bluuebunny/crossref_metadata_2025 huggingface dataset:
The Collapse under End Load of Pressurized, Axially Stiffened, Thin Cylinders
Authors: Wood W. G.
Published: February 2007

An examination is made first of the contexts in which small and large deflection theories are appropriate for dealing with the collapse of thin stiffened shells. A theory based on an energy approach is then developed to predict the collapse of pressurized axially stiffened thin cylinders under end load. The theory accounts for all observed modes of collapse and shows that, except in extreme cases of stiffener spacing and internal pressure, the collapse load is almost independent of the collapse mode. Experiments on both unstiffened and stiffened cylinders are described. Several forms of stringer section are discussed and values of collapse loads and the wavelengths of buckled stringers obtained experimentally are compared with the theoretical predictions.
Non-Steady Flow through a Square-Edged Orifice in a Pipe
Authors: Benson R. S. , Shafie H. M. F. El
Published: February 2007

One-dimensional quasi-steady flow theories for flow through an orifice in a pipe are developed. These theories are presented in a form to be used with wave action calculations using the methods of characteristics. Steady flow experiments are described for determining the effective area of the orifice and the location of the plane of the pressure recovery. Non-steady flow tests using a single unit of a pulse generator are described. The results of non-steady flow experiments in the pipe are compared with the calculated pressure diagrams using a quasi-steady flow one-dimensional theory. These showed that the theory may be used for predicting the overall wave action in the pipe. In the plane of the enlargement, downstream of the orifice, the theory did not give an exact prediction of the pressure, particularly with small orifice area to pipe area ratios and high overall pressures. For small pressure changes, however, it is considered that the theory was satisfactory and may be used as the basis for calculating instantaneous mass flows if a square-edged orifice was used in pulsating flow streams.
Flow along Tool-Chip Interface in Orthogonal Metal Cutting
Authors: Enahoro H. E. , Oxley P. L. B.
Published: February 2007

In recent papers it has been suggested that over part of the tool-chip contact zone the chip does not slide but sticks to the tool, chip flow taking place by shear within the body of the chip. Sticking contact is inconsistent with steady state cutting and in this paper a slip-line field model of chip flow is presented which does not include sticking contact and which is consistent with the relevant experimental observations.
Vibration of Rectangular Plates of Variable Thickness
Authors: Dawe D. J.
Published: February 2007

In a previous paper the application of the finite element method to plate vibration problems was discussed. It was shown that the method gave good results when applied to the vibration of plates of uniform thickness.

The present paper extends the method to include plates of variable thickness. In particular stiffness and inertia matrices are derived for an isotropic rectangular plate element of linearly variable thickness in one co-ordinate direction. These matrices are used to find the natural frequencies and mode shapes of a number of rectangular planform cantilever plates of non-uniform thickness. Experimental results provide a basis for comparison with the finite element results.
Theoretical Analysis of the Unsteady Gas Flow in the Exhaust System of an Engine
Authors: Wright E. H. , Gill K. F.
Published: February 2007

The problem studied is that of unsteady gas motion in ducts of both constant and slowly varying cross-sectional area with the effects of wall friction and heat transfer taken into account. The values of the specific heats used in the analysis are those applicable to the instantaneous gas temperature at the instant under consideration, i.e. thermal lags are ignored.

To solve the unsteady flow equations, a method is developed based on the theory of characteristics and in the application of this method a pure graphical approach is used for convenience. The plotting technique adopted is the ‘field method of solution’ in which it is assumed that a region of continually varying fluid properties can be broken into a large number of small regions for calculation purposes. The fluid properties are assumed uniform throughout each of these small regions and changes in the fluid properties can only occur across the boundaries or characteristics separating the small regions.

With a firing engine, temperature discontinuities will be established at the interface of the hot gases being discharged from the cylinder and the cooler residuals from the previous cycle. Owing to the interaction of successive points of the fundamental pressure pulse with those resulting from the reflection of previous points of the fundamental pulse, sonic velocities can be encountered at the diffuser entry section. The formation of a steep front at the diffuser entry section as a result of these rarefaction waves can produce a shock wave. A method of solution for the existence in the flow of such discontinuities as temperature and shock is included.

The general conclusions to be drawn are: (1) true application of the irreversible flow theory gives a good solution of the wave patterns occurring in both the cylinder and exhaust pipe of the engine; (2) the air mass flow can be predicted with good accuracy by application of the irreversible flow theory developed; (3) the poor correlation resulting from application of the isentropic flow theory shows caution should be exercised in the use of this simplified theory.
Simple Numerical Procedure for the Digital Computer Solution of Non-Linear Transient Heat Conduction with Changes of Phase
Authors: Lockwood F. C.
Published: February 2007

A practical numerical method is described for the solution of transient heat conduction where the thermal properties are temperature dependent and changes of phase occur. The procedure involves the use of the explicit finite difference technique, for which a stability criterion is given, in conjunction with two integral transformations.
Dynamics of a Gyroscope Having Oblique Gimbal Axes
Authors: Crawley J. , Maunder L.
Published: February 2007

The effects are considered of obliquity in the suspension axes of a free two-axis gyroscope supported in gimbals. Three principal types of obliquity are considered, namely (1) non-orthogonality of the bearing axes of the outer and inner gimbals, (2) non-orthogonality of the bearing axes of the inner gimbal and the spin axis of the rotor, in a plane Oyz defined by their usual orthogonal directions, and (3) misalignment of the spin axis of the rotor and a principal axis of the inner gimbal, in a direction out of the plane Oyz. Such obliquities or misalignments could occur as a result of manufacturing errors or they might be introduced deliberately in order to obtain particular dynamical characteristics.

