Solution Of Hydrodynamic Equations Research Articles

Features of the design and control of an underwater biomorphic robot of the tunniform type

The article describes the design and main dynamic characteristics of an underwater vehicle of the biomorphic (fish-like) type, which implements the tunniform type of locomotion for movement under water. The body of the device is made on the basis of a digital model of the body of yellowfin tuna. The movement is provided by a driv-ing device that simulates the operation of the tail fin of a fish. The robot's navigation on the surface and with a dive to a shallow depth is controlled by a remote control system, which allows you to change the dynamic characteris-tics (amplitude and frequency) of tail vibrations. In the experimental study, the dependencies of the speed of movement and energy consumption of the robot depending on these characteristics were obtained. In the theoreti-cal study, a computational model of the robot was obtained based on the solution of hydrodynamic equations. In computer modeling of swimming using the method of deformable nets, a good correspondence with experimental data was obtained. In addition, the hydrodynamic characteristics of the flow during the movement of the robot were investigated, as well as various features of the vibrations of the elements of the robot body when moving in a liquid were explained.

Calculation of the process duration of thermo-moisture treatment of semi-finished products based on animal and vegetable raw materials

Calculation of the parameters of studied systems heat treatment (the process duration, temperature distribution inside the product and in its mass change) is complicated both by external and internal moisture transfer. In this regard, a strict mathematical description of moisture and heat transfer between the surface of the semi-finished product, which must be considered as a capillary-porous body, and the surrounding medium should be based on a joint solution of hydrodynamics equations and convective heat- and mass transfer, taking into account the normal component of the mass flow on the body surface, which complicates the task. Consideration of such a task with regard to moisture transfer under the action of water content gradients, temperature and pressure is possible if the driving forces of transfer processes do not consider these potential gradients on the surface of a capillary-porous body, but the differences between potentials averaged over the surface and volume of the body. This theory successful application for widespread use in practical problems solving is complicated by the absence of a systematized database on the hygro- and hydro-mechanical equilibrium of treated semi-finished products with technological media. On the other hand, even in the presence of experimental data on hydro- and hygroscopic equilibrium, in this case there are not fields of transfer potentials, but only their average volume and mean surface values, which in principle does not allow calculating of heat treatment duration as the time to reach the required temperature in the middle of the product. Meat and fish products are treated at not too high temperatures and as a result gradients of transfer potentials inside capillary-porous bodies are not too great, therefore it can be considered that the internal moisture transfer does not change the temperature field inside meat and fish products significantly. Resource-saving modes of thermo-moisture treatment of combined products were justified: frying at t = 200 ° C, without humidification, duration - 5 min; baking at 180 ° C, water consumption for humidification (4.0-4.3)10-6 m3 / s with 10-15 minutes duration, providing a reduction in process losses of the finished product weight from 18% to 5-7%

On the finite-element-based lattice Boltzmann scheme

The finite-element-based lattice Boltzmann scheme for the computations on unstructured meshes is proposed. The scheme is based on the weighted residuals method with Galerkin approximation. The scheme is reduced to the solution of the linear algebraic system at every time step. The possibilities of application of the developed scheme for practical problems are demonstrated on the applications to two test problems of computational fluid dynamics. The investigation of the equilibrium boundary conditions for distribution functions is performed. The obtained results demonstrate that this type of boundary conditions can produced a results which are in good agreement with the results obtained from the solution of hydrodynamical equations at Re ≥ 20. The algorithm of the proposed scheme is realized in GNU license software freefem++ v.3.20. Mathematics Subject Classification: 76-04; 76M10; 65N30

A partially invariant solution of hydrodynamic equations for the atmosphere

UDC 517.944 + 532.5 The hydrodynamic equations for the atmosphere in f -plane approximation admit an infinite-dimensional Lie group of transformations. We analyze a partially invariant solution to these equations that possesses a certain functional arbitrariness. The problem of finding such a solution is reduced to the integration of the Hopf equations and finite formulas. Bibliography :8 titles. Illustrations :4 figures.

Full nonlinear dispersion model of shallow water equations on a rotating sphere

Nonlinear dispersion shallow water equations are derived, which describe propagation of long surface waves on a spherical surface with allowance for rotation of the Earth and mobility of the ocean bottom. Derivation of these equations is based on expanding the solution of hydrodynamic equations on a sphere in small parameters depending on the relative thickness of the water layer and dispersion of surface waves.

