In-Flight Aeroelastic Stability of the Thermal Protection System on the NASA HIAD, Part I: Linear Theory

Abstract

Conical shell theory and piston theory aerodynamics are used to study the aeroelastic stability of the thermal protection system (TPS) on the NASA Hypersonic Inflatable Aerodynamic Decelerator (HIAD). Structural models of the TPS consist of single or multiple orthotropic conical shell systems resting on several circumferential linear elastic supports.The shells in each model may have pinned (simply-supported) or elastically-supported edges. The Lagrangian is formulated in terms of the generalized coordinates for all displacements and the Rayleigh-Ritz method is used to derive the equations of motion. The natural modes of vibration and aeroelastic stability boundaries are found by calculating the eigenvalues and eigenvectors of a large coefficient matrix. When the in-flight configuration of the TPS is approximated as a single shell without elastic supports, asymmetric flutter in many circumferential waves is observed. When the elastic supports are included, the shell flutters symmetrically in zero circumferential waves. Structural damping is found to be important in this case. Aeroelastic models that consider the individual TPS layers as separate shells tend to flutter asymmetrically at high dynamic pressures relative to the single shell models. Several parameter studies also examine the effects of tension, orthotropicity, and elastic support stiffness. Nomenclature a n , b n , c n Modal coordinates for the three shell displacements, m D ef f Effective material bending stiffness, P a m 3 D y , D θ Shell Bending stiffness in the y and θ directions, respectively, P a m 3 D yθ Shell in-plane twisting stiffness, P a m 3 E Material Young's Modulus, P a E y , E θ Shell Young's Modulus in the y and θ directions, respectively, P a fFrequency, Hz f crit Critical frequency, at the flutter or divergence boundary, Hz G yθ Shear modulus, P a h Shell thickness, m k Circumferential wavenumber k crit Critical circumferential wavenumber, at the flutter or divergence boundary K s Spring stiffness for the circumferential elastic supports, P a K P Y R Pyrogel spring stiffness, P a/m m Shell mass per area, kg/m 2

In-Flight Aeroelastic Stability of the Thermal Protection System on the NASA HIAD, Part II: Nonlinear Theory and Extended Aerodynamics

“…To verify that the time-integration scheme has been implemented correctly, various comparisons were made with the linear theory used in Part I. 1 Note that this linear analysis was found to be consistent with previously published results on the free vibrations and flutter of conical shells. First, a buckling analysis was computed in the time domain, using the critical circumferential buckling mode (n crit = 43) found in the eigenanalysis (for the 6-meter configuration), and neglecting all nonlinear terms.…”

“…The first set of results are from validation studies, ensuring that the nonlinear buckling and aeroelastic simulations are consistent with the linear theory in Part I. 1 Next, deflection shapes and strains for a static load simulation are presented, corresponding to experimental tests performed on a 6-meter HIAD article. Aeroelastic limit cycle oscillations are then calculated for various cases, and the effects of axially-applied tension are examined for the 3-meter geometry.…”

“…Details on the thermal protection system modeling can be found in reference [1]. A brief summary of the structural models and TPS will be provided here, since the current analysis is based on the previous work.…”

“…Nonlinear aeroelastic solutions are calculated by first performing the linear analysis described in Part I. 1 Linear theory predicts a single critical circumferential mode as well as coalescence of two axial modes at the flutter dynamic pressure. A nonlinear time integration simulation is then performed with initial conditions (displacements) in the coordinates for these critical modes only.…”

“…The purpose of this report series, consisting of the current work and reference [1], is to characterize the in-flight aeroelastic behavior of a proposed thermal protection system 2 for the NASA Hypersonic Inflatable Aerodynamic Decelerator (HIAD). 3 The HIAD is an inflatable aeroshell with a diameter significantly larger than that of current rigid aeroshells.…”