bluuebunny/crossref_metadata_2025 huggingface dataset:
The Static Aeroelastic Deformation of Slender Configurations
Authors: Hancock G. J.
Published: July 2016

By consideration of a series of simple models the static aeroelasticity of conventional aircraft is first discussed and then extended to the integrated configuration combining fuselage, wing and tail. It is shown that, on the basis of linear aerodynamics, a maximum speed exists at which control is possible. Overall deformations and control forces become large at speeds approaching this critical condition. Part II, to be published, contains calculations on slender plate aircraft including non-linear aerodynamics.
The Buckling of a Reinforced Circular Plate under Uniform Radial Thrust
Authors: Cook I. T. , Parsons H. W.
Published: July 2016

An exact solution for the symmetrical buckling under uniform radial thrust is obtained for a thin circular plate having a particular type of thickness function for the cases in which the edge of the plate is either clamped or simply-supported. In both cases it is found that the critical thrust necessary to produce buckling can be increased from its value for the uniform circular plate of the same material and volume by concentrating material in the central region of the plate. For the clamped plate the increase is about 18 per cent and for the simply-supported plate about 29 per cent.
The Non-steady Irrotational Flow of an Inviscid, Incompressible Fluid, with Special Reference to Changes in Total Pressure through Flow Machines
Authors: Preston J. H.
Published: July 2016

In this paper the way in which an inviscid incompressible fluid changes its total pressure is discussed. The basic equations are set out and it is shown that changes in total pressure are essentially associated with time variable flows. Simple examples are worked to illustrate this and finally application is made to single-stage flow machines, using a simple vortex representation.
Boundary-Layer Flow Between the Attachment Lines on a Flat Plate Delta Wing at Incidence
Authors: Cooke J. C.
Published: July 2016

A three-dimensional laminar-boundary-layer calculation is carried out over the area concerned. The external flow is simplified, being calculated by slender-body theory assuming conical flow, with two point vortices above the wing, their positions and strength being determined by experiment. Attempts are made to draw transition fronts both for two-dimensional and sweep instability from this calculation. The combination of these gives fronts similar to those observed in some experiments. Because there is little or no pressure gradient over the area in question it is suggested that it is a region where distributed suction might usefully be applied in order to maintain laminar flow and reduce drag.
On the Use of Linearised Unsteady Aerofoil Theory in Arbitrarily Moving Axis Systems
Authors: Milne R. D.
Published: July 2016

A linearised, unsteady aerofoil theory is constructed which refers to an axis system which remains in the near vicinity of an aerofoil moving along an arbitrary flight path through a fluid at rest. The potential equation, the pressure equation and the boundary conditions at the aerofoil and in the wake are shown to be formally identical to those usually derived on the basis of an axis system translating uniformly through the fluid.
Shear Buckling of Clamped and Simply–Supported Infinitely Long Plates Reinforced by Transverse Stiffeners
Authors: Cook I. T. , Rockey K. C.
Published: July 2016

The paper presents a solution to the buckling of infinitely long plates clamped along the edges, together with an extension of the solution obtained by Stein and Fralich for the case when the edges are simply-supported. It is shown that, as a consequence of increasing the edge support from that of a simple support to one in which both deflection and rotation are prevented, the rigidity which an intermediate transverse stiffener must possess in order to support the plate effectively is much reduced. Agreement between the theoretical relationships and existing experimental data is good.
The Flow Close to the Surface of a Circular Cone at Incidence to a Supersonic Stream
Authors: Woods B. A.
Published: July 2016

A theory is presented describing the flow close to the surface of a circular cone at incidence to a supersonic stream, which reconciles the first order theory of Stone (on which the widely used M.I.T. Cone Tables are based) with the physically necessary condition that the entropy on the cone surface be constant.

However, the results of this “vortical layer” solution appear to invalidate the method used in Ref. 1 to apply a boundary condition at the cone surface, and so to cast doubt on the results obtained by this theory.
Shear Buckling of Clamped and Simply-Supported Infinitely Long Plates Reinforced by Closed-Section Transverse Stiffeners
Authors: Cook I. T. , Rockey K. C.
Published: July 2016

The paper presents a solution to the buckling of infinitely long plates when they are reinforced by transverse stiffeners possessing both torsional and flexural rigidity. The cases of both edges being clamped and simply-supported are dealt with. Numerical results are presented for the ratio of torsional rigidity to flexural rigidity as obtained with a thin-walled circular tube. When the stiffeners are completely rigid, in which case the individual panels are clamped along the transverse edges, the results obtained are in agreement with existing solutions for isolated rectangular plates.
The Use of an Interference-Fit Bush to Improve the Fatigue Life of a Pin-Jointed Connection
Authors: Lambert T. H. , Brailey R. J.
Published: July 2016

