bluuebunny/crossref_metadata_2025 huggingface dataset:
Stresses Round Pins in Holes
Authors: Cox H. L. , Brown A. F. C.
Published: July 2016

The existing data relating to stresses round pins in holes are reviewed and co-ordinated.

The first part of the paper deals with pins of which the diameter is less than half the plate width and which are no better than a push fit in the hole; the second section deals with larger pins; and the third section deals with interference fit of the smaller pins. The theoretical background is sketched in two appendices, and the results of three series of photoelastic measurements of the effects of clearance of the pin in the hole are described.
The Effects of Small Changes of Prandtl Number and the Viscosity-Temperature Index on Skin Friction
Authors: Young A. D.
Published: July 2016

The analytic simplifications in boundary-layer analysis that result from the assumptions that the Prandtl number σ and the viscosity-temperature index ω are unity make it desirable to be able to assess the effects of the departures of the actual values of these parameters from unity. In this paper only the effects on skin friction are considered. Formulae of acceptable validity and wide application are first used to produce generalised curves for these effects for given main-stream Mach numbers and wall temperature conditions for the case of zero external pressure gradient for both laminar and turbulent boundary layers (Figs. 1 and 2).

A number of calculated results for the laminar boundary layer with favourable and adverse pressure gradients is then analysed (Figs. 3, 4 and 5) and it is shown that these results are consistent with the assumption that, for a given wall temperature, the effects of small changes of σ and ω on skin friction are independent of the external gradient, so that the appropriate curves of Figs. 1 and 2 apply. Where the change of a- is associated with a change of wall temperature (e.g. if the heat transfer is specified as zero) then the interaction between pressure gradient and this temperature change can be significant in its effects on skin friction for the laminar boundary layer and can only be assessed if the effects of changes of wall temperature with constant σ and ω have been separately determined for the pressure distribution considered. It is inferred that in all cases, except with large adverse pressure gradients and imminent separation, the effects of changes of ω and σ for the turbulent boundary layer are reliably predicted by the zero pressure gradient curves of Figs. 1 and 2 and the effect of any associated change of wall temperature can then be reliably inferred from the zero pressure gradient formula (equation (15)) in the absence of more specific calculations covering a range of wall temperatures.
Shock-Induced Separation of a Laminar Boundary Layer in Supersonic Flow Past a Convex Corner
Authors: Curle N.
Published: July 2016

This paper presents a theoretical investigation of the interactions which occur when a laminar boundary layer on a flat surface encounters an expansive corner followed by a shock or other compressive agency. The method consists basically of two equations; the first relates deflections in the external streamlines to pressure changes and the second relates pressure changes to thickening or thinning of the boundary layer. For simplicity it is assumed that the pressure changes and streamline deflections are small.

A comparison is made with the only available experimental results, under conditions which are far outside the range of applicability of the theory. In these circumstances the agreement between the predicted and experimental pressure distributions is reasonable.
An Analysis of the Turbulent Base Pressure Problem in Supersonic Axisymmetric Flow
Authors: McDonald H.
Published: July 2016

The problem of predicting the turbulent supersonic base pressure in axisymmetric flow is treated by an extension of a method of solution to the two-dimensional problem given in Ref. 1. The solution consists principally in tracing the boundary-layer development from upstream of the base to downstream of the recompression region for a given base pressure. A unique solution is obtained by specifying the shape of the rehabilitated boundary-layer velocity profile.

A comparison with experiment in the case of the step-down cylinder problem (the sting-support problem) yields some very favourable results. It is pointed out that, while it has not been found possible to obtain a solution to the problem of a vanishingly small sting, the base pressure does not vary appreciably while the sting is decreased from about 0-3 of the base diameter down to zero. It would appear that the present analysis is capable of giving accurate results down to sting/diameter ratios of the order of 0·3.
The Fundamental Flexural Vibration of a Cantilever Beam of Rectangular Cross Section with Uniform Taper
Authors: Rao J. S.
Published: July 2016

An attempt has been made to determine the natural frequency of fundamental flexural mode of a cantilever beam with uniform taper by the Galerkin method. The method suggested considerably reduces the calculations as compared with the other methods available and the results are checked with the correction factors derived by Martin.
The Boundary Layer on a Townend Surface
Authors: Cooke J. C. , Jones O. K.
Published: July 2016

Certain three-dimensional surfaces studied by Townend have the property that at every streamwise section a supersonic air stream is compressed isentropically in the form of a reversed Prandtl-Meyer flow. If all the compressions are centred on points lying on one straight line the flow is conical. Such a surface may be of use as an engine intake. In this paper an approximate boundary-layer calculation for such a surface is made for laminar flow with zero heat transfer in the conical case. It is found that under certain circumstances a useful amount of compression can be obtained before separation occurs (a pressure ratio of 6, for instance, for an initial Mach number of 10). Limiting streamlines are drawn and displacement thickness calculated for a typical case, and the Mach number at separation is determined for a range of initial Mach numbers and angles of sweep. Instability due to sweep is considered.
Optimal Trajectories and the Accessory Minimum Problem
Authors: Bell D. J.
Published: July 2016

