A Nonlinear Hybrid Vortex Method for Wings at Large Angle of Attack

A steady and unsteady nonlinear hybrid vortex (NHV) method is developed for low aspect ratio wings at large angles of attack. The method uses vortex panels with linear vorticity distribution (equivalent to a quadratic doublet distribution) to calculate the induced velocity in the near field using closed-form expressions. In the far field, the distributed vorticity is reduced to concentrated vortex lines and the simpler Biot-Savart law is employed. The method is applied to rectangular wings in steady and unsteady flows. The numerical results show that the method accurately predicts the distributed aerodynamic loads and that it is of acceptable computational efficiency. N recent years, the development of numerical methods for predicting the steady and unsteady aerodynamic characteristics of lifting surfaces exhibiting leading- and/or side-edge separations has received considerable attention. For the steady flow problems several numerical techniques have been developed. These include the nonlinear discrete vortex1'6 (NDV) methods, higher order doublet panel methods,7"9 and nonlinear hybrid vortex (NHV) methods.10'11 For the unsteady flow problems, the literature shows fewer numerical techniques which include the NDV methods12"15 and constant doublet panel methods.16'17 The literature lacks high-order panel methods for the unsteady flow problems. For this reason, we are presenting in this paper an efficient and accurate method for the steady and unsteady flow problems of lifting surfaces at large angles of attack. In this method, vortex panels with linear vorticity distribution are used in the near field calculations. In the farfield calculations, the distributed vorticity over each far-field panel is lumped into equivalent concentrated vortex lines. In this way, accuracy is satisfied in the near field while computational efficiency is maintained in the far field. The coupling of a continuous vortex-sheet representation and a concentrated vortex-line representation for solving the nonlinear lifting surface problem is called the "nonlinear hybrid vortex'' (NHV) method.