The fatigue life of a pin-jointed connection can be optimised by using a moderately high degree of interference between the loading pin and plate. Where a joint has to be assembled in confined conditions, difficulty may be experienced in inserting the interference-fit pin and one possible solution is to use a pre-assembled interference-fit bush in the plate, leaving only a light interference-fit pin to be pressed in on assembly of the joint. It is shown that a relatively thick bush of diametral ratio 4/3 will give a reduction in shear stress concentration factor for the plate comparable with that obtained with a solid pin, but that maximum benefit is not obtained with a thinner bush of diametral ratio 8/7. Where thin bushes are essential in order to maintain the ultimate tensile and fatigue strengths of the plate and /or the ultimate and fatigue strengths of the pin, the shear stress concentration factor for the plate is reduced as the modular ratio of bush to plate is increased and as the interference fit of the loading pin in the bush is increased.
A Method for Solving Non-Linear Thermal Problems in Re-entry of Space Vehicles
Authors: Broglio Luigi
Published: July 2016

The paper considers a body, or space vehicle, of arbitrary shape, with conductivity K and specific heat c. It is first assumed that K and c are invariant with time and the body, with a given initial temperature, is assumed to be heated by a distribution of heat sources that varies with space co-ordinates and time. It is shown that a rigorous analytical solution to the problem is possible, provided that the distribution function satisfies prescribed regularity conditions.

The same problem is then considered, but with a heat-source distribution which is also a function of temperature. In this case the problem can be reduced to a Volterra-type integral equation amenable to step-by-step solution. Convective heating and radiation are specific examples of this second case.

The third case considered is that of a body whose geometry and thermal coefficients K and c are all time-dependent, and this problem is reduced to the fixed-geometry case by the addition of a hypothetical heat-source distribution which is a function of the velocity of ablation, of temperature and of its time derivative; an integral equation of Volterra type again results.

Finally, an example is given of the application of the analysis to the ablation of a conductive spherical shell.
The Polytropic Expansion of Air Through a Convergent Nozzle at Infinite Pressure Ratio—An Interesting Anomaly
Authors: Pearson H.
Published: July 2016

Previous papers have examined the implications of an assumed polytropic expansion law on the performance of nozzles. In this paper a peculiar anomaly is examined when the convergent nozzle is exhausting into a vacuum. It is shown that, on the strict assumptions of a polytropic expansion law, and the assumption that the flow will maximise for a given throat area, the thrust per pound of air increases progressively with falling polytropic efficiency, becoming infinite when the polytropic efficiency is zero. The author suggests that this anomaly is either concerned with the assumption that the flow will maximise or means that polytropic expansion efficiencies below a certain limit are theoretically impossible, but he believes that there may be some other explanation.
Mathematical Techniques Applying to the Thermal Fatigue Behaviour of High Temperature Alloys
Authors: Howe P. W. H.
Published: July 2016

During thermal fatigue testing of a specimen with a thin edge, or during rapid temperature changes in the gas flow past turbine blades, the thin edges are deformed plastically in compression during heating and subsequently creep in tension as the bulk of the specimen or blade heats up. The plastic deformation is determined from temperature distributions, which are calculated by Biot’s variational method. The creep deformation is determined as a function of time by a differential equation, which expresses the balance between increasing elastic stress and reduction of stress due to creep relaxation, and which is solved(i)by digital computer,(ii)by transformation to a Riccati equation soluble in terms of Bessel functions, or(iii)by transformation to a second-order differential equation with a periodic coefficient. Using the thermal stresses obtained from the solution of the differential equation, the theoretical thermal fatigue endurance is determined from cyclic (mechanical) stress endurance data. Agreement between theoretical and experimental thermal fatigue endurances is obtained, over ranges of temperature, strain and strain rate, or, equivalently, over ranges of temperature, edge radius and heat transfer coefficient. This agreement supports the use of the theoretical methods in wider contexts. The accuracy of the temperature distributions is better than the accuracy of other factors entering into the correlation between theoretical and experimental endurances. Improvement in the interpretation of experimental results requires consideration of the alteration of the stress cycles during the course of thermal fatigue testing. This requirement is catered for partially by the various solutions of the differential equation for thermal stress.
Losses at Sudden Expansions and Contractions in Ducts
Authors: Pearson H. , Heurteux B. M. L.
Published: July 2016

In view of the overall losses occurring in the bypass ducts of bypass engines a study has been made of the losses taking place at sudden changes of section which occur as the flow passes over compressor and turbine casings not properly faired. It has been shown that the normally estimated losses occurring at sudden contractions and expansions are greatly increased by the low discharge coefficient. When allowance is made for this, the losses at obstructions can be estimated reasonably accurately. It is shown that a fairing ahead of the blockages has to be quite extensive to produce the normally calculated loss and that all these results are reconcilable with the known losses of obstructions in semiinfinite flow. It is shown, however, that where obstructions are placed in series so that the flow areas are roughly in line, losses are much less than the total of the losses caused by the obstructions separately.
Analytical Techniques for the Optimisation of Rocket Trajectories
Authors: Lawden Derek F.
Published: July 2016

