bluuebunny/crossref_metadata_2025 huggingface dataset:
A Correlation between Pressure and Heat Transfer Distributions at Supersonic and Hypersonic Speeds
Authors: Stollery J L , Coleman G T
Published: July 2016

The “reference enthalpy” and local flat plate concepts are used to derive some simple expressions for the turbulent heat transfer rate distribution over an arbitrary body at supersonic and hypersonic speeds. The connection between pressure and heat transfer rate is established and tested against a number of experimental data.
A Reference-Plane Method for the Solution of Three-Dimensional Supersonic Flows
Authors: Camarero R
Published: July 2016

A numerical method for the solution of three-dimensional supersonic flows and the associated computer programme have been devised. The present algorithm is based on a reference-plane characteristic network. The physical region between the shock wave and the body surface is replaced by a computational mesh facilitating the incorporation of different boundary conditions and arbitrary body shapes. For reasons of stability and computing time a Hartree-type grid was used where the characteristic segments are projected upstream. The base points do not coincide with nodal points and interpolation by means of Tchebycheff polynomials is required to obtain the flow properties. Numerical differentiation is carried out by means of spline functions. The programme has been used and verified under a wide variety of flows past circular and elliptic cones, tangent ogives and a delta wing body. After a series of numerical experiments it was found that accurate solutions could be found using a 7 × 7 grid, and that the essence of the solution is preserved using a very coarse mesh of 4 × 4. Furthermore, the good agreement obtained with experimental results indicates that it could be applied successfully to problems of practical interest.
A General One-Dimensional Theory of Compressible Inviscid Swirling Flows in Nozzles
Authors: Carpenter P W
Published: July 2016

An approximate analytical method is presented for determining the swirling compressible flow through a nozzle. The method is developed from the techniques introduced by Carpenter and Johannesen. It is perfectly general in that the swirl distribution need not be specified a priori but the radial gradients of the stagnation enthalpy and entropy are assumed to be small. The principal assumption is that changes in the nozzle cross-sectional area are sufficiently gradual and smooth for the radial velocity component to be neglected at each section, i e the usual assumption of one-dimensional compressible flow theory. Analytical expressions are derived for various flow characteristics, e g mass-flux coefficient, impulse function and back-pressure ratio required for choking. The analytical results are compared to numerical results for two main classes of swirling flows. On the whole the analytical results are found to be good approximations for moderate swirl levels. The approximate numerical method is found to be reasonably successful at predicting flow reversal at the nozzle wall. The main result is that a swirl parameter is found such that, with the sole exception of the free-vortex case, the mass-flux-coefficient data for all swirling flows investigated collapse onto a single curve.
Eddy Viscosity in Turbulent Boundary Layers
Authors: Head M R
Published: July 2016

Observed variations of eddy viscosity in the outer regions of turbulent boundary layers are here explained in terms of the reorientation and stretching of vortex elements. The explanation, which is purely qualitative, gives a clear and plausible physical picture.
Some Measurements in Two-Dimensional Turbulent Wakes
Authors: Everitt K.W.
Published: July 2016

It is often assumed that the precise initial conditions exert no influence on the downstream flow development of two-dimensional wakes. A brief investigation of the wakes behind four different bodies shows the lasting influence of upstream history in such flows.
An Optical Instrument for Measuring Fluctuating Velocities in Highly Turbulent Flows
Authors: Gaster M. , Maybrey J.F.M.
Published: July 2016

Flow measurement by optical devices of various types, particularly those involving laser light sources, have received considerable attention over the last few years. Different schemes employing a wide range of optical layouts have evolved and the resulting signals have been processed in a number of ingenious ways. We report new experimental work on an optical instrument that can be considered as the forerunner of the laser anemometer in the belief that in certain circumstances this particular optical layout offers some real advantages over the majority of laser anemometers. One important advantage of this system is the ease with which both the shape and size of the sampling zone can be independently controlled. Another is the ability to position the sampling region very close to a boundary without having to contend with the surface reflection difficulties that often prevent such measurements being made with laser optics. The instrument measures the velocities of small particles suspended in the fluid in much the same way as the laser anemometer. In unsteady flows this results in a series of velocity estimates generated at random time instants. These intermittent samples of the velocity are used to form power spectral density estimates by methods recently developed for the analysis of randomly sampled records (Gaster and Roberts, 1975 & 1976). This method of analysis could well be applied to the processing of the signals generated by laser anemometers operating in the burst counter mode.
Changes in Conical Diffuser Performance by Swirl Addition
Authors: Neve R.S. , Wirasinghe N.E.A.
Published: July 2016

It has been found that the addition of a whirl velocity component to an otherwise axial flow in a conical diffuser can lead to improvements in static pressure recovery and in efficiency, according to a restricted definition. Diffusers of total conical angle 10, 20 and 30 deg. were tested in detail; improvements were evident only in the last two, which would otherwise have suffered from flow separation problems caused by their relatively large divergence angles. The agency for improvement seems to be a beneficial redistribution of axial velocities.
The Theory of Fabric Porosity as Applied to Parachutes in Incompressible Flow
Authors: Payne Peter R.
Published: July 2016

Many aspects of parachute behaviour are dominated by the permeability of the canopy cloth. Techniques employing kinematic principles to predict parachute opening behaviour, for example, must first be able to predict the air flow through the canopy material. This paper is concerned with the development of such a predictive capability.

