bluuebunny/crossref_metadata_2025_split huggingface dataset:
Solution of Navier-Stokes Equations for the Non-Linear Hydrodynamic Slider by Matrix Algebra Methods
Authors: Woodhead R. W. , Kettleborough C. F. 
Published: February 2007

The equations of viscous flow, the Navier-Stokes equations, are difficult to solve because they are non-linear, multi-variable, partial differential equations. For isothermal two-dimensional flow three equations have to be solved simultaneously, the momentum equation for each direction and the continuity equation. The usual numerical method is to replace the continuous system with the discrete representation at a number of points by the finite difference approximations to these equations, assuming that the solution to the discrete system approximates and converges with increasing point representation to the continuous solution. An iteration process, whereby the non-linear terms provide corrections to the solution of the linear portion of the equations, would tax many digital computers from the viewpoints of both storage and time. The use of matrix methods discussed in this paper enables considerable simplification and savings in both computer storage and time. Further non-linear terms present no difficulty whatsoever and are*** readily incorporated in the method of solution. This approach permits ready generalization not only to other problems in hydrodynamics but also to other non-linear differential equations. The only knowledge required is that associated with normal matrix methods and finite difference formulae applicable to numerical differentiation and integration. It is thought that the simplicity of the method will appeal to engineers in general. The first part of the paper examines the basic equations by the usual order of magnitude approach and reduces them to their simplest form with the dominant inertia terms retained. The numerical results are shown to be in good agreement with a single perturbation solution. The second part describes the numerical solution of the equations.
Design of Rectangular Tubeplates for Large Heat Exchangers
Authors: Blake C. S. , Paton A. D. 
Published: February 2007

A method is proposed for dealing with large rectangular and circular tubeplates, in which edge loading and deflection is absorbed by a bellows or a diaphragm. The simple design procedure is based on curves derived from a theory which considers a strip at the edge of the tubeplate. Specimen curves and a recommended design procedure are included. Reference is made to the ratios known as deflection and ligament efficiencies and results of tests are given which suggest that the values of these are in fact lower than those in general use. In an example it is shown that a significant saving can result by the use of a diaphragm in place of the more conventional bellows. Finally a description is given of a test rig, designed to check the values of stress and deflection in a given system of loading.
Critical-Flow Nozzle Meter and Its Application to the Measurement of Mass Flow Rate in Steady and Pulsating Streams of Gas
Authors: Kastner L. J. , Williams T. J. , Sowden R. A. 
Published: February 2007

Simple theory indicates that when critical flow of a gaseous fluid is established in a given passage, the rate of mass flow becomes dependent only on the absolute pressure and temperature upstream, and changes in downstream conditions no longer have any influence. In practice, some modifications of the theoretical conclusions may sometimes be necessary. The discharge coefficient of a simple plate orifice, for instance, is greatly dependent on the amount of jet contraction, and this may be influenced by changes in downstream pressure even under critical-flow conditions. However, a properly shaped flow nozzle is not affected in this way, and is well suited for flow measurement under critical conditions. In the experiments described, a large number of small-diameter nozzles with quadrant entrances was tested, and the effects of nozzle length/throat diameter ratio and entry radius/throat diameter ratio were carefully examined. A range of simple cylindrical nozzles was also tested. Such nozzles are easily reproduced and are to be recommended in cases where a rather low discharge coefficient is not a disadvantage. The above experiments were made with smoothed steady flows but in addition a number of trials with pulsating flows was carried out and it was found that the observed coefficients of discharge for pulsating flow differed very little from those applying to steady-flow conditions. In view of the acknowledged difficulty in metering unsteady flows, this is a most valuable property, and it is thought that critical flow meters are very suitable for measuring the output of reciprocating compressors, free piston gasifiers and other plant delivering gas at high pressure.
Effect of Pre-Strain on Yield Surfaces in Copper
Authors: Mair W. M. , Pugh H. Ll. D. 
Published: February 2007

An investigation into the effect of both tensile and torsion pre-strain is reported. A thin-walled tube was pre-strained in either tension or torsion, unloaded, and then subjected to a combination of tension and torsion to establish the yield locus in the tensile-stress-shear-stress plane corresponding to the particular pre-strain. The results for torsion pre-strain in particular support a hardening theory, proposed by Hodge, that an inflation of the yield surface is accompanied by a translation. It is shown that the method of defining yield is of prime importance. Different conclusions can be drawn about the general behaviour of the yield surfaces for a work-hardening material, depending on the definition of yield used.
Effect of High-Strain Fatigue Cycles on the Brittle-Ductile Transition of Two Mild Steels
Authors: Harris D. J. , Benham P. P. 
Published: February 2007

