Collapse of a Gas-Filled Spherical Cavity

1968 ◽  
Vol 35 (3) ◽  
pp. 579-587 ◽  
Author(s):  
W. E. Jahsman
Keyword(s):  
Spherical Cavity ◽  
Perturbation Technique ◽  
Fluid Pressure ◽  
Compressible Liquid ◽  
Adiabatic Compression ◽  
Cavity Wall ◽  
Complete Detail ◽  
Coordinate Perturbation ◽  
Wall Position ◽  
Good Agreement

The PLK coordinate perturbation technique [10] is used to obtain a solution to the problem of collapse of gas-filled spherical cavity in an infinite compressible liquid. The gas is assumed to undergo quasi-static adiabatic compression and the liquid equation of state is taken to follow the modified Tate form [11]. The approach was first outlined by Benjamin [9] and in the present paper expressions for cavity wall history and fluid pressure, density, and particle velocity are carried out in complete detail for the first three terms in the expansions. It is found that the solutions for the variables can all be written as products of functions which depend on only one of the perturbed coordinates. For the coordinate corresponding to outward traveling characteristics (first used by Whitham [12]), only two functions are required; they are associated with cavity wall position and with velocity and satisfy second-order ordinary differential equations which are readily solved by digital computer. For the remaining coordinate (perturbed radius) the functions are all polynomials. A numerical example is presented and curves of cavity wall position, pressure, and velocity histories are given for the period associated with collapse and rebound of the cavity. Results are compared with earlier work based on the Gilmore adaptation of the Kirkwood-Bethe formulation [8], and good agreement is found.

PROPAGATION OF WEAKLY NONLINEAR WAVES IN A FLUID-FILLED THIN ELASTIC TUBE

1999 ◽  
Vol 23 (2) ◽  
pp. 253-265
Author(s):  
H. Demiray
Keyword(s):  
Nonlinear Waves ◽  
Vries Equation ◽  
Perturbation Technique ◽  
Fluid Pressure ◽  
Static Field ◽  
Elastic Tube ◽  
Inviscid Fluid ◽  
Weakly Nonlinear ◽  
De Vries ◽  
Weakly Nonlinear Waves

In this work, we study the propagation of weakly nonlinear waves in a prestressed thin elastic tube filled with an inviscid fluid. In the analysis, considering the physiological conditions under which the arteries function, the tube is assumed to be subjected to a uniform pressure P0 and a constant axial stretch ratio λz. In the course of blood flow in arteries, it is assumed that a finite time dependent radial displacement is superimposed on this static field but, due to axial tethering, the effect of axial displacement is neglected. The governing nonlinear equation for the radial motion of the tube under the effect of fluid pressure is obtained. Using the exact nonlinear equations of an incompressible inviscid fluid and the reductive perturbation technique, the propagation of weakly nonlinear waves in a fluid-filled thin elastic tube is investigated in the longwave approximation. The governing equation for this special case is obtained as the Korteweg-de-Vries equation. It is shown that, contrary to the result of previous works on the same subject, in the present work, even for Mooney-Rivlin material, it is possible to obtain the nonlinear Korteweg-de-Vries equation.

Transcapillary Starling forces using membrane osmometry

1980 ◽  
Vol 238 (6) ◽  
pp. H886-H888
Author(s):  
J. L. Christian ◽  
R. A. Brace
Keyword(s):  
Osmotic Pressure ◽  
Interstitial Fluid ◽  
Subcutaneous Tissue ◽  
Fluid Pressure ◽  
Colloid Osmotic Pressure ◽  
Interstitial Fluid Pressure ◽  
Tissue Samples ◽  
Small Pore ◽  
The Difference ◽  
Good Agreement

Membrane osmometry was used to estimate the four transcapillary Starling pressures in subcutaneous tissue of rats, guinea pigs, and dogs. Isolated subcutaneous tissue samples were either placed on a large-pore or small-pore osmometer that measured the interstitial fluid pressure (Pif) and the difference between the interstitial fluid pressure and the interstitial protein osmotic pressure (Pif-pi if), respectively. The colloid osmotic pressure of the interstitial fluid (pi if) was obtained from the difference in these two pressures. A plasma sample placed on the small-pore osmometer yielded the colloid osmotic pressure of the plasma proteins (pi c). Finally the capillary pressure (Pc) was calculated from the three other Starling forces. In the rat, guinea pig, and dog, respectively, the estimated Starling forces were as follows: Pif -2.2, -2.1, and -4.8 mmHg; pi if, 7.3, 4.8, and 4.4 mmHg; pi c, 21.3, 19.5, and 19.2 mmHg; and Pc, 11.8, 12.6, and 10.0 mmHg. A comparison with data obtained in other studies using different methods shows good agreement and strongly supports membrane osmometry as a method for measuring the Starling pressures in subcutaneous tissue.

