scholarly journals Pulse Propagation in Fluid-Filled Tubes

1977 ◽  
Vol 44 (1) ◽  
pp. 31-35 ◽  
Author(s):  
J. S. Walker ◽  
J. W. Phillips
Keyword(s):  
Method Of Characteristics ◽  
Pulse Propagation ◽  
Numerical Solutions ◽  
Pulse Length ◽  
Elastic Tube ◽  
Impulsive Force ◽  
Tube Material ◽  
Thin Walled ◽  
Inviscid Compressible Fluid ◽  
Special Case

A new theory for the propagation of pressure pulses in an inviscid compressible fluid contained in a thin-walled elastic tube is presented. This theory represents an improvement over the classical waterhammer theory because the restriction that the speed of sound in the tube material must be much greater than that in the fluid has been removed and because the restriction that the pulse length must be much greater than the tube diameter has been somewhat relaxed. The new theory is applied to a water-filled copper tube with an axial impulsive force of very short duration applied either to a piston inserted in the anchored end of the tube or to a cap on the free end of the tube. Numerical solutions using the method of characteristics are presented, and comparison is made with the predictions of classical waterhammer theory. A check on the numerical solution is provided by the analytical solution for the capped tube and for the special case when the speeds of sound in the tube material and in the fluid are equal.

Pulse Propagation in Fluid-Filled Elastic Curved Tubes

1981 ◽  
Vol 103 (1) ◽  
pp. 43-49 ◽  
Author(s):  
C. K. Hu ◽  
J. W. Phillips
Keyword(s):  
Method Of Characteristics ◽  
Pulse Propagation ◽  
Elastic Tube ◽  
Governing Equations ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
The Method Of Characteristics ◽  
Continuous Waves ◽  
Fluid Transients ◽  
Inviscid Compressible Fluid

The propagation of fluid transients through elbows is studied. A set of one-dimensional governing equations for the propagation of pressure pulses in an inviscid compressible fluid contained in a thin-walled naturally curved elastic tube is formulated and solved by two different techniques. For continuous waves, reflection and transmission coefficients for elbows are determined numerically by considering periodic waves in an assemblage of straight and curved tubes. For pulse propagation, the method of characteristics is employed to solve the assemblage problem. An experimental arrangement for pulse studies is described and experimental results are compared with numerical results from the method of characteristics.

scholarly journals Numerical Boundary Conditions for Solar Magnetic Hydrodynamic Flows Using the Method of Characteristics

1996 ◽  
Vol 154 ◽  
pp. 149-153
Author(s):  
S. T. Wu ◽  
A. H. Wang ◽  
W. P. Guo
Keyword(s):  
Boundary Conditions ◽  
Method Of Characteristics ◽  
Numerical Solutions ◽  
The Self ◽  
Time Dependent ◽  
Solar Plasma ◽  
The Method Of Characteristics ◽  
Mhd Simulations ◽  
Self Consistent ◽  
Dynamic Structures

AbstractWe discuss the self-consistent time-dependent numerical boundary conditions on the basis of theory of characteristics for magnetohydrodynamics (MHD) simulations of solar plasma flows. The importance of using self-consistent boundary conditions is demonstrated by using an example of modeling coronal dynamic structures. This example demonstrates that the self-consistent boundary conditions assure the correctness of the numerical solutions. Otherwise, erroneous numerical solutions will appear.

Interactions of Nonlinear Waves in Fluid-Filled Elastic Tubes

2007 ◽  
Vol 62 (1-2) ◽  
pp. 21-28
Author(s):  
Hilmi Demiray
Keyword(s):  
Solitary Waves ◽  
Nonlinear Waves ◽  
Elastic Tube ◽  
Wave Number ◽  
Inviscid Fluid ◽  
Leading Order ◽  
Elastic Tubes ◽  
Longwave Approximation ◽  
Thin Walled ◽  
Analytical Phase

In this work, treating an artery as a prestressed thin-walled elastic tube and the blood as an inviscid fluid, the interactions of two nonlinear waves propagating in opposite directions are studied in the longwave approximation by use of the extended PLK (Poincaré-Lighthill-Kuo) perturbation method. The results show that up to O(k3), where k is the wave number, the head-on collision of two solitary waves is elastic and the solitary waves preserve their original properties after the interaction. The leading-order analytical phase shifts and the trajectories of two solitons after the collision are derived explicitly.