The development during the last two decades of analytical techniques for the solution of problems relating to the optimisation of rocket trajectories is outlined and the present position in this field of research is summarised. It is shown that the determination of optimal trajectories in a general gravitational field can be expressed as a Mayer problem from the calculus of variations. The known solution to such a problem is stated and applied, first to the special case of the launching of an artificial satellite into a circular orbit with minimum expenditure of propellant and, secondly, to the general astronautical problem of the economical transfer of a rocket between two terminals in a gravitational field. The special cases when the field is uniform and when it obeys an inverse square law of attraction to a point are then considered, and the paper concludes with some remarks concerning areas in which further investigations are necessary.
Approximate Three-Dimensional Flow Theory for Axial Turbo-Machines
Authors: Howell W. T.
Published: July 2016

The subject of three-dimensional flow in axial compressors and turbomachines has been extensively studied since 1945. This paper gives a means of calculating the approximate three-dimensional flow in an axial compressor by giving expressions for the slope of the velocity profile as a function of the axial co-ordinate. These expressions bring out the rôle of the ratio of stage inlet annulus height to stage length in the three-dimensional flow in these machines. The effect of the three-dimensional flow on the stage temperature rise at mean radius is discussed by introducing a work done factor.
Radial Flow without Swirl between Parallel Discs
Authors: Moller P. S.
Published: July 2016

An understanding of radial flow between confined boundaries is of practical importance in the design of radial diffusers and air bearings. This study presents a combined experimental and theoretical analysis of radial flow, without swirl, between parallel discs using air at incompressible speeds.

Emphasis is placed on the pressure distribution sufficiently far downstream of the channel inlet for the entry conditions to be unimportant. However, a study is also made of the main features of the flow near the inlet, particularly within the annular separation bubble.

It is shown, for both turbulent and laminar flow, that a similarity solution is possible only in special cases where certain terms in the equations of motion can be neglected. Approximate solutions are obtained for the turbulent and the laminar radial pressure distributions using an integral momentum method. Both theories agree well with experiment. The critical Reynolds number for reverse transition is found to be approximately the same as that for flow in twodimensional channels and circular pipes. With the flow separating at the channel inlet, it is established that both a suitably chosen, minimum pressure coefficient of the separation bubble and the reattachment distance are functions only of the channel width for a given inlet pipe diameter and are independent of Reynolds number and the diameter of the discs.
An Extension of the Method of Generalised Conical Flows for Lifting Wings in Supersonic Flow
Authors: Portnoy H.
Published: July 2016

The method of generalised conical flows has previously been developed subject to the condition that the upwash divided by the streamwise co-ordinate to the power ĸ, where ĸ is the order of the conical flow, must have vanishing (ĸ+1)th derivative with respect to the conical co-ordinate. In the present paper this restriction is removed. The results are also used to discuss the effect of the application of the leading edge attachment condition on the wing pressure and geometry.
Torsional Vibrations of a Solid Wing of Diamond Section
Authors: Mansfield Eric H.
Published: July 2016

An exact plate analysis is given for torsion-type modes whose wavelength and deflection pattern are repetitive in the spanwise direction. It is shown that for short wavelengths there are regions of localised curling at the leading and trailing edges.
Shear Buckling of Rectangular Plates with Mixed Boundary Conditions
Authors: Cook I. T. , Rockey K. C.
Published: July 2016

The paper presents a solution for the buckling under shear of a rectangular plate which is clamped along one edge and simply-supported along the other edges. The authors have also re-examined the case of one pair of opposite edges clamped and the other pair simply-supported.
The Effects of Vibrational Relaxation on
Hypersonic Flow Past Blunt Bodies
Authors: Blythe P. A.
Published: July 2016

The analysis of Freeman is extended to the hypersonic flow of an inviscid, vibrationally relaxing gas past a bluff body. Expressions for the shock shape, streamline shapes and stand-off distance are derived; these expressions have been evaluated for a sphere for various values of an appropriate non-equilibrium parameter Λ.
On the General Theory of Heterogeneous Aeolotropic Plates
Authors: Stavsky Yehuda
Published: July 2016

A large deflection theory is established for the bending and stretching of aeolotropic plates with elastic moduli that vary in thex, y, zdirections. The theory is formulated in terms of two simultaneous non-linear differential equations, with variable coefficients, for the transverse deflectionwand an Airy stress functionF. Small deflection heterogeneous plate theory and some other sub-classes of plate problems are formulated by specialising the general non-linear plate equations. Effects of initial irregularities and of a variable elastic foundation are considered.
A Contribution to the Analysis of Axial Compressor Performance
Authors: Pearson H.
Published: July 2016