Analysis of alternate discharge schemes for arterial crude-oil pumps based on numerical solution of hydrodynamics equations

Numerical calculations are performed for various alternate discharge schemes for an arterial crude-oil pump with an interchangeable flow-through spiral casing. Possible design solutions are analyzed for an increase in pump efficiency in cases of necessity.

Two-dimensional flows of a viscous binary fluid between moving solid boundaries

A class of exact solutions of hydrodynamic equations with additional Korteweg stresses is obtained which is characterized by a linear dependence of part of the velocity components on the space variable. In this class, exact solutions of two problems of binary fluid flow between moving flat solid boundaries was found. A family of particular exact solutions is obtained for the problem of viscous fluid flow between planes which approach or move away from each other according to a special law.

Supersonic flows with small perturbations in the presence of external effects in the flow. Part 1: “Thin body of revolution”

Axisymmetric supersonic flow about a thin body of revolution with an external energy supply and an external force localized near the body surface is considered in the linear approximation. An analytic theory is constructed for calculating spatial fields of flow parameters in this case for an arbitrary dependence of external effects on the longitudinal coordinate. Formulas are derived for the pressure ratio on the surface of the thin body of revolution. The results of calculations based on the analytic theory are in good agreement with numerical data obtained from the solution of hydrodynamic equations in the Euler approximation.

Hydrodynamical description of a hadron-quark first-order phase transition

Solutions of hydrodynamical equations are presented for the equation of state of the Van der Waals type allowing for a first-order phase transition. As an example we consider the hadron-quark phase transition in heavy-ion collisions. It is shown that fluctuations dissolve and grow as if the fluid is effectively very viscous. In the vicinity of the critical point even in spinodal region seeds are growing slowly due to viscosity, surface tension and critical slowing down. These non-equilibrium effects prevent enhancement of fluctuations in the near-critical region, which in thermodynamical approach is frequently considered as a signal of the critical endpoint in heavy-ion collisions.

Hydrodynamical description of first-order phase transitions: Analytical treatment and numerical modeling

Solutions of hydrodynamical equations are presented for an equation of state allowing for a first-order phase transition. The numerical analysis is supplemented by analytical treatment provided the system is close to the critical point. The processes of growth and dissolution of seeds of various sizes and shapes in meta-stable phases (like super-cooled vapor and super-heated liquid) are studied, as well as the dynamics of unstable modes in the spinodal region. We show that initially nonspherical seeds acquire spherical shape with passage of time. Applications to the description of the first-order phase transitions in nuclear systems, such as the nuclear gas–liquid transition occurring in low energy heavy-ion collisions and the hadron–quark transition in the high energy heavy-ion collisions are discussed. In both cases we point out the important role played by effects of viscosity and surface tension. It is shown that fluctuations dissolve and grow as if the fluid were effectively very viscous. Even in the spinodal region seeds may grow slowly due to viscosity and critical slowing down. This prevents the enhancement of fluctuations in the near-critical region, which is frequently considered as a signal of the critical point in heavy-ion collisions.

HYDRODYNAMICAL STUDY OF ADVECTIVE ACCRETION FLOW AROUND NEUTRON STARS

Here we study the accretion process around neutron stars, especially for the cases where shock does form in the accretion disk. In case of accretion flows around a black hole, close to the horizon the matter is supersonic. On the other hand for the case of neutron stars and white dwarfs, matter must be subsonic close to the inner boundary. So the nature of the inflowing matter around neutron stars and white dwarfs are strictly different from that around black holes in the inner region of the disk. Here we discuss a few phenomena and the corresponding solutions of hydrodynamic equations of matter in an accretion disk around slowly rotating neutron stars without magnetic field.

Probabilistic representation of solutions of hydrodynamic equations

It is well known that the relationships between the theory of partial differential equations (PDE) and probability theory are very deep and allow one to derive new nontrivial results concerning the behavior of random processes and properties of the solutions of boundary-value problems of PDE. It is natural to make an attempt to construct a probabilistic representation of the solution of a boundary problem for the Navier-Stokes system and other hydrodynamic equations. We construct such a representation in terms of a diffusion process. Bibliography: 16 titles.