The flow of air through cloth of gauze has been studied by many workers; since the 1850’s, in connection with filters; and since the early twenties, in connection with parachutes. Workers in each of these disciplines seemed unaware of the work being done in the other.

In the case of parachute cloth permeability we find the foundations being laid down by such eminent workers as Glauert in 1932 and Taylor in 1944. Yet most subsequent writers seem not to be aware of this, and since World War II, there have been many papers “rediscovering” basic principles; often with errors which could have been corrected by reference to the earlier authorities.

In this paper we attempt to bring together all the work which has been done in this field, and to rationalize the data by simple mathematical modelling. Individual elements of the model have been proposed before, of course.

We then examine the effect of tension on the geometric porosity of fabric, and hence the pressure loss Ap. A theoretical analysis shows that tension is likely to be a major factor. For cloths which have low porosity when unloaded our simple mathematical model shows that, for a given Ap, a stress equal to 50% of ultimate can increase the air volume flow Q by an order of magnitude. In general, the increase in permeability is greatest at the lower values of Ap, indicating that the viscous term is more influenced by tension than the dynamic term. This theoretical result is confirmed by some rather limited experiments carried out by Lashbrook and Marby. But their data also shows that a cloth made from relatively stiff glass fibers can experience areductionin permeability when loaded, due to a “closing up” of the weave. The reasons for this are discussed.
An Alternative Approach to the High Aspect Ratio Wing With Jet Flap by Matched Asymptotic Expansions
Authors: Kida T. , Miyai Y.
Published: July 2016

An alternative method is described for solving the problem of a three-dimensional jet-flapped wing with a high aspect-ratio. This method is similar to the lifting-line theory of Kerney6 or Tokuda7, but differs in that the method of matched asymptotic expansions is applied to an integral equation, derived from the lifting surface theory, rather than a partial differential equation. The advantage of the present method over those used previously is that the necessary outer solutions are obtained directly; it is not necessary to rely upon physical insight or considerable ingenuity. The final results are different from those obtained by the previous authors; it is shown that the present result is correct, by noting some errors in the earlier theories.
The Generalization of a Double Integral Method with Applications to Jets in Unbounded Co-Flows
Authors: Middleton D.
Published: July 2016

The ‘double integral’ method, employed by Squire and Trouncer to calculate the flow of a round turbulent jet in a moving stream, is generalised. Representation of the velocity profile in simple form and use of anarbitraryupper limit of integration in the second application of the momentum integral equation permits the recovery of the well-known similarity solutions for plane and axi-symmetric laminar jets issuing into a quiescent medium. Additionally, an approximation for the decay of centre-line velocity is obtained for the non-similar situation when there is an ambient co-flowing stream. This agrees well with Wygnanski’s perturbation solution for the plane laminar jet. The results of Squire and Trouncer are re-examined in the light of this generalised approach. The work has application to the operation of fluidic sensors.
The Development of High Lift, Single-Component Airfoil Sections
Authors: Kennedy J.L. , Marsden D.J.
Published: July 2016

This paper investigates the possibility of increasing the maximum lift of a single element wing section by the introduction of camber near the trailing edge. The optimum upper surface velocity distribution consists of a constant high velocity “rooftop” over the forward part of the wing section followed by transition and an optimised turbulent boundary layer recovery region to the trailing edge. The height of the rooftop, which essentially determines the maximum lift coefficient, is limited by the amount of recovery attainable without separation of the turbulent boundary layer. An increase in the upper surface velocity at the trailing edge would allow the whole top surface velocity distribution to be raised resulting in a considerable increase in maximum lift. The introduction of camber over the rear part of the wing section should produce the required increase in trailing edge velocity on the upper surface. The practical possibilities of using this technique for increased maximum lift were examined by designing a high lift wing section and testing it in the University of Alberta Low Turbulence Wind Tunnel. The results showed that the new wing section behaved qualitatively as expected. A difference of about 0.5U∞ between upper and lower surface velocities at the trailing edge was achieved, even though the thick boundary layers near the trailing edge tend to reduce the effect of camber. A maximum lift coefficient of 2.64 was measured at a Reynolds number of 1.0 × 106.
Prediction of Viscous Effects in Steady Transonic Flow Past an Aerofoil
Authors: Collyer M.R. , Lock R.C.
Published: July 2016

