bluuebunny/crossref_metadata_2025_split huggingface dataset:
A Method for Solving Non-Linear Thermal Problems in Re-entry of Space Vehicles
Authors: Broglio Luigi 
Published: July 2016

SummaryThe paper considers a body, or space vehicle, of arbitrary shape, with conductivity K and specific heat c. It is first assumed that K and c are invariant with time and the body, with a given initial temperature, is assumed to be heated by a distribution of heat sources that varies with space co-ordinates and time. It is shown that a rigorous analytical solution to the problem is possible, provided that the distribution function satisfies prescribed regularity conditions.The same problem is then considered, but with a heat-source distribution which is also a function of temperature. In this case the problem can be reduced to a Volterra-type integral equation amenable to step-by-step solution. Convective heating and radiation are specific examples of this second case.The third case considered is that of a body whose geometry and thermal coefficients K and c are all time-dependent, and this problem is reduced to the fixed-geometry case by the addition of a hypothetical heat-source distribution which is a function of the velocity of ablation, of temperature and of its time derivative; an integral equation of Volterra type again results.Finally, an example is given of the application of the analysis to the ablation of a conductive spherical shell.
The Polytropic Expansion of Air Through a Convergent Nozzle at Infinite Pressure Ratio—An Interesting Anomaly
Authors: Pearson H. 
Published: July 2016

SummaryPrevious papers have examined the implications of an assumed polytropic expansion law on the performance of nozzles. In this paper a peculiar anomaly is examined when the convergent nozzle is exhausting into a vacuum. It is shown that, on the strict assumptions of a polytropic expansion law, and the assumption that the flow will maximise for a given throat area, the thrust per pound of air increases progressively with falling polytropic efficiency, becoming infinite when the polytropic efficiency is zero. The author suggests that this anomaly is either concerned with the assumption that the flow will maximise or means that polytropic expansion efficiencies below a certain limit are theoretically impossible, but he believes that there may be some other explanation.
Mathematical Techniques Applying to the Thermal Fatigue Behaviour of High Temperature Alloys
Authors: Howe P. W. H. 
Published: July 2016

SummaryDuring thermal fatigue testing of a specimen with a thin edge, or during rapid temperature changes in the gas flow past turbine blades, the thin edges are deformed plastically in compression during heating and subsequently creep in tension as the bulk of the specimen or blade heats up. The plastic deformation is determined from temperature distributions, which are calculated by Biot’s variational method. The creep deformation is determined as a function of time by a differential equation, which expresses the balance between increasing elastic stress and reduction of stress due to creep relaxation, and which is solved(i)by digital computer,(ii)by transformation to a Riccati equation soluble in terms of Bessel functions, or(iii)by transformation to a second-order differential equation with a periodic coefficient. Using the thermal stresses obtained from the solution of the differential equation, the theoretical thermal fatigue endurance is determined from cyclic (mechanical) stress endurance data. Agreement between theoretical and experimental thermal fatigue endurances is obtained, over ranges of temperature, strain and strain rate, or, equivalently, over ranges of temperature, edge radius and heat transfer coefficient. This agreement supports the use of the theoretical methods in wider contexts. The accuracy of the temperature distributions is better than the accuracy of other factors entering into the correlation between theoretical and experimental endurances. Improvement in the interpretation of experimental results requires consideration of the alteration of the stress cycles during the course of thermal fatigue testing. This requirement is catered for partially by the various solutions of the differential equation for thermal stress.
Losses at Sudden Expansions and Contractions in Ducts
Authors: Pearson H. , Heurteux B. M. L. 
Published: July 2016

SummaryIn view of the overall losses occurring in the bypass ducts of bypass engines a study has been made of the losses taking place at sudden changes of section which occur as the flow passes over compressor and turbine casings not properly faired. It has been shown that the normally estimated losses occurring at sudden contractions and expansions are greatly increased by the low discharge coefficient. When allowance is made for this, the losses at obstructions can be estimated reasonably accurately. It is shown that a fairing ahead of the blockages has to be quite extensive to produce the normally calculated loss and that all these results are reconcilable with the known losses of obstructions in semiinfinite flow. It is shown, however, that where obstructions are placed in series so that the flow areas are roughly in line, losses are much less than the total of the losses caused by the obstructions separately.
Analytical Techniques for the Optimisation of Rocket Trajectories
Authors: Lawden Derek F. 
Published: July 2016

