| An aerodynamic model is developed for the rolling moment on a delta wing rolling about the longitudinal body-axis. The delta wing has a leading-edge sweep of 65 degrees, and the longitudinal body-axis is inclined to the flow at 30 degrees. Modeling is complicated by the presence of discontinuities in the static data, either in their value or their slope, called critical states. These critical states are associated with changes in the static flow topology, such as vortex breakdown crossing the trailing edge of the delta wing. The time scales of the flow field response to changes in roll angle vary across critical states, and lengthy transient effects often persist long after a critical state has been crossed. Modeling the rolling moment is further complicated by the presence of distinct time scales within a single flow field topology. Much of the flow field resembles that for attached flow, with a time scale inversely proportional to the convection speed, and is considered to be instantaneous for the roll rates studied. The longer time scale is an order of magnitude longer, because of the lags in the vortex breakdown locations.;This research presents the aerodynamic model in both nonlinear indicial response and state-space forms and demonstrates the relationship between the two. To accommodate the different time scales present in the flow field, the model is split into two parts, the potential and vortical components. The roll angle domain is divided into regions separated by critical states, and a separate model is determined for each region. The critical state encounters are handled by splitting the motion into two segments, one leading up to the critical state encounter and one after. Then, the transient effects are found using rolling motions that isolate a single critical state. The complete model is then assembled from its components. Comparisons to experimental data for both harmonic oscillations and ramp and hold motions that include multiple critical state crossings show that the model is a significant improvement over conventional locally-linear models. |