The free motion of the system is shown to be described by two coupled second-order non-linear equations, which are solved to first and second approximations for the three cases in which misalignment occurs separately. The first approximation determines the nutational vibration and the second the drift rate. Both are shown to be affected by each type of misalignment: the nutation varies in frequency and mode, and the drift rate in magnitude but not in direction.

The relations between misalignment of the spin axis and dynamic unbalance of the inner gimbal are also discussed.
Comparison of Unsteady Flow Discharge Coefficients for Sharp-Edged Orifices with Steady Flow Values
Authors: Trengrouse G. H. , Imrie B. W. , Mal D. H.
Published: February 2007

A simple theory, based on quasi-steady, one-dimensional flow arguments, is presented for the reflection of a compressive wave in air in a pipe when incident upon a coaxial, convergent nozzle situated at the end of the pipe.

Preliminary shock-tube experiments using quadrant arc nozzles confirm the validity of the theory, and thus enable it to be used to predict the discharge coefficients of sharp-edged orifices from pressure measurements taken in the pipe in the immediate vicinity of the orifices during further shock-tube experiments.

Steady flow discharge coefficients measured experimentally differ from the unsteady flow values by a maximum of 7 per cent.
Aerodynamic Stability of Cylinders of Various Sectional Shapes Spanning an Airstream
Authors: de Bray B. P. G. , Holt D. L.
Published: February 2007

Flexible or elastically supported cylinders (using the term in its more general sense to include bodies of any constant sectional shape, with a straight line axis) evince tendencies to oscillate when placed across an airstream.

If oscillations are constrained to one degree of freedom about an axis parallel to the cylinder axis, stability can be predicted from the steady aerodynamic properties of the sectional shape of the cylinder, but only if the axis is remote and for conditions in which vortex shedding is absent. The best-known example of this is the criterion of den Hartog for pure plunging oscillations. This criterion is readily extended to the case of an axis remote in any direction; but for cases in which the axis is near, so that angular motion becomes appreciable, it is generally considered that non-oscillatory properties do not give a guide to stability.

A theory for this case is developed for a thin flat plate, fully stalled, and its results are shown experimentally to be applicable to a range of section shapes, enabling stability to be assessed from simple measurements of the wake under steady conditions.
Thermal Stresses in a thin shell in Contact with a Smooth, Rigid Container
Authors: Parkes E. W.
Published: February 2007

General equations are given for the stresses in a thin shell subjected to temperature variation, when the shell is supported by a smooth, rigid container. A class of isothermal exact solutions is briefly considered, but the main part of the paper is concerned with the ellipsoidal shell, for which a solution is obtained in the form of an infinite double series. For calculational purposes the series can be truncated after a few terms, provided the eccentricity of the ellipse is not too great.
Flow of Incompressible Two-Phase Mixtures through Sharp-Edged Orifices
Authors: Chisholm D.
Published: February 2007

Equations are developed for the flow of gas-liquid or vapour-liquid mixtures through sharp-edged orifices under conditions where the density change of the gas or liquid through the orifice is negligible. The theoretical development differs from previous treatments in allowing for the interfacial shear force between the phases, and leads to an equation which is shown to be in good agreement with available experimental evidence. The determination by experiment of a single coefficient characterizing the pipe and orifice arrangement permits the prediction of both the two-phase flow rate and the ratio of the phase velocities for a given pressure drop and gas-liquid weight ratio. The range of conditions examined extends over weight ratios of gas to total mixture from 0·1 to 98 per cent, and ratios of downstream to upstream pressures greater than 0·99. The accuracy of correlation of two-phase flow data is now approaching that of single-phase flow.
Experiments on Pipelines and Pipe bends Subjected to Three-Dimensional Loading
Authors: Smith R. T. , Ford Hugh
Published: February 2007

The flexibility of a full-scale, three-dimensional, two-anchor pipeline has been investigated experimentally by measuring the end reactions resulting from controlled anchor movements. The results are compared with design calculations and show a satisfactory agreement.