SummaryThe development during the last two decades of analytical techniques for the solution of problems relating to the optimisation of rocket trajectories is outlined and the present position in this field of research is summarised. It is shown that the determination of optimal trajectories in a general gravitational field can be expressed as a Mayer problem from the calculus of variations. The known solution to such a problem is stated and applied, first to the special case of the launching of an artificial satellite into a circular orbit with minimum expenditure of propellant and, secondly, to the general astronautical problem of the economical transfer of a rocket between two terminals in a gravitational field. The special cases when the field is uniform and when it obeys an inverse square law of attraction to a point are then considered, and the paper concludes with some remarks concerning areas in which further investigations are necessary.
Approximate Three-Dimensional Flow Theory for Axial Turbo-Machines
Authors: Howell W. T. 
Published: July 2016

SummaryThe subject of three-dimensional flow in axial compressors and turbomachines has been extensively studied since 1945. This paper gives a means of calculating the approximate three-dimensional flow in an axial compressor by giving expressions for the slope of the velocity profile as a function of the axial co-ordinate. These expressions bring out the rôle of the ratio of stage inlet annulus height to stage length in the three-dimensional flow in these machines. The effect of the three-dimensional flow on the stage temperature rise at mean radius is discussed by introducing a work done factor.
Radial Flow without Swirl between Parallel Discs
Authors: Moller P. S. 
Published: July 2016

SummaryAn understanding of radial flow between confined boundaries is of practical importance in the design of radial diffusers and air bearings. This study presents a combined experimental and theoretical analysis of radial flow, without swirl, between parallel discs using air at incompressible speeds.Emphasis is placed on the pressure distribution sufficiently far downstream of the channel inlet for the entry conditions to be unimportant. However, a study is also made of the main features of the flow near the inlet, particularly within the annular separation bubble.It is shown, for both turbulent and laminar flow, that a similarity solution is possible only in special cases where certain terms in the equations of motion can be neglected. Approximate solutions are obtained for the turbulent and the laminar radial pressure distributions using an integral momentum method. Both theories agree well with experiment. The critical Reynolds number for reverse transition is found to be approximately the same as that for flow in twodimensional channels and circular pipes. With the flow separating at the channel inlet, it is established that both a suitably chosen, minimum pressure coefficient of the separation bubble and the reattachment distance are functions only of the channel width for a given inlet pipe diameter and are independent of Reynolds number and the diameter of the discs.
An Extension of the Method of Generalised Conical Flows for Lifting Wings in Supersonic Flow
Authors: Portnoy H. 
Published: July 2016

SummaryThe method of generalised conical flows has previously been developed subject to the condition that the upwash divided by the streamwise co-ordinate to the power ĸ, where ĸ is the order of the conical flow, must have vanishing (ĸ+1)th derivative with respect to the conical co-ordinate. In the present paper this restriction is removed. The results are also used to discuss the effect of the application of the leading edge attachment condition on the wing pressure and geometry.
Shear Buckling of Rectangular Plates with Mixed Boundary Conditions
Authors: Cook I. T. , Rockey K. C. 
Published: July 2016

SummaryThe paper presents a solution for the buckling under shear of a rectangular plate which is clamped along one edge and simply-supported along the other edges. The authors have also re-examined the case of one pair of opposite edges clamped and the other pair simply-supported.
The Effects of Vibrational Relaxation on
Hypersonic Flow Past Blunt Bodies
Authors: Blythe P. A. 
Published: July 2016

SummaryThe analysis of Freeman is extended to the hypersonic flow of an inviscid, vibrationally relaxing gas past a bluff body. Expressions for the shock shape, streamline shapes and stand-off distance are derived; these expressions have been evaluated for a sphere for various values of an appropriate non-equilibrium parameter Λ.
On the General Theory of Heterogeneous Aeolotropic Plates
Authors: Stavsky Yehuda 
Published: July 2016

SummaryA large deflection theory is established for the bending and stretching of aeolotropic plates with elastic moduli that vary in thex, y, zdirections. The theory is formulated in terms of two simultaneous non-linear differential equations, with variable coefficients, for the transverse deflectionwand an Airy stress functionF. Small deflection heterogeneous plate theory and some other sub-classes of plate problems are formulated by specialising the general non-linear plate equations. Effects of initial irregularities and of a variable elastic foundation are considered.
A Contribution to the Analysis of Axial Compressor Performance
Authors: Pearson H. 
Published: July 2016

SummaryThe concept of an idealised “unique” stage characteristic is employed to analyse and understand the performance of axial compressors. It is shown that there exists a “matching” line across the compressor characteristics at any point of which all the stages are operating at the same point of their “unique” stage characteristic, and that this matching line is readily obtainable, almost from inspection. Simple calculations lead to a derivation of both this “unique” characteristic and the effective area ratio of the compressor. The behaviour of the stages at other points than the matching line is readily understandable and presents a simpler picture of compressor performance than is often obtainable from actually measured stage characteristics.
Possible Types of Flow at Swept Leading Edges
Authors: Stanbrook A. , Squiref L. C. 
Published: July 2016