The concept of an idealised “unique” stage characteristic is employed to analyse and understand the performance of axial compressors. It is shown that there exists a “matching” line across the compressor characteristics at any point of which all the stages are operating at the same point of their “unique” stage characteristic, and that this matching line is readily obtainable, almost from inspection. Simple calculations lead to a derivation of both this “unique” characteristic and the effective area ratio of the compressor. The behaviour of the stages at other points than the matching line is readily understandable and presents a simpler picture of compressor performance than is often obtainable from actually measured stage characteristics.
Possible Types of Flow at Swept Leading Edges
Authors: Stanbrook A. , Squiref L. C.
Published: July 2016

Existing experimental data on the occurrence of attached flow around the leading edges of swept plane thin wings is summarised. It is shown that the change from separated to attached flow occurs while the Mach number normal to the leading edge is subsonic and that the Mach number required for the change increases with incidence. It is also shown that the Mach number and incidence conditions which hold on the boundaries dividing the two types of flow on wings with straight edges also apply locally at points on the leading edges of “Gothic” wings. The implications of this result on the flow over general curved-edge wings is briefly discussed.
Elastic Stress Concentrations for the Torsion of Hollow Shouldered Shafts Determined by an Electrical Analogue
Authors: Rushton K. R.
Published: July 2016

The elastic stress concentration factors for the torsion of solid and hollow shouldered shafts have been determined by means of a pure resistance electrical analogue. Fillet radii ranged from 0.05 to 1.0 times the diameter of the smaller shaft, and the shoulder diameter increased from 1.0 to 8.10 times the diameter of the smaller shaft. A comparison is made with the results of other techniques. A study has also been made of the formation of a plastic region in the neighbourhood of the fillet.
Buckling of Orthotropic Conical Shells under External Pressure
Authors: Singer J . , Fersht-Scher R.
Published: July 2016

Donnell type stability equations for thin circular orthotropic conical shells are presented and solved for external pressure loading. The solution is likewise applied to stiffened conical shells by consideration of equivalent orthotropic shells. Typical cases are computed and compared with corresponding isotropic shells. Correlation with equivalent cylindrical shells then yields a simple approximate stability analysis for orthotropic or ring-stiffened conical shells under hydrostatic pressure.
On the Confluence of Three Shock Waves in a Perfect Gas
Authors: Henderson L. F.
Published: July 2016

The paper deals with the behaviour of three shock waves meeting at a point in a perfect gas. It is shown that the equations of motion can be reduced to a single polynomial equation of degree 10. The real roots of this equation are studied to determine their physical significance. In addition, the appearance of degenerate shock systems is shown to be associated with the formation of certain multiple roots of the polynomial equation.
The Flow Past a Delta-Wing-Half-Cone Combination with Subsonic Leading Edges
Authors: Portnoy H.
Published: July 2016

The flow past an unyawed, flat, delta wing with subsonic edges, carrying a slender half-cone mounted centrally underneath, is found by using the method of supersonic conical flows. The wing plane is taken to be at zero incidence, but it is shown that wing incidence, camber, twist and thickness effects may be incorporated by superimposing on this solution the field of the isolated wing with these properties. The results are shown to agree with previous work on configurations with sonic or supersonic leading edges for the common case of sonic edges. The leading edge loading may be made zero to secure attached flow at any lift coefficient by using camber and incidence, but it is shown that there is a certain positive lift coefficient for which a negative incidence alone will suffice.
Stability of Multi-Stage Axial Flow Compressors
Authors: Howell W. T.
Published: July 2016

The following theoretical investigation is concerned with the stability of the flow through a system composed of a multi-stage axial flow compressor followed by a throttle.

Such an investigation was carried out by Pearson and Bowmer in 1949. In 1962 Pearson’s work on the analysis of axial flow compressor characteristics, and the accumulation of empirical data regarding factors affecting the surge line, re-awakened interest in the possibility of predicting the surge line of a multi-stage axial flow compressor-throttle system.

In this paper the equations governing the stability of flow at any operating point in such a system are obtained by applying Kirchhoff’s laws to the associated electric circuit at that operating point, and the analysis is applied to a wide range of flows of the calculated characteristics of a seven-stage axial flow compressor.

A study of the simplest compressor-throttle system is given, in which the equations of motion of the system are derived mechanically and electrically, and the range of validity of the equations and their stability are discussed in order to bring out the relation between the mathematics and physics of the simple system before applying these methods to multi-stage axial flow compressors.

For the relatively simple electrical representation used in this paper for an axial compressor of n stages, there are shown to be 2n possible values of p, the transient rotational frequency, and these are determined over a sufficiently wide range of flows on the seven-stage compressor studied.

As a result, a region of the compressor characteristic map can be marked out in which all the values of the transient rotational frequency have their real parts less than zero, corresponding to stability of operation, a region where at least one of the values of p is real and positive corresponding to non-oscillatory instability of operation, and an intermediate region where some of the values of the rotational frequency p are complex with positive real part, corresponding to oscillatory instability of operation.

