A new modal method capable of analysing the aeroelastic response of rotorcraft in both steady and manoeuvring flight is developed. Particular emphasis is given to the correct modelling of the dynamic interactions between the rotor and the fuselage. This is achieved via the use of complex rotor modes, which allows the effects of hub motion to be incorporated. The modal Lagrangian equation for a single rotating blade using real modes as state variables is first derived. The important non-linear terms based on an ordering scheme are retained. This aeroelastic model is then extended to adopt the complex rotor modes as state variables. This concept, which is both new and analytically demanding, is furnished with minimum algebra. A generalised proof of complex modes orthogonality and its application to the coupled rotor-fuselage dynamic system are provided. Important conclusions drawn from this proof include: A set of complex left-hand eigenvectors are required, together with the right-hand set, in order to reduce the system response equations to an uncoupled modal form suitable for a solution; and It is necessary for the modes analysis to be re-formulated as an eigenvalue problem replacing the transfer matrix solution procedure. An orthogonalisation procedure is employed to reduce the complex system response equations to the uncoupled modal form. The procedure not only simplifies the algebraic process, but also identifies exactly the forcing functions present in the dynamic system modelled. However, for consistency wi th the dynamic model, it is necessary to restrict the blade model to a straight beam with small pre-deformed angles. The need to treat both the complex coupled and reactionless mode sets simultaneously, when they are defined in different reference frames, requires special attention to the solution of the modal responses. A numerical technique is developed for filtering the applied forces and hence identifying the forcing for the respective mode types. The fundamental issue regarding the true definition of angle of attack used for aerodynamic calculation is also addressed. The second order pseudo-torsion term must be removed from the incidence expression to ensure the aerodynamic loads are calculated correctly. The determination of the blade structural loads using both Modal Summation and Force Integration methods is discussed and described. A novel numerical technique, based on curve fitting using Chebyshev polynomials coupled with analytical integration, is devised and shown for the first time to minimise the inherent numerical problems associated with Force Integration. Finally, applications of the analytical model to include the effects of hub motion on vibratory loads calculation and to determine loads in an extreme manoeuvre are successfully demonstrated. The use of rotor modes by including transmission flexibility in a rotor dynamic model in loads calculation is also provided. These correlations establish the important milestone on the ability of this model to improve vibration prediction and to simulate manoeuvring flight. They also demonstrate the potential applications of this model. Recommendations for future research are also made.

A surface shedding discrete vortex method has been developed for stimulating incompressible flows around pitching aerofoils. The method is able to predict both attached and separated flows, the latter typified by the formation and transport of large vortices. The structures of dynamic stall flow are well captured without the need for other means to predetermine the separation points. In contrast to most other vortex methods, the method presented herein can perform quantitative analysis. Throughout a wide range of incidence, the pressure distributions are smooth and the normal force and pitching moment are in good agreement with experimental data. The method is also able to predict the flow with external constraints for simulating the effects of wind tunnel blockage. In this regard quantitative results and flow structures have been obtained which are consistent with those expected. Following the review of previous work presented in the introduction, the mathematical formulation of the method is expounded. A velocity expression is theoretically derived for flows with both a moving inner boundary (aerofoil) and fixed external constraints (wind tunnel walls). To maintain both no penetration and no slip conditions, it is concluded that an external constraint parallel to the free stream can be modelled by placement of a constant vortex sheet along the boundary, and the introduction of distributed vortices next to the constraint to represent the boundary layer. The vortex sheet strength is equivalent to the free stream velocity while the strength of the vortices can be calculated in the same manner as for the internal boundary. This conclusion avoids the necessity of employing mirror vortices and iteration techniques in traditional models. The aerodynamic loads are computed from the pressure distribution. For the computation of surface pressures, the relationship between the pressure gradient and the rate of vorticity creation on the surface has been developed for a moving boundary.

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In this work, a code has been developed that solves the Navier-Stokes equations using the finite volume method with unstructured triangular grids. A cell-centred, finite volume method is used and the pressure-velocity coupling is treated using both the SMTLE and the MAC algorithms. The major advantage of using triangular grids is their applicability to complex geometry. A special treatment is developed to ensure good quality triangular elements around the boundaries. The numerical simulation of incompressible flow at low Reynolds number is studied in this thesis. A code for generating triangular grids using the tri-tree algorithm has been written and an adaptive finite volume method developed for calculating laminar fluid flow. The grid is locally adapted at each time step, with grid refinement and derefinement dependent on the vorticity magnitude. The resulting grids have fine local resolution and are economical in reducing the numerical simulation time. The discretised equations are solved by using an iterative point by point Gauss-Seidel solver. For calculating the values of velocity and pressure at vertices of triangular grids, special interpolation schemes (averaged linear-interpolation and scattered interpolation) are used to increase the accuracy. To avoid the well known checkerboard error problems, i. e., the oscillations occurring in the pressure field, third derivative terms in pressure, first introduced by Rhie-chow (1983), are added to the mass flux velocity. Convective terms are approximated using a QUICK (Quadratic Upstream Interpolation for Convective Kinematics) differencing scheme which has been developed here in for unstructured grids. Three cases of two-dimensional viscous incompressible fluid flow have been investigated: the first is channel flow, in which the numerical results are compared with the analytical solution; the second case is the backward-facing step flow; and the third case is flow past circular cylinders at low Reynolds number (Re). The numerical results obtained for the last two cases are compared with published data. The evolution of vortex shedding is presented for the case of unidirectional flow past a circular cylinder at Re=200. In addition, drag and lift force coefficients are calculated and compared for single and multiple cylinders in unidirectional flow.

