An investigation of a two-dimensional propulsive lifting system

Abstract

Several aspects of the nonhomogeneous flow associated with a system combining lifting and propulsive requirements of an aircraft are considered in detail by analytical and experimental methods. The basic geometry of the problem is that of two lifting surfaces with an actuator disk located between them. The resulting flow consists of two regions of different total energies. Propulsive lift systems are prototypes of many similar multi-energy flow problems. The principles governing flow with energy addition are examined. Basic equations and boundary conditions are developed for the complete inviscid and incompressible analysis for the two-dimensional case. The corresponding flow singularities are discussed and the integral equations which completely specify the system are derived. The two special cases of small and large energy addition are considered in detail including solutions. A numerical procedure is developed to solve the full problem including allowance for the wake deflection. Appropriate vorticity forms are used to represent the entire system. Wake vorticity is provided the freedom to move in the plane. An iterative scheme is presented which rapidly converges to a solution for the magnitude and location of the system vorticity distributions. Forces and moments are evaluated on the propulsive lift system. Analytical results are given from the numerical solution for various values of the geometric and energy parameters. Comparison of the numerical result with the solutions for extreme values of energizing is given. Results from a wind tunnel study of the two-dimensional propulsive-lift system provide a check on the importance of real effects. Comparison of the analytical and experimental results is given in detail. The experimentally determined wake development is observed to be similar to the predicted shape. In addition, the lift augmentation is similar for the theoretical and experimental cases. Further, the airfoil pressure distributions and resulting pitching moments are seen to exhibit the behavior expected from the calculations.