The necessary conditions of Clebsch and Weierstrass and of the multiplier rule in the calculus of variations, which arise from the study of the first variation of a function, are summarised. A further necessary condition associated with the second variation is stated. The latter condition is applied to two problems: (i) the determination of the thrust-time programme which maximises the altitude of a sounding rocket, (ii) the determination of the thrust direction programme for a rocket with a known propellant expenditure programme which yields a maximum range. In both problems it is found that the additional necessary condition is satisfied.
Effect of Linear Damping on Flutter Speed Part II: Systems with Three or More Degrees of Freedom
Authors: Nissim E.
Published: July 2016

An analytical discussion on the effect of linear damping on flutter speed of systems having three or more degrees of freedom is described. The study is based on energy considerations introduced in a previous paper, where binary systems were discussed.
The Instability of Buckle Pattern in Cylindrical Shells under Axial Compression
Authors: Mansfield E. H.
Published: July 2016

The repetitive pattern of buckling, common to most theoretical analyses, is shown to be itself unstable. An approximate but very simple analysis is presented to describe the true buckling behaviour.
Laminar Flow in a Uniformly Porous Channel with Large Injection
Authors: Terrill R. M.
Published: July 2016

The author has previously discussed the flow in a two-dimensional channel with porous walls through which fluid is uniformly injected or extracted. Yuan has given a solution for high injection in which certain derivatives of the axial velocity become infinite at the centre of the channel. Physically this means that there must be a viscous layer at the centre of the channel and that Yuan’s solution is ignoring the shear layer. In this paper the complete solution for large injection is obtained by the method of inner and outer expansions and therefore includes the viscous layer. The resulting series solutions are confirmed by numerical results.
Interpolation of Mode Shapes: A Matrix Scheme Using Two-Way Spline Curves
Authors: Done G. T. S.
Published: July 2016

A method of interpolating low aspect ratio lifting surface mode deflections for use in aeroelastic calculations is described. It is based on the spline curve, the numerical analogue of the draughtsman’s spline which is a thin flexible beam used for drawing a smooth curve through a set of given coordinate points. The present problem is one of surface fitting and a matrix scheme using two-way spline curves is adopted. The method of treating the case in which the data points are randomly placed, whilst retaining an exact fit at the points, is discussed, as are the results of a practical example.
On a Method for the Detection of the Important Flutter Modes
Authors: Nissim E.
Published: July 2016

A method for the detection of the important modes participating in flutter is presented in this paper. The method is based on energy considerations and is illustrated by numerical examples.
The Mixing of Turbulent Supersonic Fuel-Air Streams
Authors: Forde J. M.
Published: July 2016

An integral part of the study of supersonic combustion is the investigation of supersonic turbulent mixing of dissimilar fluids. Experimental results obtained in the course of investigating the turbulent mixing zone between supersonic streams of CO3 and air are presented. Good correlation between observation and available theories has been obtained in terms of the parameter ξ=σy/x. The correlating parameter σ defines the spreading rate of the mixing zone. The available theories, though not developed for these specific conditions, are shown to be applicable to the turbulent mixing of supersonic streams.

The correlating parameter σ was determined for three different combinations of internal and external flow Mach numbers. The values found for σ were 18, 16·3, 15·3 for constant external Mach number 1·62 and internal Mach number 1·62, 1·53, 1·47 respectively. The magnitudes of σ showed the expected trend, that is the higher value implies the least divergence of the mixing boundaries.

The reasonable agreement with experiment and the simplicity of application of the momentum integral form of solution would appear to favour the use of this approach for the theoretical prediction of the mixing conditions.
On a Class of Multi-Shock Interactions in a Perfect Gas
Authors: Henderson L. F.
Published: July 2016

The paper deals with a class of shock-wave systems that are of importance in the design and operation of supersonic intakes. It is shown that, when n− 1 wedge shocks, all of the same family, meet at a point, together with a tail shock and a bow shock, then the equations of motion which describe the flow near the shock confluence or junction are reducible to a polynomial equation of degree 10. Numerical results are obtained for the special case of the four-shock confluence and it is shown that, the number of solutions of physical interest, m4, may be 0, 2 or 4. It is found that the m4=0 solution can be interpreted physically in three different ways. These are a Guderley type flow, a confluence of three shocks with a Prandtl-Meyer expansion fan or the appearance of a shock system containing more than one confluence point. The methods developed also permit the discussion of multi-confluence wave systems and a number of examples are given. Finally, the Prandtl-Meyer compression fan is brought within the scope of the method by approximating it with a system of shock waves of weak intensity and minimum entropy.
The Effect of Jet Entrainment on Loss of Thrust for a Two-Dimensional Symmetrical Jet-Flap Aerofoil
Authors: Wygnanski I.
Published: July 2016

Jet drag, defined as the form drag associated with jet entrainment in otherwise inviscid fluid, has been analysed by replacing a two-dimensional incompressible jet with a suitable continuous distribution of sinks. Exact solutions for the jet drag, with the flow incompressible and the jet turbulent, are presented for uncambered struts of various shapes (including an ellipse and a circular cylinder), various thickness ratios, and with blowing slots of various widths in both quiescent and uniform streaming flow. In uniform streaming flow the jet is blowing in the direction of the external flow. The extension of the theory to cross-stream blowing (as in the jet flap) is discussed.