These tests were supplemented by experiments on individual pipe bends which were subjected to in-plane and out-of-plane bending while measurements were made of the resulting stresses, deflections and cross-sectional distortion. The results compared satisfactorily with calculations especially when these were modified to allow for variations of the flexibility factor.
Inertia Torques in Four-Bar Mechanisms
Authors: Marshall W. E. , Waldron P.
Published: February 2007

Four-bar mechanisms appear, in various guises, in many examples of high speed machinery, in which inertia torques may be large compared with external load torques. This paper describes the use of a digital computer to compile standard tables of inertia torques, and sets of inertia torque graphs, for use both in the analysis and the design of such mechanisms.
Heat Transfer and Pressure Drop Measurements in Channels with Whitworth Thread Form Roughness
Authors: Furber B. N. , Cox D. N.
Published: February 2007

The heat transfer and pressure drop performance of three 4-in nominal bore tubes internally roughened with Whitworth thread forms of 11, 24 and 60 threads per inch (t.p.i.) has been measured with the tubes empty and with a concentrically mounted smooth cylinder of 2·012-in diameter. The tube with the 24-t.p.i. roughness form was also tested with a concentric cylinder of 2·00-in diameter having the same geometric roughness.

The measured Stanton number and friction factors of the annuli with the smooth inner walls have been transformed using a method suggested by Hall (1)†, and compared to the empty channel and completely roughened annulus data.
Some Deductions from Bowen's Non-Newtonian Turbulent Correlation
Authors: Harris J.
Published: February 2007

Starting from Bowen's empirical correlation for non-Newtonian turbulent flow through pipes, deductions are made about the form of the velocity profile, the effective viscosity, the Reynolds number for dynamic similarity and finally the associated form of the friction factor-Reynolds number correlation.
Elastohydrodynamic Lubrication of High Pressure Face Seals
Authors: Hooke C. J. , O'Donoghue J. P.
Published: February 2007

A previous paper demonstrated that high pressure face seals have an inherent stiffness due to elastic distortions. At that time a simplified treatment of the elastic and thermal problems was presented and agreement between this theory and experimental results was found to be reasonable. Because of the predominant effect of the elastic distortions and their importance in determining the stability of a seal, the authors of this paper have determined a more accurate method of solution of the elastic problem.

The results of this theory give closer agreement with the published results obtained experimentally, and demonstrate that the simplified treatment is valid only if the seal has a large face to thickness ratio. Solutions for square-section seals are presented in non-dimensional form, leakage and parting force due to fluid pressure being expressed as ratios of the rigid values. Although only one sealing arrangement is treated the elastic solution can be applied to any body symmetrical about an axis.
The Rise of Water Level behind the Nappe of a Rectangular Weir
Authors: Vickery L.
Published: February 2007

An experimental study of the head of water behind the nappe of a rectangular weir suggests that it is linearly related to the discharge head over the weir.
Velocity of Torsional Waves in Metals Stressed Statically into the Plastic Range
Authors: Convery E. , Pugh H. LI. D.
Published: February 2007

This paper is concerned with the determination of the velocity of propagation of torsional plastic waves in metals stressed statically into the plastic range. A new method was developed in which a tubular test specimen together with a concentric bar of a brittle material was twisted slowly such that when the specimen was stressed beyond its yield the brittle bar broke suddenly and transmitted a plastic torsional stress increment along the specimen. It was found that the velocity of propagation both in copper and mild steel was the same as the elastic shear wave velocity. Although consistent with the strain-rate dependent theory, the result can be explained in terms of the strain-rate independent theory provided the stress-strain curve for the appropiate strain rate is used.
Base Pressure and Noise Produced by the Abrupt Expansion of Air in a Cylindrical Duct
Authors: Anderson J. S. , Williams T. J.
Published: February 2007

In the investigation described, the base pressure resulting from the abrupt expansion of an air jet from a circular nozzle into a concentric cylindrical duct or shroud has been measured. Stagnation pressure ratios of the forcing jet to atmospheric of up to six were used with shrouds of various lengths and diameters. As the primary or forcing jet pressure is increased and then decreased, the jet flow attaches and separates from the shroud wall and a hysteresis effect is exhibited by the pressure at the base of the shroud. With an attached flow, the base pressure attains a minimum value which depends mainly on the duct to nozzle area ratio and on the geometry of the nozzle, lower base pressures being obtained with convergent-divergent nozzles. When the jet pressure was increased beyond that required to attain the minimum value of the base pressure, it was observed that the ratio of the forcing jet pressure to base pressure remained constant.

Noise measurements of the flow from the nozzle and shroud are presented. The plot of overall noise showed a minimum value of noise at a jet pressure approximately equal to that required to produce the minimum base pressure. As the pressure was increased beyond this value, the noise from the shroud was essentially that of a subsonic jet until the flow at the shroud exit became choked. The excessive overall noise observed at low forcing pressures was due to the emission of powerful discrete tones from an organ-pipe resonance within the ducts.
Solution of Kinematic Equations by Newton's Method
Authors: Molian S.
Published: February 2007

This note describes a method of kinematic analysis generally applicable to planar mechanisms. It is illustrated by the displacement analysis of a 6-bar linkage with auxiliary gearing.
Performance of Lightly Loaded Gas Journal Bearings in the Slip-Flow and Turbulent-Flow Regimes
Authors: Wood M. D.
Published: February 2007

