bluuebunny/crossref_metadata_2025 huggingface dataset:
Approximations in Complicated Critical Buckling and Free Vibration Analyses of Prismatic Plate Structures
Authors: Williams F W
Published: July 2016

An exact method has recently been presented for computing the critical buckling loads, or the natural frequencies of vibration, of prismatic assemblies of rigidly inter-connected, thin, flat, rectangular plates. The plates can carry uniform in-plane longitudinal, transverse and shear stresses and may be isotropic or anisotropic, with the elastic coupling stiffness matrix B = 0. This method can be used even if some of the plates have curved cross sections, are non-uniformly longitudinally compressed or, in certain circumstances, have B ≠ 0. However, approximations are then involved when representing the plates. Results presented herein indicate that good answers can be obtained despite these approximations.
The Interaction of a Sonic Jet with a Surrounding Subsonic Stream
Authors: Stow Peter
Published: July 2016

An investigation has been made into the effects of a surrounding stream on an “under-expanded” sonic jet. Experiments were performed for different Mach numbers of the surrounding stream and for different ratios of the static pressure in the jet at the exit to that in the external stream. It was found that the base-flow region produced at the exit of the nozzle, due to the finite thickness of the nozzle walls, had a significant effect on the flow field. Schlieren photographs suggest that the surrounding stream has little effect on the first cell of the jet but that the second cell is, in general, lengthened when a surrounding stream is present. In most cases it is longer than the first cell. Conditions at the beginning of the second cell are probably different from those at the beginning of the first cell and it is suggested that the lengthening of the second cell is mainly a secondary effect due to the alteration in the velocity distribution of the first cell caused by the external stream. A theoretical investigation was made, using an inviscid model of the flow. The flows in the jet and the stream were calculated independently and the jet boundary determined using an iterative procedure. For the free jet, a study was made of the various approximations to the sonic exit conditions and into the errors involved in the numerical solution of the supersonic region. A comparison of the calculated length of the first cell of the jet with the experimental results showed reasonable agreement for the free jet. For a jet with a surrounding stream the inviscid model predicted that the length would be significantly increased as the Mach number of the stream was increased from zero; this effect was not found in the experiments. A modification to the model is suggested and it has been found that, using this, the results are in better agreement with the experiments.
Design of Supercritical Aerofoils
Authors: Lock R C , Fulker J L
Published: July 2016

A survey is given of experimental results on a series of aerofoils designed in recent years, first at the National Physical Laboratory and later at the Royal Aircraft Establishment, with the intention of operating at relatively high subsonic Mach numbers (around 0.8) with, on the upper surface, a large extent of supercritical flow, terminated by a weak shock wave. The paper describes the design of a basic aerofoil, together with some modifications to it which were successful in improving its performance at both high and low speeds. It is shown that the best of these aerofoils, with thickness/chord ratio 0.105, has a drag rise Mach number of 0.80 at a lift coefficient of 0.5, thus comparing favourably in this respect with other published examples; its maximum lift coefficient at low speeds, 1.2, is also satisfactory for an aerofoil of this thickness. In a final section some comparisons are given between these experimental results and some theoretical calculations by the finite-difference method of Garabedian and Korn, including a partial allowance for viscous effects. It is concluded that, although reasonable overall agreement with experiment is often obtained, further improvements in this theory are needed before it can be used with confidence for practical purposes.
Incidence Stability of Space Shuttles During Re-Entry
Authors: Arho R , Virtanen S
Published: July 2016

The equations of motion of a vehicle entering the earth’s atmosphere (space shuttle) are expanded to give the incidence oscillation equation. The stability conditions for small free oscillations are deduced. These stability conditions apply equally to short-period and long-period oscillations. A special case of critical damping is investigated and more explicit stability conditions are derived for that case.
The Effects of Recessed Lower Surface Shape on the Lift and Drag of Conical Wings at High Incidence and High Mach Number
Authors: Squire L C
Published: July 2016

For lifting re-entry there may be advantages in using wings which give as high a lift coefficient as possible at the design value of the lift/drag ratio. This paper presents the results of an experimental and theoretical study of wings with recessed lower surfaces designed to give high values of CL. The calculations show that a wide range of wing shapes can be found that give values of CL which are much larger than those on a flat wing with the same lift/drag ratio.
The Evaluation of an Integral Equation Method for Two-Dimensional Shock-Free Flows
Authors: Nixon D , Patel J
Published: July 2016

The numerical aspects of the integral equation method developed by Nixon and Hancock for two-dimensional steady shock-free flow have been rationalised; this numerically refined method is evaluated by calculating the pressure distribution around a wide range of aerofoils. These test cases include aerofoils in supercritical shock-free flow as well as subcritical flow and exact solutions are available for comparison. The computational time in the present method is significantly less than that required by the exact methods. The present results compare satisfactorily with the exact results.
The Transformation of Aerodynamic Stability Derivatives by Symbolic Mathematical Computation
Authors: Howard James C
Published: July 2016

