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Numerical Unsteady Aerodynamic and Aeroelastic Simulation

The onset of transonic shock-induced flow separation
is known to be associated with a variety of nonclassical
aeroelastic instability and response phenomena,"13 referred
to variously as: single degree of freedom flutter, limited-
amplitude flutter, limit cycle oscillations (LCO), control sur-
face buzz, shock induced oscillations ($10) and .buffeting
(onset). A characteristic of the "instabilities" involved is a
tendency to grow to a constant or bounded "limit amplitude"
which can vary from a nuisance level to levels large enough
to cause structural failure. In the latter case, the nonclassical
response, generically referred to herein as LCD, is typically
observed near the flutter boundary, making a distinction be
tween the two response mechanisms difficult. Edwardsl‘”
reviewed these features of transonic aeroelasticity, conclud-
ing that i.) computational capability for such cases would
require modeling of dynamically separating and reattaching
viscous boundary layers and ii.) such capability was not yet
mature for wings or more complete configurations.
Interactive Boundary Layer Modeling (IBLM) provides
an alternative to such direct computation of flows involving
viscous shear layers. Separate computations are made for
an inner viscous boundary layer region and an outer inviscid
flow region as illustrated in Fig. 1. Subscript “e" denotes
the “edge" of the boundary layer, while superscripts “i” and
“v" denote inviscid and viscous variables. Ref. 16 devel-
oped an integral boundary layer lag-entrainment method to
compute displacement thickness 6' which was used to up-
date the flow tangency boundary condition of the inviscid
solver. This "direct" solution method for the entrainment
equation becomes singular at flow separation and "inverse"
computation methods”22 have been developed in attempts
to treat flow separation.
Edwardsa'“ summarizes developments of such inverse
computational methods by many authorsn‘zz'zs'33 and ex-
tends the inverse method of Howlett3°33, implemented in
the CAP-TSD3‘32 (Computational Aeroelasticity Program-
Transonic Small Disturbance) potential equation code, with a
new interactive coupling procedure capable of treating tran—
sortie Shock Induced Oscillation (SIO) conditions for air-
foils. Bartels‘z'l3 has recently developed an IBLM with a
fully unsteady finite-difference boundary layer model inter-
acted with a two-dimensional version of the CAP-TSD code
and presents many SIO calculations.