The present theory compares favourably with the few available experimental results when the ratio of jet velocity to streaming-flow velocity is sufficiently large.
An Idealised Ground Effect Wing
Authors: Ando Shigenori
Published: July 2016

This paper contains a theoretical study for an idealised ground effect wing, both tips of which are close to the ground. The wing is assumed to be a simple semicircular lifting line in a transverse plane and the fluid is assumed incompressible and inviscid. When the gap between the tips and the ground tends to zero, the flow velocity through it becomes infinite. This fact is unrealistic and seems to be the reason why the theoretical ground effect is in error.
A Discrete Element Method for the Analysis of Plane Elasto-Plastic Stress Problems
Authors: Pope G. G.
Published: July 2016

A procedure is developed for the analysis of plane stress problems when yielding occurs locally. The region is divided into triangular elements and the deformation is analysed on a step-by-step basis, using the matrix notation developed by Argyris. The simple expressions which are derived for the element properties are applicable with any stress-strain relations which are stable and time-independent. Simple numerical examples are given.
A Lumped Inertia Force Method for Vibration Problems
Authors: Krishna Murty A. V.
Published: July 2016

A rational method of lumping inertia forces by considering the equilibrium of the vibrating element has been developed. This method requires the selection of a suitable displacement distribution function over each element. The closer it is to the true mode shape, the better the result.

Considering a linear displacement distribution function over each element, the natural frequencies and mode shapes are obtained for transverse vibrations of a stretched string, torsional vibrations of a cantilever shaft (fixed at one end and free at the other) and transverse vibrations of a uniform cantilever beam. It is found that, even with a few elements, a reasonable accuracy can be obtained in the natural frequency, while the mode shapes are exact in the first two cases and almost exact in the third at the points considered.

In Appendix A, it is shown that, for the torsional vibration of a uniform cantilever shaft and with a linear displacement function over each element, this method gives exact mode shapes at the points considered, while the natural frequency is always an upper bound and the error follows an inverse square law when the number of elements considered is large.

In Appendix B, it is shown that a combination of this method with the conventional lumped mass method reduces the error in the natural frequency. The error follows an inverse fourth-power law when the number of elements considered is large and the mode shapes are exact at the points considered.

This method can incorporate better displacement distribution functions, to obtain better results and convergence, and can easily be adapted to the buckling of columns, the vibration of beam columns and forced vibrations, as well as more complicated problems such as the vibration or buckling of plates and shells.
Turbulent Wall Jets on Logarithmic Spiral Surfaces
Authors: Giles J. A. , Hays A. P. , Sawyer R. A.
Published: July 2016

By considering the equations of motion it has been shown that the flow in the outer part of a two-dimensional, curved, turbulent wall jet is approximately self-preserving if the ratio of jet thickness to wall radius of curvature is constant along the jet. This condition is satisfied for a jet blowing over a surface of logarithmic spiral profile, for which the radius of curvature R increases linearly with distance s along the wall.

Measurements of velocity profiles and rates of growth of wall jets for surfaces with curvature ratios and 1 are presented. These are compared with solutions obtained using an eddy viscosity theory, and with the flow of jets round circular cylinders. The measured jets are found to be approximately self-preserving in form, and to have rates of growth which are much larger than the jets on circular cylinders with corresponding values of s/R.
A Procedure for Automated Minimum Weight Structural Design: Part I: Theoretical Basis
Authors: Gellatly Ronald A. , Gallagher Richard H.
Published: July 2016

This paper presents an approach to the determination of structural member sizes to provide minimum weight under a number of load conditions consistent with specified limitations on stress and displacement. The procedure amalgamates the disciplines of matrix displacement analysis and operations research into a scheme suitable for automatic digital computation.
The Three-Dimensional Interaction of a Shock Wave with a Turbulent Boundary Layer
Authors: McCabe A.
Published: July 2016

Experiments are described on the interaction of the shock wave generated by a wedge in a supersonic wind tunnel with the turbulent boundary layer on the side wall. It is shown that the onset of separation appears to be largely affected by the action of streamwise vorticity in the interaction region. A simple approximate theory based on this concept shows reasonable agreement with the experimental results. Comparisons have been made with two-dimensional interactions of normal shocks and boundary layers, but they did not produce any conclusive results.
Shear Buckling of a Clamped Infinitely Long Plate Reinforced by a Stiffener Mesh
Authors: Parsons H. W. , Cook I. T.
Published: July 2016