The formulation of mathematical models of aeronautical systems for simulation or other purposes, involves the transformation of aerodynamic stability derivatives. It is shown that these derivatives transform like the components of a second order tensor having one index of covariance and one index of contravariance. Moreover, due to the equivalence of covariant and contravariant transformations in orthogonal Cartesian systems of coordinates, the transformations can be treated as doubly covariant or doubly contravariant, if this simplifies the formulation. It is shown that the tensor properties of these derivatives can be used to facilitate their transformation by symbolic mathematical computation, and the use of digital computers equipped with formula manipulation compilers. When the tensor transformations are mechanised in the manner described, man-hours are saved and the errors to which human operators are prone can be avoided.
The Three-Shock Confluence Problem for Normally Impinging, Overexpanded Jets
Authors: Kalghatgi G T , Hunt B L
Published: July 2016

In this paper, a systematic study of the triple shock confluence point is presented for the case of an overexpanded jet which impinges on a perpendicular flat plate at small displacements from the nozzle. The jet is uniform upstream of the free jet shock wave. Non-homentropic effects are taken into account and lead to modifications to the accepted flow patterns at a triple point for the case of strong incident shock waves. Where more than one thermodynamically possible solution to the triple point equations exists, the alternative solutions are re-examined, taking non-homentropic effects into consideration. Some discussion of the possibility of infinite shock curvatures is also included. Qualitative flow patterns of the impinging flow are constructed, based on the triple point solutions and the known boundary conditions. The interesting cases where the tail shock flow is supersonic are given particular attention and two possible flow patterns are distinguished. Finally, some experimental evidence in the form of schlieren pictures is presented. Although not conclusive, this evidence supports the theory.
Inviscid Hypersonic Source Flow, over Slender Power-Law Bodies
Authors: Yasuhara M , Watanabe S
Published: July 2016

Hypersonic small-disturbance theory is applied to the source flow over power-law slender bodies with conical or wedge type asymptote. The results for a point source flow with λ=2 over power-law cones of revolution show that the dominating equations in the first and second approximations are essentially the same as the ones for the parallel flow over power-law bodies of revolution. In the special case of a cone, results of a source flow and of a parallel flow are compared and it is shown that the surface pressure in a source flow at the nose is the same as the constant cone pressure in a parallel flow, but systematically decreases in the rear part. This is confirmed by comparison with a shock tunnel experiment.
Hole Reinforcement in Isotropic and Orthotropic Plates Using Filament-wound Discs
Authors: McKenzie D O , Webber J P H
Published: July 2016

A theoretical and experimental study is made of the stresses and strains around circular holes in plates reinforced with carbon fibre filament-wound discs. An analytical solution is given for infinite isotropic plates subjected to uniform tension, but for orthotropic carbon fibre plates the finite-element displacement method of analysis is used. The filament-wound discs are found to be efficient in reducing the stresses around the holes with the principal stresses being taken, in the main, by the strong fibres. There is reasonable agreement with the experimental results for the uniform tension cases, but results from tests on bolt-loaded holes do not correlate as well with theory.
A New Exact Solution for Compressible Swirling Flow
Authors: Greitzer E M
Published: July 2016

An exact analytic solution is presented for axisymmetric compressible swirling flow in an annular passage. The solution is given in terms of simple expressions for the streamline shapes. The results can be used to describe an irrotational flow as well as a class of rotational flows in annular passages, such as might be encountered in turbomachinery components. The solution could be applied as a test case for numerical computations of flows in turbomachines.
Flow Regimes over Delta Wings at Supersonic and Hypersonic Speeds
Authors: Squire L C
Published: July 2016

This paper concerns the boundaries between flow regimes for sharp-edged delta wings in supersonic flow and the relation of some predictions of thin-shock-layer theory to these boundaries. In particular, it is shown that the theory predicts that the attachment lines on the lower surface of a thin delta wing at supersonic speeds suddenly jump from just inboard of the leading edges to the centre line in certain flight conditions. In general there is close agreement between the conditions for this jump and the flight conditions corresponding to the change-over from attached flow to the leading-edge separation on the upper surface. Since the movement of the attachment lines on the lower surface must change the position of the sonic line and the nature of the expansion around the edge, it is suggested that the two phenomena are directly related. Thus thin-shock-layer theory can be used to establish the boundaries of the various flow regimes for a wide range of Mach number, incidence and wing sweep. The theory can also be used to predict the effects of wing thickness on leading-edge separation, but here the experimental data is very sparse and somewhat contradictory, so the value of the prediction in the case of thickness requires further investigation.
Some Notes on Coleman Instability
Authors: Simpson A
Published: July 2016