The note compares recently published versions of the governing gas film equations for slip-flow and turbulent flow with Reynolds equation for laminar flow. The comparison shows how approximate values of steady-state and dynamic performance parameters may be deduced for the new conditions from existing data.
Equilibrium-Turbulent Boundary Layer Prediction for a Proposed Prandtl Mixing Length Distribution
Authors: Lockwood F. C.
Published: February 2007

The momentum equation is solved numerically for a suggested ramp variation of the Prandtl mixing length across an equilibrium-turbulent boundary layer. The predictions of several important boundary-layer functions are compared with the equilibrium experimental data. Comparisons are also made with some recent universal recommendations for turbulent boundary layers since the equilibrium experimental data are limited. Good agreement is found between the predictions, the experimental data, and the recommendations.
Improved Application of the Von Karman Similarity Hypothesis to Turbulent Flow in Ducts
Authors: Quarmby Alan
Published: February 2007

It is shown that Von Karman's similarity hypothesis can be used to deduce the Reynolds number dependence of the nor-dimensional turbulent velocity profile in both the circular tube and parallel plate channel. The analysis uses a two part model of a sub-layer and a main stream and ensures that there are no discontinuities in the profile gradient and that it fulfils the correct centre-line boundary condition. There is good agreement with experimental results in both configurations.
Stress-Strain Behaviour of a Low Density Polyethylene under Complex Strain
Authors: Wriggles J. D. , Williams J. G.
Published: February 2007

A description of a simple non-linear form of viscoelasticity in terms of logarithmic strain is given together with a correction factor. Apparatus is described for determining relaxation data in simple tension and results are given for a low density polyethylene. These results are then used in conjunction with the theory to predict behaviour in simple tension at various strain rates, at various constant strain ratios in loading only, stress relaxation under complex stress and in tests with varying strain ratios. An apparatus is described to obtain such data and the results are compared with the theoretical predictions.
Parametrically Excited Lateral Vibrations of an Asymmetric Slender Shaft in Asymmetrically Flexible Bearings
Authors: Black H. F.
Published: February 2007

The lateral motion of a multi-degree-of-freedom shaft with cross-sectional asymmetry having common principal planes, mounted on asymmetrically flexible bearings having fixed common principal planes, is analysed in terms of a generating system consisting of a symmetric shaft with the mean cross-sectional rigidity mounted on the asymmetric bearings. Equations of motion are developed in terms of the principal co-ordinates and modes of the generating system, the shaft asymmetry producing coupling terms with periodic coefficients. The equations are solved by the perturbation-variation method of Hsu, leading to simple explicit formulae for instability bands in many practically important cases. The solutions are limited to small shaft asymmetry; any degree of bearing asymmetry is admissible.
Nonlinear Behaviour, Including Jump Resonance, of Hydraulic Servomechanisms
Authors: Davies A. M. , Davies R. M.
Published: February 2007

The harmonic response of an electrohydraulic servomechanism operated under certain conditions is investigated. Its nonlinear characteristics are apparent in the experimental results and include among its peculiarities the jump phenomenon. It is shown that the nonlinear effects of interest are contained in the equations which are formulated. The mathematical model is modified to a form which allows of a simplified analogue programme and of analytical treatment by the application of Duffing's method to the open loop. Closed loop behaviour is then predictable by the use of the authors' general method. Finally, general criteria are obtained for the occurrence of the jump phenomenon and for the boundaries of linear operation in hydraulic servos.
Plastic Behaviour of Thin Cylindrical Pressure Vessels with Circular Cutouts and Radial Branches
Authors: Calladine C. R. , Goodall I. W.
Published: February 2007

Pressure tests were performed on four thin cylindrical aluminium vessels with circular cutouts and cover plates, and on two vessels with radial branches. In all cases a fairly well defined ‘limit pressure’ was observed—corresponding to plastic deformation in the vicinity of the cutout or branch—together with a moderate increase in pressure as deformation proceeded, which may be interpreted as a moderately strong ‘geometry-change effect’.

The limit pressures observed for vessels with cutouts agree well with a lower-bound analysis which is described in outline. In general the observed limit pressures fit in well with those observed by other workers for vessels of different proportions. Correlation of geometry-change effects is not so simple, but a fairly clear picture of trends emerges from the study.

The question of appropriate geometrical parameters for correlation of results is discussed, and a suggestion is made for taking into account any ‘extra’ cross-sectional area at the junction weld.
Transient Thermal Stresses in Elasto-Plastic Discs
Authors: Odenö H.
Published: February 2007

A thin circular disc of elastic-perfectly plastic material, subjected to an axially symmetric transient temperature distribution, is treated analytically. All material parameters are assumed to be independent of the temperature. Poisson's ratio is taken to be one-half. The Tresca yield condition with associated flow rule is employed.

The temperature distribution is that which appears when the outer rim surface of the disc receives a rapid temperature increase and it is solved approximately by the collocation method.