An account is given of a numerical method for calculating transonic flow past an aerofoil with an allowance for viscous effects, providing that the boundary layer remains fully attached over the aerofoil surface. The method has been developed by combining, in an iterative manner, calculations of the inviscid flow with calculations of the compressible boundary layer and wake. The solution for the inviscid flow is obtained by an iterative scheme, originally established by Garabedian & Korn, which has been modified to give a more realistic representation of shock waves. The boundary-layer development is treated as laminar initially; at a certain transition position a turbulent boundary layer is assumed to develop, and this is determined by the lag-entrainment method of Green et al. Comparisons of the results from the numerical scheme with some experimental measurements are shown for various examples in which shock waves of moderate strength are present. The method predicts, with reasonable accuracy, both the detailed pressure distribution and the variation of drag coefficient with lift coefficient.
Derivation by a Transform Method of Integral Equations of Unsteady Lifting Surface Theory in Subsonic and Supersonic Flow
Authors: Ando Shigenori , Ichikawa Akio
Published: July 2016

Applications of “integral transforms of in-plane coordinate variables” in order to formulate unsteady planar lifting surface theories are demonstrated for both sub- and supersonic inviscid flows. It is concise and pithy. Fourier transforms are exclusively used, except for only Laplace transform in the supersonic streamwise direction. It is found that the streamwise Fourier inversion in the subsonic case requires some caution. Concepts based on the theory of distributions seem to be essential, in order to solve the convergence difficulties of integrals. Apart from this caution, the method of integral transforms of in-plane coordinate variables makes it be pure-mathematical to formulate the lifting surface problems, and makes aerodynamicist’s experiences and physical models such as vortices or doublets be useless.
Stability Derivatives of Blunt Slender Cones at High Mach Numbers
Authors: Khalid M. , East R.A.
Published: July 2016

This paper presents a semi-empirical theoretical model for calculating the effect of nose bluntness on the stability derivatives of oscillating slender cones at hypersonic Mach numbers. It is based on a hybrid blast wave analogy/shock-expansion flow model and is used to obtain closed form analytic expressions for the derivatives for oscillating slender cones. Two models based on zero thickness and finite thickness entropy layers are proposed which are seen to be appropriate to the cases of very small and large nose bluntnesses, respectively. The results are compared with new and existing experimental data and with the predictions of previous theoretical methods.
The Effect of Mean Loading on the Fluctuating Loads Induced on Aerofoils by a Turbulent Stream
Authors: Mckeough P.J. , Graham J.M.R.
Published: July 2016

This paper analyses the unsteady lift produced on a thin aerofoil by an arbitrary three-dimensional gust. In particular, it evaluates the effects of α, the angle of incidence of the aerofoil to the mean stream. A thin aerofoil theory which includes the effects of distortion of the turbulence by the mean flow field of the aerofoil is applied to the case of an aerofoil in isotropic turbulence. Some computed results are compared with measurements made on a NACA 0015 aerofoil in grid turbulence in a wind tunnel. It is shown that for isotropic turbulence the effect of mean incidence on the lift spectrum is of order α2, and is significant at low frequencies for the length scale ratios tested.
An Inviscid-Viscous Interaction Method to Predict the Blade-to-Blade Performance of Axial Compressors
Authors: Calvert W.J. , Herbert M.V.
Published: July 2016

An inviscid-viscous interaction method has been developed to predict the blade-to-blade flow in axial compressors. The method is primarily intended for high deflection, transonic (but substantially shock-free) blades where the suction surface boundary layer may be separated near the trailing edge. The inviscid flow is calculated by a time marching method and the viscous flow by integral methods for laminar and turbulent boundary layers. A mixing calculation is then carried out to determine the blade deviation angle and pressure loss coefficient. Predictions have been compared with test results for three high deflection, transonic cascades and there is generally good agreement.
Numerical Computation of Transonic Potential Flow Through Nozzles
Authors: Baker T.J.
Published: July 2016

A numerical method for computing potential flow through either a planar or axisymmetric nozzle is described. Some results obtained from a computer program based on this method are presented and compared with experimental data.
On an Approximation to the Flow Through Axi-Symmetric Contracting Ducts
Authors: Jordinson R. , Rodger J.G.
Published: July 2016

A method is given for the calculation of incompressible, inviscid flow through an axi-symmetric contracting duct for which the two dimensional flow with the same meridianal boundaries is known. The method, which is based on Whitehead, Wu and Waters original proposal, assumes that the contraction consists of two separate portions, upstream and downstream respectively. The flow in each portion is calculated and the two portions matched to produce a contraction of given area ratio with preassigned values of the two dimensional ‘overshoot’ and ‘undershoot’ parameters. It is worth emphasizing that in practice it is only necessary to do the calculations once to predict wall velocities for a family of contraction shapes with different area ratios provided they share a common upstream or downstream portion. The results given here show reasonable agreement with the pressure coefficients obtained in experiment for the upstream end of a small scale contraction of area ratio 16:1. There is however a discrepancy between theory and experiment at the downstream end and a qualitative explanation is advanced for this.
The Effects of Swirl on the Performance of Supercritical Convergent-Divergent Nozzles
Authors: Carpenter P.W.
Published: July 2016

