bluuebunny/crossref_metadata_2025_split huggingface dataset:
A Contribution to the Theory of Flow Stability in Multi-Stage Axial Compressors
Authors: Carter A. D. S. 
Published: July 2016

SummaryPrevious theories on the surging of axial compressors have been based on a quasi-static theory, whereas a finite rate of growth of the circulation around each blade must occur in practice. An examination of this factor is made in the paper, studying the stability with respect to small changes in speed instead of mass flow as in the normal approach. Effects of capacity are neglected. It is concluded that an instability occurs in the last stage of the compressor, even when that stage is itself unstalled, which could give rise to surge. It has been found necessary to introduce one empirical factor into the analysis but, when this is given a value compatible with other experimental and theoretical evidence, reasonably good agreement with experimental results is obtained.
The Estimation of Laminar Skin Friction, including the Effects of Distributed Suction
Authors: Curle N. 
Published: July 2016

SummaryStratford's analysis of the laminar boundary layer near separation uses two physical ideas. In the outer part of the boundary layer, where viscous effects are small, the development is given by the condition that the total head is constant along streamlines, apart from a second-order correction for viscosity. Near the wall, however, viscous forces must balance the pressure forces, and the profile adjusts itself accordingly. Quantitatively these ideas yield a simple formula for predicting separation, which has been found to be particularly accurate.In this paper it is indicated how the same approach may be used to yield the full distribution of skin friction along the wall. Further, the effects of suction may be incorporated into the method. Physically, suction affects the outer part of the boundary layer in that the streamlines are drawn towards the wall when suction is applied. At the wall, the balance between viscous and pressure forces is influenced by the momentum of the fluid which is sucked away. When these effects are accounted for quantitatively, the resulting formula for the skin friction is still very simple.Several examples are considered, and comparison is made with exact theory and with approximate results by other methods. It is indicated that the method has a useful range of validity.
Vibration of Rectangular Plates Point-Supported at the Corners
Authors: Cox Hugh L. , Boxer Jack 
Published: July 2016

SummaryThe fundamental frequencies of flexural vibration are determined for uniform isotropic rectangular plates that have free edges and pinpoint supports at the four corners. For the particular case of a square plate the lowest five frequencies and mode shapes have been determined. The second frequency is most unusual, since an infinite number of mode shapes exist with identical frequencies. Finite difference expressions, which simplify the treatment of the free boundaries for definite values of Poisson's ratio, are used in conjunction with extrapolation procedures to obtain the approximate solutions.
The Pressure Distribution on a Wing with a Subsonic Leading Edge in the Presence of Anti-symmetric Body Shaping
Authors: Jones J. G. 
Published: July 2016

SummaryThe pressure distribution on the wing of a centrally mounted wingbody combination due to anti-symmetrical body shaping (with respect to the wing plane) can be calculated in the case where the wing leading edge is supersonic by using the fact that the upper and lower halves of the flow field are independent and that each half can be treated by quasi-cylinder theory. When the leading edge is subsonic the anti-symmetric body shaping produces flow round the leading edge. This paper is concerned with wing pressure distributions including the effect of this flow round the leading edge.
A Theoretical Approach to the Aerodynamically Significant Properties of Roughness from Insects
Authors: Coleman W. S. 
Published: July 2016

SummaryIn Reference 3, attention is drawn to the difficulties of measuring the streamwise extent of the roughness from insects. The present paper deals with the problem theoretically for an aerofoil in two-dimensional, incompressible flow. A tentative approach to the determination of effective excrescence height downstream of the leading-edge zone is also advanced. The application of these investigations, in conjunction with the analysis from Ref. 3 regarding the critical conditions for premature transition, leads to estimates of the amount of significant roughness which are in good agreement with flight observation.
Further Comments on High-Lift Testing in Wind Tunnels with Particular Reference to Jet-Blowing Models
Authors: Butler S. F. J. , Williams J. 
Published: July 2016

SummaryThis paper discusses some of the special problems of wind-tunnel testing which arise with high-lift jet-blowing models, supplementing earlier comments. Further detailed remarks are made about recent developments on tunnel-wall interference, test rigs and methods of minimising constraints from air-feeds to models, and on general test and model design techniques.
The Behaviour of a Clamped Circular Plate in Compression
Authors: Sherbourne A. N. 
Published: July 2016

SummaryA theoretical solution is presented for the problem of the clamped circular plate loaded in uniform compression. The solution employs a numerical method programmed for a digital computer. Instead of solving the classical von Kármán large deflection equations, a step-by-step integration of the elastic differential equations of equilibrium is carried out until suitable boundary conditions are attained. The method is an extension of one developed earlier to explain the behaviour of the simply-supported plate.
The Axial Decay and Radial Spread of a Supersonic Jet Exhausting into Air at Rest
Authors: Frauenberger J. H. , Forbister J. G. 
Published: July 2016