Low endurance fatigue curves were obtained for grades A and D mild steel under the following axial conditions: reversed load cycling—plain specimens; repeated tensile load cycling—plain specimens (grade A only); reversed strain cycling—plain material; reversed strain cycling—notched material. Some results were also obtained for reversed strain cycling in bending of notched specimens. The fatigue results were generally as expected, the grade D steel showing a slightly superior fatigue strength. The major part of the programme was then concerned with the effect of plastic strain cycling on the brittle fracture transition behaviour. Prior axial strain cycling initiated fairly blunt fatigue cracks after only a few cycles in all notched specimens and the Tipper test transition was lowered by about 10°C for the grade A steel, but there was little effect on the grade D material. The Charpy transition temperature was raised by various amounts (20°C maximum), depending on the cyclic strain range, number of cycles and type of steel.
Pressure Waves in Horizontal Liquid-Filled Flexible Tubes
Authors: Paidoussis M. P. 
Published: February 2007

This paper deals with the velocity of propagation of waves in flexible liquid-filled tubes lying on a flat horizontal surface. The tubes considered are of sufficiently small rigidity that their cross-sectional shape is determined by the internal hydrostatic pressure, lying quite flat when empty. It is shown that at low internal pressures very long waves propagate essentially as gravity waves in a canal. The wave velocity increases with the internal pressure and, at the same time, is increasingly affected by the extensibility of the tube wall. At very high pressures, long waves propagate essentially as axisymmetric waves in distensible circular cylinders. The calculated and measured velocities of propagation of very long waves are in substantial agreement. The system is frequency dispersive and the wave velocity rapidly increases with the wave number. An approximate analysis is presented, applying only when the tube contains little liquid, establishing the mechanism underlying this behaviour. This is qualitatively supported by experimental observations.
Limited Life of Shells of Revolution Subjected to Severe Local Bending
Authors: Marcal P. V. , Turner C. E. 
Published: February 2007

Tests were performed on axially loaded expansion bellows in order to obtain the relationship between maximum strain, load and deflection in the plastic region. A numerical method, previously proposed by the authors, was also used to investigate the behaviour of the bellows. The experimental and calculated results were found to be in reasonable agreement. The strains measured at collapse did not exceed three and a half times the strain at first yield while the strains after collapse were of a higher order of magnitude. The bellows were finally tested to failure in the low-cycle regime. The results agreed with fatigue tests on the parent material. A simple model based on the behaviour of the bending of a beam is proposed for predicting the strains in a shell of revolution with severe local bending. This model is used to classify the types of loading which lead to different modes of failure in the plastic region. The proposed design procedures are then used in case studies of the limited-life design of bellows and pipe bends, and comparison made with the observed fatigue lives.
Effects of Fluid Inertia and Compressibility on the Performance of Valves and Flow Meters Operating under Unsteady Conditions
Authors: McCloy D. 
Published: February 2007

Incompressible flow theory is used in the investigation of the effects of fluid inertia on unsteady flow through valves and flow meters. Two types of oscillatory disturbance are considered, one being due to valve oscillation at constant pressure drop and the other to pressure pulsation at constant orifice area. With the former type of disturbance it is shown that the mean flow rate decreases with frequency of oscillation. When the pressure drop pulsates the mean flow rate increases with frequency. These phenomena are shown to be of importance in hydraulic servomechanisms and in dynamic flow measurement. Compressibility effects are considered and it is shown that cavitation can occur at the valve during oscillation.
Theoretical Estimation of the Frictional Energy Dissipation in a Simple Lap Joint
Authors: Earles S. W. E. 
Published: February 2007

Some recent work on fretting fatigue in lap joints has shown that certain treatments of the joint contact surfaces greatly improve the fatigue life of the joint, and suggests that maximum benefit may be obtained by arranging for force transference within the joint to take place only by frictional resistance. A simple theoretical analysis of a simple lap joint is here presented which estimates the frictional energy dissipation, and concludes that, for any pressure distribution imposed along the joint faces by the rivet clamping force, the damping capacity of the joint is a maximum when force transference is only by friction throughout the joint.
Resistance to Steady Laminar Flow of Pseudoplastic Fluids through Pipes and Valves
Authors: Ury J. F. 
Published: February 2007

The well-known logarithmic friction factor diagram for laminar pipe flow can be extended in the following two respects: For application to non-Newtonian fluids, by incorporating in the plot a modified form of the consistency curve for a given material. Methods are discussed of obtaining these curves, and of transforming them into the required shape. For prediction of flow resistance through valves and fittings, by use of an auxiliary diagram based on results of appropriate tests. The general procedure is outlined, and it is stressed that results cannot be relied on quantitatively, until test data are obtained for wider ranges of sizes and types than hitherto available.
Self-Damped Pneumatic Isolator for Variable Frequency Excitation
Authors: Soliman J. I. , Tajer-Ardabili D. 
Published: February 2007

