A method for the calculation of steady or unsteady compressible flows is presented. The procedure, based on a cartesian cut cell approach and multi-dimensional high resolution upwind finite volume scheme, can cope with static or moving body problems having arbitrarily complex geometries. The method is described in two parts. In Part A, we discuss the cartesian cut cell approach and upwind finite volume scheme for static body problems. The method is validated on test problems involving both steady and unsteady compressible flows and then applied to some practical problems. The extension of the method to moving body problems is presented in Part B (pp 57-65).

A cartesian cut cell method for static body problems was presented in Part A (pp 47-56). Here, we extend the method to unsteady compressible flows involving arbitrarily moving bodies. The moving bodies are allowed to cross a stationary background cartesian mesh. So problems such as mesh distortion and/or restrictions on body motion which may affect other mesh approaches do not occur.

A MUSCL-Hancock finite volume scheme has been modified for moving boundary problems. The upwind fluxes on the interfaces of static cells are updated using an HLLC approximate Riemann solver and an exact Riemann solution for a moving piston is used to update moving solid boundaries (faces). A cell merging technique has been developed to maintain numerical stability in the presence of arbitrarily small cut cells and to retain strict conservation at moving boundaries.

The method has been validated against some well-known two dimensional test problems and applied to practical examples involving an exploding pressure vessel and a store release into a Mach 1.5 stream.

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.

A computer program for use in the conceptual stage of aircraft design has been developed. The program obtains minimum mass designs for high aspect ratio, composite wings, subject to constraints on flutter speed, divergence speed and material stress. The wing is modelled as a series of composite beam elements and both flutter speed and divergence speed are calculated using a normal mode approach. Modal analysis is carried out by applying the Wittrick-Williams algorithm to the dynamic stiffness method, whereas unsteady aerodynamic loads are calculated from strip theory, although an option which uses lifting-surface theory is also presented. A previously published example is given to validate the analysis. Single level optimisation is carried out using a sequential quadratic programming strategy combined with the modified methods of feasible directions optimizer, for which flutter sensitivities are obtained by an efficient determinant interpolation technique. Design variables include topological variables such as spar and engine positions as well as layer thicknesses, which are modelled using quadratic functions. The wing of a regional turboprop aircraft is optimized to illustrate the use of the program. The problem was modelled using 10 elements and had 43 design variables, 162 constraints and required just over 20 minutes of CPU time on a workstation. This, coupled with the fact that a full three-dimensional FE model of the same wing would require over 1000 elements, illustrates the suitability of the dynamic stiffness method to the conceptual design stage.

A windtunnel study was undertaken to determine the effects of delta planform tip sails (DPTS) on the aerodynamic characteristics of a planar blunt edged wing. In the investigation, the sail incidence and chordwise attachment position were varied. The results indicate that significant performance improvements can be obtained with DPTS. For all DPTS variations, increases of lift curve slope, maximum lift coefficient and Oswald efficiency factor were recorded and compared to the basic wing.

Energy considerations are used to find the spanwise circulatory lift distribution yielding minimal induced resistance for a harmonically oscillating planar wing in a steady incompressible flow. Under the restriction that the time-averaged and oscillatory constituents of the wing's circulatory lift are known, the optimal distribution is such that its time-averaged constituent is elliptical, but the oscillatory one is generally not. The latter varies from elliptical to rectangular as the frequency of the oscillations increases. When the oscillatory part of the lift is not prescribed, present results infer that its reduction — as, for example, by an elastic twist — will typically reduce the drag, even if the twist yields a non-optimal (for that lift) lift distribution.