It is suggested that the non-oscillatory instability found here is associated with the surge and the line of inception of non-oscillatory instability with the surge line.
Maximum Stability Characteristics of a Simple Flameholder in High Velocity Gaseous and Liquid Fuel/Air Streams
Authors: Walburn Peter G.
Published: July 2016

The same fluid kinetic-chemical parameter is shown to describe the peak velocity conditions at which cylindrical flameholders can sustain a flame in both gaseous and liquid fuel/air mixtures. Experimental data indicate the existence of three possible aerodynamic conditions which may aflect the flame stabilisation process. In both gaseous and liquid fuel flame stabilisation an increase in stabiliser size is shown to increase the peak stable burning velocity.
Pseudo-Radial Equilibrium in Flared Annuli
Authors: Horlock J. H.
Published: July 2016

A simple method of calculating the flow in turbo-machines with flared annuli is given. Approximate solutions are derived for the compressible swirling flow between the blade rows. Originally received February 1964.
Structure of the Flow Associated with a Two-Dimensional Supersonic Intake
Authors: Henderson L. F.
Published: July 2016

The intake is conceived as a device that generates a shock system and a subsonic patch within a supersonic field. The object of the paper is to obtain a qualitative description of this flow structure. The analytical procedure is a simple but fairly powerful mapping technique. Several examples are discussed and these show how the flow on the intake alters under the influence of gradually changing boundary conditions.
General Instability of Stiffened Circular Conical Shells under Hydrostatic Pressure
Authors: Baruch M. , Singer J.
Published: July 2016

Donnell type equilibrium and stability equations are derived for stiffened thin conical shells. The stiffeners are considered closely spaced and are therefore assumed to be “distributed” over the whole surface of the shell. In the proposed theory the stiffeners and their spacing may vary in any prescribed manner, but here only equal and equally spaced stiffeners are dealt with. The force- and moment-strain relations of the combined stiffener-sheet cross section are determined by the assumption of identical normal strains at the contact surface of stiffener and sheet.

The stability equations are solved for general instability under hydrostatic pressure by the method of virtual displacements. The solution used earlier for unstiffened conical shells, which satisfies some of the boundary conditions of simple supports only approximately, is again applied here. The effect of this incomplete compliance with boundary conditions is shown to be negligible by consideration of “boundary work”. The solution proposed for stiffened conical shells involves the concepts of “correcting coefficients” and minimisation of corresponding “error loads”.

Typical examples are analysed and the effect of eccentricity of stiffeners is investigated. Simplified approximate formulae for the critical pressure of frame-stiffened conical shells are also proposed.
An Application of Conformal Mapping to a Three-Dimensional Unsteady Heat Conduction Problem
Authors: Laura Patricio A. , Chi M.
Published: July 2016

This paper deals with an unsteady-state three-dimensional heat conduction problem in a prismatic body which has a complicated boundary shape. Numerical techniques such as a relaxation method must be used to solve a problem of this type; this method, however, requires unusually large amounts of labour. The method used in this paper consists of the application of conformal mapping and numerical solution of a partial differential equation and is applied first to a prismatic body of square cross section for which the exact solution is well known. As a second application, the approximate solution for a problem involving a star-shaped cross section is presented.
Radial Flow of Compressible Fluids Between Discs
Authors: Na Tsung Yen
Published: July 2016

Numerical solutions are obtained for the one-dimensional radial flow of a compressible fluid between parallel discs. A general discussion of the variations of pressure, density, velocity and temperature along the radius of the disc is then given. The present investigation covers both subsonic and supersonic flows, a range not previously covered in the literature.
The Random Vibration Response of a System Having Many Degrees of Freedom
Authors: Robson J. D.
Published: July 2016

The paper treats the general problem of the response to multiple random excitation of a system having n degrees of freedom. Analysis is developed which connects the spectral density matrix of a set of generalised coordinates with that of corresponding generalised forces, and makes explicit the contributions of the various normal modes. The case of two degrees of freedom is considered in detail. The importance of cross-correlations between modes is shown by determining their effects on spectra and on mean-square response.
An Analytical and Experimental Study of Cylindrical Shells under Localised Impact Loads
Authors: Yao John C.
Published: July 2016

Non-symmetric response of elastic shells to localised impact loads is studied. Closed-form solutions for the response to four particular kinds of pulse shapes are given. Experimentally measured values of the strain response of a cylinder to impact loads are obtained which compare satisfactorily with theoretical predicted values.
Stress-Concentration Factors at a Doubly-Symmetric Hole
Authors: Mitchell L. H.
Published: July 2016

The stress-concentration factor is calculated for an infinite plate in tension containing a doubly-symmetrical hole whose boundary consists of parts of three intersecting circles. A suggestion is made for modifying the results to apply to a strip.
Non-Linear Theory for Slender Wings in Sudden Plunging Motion
Authors: Dore B. D.
Published: July 2016

A theoretical treatment is considered for the flow past slender wings in sudden plunging motion when leading-edge vortices are present. A form of slender-wing theory is used and, although the basis of the theory involves no restriction on compressibility, it has proved possible to make calculations only for an incompressible fluid.

