By considering the equations of motion it has been shown that the flow in the outer part of a two-dimensional, curved, turbulent wall jet is approximately self-preserving if the ratio of jet thickness to wall radius of curvature is constant along the jet. This condition is satisfied for a jet blowing over a surface of logarithmic spiral profile, for which the radius of curvature R increases linearly with distance s along the wall.

Measurements of velocity profiles and rates of growth of wall jets for surfaces with curvature ratios and 1 are presented. These are compared with solutions obtained using an eddy viscosity theory, and with the flow of jets round circular cylinders. The measured jets are found to be approximately self-preserving in form, and to have rates of growth which are much larger than the jets on circular cylinders with corresponding values of s/R.

Real-time flight data from the Automatic Dependent Surveillance–Broadcast (ADS-B) has been integrated, through a data interface, with a flight performance computer program to predict aviation emissions at altitude. The ADS-B, along with data from Mode-S, are then used to ‘fly’ selected long-range aircraft models (Airbus A380-841, A330-343 and A350-900) and one turboprop (ATR72). Over 2,500 flight trajectories have been processed to demonstrate the integration between databases and software systems. Emissions are calculated for altitudes greater than 3,000 feet (609m) and exclude landing and take-off cycles. This proof of concept fills a gap in the aviation emissions inventories, since it uses real-time flights and produces estimates at a very granular level. It can be used to analyse emissions of gases such as carbon dioxide ($\mathrm{CO}_2$), carbon monoxide (CO), nitrogen oxides ($\mathrm{NO}_x$) and water vapour on a specific route (city pair), for a specific aircraft, for an entire fleet, or on a seasonal basis. It is shown how $\mathrm{NO}_x$ and water vapour emissions concentrate around tropospheric altitudes only for long-range flights, and that the cruise range is the biggest discriminator in the absolute value of these and other exhaust emissions.

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.

This paper presents results of an investigation of the wake flow of a series of two-dimensional bluff bodies with different boundary-layer separation angles. These results are compared with the results of an earlier investigation of a similar series of axisymmetric bodies. It is found that when the same length scales characterising the wakes that were proposed for the axisymmetric case are used in the current investigation, then there is good agreement between the two cases in the variation of the length scales with boundary-layer separation angle. The universal Strouhal number previously proposed for axisymmetric bodies is derived for the two-dimensional bodies under investigation and is found to remain a constant for the different bodies, but at a different numerical value from that found for the axisymmetric bodies.

After a brief discussion of alternative ways in which the drag of an aircraft wing can be derived theoretically, attention is focused on a technique whereby the separate ‘far-field’ components of drag — viscous, trailing-vortex (induced) and wave — are calculated separately. In particular, a new approximate method is described for estimating the wave drag. Based on an exact two-dimensional analysis involving the flow conditions just upstream of the shock wave, a simple formula is derived which, to first order, involves only a knowledge of the Mach number distribution on the surface of the aerofoil ahead of the shock and of the surface geometry at its foot. The accuracy of this formula is assessed for aerofoils by comparison with more exact theoretical results and with experiment. A ‘strip theory’ extension to swept wings is proposed and illustrated by applying it to a particular transport-type wing body combination. Using experimental pressure measurements as input, all three components of drag are estimated theoretically, and by adding their sum to separate balance measurements of the body drag comparisons between ‘theory’ and experiment for the overall drag can be made. These show a satisfactory standard of accuracy, the error varying between —5% and — 1% of the total drag over a wide range of Mach number and lift coefficient.

The discrete element displacement method is used to analyse the instability of flat rectangular plates subjected to arbitrary systems of in-plane loading. Critical load intensities calculated in a range of applications, some of which include discrete reinforcing members, are compared with the predictions of past investigators and demonstrate the accuracy of the procedure.

It is generally accepted that the displacement patterns chosen to represent the deformation of a finite element should be such that there is complete compatibility with adjacent elements. Although some writers have doubted the necessity for the complete satisfaction of compatibility away from the reference nodes, provided the displacement pattern is capable of assuming certain uniform strain states, the desirability of complete compatibility is not in question. The displacement fields suggested in this note satisfy complete compatibility.