The quasi-one-dimensional theory due to Carpenter and Johannesen is applied to supercritical swirling flows in convergent-divergent nozzles. Only flows with uniformly constant stagnation pressure and entropy are considered. Values of exit impulse function and area ratio are given for various types of swirling flow with a range of back-pressure ratios. Thrust coefficients are calculated using these values and specific thrust coefficients plotted against maximum swirl velocity for various cases. In some cases the specific thrust for swirling nozzle flows very slightly exceeds the no-swirl value. The effects of nozzle wall curvature and flight speed on swirling nozzle flows are discussed. The contribution of post-exit thrust to the total thrust is estimated for swirling flow. Finally, the implications are considered of using swirl at the cruise conditions of a typical SST.
Measured Pressure Distributions and Shock Shapes on a Simple Delta Wing
Authors: Squire L.C.
Published: July 2016

This note presents the results of an experimental investigation of the flow over a simple delta wing designed for a Mach number of 3.5. Complete pressure distributions were measured for incidences of 0°, 10° and 20° at Mach numbers of 2.5 and 3.5. A number of schlieren photographs of the shock system around the wing were obtained at the same conditions and surface streamline patterns were studied at M = 3.5. The measurements were made to support numerical calculations which use this wing as a test case.
Forced Convection Near Laminar Separation
Authors: Akinrelere E.A.
Published: July 2016

The singular behaviour of an incompressible boundary layer at separation has been well established by the works of Howarth (1938), Goldstein (1948), Stewartson (1958), Curie (1958) and Terrill (1960). Stewartson (1962) remarked that the existence of the singularity at separation can be regarded as fully established and understood. The skin friction vanishes like where x is the distance to separation, and the stream function close to the wall is described by a series of powers of , with coefficients that are functions of , where y measures distance normal to the wall. At some stages in the expansion of the stream function, terms in log x have to be included. The case of the compressible flow is less satisfactory. Stewartson (1962) was unable to establish singularity at separation and concluded that the general compressible boundary layer cannot have a singularity at separation unless there is no heat transfer from the wall. This has been contradicted by the works of Merkin (1968) and Buckmaster (1970). Curie (1958) also reported that the difficulty encountered in computing the temperature field right down to the point of separation might be due to the singularity there. In this paper, the Goldstein-Stewart son approach is applied to laminar boundary layer flow at low speeds in which density is sensibly constant and the Prandtl number σ is taken as unity. Singularity is established at separation for the temperature field. The heat transfer does not vanish at separation point and is of the form
Some Techniques for Extending the Application of the Discrete Vortex Method of Flow Simulation
Authors: Bromilow I.G. , Clements R.R.
Published: July 2016

Simulations of vortex sheet dynamics by the discrete vortex method have often shown a growing randomness of the discrete vortices. This paper describes two techniques which attempt to mitigate this tendency whilst preserving the overall structure of the vortex sheet. Clusters of vortices near the points of concentration are amalgamated into a single equivalent vortex and a process of repeated rediscretization of the remaining part of the sheet maintains the integrity of its representation. Use of these techniques allow the flow model to be followed beyond previous expectations, without undue randomisation of the vortex positions. The effects of using these techniques on the overall vortex sheet development are fully investigated in order to validate their use in future investigations.
A Normal Flat Plate Close to a Large Plane Surface
Authors: Everitt K.W.
Published: July 2016

The flow around a normal flat plate close to a large plane surface has been investigated for a range of boundary-layer thickness on the plane surface of 0.72 to 2.53 times the plate height, h. As the gap between the plate and the plane surface is reduced below about 0.55h vortex shedding from the plate is inhibited by the presence of the plane surface. Boundary layer thickness has little effect on the gap at which this occurs, but does affect the strength and frequency of vortex shedding at greater gaps. As the gap between the plate lower edge and the plane surface is decreased towards the critical value of 0.55h, both vortex strength and Strouhal number are more significantly affected when the approaching boundary layer is thin. It is not clear whether this is a result of shear or increased turbulent intensity.
Turbulent Boundary-Layer Development on a Two-Dimensional Aerofoil with Supercritical Flow at low Reynolds Number
Authors: Baker C.J. , Squire L.C.
Published: July 2016

Detailed measurements have been made of the boundary-layer development on a small two-dimensional aerofoil with supercritical flow and a weak shock wave, together with similar measurements on the tunnel side wall opposite the aerofoil surface. The Reynolds number of the test is similar to that found in the turbines of jet engines and there is a strong favourable pressure gradient ahead of the interaction of the shock with the boundary layer as often occurs in turbine blade passages. However, whereas the boundary layer on the aerofoil is thin and of the same thickness as that on a turbine blade, the thicker boundary layer on the wall is more typical of that on the hub or casing. The experimental results are compared with results from a wide range of calculation methods. One interesting conclusion from these comparisons is the fact that prediction methods which perform well for the thin boundary layers on the aerofoil do not necessarily perform as well for the thicker boundary layers on the wall.
On the Impingement of Supersonic Jet on a Normal Flat Surface
Authors: Pamadi B.N.
Published: July 2016