The equations of motion of a highly idealised model of a helicopter with a simple lag-hinged rotor are derived by Lagrange’s method. It is shown that the transformed equations governing Coleman instability (ground resonance) have a regular form involving wholly symmetric and skew-symmetric matrices. The work input to the unstable motions derives wholly from the torque applied to the rotor by the engine, but the torque equation is superfluous as far as the eigenvalues are concerned. Approximate stability criteria show that chassis and lag dampingsper seare destabilising relative to the undamped reference condition and can lead to a substantial lowering of the critical rotor speed for instability onset. A necessary condition for instability (dynamic) is that two eigenvalues of thestiffnessmatrix are simultaneously negative.
Supersonic Flow Past a Slender Delta Wing. An Experimental Investigation Covering the Incidence Range –5° ≤ α ≤ 50°
Authors: Richards I C
Published: July 2016

A detailed survey of a delta wing of 70° sweep has been performed at M = 2.5. The measurements include upper- and lower-surface pressure distributions, schlieren photographs, vapour-screen photographs and surface oil-flow visualisation. The results have been compared with thin-shock-layer theory and various other predictions.
The Origin and Nature of the Lift Force on the Leeward of Two Bluff Bodies
Authors: Price S J
Published: July 2016

This paper deals with the force coefficients on the leeward of two bluff bodies, in particular with the origin and nature of the lift force. Initially a general description of the characteristics of the force coefficients, plus the effect of parameters such as free-stream turbulence and surface roughness in the form of stranding, is given.

A resume of all the known suggestions for the origin of the lift force is listed and a series of experiments, attempting to test these suggestions using simple methods, is described. These methods consist mainly of force measurement, involving force measurement on the leeward conductor using different shapes for the leeward and windward bodies. However, static pressure tapping and flow visualisation are also employed to a small degree.

It is shown that none of the suggestions gives a satisfactory explanation for the origin of the lift force. However, several interesting points were noted; for instance the dependence of the lift profiles for the leeward body on its own characteristics in the wake and not particularly on the wake characteristics. Hence it is shown that the use of wake parameters, measured without the presence of the leeward body when attempting to assess the forces thereon, is an over-simplification of the situation as far as lift is concerned while appearing to work quite well for drag.
The Occurrence of Stagnation Bubbles in Supersonic Jet Impingement Flows
Authors: Kalghatgi G T , Hunt B L
Published: July 2016

This paper reports an experimental investigation into the stagnation bubbles found in the shock layers of some supersonic jets impinging on perpendicular flat plates at small nozzle-to-plate distances. The experiments used twelve contoured nozzles within the Mach number range 1.42 to 2.83. Surface pressures were measured on the plate and free-jet pitot pressure distributions were obtained at the level of the centre of the plate shock. Schlieren pictures were taken of both impinging and free jets. It was found that the bubbles result from the interaction of the plate shock with very weak shock waves which are produced in the jet either by small imperfections in the nozzle wall or by slight inaccuracies in the design or production of the nozzle contour. The bubbles can be eliminated by suitable improvements to the nozzle. Other anomalous flows produced by shock interactions are described and explanations offered. It is shown that the bubbles sometimes encountered at close plate spacings with conical nozzles are also due to shock waves. However, for wide-angled nozzles, internal shocks can be an inherent part of the flow from the nozzle and the bubbles which they produce are thus an inherent part of the impingement flow. From physical arguments concerning the main factors involved in producing a bubble, a parameter is constructed whose values are shown to be a good criterion for whether a bubble occurs or not.
Supersonic Cone with Surface Blowing
Authors: Carafoli E , Berbente C
Published: July 2016

The velocity field around a circular cone in supersonic flow is determined by considering fluid injection and suction through the porous wall of the body. By using a new method of linearisation of the equations of motion, analytical formulae are obtained which yield almost exact results, as compared with numerical calculations. In addition, the method proposed suggests new problems related to fluid injection and suction which are important for practical applications.
Post-Buckling Behaviour of Simply-Supported Cross-Ply Rectangular Plates
Authors: Prabhakara M K
Published: July 2016

An analysis is presented for the post-buckling behaviour of simply-supported, laminated cross-ply rectangular plates subjected to biaxial compression. The solution to von Kármán-type large deflection equations of the plate is expressed as a double sine series for the transverse deflection and a double series of clamped-clamped beam functions for the force function. All the boundary conditions, including those involving the normal bending moment at the edges, are satisfied exactly. The series solution is found to converge rapidly. Using only the first few terms in the series, numerical results for square graphite-epoxy unsymmetric laminates under uniaxial compression is presented graphically.
The Confluence of Three Shock Waves in Three-Dimensional Flow
Authors: Hunt B.L. , Lamont P.J.
Published: July 2016

This paper presents a theoretical study of the confluence of three shock waves in three-dimensional flow. A suitable transformation reduces the problem to that of a planar confluence point for which the theory already exists. Expressions relating the two flows are developed and successfully applied to an experimentally observed intersection. It is found that the three-dimensional flow can have an entirely supersonic downstream flow, unlike its two-dimensional counterpart, and that the flows in the two downstream regions need not be parallel.
Effects of Stream Turbulence on Free Shear Flows
Authors: Patel Rajni P.
Published: July 2016