SummaryThe distribution of total pressure, stagnation temperature and gas velocity is determined for the subsonic region of a supersonic jet emerging from a solid propellant rocket motor into air at rest. Measurements of Pitot pressures in the supersonic flow region have shown that the flow follows the axis of an inclined nozzle within the order of accuracy of the measurements. Nozzle cone angle, and probably the expansion ratio, affect the jet distribution significantly.
A Comparison of the Characteristic Equations in the Theory of Circular Cylindrical Shells
Authors: Houghton D. S. , Johns D. J. 
Published: July 2016

SummaryCharacteristic equations are derived for thin circular shells, based on various approximations to the linear elastic theory of small deformations. By representing the deformation in a Fourier series in the circumferential direction, the roots of these equations are computed for a range of the significant parameters and compared.
A Study of the Various Boundary Conditions for Electrical Analogue Solutions of the Extension and Flexure of Flat Plates
Authors: Redshaw S. C. , Rushton K. R. 
Published: July 2016

SummaryThe application of electrical analogue methods to the analysis of the extension and flexure of flat plates is reviewed and the difficulties encountered in the satisfaction of the various boundary conditions are discussed. A new method for treating certain boundary conditions and the operation of the electrical analogue is described. New experimental results for two cases which present great analytical difficulty, the flexure of a plate with a free edge and a plate supported on columns, are given.
The Effects of Heat Transfer on Laminar-Boundary-Layer Separation in Supersonic Flow
Authors: Curle N. 
Published: July 2016

SummaryBy generalising earlier work, an approximate method is derived for calculating compressible laminar boundary layers with an unfavourable pressure gradient, with the wall temperature and Prandtl number arbitrary and some allowance made for the viscosity-temperature law. The method merely requires two quadratures and uses tables of universal functions. On the basis of this method it is suggested that when the wall is at uniform temperature the viscosity-temperature law should make little difference to the results, and that, when the wall temperature varies spatially by a factor of two, the use of a linear relationship may introduce errors of order 4 per cent in the momentum thickness. It is further suggested that the effects of Prandtl number differing from unity will increase as either the Mach number is increased or the wall is cooled. These general conclusions are borne out by detailed numerical calculations in a few selected cases.
The Influence of the Coefficient of Friction on the Elastic Stress Concentration Factor for a Pin-Jointed Connection
Authors: Lambert T. H. , Brailey R. J. 
Published: July 2016

SummaryThe benefit to be obtained by using an interference fit between the pin and plate in a pin-jointed connection has already been established. An examination of the published results shows that some non-linearity occurs in the mechanism of load transference from the pin to the plate since, except at very high initial interference, doubling the load on the joint more than doubles the maximum shear stress in the plate. An examination of the stress-load relationship shows a distinct discontinuity, the load at which this discontinuity occurs being dependent upon both the initial interference and the coefficient of friction between the pin and the plate. It is shown that the results hitherto published correspond to a coefficient of friction between the pin and the plate of 0.3 and results for lower and higher coefficients are given.
The Deformational Behaviour of Low Aspect Ratio Multi-Web Wings
Authors: Gallagher R. H. , Rattinger I. 
Published: July 2016

SummaryResults of a study of the accuracy attainable from various approaches to low aspect ratio wing deformational analyses are described. Seven model multi-web wings, representing a restricted range of sweep angles, aspect ratios and other geometric factors, were tested for deflection influence coefficients; Part I gave experimental data. This paper describes, applies, and compares certain elementary and plate bending theories. A subsequent paper will deal with discrete element idealisations commonly employed in matrix structural analysis.
The Elastic Stress Concentration Factors in Shouldered Shafts
Authors: Allison I. M. 
Published: July 2016

The description of a photoelastic investigation, initiated by the Structures Committee of the Royal Aeronautical Society, into the elastic stress concentration factors associated with shouldered shafts subjected to various simple forms of loading is completed in this part of the paper. A general description of the manufacture of the models, the photoelastic techniques employed to evaluate the s.c.f. and the results of the tests on shouldered shafts subjected to torsion and to bending have been given in the previous two parts.The present paper includes the results of the tests on shafts subjected to axial load, together with details of a supplementary investigation into the limiting value of the s.c.f., for a particular shoulder radius, as the depth of the shoulder is increased to infinity. A summary of the general conclusions for all forms of loading is given at the end of the paper.
The Deformational Behaviour of Low Aspect Ratio Multi-Web Wings
Authors: Gallagher R. H. , Rattingerj I. 
Published: July 2016