An improved method, based on one strip approximation of the method of integral relations which was reported originally by Belov, Ginzburg and Shub, is presented for the calculation of flow parameters in the impingement region of a supersonic, underexpanded jet striking a normal surface located within the first cell. The results are presented for two impingement conditions and found to be in good agreement with the experimental data.
The Unsteady Lift on Bluff Cylindrical Bodies in Unsteady Flow
Authors: Stapountzis H. , Graham J.M.R.
Published: July 2016

The unsteady lift generated on a NACA 0015 aerofoil, a D cylinder (with the flat face down-stream) and an elliptic cylinder was measured when these bodies were exposed to a flow with a two-dimensional sinusoidal upwash at reduced frequencies 0.05 to 0.8. The mean flow Reynolds numbers were in the range 1.2 × 105 to 3 × 105. Unsteady thin aerofoil theory was used in an attempt to predict the unsteady lift on the bluff bodies, as well as the aerofoil section for fequencies in the low range below the vortex shedding frequency. The results were quite accurate for the aerofoil and the D cylinder, but the aerodynamic admittance predicted by this theory for the elliptic cylinder was significantly above that measured experimentally. The movement of the two free separation points was found to play an important role in the characteristic lift behaviour of the elliptic cylinder.
A Laser-Interferometer Method for Determining the Forces on a Freely-Flying Model in a Shock-Tunnel
Authors: Bernstein L. , Stott G.T.
Published: July 2016

Conventional force-balances, “accelerometer balances” and photographic monitoring of freely-flying models are not suitable for use in the Q.M.C. shock tunnel where the force levels are of order 10N for flow durations of about 1 ms. An interferometric method has therefore been developed for following the trajectory of a weakly-restrained model. The prototype system consists of two simple Michelson interferometers, a single He-Ne laser being employed to provide two measurement and two reference beams so that the motion of two points on the model can be followed. The measurement beams are returned by corner-cube retroreflectors carried on the model which ensures that for each measurement arm the reference and measurement beams recombine at the surface of a photo-detector. As the model moves, interference fringes are produced at the detectors, the cycle dark-light-dark corresponding to a model displacement along the measurement beam of ½λ, about 0.3μm. The frequency-modulated wave-trains produced are recorded using two transient recorders, the data being subsequently played back to a two-channel pen recorder giving a record 500 mm in length corresponding to the test time. The fringe number as a function of time is read manually, and the data analysed by curve fitting to a parabola which yields the accelerations of the measurement points. A knowledge of the inertial characteristics of the model then gives the forces on it. By suitably aligning the beams, lift and pitching moment for a ridge-delta of aspect-ratio 1 were obtained. Two models of the same geometric size but of different inertia were tested. All the data were obtained for model displacements less than 1 mm and pitch rotations less than 0.1°.
An Experimental Investigation of the Wake of an Axisymmetric Body with a Slanted Base
Authors: Xia X.J. , Bearman P.W.
Published: July 2016

The effect of base slant on the base pressure distribution, drag coefficient and vortex shedding characteristics of a model consisting of an axisymmetric main body with an ellipsoidal nose have been investigated for three fineness ratios; 3, 6 and 9. A sudden change in the drag coefficient and separated flow pattern is observed at a critical slant angle (for constant incidence) or at a critical angle of incidence (for a constant base slant angle). The tests confirm that the value of the maximum drag coefficient is extremely sensitive to angle of incidence. Measurements of the frequency of vortex shedding are presented and the structure of the wake is investigated using smoke visualization and hot-wire correlation measurements. The wake is found to be far less stable than that from a two-dimensional bluff body and the vortex structures are sometimes in-phase and sometimes out of phase across the wake. The effect of free-stream turbulence on this family of body shapes is observed to be different to that on three-dimensional blunt-faced bluff bodies. Free-stream turbulence is found to have a minimal effect on base pressure for slant angles giving a recirculating type near wake flow. When longitudinal vortices are present the addition of free-stream turbulence slightly reduces the magnitude of the peak suctions recorded on the base but has little effect on base drag.
Effect of Initial Conditions on Constant Pressure Mixing Between Two Turbulent Streams
Authors: Kangovi Sachidananda
Published: July 2016

A study of the process of mixing and wake development has varied applications in wide ranging fields like jet ejectors, wake signatures, base pressure control, combustors, flow over cut-outs, jet noise and jet interactions. In real flows the wake is usually divided into two zones namely, the near field and the far field. The near field is usually controlled by initial conditions which involve two back-to-back boundary layers separating from the trailing edge of a solid surface. In the far field the flow becomes fully developed and assumes self similarity. The properties of fully developed far field have been well established but little is known about the near field. This paper describes the application of an integral analysis to study the effects of initial conditions like velocity ratio, initial boundary layer thickness, compressibility and temperature ratio on the development of near field of the turbulent mixing layer between two compressible, non-isoenergetic streams at constant pressure. Results include velocity and temperature profiles and the location of jet boundary line in the mixing layer. These results show the gradual approach of the mixing layer to self-preservation.
The Swirl in an S-Duct of Typical Air Intake Proportions
Authors: Guo R.W. , Seddon J.
Published: July 2016