Recently attention has been given to the effects of the stream turbulence on the characteristics of the turbulent boundary layers and the turbulent shear flows. For the boundary layers considerable information on the effects of the stream turbulence is available but for the shear flows it is limited. This paper describes an experimental investigation for the effects of stream turbulence on the development of an asymmetric jet and a plane mixing layer. It is shown that the characteristics of these flows are considerably affected by the stream turbulence but for the measurements in the plane mixing layers at large downstream distances the influence of the stream turbulence is negligible provided the intensities are less than 0.6%. For the plane mixing layer the results show that the flow characteristics are not affected significantly by the initial boundary layers, the acoustic disturbances and the boundary conditions imposed by the end plates.
The Attachment of a Ventilated Plane Jet to an Inclined Plane Wall
Authors: Marsters G.F.
Published: July 2016

The behaviour of a plane jet issuing in the neighbourhood of a plane wall has been studied experimentally. Such arrangements may find application in jet augmented flaps for STOL aircraft development. The essential features of this configuration are the gap between the wall and the jet nozzle, permitting entrainment of secondary flow, and the inclination of the plane wall with respect to the nozzle axis.

Measurements of velocity profiles, wall static pressure distributions and turbulence intensities reveal the presence of extensive regions of low pressure over the wall, strong pressure gradients resulting in the highly curved flow, a fair degree of self-preservation of the mean velocities, but no particularly unusual features observed in the turbulence quantities. The size of the gap, the wall angle and the wall length all influence the reattachment location, and limits of gap, angle and length for which reattachment occurs are shown. The sub-ambient static pressure regions give rise to significant forces on the wall; these forces are primarily due to the entrainment feature.
Buckling of Simply Supported Orthotropic Skew Plates
Authors: Kennedy J.B. , Prabhakara M.K.
Published: July 2016

A double Fourier series solution is presented for the buckling of simply supported orthotropic and isotropic skew plates, subjected to in-plane compressive and shear edge loads. All the boundary conditions, including the vanishing of the normal bending moment along the edges, are satisfied. Numerical results, suitable for design purposes, are presented graphically for a number of independent parameters such as skew angle, ratio of flexural rigidities and aspect ratio. The results show that the buckling strength is substantially effected by the skew angle, and to a lesser extent, by the ratio of the flexural rigidities and aspect ratio. In contrast with positive shear edge loads, which tend to decrease the skew angle, negative shear edge loads appear to reduce the buckling strength of orthotropic and isotropic skew plates.
Some Low Speed Experimental Results on the Effects of Swirl and Velocity Distribution on an Axi-Symmetric Jet
Authors: Young A.D. , Rao K.N.
Published: July 2016

The flows resulting from a number of different methods for producing swirl in an axi-symmetric jet have been investigated. These methods include upstream vanes, tangential injection, a twisted plastic sheet and rotation of part of the jet pipe. Tests were also made with the first two types of swirl device in association with a radial distribution of axial velocity in the jet which had a minimum on the axis produced by a suitably graded wire grid or web inserted in the jet pipe. The measurements covered the mean (axial and swirl) velocity distributions as well as the main turbulence quantities at various stations downstream of the jet exit. It was found that the swirl considerably enhanced the rate of growth of the mixing region as previous workers have shown, but there was a significant reduction of this enhancement when the axial velocity increased from the centre outwards. This is in accordance with current concepts on the stability of curved turbulent shear flows.
Hypersonic Flow Over Conical Wing-Body Combinations
Authors: Hillier R.
Published: July 2016

This paper shows how thin shock layer theory may be applied to wing-body combinations and also to yawed wings of caret and diamond section. The common feature of these cases is the interaction of the crossflow with the body slope discontinuity and the manner in which the resulting disturbances propagate through the shock layer. Practical computation of surface pressures is straightforward and comparison with experiment appears to be fairly good for the limited results available.
The Effect of Chordwise Flexibility on the Lift of a Rapidly Accelerated Airfoil
Authors: Katz J. , Weihs D.
Published: July 2016

The effects of finite chordwise flexibility on the development of lift on a rapidly started airfoil are studied. This is a generalization of the so-called Wagner problem of unsteady aerodynamics. It is found that the lift varies with time in a non-monotonous fashion, including more than one extremum. The lift at large times is found to be lower, the more flexible the foil. Changes in the wake vortex sheet are also discussed.
Effect of Base Cavities on the Aerodynamic Drag of an Axisymmetric Cylinder
Authors: Morel Thomas
Published: July 2016

Base cavities (hollow extensions mounted behind the rear end of a bluff body) are known to reduce substantially the aerodynamic drag of two-dimensional bodies. For axisymmetric bodies their effect is not well established, and the objective of this work was to assess their drag-reducing potential. Experiments were performed using three different types of base cavities, one solid walled and two ventilated, each with six different depths ranging from 0.1 to 0.9 body diameters. All three types of cavities reduced the body drag for small cavity depths, with a maximum drag coefficient reduction of 0.027 being obtained with a ventilated cavity 0.2 diameters deep. The reductions are an order of magnitude lower than those reported for two-dimensional bodies, but are achieved with a much shorter cavity depth. Although the ventilated cavities had a beneficial effect for small depths, at large depths (greater than 0.5 diameters) they had an opposite effect – a very large drag increase. The cause of this increase is as yet not understood. Hot-wire investigation revealed that base cavities suppress wake periodicity. For cavities of small depth this correlated with a reduction in drag, but for large cavity depths the trends of the intensity of the periodic motion and of drag were not always the same.
The Fibre Composite Helicopter Blade
Authors: Mansfield E.H. , Sobey A.J.
Published: July 2016