A theoretical solution to the initial buckling under shear stress of a long clamped plate with parallel edges reinforced by a stiffener mesh is obtained. The mesh is formed by two families of stiffeners each evenly spaced. One family consists of longitudinal stiffeners parallel to the edges of the plate and the other consists of diagonal stiffeners inclined to the parallel edges. The flexural and torsional rigidity of the stiffeners are included in the analysis. Numerical results are given for the special case in which the longitudinal stiffeners are absent and the diagonal stiffeners have flexural rigidity only.
The Free-Piston Shock Tube
Authors: Stalker R. J.
Published: July 2016

A study of shock tube operation with free-piston compression of the driver gas is presented. It is shown theoretically and experimentally that shock Mach numbers exceeding 30 in air may be obtained with an apparatus of moderate size. The operating limitations imposed by the maximum pressures allowed in the apparatus, by the ratio of the volume of the shock tube to the volume of the compression tube, and by the maximum pressure available for driving the piston are all explored theoretically. The compression process is studied experimentally, and results for three different compression tubes are used to indicate empirical rules for maximising the efficiency of the compression process. Streak photographs of the movement of the luminous gas behind the shock wave in a 1 in diameter shock tube are used to demonstrate the quality of the shock-wave motion produced.
Deformation of Rectangular Slender Webplates with Boundary Members Flexible in the Webplate Plane
Authors: Djubek J.
Published: July 2016

The paper presents a solution of the non-linear problem of the deformation of slender rectangular plates which are stiffened along their edges by elastically compressible stiffeners flexible in the plane of the plate. The webplate is assumed to be simply-supported along its contour. Numerical results showing the effect of flexural and normal rigidity of stiffeners are given for a square webplate loaded by shear and compression.
Lower Bounds for Sonic Bangs in the Far Field
Authors: Jones L. B.
Published: July 2016

In this paper lower bounds are obtained for the intensity of the sonic bang resulting from a slender aircraft flying straight and level at supersonic speeds. The lower bounds are obtained for an aircraft subject to various constraints on its total lift, volume, area distribution and centre-of-pressure position. The work described proves the results quoted in an earlier paper, corrects the results given in that paper for the general configuration, and extends the results to cover more constraints, mainly the centre-of-pressure position.
The Calculation of Three-Dimensional Turbulent Boundary Layers: Part I: Flow over the Rear of an Infinite Swept Wing
Authors: Cumpsty N. A. , Head M. R.
Published: July 2016

A method of calculation has been developed in which all terms in the momentum integral equations in the streamwise and cross-flow directions are taken into account so that no restriction to small cross-flows is imposed. The essential feature of the method is the use of an entrainment equation which enables the development of the streamwise form parameter to be calculated along with the streamwise and cross-flow momentum thicknesses. Mager’s quadratic expression is used to relate streamwise and cross-flow profiles. The method has been applied to the idealised case of an infinite swept wing with free-stream velocity over the forward part of the chord and a linear adverse velocity gradient over the rear. The position of separation, the directions of the surface streamlines and the development of streamwise and cross-flow profiles have been calculated for a series of angles of sweep and for adverse pressure gradients of varying severity.
Decay of a Velocity Maximum in a Turbulent Boundary Layer
Authors: Escudier M. P. , Nocoll W. B. , Spalding D. B. , Whitelaw J. H.
Published: July 2016

The paper describes an “explicit” method of predicting the flow properties of a turbulent boundary layer; particular attention is paid to the region in which the growth of the layer is characterised by the decay of a velocity maximum. The validity of the method is tested against the data of Wieghardt and against new data of the present authors; it is shown to be satisfactory. The integral flow properties predicted by the method are used, together with a further assumption, to predict velocity profiles; these closely resemble the measured ones.
Simple Expressions for the Spread of Turbulent Jets
Authors: Bradbury L. J. S.
Published: July 2016

Simple expressions are derived for predicting the spread of turbulent jets issuing into parallel moving airstreams. Difficulties with applying these expressions to practical problems are discussed and comparisons with experimental results are given.
On the Flow Along Swept Leading Edges
Authors: Gaster M.
Published: July 2016

Flight tests on the Handley Page suction wing showed that turbulence at the wing root can propagate along the leading edge and cause the whole flow to be turbulent. The flow on the attachment line of a swept wing was studied in a low speed wind tunnel with particular reference to this problem of turbulent contamination.

The critical Reynolds number, RθL, of the attachment-line boundary layer for the spanwise spread of turbulence was found to be about 100 for sweep angles in the range 40°–60°. A device was developed to act as a barrier to the turbulent root flow so that a clean laminar flow could exist outboard. This device was shown to be effective up to an Rθ of at least 170, so that experiments were possible on a laminar boundary layer at Reynolds numbers above the lower critical value. A spark was used to introduce spots of turbulence into the attachment-line boundary layer and the propagation speeds of the leading and trailing edges were measured. The spots expanded, the leading edge moving faster than the trailing edge, at high Reynolds numbers, and contracted at low values.