The effect of multigrid acceleration implemented within an upwind-biased Euler method for hovering rotor flows is presented. The requirement to capture the vortical wake development over several turns means a long numerical integration time is required for hovering rotors, and the solution (wake) away from the blade is significant. Furthermore, the flow in the region near the blade root is effectively incompressible. Hence, the solution evolution and convergence is different to a fixed wing case where convergence depends primarily on propagating errors away from the surface as quickly as possible, and multigrid acceleration is shown to be less effective for hovering rotor flows. It is found that a simple V-cycle is the most effective, smoothing in the decreasing mesh density direction only, with a relaxed trilinear prolongation operator. Results are presented for multigrid computations with 2, 3, 4, and 5 mesh levels, and a CPU reduction of approximately 80% is demonstrated for five mesh levels.

Carbon fibres with high tensile strength are being increasingly utilised in the manufacture of advanced composite aerostructures. A Modified Compact Tension (MCT) specimen is often deployed to measure the longitudinal intralaminar fracture toughness but a high tensile strength often leads to premature damage away from the crack tip. We present an approach whereby the MCT specimen is supported by external fixtures to prevent premature damage. In addition, we have developed a novel measurement technique, based on the fibre failure strain and C-scanning, to determine the crack length in the presence of surface sublaminate delamination which masks the crack tip location. A set of cross-ply specimens, with a ((90/0)s)4 layup, were manufactured from an IMS60/epoxy composite system Two different data reduction schemes, compliance calibration and the area method, are used to determine the fibre-dominated initiation and propagation intralaminar fracture toughness values. Propagation values of fracture toughness were measured at 774.9 ± 5.2% kJ/m2 and 768.5 ± 4.1% kJ/m2, when using the compliance calibration method and the area method, respectively. Scanning Electron Microscopy (SEM) is carried out on the fracture surface to obtain insight into the damage mechanism of high-tensile-strength fibre-reinforced unidirectional composites. The measured tensile fracture toughness value is used in a fully validated computational model to simulate the physical test.

The finite element method is extended to the problem of finite plane strain of elastic solids. A highly elastic body subjected to two-dimensional deformations is represented by an assembly of triangular elements of finite dimension. The displacement fields within each element are approximated by linear functions of the local coordinates. Non-linear stiffness relations involving generalised node forces and displacements are derived from energy considerations. For demonstration purposes, the non-linear stiffness equations are applied to the problems of finite simple shear and generalised shear. For finite simple shear, it is shown that these relations are in exact agreement with finite elasticity theory. Convergence rates of finite element representations of these problems are briefly examined.

The computation of slowly moving Shockwaves is considered. A numerical error is introduced into the solution during an explicit computation, which results in the generation of spurious entropy. The generation of this spurious entropy and its effect on the pressure wave in Euler flows is examined, in one dimension by considering a moving shock in a constant area duct, and in two dimensions by considering an unsteady aerofoil flow. An efficient temporal discretisation is presented, whose advantages over the explicit scheme are two-fold. First, the numerical entropy generation due to shock motion is eliminated, and second, the CPU requirements for a two-dimensional unsteady computation are reduced by a factor of five from that required for the explicit scheme, for no loss of accuracy.

Fitting a spike on a blunt body provides a drag reduction at supersonic and hypersonic speeds. In this study, the laminar flow over a spiked, conical body terminated by a spherical cap, inspired by the Apollo re-entry capsule design, was investigated using a hypersonic wind tunnel. Schlieren pictures revealed the absence of flow unsteadiness for the range of spike lengths tested, and force measurements showed a maximum reduction of 77% of the unspiked body drag.

A simple theoretical model based on the pressure drag generated by a solid cone showed good agreement with the experimental data. The measured shock stand-off distance agreed well with predictions.

From Lanchester to the A380; from the era of the great pioneers to the integrated engineering teams and sophisticated analyses required to develop todays airliner. The ‘art’ of Aerodynamics has progressed a long, long way in the intervening century, but even with todays computational power it is still relevant to understand the basics and the early theories as developed by Lanchester and his contemporaries. In this lecture, the relevance of some of that early work and the compromises that must be made in optimising a modern wing design will be presented. These will include optimisation of spanwise loading, including trimming effects and winglets, and high and low speed aerodynamic and structural interactions, with examples drawn from the author's career in helping to develop the wings for the HS146 (now the RJX) and the Airbus family.