In Part 1 expressions are derived for the coupled torsional, extensional and flexural stiffnesses of a fibre composite tube, such as a helicopter blade, which is subjected to torsion, longitudinal tension, chordwise and flapping bending moments and shear. The theory is an extension of Batho-Bredt engineering analysis and is valid for a cylindrical tube of arbitrary cross-section with an arbitrary circumferential distribution of fibre composite plies. Particular attention is paid to the coupling effects in which an asymmetric fibre lay-up results in a twisting of the tube under bending and/or tension. Consideration is also given to the influence on the stiffness characteristics of an initial twist in the tube.

In Part 2 the analysis of Part 1 is developed numerically for tubes representative of GFRP blades. Static and dynamic aspects are considered which pave the way for aeroelastic tailoring studies of such blades.
Shockwave and Boundary Layer Interaction in the Presence of an Expansion Corner
Authors: Chew Y.T.
Published: July 2016

An investigation has been carried out to examine one aspect of supersonic jet-engine inlet flow, namely shock-wave and boundary-layer interaction in the presence of an expansion corner. The experiment was undertaken at Mach numbers of 1.8 and 2.5. The local Reynolds number per metre varied from 2.79 to 3.13 × 107 for M = 1.8 and from 4.20 to 6.4-8 × 107 for M = 2.5. Adiabatic turbulent boundary layers of about 6 mm thick on an expansion-corner plate were disturbed at different streamwise positions by oblique shocks with deflection angles of 4°, 6° and 8°. The pressure distributions, wave patterns and the extent of the separation regions were strongly influenced by the presence of the expansion corner, especially when the shock impingement positions were upstream of the corner. The pressure rise induced by the incident shock began to decrease in level when the shock impingement position was about 3-4 boundary-layer thicknesses upstream of the corner. As the incident shock moved towards the corner, the pressure rise and the extent of the separation region decreased. When the shock impingement position was at the corner, the reflected shock was effectively neutralised by the Prandtl-Meyer expansion; especially when the deflection angle of incident shock matched that of the expansion corner. The three dimensionality of the incident shock and separation region is due to the interactions between the glancing oblique incident shock and the tunnel’s sidewall boundary layers.
Transition in the Infinite Swept Attachment Line Boundary Layer
Authors: Poll D.I.A.
Published: July 2016

The transition behaviour of the boundary layer which is formed along an infinite swept attachment line has been studied experimentally. Circular trip wires and turbulent flat plate boundary layers have been used as sources of disturbance and the range of parameters covered has been such that the results are directly applicable to full scale flight conditions. Simple criteria have been deduced which allow the state of the boundary layer to be determined for given geometric and free stream properties. Sample calculations for typical swept wing configurations suggest that the majority of civil aircraft will have turbulent attachment lines in the cruise and that subsequent relaminarisation in regions of favourable pressure gradient is unlikely.
A Simplified Theory of Oscillating Aerofoils in Transonic Flow: Review and Extension
Authors: Dowell E.H.
Published: July 2016

Significant new results are presented to show to what extent a simplified theory for transonic flow may be used. Solutions are obtained by classical techniques and compared with experiment. Results are given for two-dimensional and three-dimensional, steady and unsteady flow. The effects of flow separation and improvements in Bernoulli’s equation and the surface boundary condition are also briefly discussed.
The Influence of Aspect Ratio on Incompressible, Turbulent Flows From Rectangular Slots
Authors: Marsters G.F. , Fotheringham J.
Published: July 2016

Jets issuing from rectangular slots cut in thin plates exhibit some unusual features, including unequal spreading rates in the spanwise and transverse directions, the appearance of velocity peaks near the “ends” of the jet and changing rates of centreline velocity decay in the downstream direction. This study examines the effects of aspect ratio on such flows. The flow field has been investigated using both total head tubes and hot wire anemometry. The results are presented in the form of three-dimensional plots of total pressure and contour maps of constant velocity, streamwise turbulence intensity and the Reynolds shear stresses. The decay of mean velocity and stream-wise turbulence intensity along the centreline are presented. The rates of spanwise spreading and the location of the velocity peaks at various downstream stations are discussed. If the aspect ratio is small enough, spanwise peaks in the mean velocity distribution are suppressed.
Measurements of Dynamic Stability Derivatives of Hyperballistic and Conic Shapes at M = 6.85
Authors: Qasrawi A.M.S. , East R.A.
Published: July 2016