The behaviour of Tollmien-Schlichting waves was also investigated by exciting the flow with sound emanating from a small hole on the attachment line. Measurements of the perturbation phase and amplitude were made downstream of the source and, although accurate values of wave length and propagation speed could be found, difficulties were experienced in evaluating the amplification ratio. Nevertheless, all small disturbances decayed at a sufficient distance from the source hole up to the highest available Reynolds number of 170.
A Simple Method for Predicting the Performance of Cascades of Low Solidity
Authors: Tanabe K. , Horlock J. H.
Published: July 2016

A simple potential theory for flow through cascades of low solidity is developed. The analysis is an extension of Glauert’s theory for single aerofoils. The variation of outlet angle and lift coefficient with space/chord ratio and stagger angle is predicted. The simple analysis is shown, by comparison with other methods of computation, to be valid for cascades of space/chord ratio in excess of 1·5 and staggers over 50 degrees.
Approximate Calculations of the Incompressible Laminar Boundary Layer
Authors: Head M. R. , Hayasi N.
Published: July 2016

A recent calculation method proposed by Curle has been applied to the flow U=U0ξe-ξ for which a computer solution exists. An earlier approximate method due to Head, presented here in a simplified form, has been applied to the same problem. All three solutions are found to be in close agreement. A further problem, already examined by Curle, is treated by Head’s method. Again the results are in good agreement with each other and with an exact solution obtained subsequently.
Base Pressure Measurements on Elliptic Cones in Supersonic Flow
Authors: Stahl W. , Grauer-Carstensen H.
Published: July 2016

At the Aerodynamische Versuchsanstalt Gottingen (AVA), base pressure measurements were made on five elliptic cones. The ratios of the axes of the ellipses were: 1:12, 1:3, 1:1, 3:1, and 12:1. All the cones had the same volume and the same length. The investigations were carried out for Mach numbers M∞=1·50, 1·73, and 1·98 at angles of incidence between about —2 degrees and about 8 degrees. Reynolds numbers, based on a mean length,lm, varied from 2·5×106to 3·0×106; the boundary layer approaching the base was turbulent. The base pressure coefficients are given as a function of geometry. Some of the results were compared with the base-flow theory of Korst and reasonable agreement was found.
On the Performance of the Hovercraft Single-Wall Skirt
Authors: West A. A.
Published: July 2016

A simple analysis is presented for the air flow and nozzle power requirements of hovercraft fitted with skirts on which the peripheral jet is blown down the inner skirt face—the “single-wall” type. The theory, which utilises experimental wall-jet data, is applicable to the equilibrium jet state.

A comparison is made with analyses for the air flow and nozzle power requirements of plenum chamber craft and hovercraft fitted with twin-wall skirts. It is concluded that, for a given gap between the skirt bottom and the terrain, at normal operating conditions the order of merit is twin-wall skirt, single-wall skirt, plenum chamber.
On a Convergent Multi-Moment Method for the Laminar Boundary Layer Equations
Authors: Bethel Howard E.
Published: July 2016

This paper presents a summary of a multi-moment method for solving the laminar boundary layer equations. Results obtained with the method tend to converge to the exact values as higher moments are used. Both similar and non-similar external flow fields are considered. The present results are compared with those obtained by another multi-moment method, a finite-difference method and a refined Pohlhausen-type method.
An Asymptotic Solution for the Centre of a Rolled-up Conical Vortex Sheet in Compressible Flow
Authors: Brown Susan N. , Mangler K. W.
Published: July 2016

The asymptotic solution, valid near the centre of a rolled-up vortex sheet, obtained by Mangier and Weber, is generalised to include the effects of compressibility. The vortex sheet is taken to be embedded in a potential flow, and the flow field is assumed to be conical.
Nodal Lines for Long Plates in Combined Shear and Compression with Sinusoidal Edge Rotations
Authors: Wittrick W. H. , Curzon P. L. V.
Published: July 2016

The work described in this paper forms part of a programme on the local buckling of long thin flat-walled structures, such as integrally stiffened panels or corrugated core sandwich panels, with the individual flats subjected to combined longitudinal compression and shear. When buckling occurs, the line junctions between adjoining flats remain straight, but rotations occur about the junctions. These rotations vary sinusoidally in the longitudinal direction but, because of the shear, the rotations at the two edges of an individual flat are out of phase with each other. In order to picture the buckling mode it is essential to have at least a qualitative idea of the shape of the nodal lines in the flats. The analysis of this paper is entirely concerned with this problem.
An Experimental Study of the Flexure of Some Triangular Sections
Authors: Nath B.
Published: July 2016

This paper presents the flexure functions of some triangular sections, subjected to terminal loads, obtained by using a simple electric analogy technique. The effect on the flexure function of both the shape of the section and Poisson’s ratio of the material has been investigated; examples also include some interesting doubly-connected sections. Flexibility of the analogy technique is indicated.
Vibration Characteristics of Straight Blades of Asymmetrical Aerofoil Cross-Section
Authors: Carnegie W. , Dawson B.
Published: July 2016