Vibrations of microemulsion droplets and vesicles with compressible surface layer

The surface vibration spectra of liquid droplets with flexible interfaces, like microemulsion droplets or vesicles, are studied. As distinct from the previous theories, we proceed with exact solutions of hydrodynamic equations for incompressible bulk fluids inside and outside the droplet. The dynamical equations for the interface are those obtained by Lebedev and Muratov @JETP 68, 1011 ~1989!# but with the improved continuity equation for the surface layer. Within the Helfrich’s concept of the interfacial elasticity and taking into account the compressibility of the surface layer, the exact equation is obtained for the frequencies of the droplet vibrations. The equation describes uniformly a broad region of frequencies from the lowest, almost purely relaxation modes, up to the modes determined mainly by the change of the area per molecule of the layer. The dispersion laws for some of the modes are obtained analytically in the limits of large and small penetration depths of the corresponding waves. Our analysis corrects the previous results concerning the relaxation modes, the capillary wave frequency and the frequency of the mode connected with the fluctuations of molecules in the surface layer. An additional mode of this kind is obtained for almost incompressible layers. In the region corresponding to large penetration depths, a couple of modes exist with frequencies depending both on the surface elasticity and compressibility. In the limit of infinite compressibility of the layer, the lower of the two modes disappears. The conditions necessary for the existence of all the modes were specified. Some representative numerical solutions of the obtained equation are presented as depending on various values of the model parameters including those for realistic microemulsion systems. @S1063-651X~98!06812-3#

Appearance intensities for multiply charged ions in a strong laser field.

We study multiple ionization of atoms by a strong laser field using a time-dependent approach based on the Thomas-Fermi model. The evolution of the electron density under the influence of a transient, linearly polarized radiation field is determined by numerical solution of hydrodynamic equations on a two-dimensional grid. We find a threshold ``appearance intensity'' for a given charge state, i.e., the laser intensity at which such a charge state first appears, which is in reasonable agreement with experimental results for high charge states.

DISTRIBUTIONS OF TEMPERATURE, VELOCITY AND VISCOSITY AT SYMMETRICAL AXIS OF CYLINDRICAL PLUME IN EARTH'S MANTLE WITH VARIABLE VISCOSITY

The parameters at the symmetrical axis of a cylindrical plume characterize the strength of this plume and provide a boundary condition which must be given to investigate the structure of a plume. For Newtonian fluid with a temperature-and pressure-dependence viscosity, an asymptotical solution of hydrodynamic equations at the symmetrical axis of the plume is found in the present paper. The temperature, upward velocity and viscosity at the symmetrical axis have been obtained as functions of depth, The calculated results have been given for two typical sets of Newtonian rheological parameters. The results obtained show that the temperature distribution along the symmetrical axis is nearly independent of the theological parameters. The upward velocity at the symmetrical axis, however, is strongly dependent on the rheological parameters.

An asymptotic solution of hydrodynamic equations at the mid-plane of a plume in the Earth's mantle

From the partial differential equations of hydrodynamics governing the movements in the Earth's mantle of a Newtonian fluid with a pressure- and temperature-dependent viscosity, considering the bilateral symmetry of velocity and temperature distributions at the mid-plane of the plume, an analytical solution of the governing equations near the mid-plane of the plume was found by the method of asymptotic analysis. The vertical distribution of the upward velocity, viscosity and temperature at the mid-plane, and the temperature excess at the centre of the plume above the ambient mantle temperature were then calculated for two sets of Newtonian rheological parameters. The results obtained show that the temperature at the mid-plane and the temperature excess are nearly independent of the rheological parameters. The upward velocity at the mid-plane, however, is strongly dependent on the rheological parameters.

Laser Fusion Hydrodynamics Calculations

Laser fusion hydrodynamics calculations include both the solution of the plasma hydrodynamics equations and transport equations for various nonthermal particles. The solution of the hydrodynamics equations is usually a combination of an explicit technique for the hyperbolic equation-of-motion and an implicit method for parabolic temperature equations. Transport equations are solved using fully implicit techniques to allow their time step to be as large as the time step used in the solution of the hydrodynamics equations.Multigroup flux-limited diffusion theory is often used to model the time-dependent transport problem. In this method, the diffusion coefficient is “adjusted” to provide a physically plausible result in the free streaming limit. The energy dependence of the distribution function is modeled using multigroup theory. Another method of solving the transport problem, time-dependent particle tracking, approximates the trajectory of the charged particles as straight lines, from creation to thermalization. This simple method accurately describes the slowing down of thermonuclear reaction products, while the flux-limited diffusion technique is more applicable to the transport of electrons and photons.

A method of introducing “pseudoviscosity” and its use for improving the difference solutions of hydrodynamic equations

A method of introducing “pseudoviscosity” and its use for improving the difference solutions of hydrodynamic equations