The paper presents the results of measurement of the static pressure, total pressure and swirl in the flow through an S-shaped duct of typical air intake proportions mounted in a wind tunnel and tested at different incidences and different through-flow ratios. In order to reduce the magnitude of swirl at high incidence, two methods have been studied - one, to change the distribution of pressures by means of a spoiler and two, to re-energize the separated flow with an inflow of free stream air through auxiliary inlets. Measurements were also made, at 0° incidence, with a perforated spoiler intended to simulate roughly the taking in of low energy flow from the fuselage boundary layer. The results show a small degree of swirl at low incidence which takes the classical pattern of two contra-rotating flows, and a large degree of swirl at high incidence, in the form of a single rotating flow. Of the anti-swirl devices, the spoiler is the more powerful and can be sized either to reverse the swirl direction or to eliminate the swirl completely. A parameter of swirl coefficient, SC60, has been suggested. Values of SC60 at 30° incidence are 0.188 for the duct as designed, 0.068 for the arrangement with auxiliary inflow and −0.039 with a solid spoiler of width 0.15 times throat width. The various arrangements tested, together with results of an earlier study, shed useful light on the general nature of swirl in an S-duct, its method of generation and its final form and magnitude. A further experiment will be made on a duct having both a horizontal and a vertical offset.
Annular Jets of Different Diameter Ratios
Authors: Ko N.W.M. , Chu F.C.
Published: July 2016

This paper describes part of a detailed study of annular jets of different diameter ratios. From the overall pressure and spectral measurements of conical and basic annular jets of five diameter ratios the coherent structures of the standing vortices, wake vortices, jet vortices, lower wake induced vortices and wake induced vortices can be isolated and their effects assessed. The findings are supported by the available multi-exposed schlieren photographs of both the conical and basic annular jets. The causes for the presence or absence of the additional trains of vortices in the jet flow can also be evaluated by the variation of the diameter ratio. For the standing vortices and wake vortices within the flow behind the interface good correlation is found with the available pressure behind the interface.
An Investigation of the Effects of Incidence on the Flow Around a Square Section Cylinder
Authors: Obasaju E.D.
Published: July 2016

A study has been made of the changes that take place in the flow around a square section cylinder as the angle of incidence is increased from 0° to 45°. Measurements of the Strouhal number, S, and the vortex longitudinal spacing, a/d, are presented and used to estimate the vortex strength,, and vortex street spacing ratio, b/a.is found to vary between about 1.2 and 1.7 depending on incidence, and is given approximately by 0.52(1 - Cpb)/2πS, where Cpbis the mean base pressure coefficient. As the incidence is increased from 0°, S at first decreases slightly and then rises sharply to a maximum at 13.5° incidence, which is the incidence where reattachment of the shear layer, in some mean sense, is expected to commence. The spectra of pressure and velocity fluctuations were measured and subharmonic peaks were found in both spectra at 5° and 10° incidence. It is suggested that they may have been caused by an interaction between a vortex and a trailing edge corner. The degree of organisation of the vortex shedding process was estimated by calculating the sharpness factor, Q, of the spectral peaks at the vortex shedding frequency. In general Q fluctuated with changes in incidence. High values of Q occurred at angles of incidence where the rate of change of the mean base pressure coefficient with incidence is very small whereas low values occurred where the flow is changing to a different state.
Some Effects of Mechanical Damping on the Self-Induced Aeroelastic Oscillations of an Axial Compressor Blade
Authors: Davidson I. M.
Published: July 2016

By a slight modification to den Hartog’s classical theory of harmonically forced vibration off resonance it is shown that, with such distorted forcing wave forms as might be encountered in the stalling or choking flutter of an aerofoil in cascade, the influence of damping on the amplitude of motion can still be assessed with considerable accuracy by the assumption of an equivalent harmonic excitation. The result is valid for any amount of Coulomb damping at which motion is significant in the presence of any “ velocity ” damping coefficient up to that defined by a logarithmic decrement of about 1-3, the formal conclusion of the argument being stated in Section 4.
The Aiming Problem in Aerial Gunnery
Authors: Hancock M.
Published: July 2016

The aiming problem in aerial gunnery has formerly been analysed by approximate methods which allow results of sufficient accuracy for practical requirements to be obtained from a very simple mathematical treatment. There has therefore been no practical demand for any more elaborate analysis, although the development of a more exact treatment of the problem is not without interest from the academic point of view. In this paper a more complete analysis is developed in a form which is generally applicable to a broader class of aiming problems. The relevant parts of the standard external ballistic analysis for projectiles fired from guns are also included for the sake of completeness, and the earlier simplified analysis of the aiming problem is also presented to allow comparison of the results with those of the more complete analysis. Finally, a section on the gunner's view of the aiming problem is included, to provide an explanation of certain difficulties which frequently arise through neglect of the important differences between the points of view of an observer moving with the gun and an observer at rest in the air.
A Finite Series Solution for Grillages under Normal Loading
Authors: Holman D. F.
Published: July 2016