Theoretical and experimental natural frequencies and modal shapes up to the fifth mode of vibration are given for a straight blade of asymmetrical aerofoil cross-section. The theoretical procedure consists essentially of transforming the differential equations of motion into a set of simultaneous first-order equations and solving them by a step-by-step finite difference procedure. The natural frequency values are compared with results obtained by an analytical solution and with standard solutions for certain special cases. Good agreement is shown to exist between the theoretical results for the various methods presented. The equations of motion are dependent upon the coordinates of the axis of the centre of flexure of the beam relative to the centroidal axis. The effect of variations of the centre of flexure coordinates upon the frequencies and modal shapes is shown for a limited range of coordinate values. Comparison is made between the theoretical natural frequencies and modal shapes and corresponding results obtained by experiment.
Transfer Matrices for Beams Loaded Axially and Laid on an Elastic Foundation
Authors: Djodjo B. A.
Published: July 2016

Using a modified model of the axially-loaded Timoshenko beam, nine field transfer matrices for the homogeneous case and three field matrices for the non-homogeneous case have been derived, covering thus all the “cases of state” of continuous beams loaded axially and laid on an elastic foundation. The loads and restraints (translatory and rotatory) may be both concentrated and distributed. The matrices make possible a simultaneous treatment of free vibrations, forced vibrations, statics and buckling.
Minimum Induced Drag of Non-Planar Ground Effect Wings with Small Tip Clearance
Authors: Kida T , Miyai Y
Published: July 2016

This paper treats theoretically the problem of the minimum induced drag of non-planar ground effect wings with both tips very close to the ground, within the limitations of the linearised lifting-line theory. The gap clearance between the wing tip and the ground is assumed to be very small and, using this small parameter, an approximate theory, which yields the minimum induced drag of a non-planar ground effect wing, is formulated by the method of matched asymptotic expansions. As a check on the accuracy of the method, this theory is compared with the exact theory for a semicircular wing. This shows that the present method is accurate within the small gap clearance. Moreover, the present method is applied to other wing configurations, such as semi-elliptic wings and wings with endplates, circular arc wings in a tube and circular arc wings. These computations show the theory to be very effective and it can be easily extended to various spanwise cambers.
A Stagnation Pressure Probe for Supersonic and Subsonic Flows
Authors: Goodyer M J
Published: July 2016

The usefulness of a probe which can sense the absolute value of the stagnation pressure in supersonic flow has long been recognised. In the past such a probe has not been available and therefore it has been necessary to infer this fundamentally important flow property from measurements of other properties. This paper describes a probe which has been developed specifically to measure accurately the stagnation pressure of a supersonic gas stream. Measurements of the performance of the probe to date show that it is capable of measuring absolute stagnation pressure with an accuracy of 0.1 per cent in the Mach number range 1.5 to 2.1. No measurements have yet been made in the transonic range, but at low subsonic speeds the probe has demonstrated its ability to measure dynamic pressure within an accuracy of 0.1 per cent at a Mach number of approximately 0.13. The permissible range of misalignment in pitch and yaw before the pressure recovery begins to deteriorate are functions of free-stream Mach number and are usefully wide.
A Study of the Mechanics of Flapping Wings
Authors: Betteridge D S , Archer R D
Published: July 2016

A method for the analysis of flapping-wing flight using lifting-line theory and actuator disc theory is proposed for the prediction of aerodynamic loads, propulsive efficiencies and optimum lift distributions.
Measurement of the Mean Pressure Distribution About a Double-wedge Strut in Turbulent Shear Flow
Authors: Turner J T , Turner M H , Williams K J
Published: July 2016

Surface pressure distributions have been measured on a cylinder with a double-wedge cross section in a two-dimensional channel flow. The flow is sheared in the direction of the cylinder axis, using a grid of parallel wires with variable spacing, in order to simulate the type of geometry and velocity variation which occur for annulus support struts in turbomachines. The strut had a 38° included angle at the leading and trailing edges and an aspect ratio of 1.33 based on the maximum thickness. This was fixed between the parallel walls of a rectangular wind tunnel with end leakage eliminated. Surface pressure distributions were measured over a Reynolds number range of 0.5 × 105 to 1.5 × 105 for three different shear flow conditions. Despite the presence of sharp edges at the mid-chord position, delayed boundary-layer separation beyond the plane of maximum thickness has been found for sufficiently high spanwise shear in the upstream flow. Surprisingly, therefore, some similarity with previous results for struts of circular cross section appears to exist. The influence of the shear flow conditions on the pressure drag force has been determined by numerical integration of the data. Only a slight dependence on the upstream flow conditions is found, although the effect of secondary velocity components may still be observed if the spanwise variations in the local drag force are examined.
Critical Buckling of Some Stiffened Panels in Compression, Shear and Bending
Authors: Plank R J , Williams F W
Published: July 2016