Use is made of an analogy between the unsteady flow and related steady flows. In the incompressible case, an extension of the theory of Brown and Michael is given to determine the strength of the vortex and its path from the leading edge to the final steady-state position. A qualitative comparison with experiment is made of the instantaneous position of the vortex. In a typical case the lift is calculated to remain within one per cent of its final value after the vortex strength has reached 55 per cent of its final value.
Calculation of Heat Transfer Coefficients in Cooled Turbine Cascades
Authors: Harris H. D. , Luxton R. E.
Published: July 2016

An approximate method is presented for the calculation of heat transfer rates to cooled turbine blades. The method is based on a combination and extension of methods which have been developed in recent years for the calculation of the skin friction and heat transfer coefficients on wings in high speed flight. The use of the method is demonstrated by application to a specific cascade for which an experimental determination of overall heat transfer coefficient is known. Very close agreement with the experimental results is found over the range of Reynolds number tested. The calculated distribution of local heat transfer coefficient indicates that local pressure gradients have a marked effect on the heat transfer. A first-order estimate of the effect of blade cooling on the rate of mass flow through a blade passage shows that an increase of the order of one per cent in the mass flow rate may be obtained by a reasonable degree of blade cooling.
A ‘Pseudo-Viscosity’ Method for Calculating Two-Dimensional Flow Fields
Authors: Walkden F. , Sellars J. E.
Published: July 2016

A scheme that uses an implicit system of finite-difference equations to obtain solutions of the equations governing the two-dimensional supersonic motion of an inviscid gas is described. The method relies on pseudo-viscosity in order to calculate shock waves. Compared with characteristics methods, pseudo-viscosity methods have certain advantages. For example, shock waves are calculated automatically without special procedures and pseudo-viscosity methods are easily generalised so that problems with three or more independent variables may be considered. Pseudo-viscosity methods have not been used extensively in the field of aerodynamics, partly because of the difficulty in obtaining sufficiently accurate solutions in the neighbourhood of a boundary. The main purpose of this paper is to show how this difficulty can be overcome. The problem of integrating the equations of motion when a boundary condition has to be satisfied on an arbitrary curve is considered. Streamlines are used as one of the independent variables so that the boundary curve is a coordinate curve, and the equations of motion are used in a form which leads to a simple procedure at the wall. For a given system of partial differential equations it is possible to introduce pseudo-viscous terms in many ways, not all of which are satisfactory. The results presented show that the method proposed in this paper is adequate. The calculated results are accurate and vary smoothly in the neighbourhood of the boundary.
Asymptotic Expansion for Transient Forces from Quasi-Steady Subsonic Wing Theory
Authors: Garner H. C. , Milne R. D.
Published: July 2016

A simple general expression is obtained for the rate of change of generalised aerodynamic damping coefficients with respect to frequency parameter in the limit as frequency tends to zero. The expression is directly proportional to aspect ratio and does not depend explicitly on Mach number. The result is consistent with calculated pitching derivatives from finite-frequency theory.

This extension of quasi-steady theory is applied to determine the leading transient term of the asymptotic expansion for large time of generalised forces due to an indicial upwash field. The expansion has direct relevance to the use of quasi-steady aerodynamic derivatives in the field of stability and control.
The Effect of Base Bleed on the Flow behind a Two-Dimensional Model with a Blunt Trailing Edge
Authors: Bearman P. W.
Published: July 2016

The effects of base bleed on the flow about a two-dimensional model with a blunt trailing edge were examined at Reynolds numbers, based on model base height, between 1·3×104 and 4·1×104. The ratio of boundary layer thickness at the trailing edge to half the model base height was approximately 0·4. Measurements were made of base pressure, vortex shedding frequency and the distance to vortex formation. With a sufficiently large bleed quantity the regular vortex street pattern disappeared and the base drag of the section was reduced to about a third of its value without bleed. The base pressure was found to vary linearly with the inverse of the vortex formation distance. Results of a previous splitter plate investigation were found to agree closely with those of the present experiments.
Experiments on the Reattachment of a Turbulent Axisymmetric Shear Layer
Authors: Finley P. J.
Published: July 2016

Some experiments are described in which an axisymmetric free shear layer attaches to a spherical surface, the exterior flow Mach number ranging from 0-75 to 207. The Chapman-Korst reattachment model is shown to correlate the results very well. The relation between the quantities measured and the numerical predictions of the model is discussed in detail and it is shown that the pressure changes which occur just downstream of reattachment are significantly different from those observed on flat walls.
A Note on the Shear Stress Criterion for Fatigue Failure under Combined Stress
Authors: Little R. E.
Published: July 2016

Nishihara’s combined bending and torsion out-of-phase fatigue limit data are analysed. The Tresca shear stress failure criterion predicts strengths up to 30 per cent higher than observed. It thus appears that renewed attention should be given to the basic problem of developing reliable combined stress failure criteria. It is suggested that new test methods will be required for this purpose.
Measurements of the Flow Field on a 15° Semi-Vertex Angle Blunt Cone at M=8.6
Authors: Wood N. B.
Published: July 2016