A method has been given by Klitchieff for analysis of grillages of intersecting beams under lateral loading. Klitchieff's solution was in the form of infinite Fourier series and the expressions for bending moments converged approximately as Σ n–2, making numerical computation difficult. This paper shows that, for grillages in which one set of beams are evenly spaced, Klitchieff’s solution can be adapted to give finite series for deflections arid bending moments at the intersections of the beams. The number of terms in the series is not greater than the number of beams in the equally spaced set (referred to in this paper as set “ A ”). A numerical example is given and an accurate solution is obtained with appreciably less computation than other known methods would entail.
Stability and Response of Systems Satisfying a Second-Order Linear Differential Equation with Time-Dependent Coefficients
Authors: Babister A. W.
Published: July 2016

The differential equation considered is

where all the a’s and b’s are real constants.

The nature of the solution is investigated in the neighbourhood of the singular point and the conditions are found for logarithmic terms to be absent.

The conditions for stability for large values of τ are determined; the system is stable if

are all positive for large values of τ.

The form of the response is considered and its oscillatory (or non-oscillatory) nature investigated. The Sonin-Polya theorem is used to determine simple inequalities which must hold between the coefficients of the differential equation in any interval for the relative maxima of | x | to form an increasing or decreasing sequence in that interval.
On the Measurement of Supersonic Aerofoil Drag by Pressure Traverse
Authors: Meyer R. E.
Published: July 2016

The drag in two-dimensional flow is expressed in terms of the distributions of static and stagnation pressures along a traverse line downstream of the aerofoil. Sources of error are discussed with regard to their effect on the accuracy of drag measurement in small tunnels at medium Mach numbers.
A Reduction Method for Buckling Problems of Orthotropic Plates
Authors: Shuleshko P.
Published: July 2016

Several plate buckling problems are solved, using a reduction method. By this method the solution of an orthotropic plate can be reduced to the solution of an isotropic plate and the solution of a plate with bi-axial loading can be reduced to the solution of a plate with uni-axial loading and so on. Plates with simply-supported ends and various boundary conditions at the sides with uni-axial and bi-axial loading are considered and the necessary reduction equations are given.
A Solution of the Flutter Determinant on a General Purpose Electronic Digital Computer
Authors: Gillies D. B. , Hunt P. M.
Published: July 2016

A method is given for the solution of the flutter determinant on a general purpose electronic digital computer. The method has been programmed for the N.R.D.C. 401 Computer and details of this programme are given. A quicker programme, applicable when only structural damping is present and there are two degrees of freedom, is also discussed. Appendix I discusses in detail the types of errors which occur when the method is applied and Appendix II considers the anticipated loss of accuracy which will be encountered when using the method in cases where the number of degrees of fredom is large.
Analysis of a Vector Field and Some Applications to Fluid Motion
Authors: Duncan W. J.
Published: July 2016

The paper first discusses the analysis of a general vector field with the aid of the concept of the field line with its tangent, principal normal and binormal. Detailed applications are made to the motion of inviscid and of viscous fluids.
The Oscillating Two-Dimensional Aerofoil Between Porous Walls
Authors: Drake D. G.
Published: July 2016

The compressible flow past an oscillating two-dimensional aerofoil in a wind tunnel with porous walls is considered, using linearised theory. The porous wall is assumed to have the property that the ratio of the normal velocity at the wall to the pressure drop across the wall is constant. Transform theory is used to find the supersonic longitudinal stability derivatives, and an extension of Possio's integral equation for the quasi-stationary case in subsonic flow.
An Experimental Investigation of the Secondary Flow Occurring in a Compressor Cascade
Authors: Armstrong W. D.
Published: July 2016

When a non-uniform stream flows through a cascade of compressor blades a three-dimensional secondary motion is generated in the outlet stream. This motion, which consists of a spanwise re-orientation of the Bernoulli planes, together with the effects of vorticity components in the stream direction, may be predicted theoretically. In this paper experimental results obtained on a 6 in. chord cascade are reported. The experimental and computed outlet angles are compared and the discrepancies are explained qualitatively. Additional particle track and visualisation experiments were designed to investigate the local blade flows and the effects of the nose vortices.
Approximate Methods for Predicting Separation Properties of Laminar Boundary Layers
Authors: Curle N. , Skan S. W.
Published: July 2016

