bluuebunny/crossref_metadata_2025_split huggingface dataset:
Calculation of Heat Transfer Coefficients in Cooled Turbine Cascades
Authors: Harris H. D. , Luxton R. E. 
Published: July 2016

SummaryAn approximate method is presented for the calculation of heat transfer rates to cooled turbine blades. The method is based on a combination and extension of methods which have been developed in recent years for the calculation of the skin friction and heat transfer coefficients on wings in high speed flight. The use of the method is demonstrated by application to a specific cascade for which an experimental determination of overall heat transfer coefficient is known. Very close agreement with the experimental results is found over the range of Reynolds number tested. The calculated distribution of local heat transfer coefficient indicates that local pressure gradients have a marked effect on the heat transfer. A first-order estimate of the effect of blade cooling on the rate of mass flow through a blade passage shows that an increase of the order of one per cent in the mass flow rate may be obtained by a reasonable degree of blade cooling.
A ‘Pseudo-Viscosity’ Method for Calculating Two-Dimensional Flow Fields
Authors: Walkden F. , Sellars J. E. 
Published: July 2016

SummaryA scheme that uses an implicit system of finite-difference equations to obtain solutions of the equations governing the two-dimensional supersonic motion of an inviscid gas is described. The method relies on pseudo-viscosity in order to calculate shock waves. Compared with characteristics methods, pseudo-viscosity methods have certain advantages. For example, shock waves are calculated automatically without special procedures and pseudo-viscosity methods are easily generalised so that problems with three or more independent variables may be considered. Pseudo-viscosity methods have not been used extensively in the field of aerodynamics, partly because of the difficulty in obtaining sufficiently accurate solutions in the neighbourhood of a boundary. The main purpose of this paper is to show how this difficulty can be overcome. The problem of integrating the equations of motion when a boundary condition has to be satisfied on an arbitrary curve is considered. Streamlines are used as one of the independent variables so that the boundary curve is a coordinate curve, and the equations of motion are used in a form which leads to a simple procedure at the wall. For a given system of partial differential equations it is possible to introduce pseudo-viscous terms in many ways, not all of which are satisfactory. The results presented show that the method proposed in this paper is adequate. The calculated results are accurate and vary smoothly in the neighbourhood of the boundary.
Asymptotic Expansion for Transient Forces from Quasi-Steady Subsonic Wing Theory
Authors: Garner H. C. , Milne R. D. 
Published: July 2016

SummaryA simple general expression is obtained for the rate of change of generalised aerodynamic damping coefficients with respect to frequency parameter in the limit as frequency tends to zero. The expression is directly proportional to aspect ratio and does not depend explicitly on Mach number. The result is consistent with calculated pitching derivatives from finite-frequency theory.This extension of quasi-steady theory is applied to determine the leading transient term of the asymptotic expansion for large time of generalised forces due to an indicial upwash field. The expansion has direct relevance to the use of quasi-steady aerodynamic derivatives in the field of stability and control.
The Effect of Base Bleed on the Flow behind a Two-Dimensional Model with a Blunt Trailing Edge
Authors: Bearman P. W. 
Published: July 2016

SummaryThe effects of base bleed on the flow about a two-dimensional model with a blunt trailing edge were examined at Reynolds numbers, based on model base height, between 1·3×104 and 4·1×104. The ratio of boundary layer thickness at the trailing edge to half the model base height was approximately 0·4. Measurements were made of base pressure, vortex shedding frequency and the distance to vortex formation. With a sufficiently large bleed quantity the regular vortex street pattern disappeared and the base drag of the section was reduced to about a third of its value without bleed. The base pressure was found to vary linearly with the inverse of the vortex formation distance. Results of a previous splitter plate investigation were found to agree closely with those of the present experiments.
Experiments on the Reattachment of a Turbulent Axisymmetric Shear Layer
Authors: Finley P. J. 
Published: July 2016

SummarySome experiments are described in which an axisymmetric free shear layer attaches to a spherical surface, the exterior flow Mach number ranging from 0-75 to 207. The Chapman-Korst reattachment model is shown to correlate the results very well. The relation between the quantities measured and the numerical predictions of the model is discussed in detail and it is shown that the pressure changes which occur just downstream of reattachment are significantly different from those observed on flat walls.
A Note on the Shear Stress Criterion for Fatigue Failure under Combined Stress
Authors: Little R. E. 
Published: July 2016

SummaryNishihara’s combined bending and torsion out-of-phase fatigue limit data are analysed. The Tresca shear stress failure criterion predicts strengths up to 30 per cent higher than observed. It thus appears that renewed attention should be given to the basic problem of developing reliable combined stress failure criteria. It is suggested that new test methods will be required for this purpose.
Measurements of the Flow Field on a 15° Semi-Vertex Angle Blunt Cone at M=8.6
Authors: Wood N. B. 
Published: July 2016