SummaryResults of a study of the accuracy attainable from various approaches to low aspect ratio wing deformational analysis are described. Seven model multi-web wings, representing a restricted range of sweep angles, aspect ratios and other geometric factors, were tested for deflection influence coefficients and various analytical approaches were applied in the prediction of these results. Part I gave the experimental data; Part II dealt with analyses based on elementary and plate bending theories. This part describes and applies certain discrete element idealisations common to matrix structural analysis. The merits and shortcomings of the theories studied herein are reviewed and other promising approaches are discussed.
Decay of a Viscous Trailing Vortex
Authors: Dosanjh D. S. , Gasparek E. P. , Eskinazi S. 
Published: July 2016

SummaryAn experimental investigation of the viscous decay of a steady, three-dimensional, helical vortex is presented. The vortex was generated by a rectangular, symmetrical half aerofoil (N.A.C.A. 0009) of 10·5 in. span, 3 in. chord, cantilevered from the wall of the circular test section of a low speed wind tunnel. Only the local total head and flow directions were measured with a five-hole pressure sensitive probe at one to eight chord lengths behind the trailing edge of the aerofoil, and the radial, tangential and axial velocity distributions in the trailing vortex were derived. The static pressure variation in the vortex flow and the difficulties in its accurate measurement are discussed. All tests were performed at a Reynolds number based on the free-stream velocity and chord length of the aerofoil of 10,000.The various experimental velocity distributions in the vortex were in good agreement with a linearised, axi-symmetric, laminar, incompressible, viscous vortex due to Newman. The decay of velocity and geometry parameters, however, were found to be approximately eight to ten times faster than predicted by the analysis based on a laminar kinematic viscosity. It was also observed that the amount of circulation which actually rolled up in the trailing vortex was only about 58 per cent of that expected around the (N.A.C.A. 0009) aerofoil used for this investigation.
Heat Transfer Through a Compressible Laminar Boundary Layer
Authors: Curle N. 
Published: July 2016

SummaryA simple method is presented for calculating the heat transfer rate through a compressible laminar boundary layer. The temperature of the wall is assumed to be uniform, the viscosity being proportional to the absolute temperature with a ratio which may vary in an appropriate manner with position along the wall; the Prandtl number is arbitrary but greater than about 0·5.The method assumes, following Lighthill, that heat transfer rates are determined mainly by the form of the velocity field in regions close to the wall. After applying the Ulingworth-Stewartson transformation the velocity is expanded in powers of the distance Y normal to the wall, three terms being retained. The first term, proportional to the skin friction, is zero near to a position of boundary layer separation. The second term is proportional to the pressure gradient and also to the wall temperature. Accordingly it can become close to zero when the wall is sufficiently cooled. The third term becomes important only when the first two are simultaneously close to zero and is proportional to the heat transfer rate. Since the three terms cannot, in fact, ever be all zero at the same position they form a uniformly valid non-trivial approximation to the velocity close to the wall.With this velocity profile, and following similarity arguments first given by Liepmann, it is possible to reduce the integrated thermal energy equation to a first-order ordinary differential equation for the heat transfer rate, which is easily solved.A comparison with an accurate solution of Poots, for a particular pressure gradient and wall temperature, yields agreement to within 1 per cent at one third of the distance from leading edge to separation and 3 per cent at twice this distance, with the error rising to 16 per cent at separation where the heat transfer rate is, of course, very low. The modesty of this error is very encouraging.
Approximate Methods of Solving the Laminar Boundary-Layer Equations
Authors: Terrill R. M. 
Published: July 2016

SummaryCurie and Skan have modified the approximate methods of Thwaites and Stratford to predict separation properties of laminar boundary layers for flow over an impermeable surface. The work of Curie and Skan has been extended by Curle to include the estimation of laminar skin friction for the whole flow. The purpose of the following note is to compare the approximate methods of Curie and Skan and Curle with the numerical results given by the author for flow past a circular cylinder. It is found that there is remarkable agreement between these approximate methods and the exact numerical solutions. This indicates that these methods can be used widely, both on account of their simplicity and their accuracy.
Buckling of Tapered Rectangular Plates in Compression
Authors: Wittrick W. H. , Ellen C. H. 
Published: July 2016

SummaryThe problem considered is the buckling of a rectangular plate, tapered in thickness in a direction parallel to two sides, and uniformly compressed in that direction. Curves are presented showing the variation of buckling stress coefficient with the side ratio and the amount of taper, for each of two types of thickness variation, namely exponential and linear, and for each of two sets of boundary conditions, namely all edges simply-supported, and ends clamped and sides simply-supported. It is shown that, unlike the case of a uniform plate, there are no discontinuous changes of buckling mode.
Some Observations on the Compressive Buckling of Rectangular Plates
Authors: Wittrick W. H. 
Published: July 2016