Some new solutions for steady incompressible laminar boundary layer flow, obtained by Gortler, have been used to test the accuracy of two methods which are commonly used to predict separation. A modification of Stratford's criterion for separation is given in this paper and is probably the most accurate and the simplest of all methods at present in use. Modified numerical functions are also given for Thwaites's method of predicting the main characteristics of the boundary layer over the whole surface, which improve the accuracy of the method.
Noise Measurements on Cold Jets using Convergent-Divergent Nozzles
Authors: Franklin R. E.
Published: July 2016

Tests have been carried out on a series of convergent-divergent nozzles and the results compared with those from a test on a convergent nozzle. At the design pressure ratio, reductions in the noise were found, particularly at 90° to the jet direction. For lower forward pressures the noise is also less, but above the design pressure the noise rises rapidly to the same level as that with a convergent nozzle. In the experiments cold jets were used, but the results are probably applicable in certain respects to hot jets.
Flow about Cones at Very High Speeds
Authors: Zienkiewicz H. K.
Published: July 2016

Effects of vibrational excitation and dissociation of air on inviscid high speed flow past a circular cone, at zero incidence, with an attached shock wave, are studied on the assumption of thermal equilibrium. A numerical solution of the problem is outlined and an approximate analytic solution for the flow between the surface of the cone and the shock wave is developed. Two numerical examples are given as an illustration and compared with the corresponding solutions assuming constant air properties.
The Design of Intermediate Vertical Stiffeners on Web Plates Subjected to Shear
Authors: Mitchell L. H. , Rockey K. C.
Published: July 2016

Dr. Rockey, in his interesting paper on the design of vertical stiffeners for shear webs, perpetuates the idea of Timoshenko (Theory of Elastic Stability, McGraw-Hill, New York, 1936) that for stiffener rigidities above a certain value the stiffeners remain straight and the rigid stiffener buckling load is reached. It is my opinion that this is only so when the stiffeners happen to be placed along a straight node of one of the harmonics of the buckling pattern of the unstiffened plate. With unstiffened plates under shear loads, the nodes are not straight and consequently the buckling load will theoretically always increase with increase of stiffener rigidity, i.e. no buckling mode exists such that stiffeners of finite rigidity remain straight. It is suspected that Timoshenko was led to his conclusion by over-estimated buckling loads obtained by energy methods.
Flexural Vibrations of a Thin-Walled Cylinder of Rectangular Cross Section
Authors: Mansfield E. H.
Published: July 2016

The natural transverse vibrations of a long cylindrical box of doubly symmetrical rectangular cross section are considered. Explicit stress-function solutions are obtained for the webs and the top and bottom surfaces so that the effects of shear lag and shear deflection are inherently included. The results are expressed simply in terms of an effective flexural rigidity, which may be determined with the aid of a number of graphs.
A Rapid Method for Calculating the “Off-Design” Performance of Compressors and Turbines
Authors: Horlock J. H.
Published: July 2016

A model for the calculation of the “off-design” performance of turbo-machines has been suggested by Mellor, who proposed that the machine be split into an infinite number of stages, each producing a small change in stagnation enthalpy. This note suggests that the overall performance of a machine may be obtained in an integral form which permits a rapid calculation of performance maps for rotational speeds and flow rates not greatly different from design values. The method may be of use in preliminary design studies of multi-stage compressors and turbines.
Matrix Analysis of Shell Structures with Flexible Frames
Authors: Przemieniecki J. S.
Published: July 2016

A simple matrix method is presented for the deflection and stress analysis of cylindrical shell structures of arbitrary cross section stiffened by flexible frames. The method is an extension to fuselage structures of the Matrix Force Method developed by Argyris, in which the internal load system in the structure consists of two parts:—(a) synthetic load distribution, represented by the matrix b0, satisfying the external and internal equations of equilibrium, and(b)self-equilibrating load systems, represented by the matrix b1, which are introduced to satisfy compatibility conditions. The magnitudes of these self-equilibrating load systems are determined from the generalised compatibility equations formulated using the flexibility matrix f for the un-assembled elements of the structure. The self-equilibrating systems are non-orthogonal, but are arranged in such a way that the mixing between one system and another is kept to a minimum and, consequently, the resulting compatibility equations are well-conditioned. The three basic matrices, b0, b1;and f, are compiled using only very simple formulae. The matrices b0and b1depend on the geometry of the structure, while the flexibility matrix f is a function of geometry and elastic properties. The present analysis is applied to cut-out problems in fuselage structures. It can also be used for problems involving thermal loading and diffusion of loads in curved panels stiffened by flexible frames.
Some Simple Results for Two-Dimensional Jet-Flap Aerofoils
Authors: Spence D. A.
Published: July 2016

It is shown from elementary considerations that the lift coefficient of a thin two-dimensional wing at zero incidence, with a narrow high-velocity jet of momentum coefficient Cj issuing from its trailing edge at a (small) downward inclination τ, is given by

and the loading on the chord line (0<x<1) by

(except in a certain neighbourhood of the trailing edge), for small values of Cj. These formulae agree well with known measurements. Interpolation formulae for derivatives of CL at larger values of CJ based on earlier work, are also given: