scholarly journals Impact of liquids with different densities

2015 ◽  
Vol 766 ◽  
pp. 5-27 ◽  
Author(s):  
Y. A. Semenov ◽  
G. X. Wu ◽  
A. A. Korobkin
Keyword(s):  
Velocity Potential ◽  
Normal Component ◽  
Mapping Function ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Complex Conjugate ◽  
Hodograph Method ◽  
Velocity Magnitude ◽  
Complex Velocity Potential ◽  
The Impact

AbstractThe collision of liquids of different densities is studied theoretically for the case of liquids having wedge-shaped configuration before the impact. Both liquids are assumed to be ideal and incompressible, and the velocity potential theory is used for the flow of each liquid. Surface tension and gravity effects are neglected. The problem is decomposed into two self-similar problems, one for each liquid. Across the interface between the liquids, continuity of the pressure and the normal component of the velocity is enforced through iteration. This determines the shape of the interface and other flow parameters. The integral hodograph method is employed to derive the solution consisting of analytical expressions for the complex-velocity potential, the complex-conjugate velocity, and the mapping function. They are all defined in the first quadrant of a parameter plane, in which the original boundary-value problem is reduced to a system of integro-differential equations in terms of the velocity magnitude and the velocity angle relative to the flow boundary. They are solved numerically using the method of successive approximations. The results are presented through streamlines, interface and free-surface shapes, the pressure and velocity distributions. Special attention is given to the structure of the splash jet rising as a result of the impact.

scholarly journals Asymmetric impact between liquid and solid wedges

2013 ◽  
Vol 469 (2150) ◽  
pp. 20120203 ◽  
Author(s):  
Y. A. Semenov ◽  
G. X. Wu
Keyword(s):  
Free Surface ◽  
Velocity Potential ◽  
Mapping Function ◽  
Solution Procedure ◽  
Contact Angles ◽  
The Body ◽  
Surface Shape ◽  
Parameter Plane ◽  
Complex Velocity Potential ◽  
The Impact

The hydrodynamic problem of impact between a solid wedge and a liquid wedge is analysed. The liquid is assumed to be ideal and incompressible; gravity and surface tension effects are ignored. The flow generated by the impact is assumed to be irrotational and therefore can be described by the velocity potential theory. The solution procedure is based on the analytical derivation of the complex-velocity potential in a parameter plane and the function mapping conformally the parameter plane onto the similarity plane. The mapping function is found as a combination of the derivatives of the complex potential in the similarity and parameter planes, through the integral equations for mixed and homogeneous boundary-value problems in terms of the velocity modulus and the velocity angle with the fluid boundary, together with the dynamic and kinematic boundary conditions. These equations are solved through a numerical method. The procedure is first verified through comparisons with some known results. Simulations are then made for a variety of cases, and detailed results are presented in terms of the free surface shape, streamlines, pressure distribution on the wetted solid surface, and contact angles between the free surface and the body surface.

ANALYSIS OF THE NETWORK WITH MULTIPLE CLASSES OF POSITIVE AND NEGATIVE CUSTOMERS AT A TRANSIENT REGIME

2018 ◽  
Vol 33 (2) ◽  
pp. 172-185 ◽  
Author(s):  
Mikhail Matalytski
Keyword(s):  
Transient Regime ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Stationary Probability Distribution ◽  
Negative Customers ◽  
Network Systems ◽  
Modified Method ◽  
Computer Calculations ◽  
Network States ◽  
The Impact

This paper is devoted to the investigation of the G-network with multiple classes of positive and negative customers. The purpose of the investigation is to analyze such a network at a transient regime, to find the state probabilities of the network that depend on time. In the first part, a description of the functioning of G-networks with positive and negative customers is provided, when a negative customer when arriving to the system destroys a positive customer of its class. Streams of positive and negative customers arriving at each of the network systems are independent. Services of positive customers of all types occur in accordance with a random selection of them for service. For nonstationary probabilities of network states, a system of Kolmogorov's difference-differential equations (DDE) has been derived. A method for their finding is proposed. It is based on the use of a modified method of successive approximations, combined with the method of series. It is proved that successive approximations converge with time to a stationary probability distribution, the form of which is indicated in this paper, and the sequence of approximations converges to the unique solution of the DDE system. Any successive approximation is representable in the form of a convergent power series with an infinite radius of convergence, the coefficients of which satisfy recurrence relations, which is convenient for computer calculations. A model example illustrating the determination of the time-dependent probabilities of network states using this technique has been calculated. The obtained results can be applied in modeling the behavior of computer viruses and attacks in information and telecommunication systems and networks, for example, as a model of the impact of some file viruses on server resources. variable.

scholarly journals Impulsive Motion Inside a Cylindrical Cavity

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 192
Author(s):  
Yuriy Savchenko ◽  
Georgiy Savchenko ◽  
Yuriy A. Semenov
Keyword(s):  
Cylindrical Cavity ◽  
Experimental Studies ◽  
Added Mass ◽  
Axisymmetric Body ◽  
The Body ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Main Concern ◽  
Free Boundaries ◽  
Hodograph Method

