AIAA 2000-4321 Steady–State Computation of Constant Rotational Rate Dynamic Stability Derivatives

Dynamic stability derivatives are essential to predicting the open and closed loop performance, stability, and controllability of aircraft. Computational determination of constant-rate dynamic stability derivatives (derivatives of aircraft forces and moments with respect to constant rotational rates) is currently performed indirectly with finite differencing of multiple time-accurate computational fluid dynamics solutions. Typical time-accurate solutions require excessive amounts of computational time to complete. Formulating Navier-Stokes (N-S) equations in a rotating, noninertial reference frame and applying an automatic differentiation tool to the modified code has the potential for directly computing these derivatives with a single, much faster steady-state calculation. The ability to rapidly determine static and dynamic stability derivatives by computational methods can benefit multidisciplinary design methodologies and reduce dependency on wind tunnel measurements. The CFL3D thin-layer N-S computational fluid dynamics code was modified for this study to allow calculations on complex three-dimensional configurations with constant rotation rate components in all three axes. These CFL3D modifications also have direct application to rotorcraft and turbomachinery analyses. The modified CFL3D steady-state calculation is a new capability that showed excellent agreement with results calculated by a similar formulation. The application of automatic differentiation to CFL3D allows the static stability and body-axis rate derivatives to be calculated quickly and exactly. Graduate Student, NASA Langley Research Center, Multidisciplinary Optimization Branch, MS 159, Hampton, Virginia, Member AIAA Research Scientist, Multidisciplinary Optimization Branch, MS 159, Senior Member AIAA Copyright  2000 by the American Institute of Aeronautics, Inc. No copyright is asserted in the United States under Title 17, U.S. Code. The Government has royalty-free license to exercise all rights under the copyright claimed herein for government purposes. All other rights reserved by the copyright owner. Introduction Dynamic derivatives quantify the aerodynamic damping of aircraft motions and are used to predict the longitudinal short period, lateral pure roll, and lateral Dutch roll behavior of the configuration. Analytical, empirical, and vortex lattice methods of estimating these derivative values are not suited to unconventional configurations or high-speed, compressible flows dominated by viscous effects. Evaluating unconventional configurations is of growing interest due to the design and analysis of next generation attack, transport, and reusable launch vehicles. Examples of these new, unconventional designs are the blended wing body and the X-33 configurations. A methodology of using high fidelity, noninertial Euler and Navier-Stokes (N-S) calculations gives improved capability in predicting these dynamic stability derivative values in compressible flow on conventional or unconventional designs. Due to cost and time limitations, it is impractical to construct and test numerous wind tunnel models during initial prototyping. Therefore, measurement of the effects of aircraft dynamics on preliminary configuration aerodynamic forces and moments is limited. The application of automatic differentiation to a noninertial reference frame Euler and N-S code has potential for providing designers with insight, gained from higher fidelity codes, into aircraft dynamics at the preliminary design stage. This design stage is when control surface size and preliminary control laws are being evaluated. Computational determination of these derivatives is cheaper and faster than performing wind tunnel measurements and will aid rapid prototyping and multidisciplinary design. The modification of the CFL3D (Computational Fluids Laboratory Three-Dimensional) computational fluid dynamics (CFD) code to perform calculations in a noninertial, rotating reference frame has the potential to reduce the reliance on forced-motion wind tunnel and free-flight wind tunnel tests. Considerable previous work performed on turbomachinery has demonstrated noninertial, rotating reference frame