The analysis shows that under certain circumstances, plastic deformation will occur in a moving annular region. This region starts to develop at the exterior surface and moves inward, while changing its width. After a certain finite time its width shrinks to zero. Except for a residual constant state of strain, the strain field is then again elastic.

An application to the method of separating the ring and the shaft in a shrink-fit is carried out numerically. The residual stresses in the ring are calculated.
Numerical Integration Procedure for the Steady State Navier-Stokes Equations
Authors: Runchal A. K. , Wolfshtein M.
Published: February 2007

A procedure is proposed for the integration of the full Navier-Stokes equations for constant-property two-dimensional flows. In contrast with earlier procedures, the present one is capable of dealing with cases of very high Reynolds number. The power of the new procedure is demonstrated in two cases: (1) the square recirculating eddy, for which no solution was previously available for Reynolds numbers larger than about 400, and (2) an impinging jet, for which no solution was available previously. The procedure has also been applied to the square cavity at Reynolds numbers below 400; it gives results of an accuracy comparable with that of previous solutions, but with a smaller computing time.
Development of a Steam Generator and Calorimeter for Property Measurement at Advanced Conditions
Authors: Burnside B. M. , Mackie W. W. , Nisbet S. K.
Published: February 2007

The development of a once-through steam generator and calorimeter to obtain measurements of the specific heat capacity at advanced conditions is described. The construction and operation of the steam generator to produce 14 g/s at 70 000 kN/m2 and 750°C is detailed. The feasibility of using a differential calorimeter was investigated by measurements at 6000 kN/m2 and 400°C. The heat leak correction was found to be larger than anticipated owing to the heat leak being mass flow dependent. This was possibly due to operation at transitional Reynolds numbers. Some methods of determining the heat leak correction are described.
Narrow Band Random Fatigue Testing with Amsler Vibrophore Machines
Authors: White D. J. , Lewszuk J.
Published: February 2007

A description is given of modifications made to Amsler Vibrophore machines to permit narrow band random fatigue tests to be made. In this mode of working, the machine electromagnet is excited by means of a random generator and a complete control loop is effected by connecting the output of the inductive transducer of the machine dynamometer to the automatic output regulator (compressor circuit) of the random generator. The dynamometer was strain-gauged and calibrated to read r.m.s. load. Under compressor circuit control, the stress peaks in a specimen followed the Rayleigh distribution at least up to four times the r.m.s. value.

As in constant amplitude sinusoidal loading, these machines are capable of applying mean stress when working in random loading. Some practically occurring stress spectra may be synthesized by applying sequences consisting of a number of stepped r.m.s. loads, each step being applied for a predetermined time.
Effect of Position on the Stability of Pneumatic Servomechanisms
Authors: Burrows C. R.
Published: February 2007

The analysis of a proportional controlled pneumatic servomechanism has been extended to consider motion about any initial position along the stroke. It is shown that there is an inherent damping effect which is dependent upon position and this supports previously published experimental work.
Analysis of Externally Pressurized Gas Journal Bearing
Authors: Majumdar B. C.
Published: February 2007

An externally pressurized gas journal bearing with multiple supply holes is analysed theoretically by numerical method of solution. The load and flow are predicted by considering both axial and circumferential flow. These load and flow expressed in dimensionless factors are presented for different bearing design parameters. The results are compared with the similar available approximate method.
Synthesis of Linear Lumped-Parameter Vibrating Systems by an Inverse Holzer Technique
Authors: Porter B.
Published: February 2007

This paper describes a simple method of synthesizing linear lumped-parameter vibrating systems so that one mode (usually that with the highest or lowest natural frequency) has a prescribed natural frequency and mode shape. This synthetic method may be regarded as an inversion of the classical Holzer analytic technique. Its use is illustrated by means of two examples.
Empirical Treatment of Hydrodynamic Journal Bearing Performance in the Superlaminar Regime
Authors: Black H. F.
Published: February 2007

The application of a perturbation in terms of simple correlations for friction in turbulent Couette and ‘screw’ flows, together with a further empirical assumption consonant with the experimental work of Smith and Fuller (1), leads to a pressure field equation identical in form with the Reynolds equation. The load capacity of journal bearings throughout most of the superlaminar range may be represented by a single curve, and existing laminar solutions may be applied with the parameters modified by Reynolds number. The theory is compared with published experimental results, and with the most successful theoretical treatment (4). The correlations obtained confirm the adequacy of the theory to predict performance in the superlaminar régime.
Geometry of Spherical Flame Propagation in a Disc-Shaped Combustion Chamber
Authors: Annand W. J. D.
Published: February 2007

In performing synthesis or analysis of the combustion process in spark-ignition engines by digital computer, it is necessary to know the enflamed volume, the flame front area, and the area of the chamber surface in contact with the enflamed material, as functions of flame travel distance. This Note examines the case of spherical flame propagation in a disc-shaped chamber, with origin at any point on one of the flat surfaces. An ‘exact’ method of computation is outlined, and a simple approximate procedure, giving high accurary for this particular case, is described.
Fully Developed Heat Transfer to a Gaseous Suspension of Particles Flowing Turbulently in Ducts of Different Size
Authors: Boothroyd R. G. , Haque H.
Published: February 2007

This paper is a sequel to two earlier studies of friction (I)† and eddy diffusion (2) carried out for the same flow conditions as in the present study of heat transfer. Heat was transferred to an upward flowing suspension of 0-40 μ zinc particles in pipes of 1, 2 and 3 in bore. The solids/gas flow rate was in the range 0 < Ws/ W g< 17 and the pipe Reynolds number in the range 3·5 × 104< Re < 105.

