Traditionally, approximate solutions of these problems are found by "cut and try" methods, combining a designer's engineering experience with repeated experimental testing. Current methods take advantage of computational advances to compute the optimal design directly. Application of the sensitivity equation method is studied in this work.
The test problem below is motivated by the free-jet test facility at the Arnold Engineering Development Center (AEDC). This facility is used to test commercial and military jet engines under air flow conditions they would receive in flight. This facility consists of:
The design of the forebody simulator is an important step in any test, since it shapes the flow profile to the engine inlet. In this study, we consider a two dimensional analogue of this problem.
Modeling assumptions:
We then seek a shortened forebody shape (half the length of the original forebody) which simulates the effect of the original forebody on the outflow.
Shortened Forebody (shape to be determined)
Since we have restricted ourselves to using a shortened forebody, we don't expect to match the outflow exactly. Therefore we create a measure of how close we are. This measure is the least squares error in the density, momentum and pressure at the outflow.
The sensitivity equation method was used to solve this problem.
The optimization was performed starting with the parameters:
View either an mpeg movie or a quicktime movie of the iterations to convergence.
It was observed that the first Bezier parameter converges first producing a blunter forebody which forces the shock to emminate from in front of the forebody. The shock then slides up the outflow boundary to match the shock location of the long forebody.
The second Bezier parameter increases at first to help produce a blunt forebody, then later in the iteration, decreases to better match the flow closer to the forebody.
The iteration converged quickly due in part to the presence of the shock (investigated in related work).
For more details, please consult:
Borggaard, J. and Burns, J., A Sensitivity Equation Approach to
Shape Optimization in Fluid Flows , in Flow Control,
M. Gunzburger editor, Springer-Verlag, pages 49-78 (1995).
(Also appeared as
ICASE Report No. 94-8)
This research was joint work with:
Funding was provided by the Air Force Office of Scientific Research under grants F49620-92-J-0078 and F49620-93-1-0280.
Some of the multimedia on this page was generated as a project for Scientific Visual Analysis with Multimedia (ESM 4714/5984).