Stall Cell Prediction Using a Lifting-Surface Model

Abstract

This paper investigates the use of a lifting surface method coupled with a nonlinear lift curve, the nonlinear vortex lattice method (NL-VLM), toward the study of stall cells on wings. First, Spalart’s spectral lifting line model is thoroughly investigated. It is found that the Gaussian filter leads to the existence of two different solutions, one directly interpolated in the lift polar and the other retrieved from the circulation distribution. Then the NL-VLM method is applied to the canonical cases of the infinite and the elliptic wing. In this model, the stall cells is represented as a sharp transition between stalled and prestalled wing section, meaning that no wing section effectively sees a negative slope of the lift against angle-of-attack relation. This sharp transition can be smoothed by introducing an artificial dissipation that also results in two separated solutions, without changing the underlying characteristics of the model. The effect of several parameters, like the grid spacing and the relaxation factor, is studied, with little effect on the wavelength of the predicted stall cells. The effect of specific parameters of the lift polar like the magnitude of the negative slope in the stall regime and the trend in the deep stall range is also investigated. It is observed that the slope of the lift versus angle of attack must not stay negative when the angle of attack goes to infinity for the system of equations to have a steady solution. The amplitude of the negative lift-curve slope has an effect on the wavelength of the cells explaining why the stall cells would not be observed for a leading-edge-type stall. Finally rectangular wings are studied for comparison to experimental data and higher-fidelity numerical simulations, showing the predictive capability of the proposed low-order model.