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.

On the theory of hypersonic flow past plane and axially symmetric bluff bodies

1956 ◽  
Vol 1 (4) ◽  
pp. 366-387 ◽  
Author(s):  
N. C. Freeman
Keyword(s):  
Hypersonic Flow ◽  
The Body ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Radius Of Curvature ◽  
Bluff Bodies ◽  
Axially Symmetric ◽  
Nose Radius ◽  
Flow Past ◽  
Past Plane

The ‘Newtonian-plus-centrifugal’ approximate solution (Busemann (1933) and Ivey (1948)) for hypersonic flow past plane and axially symmetric bluff bodies in gases with the ratio of the specific heats λ constant and equal to unity is rederived using ‘boundary layer’ techniques together with the von Mises variables x and ψ. A method of successive approximations then gives a closer approximation to this solution for ε (λ − 1)/(λ + 1) small and the free-strea Mach number infinite. Formulae for the streamlines, shock shape and pressure distribution are determined to this approximation. These formulae are valid for any plane or axially symmetric shape, giving the ‘stand-off’ distance of the shock wave from the body as ½εlog(4|3ε) and ε times the nose radius of curvature for plane and axially-symmetric flows respectively. Particular results are computed for a number of special shapes. For certain shapes, the theory has a singular point where the first approximation to the pressure vanishes (θ = 60° for a sphere). Actually, the theory is not applicable where the pressure becomes too small. The corresponding theory for gases of general thermodynamic properties is deduced, the approximation being valid provided the total energy of the gas is large compared with the energy contained in the translational modes of the gas molecules.

The absorption of wave energy by a three-dimensional submerged duct

1981 ◽  
Vol 104 ◽  
pp. 189-215 ◽  
Author(s):  
J. R. Thomas
Keyword(s):  
Three Dimensional ◽  
Added Mass ◽  
Axisymmetric Body ◽  
The Body ◽  
Forced Oscillations ◽  
Radiation Problem ◽  
Absorption Length ◽  
Damping Coefficients ◽  
Sea Bed ◽  
Linear Spring

It has been shown (Evans 1976) that the power absorbed by a general, axisymmetric body depends solely upon the added-mass and damping coefficients. These coefficients are fundamental properties of the body, representing the component of the force on the body proportional to the acceleration and velocity of the body respectively in the radiation problem, where the body is forced to oscillate in the absence of incoming waves.In the present paper these coefficients are determined by solution of the radiation problem, for a mouth-upward cylindrical duct situated on the sea bed and fitted with a piston undergoing forced oscillations. The added-mass and damping coefficients are then used to study the power absorption properties of the duct when the power take-off is modelled by a linear-spring–dashpot system attached to the piston. Curves of the added mass, damping coefficients and absorption length (a measure of the power absorbed) as functions of wavenumber are presented, for different duct diameters and different depths of submergence.

scholarly journals MODELING OF STRESS-DEFORMED STATE OF BENDED REINFORCED CONCRETE ELEMENTS IN ZONES OF CLEAN AND TRANSVERSE BEND

2021 ◽  
Vol 11 (1) ◽  
pp. 26-33
Author(s):  
Anatoly A. PROKOPOVICH ◽  
Yana A. BUZOVSKAYA
Keyword(s):  
Reinforced Concrete ◽  
Experimental Studies ◽  
Element Model ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Concrete Element ◽  
Nite Element ◽  
Deformed State ◽  
System Of Cracks ◽  
Concrete Elements

The article deals with the analysis of the stress-strain state (SSS) of a bent reinforced concrete element in zones of pure and transverse bending. It is assumed that a bent element in the process of loading (after the formation of normal and oblique cracks) is divided into blocks, united by uncracked concrete and reinforcement that has adhesion to concrete. SSS was formed using the results of experimental studies of special prototypes in the PC “Lira-SAPR”. A fi nite element model of a prototype has been developed in the form of a reinforced concrete rectangular beam loaded with two identical concentrated forces in the span. By the method of successive approximations, the process of formation and formation of a system of cracks is realized, with which the beam is divided into blocks during loading. The results of calculating the fi nite element model and their comparison with experimental data are presented.

Flow Near the Stagnation Point of a Body Which Undergoes a Sudden Change in a Steady Stream

1973 ◽  
Vol 40 (1) ◽  
pp. 37-42 ◽  
Author(s):  
K. Nanbu
Keyword(s):  
Stagnation Point ◽  
Equations Of Motion ◽  
Sudden Change ◽  
Order Theory ◽  
Small Time ◽  
The Body ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
First Order Theory ◽  
Time Solution

Unsteady laminar boundary layers near the stagnation point of a body which undergoes a sudden change in a steady stream are analyzed by the method of successive approximations. It is shown that the second approximation which includes the effect of nonlinear convective terms of the equations of motion improves remarkably the first-order theory by the earlier investigators. Also, it seems that when the body is started with velocity increasing gradually with increasing time, the small-time solution obtained thus connects smoothly with the existing large-time solution.

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.

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.

Experimental Studies on Diesel Engine with Piston Crown Modification Using an Optimum Alternative Fuel

2015 ◽  
Vol 813-814 ◽  
pp. 830-835
Author(s):  
Akkaraju H. Kiran Theja ◽  
Rayapati Subbarao
Keyword(s):  
Diesel Engine ◽  
Combustion Chamber ◽  
Experimental Studies ◽  
Alternative Fuel ◽  
Air Gap ◽  
The Body ◽  
Injection Timing ◽  
Positive Trend ◽  
Piston Crown ◽  
Karanja Oil

The drawbacks associated with bio-fuels can be minimized by making modifications to combustion chamber. Modification of combustion chamber is achieved by providing an air gap in between the crown and the body of the piston with the top crown made of low thermal conductivity material. Experimentation is carried on a diesel engine with brass as piston crown material and karanja as test fuel, which is found to be a better alternative fuel based on the tests carried out prior to modification. Investigations are carried out on the performance of the engine with modified combustion chamber consisting of air gap insulated piston with 2 mm air gap with brass crown when fuelled with karanja oil. Comparative studies are made between the two configurations of engine with and without modification at an injection timing of 29obTDC. Performance, heat balance and emission plots are made with respect to brake power. Fuel consumption increased with modification. The mechanical and volumetric efficiencies are similar in both the cases. Indicated and brake thermal efficiencies got reduced with modification. But, it is good to see that HC and CO emissions are showing positive trend. Thus, the present investigation hints the possibility of improvements while making piston modification and providing air gap insulation.

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