SummaryMeasurements of the pitot pressure between the body and shock on a 15° semi-vertex angle, spherically blunted cone were made in the RARDE Hypersonic Gun Tunnel at a Mach number of 8·6. Using these measurements, together with the measured shock shape, the other flow field parameters were calculated. The results were compared with results of inviscid theoretical calculations for a similar cone at a Mach number of 10.
Displacement Effects on Pitot Tubes with Rectangular Mouths
Authors: Quarmby Alan , Das H. K. 
Published: July 2016

SummaryThe displacement effects on a set of five rectangular mouthed pitot tubes of a constant thickness ratio, 0-6, were investigated in fully developed turbulent flow in a plain tube. The results show that the displacement due to shear only, δ1, is given by δ1/b=0.19, where b is the outside thickness of the pitot tube. The additional wall effect is found to have a dependence on Reynolds number or, equivalently, wall shear within the range investigated of 27 500 < Rev < 58 300. The wall effect results may be presented as a single curve, however, if consideration is given to the distance up to which the wall effect is present.
Correlation of Constant Pressure Turbulent Boundary Layer Measurements on Insulated Walls
Authors: Stoddart J. A. P. 
Published: July 2016

SummaryMeasured characteristics of compressible constant pressure adiabatic turbulent boundary layers are correlated in an incompressible frame of reference with the aid of a modification of the well known Mager compressibility transformation. Quite good data collapse is obtained although the transformation is shown to be deficient in the outer regions of the boundary layer. The results will be used to produce data sheets of constant pressure adiabatic turbulent boundary layer properties.
The Post-Buckling Behaviour of Simply-Supported Square Plates
Authors: Walker A. C. 
Published: July 2016

SummaryThe post-buckling behaviour of flat square plates loaded along two opposite straight edges is analysed using the von Kármán equations, trigonometric series and Galerkin’s method. The unloaded edges are considered to be either free to distort in the plane of the plate or maintained straight but allowed to move bodily; all edges are simply-supported in the out-of-plane direction. The non-linear algebraic equations are solved approximately using a McLaurin’s series expansion technique which facilitates the development of explicit expressions for ultimate load, end shortening and stiffness. The effects of initial geometric imperfections are also studied and it is shown that the results for ultimate load prediction and end shortening are in good agreement with test results.
The Effect of End-Plates on the Two-Dimensionality of a Vortex Wake
Authors: Graham J. M. R. 
Published: July 2016

SummarySpanwise velocity correlations of the turbulent vortices shed by a two-dimensional bluff body of D-section are presented for different aspect ratios of the shedding body between end-plates. From these it is shown that the vortices are only shed two-dimensionally when the gap between the end-plates is less than or equal to four times the base height of the shedding body.
Laminar Boundary Layers over Permeable Curved Surfaces
Authors: Clayton B. R. , Massey B. S. 
Published: July 2016

SummarySteady, constant-density, two-dimensional flow in a laminar boundary layer is considered over a permeable curved surface, for conditions such that the equation of motion has similar solutions. Account is also taken of the displacement of the main stream by the boundary layer.Integration of the equation of motion on a digital computer yields results indicating that, for given values of curvature and longitudinal pressure gradient, suction reduces the boundary-layer thickness and increases skin friction. Blowing has the reverse effects. The amount of suction or blowing required to produce neutral stability is independent of curvature and so may be deduced from data for flat surfaces.For a given curvature, blowing reduces, whereas suction increases, the magnitude of the adverse pressure gradient which the boundary layer can withstand before separation occurs. For a surface through which there is blowing or only a small amount of suction, convex curvature also reduces the magnitude of the adverse pressure gradient producing separation; but for larger amounts of suction the effect of surface curvature on separation is reversed.
An Improved Method of Matrix Displacement Analysis in Vibration Problems
Authors: Carnegie W. , Thomas J. , Dokumaci E. 
Published: July 2016

SummaryThis paper presents a method with strong convergence characteristics for the determination of eigenvalues and eigenvectors of continuous systems. The limitation on the number of undetermined constants in the displacement functions introduced by the conditions at the ends of a segment is removed by the introduction of points of freedom within the segment.This improves the convergence of eigenvalues and eigenvectors very rapidly with the number of segments, especially in torsional vibration problems where the convergence with the usual Matrix Displacement method is very poor. The continuous medium is successively approximated by the use of sub-systems with finite numbers of degrees of freedom. The principles upon which the method is based and the convergence of the results are discussed and illustrated by a series of examples.
Flow between a Rotating and a Stationary Disc
Authors: Bayley F. J. , Owen J. M. 
Published: July 2016

SummaryThis paper deals with the effects of a superimposed radial outflow upon the motion of the fluid between a rotating and a stationary plane disc. This is an idealisation of the situation found in advanced turbo-machinery in which cooling of the rotor faces is necessary. The boundary layer approximations to the equations of fluid motion are integrated by an extension of the numerical technique proposed in Ref. 11. Predictions of drag torque and radial pressure distributions are compared with experimental results from a 30 in (762 mm) diameter system, using a range of speeds up to 4000 rev/min, while varying the axial spacing and rate of imposed radial flow. Qualitative agreement was satisfactory throughout the range, but quantitative discrepancies in the estimates of drag and in the pressure distributions at certain flow conditions suggest that the simple mixing length hypothesis used in this analysis for the turbulent shear terms in the equations of motion is not universally adequate.
Long Cylindrical Tube Subjected to Two Diametrically Opposite Loads
Authors: Yao J. C. 
Published: July 2016

