Prediction of pitch-damping aerodynamic derivatives using Navier-Stokes computational techniques

A computationally based, multi-disciplinary approach for predicting the pitch-damping aerodynamic derivatives for symmetric flight bodies has been developed and validated for flight velocities from high subsonic/low transonic through high supersonic velocities. Although the pitch-damping aerodynamic derivatives are normally associated with unsteady or time-dependent motions, the approach presented here utilizes steady motions that result in steady flow fields to produce the aerodynamic forces and moments of interest. These motions include coning motion, looping motion and two forms of helical motion. The four motions allow the pitch-damping coefficient sum and its individual components to be determined.;The technique has been extensively validated with experimental data and comparisons with simpler theories show significant improvements in the prediction accuracy. The versatility of the technique has been demonstrated by application to a wide variety of flight body geometries over a range of flight velocities including high subsonic, transonic and supersonic velocities.;To predict the aerodynamic forces and moments of interest, a sophisticated computational capability based on the thin-layer Navier-Stokes equations has been developed. The technique allows the three-dimensional turbulent viscous flow field acting on the body in response to the applied motions to be determined. The aero-dynamic forces and moments can then be computed from the integrated effects of the pressure and viscous stresses acting on the body. A key feature of the technique is the use of a body-fixed rotating coordinate frame that allows the flow field to be viewed from a steady frame. Because this is a non-inertial coordinate frame, the governing equations have been modified to include the centrifugal and Coriolis body forces due to the coordinate system rotation. Two computational techniques have been implemented to cover the envelope of flight velocities. For high subsonic, transonic or low supersonic flows, a time-marching thin-layer Navier-Stokes technique is utilized to obtain the solution in a time-iterative manner. At supersonic velocities, a space-marching parabolized Navier-Stokes technique is applied to determine the flow field from a single pass through the computational grid.