Tube Hydroforming (THF): Process Optimization of an Automotive Component

2013 ◽  
Vol 549 ◽  
pp. 141-148
Author(s):  
Aldo Attanasio ◽  
Elisabetta Ceretti ◽  
Giancarlo Maccarini
Keyword(s):  
Fluid Pressure ◽  
Tube Hydroforming ◽  
Experimental Tests ◽  
Side Impact ◽  
Pressure Curve ◽  
Part Geometry ◽  
Italian Government ◽  
Working Solution ◽  
Hydroforming Process ◽  
Good Agreement

This paper reports the results obtained during a research project funded by the Italian Government and involving several Italian Universities (PRIN INTEMA). The activities have been focused on side impact bar manufacturing by means of Tube Hydroforming process (THF). Punch movement paths and fluid pressure curve were optimized by means of FEM software (LS-DYNA) to guarantee tube sealing and material feeding during the tube deformation. The side impact bar geometry was optimized till reaching the shape guaranteeing the obtainment of safe parts with the best compromise in terms of final part geometry and thickness reduction. Different fluid pressure and punch movement paths were investigated. Once accomplished all the simulations and identified the best working solution, experimental tests were performed setting the process parameters according to the values defined during the simulation phase. Good agreement between FEM and experimental results were highlighted.

Penetration of Strain-Hardening Targets With Rigid Spherical-Nose Rods

1991 ◽  
Vol 58 (1) ◽  
pp. 7-10 ◽  
Author(s):  
M. J. Forrestal ◽  
N. S. Brar ◽  
V. K. Luk
Keyword(s):  
Closed Form ◽  
Strain Hardening ◽  
Spherical Cavity ◽  
Cavity Expansion ◽  
Rigid Rods ◽  
Engineering Models ◽  
Spherical Nose ◽  
Spherical Cavity Expansion ◽  
Penetration Depths ◽  
Good Agreement

We developed engineering models that predict forces and penetration depth for long, rigid rods with spherical noses and rate-independent, strain-hardening targets. The spherical cavity expansion approximation simplified the target analysis, so we obtained closed-form penetration equations that showed the geometric and material scales. To verify our models, we conducted terminal-ballistic experiments with three projectile geometries made of maraging steel and 6061-T651 aluminum targets. The models predicted penetration depths that were in good agreement with the data for impact velocities between 0.3 and 1.0 km/s.

Nonaxisymmetric Flow in the Narrow Gap Between a Rotating and a Stationary Disk

1976 ◽  
Vol 98 (2) ◽  
pp. 217-223 ◽  
Author(s):  
M. Bein ◽  
A. Shavit ◽  
A. Solan
Keyword(s):  
Flow Field ◽  
Perturbation Technique ◽  
Fluid Pressure ◽  
Rotating Disk ◽  
Operating Conditions ◽  
Narrow Gap ◽  
Stationary Disk ◽  
Flow Maps ◽  
Pass Through ◽  
Rotary Vane Compressor

The flow between a rotating disk and a stationary disk, with nonaxisymmetric boundary conditions is studied. A flow field of this type exists in the narrow gap between the rotor and side plates of a rotary vane compressor. Fluid is admitted into the gap in the center of the disk for the purpose of sealing against leakage due to the nonaxisymmetric pressure distribution externally imposed on the disk circumference. The flow is solved analytically by a perturbation technique. Flow maps and pressure maps are obtained for various operating conditions. The effectiveness of the fluid seal is evaluated for these conditions by calculating the flow rates that pass through the gap. The flow field is simulated on a test apparatus and experimental verification is given to the analytical results. The results obtained indicate the possibility of appreciably reducing the leakage through the gap by a proper selection of the fluid pressure and the disk geometry.

Forced Oscillations of Non-Linear Two-Degree-of-Freedom Systems

1966 ◽  
Vol 8 (3) ◽  
pp. 252-258 ◽  
Author(s):  
G. N. Bycroft
Keyword(s):  
Numerical Integration ◽  
Transient Response ◽  
Internal Resonance ◽  
Perturbation Technique ◽  
Degree Of Freedom ◽  
Forced Oscillations ◽  
Oscillatory Systems ◽  
Non Linear ◽  
Two Degree Of Freedom ◽  
Good Agreement

This paper shows how the Lighthill-Poincaré perturbation technique may be used to determine the transient response of ‘lightly coupled’ non-linear multi-degree-of-freedom oscillatory systems subject to arbitrary forcing functions. The results in general are complex but simplify in many important cases. A comparison is made between the analytical results and results obtained by a numerical integration of the equations on a computer. Good agreement is noted. The method fails under conditions of ‘internal resonance’ of the system.