Previous papers by the authors and others have developed exact methods for computing the critical buckling loads of prismatic assemblies of rigidly interconnected thin flat rectangular plates. The plates may be isotropic or anisotropic and can carry uniform in-plane shear stresses and transverse stresses in addition to a longitudinal stress which varies linearly over the cross section but is longitudinally invariant. Published results obtained using these methods have only covered a few of the types of structure and loading which are of interest. This paper presents results which complement those already published. For instance, interaction curves are given for common types of panel in combined in-plane shear and longitudinal compression and bending. About half of these curves are nearly parabolic while some others differ greatly from the parabola, which errs on the safe side for all the results presented. Other results cover critical loads other than the lowest, panels with bulb flat stiffeners, as used for bridge decks, and the effects of assumptions usually made when idealising real panels before computation.
A Two-Dimensional Aerofoil with a Control Surface Oscillating at Low Frequency in High Subsonic Flow
Authors: Nixon D
Published: July 2016

The aerodynamic derivatives for a two-dimensional aerofoil with an oscillating control surface in a high subcritical flow are calculated using the method of Nixon. The aerofoil is assumed to be symmetric and at zero incidence with a zero mean control surface deflection angle. With the exception of the control surface stiffness derivative the magnitudes of the aerodynamic derivatives are greater than the corresponding linear values by between 15–35 per cent; the greatest difference occurs for low values of the frequency parameter. The magnitude of the control surface stiffness derivative is less than the corresponding linear value by the order 10–15 per cent.
The Prediction of Turbulent Boundary Layer Parameters in Conical Diffuser Flows
Authors: Wirasinghe N E A , Neve R S
Published: July 2016

The methods suggested by Ross and by Fraser for dealing with turbulent boundary layers in adverse pressure gradients using semi-empirical data are extended to the prediction of boundary layer growth in conical diffusers, the new method making no recourse to measured static pressures, as previously required. Predictions agree closely with published experimental data by Fraser and give some justification for the use of the Ross model for the turbulent boundary layer in a diffuser provided that the diffuser is not too long and that the inlet boundary layer is thin.
The Boundary Layer on a Plane of Symmetry
Authors: Head M R , Prahlad T S
Published: July 2016

For the turbulent boundary layer it is shown that, if an initial velocity profile is given, along with the local pressure gradient and shear-stress distribution through the layer, then the shape of the velocity profile a short distance downstream is unaffected by flow convergence or divergence, provided this is constant through the layer. For flow approaching an obstacle, increased divergence close to the surface is shown to account for the marked changes in profile shape that have been observed.
Simple Formulae for Supersonic Flow past a Cone
Authors: Hui W H
Published: July 2016

The problem of the supersonic flow with attached shock wave past a circular cone at zero angles of attack is treated, using the thin-shock-layer expansion. The solution is calculated to the fourth approximation. A simple formula is then derived for the surface pressure coefficient by the application of the parameter-straining technique and it is shown to be very accurate for the whole Mach number range for which the shock remains attached to the cone vertex.
Orbital and Attitude Stability of Space Shuttles in Parking Orbits
Authors: Arho R
Published: July 2016

A unified treatment is given of the orbital and attitude stability of space shuttles in parking orbits (in vacuo) in the earth’s gravitational field. A shuttle in a circular orbit with a principal axis aligned with the horizontal in the orbital plane is found to be in stationary geostatic equilibrium. The demand for stability leads to a condition which must be satisfied by the principal moments of inertia. The stability which is achieved is not asymptotic without control. The stationary state is a stable centre about which a bounded perturbation oscillation without damping may exist.
The Application of a Lifting-Surface Method to Large, Steady or Oscillating Models in Subsonic, Closed, Open or Slotted Wind Tunnels
Authors: Streather R A
Published: July 2016

A subsonic, lifting-surface method is extended to apply to low-frequency oscillations of wind-tunnel models, taking into account both longitudinal and lateral variations of tunnel lift interference. Rectangular sectioned tunnels with closed, slotted or open roof and floor and closed sidewalls are considered. A comparison is made between the aerodynamic derivatives obtained by this method and those calculated with the assumption that the model span is small compared to the tunnel width. Three models of aspect ratio 2.67 and different sweepback are considered in rigid pitching oscillations in tunnels of width/height ratio 2.5. The greatest differences between the results from the two methods occur for the tunnel with closed roof and floor and for the unswept planform. The least differences occur for the slotted tunnel and for the planform of greatest sweepback. The results indicate that, for models of conventional size [up to span/(tunnel width) ratio of 0.4], the “small-span” assumption is satisfactory in tunnels with slotted roof and floor and closed side walls, but not in fully closed tunnels.
An Extension of One-Dimensional Theory to Inviscid Swirling Flow through Choked Nozzles
Authors: Carpenter P W , Johannesen N H
Published: July 2016

