Accurately and efficiently predicting the unsteady dynamics of coupled, fluid-structure systems significantly reduces the cost of designing, testing, and maintaining fixed-wing aircraft, rotorcraft, and turbomachinery. It also improves safety. Organizations can realize substantial savings by understanding these dynamics, because aeroelastic loading increases fatigue cycling and reduces vehicle operating life. Further savings come from designing for lower fleet sustainment costs without incurring additional flight-test expenses. For example, aircraft with weapons stores require certification flight tests for each stores configuration. Replacing flight tests with computational simulations could significantly lower acquisition costs.

Accurate methods of predicting aeroelasticity are also essential in non-aerospace applications where fluid-structure interaction relates to efficient product operation and such important issues as noise control. Engineers can use fluid-structure interaction models to design products that accommodate fluid flow and moving boundaries during operations. Examples range from ink-jet printers with vibrating-diaphragm injection systems to nuclear reactors with flexible fuel rods suspended in high-speed coolant flows.

The problem of fluid-structure interaction is characterized by two dynamic subsystems — fluid and structure — each with its own inertia, stiffness, and damping. The forces that each exerts on the other couple the subsystems. Engineers are concerned with the temporal dynamics of this coupled system. In the case of a lifting surface, the engineer must determine system stability over a range of such operating conditions as Mach number, altitude, and angle of attack.

Inherent difficulties in the problem leave the engineer with two imperfect ways of modeling the coupled system. The difficulties center on the forcing terms that couple the two systems and how the engineer characterizes and then introduces the terms into the equations that govern the fluid and structure. One modeling approach estimates structural deflection growth rates using linearized approximations of the aerodynamic loads. This method follows the tack of modern stability analysis — with approximations to viscous fluid force that limit the scope of application. A second method iteratively marches the model of the fluid and the model of the structure forward in time. This "brute force" approach demands computational resources that can easily become prohibitively expensive.

AeroMechanics is a patent-pending program that predicts and ultimately lets one control the unsteady dynamics of aeroelastic systems. Through a general, curvilinear coordinate transformation, the program achieves exact coupling between the fluid and structure without compromising the effects of viscosity, separation, shocks, and shock-boundary layer interaction. The computational formulation enables a comprehensive approach to the analysis of system dynamics: capturing weak nonlinearities in an eigensystem formulation, strong nonlinearities using the full nonlinear system and dynamic systems methods, and detailed flow dynamics in time-marched simulations of the fully-coupled model.

The eigensystem predicts the stability of the physical system in the presence of weak nonlinearities. The computed eigenvalue of each variable determines its time-dependent behavior — growth, decay, oscillation, oscillatory growth, or oscillatory decay. Therefore, the model can predict the dynamic behavior of the fully-coupled system without iterative time marching, re-meshing, and with no limiting approximations. Time-marched simulations require many CPU hours; even smaller problems like flow over a two-dimensional airfoil require 15 or more CPU hours to predict system dynamics from an initial state to equilibrium. Within minutes, AeroMechanics accurately predicts system stability, enabling a complete exploration of the design early in the process. The computational model has been validated by comparing data from simulations with known, exact solutions and with independent computational data. Maximum relative differences between known, exact solutions and data from the model are consistently small — less than one percent.

This work was done by H. A. Carlson and R. E. Miller of Beam Technologies, Inc. for the Aeroelasticity Branch at NASA's Langley Research Center. For more information, contact

Beam Technologies,
404 Wyman St., Suite 355,
Waltham, MA 02451;
(781) 890-5091