The correct amount of damping is very important for the proper functioning of isolation systems. Isolation systems with a small amount of damping are unable to protect the equipment from damaging resonance build-up and excessive damping reduces the isolation effectiveness at high disturbing frequencies. In this paper it is shown that when pneumatic isolators are used, damping can be provided simply by ‘transient pressure feedback’. The main advantage of this method of damping is that it is dependent on the disturbing frequency and, therefore, it is possible to have a large amount of damping at resonant frequency and a decreasing amount of damping as the frequency of vibration increases.
Comparison of Constant-Load and Constant-Stress Tensile Creep Data for an Aluminium-0.07 Percent Titanium Alloy at 250°C
Authors: Fairbairn J. 
Published: February 2007

Constant-stress tensile creep data were obtained from an aluminium-0.07 per cent titanium alloy at 250°C and correlated using a power law of the form: To obtain a better fit to the experimental data in the higher strain regions a modified time function was selected and the experimental data correlated using an equation of the form: This equation was used to obtain theoretical constant-load curves which are compared with experimental constant-load data previously obtained from the same billet of material.
Gyroscopic Whirl of a Rotating Bobbin Mounted on a Swing-Arm
Authors: Beddoe B. 
Published: February 2007

A bobbin mounted transversely at one end of a flexible arm which is pivoted at the other end, is represented by four degrees of freedom. The frequency equation is derived in non-dimensional form and changes in the frequencies of free vibration due to gyroscopic effects are discussed. Four of a possible 20 sets of frequency curves are illustrated. The analysis was prompted by vibration of a machine for winding synthetic yarn.
The Railway Wheelset and Suspension Unit as a Closed-Loop Guidance Control System: A Method for Performance Improvement
Authors: Benington C. K. 
Published: February 2007

Using a simplified mathematical model, the conventional railway wheelset and suspension unit is shown to behave as a closed-loop guidance control system. The centre-line of the track corresponds to the input, and the lateral position of the centroid of the wheelset to the output. Analysis of the system shows that, while it may be made stable at up to high speeds, the performance in the stable region is unsatisfactory in certain respects. This is attributed to the large forces of interaction between the wheels and rails at the points of contact, arising, in the case of the conventional wheelset, from creepage. These forces may be reduced and controlled by interposing a coupling having viscous characteristics between the wheels, in place of the rigid axle. The new arrangement is shown to be much more flexible, and capable of fulfilling a wide range of performance requirements.
Steady-Amplitude, Self-Excited Oscillations of Hydraulic Spool Valves
Authors: Foster K. , Kulkarni M. M. 
Published: February 2007

The free oscillations of an inertia-loaded hydraulic spool valve are examined by obtaining first the theoretical conditions for a steady amplitude oscillation of a three-way valve working at low pressures where compressibility of the fluid is unimportant. The predictions are confirmed qualitatively, in experimental work on valves, but quantitatively there is some discrepancy between the experimental and theoretical negative damping forces for short valves. This theory is then extended to the case where compressibility creates a distributed parameter effect in the inlet pipe, and it is shown that jumps in frequency and amplitude occur when the length of the inlet pipe is near to odd multiples of one-eighth of a wavelength. Another resonant system on the output of the valve also occurs when fluid compressibility combines with the inertia of a load on an output actuator, and again the agreement between the theory and experiment is good. It is concluded from the work that a freely oscillating valve could be used as an oscillator, but the control over frequency of oscillation would be poor. Changing load conditions have a marked effect on both frequency and amplitude of oscillation.
Modal Curves of Pre-Twisted Beams of Rectangular Cross-Section
Authors: Dawson B. , Carnegie W. 
Published: February 2007

An important aspect of the theoretical study of the vibrational characteristics of turbine and compressor blading is the prediction of the modal curves from which the stresses along the length of the blading can be determined. The accurate prediction of the modal curves allowing for such factors as pre-twist, camber, size of cross-section, centrifugal tensile effects, aerodynamic effects, etc., is still not possible. However, a better understanding of the effects of some of these parameters can be obtained by a study of the modal curves of relatively simple idealized models. In this work the theoretical mode shapes of vibration of pre-twisted rectangular cross-section beams for various width to depth ratios and pre-twist angle in the range 0-90° are examined. The theoretical results are obtained by the transformation method given by Carnegie, Dawson and Thomas (1)† and the accuracy of these results is verified by comparison with results obtained by Dawson (2) using the Ritz method. The theoretical results are compared to modal curves determined experimentally and good agreement is shown between them. A physical explanation of the effects of the pre-twist angle upon the modal curves is given for the first three modes of vibration.
One-Way Buckling of Elastically Restrained Columns
Authors: Allan T. 
Published: February 2007