A method is presented for determining the swirling compressible flow through a nozzle, given conditions at a reference section. The principal assumption is that changes in the nozzle cross-sectional area are sufficiently gradual for the radial velocity component to be neglected at each section, i e, the usual assumption of one-dimensional compressible flow theory. This method is used to determine choked-flow conditions in the case where there is solid-body rotation at the throat for a range of swirl intensities with the ratio of the specific heats taking various values. Mass-flux coefficients and impulse functions are determined. Sonic surfaces, velocity profiles and other characteristics of interest are also presented. An approximate analysis valid for low swirl intensities is developed and analytical formulae are derived for most quantities of interest. The main conclusion of practical importance is that the introduction of swirl to compressible nozzle flows need not lead to a significant reduction in specific thrust. Further exploration of the possible effects of swirl on noise during the relatively short take-off and landing periods cannot therefore be ruled out on the grounds that swirl would lead to excessive thrust losses.
Analysis of High-Lift Wing Systems
Authors: Goradia Suresh H , Colwell Gene T
Published: July 2016

A method which can be used for the design of blown or unblown wing sections is described in this paper. A brief description of a variety of theoretical methods for computation of different fluid flow phenomena encountered on high-lift wing systems is presented. The most significant type of viscous flow - a confluent boundary layer flow, which is present on the upper surface of the flap, the vane and the main component of a high-lift system – is described and its importance to the performance of high-lift systems is illustrated. Results of computation of pressure distribution, boundary-layer characteristic, and lift coefficient for two-dimensional high-lift systems are compared with experimental data in order to establish the validity and limitations of the method.
Eddy Viscosity and Mixing Length from Measured Boundary Layer Developments
Authors: Galbraith R A McD , Head M R
Published: July 2016

To obtain profiles of shear stress and eddy viscosity, the boundary-layer equations in finite-difference form have been applied to published turbulent-boundary-layer developments measured in nominally two-dimensional conditions. In applying this procedure, measured velocity profiles have been represented by members of Thompson’s profile family. Except close to separation, these representations are very satisfactory, and derived shear-stress profiles are generally in good agreement with direct measurements. Various eddy-viscosity and mixing-length models are compared with the results of the analysis and are found in general to differ widely among themselves and from the present results. The widely used assumption,l= ky in the wall region, appears to be invalid.
Extension of the Wagner Torsion Bending Theory to Allow for General Systems of Loading
Authors: Megson T H G
Published: July 2016

This paper extends the Wagner torsion bending theory for open section tubes to general systems of applied loading. An illustrative example is also included involving the calculation of the twisting and direct stress distribution in an axially loaded Z-section column.
The Flow Over a “High” Aspect Ratio Gothic Wing at Supersonic Speeds
Authors: Narayan K Yegna
Published: July 2016

Results are presented of an experimental investigation on a non-conical wing which supports an attached shock wave over a region of the leading edge near the vertex and a detached shock elsewhere. The shock detachment point is determined from planform schlieren photographs of the flow field and discrepancies are shown to exist between this and the one calculated by applying the oblique shock equations normal to the leading edge. On a physical basis, it is argued that shock detachment has to obey the two-dimensional law normal to the leading edges. From this, and from other measurements on conical wings, it is thought that the planform schlieren technique may not be particularly satisfactory for detecting shock detachment. Surface pressure distributions are presented and are explained in terms of the flow over related delta wings which are identified as a vertex delta wing and a local delta wing. The forces acting on the wing are calculated and are shown to be very close to the two-dimensional wedge values over a wide range of incidence. In particular, it is shown that this wing, compared to one which supports a fully detached shock wave, generates a higher lift/(pressure drag) ratio at a given lift coefficient.
Numerical Computations of the Flow in Curved Ducts
Authors: Pratap V S , Spalding D B
Published: July 2016

The paper describes the application of a recently developed numerical scheme to the computation of the flow in a curved duct. The flow situation is partially-parabolic in nature as there are significant elliptic effects, which are transmitted through the pressure field. The turbulence model used comprises two differential equations, one for the kinetic energy of turbulence and the other for its dissipation rate. It has been observed that the predictions using the new procedure agree very satisfactorily with the experimental data. Comparisons are also made with the predictions of a fully-parabolic calculation procedure.
Blockage Effects on Two-dimensional Bluff Body Flow
Authors: Fackrell J E
Published: July 2016

The time mean flow past a two-dimensional bluff body in a wind-tunnel is modelled by an adaptation of the numerical free-streamline method of Bearman and Fackrell. Provided the base pressure and separation positions are specified in advance, the method allows the calculation of the flow field outside the wake and in particular of the pressures on the wetted surface of the body. Good agreement of the predicted pressures with experimental results is obtained for a flat plate, wedge and circular cylinder at various blockage ratios. In addition to predicting the confined flow, it is shown that a free-air base pressure can be simply deduced from the confined base pressure. With an assumption that the separation positions are unaffected by blockage, this allows the free-air flow field to be calculated. By using an analogy to Roshko’s Strouhal number, which has been found to be invariant under constraint, a free-air Strouhal number can also be deduced.