SummaryThe problem considered is the buckling of a rectangular plate under uniaxial compression. The ends may be either both clamped, both simply-supported or a mixture of the two. The sides may be elastically restrained against both deflection and rotation with any stiffnesses whatsoever. It is shown that the curve of buckling stress coefficient versus side ratio can be deduced in a simple manner from that of a plate with the same end conditions but with both sides simply-supported, provided only that the buckling stress coefficient and wavelength for an infinite strip with the same side conditions are known. Some correlations between the curves for the three types of end condition are discussed. It is also shown that if, for some given side ratio, the buckling mode is known, then it is always possible to deduce the rate of change of buckling stress coefficient with side ratio at that point. The argument is based upon an assumption which is shown to give very accurate results in a wide range of cases.
Some Remarks on Glauert's General Interference Theorem
Authors: Garner H. C. 
Published: July 2016

SummaryAfter a retrospective discussion of Glauert's theorem concerning the wall interference on a small lifting aerofoil in a wind tunnel with mixed boundaries, a simple proof of the theorem is given for a tunnel having one rigid and one free boundary. It is shown that the theorem does not necessarily hold when there are two rigid walls and two free boundaries.
The Ludwieg Pressure-Tube Supersonic Wind Tunnel
Authors: Cable A. J. , Cox R. N. 
Published: July 2016

SummaryA description is given of a supersonic pressure-tube wind tunnel which has been constructed at A.R.D.E. This is a blow-down tunnel which uses as a reservoir a long tube filled with gas under pressure. A quasi-steady supersonic flow is achieved by expanding in a convergent-divergent nozzle the subsonic flow behind rarefaction waves which propagate down the tube when a diaphragm at the nozzle exit is burst. The theory of the operation of the tunnel is given and calculations are made of the boundary-layer growth along the tube. Pressure-time records were obtained in the tube, and a high speed camera was used to obtain pictures of the flow round a model. Measurements also included a pitot-tube traverse of the nozzle exit, and the Mach number distribution was determined from the ratio of the pitot to the stagnation pressure. Tests showed that, as predicted, a constant stagnation pressure was obtained ahead of the nozzle, and it is considered that a tunnel of this type would be a cheap and simple way of obtaining an intermittent tunnel with adequate running time for many types of test, and capable of operating at a Reynolds number of more than 107 per inch at a Mach number of about 3·5.
Compressive Buckling of Infinite Strips with Elastically Restrained Edges
Authors: Wittrick W. H. , Bodley W. E. 
Published: July 2016

SummaryIt has been shown in another paper that the relation between the compressive buckling stress coefficient and side ratio for a rectangular plate with the sides elastically restrained against deflection and rotation can be obtained from the corresponding curve for a plate with the same end conditions but with both sides simply-supported, provided only that the buckling stress coefficient and wavelength of the buckle are known for an infinite strip with the given side conditions. This paper presents these numerical values for infinite strips with a wide range of edge stiffnesses.
Flight Efficiency of Air-Breathing Engines
Authors: Bragg S. L. 
Published: July 2016

SummaryThe overall effective efficiency of a jet-propelled flight may be defined as the net useful work that is done in accelerating the vehicle, raising it to height and combating its drag, divided by the calorific value of the propellants used. The analysis presented here shows that for a single-stage vehicle this overall efficiency is equal to the integral of the fractionwith respect to each element of propellants used. In this expression u'is the effective jet velocity (allowing for jet deflection, this is √(1 + k2) times the actual exhaust velocity), υ the vehicle velocity, q the fuel/air ratio and H the calorific value of the fuel in dynamic units. The mean lift/drag ratio of the vehicle is taken as 1/k, so that the last three terms of the numerator represent the work lost in dragging, raising and accelerating each element of propellant to the range R, height h and flight velocity υ at which it is burnt. The fraction may therefore be considered as the efficiency with which that element of propellant is used with respect to the whole flight plan.For advanced air-breathing projects—by-pass engines up to aircraft speeds around Mach 2 and ramjets between Mach 4 and 9—the analysis shows that the sum of the υ-dependent terms in the efficiency factor is practically constant. The potential energy term is insignificant in the normally accepted flight corridor. Thus the overall efficiency with which propellants are consumed in covering a range R1 at flight speed υ js closely approximated to by the fractionand the useful work done by the mass mm of propellants isThe vehicle mass (including engine, payload, and so on) that can be dragged over the range R1 by unit mass of propellants can then be calculated.Although such simplified expressions cannot substitute for the final detailed analysis of a projected flight plan, it is hoped that they will prove more useful in preliminary analysis than the figures based entirely on cruise performance which have often been quoted in the past.
The Effect of the Boundary Layer on the Lift of Finite Wings
Authors: Squire L. C. 
Published: July 2016

SummaryThe vorticity shed behind a finite wing has been studied and a condition found for steady circulation. This condition is then combined with three-dimensional boundary layer theory to find the lift of a finite wing. An example shows that on a thin ellipsoid of aspect ratio 6·37 the lift as found by the present method is 2 per cent lower than the lift obtained using a sectional boundary layer approach.