probability One of Equilibrium of Ideal Incompressible Liquid Situated in a Vertical Cylinder under Its Random Coaxial Vibration

Development of a method for numerical modeling of the separation flow at the entrance to a rectangular exhaust channel with sharp edges

We have developed a method for mathematically simulating flow separation at the entrance to the exhaust channels of rectangular shape, using stationary discrete vortices in an ideal incompressible liquid in full spatial setting. When designing the discrete model, straight and curvilinear quadrangular vortex frames, straight and curvilinear horseshoe-shaped vortices were used. Using the developed computational procedure and computer program, the outline of vortex zone at the entry to the rectangular exhaust channel with sharp edges and the axial velocity of the air flow are determined. The results were compared with studies by different authors, as well as calculations by the methods of the theory of functions of a complex variables for the slotted exhausts and with results earlier obtained by us for calculation the square exhaust opening by means of discrete vortices in non-stationary and quasi-symmetric setting. The further direction of research will be related to the investigation of flows detached at the entrance to the rectangular exhaust hoods by the developed method, as well as by CFD methods. Then it is necessary to identify the regularities of the change of the local resistance coefficient at the entrance to the exhaust hood, shaped by the found outlines of the vortex zones.

Effect of paragliding wing dome shape on its aerodynamic characteristics

Double-membrane gliding parachutes (DGP) obtain their wide variety of application, including the solution of cargo transportation problems. This parachute is a flexible canopy, which shape is maintained by ram air. In terms of the aerodynamic performance calculation and analysis when operating, DGP is the most complex aero elastic system. The computation of DPG aerodynamic performance is only possible, utilizing the methods of nonlinear aerodynamics and the nonlinear theory of elasticity methods.This paper investigates the aerodynamic characteristics of stable geometric shapes for various gliding parachutes, taking into account their dome shape both chord-wise and span-wise. Notably, the volumetric parachute profile is modeled by its median surface. The research, conducted by the authors, showed that such an aero elastic model of DGP allows you to obtain results that reflect correctly the qualitative effects of detached and free streamline flow. To solve the problem about the airflow over a gliding parachute, considering its canopy curvature, the method of discrete vortices with closed frames is employed, which allows you to calculate the paragliding wing aerodynamic performance within a wide range of angles of attack. There is also a possibility of flow separation simulation. The ideal incompressible liquid flow over the median surface of a stable shape for a double-membrane gliding parachute is regarded. The parachute fabric porosity is not analyzed, since the upper and lower DGP panels are made of either the low permeable or non-porous fabric. In the separated flow past, the aerodynamic coefficients are identified by time averaging to its large values after computing. The DGP aerodynamic performance computation results are given at a different value of its dome shape, as in the free streamline flow as in the flow separation. The computed coefficients, that allow us to consider the influence of canopy dome shape on its aerodynamic characteristics, are obtained. The proposed technique can be used for operational estimates of aerodynamic forces while designing and planning a pipe experiment.

Topology of the isoenergy manifolds of the Kirchhoff rigid body case on e(3)

Our aim is to study topology of the Kirchhoff case of rigid body motion in an ideal incompressible fluid. We introduce the reduced potential for general Hamiltonian systems on e(3) with mixed quadratic terms. In application to the Kirchhoff case, we describe the Reeb graphs of the reduced potential. We provide a complete topological description of the three-dimensional isoenergy manifolds for that system, based on a combinatorial study of the Reeb graphs. Studying its momentum map, we describe the points of ranks zero and one. The Poincaré model of a rigid body with an ellipsoidal cavity filled with an ideal incompressible liquid has a Hamiltonian of the same form as the Kirchhoff Hamiltonian, with the underlying Poisson algebra being so(4). A similar analysis of bifurcations of the momentum map is presented in the Poincaré case as well.

Медленные движения кругового цилиндра в жидкости после отрывного удара

The plane problem of the separation impact of a circular cylinder completely immersed in an ideal incompressible heavy liquid is considered. It is assumed that after the impact, the cylinder moves horizontally at a constant speed. An attached cavity is formed behind the body, the shape of which depends on the physical and geometric parameters of the problem. It is required to study the process of collapse of the cavity at low velocities of the cylinder, which correspond to small Froude numbers. The solution to the problem is constructed using asymptotic expansions in a small parameter, which is the dimensionless speed of the cylinder. In this case, as the characteristic speed of the problem, a value is chosen equal to the square root of the product of the radius of the cylinder and the acceleration of gravity. As a result of this choice, the indicated small parameter coincides with the Froude number, and therefore, we can assume that the asymptotics of the problem is constructed for small Froude numbers. In the leading asymptotic approximation, a mixed problem of potential theory with one-sided constraints on the surface of the body is formulated. With its help, the position of the separation points at each moment of time is determined and the time of collapse of a thin cavity is found. The results obtained can be used to solve practical problems of ship hydrodynamics, in which it is necessary to take into account the phenomenon of cavitation.