It was found that the fractional increase in heat transfer coefficient due to the presence of solids was always less than the increase in the friction factor. Minimum values of both these parameters are often observed in the range 1 < W s/ W q< 2·5. This paper gives further evidence that turbulence is suppressed by the particles, particularly when the duct is small and Re is large; in this case the wall Nusselt number, Nu s, is markedly reduced below the value when gas flows alone. However, when the pipe is large and Re is low, Nu s can be substantially higher than the value for gas alone. In this case the suspension is a superior coolant to the flow of gas alone.
Method of Brittle Fracture Analysis in Turbine Rotors during Cold Starts
Authors: Chow C. L.
Published: February 2007

Design requirements of turbine rotors capable of performing cyclic operations demand the need of both brittle and ductile fracture analyses. This paper presents a method of brittle analysis in turbine rotors. In another paper the author has dealt with the problem of ductile analysis. Generalized equations for different types of defect configurations commonly observed in defective rotors are formulated and discussed in terms of the computed average bursting strength and fatigue life. The computer results are presented in graphical form to facilitate design procedures and acceptance standards. A design criterion concerning the necessity of bore-holes in turbine rotors is proposed. It is intended to improve the present practice of indiscriminate use of costly rotor boring processes. The brittle fracture analysis devised is applied to a marine turbine rotor during its typical cold start and the results computed are found to be satisfactory.
Influence of Residual Stresses and of Mean Stress on the Fatigue Strength of Specimens with Longitudinal Non-Load-Carrying Fillet Welds
Authors: Gurney T. R.
Published: February 2007

Using results obtained in work on fatigue crack propagation in unwelded sheet specimens, an analysis has been made of fatigue test results for specimens with longitudinal non-load-carrying fillet welds tested in the as-welded and stress relieved conditions and also after treatment by local compression and by spot heating. It is shown that, by this means, it is possible to provide a quantitative explanation of the effect of residual stresses and applied stress ratio on fatigue strength, since all the results can be normalized on the basis of an effective stress range. In the course of the work it has been shown that the gross stress concentration factor for this type of joint is approximately 2·57. It has also again been demonstrated that the beneficial effect of spot heating on fatigue strength is a direct result of induced compressive residual stresses.
Lubrication of Angular Contact Bearings
Authors: Snidle R. W. , Archard J. F.
Published: February 2007

In angular contact bearings the motion of the ball on the race involves both rolling and spinning. Recent work provides theories of the generation of a lubricant film, by hydrodynamic mechanisms, for each of these motions considered in isolation. By comparison of these theories, and using knowledge of the kinematics of bearings, it has been possible to provide an estimate of the relative importance of the rolling and spinning motions for film generation in angular contact bearings.
Empirically Determined Model for Polarized Relays
Authors: Barnes R. N. , Burrows C. R.
Published: February 2007

Theoretical determination of a mathematical model to describe a polarized relay requires knowledge of the relay characteristics, i.e. the inductance, resistance and armature dynamics. Unless the data are supplied by the manufacturer determination of the characteristics is time-consuming and may present problems, especially if the inductance is required at low frequencies.

A technique is presented here which overcomes measurement difficulties at low frequency and allows an approximate model to be rapidly determined.
Stress Corrosion Cracking of En 31 Ball Race Steel Using Fracture Mechanics Methods of Analysis
Authors: Cox B. G. , Ellison E. G.
Published: February 2007

Subcritical crack growth was studied in an En 31 ball race steel subjected to various fluids, some of which are suitable for possible use in high pressure applications. Using fracture mechanics techniques of measurement and analysis, it was found that Esso Univis P38, Shell Tellus 15, and a 25 per cent glycerine–ethylene glycol mixture caused subcritical crack growth with a corrosion stress intensity threshold approximately half that obtained in air. Diesel oil had no effect. Evidence of blunting of the crack system and some effects of history were found.
The Post-Buckling Behaviour of Thin Flat Plates in Compression with the Unloaded Edges Elastically Restrained against Rotation
Authors: Rhodes J. , Harvey J. M.
Published: February 2007

Details of a theoretical analysis of the post-buckling behaviour of thin plates loaded in compression are presented. The loaded ends are simply supported and the unloaded edges are restrained elastically against rotation. The results obtained are compared in some cases with results obtained by other authors.
Natural Convection of a Heat Generating Fluid in a Closed Vertical Cylinder: An Examination of Theoretical Predictions
Authors: Watson A.
Published: February 2007