Experimental measurement of the pitching stability derivatives and of AGARD hyperballistic standard models HB1 and HB2, a hemisphere-cylinder double flared configuration designated HBS and three 10° semi angle cones of bluntness ratios 0.0, 0.2 and 0.4 are reported. Data were obtained at a Mach number of 6.85 in a short duration light piston tunnel using the small amplitude free oscillation technique. The tests were conducted at Reynolds numbers from 0.2 × 106 to 0.85 × 106, based on centre-body diameter, for the hyperballistic shapes and from 1.45 × 1016 to 2.17 × 106, based on base diameter, for the conical shapes. The mean angle of attack was varied from 0 to 17.0 degrees and the frequency parameter from 0.0020 to 0.0043 for the hyperballistic shapes and from 0.0018 to 0.0092 for the cones. All models tested were found to be dynamically stable for all positions of the axis of oscillation considered. The significant observed non linear variations of the damping derivative with angle of attack for the 0.2 and 0.4 bluntness cones and the HB2 shape could be partially accounted for qualitatively by boundary layer transition induced effects. The variation of the derivatives with angle of attack for the pointed cone were consistent with a fully turbulent boundary layer, whereas it was probable that for the HB1 and HBS models the boundary layer remained laminar throughout. Variation of the frequency parameter resulted in no significant effect on the measured stability derivatives.
On the Decay of Laminar Jets in Ambient Streams
Authors: Middleton D.
Published: July 2016

Earlier analysis, Middleton, of the laminar discharge of a ‘strong’ incompressible jet, due to a line or point source of momentum, into an unbounded co-flowing stream of the same density, is extended to the case of plane and round ‘weak’ jets the velocity in which only slightly exceeds the ambient velocity. In addition to recovering Goldstein’s solutions for ‘wake-like’ flows, use of the momentum integral equation provides approximate relationships for the decay of the centre velocities from the strong to the weak situations. Comparison is made with Wygnanski’s perturbation approach, suitably extended, and it is concluded that for the plane jet case, for which the agreement is better, the curve for the centre-plane velocity is correct to within about 12% throughout its range. The present approach is applicable to any flow for which a similarity solution exists as a first order solution, and is especially suitable when two such solutions exist for large and small values of an appropriate parameter. Its use also throws light on the form to be adopted for a perturbation expansion.
Part I: Chordwise Distribution of Fluctuating Pressure
Authors: Wilkinson R.H.
Published: July 2016

The fluctuating loading on a cylindrical bluff body due to vortex shedding increases if the body is capable of vibration. This is a result of amplification of the fluctuating pressures around a two-dimensional section of the body together with an improvement of the spanwise correlation of the vortex shedding. Measurement of the fluctuating forces on the cylinder during this process gives no guide as to the relative magnitude of these effects. In this paper, root mean square fluctuating pressure distributions and pressure correlations across a chord are presented for a square cylinder with front face normal to the approach flow whilst stationary and during forced vibration. The fluctuating lift coefficient for a two-dimensional section of the cylinder and its maximum amplification during vibration are calculated.
Evaluation of Two-Dimensional Subsonic Oscillatory Airforce Coefficients and Loading Distributions
Authors: Salmond Deborah J.
Published: July 2016

A method is described for calculating numerically the aerodynamic stiffness and damping coefficients and loading distributions for a two-dimensional thin aerofoil oscillating harmonically in subsonic flow, from the Possio Integral Equation by approximating the loading by a finite series of basis functions. Sample loading distributions obtained by using the method are presented for a Mach number of 0.9 and a frequency parameter of 0.4.
Two-Dimensional Flow at Right Angles to a Flexible Membrane
Authors: Newman B.G. , Low H.T.
Published: July 2016

Incompressible flow perpendicular to a flexible, impervious membrane has been studied for two-dimensional conditions. The membrane was mounted on relatively thin supports spaced c apart. Measurements of drag, base pressure and the frequency of membrane oscillation are presented for various lengths ℓ, and for two densities, of membrane. These parameters are related to one another theoretically and in particular Bearman′s universal correlation for Strouhal number agrees with the experimental results. It is found that for values of< 0.50 the drag is independent of membrane density. The drag decreases at larger values ofand this is related to a periodic reattachment of the separated flow to the back of the membrane. For a given ℓ the drag is greatest whenis very small and the membrane is almost flat.
Streamwise Corners with Curvature Independent of Streamwise Distance
Authors: Barclay W.H. , Ridha A.H.
Published: July 2016

A two parameter approximate solution is presented for the flow along a streamwise corner having large, possibly infinite, curvature in its region of transition between the two quarter infinite planes which form its asymptotes. The two parameters are the angle between the asymptotes and a quantity proportional to the ratio of the local two-dimensional boundary layer thickness and the radius of curvature of the corner at the symmetry plane. Relative to the corner of infinite curvature (sharp corner) a finite curvature always tends to modify the solution towards that for a flat plate. This implies that for corner angles less than 180° the corner layer thickness in the symmetry plane is less than that for the sharp corner of the same angle and the shear stress is higher, the converse holding for angles greater than 180°. The flow in planes normal to the free stream direction is rather complex and typically there is a reversal in its direction within the symmetry plane.
The Effect of Disturbed Turbulence Structure on the Preston-Tube Method of Measuring Wall Shear Stress
Authors: Kiske S. , Ram V. Vasanta , Pfarr K.
Published: July 2016