SummaryA theoretical study is made of the problem of a long, thick cylindrical tube subjected to two equal and diametrically opposite normal loads. The stress state is analysed by the three-dimensional theory of elasticity, with the Papkovich and Neuber stress-function approach. Numerical results for stresses and radial displacement are obtained to show the nature of stress concentration in the neighbourhood of the load. Some related experiments using the photoelasticity technique are also accomplished. Favourable correlation is shown between the theory and the test results.
The Supersonic Flow Past an Elliptic Cone
Authors: Woods B. A. 
Published: July 2016

SummaryThe supersonic flow past an elliptic cone of small eccentricity is treated as a pertubation of the axially-symmetric conical flow. The perturbation is singular; a uniformly valid solution is constructed by formulating the problem in sphero-conal coordinates (in which the cone surface is always a level surface of one of the coordinates) and by using the method of matched asymptotic expansions. This formulation enables first-order results to be obtained economically. In a numerical example for the flow past a cone of quite large eccentricity at incidence, it is shown that the present first-order solution (of three terms) agrees as well with experiment as a ten-term approximation obtained by Martellucci using the method of linearised characteristics.
Solution of the Non-Linear Differential Equations for Finite Bending of a Thin-Walled Tube by Parameter Differentiation
Authors: Na T Y , Turski C E 
Published: July 2016

SummaryThe method of parameter differentiation is applied to the solution of the non-linear, two-point, ordinary differential equations resulting from an analysis of the finite bending of a thin-walled tube. Starting from a given set of solutions of the differential equations for a particular value of the curvature parameter α, solutions for a range of values of α can be obtained by this method non-iteratively. Very close agreement was obtained with solutions using iterative numerical methods.
A Simple Integral Method for the Calculation of Thick Axisymmetric Turbulent Boundary Layers
Authors: Patel V C 
Published: July 2016

SummaryA simple integral method is described for the calculation of a thick axisymmetric turbulent boundary layer. It is shown that the development of the boundary layer can be predicted with acceptable accuracy by using an approximate form of the momentum-integral equation, an appropriate skin-friction law, and an entrainment equation obtained for axisymmetric boundary layers. The method also involves the explicit use of a velocity profile family in order to interrelate some of the integral parameters. Available experimental results have been used to demonstrate the general accuracy of the method.
Higher-Order Solutions for Unsteady Hypersonic and Supersonic Flow
Authors: Hui W H , Hamilton J 
Published: July 2016

SummaryThe problem of unsteady hypersonic and supersonic flow with attached shock wave past wedge-like bodies is studied, using as a basis the assumption that the unsteady flow is a small perturbation from a steady uniform wedge flow. It is formulated in the most general case and applicable for any motion or deformation of the body. A method of solution to the perturbation equations is given by expanding the flow quantities in power series in M−2, M being the Mach number of the steady wedge flow. It is shown how solutions of successive orders in the series may be calculated. In particular, the second-order solution is given and shown to give improvements uniformly over the first-order solution.
The Prediction of the Axisymmetric Turbulent Jet Issuing into a Co-Flowing Stream
Authors: Antonia R A , Bilger R W 
Published: July 2016

SummaryThree analyses are presented for predicting the development of an axisymmetric turbulent jet issuing into a co-flowing external air stream. The first analysis is analogous to a method used by Patel to predict the growth of a two-dimensional jet in an external air stream. The method is found to be inadequate when the excess velocity on the axis of the jet becomes small compared with the external stream velocity. The second analysis assumes that the turbulence structure is similar at different streamwise stations but it breaks down when the advection of turbulent energy becomes comparable with the turbulent energy production. In the third approach, a two-parameter model of turbulence developed by Rodi and Spalding, which uses two differential equations for the turbulent energy and the length scale of the turbulence respectively, is found to predict closely the experimental results of Antonia and Bilger for a ratio of jet to external stream velocity of 3.0. The success of this last method emphasises the non-similar character of turbulence.
Simple Finite Elements for Pre-Twisted Blading Vibration
Authors: Thomas J , Dokumaci E 
Published: July 2016

SummaryA simple formulation is established for the determination of vibration characteristics of pre-twisted beams by the matrix displacement method. An important point in the analysis is the assumption of complete polynomial displacement distribution in the principal directions. In particular, two twisted elements which employ quintic polynomials are introduced and used in the calculation of natural frequencies of pre-twisted beams for several boundary conditions. The results demonstrate rapid convergence.
Approximations in Complicated Critical Buckling and Free Vibration Analyses of Prismatic Plate Structures
Authors: Williams F W 
Published: July 2016

SummaryAn 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

SummaryAn 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

SummaryA 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

SummaryThe 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

SummaryFor 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

SummaryThe 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.