SummaryExisting experimental data on the occurrence of attached flow around the leading edges of swept plane thin wings is summarised. It is shown that the change from separated to attached flow occurs while the Mach number normal to the leading edge is subsonic and that the Mach number required for the change increases with incidence. It is also shown that the Mach number and incidence conditions which hold on the boundaries dividing the two types of flow on wings with straight edges also apply locally at points on the leading edges of “Gothic” wings. The implications of this result on the flow over general curved-edge wings is briefly discussed.
Elastic Stress Concentrations for the Torsion of Hollow Shouldered Shafts Determined by an Electrical Analogue
Authors: Rushton K. R. 
Published: July 2016

SummaryThe elastic stress concentration factors for the torsion of solid and hollow shouldered shafts have been determined by means of a pure resistance electrical analogue. Fillet radii ranged from 0.05 to 1.0 times the diameter of the smaller shaft, and the shoulder diameter increased from 1.0 to 8.10 times the diameter of the smaller shaft. A comparison is made with the results of other techniques. A study has also been made of the formation of a plastic region in the neighbourhood of the fillet.
Buckling of Orthotropic Conical Shells under External Pressure
Authors: Singer J . , Fersht-Scher R. 
Published: July 2016

SummaryDonnell type stability equations for thin circular orthotropic conical shells are presented and solved for external pressure loading. The solution is likewise applied to stiffened conical shells by consideration of equivalent orthotropic shells. Typical cases are computed and compared with corresponding isotropic shells. Correlation with equivalent cylindrical shells then yields a simple approximate stability analysis for orthotropic or ring-stiffened conical shells under hydrostatic pressure.
On the Confluence of Three Shock Waves in a Perfect Gas
Authors: Henderson L. F. 
Published: July 2016

SummaryThe paper deals with the behaviour of three shock waves meeting at a point in a perfect gas. It is shown that the equations of motion can be reduced to a single polynomial equation of degree 10. The real roots of this equation are studied to determine their physical significance. In addition, the appearance of degenerate shock systems is shown to be associated with the formation of certain multiple roots of the polynomial equation.
The Flow Past a Delta-Wing-Half-Cone Combination with Subsonic Leading Edges
Authors: Portnoy H. 
Published: July 2016

SummaryThe flow past an unyawed, flat, delta wing with subsonic edges, carrying a slender half-cone mounted centrally underneath, is found by using the method of supersonic conical flows. The wing plane is taken to be at zero incidence, but it is shown that wing incidence, camber, twist and thickness effects may be incorporated by superimposing on this solution the field of the isolated wing with these properties. The results are shown to agree with previous work on configurations with sonic or supersonic leading edges for the common case of sonic edges. The leading edge loading may be made zero to secure attached flow at any lift coefficient by using camber and incidence, but it is shown that there is a certain positive lift coefficient for which a negative incidence alone will suffice.
Stability of Multi-Stage Axial Flow Compressors
Authors: Howell W. T. 
Published: July 2016

SummaryThe following theoretical investigation is concerned with the stability of the flow through a system composed of a multi-stage axial flow compressor followed by a throttle.Such an investigation was carried out by Pearson and Bowmer in 1949. In 1962 Pearson’s work on the analysis of axial flow compressor characteristics, and the accumulation of empirical data regarding factors affecting the surge line, re-awakened interest in the possibility of predicting the surge line of a multi-stage axial flow compressor-throttle system.In this paper the equations governing the stability of flow at any operating point in such a system are obtained by applying Kirchhoff’s laws to the associated electric circuit at that operating point, and the analysis is applied to a wide range of flows of the calculated characteristics of a seven-stage axial flow compressor.A study of the simplest compressor-throttle system is given, in which the equations of motion of the system are derived mechanically and electrically, and the range of validity of the equations and their stability are discussed in order to bring out the relation between the mathematics and physics of the simple system before applying these methods to multi-stage axial flow compressors.For the relatively simple electrical representation used in this paper for an axial compressor of n stages, there are shown to be 2n possible values of p, the transient rotational frequency, and these are determined over a sufficiently wide range of flows on the seven-stage compressor studied.As a result, a region of the compressor characteristic map can be marked out in which all the values of the transient rotational frequency have their real parts less than zero, corresponding to stability of operation, a region where at least one of the values of p is real and positive corresponding to non-oscillatory instability of operation, and an intermediate region where some of the values of the rotational frequency p are complex with positive real part, corresponding to oscillatory instability of operation.It is suggested that the non-oscillatory instability found here is associated with the surge and the line of inception of non-oscillatory instability with the surge line.
Maximum Stability Characteristics of a Simple Flameholder in High Velocity Gaseous and Liquid Fuel/Air Streams
Authors: Walburn Peter G. 
Published: July 2016

