Dynamics of a Body with a Sharp Edge in a Viscous Fluid
Russian Journal of Nonlinear Dynamics, 2018, vol. 14, no. 4, pp. 473-494
Abstract
pdf (835.37 Kb)

This paper addresses the problem of plane-parallel motion of the Zhukovskii foil in a viscous
fluid. Various motion regimes of the foil are simulated on the basis of a joint numerical solution
of the equations of body motion and the Navier – Stokes equations. According to the results
of simulation of longitudinal, transverse and rotational motions, the average drag coefficients
and added masses are calculated. The values of added masses agree with the results published
previously and obtained within the framework of the model of an ideal fluid. It is shown that
between the value of circulation determined from numerical experiments, and that determined
according to the model of and ideal fluid, there is a correlation with the coefficient $\mathcal{R} = 0.722$.
Approximations for the lift force and the moment of the lift force are constructed depending
on the translational and angular velocity of motion of the foil. The equations of motion of
the Zhukovskii foil in a viscous fluid are written taking into account the found approximations and the drag coefficients. The calculation results based on the proposed mathematical model
are in qualitative agreement with the results of joint numerical solution of the equations of body
motion and the Navier – Stokes equations.

Mamaev I. S., Tenenev V. A., Vetchanin E. V., Dynamics of a Body with a Sharp Edge in a Viscous Fluid, Russian Journal of Nonlinear Dynamics, 2018, vol. 14, no. 4, pp. 473-494

Controlling the movement of the body using internal masses in a viscous liquid
Computer Research and Modeling, 2018, vol. 10, no. 4, pp. 445-460
Abstract
pdf (523.34 Kb)

This article is devoted to the study of self-propulsion of bodies in a fluid by the action of internal
mechanisms, without changing the external shape of th
e body. The paper presents an overview of theoretical
papers that justify the possibility of this displacement in ideal and viscous liquids.
A special case of self-propulsion of a rigid body along the surface of a liquid is considered due to the
motion of two internal masses along the circles. The paper presents a mathematical model of the motion of
a solid body with moving internal masses in a three-dime
nsional formulation. This model takes into account the
three-dimensional vibrations of the body during motion,
which arise under the action of external forces-gravity
force, Archimedes force and forces acting on the body, from the side of a viscous fluid.
The body is a homogeneous elliptical cylinder with a k
eel located along the larger diagonal. Inside the
cylinder there are two material point masses moving along the circles. The centers of the circles lie on the
smallest diagonal of the ellipse at an equal distance from the center of mass.
Equations of motion of the system (a body with two mater
ial points, placed in a fluid) are represented as
Kirchhoff equations with the addition of external for
ces and moments acting on the body. The phenomenological
model of viscous friction is quadratic in velocity used
to describe the forces of resistance to motion in a fluid.
The coefficients of resistance to movement were determ
ined experimentally. The forces acting on the keel were
determined by numerical modeling of the keel oscillations in a viscous liquid using the Navier – Stokes equations.
In this paper, an experimental verification of the
proposed mathematical model was carried out. Several
series of experiments on self-propulsion of a body in a liquid by means of rotation of internal masses with
different speeds of rotation are presented. The dependence of the average propagation velocity, the amplitude of
the transverse oscillations as a function of the rotational speed of internal masses is investigated. The obtained
experimental data are compared with the results obtai
ned within the framework of the proposed mathematical
model.

Keywords:

motion in a fluid, self-promotion, the equations of movement, above-water screwless robot, Navier – Stokes equations

Citation:

Kilin A. A., Klenov A. I., Tenenev V. A., Controlling the movement of the body using internal masses in a viscous liquid, Computer Research and Modeling, 2018, vol. 10, no. 4, pp. 445-460

Optimal control of the motion in an ideal fluid of a screw-shaped body with internal rotors
Computer Research and Modeling, 2017, vol. 9, no. 5, pp. 741-759
Abstract
pdf (567.52 Kb)