This paper is an extension of the author's work on one-way buckling phenomena. The effect of an elastic lateral restraint ( Ky) is considered in this paper and an analysis of a long thin beam subject to point loading and of a long thin column subject to axial loading is presented. This shows that the behaviour in such cases is similar and rather unique in that a single discrete wave or buckle forms in the member. This has a wavelength independent of the length of the member. In the case of the column it is quite possible for several of these waveforms to appear along the column length, but they neither need to be joined to each other nor do they need to fill the whole length of the column. In practice, however, it is more usual for a single buckle wave to form. The axial load at which buckling occurs is shown to be independent of the amplitude of the buckle wave. An experimental investigation is also reported which is in general agreement with the analysis. By combining the ‘elastic’ and ‘constant load’† lateral restraint conditions, the author presents a strip column buckling analysis which will be found to be useful in appreciating the phenomena of certain shell buckling configurations.
Limit Pressures for Cylindrical Shells with Unreinforced Openings of Various Shapes
Authors: Kitching R. , Davis J. K. , Gill S. S. 
Published: February 2007

Experimental limit pressures have been determined and compared for cylindrical shells with unreinforced openings of 26 different shapes and sizes. Deformation patterns were also studied. The shapes included circles (radius r = c), squares (side 2 c), rectangles (longitudinal side 2 c, circumferential side 2 a) and ellipses (longitudinal and circumferential semi-axes c and a respectively). Specimens of the different shapes but where dimension c was common were found to behave similarly and to have closely related limit pressures. This was predicted for specimens having rectangular and square openings by a lower bound analysis which led to a simple mathematical relationship between limit pressure and the non-dimensional parameter c/√RT, R and T being respectively the radius and thickness of the cylinder. The results are important in predicting limit pressures for cylinders having openings of shapes corresponding to curves formed by the intersection of the shell by oblique branches.
Experiments in Plate Cutting by Shaped High Explosive Charges
Authors: Zaid A. I. O. , Hawkyard J. B. , Johnson W. 
Published: February 2007

Although axisymmetrical lined cavity shaped charges have received considerable development and analytical treatment in the past, mainly in connection with armour piercing projectiles, relatively little attention appears to have been directed towards the linear system. This finds limited application in the cutting of plates, sections and pipes, in demolition and emergency rescue work for example. Experiments into the linear cutting system are described in this paper, to investigate the influence of liner and charge geometry. Steel plates up to 2 in thickness are cut, using charge weights up to 50 g per inch of cut. To investigate the theories available for the development of the very high velocity cutting jet and its penetration of the target, experiments are performed on a range of liner and target materials to achieve variations in density and yield strength.
Estimation of the Fatigue Life of a Thick-Walled Cylinder Subjected to Repeated Internal Pressure
Authors: Haslam G. H. 
Published: February 2007

Experimental data available on fatigue crack growth may be described by an equation of the form d a/d N = B(Δ K) m, where d a/d N is the rate of crack growth per stress cycle, Δ K is the range of stress intensity factor, and B and m are material properties. This relationship has been used to estimate the fatigue crack propagation lives of thick-walled cylinders subjected to repeated internal pressure. By using an approximate value for the stress intensity factor, and considering the high local stresses at the crack due to pressurized oil, close correlation is obtained between the estimated and experimental fatigue lives. Design curves are obtained, by which the fatigue life of such a cylinder may be estimated from a knowledge of the transverse uniaxial fatigue limit and fracture toughness properties of the cylinder material, as well as the diameter ratio of the cylinder and the repeated pressure.
Pitch Information from Single Flank Tests
Authors: Sharpe J. E. , Smith J. D. 
Published: February 2007

Techniques for sampling single flank test results on grating equipment are discussed. The methods of analysis of the resultant pitch errors to separate out the errors of the two gears are given with a suitable computer programme. Master gear pitch errors can be eliminated by this approach, both for single and dual flank checkers. The theoretical and practical problems of extending the method to complete car gearboxes with two meshes are discussed and suitable solutions given.
Synthesis of Single-Ratio and Multi-Ratio Epicyclic Gear Trains
Authors: Fitzgeorge D. 
Published: February 2007

A class of epicyclic gears based on coaxially mounted plane trains is defined. The class is restricted to those gears in which planetary gears of adjacent trains are coupled. The type of epicyclic multi-ratio gearbox in which the input and output members are always the same is selected for consideration. The basic kinematics of the planetary member are then reduced to a single equation which is subsequently expressed as a chart, covering all ratio possibilities and directly applicable as the basis of synthesis. The chart is shown to offer an arbitrary means of describing the various forms of gear by a number-and-letter code. The application of the chart to the synthesis of trains incorporating planetary idlers and multi-ratio trains is explained.