An Evaluation of Material Weight and Contained Fluid Volume for Eccentric Intersecting Cylinders of Arbitrary Size

1989 ◽  
Vol 111 (3) ◽  
pp. 342-347
Author(s):  
Y. J. Chao ◽  
M. A. Sutton
Keyword(s):  
Vessel Diameter ◽  
Fluid Volume ◽  
Wide Range ◽  
Single Integral ◽  
Material Volume ◽  
Thin Walled ◽  
Special Case ◽  
Range Of Values ◽  
Engineering Personnel ◽  
Quantities Of Interest

Engineering personnel in industries which use pressurized containment vessels having attached nozzles are required not only to design portions of the lifting mechanism, but also to estimate the fluid volume which the vessel and nozzles will contain; most designers use simplified formulas for computing the quantities of interest. Typically, these formulas are valid approximations when the nozzle diameter is much smaller than the vessel diameter. The enclosed work develops three single-integral expressions which can be programmed and numerically integrated to obtain accurate estimates for both the material volume and also the containment volume present in a pair of eccentrically, or concentrically, intersecting thin-walled cylinders of arbitrary diameters. A table of such values is presented for a wide range of values of the standard nozzle pipe diameter and vessel diameter, for the special case of a concentric nozzle. In addition, an example is presented which compares the numerically integrated values for both the material volume and the containment volume to simplified upper and lower-bound estimates.

scholarly journals Motion of a tightly fitting axisymmetric object through a lubricated elastic tube

2021 ◽  
Vol 926 ◽  
Author(s):  
Bhargav Rallabandi ◽  
Jens Eggers ◽  
Miguel Angel Herrada ◽  
Howard A. Stone
Keyword(s):  
Numerical Simulations ◽  
Numerical Solutions ◽  
Elastic Tube ◽  
Direct Numerical Simulations ◽  
Fluid Film ◽  
Square Root ◽  
Membrane Tension ◽  
Relative Speed ◽  
Thin Fluid ◽  
Thin Fluid Film

We consider the translation of a rigid, axisymmetric, tightly fitting object through a cylindrical elastic tube filled with viscous fluid, using a combination of theory and direct numerical simulations. The intruding object is assumed to be wider than the undeformed tube radius, forcing solid–solid contact in the absence of relative motion. The motion of the object establishes a thin fluid film that lubricates this contact. Our theory couples lubrication theory to a geometrically nonlinear membrane description of the tube's elasticity, and applies to a slender intruding object and a thin tube with negligible bending rigidity. We show using asymptotic and numerical solutions of the theory, that the thickness of the thin fluid film scales with the square root of the relative speed for small speeds, set by a balance of hoop stresses, membrane tension and fluid pressure. While membrane tension is relatively small at the entrance of the film, it dominates near the exit and produces undulations of the film thickness, even in the limit of vanishing speeds and slender objects. We find that the drag force on the intruding object depends on the slope of its surface at the entrance to the thin fluid film, and scales as the square root of the relative speed. The predictions of the lubricated membrane theory for the shape of the film and the force on the intruder are in quantitative agreement with three-dimensional direct numerical simulations of the coupled fluid–elastic problem.

An Elongating String Under the Action of a Transverse Force

1957 ◽  
Vol 24 (4) ◽  
pp. 609-616
Author(s):  
Werner Goldsmith
Keyword(s):  
Method Of Characteristics ◽  
Numerical Solutions ◽  
Transverse Force ◽  
Transverse Displacement ◽  
Fixed Frequency ◽  
Constant Acceleration ◽  
Forcing Function ◽  
Subsonic Regime ◽  
Arbitrary Amplitude ◽  
Analytical Expressions

Abstract The motion of a uniform undamped flexible string whose length increases with time has been investigated when an arbitrary time-dependent force acts transversely at the free end. The method of characteristics has been employed to derive analytical expressions for the transverse displacement in the subsonic regime. Cases are considered when the free end of the wire moves either at constant velocity or at constant acceleration. Numerical solutions are presented in dimensionless form for a sinusoidal forcing function of arbitrary amplitude and fixed frequency. The possibility of the existence of resonances in the string has been examined.