Coordinate perturbation and multiple scale in gasdynamics

1972 ◽  
Vol 272 (1222) ◽  
pp. 275-301 ◽  
Keyword(s):  
Flow Field ◽  
Perturbation Technique ◽  
Leading Edge ◽  
Multiple Scale ◽  
Initial Disturbance ◽  
Two Dimensional ◽  
Third Order ◽  
Closed Tube ◽  
Coordinate Perturbation

Usually, the application of the coordinate perturbation technique consists in transforming the equations to perturbed coordinates, and determining from the transformed equations the amount of coordinate straining appropriate to obtain a uniformly valid expansion. However, the transformed equations may become unwieldy with increasing order of the system, number of variables, and order of the approximation. There exists a much simpler way of applying the technique, which bypasses the transformed equations and provides the appropriate coordinate stretching by simple algebraic manipulations on the nonuniformly valid expansion obtained by straightforward expansion from the original equations. Interesting results are obtained by applying the procedure to two gasdynamical problems. In the first the flow field around a supersonic two-dimensional wing is determined up to third order, including a uniformly valid representation of the front shock shape, valid even when the shock does not start at the leading edge. The second problem concerns the oscillations in a closed tube following an arbitrary initial disturbance, both when the two ends are closed, and when one of the two ends contains an oscillating piston (the inviscid Chester problem). In both problems the uniformly valid expansions are substantially simpler than the non-uniformly valid. But most interesting is the result that the uniformly valid expansions cannot be obtained without supplementing the coordinate perturbation technique by the multiple scale technique.

A Methodology of Predicting Cavity Geometry Based on Scanned Surface Temperature Data—Prescribed Surface Temperature at the Cavity Side

1980 ◽  
Vol 102 (2) ◽  
pp. 324-329 ◽  
Author(s):  
C. K. Hsieh ◽  
K. C. Su
Keyword(s):  
Surface Temperature ◽  
Three Dimensional ◽  
Mesh Size ◽  
Front Surface ◽  
Temperature Data ◽  
Cavity Wall ◽  
Back Surface ◽  
Measured Temperature ◽  
Surface Temperature Data ◽  
Wall Position

The scanned surface temperature data from a body are used to predict the cavity lying underneath the surface. The basic system under investigation is a plane wall having a rectangular cavity at the back surface. The front surface dissipates heat by convection; this is also the surface whose temperature is scanned. For a prescribed surface temperature specified on the cavity side, a numerical solution is found convenient to predict the cavity top and the approximate location of the cavity wall. A recheck of the cavity wall position calls for matching the recalculated surface temperature with the measured temperature. The data are found to be well behaved to the extent that an interpolation is possible when the mesh size chosen happens to miss the wall position. The methodology can also be extended to prediction of holes in a three-dimensional body.

Large Deflection of Unsymmetric Cross-Ply and Angle-Ply Plates

1976 ◽  
Vol 18 (4) ◽  
pp. 179-183 ◽  
Author(s):  
C. Y. Chia ◽  
M. K. Prabhakara
Keyword(s):  
Boundary Conditions ◽  
Large Deflection ◽  
Perturbation Technique ◽  
Transverse Load ◽  
Load Force ◽  
Rectangular Plates ◽  
Linear Partial Differential Equations ◽  
Transverse Deflection ◽  
Anisotropic Rectangular Plates ◽  
Good Agreement

An approximate solution to the von Karman-type large-deflection equations of unsymmetrically laminated, anisotropic, rectangular plates under uniform transverse load is formulated by the perturbation technique. The membrane boundary conditions are the zero normal and shear boundary forces. By expressing the load, force function and transverse deflection in the form of series, the governing equations and boundary conditions are reduced to a series of linear partial differential equations and boundary conditions. In each approximation a solution is assumed in the form of polynomials which satisfy the associated boundary conditions and physical requirements for deflection and and three membrane forces in unsymmetric cross-ply and angle-ply plates. Taking the first three terms in the truncated series, numerical results are graphically presented for the load-deflection relations, bending moments and membrane forces in unsymmetric cross-ply and angle-ply plates with various values of aspect ratio and total number of layers. The present third approximation is in good agreement with the existing solutions for large deflections of isotropic and unsymmetric angle-ply plates having the ratio of central deflection to thickness up to the value of 2.

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