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The work presented in this thesis attempts to provide a deeper understanding of the physical phenomena associated with the dynamic stall process on finite wing planforms. The work involves the analysis of data from the Glasgow University unsteady aerodynamics database that has been built up over a number of years through contributions from a range of researchers. Analysis focuses on two finite wing models; one a rectangular wing of aspect ratio three and the other with the same overall dimensions but with 60o swept tips. However, as most research to date has focused on nominally two-dimensional data, the results are referenced to measurements made on a nominally two-dimensional NACA 0015 aerofoil model. This is appropriate as this aerofoil was used as the wing section of both of the three-dimensional wing models. Flow visualisation images collected in a previous study also provide valuable information to supplement the pressure analysis. It is shown that, although the flow at the mid span sections of the finite wings exhibit many of the features of the two-dimensional case, there are some significant differences. In particular, the three-dimensional flow is dominated by the downwash from the wing tips. This causes the normal force response during pitching to lag the static normal force curve. This is in complete contrast to the two-dimensional case where the shed vorticity induces the opposite effect. The downwash also influences the incidence of lift stall but it does so in a manner that is dependent on the reduced pitch rate. Despite these effects, it is established that the flow behaviour in the mid-span region is almost two-dimensional prior to vortex inception. This provides an opportunity to examine the relationship between the generation of vorticity, or vorticity flux, in the leading edge region and the origins of the dynamic stall vortex at specific span locations in location. The vorticity flux distributions around the leading edges of the nominally two-dimensional NACA 0015 aerofoil and the two finite wings are then examined for pitching cases. On this basis a link is established between the peak vorticity flux and the dynamic stall vortex formation. This is confirmed by comparison of the vorticity flux measurements with a previous dynamic stall vortex detection method. The two methods are shown to five almost identical results in situations where the flow may be considered nominally two-dimensional. This suggests that monitoring vorticity flux may provide a practical method of dynamic stall vortex detection. In regions of the finite wings that exhibit strong three-dimensional flow effects, i.e. away from the mid-span, the peak vorticity flux is achieved after the dynamic stall vortex forms. This suggests that vortex formation is triggered by interference from adjacent sections of the wing. To examine this possibility, the vorticity flux is compared to a criterion used to detect the initial instability of the boundary layer at the leading edge. It is shown that the relationship between this criterion and the peak vorticity flux is the same along the span of the wing. This is a significant result as it demonstrates that, although the leading edge response determines the incidence of vortex onset near the mid-span, the formation of the vortex on sections of the wing closer to the tips occurs before the leading edge becomes critical. The implications of this for dynamic stall modelling of two-dimensional dynamic stall predictors with lifting line formulations will not capture this effect.

Non-linear unsteady aerodynamic effects present major modelling difficulties in the analysis of aeroelastic response and in the subsequent design of appropriate controllers. As the direct use of the basic fluid mechanic equations is still not practical for aeroelastic applications, approximate models of the non-linear unsteady aerodynamic response are required. A rigorous mathematical framework, that can account for the complex non-linearities and time-history effects of the unsteady aerodynamic response, is provided by the use of functional representations. A recent development, based on functional approximation theory, has provided a new functional form; namely, multi-layer functionals. Moreover, the multi-layer functional representation for time-invariant, infinite memory systems is shown to be realisable in terms of temporal neural networks. In this work, a multi-layer functional representation of non-linear motion-induced unsteady aerodynamic response is presented. A discrete-time, finite memory temporal neural network, in the form of a finite impulse response (FIR) neural network, is used as a practical realisation of a multi-layer functional. This model form permits the identification of parametric input-output models of the non-linear motion-induced unsteady aerodynamic response. Identification of an appropriate FIR neural network model is facilitated by means of a supervised training process using multiple sets of motion-induced unsteady aerodynamic response. The training process is based on a conventional genetic algorithm to optimise the FIR neural network architecture, and is combined with a simplification of the simulated annealing algorithm to update weight and bias values.

The thesis traces the history of missile aerodynamic prediction methods and defines the aerodynamic requirements for the subsonic free-flight projectiles configurations under consideration. Different types of trajectory model are described with the aerodynamic input requirement being analysed. Methods of generating the required aerodynamic data for the trajectory models are discussed emphasising the aerodynamic models capabilities, weaknesses and ease of use. The method of masses aerodynamic prediction method is defined, highlighting the adaptations to the method that were carried out to generate the aerodynamic stability data required for subsequent projectile trajectory analysis. An assessment of the sensitivity and accuracy of the simulated data is carried out using experimental flight trial data on different projectile configurations. Finally, using the simulation models developed in previous chapters, a parametric analysis is carried out on different projectile configurations to optimise the trajectory performance.

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