A New Compressibility Correction Method to Predict Aerodynamic Interaction between Lifting Surfaces

A new extension to the vortex-lattice method is presented to properly account for the effect of compressibility on the downwash interaction between two or more lifting surfaces. This method is based on a compressibility-correction factor (κ) that is found from the ratio of lift-curve slopes in compressible and incompressible conditions for a given isolated lifting surface. It is shown that this ratio can be found from empirical, numerical, or experimental estimations. To predict the effect of compressibility on downwash interaction, the relative distance between lifting surfaces is scaled by 1/κ resulting in a modified influence matrix. It is demonstrated that by extracting κ values from isolated-wing Euler-CFD predictions, this modified vortex-lattice method is capable of predicting downwash interaction with great precision. For a wing-horizontal tail system, the error with respect to an Euler prediction is shown to be no more than 3% for the horizontal-tail lift-curve slope at M∞ = 0.6. Furthermore, for canard-wing interaction, the prediction of the spanwise lift distribution demonstrates that the accuracy of the modified vortex-lattice prediction is dependent on how close the tip vortex from the canard passes from the main wing. Overall agreement with Euler predictions was good up to the highest Mach number (M∞ = 0.7). Comparison of predicted lift coefficients between VLM-κ-r and Euler showed differences in canard lift coefficient of no more than 1.6%, while the difference in wing lift coefficient was no more than 0.8%.