Machine Learning and transcritical sprays: A demonstration study of their potential in ECN Spray-A

The present work investigates the application of Machine Learning and Artificial Neural Networks for tackling the complex issue of transcritical sprays, which are relevant to modern compression-ignition engines. Such conditions imply the departure of the classical thermodynamic perspective of ideal gas or incompressible liquid, necessitating the use of costly and elaborate thermodynamic closures to describe property variation and simulation methods. Machine Learning can assist in several ways in speeding up such calculations, either as a compact, trained thermodynamic model that can be coupled to the flow solver, or as a surrogate predictive tool of spray characteristics. In this work, such applications are demonstrated and their performance is assessed against more traditional approaches. Such applications involve the prediction of macroscopic spray characteristics, for example, the spray penetration over time, or the spray distribution in space and time, and predictions of fluid properties for the thermodynamic states encountered in such applications. Macroscopic characteristics can be adequately predicted by relatively simple network structures, involving just a hidden layer of 3–4 neurons, whereas prediction of thermodynamic states requires several layers of 5–20 neurons each. The results of integrating Artificial Neural Networks in transcritical sprays are rather promising; prediction of thermodynamic properties at pressures greater than 1bar has effectively zero error, yielding simulations indistinguishable from standard tabulated approaches with minimal overhead. When used as a regression method for time-histories either of spray characteristics or spray distributions, the results are within experimental uncertainty of similar experiments, not included in the training dataset.

Метод годографа для решения задачи о мелкой воде под твердой крышкой

One of the mathematical models describing the behavior of two horizontally infinite adjoining layers of an ideal incompressible liquid under a solid cover moving at different speeds is investigated. At a large difference in the layer velocities, the Kelvin-Helmholtz instability occurs, which leads to a distortion of the interface. At the initial point in time, the interface is not necessarily flat. From a mathematical point of view, the behavior of the liquid layers is described by a system of four quasilinear equations, either hyperbolic or elliptic, in partial derivatives of the first order. Some type shallow water equations are used to construct the model. In the simple version of the model considered in this paper, in the spatially one-dimensional case, the unknowns are the boundary between the liquid layers h(x,t) and the difference in their velocities γ(x,t). The main attention is paid to the case of elliptic equations when |h|<1 and γ>1. An evolutionary Cauchy problem with arbitrary sufficiently smooth initial data is set for the system of equations. The explicit dependence of the Riemann invariants on the initial variables of the problem is indicated. To solve the Cauchy problem formulated in terms of Riemann invariants, a variant of the hodograph method based on a certain conservation law is used. This method allows us to convert a system of two quasilinear partial differential equations of the first order to a single linear partial differential equation of the second order with variable coefficients. For a linear equation, the Riemann-Green function is specified, which is used to construct a two-parameter implicit solution to the original problem. The explicit solution of the problem is constructed on the level lines (isochrons) of the implicit solution by solving a certain Cauchy problem for a system of ordinary differential equations. As a result, the original Cauchy problem in partial derivatives of the first order is transformed to the Cauchy problem for a system of ordinary differential equations, which is solved by numerical methods. Due to the bulkiness of the expression for the Riemann-Green function, some asymptotic approximation of the problem is considered, and the results of calculations, and their analysis are presented.

Mathematical model of the flotation complex particle–bubble within the framework of Lagrangian formalism

A model of the interaction of a spherical gas bubble and a rigid particle is derived as a coupled system of second-order differential equations using Lagrangian mechanics. The model takes into account oscillations of the bubble surface and the attached to it solid cylindrical particle in infinite volume of ideal incompressible liquid. The capillary force holding the particle on the bubble is due to the shape of the meniscus surface, which determines the wetting edge angle. The series with respect Legendre polynomials is used to present small axisymmetric oscillations of the particle-bubble system. Potential and kinetic energies are expressed through coefficients of this series. Particle adhesion condition to bubble surface is implemented through Lagrange multipliers. The dependence of the particle size and its density is demonstrated as a result of the numerical integration of the resulting dynamic system of differential equations.