Lobar Buckling of Thin-Walled Cylindrical and Truncated Conical Shells Under External Pressure

1974 ◽  
Vol 18 (04) ◽  
pp. 272-277
Author(s):  
C. T. F. Ross
Keyword(s):  
Finite Element ◽  
Circular Cylinder ◽  
Numerical Solutions ◽  
External Pressure ◽  
Element Solution ◽  
Conical Shells ◽  
Varying Thickness ◽  
Complex Boundary ◽  
Thin Walled ◽  
Unsymmetrical Loading

Numerical solutions have been produced for the asymmetric instability of thin-walled circular cylindrical and truncated conical shells under external pressure. The solutions for the circular cylinder have shown that the assumed buckling configurations of Nash [l]2 and Kaminsky [2] were quite reasonable for fixed ends. Comparison was also made of the finite-element solution of conical shells with other analyses. From these calculations, it was shown that the numerical solutions were superior to the analytical ones, as the former could be readily applied to vessels of varying thickness or those subjected to unsymmetrical loading or with complex boundary conditions.

Comparative Evaluation of Analytical Methods for the Determination of Coefficients of Friction and Stresses when Wire Rod Drawing

2018 ◽  
Vol 284 ◽  
pp. 247-252 ◽  
Author(s):  
Sergei I. Platov ◽  
V.A. Nekit ◽  
Nikolay N. Ogarkov
Keyword(s):  
Plastic Deformation ◽  
Comparative Evaluation ◽  
Method Of Characteristics ◽  
Circular Cross Section ◽  
Wire Drawing ◽  
Work Piece ◽  
Relative Height ◽  
Plane Plastic ◽  
Special Case

The article discusses the process of wire drawing of circular cross-section. The study of stresses of wire drawing in conditions of plane plastic flow was held. As theoretical framework the study was adopted the method of characteristics, a special case, having the definitive decision. Stresses during wire drawing are defined by decomposing the decision into two components of plane strain and the superposition of these decisions. The results of theoretical solution of the problem of wire drawing were used to determine the coefficients of friction on the surface of contact of the tool and the work piece during the deformation of steel with a diameter of 5.5 mm. It is recommended to use two-dimensional methods of solution in the analysis of the process of wire drawing in conditions with a high hearth of plastic deformation (with the relative height of the hearth of plastic deformation 2 and bigger). The theoretical dependences between the friction coefficients at the contact surface of the work piece and the tool was obtained. The obtained values of coefficients of friction can be used over solving the task of the wire drawing in conditions with a high hearth of plastic deformation.

scholarly journals Geometry of Hamiltonian Dynamics with Conformal Eisenhart Metric

2011 ◽  
Vol 2011 ◽  
pp. 1-26 ◽  
Author(s):  
Linyu Peng ◽  
Huafei Sun ◽  
Xiao Sun
Keyword(s):  
Hamiltonian System ◽  
Geometric Structure ◽  
Degrees Of Freedom ◽  
Numerical Solutions ◽  
Hamiltonian Dynamics ◽  
Jacobi Field ◽  
Linear Hamiltonian System ◽  
Conformal Metric ◽  
Jacobi Equations ◽  
Special Case

We characterize the geometry of the Hamiltonian dynamics with a conformal metric. After investigating the Eisenhart metric, we study the corresponding conformal metric and obtain the geometric structure of the classical Hamiltonian dynamics. Furthermore, the equations for the conformal geodesics, for the Jacobi field along the geodesics, and the equations for a certain flow constrained in a family of conformal equivalent nondegenerate metrics are obtained. At last the conformal curvatures, the geodesic equations, the Jacobi equations, and the equations for the flow of the famous models, anNdegrees of freedom linear Hamiltonian system and the Hénon-Heiles model are given, and in a special case, numerical solutions of the conformal geodesics, the generalized momenta, and the Jacobi field along the geodesics of the Hénon-Heiles model are obtained. And the numerical results for the Hénon-Heiles model show us the instability of the associated geodesic spreads.

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