In this paper we consider the controlled motion of a helical body with three blades in an ideal fluid, which is executed by rotating three internal rotors. We set the problem of selecting control actions, which ensure the motion of the body near the predetermined trajectory. To determine controls that guarantee motion near the given curve, we propose methods based on the application of hybrid genetic algorithms (genetic algorithms with real encoding and with additional learning of the leader of the population by a gradient method) and artificial neural networks. The correctness of the operation of the proposed numerical methods is estimated using previously obtained differential equations, which define the law of changing the control actions for the predetermined trajectory.
In the approach based on hybrid genetic algorithms, the initial problem of minimizing the integral functional reduces to minimizing the function of many variables. The given time interval is broken up into small elements, on each of which the control actions are approximated by Lagrangian polynomials of order 2 and 3. When appropriately adjusted, the hybrid genetic algorithms reproduce a solution close to exact. However, the cost of calculation of 1 second of the physical process is about 300 seconds of processor time.
To increase the speed of calculation of control actions, we propose an algorithm based on artificial neural networks. As the input signal the neural network takes the components of the required displacement vector. The node values of the Lagrangian polynomials which approximately describe the control actions return as output signals . The neural network is taught by the well-known back-propagation method. The learning sample is generated using the approach based on hybrid genetic algorithms. The calculation of 1 second of the physical process by means of the neural network requires about 0.004 seconds of processor time, that is, 6 orders faster than the hybrid genetic algorithm. The control calculated by means of the artificial neural network differs from exact control. However, in spite of this difference, it ensures that the predetermined trajectory is followed exactly.

Keywords:

motion control, genetic algorithms, neural networks, motion in a fluid, ideal fluid

Citation:

Vetchanin E. V., Tenenev V. A., Kilin A. A., Optimal control of the motion in an ideal fluid of a screw-shaped body with internal rotors, Computer Research and Modeling, 2017, vol. 9, no. 5, pp. 741-759

Describing the Motion of a Body with an Elliptical Cross Section in a Viscous Uncompressible Fluid by Model Equations Reconstructed from Data Processing
Technical Physics Letters, 2016, vol. 42, no. 9, pp. 886-890
Abstract
pdf (508.12 Kb)

From analysis of time series obtained on the numerical solution of a plane problem on the motion
of a body with an elliptic cross section under the action of gravity force in an incompressible viscous fluid, a
system of ordinary differential equations approximately describing the dynamics of the body is reconstructed.
To this end, coefficients responsible for the added mass, the force caused by the circulation of the velocity
field, and the resisting force are found by the least square adjustment. The agreement between the finitedimensional
description and the simulation on the basis of the Navier–Stokes equations is illustrated by
images of attractors in regular and chaotic modes. The coefficients found make it possible to estimate the
actual contribution of different effects to the dynamics of the body.

Citation:

Borisov A. V., Kuznetsov S. P., Mamaev I. S., Tenenev V. A., Describing the Motion of a Body with an Elliptical Cross Section in a Viscous Uncompressible Fluid by Model Equations Reconstructed from Data Processing, Technical Physics Letters, 2016, vol. 42, no. 9, pp. 886-890

Chaotic dynamics in the problem of the fall of a screw-shaped body in a fluid
Russian Journal of Nonlinear Dynamics, 2016, vol. 12, no. 1, pp. 99-120
Abstract
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This paper is concerned with the process of the free fall of a three-bladed screw in a fluid. The investigation is performed within the framework of theories of an ideal fluid and a viscous fluid. For the case of an ideal fluid the stability of uniformly accelerated rotations (the Steklov solutions) is studied. A phenomenological model of viscous forces and torques is derived for investigation of the motion in a viscous fluid. A chart of Lyapunov exponents and bifucation diagrams are computed. It is shown that, depending on the system parameters, quasiperiodic and chaotic regimes of motion are possible. Transition to chaos occurs through cascade of period-doubling bifurcations.

Keywords:

ideal fluid, viscous fluid, motion of a rigid body, dynamical system, stability of motion, bifurcations, chart of Lyapunov exponents

Citation:

Tenenev V. A., Vetchanin E. V., Ilaletdinov L. F., Chaotic dynamics in the problem of the fall of a screw-shaped body in a fluid, Russian Journal of Nonlinear Dynamics, 2016, vol. 12, no. 1, pp. 99-120

The dynamics of vortex rings: leapfrogging in an ideal and viscous fluid
Fluid Dynamics Research, 2014, vol. 46, no. 3, 031415, 16 pp.
Abstract
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We consider the problem of motion of axisymmetric vortex rings in an ideal incompressible and viscous fluid. Using the numerical simulation of the Navier–Stokes equations, we confirm the existence of leapfrogging of three equal vortex rings and suggest the possibility of detecting it experimentally. We also confirm the existence of leapfrogging of two vortex rings with opposite-signed vorticities in a viscous fluid.