On Investigation of Liquid Sloshing in Cylindrical Tanks With Single and Multiply Connected Domains Using Isogeometric Boundary Element Method

Abstract This paper explores an isogeometric boundary element method (IGA-BEM) for sloshing problems in cylindrical tanks with single and multiply connected domains. Instead of the Lagrange basis functions used in the standard BEM, the nonuniform rational B-splines (NURBS) basis functions are introduced to approximate the geometries of the problem boundaries and the unknown variables. Compared with the Lagrange basis functions, NURBS basis functions can accurately reconstruct the geometric boundary of analysis domain with almost no error, and all the data information for NURBS basis functions can be directly obtained from the computer-aided design (cad) or computer-aided engineering (cae) commercial software, which implies the modeling process of IGA-BEM is more simple than that of the standard BEM. NURBS makes it possible for the IGA-BEM to realize the seamless connection between cad and cae software with relative higher calculation accuracy than the standard BEM. Based on the weighted residual method as well as the divergence theorem, the IGA-BEM is developed for the single and multiply connected domains, whose boundaries are separately defined in the parameter space by different knot vectors. The natural sloshing frequencies of the liquid sloshing in a circular cylindrical tank with a coaxial or an off-center circular pipe, an elliptical cylindrical tank with an elliptical pipe, a circular cylindrical tank with multiple pipes are estimated with the introduced method by assuming an ideal (inviscid and incompressible) liquid, irrotational small-amplitude sloshing, and the linear free-surface condition. The comparison between the results obtained by the proposed method and those in the existing literatures shows very good agreements, which verifies the proposed model well. Meanwhile, the effects of radius ratio, liquid depth, number, and location of internal pipe (pipes) on the natural sloshing frequency and sloshing mode are analyzed carefully, and some conclusions are outlined finally.

Алгоритм движения точечных вихрей в ограниченной области

The problem of calculating the paths of motion of a set of point vortices in an ideal incompressible liquid in a limited area is considered. The area is supposed to be piecewise smooth. The stream function at any given time is presented as a sum: the stream functions of point vortices and the potential of a simple layer, the density of which - the density of vortexes on the border - is required to determine. Regardless of time, the stream function harmoniously extends into the exterior of the area and is identically equal to a constant at the boundary, and, therefore, is a Roben potential. Briefly, the paper describes an algorithm for calculating the Roben potential. The unknown density of vortices is sought in the form of a linear combination of a complete system of potentials, and the coefficients are determined by the values of the Roben potential, as a solution to the inverse problem; determination of the coefficients reduces to solving a system of linear equations with a Gram matrix for a linearly independent system of functions. By the function of stream by tangents determine the trajectories of movements of vortices. The results of computational experiments of the motion of several point vortices in a square are presented. A computer analysis of the movement was carried out: two, four and eight point vortices, calculated the trajectories of their movement and found stationary and periodic, stable and unstable configurations.

Vibrations of Two-Layer Ideal Liquid in a Rigid Cylindrical Vessel with Elastic Bases

We analyze the frequency equation of natural vibrations of a heavy ideal two-layer incompressible liquid placed in a rigid circular cylindrical vessel with elastic bases in the form of fixed thin circular plates. We consider the cases of axially symmetric (longitudinal) and asymmetric (transverse) vibrations of the liquid and plates and different limiting cases (degeneration of the plates into membranes, absolutely rigid plates, and the absence of the top plate). It is shown that the frequency spectrum of coupled asymmetric vibrations of the elastic bases and two-layer ideal liquid consists of three sets of frequencies corresponding to the vibrations of the top and bottom elastic bases and to the vibrations of the inner interface of liquids. The frequency spectrum of coupled axially symmetric vibrations consists of the same three sets as for the asymmetric vibrations and an additional frequency of vibration of the liquid column as a single whole. As an example, we perform the analytic and numerical investigations of the frequency spectrum of a homogeneous liquid with free surface and elastic bottom in the form of a membrane.