The subject of this paper is the effect of a disturbance to the turbulence structure of the flow on the reading of a Preston tube used to measure wall shear stress. Two kinds of disturbance have been studied experimentally, one caused by reattachment and the other by an abrupt change in wall roughness. The apparent wall shear stress measured by the Preston tube both in channel and boundary layer flows with these kinds of disturbance has been compared with the wall shear stress measured by a sublayer fence. The results give an idea of the magnitude of the error that is likely to arise when the Preston tube is used in a flow with disturbed turbulence structure.
Characteristics of Poiseuille Flow in a Divided Channel
Authors: Zamir M. , Camiletti S.E.
Published: July 2016

The problem considered is that of Poiseuille flow in a two dimensional channel impinging on a flat plate placed symmetrically between the two channel walls so as to bifurcate the channel into two equal branches. The results of a theoretical study of the problem are presented and analysed to portray in full details the characteristics of the flow before and after the bifurcation point. In particular the effects of the flow divider on the flow near the channel walls and the effects of the channel walls on the flow near the flow divider are examined.
Pitch/Yaw Coupling Due to Roll of an Axisymmetric Missile with Autopilot
Authors: Fortescue P.W.
Published: July 2016

The types of pitch/yaw coupling which may result from roll motion of a conventional tail-controlled cartesian missile have been categorised. The consequences of the couplings upon:

(a)

the response to a step demand for manoeuvre, and

(b)

the decay of error in a beam-rider system are presented.

Potentially the most damaging forms of coupling are due to

(a)

mis-match of the Invariant Frames of airframe and servos,

(b)

angular mismatch between parts of the system, and

(c)

gyroscopic coupling.
Asymmetric Vortex Formation from Cones at Incidence – a Simple Inviscid Model
Authors: Dyer D.E. , Fiddes S.P. , Smith J.H.B.
Published: July 2016

An inviscid model, originally proposed by Bryson to describe the formation of laterally-symmetric vortices above bodies of revolution at large angles of incidence, is extended to describe flows without lateral symmetry. Each vortex is represented by a single line-vortex and conditions of cross-flow stagnation are applied at the postulated separation lines. The transverse component of the force acting on each vortex is balanced by an equal and opposite force acting on the cut connecting it to the adjacent separation line. It is shown that this model allows asymmetrical vortices to form in the flow over slender circular cones even when the separation lines are disposed symmetrically.
Swirl Characteristics of an S-Shaped Air Intake with both Horizontal and Vertical Offsets
Authors: Guo R.W. , Seddon J.
Published: July 2016

As part of a series of investigations of the swirl in S-ducts, the present paper gives the results of tests on a duct with both horizontal and vertical offsets, for comparison with earlier work on ducts with horizontal offset only. Results obtained bear a similarity to those of Reference 2, for which the duct had the same cross-sectional shapes and areas, but the addition of a vertical offset magnifies the resultant swirl considerably. As before, the swirl is found to be sensitive to entry conditions, in that a solid spoiler, blocking off 15% of entry width from the inside wall, reverses the sense of the final swirl. Taken overall, the results throw additional light on the nature of the swirl problem. A particularly interesting and potentially important correlation is obtained between the final swirl (in magnitude and sense of rotation) and a pressure difference between the top and bottom walls of the duct, taken in the end plane of the second bend.
On the Energy Characteristics of the Aerodynamic Matrix and the Relationship to Possible Flutter
Authors: Jones J.G.
Published: July 2016

The problem of energy transfer between an airstream and a wing in sinusoidal motion has been investigated by a series of authors beginning with Frazer who in 1939 considered the power input required to maintain forced oscillations of an aeroplane wing in flight. More recently Nissim introduced an ‘aerodynamic energy concept’ as the basis for the design of active control systems for flutter suppression. In this paper the author reconsiders the energy characteristics of the aerodynamic matrix in terms of the network concepts of resistive and reactive elements, corresponding to energy dissipation and energy storage respectively. A dual formulation of Nissim’s method is described and an extension proposed that takes account of aerodynamic energy storage in addition to aerodynamic energy dissipation.
Added Fluid Mass and the Equations of Motion of a Parachute
Authors: Eaton John A.
Published: July 2016

