Aeroelastic Calculations Using CFD for a Typical Business Jet Model
Two time-accurate Computational Fluid Dynamics (CFD) codes were used to compute several flutter points for a typical business jet model. The model consisted of a rigid fuselage with a flexible semispan wing and was tested in the Transonic Dynamics Tunnel at NASA Langley Research Center where experimental flutter data were obtained from M(sub infinity) = 0.628 to M(sub infinity) = 0.888. The computational results were computed using CFD codes based on the inviscid TSD equation (CAP-TSD) and the Euler/Navier-Stokes equations (CFL3D-AE). Comparisons are made between analytical results and with experiment where appropriate. The results presented here show that the Navier-Stokes method is required near the transonic dip due to the strong viscous effects while the TSD and Euler methods used here provide good results at the lower Mach numbers.
Calculation of AGARD Wing 445.6 Flutter Using Navier-Stokes Aerodynamics
The flutter characteristics of the first AGARD standard aeroelastic configuration for dynamic response, Wing 445.6, are studied using an unsteady Navier-Stokes algorithm in order to investigate a previously noted discrepancy between Euler flutter characteristics and the experimental data. The algorithm, which is a three-dimensional, implicit, upwind Euler/Navier-Stokes code (CFL3D Version 2.1), was previously modified for the time-marching, aeroelastic analysis of wings using the unsteady Euler equations. These modifications include the incorporation of a deforming mesh algorithm and the addition of the structural equations of motion for their simultaneous time integration with the governing flow equations. In this paper, the aeroelastic method is extended and evaluated for applications that use the Navier-Stokes aerodynamics. The paper presents a brief description of the aeroelastic method and presents unsteady calculations which verify this method for Navier-Stokes calculations. A linear stability analysis and a time-marching aeroelastic analysis are used to determine the flutter characteristics of the isolated 45° swept-back wing. Effects of fluid viscosity, structural damping, and number of modes in the structural model are investigated. For the linear stability analysis, the unsteady generalized aerodynamic forces of the wing are computed for a range of reduced frequencies using the pulse transfer-function approach. The flutter characteristics of the wing are determined using these unsteady generalized aerodynamic forces in a traditional V-g analysis. This stability analysis is used to determine the flutter characteristics of the wing at free-stream Mach numbers of 0.96 and 1.141 using the generalized aerodynamic forces generated by solving the Euler equations and the Navier-Stokes equations. Time-marching aeroelastic calculations are performed at a free-stream Mach number of 1.141 using the Euler and Navier-Stokes equations to compare with the linear V-g flutter analysis method. The V-g analysis, which is used in conjunction with the time-marching analysis, indicates that the fluid viscosity has a significant effect on the supersonic flutter boundary for this wing while the structural damping and number of modes in the structural model have a lesser effect.
Mechanics of deformable directed surfaces
Abstract The paper develops a simple, yet complete and consistent non-linear dynamic thermo-elastic shell theory based on the concepts of a two-dimensional directed continuum. The constitutive equations are postulated in a general form. Stress-strain relations are derived using the equation of energy balance and the two entropy production inequalities, which are rewritten in a special form. The linear theory is discussed in detail. The structure of the stress-strain relations is presented in the most general form and then specialized to concrete examples, in particular, to the classical shell theory, using their invariance properties with respective to certain symmetry groups. The elastic moduli are determined by demanding the coincidence of the frequency dispersion surfaces obtained using the two-dimensional theory with the lowest foils of the corresponding surfaces resulting from the three-dimensional theory of elasticity.