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The goal of the present work is the development of a numerical method for compressible viscous flows on mixed unstructured grids. The discretisation is based on a vertex-centred finite-volume method. The concept of grid transparency is developed as a framework for the discretisation on mixed unstructured grids. A grid-transparent method does not require information on the cell types. For this reason, the numerical method developed in the present work can be applied to triangular, quadrilateral, and mixed grids without modification. The inviscid fluxes are discretised using the approximate Riemann solver of Roe. A limited linear-reconstruction method leads to monotonic capturing of shock waves and second-order accuracy in smooth regions of the flow. The discretisation of the viscous fluxes on triangular and quadrilateral grids is first studied by reference to Laplace's equation. A variety of schemes are evaluated against several criteria. The chosen discretisation is then extended to the viscous fluxes in the Navier-Stokes equations. A careful study of the various terms allows a form to be developed which may be regarded as a thin-shear-layer approximation. In contrast to previous implementations, however, the present approximation does not require knowledge of normal and tangential coordinate directions near solid surfaces. The effects of turbulence are modelled through the eddy-viscosity hypothesis and the one-equation model of Spalart and Allmaras. The discrete equations are marched to the steady-state solution by an explicit Runge-Kutta method with local time-stepping. The turbulence-model equation is solved by a point-implicit method. To accelerate the convergence rate, an agglomeration multigrid method is employed. In contrast to previous implementations, the governing equations are entirely rediscretised on the coarse grid levels. The solution method is applied to various inviscid, laminar, and turbulent flows. The performance of the multigrid method is compared for triangular and quadrilateral grids. Care is taken to assess numerical errors through grid-refinement studies or comparisons with analytical solutions or experimental data. The main contributions of the present work are the careful development of a solution method for compressible viscous flows on mixed unstructured grids and the comparison of the impact of triangular, quadrilateral, and mixed grids on convergence rates and solution quality.

Numerical analysis conducted using Callisto, which is Airbus’s three-dimensional momentum integral boundary layer code coupled with Green’s lag-entrainment method has shown that there might be a small but worthwhile form drag reduction through attachment line control, up to about 0:4-0.6 counts for an aircraft. However, in order to overcome numerical issues in the modelling a few approximations have been made in the method while calculating the flow very near the leading ledge. The detail of the leading edge flow needs to be verified if the drag results are to be trusted. Therefore, an experiment carried out, aiming to capture the velocity profiles starting from the attachment line and up to about 3% chord downstream. In order to design the experimental model, a systematic approach was used based on previous semi-empirical work on the attachment line flow. The model was designed so that the attachment line boundary layer is turbulent due to contamination from the turbulent boundary layer from the wall (floor) of the wind tunnel and thick enough to give a sensible experimental domain size including sufficient chord wise extent for hot-wire measurement. The velocity profiles were captured by means of hot wire anemometry using a micro displacement traverse designed and manufactured in-house.

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No description available.

No description available.