Measurements of the pitot pressure between the body and shock on a 15° semi-vertex angle, spherically blunted cone were made in the RARDE Hypersonic Gun Tunnel at a Mach number of 8·6. Using these measurements, together with the measured shock shape, the other flow field parameters were calculated. The results were compared with results of inviscid theoretical calculations for a similar cone at a Mach number of 10.
Displacement Effects on Pitot Tubes with Rectangular Mouths
Authors: Quarmby Alan , Das H. K.
Published: July 2016

The displacement effects on a set of five rectangular mouthed pitot tubes of a constant thickness ratio, 0-6, were investigated in fully developed turbulent flow in a plain tube. The results show that the displacement due to shear only, δ1, is given by δ1/b=0.19, where b is the outside thickness of the pitot tube. The additional wall effect is found to have a dependence on Reynolds number or, equivalently, wall shear within the range investigated of 27 500 < Rev < 58 300. The wall effect results may be presented as a single curve, however, if consideration is given to the distance up to which the wall effect is present.
Correlation of Constant Pressure Turbulent Boundary Layer Measurements on Insulated Walls
Authors: Stoddart J. A. P.
Published: July 2016

Measured characteristics of compressible constant pressure adiabatic turbulent boundary layers are correlated in an incompressible frame of reference with the aid of a modification of the well known Mager compressibility transformation. Quite good data collapse is obtained although the transformation is shown to be deficient in the outer regions of the boundary layer. The results will be used to produce data sheets of constant pressure adiabatic turbulent boundary layer properties.
The Post-Buckling Behaviour of Simply-Supported Square Plates
Authors: Walker A. C.
Published: July 2016

The post-buckling behaviour of flat square plates loaded along two opposite straight edges is analysed using the von Kármán equations, trigonometric series and Galerkin’s method. The unloaded edges are considered to be either free to distort in the plane of the plate or maintained straight but allowed to move bodily; all edges are simply-supported in the out-of-plane direction. The non-linear algebraic equations are solved approximately using a McLaurin’s series expansion technique which facilitates the development of explicit expressions for ultimate load, end shortening and stiffness. The effects of initial geometric imperfections are also studied and it is shown that the results for ultimate load prediction and end shortening are in good agreement with test results.
The Effect of End-Plates on the Two-Dimensionality of a Vortex Wake
Authors: Graham J. M. R.
Published: July 2016

Spanwise velocity correlations of the turbulent vortices shed by a two-dimensional bluff body of D-section are presented for different aspect ratios of the shedding body between end-plates. From these it is shown that the vortices are only shed two-dimensionally when the gap between the end-plates is less than or equal to four times the base height of the shedding body.
Laminar Boundary Layers over Permeable Curved Surfaces
Authors: Clayton B. R. , Massey B. S.
Published: July 2016

Steady, constant-density, two-dimensional flow in a laminar boundary layer is considered over a permeable curved surface, for conditions such that the equation of motion has similar solutions. Account is also taken of the displacement of the main stream by the boundary layer.

Integration of the equation of motion on a digital computer yields results indicating that, for given values of curvature and longitudinal pressure gradient, suction reduces the boundary-layer thickness and increases skin friction. Blowing has the reverse effects. The amount of suction or blowing required to produce neutral stability is independent of curvature and so may be deduced from data for flat surfaces.

For a given curvature, blowing reduces, whereas suction increases, the magnitude of the adverse pressure gradient which the boundary layer can withstand before separation occurs. For a surface through which there is blowing or only a small amount of suction, convex curvature also reduces the magnitude of the adverse pressure gradient producing separation; but for larger amounts of suction the effect of surface curvature on separation is reversed.
An Improved Method of Matrix Displacement Analysis in Vibration Problems
Authors: Carnegie W. , Thomas J. , Dokumaci E.
Published: July 2016

This paper presents a method with strong convergence characteristics for the determination of eigenvalues and eigenvectors of continuous systems. The limitation on the number of undetermined constants in the displacement functions introduced by the conditions at the ends of a segment is removed by the introduction of points of freedom within the segment.

This improves the convergence of eigenvalues and eigenvectors very rapidly with the number of segments, especially in torsional vibration problems where the convergence with the usual Matrix Displacement method is very poor. The continuous medium is successively approximated by the use of sub-systems with finite numbers of degrees of freedom. The principles upon which the method is based and the convergence of the results are discussed and illustrated by a series of examples.
Flow between a Rotating and a Stationary Disc
Authors: Bayley F. J. , Owen J. M.
Published: July 2016