With the exponentially increasing computer power available over the last 30 years, the ‘art of compromise’ has progressively become the ‘science of optimisation’ and the lecture closes with a brief reference to techniques used to optimise current wing designs for the Airbus family.

Large deflection analysis of a cantilever beam under a tip concentrated rotational load governed by a second order non-linear differential equation is solved using a fourth-order Runge-Kutta integration scheme. Initially the two point boundary value problem is converted to an initial value problem by estimating one of the two required initial conditions in an iterative process, so as to satisfy the other boundary condition. The details of load deflection curves are presented.

The value of computational fluid dynamics, CFD, delivered to date has mainly been related to its application to high-speed cruise design. To increase its applicability CFD must apply to the full flight envelope frequently characterised by large regions of separated flows. These flows are encountered by transport aircraft at low speed with deployed high lift devices, at their structural design loads conditions, or subjected to in-flight upsets that expose them to speed and/or angle-of-attack conditions outside the envelope of normal flight conditions to name a few. Such flows can only be characterised by the Navier-Stokes equations. This paper will report the progress toward CFD for full flight envelope. The CFD methods in use at Boeing will be described. Examples presented will address high-lift, loads and stability and control concerns including Reynolds scaling from wind tunnel to flight, vortex generator simulation, spoiler and horizontal tail effectiveness. In general, results shown are in ‘good enough’ agreement with experimental data. Deficiencies and the need for further algorithm and process improvement are noted. The need for automation to enable the large scale use of CFD will also be discussed.

This work presents a method for selecting the gain parameters of a C* control law for an aircraft’s longitudinal motion. The design incorporates various handling quality requirements involving modal, time- and frequency-domain criteria that were fixed by the aircraft manufacturer. After necessary model order-reductions, the design proceeds in essentially two-steps: stability augmentation system (SAS) loop design and control augmentation system (CAS) loop design. The approach partly relies on the use of guardian maps to characterise, in each case, the set of gain parameters for which desired handling quality requirements are satisfied. The approach is applied throughout the full flight envelope of a business jet aircraft and yields satisfactory results.

Results of a comparison of dynamic stall onset are presented, as assessed from low Mach number windtunnel data contained in the University of Glasgow's database and that from the well established Beddoes’ model. The model, which was originally developed to reconstruct higher Mach number dynamic stall characteristics, exhibited a lower stall onset incidence than that assessed from the windtunnel data. The differences and speculations on the physical reasoning underlying the two assessments are discussed. An addition to the Beddoes model is proposed which yields an improved reconstruction of the Glasgow windtunnel data.

Recent experimental and computational studies have indicated that rearward curvature of a wing can reduce the induced drag factor to values less than that obtained from the unswept elliptical wing considered optimal in classical wing theory. Wake non-planarity associated with a wing with aft swept tips has been suggested as a reason for this behaviour. This paper provides a systematic examination of the wake non-planarities induced by a variety of wing planforms and quantifies the induced drag reductions which may be expected. Results suggest a dependence of induced drag factor upon angle of attack, and therefore upon lift coefficient. The crescent wing is identified as the planform to derive the most benefit from its non-planar wake shape, typically a 4% reduction in induced drag factor at moderate angle of attack.

This paper reviews the research on Gurney flaps and related high lift trailing edge devices. It investigates aerofoil performances at Reynolds numbers Re ≅ 105 and below, both with the clean configuration and various Gurney flap sizes. The device height is optimised, and a semi-empirical formula linking flap height to free stream speed and aerofoil chord is proposed. The analysis shows that the optimal size of the device is always below the boundary-layer thickness at the trailing edge. Discussion of results includes analysis of hysteresis loops occurring in the L/D performances. These are mostly due to large changes in drag and small changes in lift, which occur when the aerofoil is restored to the reference angle of attack.

A procedure is developed for the analysis of plane stress problems when yielding occurs locally. The region is divided into triangular elements and the deformation is analysed on a step-by-step basis, using the matrix notation developed by Argyris. The simple expressions which are derived for the element properties are applicable with any stress-strain relations which are stable and time-independent. Simple numerical examples are given.