The present report discusses the development of a time-dependent Navier-Stokes code for use in predicting transonic shock-wave boundary layer interaction. In addition, various test cases which have been performed are discussed. The algorithm used to solve the equations is based upon the consistently split linearized block implicit method of Briley and McDonald (15, 16). The philosophy and use of a solution adaptive mesh is also described. The test cases studied in this report are: normal shock wave boundary layer interaction in a constant area circular pipe, steady transonic flow over an axisymmetric bump, unsteady flow over an axisymmetric bump, supersonic flow over an axisymmetric compression corner and oblique shock wave impingement on a flat plate boundary layer. (Author).

The hybrid finite difference code developed by MacCormack was applied to the investigation of transonic normal-shock turbulent boundary layer interactions. The computations were performed for the half plane of a symetric two dimensional duct by establishing a symmetry boundary condition at the upper boundary. Both first and second order center line boudnary conditions were imposed with no measurable difference observed. A two-point linear extrapolation of the primative variable was unsuccessfully attempted at the subsonic outflow boundary, but a simple zero gradient condition gave satisfactory results at four different outflow boundary positions relative to the shock wave. Numerical results (M = 1.51, 1.40 and 1.3 Re = 3,000,000 per ft) were compared with the experimental data reported by Abbiss and East. Even though the data exhibit three-dimensional effects, the two-dimensional computations show agreement within approximately 10%. The differences observed in the numerical-experimental comparisons were all consistent with expected three-dimensional trends. Although not conclusive, the potential of adding simple three-dimensional corrections to the two-dimensional code shows promise for improving the experimental-numerical agreement. (Author).

Shock wave-boundary-layer interaction (SBLI) is a fundamental phenomenon in gas dynamics that is observed in many practical situations, ranging from transonic aircraft wings to hypersonic vehicles and engines. SBLIs have the potential to pose serious problems in a flowfield; hence they often prove to be a critical - or even design limiting - issue for many aerospace applications. This is the first book devoted solely to a comprehensive, state-of-the-art explanation of this phenomenon. It includes a description of the basic fluid mechanics of SBLIs plus contributions from leading international experts who share their insight into their physics and the impact they have in practical flow situations. This book is for practitioners and graduate students in aerodynamics who wish to familiarize themselves with all aspects of SBLI flows. It is a valuable resource for specialists because it compiles experimental, computational and theoretical knowledge in one place.

A transonic interaction between a shock wave and a turbulent boundary layer is experimentally and theoretically investigated. The configuration is a channel flow over a bump, where a shock wave causes the separation of the boundary layer and a recirculating bubble is observed downstream of the shock foot.The mean flow is experimentally investigated by means of PIV, then different techniques allows to identify the main unsteadiness of this shock-wave/boundary-layer interaction. As recognised in similar configurations, the flow presents two distinguished characteristic frequencies, whose origins are still unknown.Numerical simulations are performed solving RANS equations. Results are in good agreement with the experimental mean flow, but the approach fails to predict the unsteady. The solution of RANS equations is then considered as a base flow, and a global stability analysis is performed. Eigenvalue decomposition of the Navier-Stokes operator indicates that the interaction is stable, and the dynamics cannot be described by unstable global modes.A linearised approach based on a singular-value decomposition of the Resolvent is then proposed: the noise-amplifier behaviour of the flow is highlighted by the linearised approach. Medium-frequency perturbations are shown to be the most amplified in the mixing layer, whilst the shock wave behaves as a low-pass filter.The same approach is then applied to a transonic flow over a profile, where the flow can present high-amplitude shock oscillations. The stability analysis can describe both the buffet phenomenon when an unstable mode is present, and the convective instabilities responsible of medium-frequency unsteadiness.

A strong viscous-inviscid interaction model has been developed for predicting the detailed properties of the flow in the vicinity of an imbedded transonic shock wave interacting with a turbulent boundary layer in cases where the shock wave is of sufficient strength to result in flow separation. In this interaction model the inviscid flow is analyzed with a compressible stream function analysis specifically developed for mixed subsonic-supersonic flow regions. In the present effort this analysis has been extended to include upstream vorticity effects and the boundary-layer displacement effects. Numerous calculations are presented which demonstrates the capability of this analysis to predict transonic rotational flow. The viscous analysis in this interaction model is a newly developed inverse boundary-layer analysis which accounts for normal pressure gradients and imbedded shock waves. The equations are solved with a coupled implicit finite-difference scheme subject to the condition that the flow at the edge of viscous layer merges asymptotically with the outer inviscid flow. A model problem has been analyzed with this generalized inverse boundary-layer procedure and no stability problems were encountered.