SummaryThe same fluid kinetic-chemical parameter is shown to describe the peak velocity conditions at which cylindrical flameholders can sustain a flame in both gaseous and liquid fuel/air mixtures. Experimental data indicate the existence of three possible aerodynamic conditions which may aflect the flame stabilisation process. In both gaseous and liquid fuel flame stabilisation an increase in stabiliser size is shown to increase the peak stable burning velocity.
Structure of the Flow Associated with a Two-Dimensional Supersonic Intake
Authors: Henderson L. F. 
Published: July 2016

SummaryThe intake is conceived as a device that generates a shock system and a subsonic patch within a supersonic field. The object of the paper is to obtain a qualitative description of this flow structure. The analytical procedure is a simple but fairly powerful mapping technique. Several examples are discussed and these show how the flow on the intake alters under the influence of gradually changing boundary conditions.
General Instability of Stiffened Circular Conical Shells under Hydrostatic Pressure
Authors: Baruch M. , Singer J. 
Published: July 2016

SummaryDonnell type equilibrium and stability equations are derived for stiffened thin conical shells. The stiffeners are considered closely spaced and are therefore assumed to be “distributed” over the whole surface of the shell. In the proposed theory the stiffeners and their spacing may vary in any prescribed manner, but here only equal and equally spaced stiffeners are dealt with. The force- and moment-strain relations of the combined stiffener-sheet cross section are determined by the assumption of identical normal strains at the contact surface of stiffener and sheet.The stability equations are solved for general instability under hydrostatic pressure by the method of virtual displacements. The solution used earlier for unstiffened conical shells, which satisfies some of the boundary conditions of simple supports only approximately, is again applied here. The effect of this incomplete compliance with boundary conditions is shown to be negligible by consideration of “boundary work”. The solution proposed for stiffened conical shells involves the concepts of “correcting coefficients” and minimisation of corresponding “error loads”.Typical examples are analysed and the effect of eccentricity of stiffeners is investigated. Simplified approximate formulae for the critical pressure of frame-stiffened conical shells are also proposed.
An Application of Conformal Mapping to a Three-Dimensional Unsteady Heat Conduction Problem
Authors: Laura Patricio A. , Chi M. 
Published: July 2016

SummaryThis paper deals with an unsteady-state three-dimensional heat conduction problem in a prismatic body which has a complicated boundary shape. Numerical techniques such as a relaxation method must be used to solve a problem of this type; this method, however, requires unusually large amounts of labour. The method used in this paper consists of the application of conformal mapping and numerical solution of a partial differential equation and is applied first to a prismatic body of square cross section for which the exact solution is well known. As a second application, the approximate solution for a problem involving a star-shaped cross section is presented.
Radial Flow of Compressible Fluids Between Discs
Authors: Na Tsung Yen 
Published: July 2016

SummaryNumerical solutions are obtained for the one-dimensional radial flow of a compressible fluid between parallel discs. A general discussion of the variations of pressure, density, velocity and temperature along the radius of the disc is then given. The present investigation covers both subsonic and supersonic flows, a range not previously covered in the literature.
The Random Vibration Response of a System Having Many Degrees of Freedom
Authors: Robson J. D. 
Published: July 2016

SummaryThe paper treats the general problem of the response to multiple random excitation of a system having n degrees of freedom. Analysis is developed which connects the spectral density matrix of a set of generalised coordinates with that of corresponding generalised forces, and makes explicit the contributions of the various normal modes. The case of two degrees of freedom is considered in detail. The importance of cross-correlations between modes is shown by determining their effects on spectra and on mean-square response.
An Analytical and Experimental Study of Cylindrical Shells under Localised Impact Loads
Authors: Yao John C. 
Published: July 2016

SummaryNon-symmetric response of elastic shells to localised impact loads is studied. Closed-form solutions for the response to four particular kinds of pulse shapes are given. Experimentally measured values of the strain response of a cylinder to impact loads are obtained which compare satisfactorily with theoretical predicted values.
Non-Linear Theory for Slender Wings in Sudden Plunging Motion
Authors: Dore B. D. 
Published: July 2016

SummaryA theoretical treatment is considered for the flow past slender wings in sudden plunging motion when leading-edge vortices are present. A form of slender-wing theory is used and, although the basis of the theory involves no restriction on compressibility, it has proved possible to make calculations only for an incompressible fluid.Use is made of an analogy between the unsteady flow and related steady flows. In the incompressible case, an extension of the theory of Brown and Michael is given to determine the strength of the vortex and its path from the leading edge to the final steady-state position. A qualitative comparison with experiment is made of the instantaneous position of the vortex. In a typical case the lift is calculated to remain within one per cent of its final value after the vortex strength has reached 55 per cent of its final value.