bluuebunny/crossref_metadata_2025_split huggingface dataset:
The Fundamental Flexural Vibration of a Cantilever Beam of Rectangular Cross Section with Uniform Taper
Authors: Rao J. S. 
Published: July 2016

SummaryAn 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

SummaryCertain 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

SummaryThe 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.
Laminar Flow in a Uniformly Porous Channel with Large Injection
Authors: Terrill R. M. 
Published: July 2016

SummaryThe 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

SummaryA 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.
The Mixing of Turbulent Supersonic Fuel-Air Streams
Authors: Forde J. M. 
Published: July 2016

SummaryAn 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

SummaryThe 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

SummaryJet 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

SummaryThis 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

SummaryA 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

SummaryA 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

SummaryBy 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

SummaryThis 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

SummaryExperiments 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

SummaryA 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

SummaryA 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

SummaryThe 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

SummaryIn 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

SummaryA 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

SummaryThe 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.
On the Flow Along Swept Leading Edges
Authors: Gaster M. 
Published: July 2016

SummaryFlight 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

SummaryA 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

SummaryA 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

SummaryAt 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

SummaryA 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

SummaryThis 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

SummaryThe 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

SummaryThe 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

SummaryThis 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.