This paper deals with the effects of a superimposed radial outflow upon the motion of the fluid between a rotating and a stationary plane disc. This is an idealisation of the situation found in advanced turbo-machinery in which cooling of the rotor faces is necessary. The boundary layer approximations to the equations of fluid motion are integrated by an extension of the numerical technique proposed in Ref. 11. Predictions of drag torque and radial pressure distributions are compared with experimental results from a 30 in (762 mm) diameter system, using a range of speeds up to 4000 rev/min, while varying the axial spacing and rate of imposed radial flow. Qualitative agreement was satisfactory throughout the range, but quantitative discrepancies in the estimates of drag and in the pressure distributions at certain flow conditions suggest that the simple mixing length hypothesis used in this analysis for the turbulent shear terms in the equations of motion is not universally adequate.
Long Cylindrical Tube Subjected to Two Diametrically Opposite Loads
Authors: Yao J. C.
Published: July 2016

A theoretical study is made of the problem of a long, thick cylindrical tube subjected to two equal and diametrically opposite normal loads. The stress state is analysed by the three-dimensional theory of elasticity, with the Papkovich and Neuber stress-function approach. Numerical results for stresses and radial displacement are obtained to show the nature of stress concentration in the neighbourhood of the load. Some related experiments using the photoelasticity technique are also accomplished. Favourable correlation is shown between the theory and the test results.
The Supersonic Flow Past an Elliptic Cone
Authors: Woods B. A.
Published: July 2016

The supersonic flow past an elliptic cone of small eccentricity is treated as a pertubation of the axially-symmetric conical flow. The perturbation is singular; a uniformly valid solution is constructed by formulating the problem in sphero-conal coordinates (in which the cone surface is always a level surface of one of the coordinates) and by using the method of matched asymptotic expansions. This formulation enables first-order results to be obtained economically. In a numerical example for the flow past a cone of quite large eccentricity at incidence, it is shown that the present first-order solution (of three terms) agrees as well with experiment as a ten-term approximation obtained by Martellucci using the method of linearised characteristics.
Solution of the Non-Linear Differential Equations for Finite Bending of a Thin-Walled Tube by Parameter Differentiation
Authors: Na T Y , Turski C E
Published: July 2016

The method of parameter differentiation is applied to the solution of the non-linear, two-point, ordinary differential equations resulting from an analysis of the finite bending of a thin-walled tube. Starting from a given set of solutions of the differential equations for a particular value of the curvature parameter α, solutions for a range of values of α can be obtained by this method non-iteratively. Very close agreement was obtained with solutions using iterative numerical methods.
A Simple Integral Method for the Calculation of Thick Axisymmetric Turbulent Boundary Layers
Authors: Patel V C
Published: July 2016

A simple integral method is described for the calculation of a thick axisymmetric turbulent boundary layer. It is shown that the development of the boundary layer can be predicted with acceptable accuracy by using an approximate form of the momentum-integral equation, an appropriate skin-friction law, and an entrainment equation obtained for axisymmetric boundary layers. The method also involves the explicit use of a velocity profile family in order to interrelate some of the integral parameters. Available experimental results have been used to demonstrate the general accuracy of the method.
Higher-Order Solutions for Unsteady Hypersonic and Supersonic Flow
Authors: Hui W H , Hamilton J
Published: July 2016

The problem of unsteady hypersonic and supersonic flow with attached shock wave past wedge-like bodies is studied, using as a basis the assumption that the unsteady flow is a small perturbation from a steady uniform wedge flow. It is formulated in the most general case and applicable for any motion or deformation of the body. A method of solution to the perturbation equations is given by expanding the flow quantities in power series in M−2, M being the Mach number of the steady wedge flow. It is shown how solutions of successive orders in the series may be calculated. In particular, the second-order solution is given and shown to give improvements uniformly over the first-order solution.
The Prediction of the Axisymmetric Turbulent Jet Issuing into a Co-Flowing Stream
Authors: Antonia R A , Bilger R W
Published: July 2016

Three analyses are presented for predicting the development of an axisymmetric turbulent jet issuing into a co-flowing external air stream. The first analysis is analogous to a method used by Patel to predict the growth of a two-dimensional jet in an external air stream. The method is found to be inadequate when the excess velocity on the axis of the jet becomes small compared with the external stream velocity. The second analysis assumes that the turbulence structure is similar at different streamwise stations but it breaks down when the advection of turbulent energy becomes comparable with the turbulent energy production. In the third approach, a two-parameter model of turbulence developed by Rodi and Spalding, which uses two differential equations for the turbulent energy and the length scale of the turbulence respectively, is found to predict closely the experimental results of Antonia and Bilger for a ratio of jet to external stream velocity of 3.0. The success of this last method emphasises the non-similar character of turbulence.
Simple Finite Elements for Pre-Twisted Blading Vibration
Authors: Thomas J , Dokumaci E
Published: July 2016

A simple formulation is established for the determination of vibration characteristics of pre-twisted beams by the matrix displacement method. An important point in the analysis is the assumption of complete polynomial displacement distribution in the principal directions. In particular, two twisted elements which employ quintic polynomials are introduced and used in the calculation of natural frequencies of pre-twisted beams for several boundary conditions. The results demonstrate rapid convergence.