Experimental studies of supercavitating models moving at speeds in the range from 400 m/s to 1000 m/s revealed a regime of bouncing motion, in which the rear part of an axisymmetric body periodically bounces against the free boundaries of the supercavity. The impulsive force generated by the impacts is the main concern in this paper. The analysis is performed in the approximation of two-dimensional potential flow of an ideal and incompressible liquid with negligible surface tension effects. The primary interest of the study is to determine the added mass taking into account the shape of the cavity. The theoretical study is based on the integral hodograph method, which makes it possible to obtain analytic expressions for the flow potential and for the complex velocity in an auxiliary parameter plane and obtain a parametric solution to the problem. The problem is reduced to a system of two integro-differential equations in two unknowns: the velocity magnitude on the cavity boundary and the slope of the velocity angle to the body. The equations are solved numerically using the method of successive approximations. The obtained results show that the added mass of an arc impacting a cylindrical cavity depends heavily on the arc angle. As the angle tends to zero or the radius of the cavity tends to infinity, the obtained solution predicts the added mass corresponding to a plate impacting a flat free surface.

Numerical Methods for Solving Physically Nonlinear Problems for Inhomogeneous Thick-Walled Shells

2017 ◽  
Vol 865 ◽  
pp. 325-330 ◽  
Author(s):  
Vladimir I. Andreev ◽  
Lyudmila S. Polyakova
Keyword(s):  
Numerical Method ◽  
Nonlinear Problems ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Deformation Diagram ◽  
Method Of Solution ◽  
Properties Of Materials ◽  
Physical Fields ◽  
Cylinders And Spheres ◽  
Numerical Method Of Solution

The paper proposes the numerical method of solution the problems of calculation the stress state in thick-walled cylinders and spheres from physically nonlinear inhomogeneous material. The urgency of solved problem due to the change of mechanical properties of materials under the influence of different physical fields (temperature, humidity, radiation, etc.). The deformation diagram describes the three-parameter formula. The numerical method used the method of successive approximations. The results of numerical calculation are compared with the test analytical solutions obtaining the authors with some restrictions on diagram parameters. The obtained results can be considered quite satisfactory.

On a sphere performing linear and torsional oscillations in a viscous fluid

1988 ◽  
Vol 66 (7) ◽  
pp. 576-579
Author(s):  
G. T. Karahalios ◽  
C. Sfetsos
Keyword(s):  
Boundary Layer ◽  
Viscous Fluid ◽  
Secondary Flow ◽  
Small Amplitude ◽  
Equations Of Motion ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Time Varying ◽  
Torsional Oscillations

A sphere executes small-amplitude linear and torsional oscillations in a fluid at rest. The equations of motion of the fluid are solved by the method of successive approximations. Outside the boundary layer, a steady secondary flow is induced in addition to the time-varying motion.

scholarly journals Green’s Function In Free Axisymmetric Vibration Analysis Of Annular Thin Plates With Different Boundary Conditions

2015 ◽  
Vol 20 (4) ◽  
pp. 939-951
Author(s):  
K.K. Żur
Keyword(s):  
Power Series ◽  
Vibration Analysis ◽  
Free Vibration Analysis ◽  
Thin Plates ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Axisymmetric Vibration ◽  
Annular Plates ◽  
The Core ◽  
Analytical Frequency

Abstract Free vibration analysis of homogeneous and isotropic annular thin plates by using Green’s functions is considered. The formula of the influence function for uniform thin circular and annular plates is presented in closed-form. The limited independent solutions of differential Euler equation were expanded in the Neumann power series based on properties of integral equations. The analytical frequency equations as power series were obtained using the method of successive approximations. The natural axisymmetric frequencies for singularities when the core radius approaches zero are calculated. The results are compared with selected results presented in the literature.

scholarly journals A new method of successive approximations when calculating elements of electromechanical machines

2020 ◽  
Vol 5 (2) ◽  
pp. 168-172
Author(s):  
K. Ismayilov ◽  
◽  
S.T. Suleymanov ◽  
S.T. Ruziev ◽  
M.B. Aripjanova ◽  
...  
Keyword(s):  
New Method ◽  
Successive Approximations ◽  
Method Of Successive Approximations

scholarly journals The Two-Phase Hell-Shaw Flow: Construction of an Exact Solution

2013 ◽  
Vol 18 (1) ◽  
pp. 249-257
Author(s):  
K.R. Malaikah
Keyword(s):  
Exact Solution ◽  
Velocity Potential ◽  
Time Dependent ◽  
Computational Domain ◽  
Phase Problem ◽  
Complex Velocity ◽  
Two Phase ◽  
Interface Evolution ◽  
Complex Velocity Potential ◽  
Branch Cuts

We consider a two-phase Hele-Shaw cell whether or not the gap thickness is time-dependent. We construct an exact solution in terms of the Schwarz function of the interface for the two-phase Hele-Shaw flow. The derivation is based upon the single-valued complex velocity potential instead of the multiple-valued complex potential. As a result, the construction is applicable to the case of the time-dependent gap. In addition, there is no need to introduce branch cuts in the computational domain. Furthermore, the interface evolution in a two-phase problem is closely linked to its counterpart in a one-phase problem

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