Airfoil

Abstract: An algebraic turbulence model for two- and three-dimensional separated flows is specified that avoids the necessity for finding the edge of the boundary layer. Properties of the model are determined and comparisons made with experiment for an incident shock on a flat plate, separated flow over a compression corner, and transonic flow over an airfoil. Separation and reattachment points from numerical Navier-Stokes solutions agree with experiment within one boundary-layer thickness. Use of law-of-the-wall boundary conditions does not alter the predictions significantly. Applications of the model to other cases are contained in companion papers.

Abstract: Preface Acknowledgements List of main symbols List of figures List of tables 1. Introduction: a history of helicopter flight 2. Fundamentals of rotor aerodynamics 3. Blade element analysis 4. Rotating blade motion 5. Basic helicopter performance 6. Conceptual design of helicopters 7. Rotor airfoil aerodynamics 8. Unsteady aerodynamics 9. Dynamic stall 10. Rotor wakes and tip vortices Appendix Index.

Abstract: The aerodynamic forces on an oscillating airfoil or airfoil-aileron combination of three independent degrees of freedom were determined. The problem resolves itself into the solution of certain definite integrals, which were identified as Bessel functions of the first and second kind, and of zero and first order. The theory, based on potential flow and the Kutta condition, is fundamentally equivalent to the conventional wing section theory relating to the steady case. The air forces being known, the mechanism of aerodynamic instability was analyzed. An exact solution, involving potential flow and the adoption of the Kutta condition, was derived. The solution is of a simple form and is expressed by means of an auxiliary parameter k. The flutter velocity, treated as the unknown quantity, was determined as a function of a certain ratio of the frequencies in the separate degrees of freedom for any magnitudes and combinations of the airfoil-aileron parameters.

Abstract: Calculation procedures for viscous/inviscid analysis and mixed-inverse design of subcritical airfoils are presented. An inviscid linear-vorticity panel method with a Karman-Tsien compressiblity correction is developed for direct and mixed-inverse modes. Source distributions superimposed on the airfoil and wake permit modeling of viscous layer influence on the potential flow. A two-equation lagged dissipation integral method is used to represent the viscous layers. Both laminar and turbulent layers are treated, with an e 9-type amplification formulation determinining the transition point. The boundary layer and transition equations are solved simultaneously with the inviscid flowfield by a global Newton method. The procedure is especially suitable for rapid analysis of low Reynolds number airfoil flows with transitional separation bubbles. Surface pressure distributions and entire polars are calculated and compared with experimental data. Design procedure examples are also presented.

Abstract: 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 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.