An analysis of the natural convection of a heat generating fluid in a semi-infinite vertical cylinder has been seen, in a previous publication, to give good agreement with experimental measurement. The analytical method used was that of solving the integrated equations of continuity, motion and energy, a technique which is frequently applied to internal natural convection problems and which has a reputation for being insensitive to thermal boundary conditions and the profile assumptions needed. The boundary conditions assumed for the analysis were not those of the experiment, and this paper is the result of an examination of the sensitivity of the prediction to the assumed conditions. A new analysis has been carried out with the boundary conditions of the experiment, and with profile assumptions closer to the experimental data. The new predictions show much less favourable agreement. It is concluded that the agreement obtained in the earlier analysis should not be used as a recommendation of the integral technique.
Stability of a Four-Bar Linkage with Flexible Coupler
Authors: Smith M. R. , Maunder L.
Published: February 2007

The undamped transverse vibration of a flexible coupler in a crank and rocker four-bar linkage is shown to be governed by an inhomogeneous Hill's equation. Analysis of the corresponding homogeneous equation shows that the vibration may be unstable and that at a prescribed input speed stability depends on the inertia effects of the follower as well as on the characteristics of the coupler. Stability boundaries may be determined by digital computation, and an illustrative chart is worked out for a particular case.
A Heat-Mass Transfer Analogy Applied to Fully Developed Turbulent Flow in an Annulus
Authors: Lewis J. S.
Published: February 2007

A heat-mass transfer analogy based on the ‘universal’ velocity profile applied to an annulus is compared with analogy values based on similar but more sophisticated expressions for the eddy diffusivity and hence velocity profile. The difference between these analogy values and those of Chilton and Colburn (I)† are noted to be appreciable and to increase with increasing Reynolds number.

Heat transfer predictions from mass transfer measurements using ‘universal’ velocity profile type analogies are compared with established results.

Friction factor measurements were made and found to be up to 10 per cent higher than the values for flow in a round tube at the corresponding Reynolds number.
Spontaneous Hot Zone Formation in Oil Flow
Authors: Polak P.
Published: February 2007

This paper discusses a thermally unstable situation in viscous flow of any fluid whose viscosity falls with rising temperature. The existence of the effect is demonstrated by passing oil through small pipes and observing the temperature rise of the pipe wall. The pressure loss is shown to be lower than that predicted by simple theory assuming fluid properties to be constant across the flow.
The Uniqueness of Turbomachinery Flow Calculations Using the Streamline Curvature and Matrix Through-Flow Methods
Authors: Marsh H.
Published: February 2007

When calculating the flow through turbomachines by an iterative procedure, it is assumed that on each cycle of iteration there is only one solution for the flow pattern. The uniqueness of the solution obtained by the method of streamline curvature is examined and a set of Mach number conditions are derived which are sufficient to ensure that the flow pattern is unique. The Mach number limitations are the same as those which are necessary to avoid ambiguity in the matrix through-flow analysis. An alternative procedure is then described in which the solution for the flow pattern is always unique.
Finite Element Solution of Heat Transmission in Steel Ingots
Authors: Soliman J. I. , Fakhroo E. A.
Published: February 2007

A mathematical study of the solidification of steel ingots using, for the first time, the finite element method.
Elastohydrodynamic Lubrication of Soft, Highly Deformed Contacts
Authors: Hooke C. J. , O'Donoghue J. P.
Published: February 2007

Part 1 presents a theoretical solution to the problem of lubrication of soft, highly deformed surfaces. It is argued that with this type of contact the inlet and outlet regions can be separated and analysed independently. This approach leads to a single value of non-dimensional film thickness at the point of maximum contact pressure and to a non-dimensional minimum film thickness dependent on the relationship between the inlet and outlet parameters.

In Part 2, these results are applied to the problems of a cylinder sliding on an elastomer lined surface, an elastomer lined journal bearing and a sliding O-ring seal.
Dynamic Analysis of Axially Non-Uniform Thin Cylindrical Shells
Authors: Lakis A. A. , Paidoussis M. P.
Published: February 2007

Part 1 of this paper presents a new theory for the dynamic and static analysis of axially non-uniform, thin cylindrical shells. It is a hybrid of finite element and classical shell theories: the shell is subdivided into cylindrical finite elements, and the displacements within each (expressed in terms of nodal displacements), i.e., the displacement functions, are obtained using Sanders' equations for thin cylindrical shells in full. Sanders' theory gives zero strains for small rigid-body motions, so that displacement functions based on it satisfy the convergence criteria of the finite-element method.

Expressions for the mass, stiffness and stress-resultant matrices are obtained, and the method for constructing the equivalent global matrices is given. This paper is supported by Part 2, where the eigenvalues of a number of shells are calculated and compared with other theories and experiments.

