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A method of accurately calculating transonic and low Reynolds number airfoil flows, implemented in the viscous-inviscid design/analysis code ISES, is presented. The Euler equations are discretized on a conservative streamline grid and are strongly coupled to a two-equation integral boundary-layer formulation, using the displacement thickness concept. A transition prediction formulation of the e 9 type is derived and incorporated into the viscous formulation. The entire discrete equation set, including the viscous and transition formulations, is solved as a fully coupled nonlinear system by a global Newton method. This is a rapid and reliable method for dealing with strong viscous-inviscid interactions, which invariably occur in transonic and low Reynolds number airfoil flows. The results presented demonstrate the ability of the ISES code to predict transitioning separation bubbles and their associated losses. The rapid airfoil performance degradation with decreasing Reynolds number is thus accurately predicted. Also presented is a transonic airfoil calculation involving shock-induced separation, showing the robustness of the global Newton solution procedure. Good agreement with experiment is obtained, further demonstrating the performance of the present integral boundary-layer formulation.

SUMMARYThe present work predicts the formation of laminar separation bubbles at low Reynolds numbers and the related transition to turbulence by means of Implicit Large Eddy Simulations with a high-order Discontinuous Galerkin method. The flow around an SD7003 infinite wing at an angle of attack of 4 • is considered at Reynolds numbers of 10 000, 22 000, and 60 000 in order to gain insight into the characteristics of the laminar and turbulent regimes. At the lowest Reynolds number studied, the flow remains laminar and two dimensional over the wing surface, with a periodic vortex shedding. For higher Reynolds numbers, the flow is unsteady over the upper wing surface and exhibits a separation bubble along which the flow transitions to turbulence. Tollmien-Schlichting (TS) waves are observed in the boundary layer, and transition is found to be caused by unstable TS modes as revealed by the growth of the stream-wise amplification factor.

A control volume analysis of the compressible viscous flow about an aircraft is performed, including integrated propulsors and flow control systems. In contrast to most past analyses which have focused on forces and momentum flow, in particular thrust and drag, the present analysis focuses on mechanical power and kinetic energy flow. The result is a clear identification and quantification of all the power sources, power sinks, and their interactions which are present in any aerodynamic flow. The formulation does not require any separate definitions of thrust and drag, and hence it is especially useful for analysis and optimization of aerodynamic configurations which have tightly integrated propulsion and boundary layer control systems. x, y, z cartesian axes