On the Stability of the rotation under the action of constant momentum Lagrangian top with perfect fluid in a resisting medium

The rotation around a fixed point of a heavy dynamically symmetric solid body with an arbitrary asymmetric cavity completely filled with an ideal in-compressible liquid is considered. The stability of a uniform rotation of a Lagrang' top with the ideal liquid in a resisting medium under condition of a given constant moment is investigated. The equation of the perturbed motion of the Lagrang' top with the ideal liquid is presented. It is proved the follow-ing: the asymptotic stability of uniform rotation for an ellipsoidal cavity will be only for a compressed ellipsoidal cavity. It has been observed that most practically important cases consider the main effect of the ideal liquid influence on the motion of a solid can be researched by means of considering only the fundamental tone of the liquid oscillation. Conditions of uniform rotation asymptotic stability in a resistive medium under the action of the Lagrange top' constant moment with an arbitrary axisymmetric cavity containing an ideal liquid are obtained. Stability conditions are derived with provisions for the main and additional tones of liquid oscillations. The heavy solid body with the fixed-point value is ex-posed to the action of a constant moment in the inertial coordinate system. Analytic and numerical investigations of the main and additional tones of liquid oscillations influence, over-turning, restoring, dissipative and constant moments on the conditions of the asymptotic stability of the uniform rotation of the Lagrange top with an ideal liquid are carried out. It is stated the following: cubic and square inequalities presented in the paper are conditions of asymptotic stability if the basic tone of liquid fluctuations will be mentioned. Stability region numerical studies have been carried out on the example of an ellipsoidal cavity. It is presented that increasing of the equatorial moment of inertia of the solid body de-creases its stability region as well as the increasing of the solid body inertia axial moment in-creases the last one.

Boundary element method in nonlinear sloshing analysis for shells of revolution under longitudinal excitations

Processes of liquid sloshing in rigid shells of revolution filled with an ideal incompressible liquid are studied. The shells are subjected to longitudinal excitations. The liquid motion in these containers is supposed to be irrotational. The problems of liquid sloshing are considered in weakly nonlinear formulations when the free surface elevation is small compared with the shell radius. The spectral boundary problem on natural sloshing modes and frequencies is solved using the in-house computational tool based on boundary element methods. The linear and constant interpolations of unknown functions inside boundary elements are involved. The modes obtained are considered as basic functions for analysis of forced liquid vibrations. The numerical procedure based on boundary element method and the multimodal approach is developed for numerical analysis of nonlinear sloshing effects in rigid shells of revolution under longitudinal excitations. The free-surface elevation and velocity potential are expanded into infinite series with obtained basic functions and unknown time-dependent coefficients. The problems of liquid vibrations are reduced to solving nonlinear systems of second order ordinary differential equations about these coefficients that in linear formulation turns to the system of uncoupled Mathieu equations. The parametric oscillations are considered both in linear and nonlinear statements.

Temporary Evolution of the Amplitudes of Capillary Waves on the Surface of a Charged Jet, Moving Relative to a Material Dielectric Medium

A solution to the problem of calculating the temporary evolution of amplitudes of capillary waves of an arbitrary symmetry on the surface of a cylindrical jet of an ideal incompressible conductive liquid moving relative to an ideal incompressible dielectric medium is offered, taking into account multimodal initial conditions. Analytical expressions for the temporary evolution of the amplitudes of waves on a jet, amplitude values of hydrodynamic potentials of velocity fields on a jet and in a medium, and the electric potential of the field in the neighborhood of the jet. An assessment of the characteristic time of a separation of a drop from a jet is performed.

Instability Increments for Waves with Different Symmetries on a Space-Charged Jet Moving Relative to a Material Medium

We have studied the instability increments of capillary waves with an arbitrary symmetry (arbitrary azimuthal numbers m) on the surface of a space-charged cylindrical jet of an ideal incompressible dielectric liquid moving relative to an ideal incompressible material dielectric medium. It is shown that for not very high jet velocities, the axisymmetric mode (m = 0) is the first to become unstable upon an increase in the space charge density, and then the kink mode (m = 1) and flexural-strain mode (m = 2) exhibit instability. It is this sequence of realization of instability of azimuthal modes that determines the regularities of charged jet dispersion in experiments. For jet velocities comparable with those critical for aerodynamic instability realization, the mode with m = 1 is the first to lose its stability. The dependences of maximal increments on wavenumbers have been determined for all azimuthal modes.

Numerical Study of Interaction of Two Deformable Bubbles in an Acoustic Field

Three-dimensional deformation of two bubbles and bubbles in a cluster in an ideal incompressible liquid in an acoustic field is investigated using the boundary element method for potential flows. The dependence of the dynamics of two interacting bubbles on the frequency and amplitude of the acoustic field and the distance between bubbles is studied. The parameters of the acoustic field and the cluster for which jets are formed and the bubbles are deformed or remain spherical are determined. The behavior of two central bubbles in a structured cluster in an acoustic field with different frequency and amplitude is investigated as a function of the distance between bubbles in the cluster. A comparative analysis of the deformation of the investigated bubbles in the presence and absence of adjacent bubbles is performed.