While it has long been known that added fluid mass may be important in the dynamics of parachutes, due to inadequate or incorrect derivation and/or implementation of the added mass tensor its full significance in the stability of parachutes has yet to be appreciated. The concept of added mass is outlined and some general conditions for its significance are presented. Its implementation in the parachute equations of motion is reviewed, and the equations used in previous treatments are shown to be erroneous. A general method for finding the equivalent external forces and moments due to added mass is given, and the correct, anisotropic forms of the added mass tensor are derived for the six degree-of-freedom motion in an ideal fluid of rigid body shapes with planar-, twofold- and axisymmetry, These derivations may also be useful in dynamic stability studies of other low relative density bodies such as airships, balloons, submarines and torpedoes. Full nonlinear solutions of the equations of motion for the axisymmetric parachute have been obtained, and results indicate that added mass effects are more significant than previously predicted. In particular, the component of added mass along the axis of symmetry has a strong influence on stability. Better data on unsteady forces and moments on parachutes are needed.
Approximate Displacements of Exact Membrane Actions in a Shell Triangular Element
Authors: Morley L.S.D.
Published: July 2016

Exact stress functions which satisfy the homogeneous differential equations of equilibrium for membrane actions are available from the static geometric analogue of previously derived exact displacements of inextensional bending. For finite element evaluation it is necessary to know the displacements (and rotations) caused by these membrane actions. A method of calculating approximate displacements is described which uses the principle of minimum potential energy. Results are given for specimen triangular elements with positive, zero and negative Gaussian curvatures. A listing is appended of a Fortran computer program which allows calculation of these approximate displacements, rotations and other physical quantities for other element shapes.
A Model for Studying the Stress-Field around Simple Fractures in Human Patella
Authors: Misra J.C. , Murti V.V.T.N.
Published: July 2016

A mathematical model for estimating the stress-field in the vicinity of cracks in human patella has been studied. In conformity with experimental observations with regard to the mechanical properties of osseous tissues, elasticity and anisotropy of the patella have been paid due consideration. The present study being analytical, the problem is first formulated mathematically, and posed as a boundary value problem. Using Mellin transforms technique, the problem is reduced to solving a Fredholm integral equation which is treated numerically by employing Chebyshev quadrature formula. Numerical results are presented. It is suggested that the techniques used may also find application to engineering structures.
The Distribution of Pressure on an Aerofoil, in a Stream with a Spanwise Velocity Gradient
Authors: Mair W. A.
Published: July 2016

Pressure measurements were made at one section of an aerofoil of constant chord spanning a wind tunnel. A flat plate was mounted in the tunnel upstream of the aerofoil, so that the wake from the plate produced a spanwise velocity gradient at the aerofoil. By traversing the plate across the tunnel the position of the wake could be altered relative to the pressure holes in the aerofoil, so that the complete pressure distribution over the aerofoil in the neighbourhood of the wake could be found. The results showed that, because of the secondary flow produced by the interaction between the aerofoil and the wake, the variation of pressure across the wake for a given chordwise position was very small, except close to the leading edge. Thus the lift coefficient, based on the velocity outside the wake, was nearly constant across the wake. The form drag coefficient, based on the same velocity, was considerably reduced in the wake. Even when the form drag coefficient was based on the local velocity of the stream, a considerable reduction was found in the wake.
Experiments with an Electrical Analogue for the Extension and Flexure of Flat Plates
Authors: Palmer P. J. , Redshaw S. C.
Published: July 2016

Details of the design, construction and use of an electrical resistance network for solving certain of the problems encountered in the flexure and extension of flat plates are given. Some typical experiments have been carried out with the aid of this network and the method of operation of the analogy is described. The results of these experiments are presented and they are compared with the corresponding theoretical values. The comparison is as good as could be expected in view of the limitations imposed by the very coarse mesh which was used; essentially the same results would have been obtained by the exercise of a relaxation computation, using the same size of net. No practical difficulties would be encountered in building a large network having a very fine mesh.
The Drag of Non-Planar Thickness Distributions in Supersonic Flow
Authors: Graham E. W. , Beane B. J. , Licher R. M.
Published: July 2016

For many conventional aircraft, the thickness of the wing and fuselage can be represented approximately by source distributions in the plane of the wing and on the axis of the fuselage. Such aircraft may be considered as having essentially planar thickness distributions. However, missiles with cruciform wings, biplane arrangements, “ ring ” wings and so on, require non-planar source distributions to represent the wing and fuselage thickness. For this reason, the term “ spatial thickness distribution ” is used.

To simplify the investigation of spatial thickness distributions, a singularity representing an element of volume is introduced. It is shown that the optimum distribution of such elements in a prescribed space gives rise to a minimum wave drag value consistent with that obtained for a Sears- Haack optimum body of revolution.
The Buckling and Bending of Orthotopic Sandwich Panels With All Edges Simply-Supported
Authors: Robinson J. R.
Published: July 2016

A formula is derived for the buckling in compression of an orthotropic sandwich panel, with all edges simply-supported. Two special types of symmetrical sandwiches, that of a sandwich having zero core flexural stiffnesses and of a corrugated core sandwich, are considered, and curves giving the critical buckling end load per inch are presented. An approximate theory is also given for the bending of sandwich panels under the action of an axial compressive load and a uniform lateral pressure. Curves are presented giving the maximum bending moments in a corrugated core sandwich panel.