In Part 2, the free flexural vibration characteristics of thin cylindrical shells are studied by this new, hybrid finite-element theory, where the displacement functions are determined by solution of the cylindrical thin-shell equations. Uniform shells with simply-supported, clamped and free ends are studied, as well as ring-stiffened shells and shells with thickness discontinuities. The frequencies of vibration are compared with those obtained by other theories and with the experiments of others. Agreement with other theories is good and, in the majority of cases, is even better with the experiments.
The Non-Linear Performance of Squeeze-Film Bearings
Authors: Holmes R.
Published: February 2007

The purpose of this research note is to consider the non-linear vibration performance of squeeze-film bearings with a view to investigating their feasibility as load-carrying members for aircraft gas-turbine rotors.
Interpretation of Pitot Pressure in Compressible Two-Phase Flow
Authors: Crane R. I. , Moore M. J.
Published: February 2007

An analysis is presented of the dynamics of small droplets near the mouth of a purged or unpurged pitot tube in two-phase flow. Under certain conditions, that part of the total pressure which is attributable to loss of droplet momentum is shown to be only weakly dependent upon droplet size and density, vapour viscosity, tube size and purging rate. A new method is formulated for calculating the velocity from measured static and total pressures in compressible flow, which does not include the assumption that the fluid behaves as a homogeneous equilibrium mixture. When compared with results based upon the mixture assumption, for condensing flows of steam at low pressures, the new method yields velocities which are greater by one or two per cent and which approach the dry vapour values as the wetness fraction tends to zero. The absolute accuracy of the method has yet to be determined through experiment.
Geometric Stability Charts for the Centreless Grinding Process
Authors: Rowe W. B. , Richards D. L.
Published: February 2007

Experiments and theoretical analyses by previous workers have shown the critical importance of the geometrical configuration on the ability to produce round workpieces. Resonances in the machine tend to worsen geometrical instability and it is therefore necessary to be able to predict geometrical instabilities in order to avoid unfavourable operating conditions. The theory presented in this paper is nearer to being rigorous than previous treatments and an improved method is demonstrated for indicating conditions of instability. Experimental results are quoted which show good correlation with the information on the stability charts.
Thermal Performance of Cross-Inclined Tube Bundles Measured by a Transient Method
Authors: Smith E. M. , Coombs B. P.
Published: February 2007

By considering both theoretical and experimental aspects of an exponential inlet temperature response, significant improvement in the transient single blow method for measurement of heat transfer coefficients in matrices becomes possible. Specific requirements for success with the method were met in a test programme to evaluate the shell side thermal performance of a variety of tube bundle configurations. Results for conventional geometries of known worth confirm the precision of the technique, and new data on cross-inclined tube bundles are presented.
Surface Vorticity Theory for Axisymmetric Potential Flow past Annular Aerofoils and Bodies of Revolution with Application to Ducted Propellers and Cowls
Authors: Lewis R. I. , Ryan P. G.
Published: February 2007

The well known surface vorticity method originally due to Martensen for calculating two-dimensional aerofoil and cascade flows is extended to axisymmetric flows past annular aerofoils, bodies of revolution and interacting combinations of these. A variety of solutions is presented in comparison with experimental test or classical solutions. A generalized surface vorticity integral equation for fully three-dimensional flow is developed in curvilinear co-ordinates from which the two-dimensional axisymmetric equations are shown to be reducible. This paper is aimed at ship ducted propeller problems but is of wider application to fan cowls, nozzles, bodies of revolution or engine intakes.
Pressure Distributions in Manifolds with Return Ducts
Authors: Kimber G. R. , Hollingsworth M. A.
Published: February 2007

Longitudinal static pressure distributions in air flow have been measured in manifolds with untapered inlet and outlet ducts, closed at one end and interconnected by a large number of identical ports. The transfer of air through these ports causes the static pressure to rise towards the closed end of the inlet duct, although friction reduces this rise to about 50 per cent of its ideal value. For very long ducts the pressure initially decreases near the inlet end. In the outlet duct the ideal drop in pressure from the closed end is increased by about 15 per cent. Theoretical distributions in good agreement with measurements are obtained assuming constant values for the frictional losses for each configuration and meaningful predictions may be made at the design stage since pressure distributions are found to be relatively insensitive to these values.
Synthesis of Multiple-Speed Transmissions of the Planetary-Gear Type
Authors: Sanger D. J.
Published: February 2007

Techniques for the structural and numerical synthesis of multiple-speed planetary transmissions are described. The characteristics which describe the structure of each train are tabulated, and a numerical example is included to illustrate the use of the methods.
Wall Boundary Layers in Turbomachines
Authors: Marsh H. , Horlock J. H.
Published: February 2007

Equations for the passage-averaged flow in a cascade are used to derive the momentum integral equations governing the development of the wall boundary layer in turbomachines. Several existing methods of analysis are discussed and an alternative approach is given which is based on the passage-averaged momentum integral equations. The analysis leads to an anomaly in the prediction of the cross flow and to avoid this it is suggested that for the many-bladed cascade there should be a variation of the blade force through the boundary layer. This variation of the blade force can be included in the analysis as a force deficit integral. The growth of the wall boundary layer has been calculated by four methods and the predictions are compared with two sets of published experimental results for flow through inlet guide vanes.