Citation:

Borisov A. V., Kilin A. A., Mamaev I. S., Tenenev V. A., The dynamics of vortex rings: leapfrogging in an ideal and viscous fluid , Fluid Dynamics Research, 2014, vol. 46, no. 3, 031415, 16 pp.

The Self-propulsion of a Body with Moving Internal Masses in a Viscous Fluid
Regular and Chaotic Dynamics, 2013, vol. 18, no. 1-2, pp. 100-117
Abstract
pdf (1.71 Mb)

An investigation of the characteristics of motion of a rigid body with variable internal mass distribution in a viscous fluid is carried out on the basis of a joint numerical solution of the Navier–Stokes equations and equations of motion for a rigid body. A nonstationary three-dimensional solution to the problem is found. The motion of a sphere and a drop-shaped body in a viscous fluid in a gravitational field, which is caused by the motion of internal material points, is explored. The possibility of self-propulsion of a body in an arbitrary given direction is shown.

Keywords:

finite-volume numerical method, Navier–Stokes equations, variable internal mass distribution, motion control

Citation:

Vetchanin E. V., Mamaev I. S., Tenenev V. A., The Self-propulsion of a Body with Moving Internal Masses in a Viscous Fluid, Regular and Chaotic Dynamics, 2013, vol. 18, no. 1-2, pp. 100-117

Motion control of a rigid body in viscous fluid
Computer Research and Modeling, 2013, vol. 5, no. 4, pp. 659-675
Abstract
pdf (359.11 Kb)

We consider the optimal motion control problem for a mobile device with an external rigid shell moving along a prescribed trajectory in a viscous fluid. The mobile robot under consideration possesses the property of self-locomotion. Self-locomotion is implemented due to back-and-forth motion of an internal material point. The optimal motion control is based on the Sugeno fuzzy inference system. An approach based on constructing decision trees using the genetic algorithm for structural and parametric synthesis has been proposed to obtain the base of fuzzy rules.

Vetchanin E. V., Tenenev V. A., Shaura A. S., Motion control of a rigid body in viscous fluid, Computer Research and Modeling, 2013, vol. 5, no. 4, pp. 659-675

The motion of a body with variable mass geometry in a viscous fluid
Russian Journal of Nonlinear Dynamics, 2012, vol. 8, no. 4, pp. 815-836
Abstract
pdf (15.9 Mb)

An investigation of the characteristics of motion of a rigid body with variable internal mass distribution in a viscous fluid is carried out on the basis of a joint numerical solution of the Navier–Stokes equations and equations of motion. A non-stationary three-dimensional solution to the problem is found. The motion of a sphere and a drop-shaped body in a viscous fluid, which is caused by the motion of internal material points, in a gravitational field is explored. The possibility of motion of a body in an arbitrary given direction is shown.

Keywords:

finite-volume numerical method, Navier-Stokes equations, variable internal mass distribution, motion control

Citation:

Vetchanin E. V., Mamaev I. S., Tenenev V. A., The motion of a body with variable mass geometry in a viscous fluid, Russian Journal of Nonlinear Dynamics, 2012, vol. 8, no. 4, pp. 815-836

Motion control simulating in a viscous liquid of a body with variable geometry of weights
Computer Research and Modeling, 2011, vol. 3, no. 4, pp. 371-381
Abstract
pdf (594.85 Kb)

Statement of a problem of management of movement of a body in a viscous liquid is given. Movement bodies it is induced by moving of internal material points. On a basis the numerical decision of the equations of movement of a body and the hydrodynamic equations approximating dependencies for viscous forces are received. With application approximations the problem of optimum control of body movement dares on the set trajectory with application of hybrid genetic algorithm. Possibility of the directed movement of a body under action is established back and forth motion of an internal point. Optimum control movement direction it is carried out by motion of other internal point on circular trajectory with variable speed

Keywords:

optimum control, the equations of movement, Navier–Stokes equations, numerical methods, fuzzy decision trees, genetic algorithm

Citation:

Vetchanin E. V., Tenenev V. A., Motion control simulating in a viscous liquid of a body with variable geometry of weights, Computer Research and Modeling, 2011, vol. 3, no. 4, pp. 371-381