The NASA Lewis Research Center is developing analytical methods
and software tools to create a bridge between the controls and
computational fluid dynamics (CFD) disciplines. Traditionally,
control design engineers have used coarse nonlinear simulations
to generate information for the design of new propulsion system
controls. However, such traditional methods are not adequate for
modeling the propulsion systems of complex, high-speed vehicles
like the High Speed Civil Transport. To properly model the relevant
flow physics of high-speed propulsion systems, one must use simulations
based on CFD methods. Such CFD simulations have become useful
tools for engineers that are designing propulsion system components.
The analysis techniques and software being developed as part of
this effort (ref. 1) are an attempt to evolve CFD into a useful
tool for control design as well.
One major aspect of this research is the generation of linear
models from steady-state CFD results. CFD simulations, often used
during the design of high-speed inlets, yield high-resolution
operating point data. Under a NASA grant, the University of Akron
has developed analytical techniques and software tools that use
these data to generate linear models for control design. The resulting
linear models have the same number of states as the original CFD
simulation, so they are still very large and computationally cumbersome.
Model reduction techniques have been successfully applied to reduce
these large linear models by several orders of magnitude without
significantly changing the dynamic response. The result is an
accurate, easy to use, low-order linear model that takes less
time to generate than those generated by traditional means.
The development of methods for generating low-order linear models
from steady-state CFD is most complete at the one-dimensional
level (ref. 2), where software is available to generate models
with different kinds of input and output variables. One-dimensional
methods have been extended somewhat so that linear models can
also be generated from two- and three-dimensional steady-state
results. Standard techniques are adequate for reducing the order
of one-dimensional CFD-based linear models. However, reduction
of linear models based on two- and three-dimensional CFD results
is complicated by very sparse, ill-conditioned matrices. Some
novel approaches are being investigated to solve this problem.
Currently available software uses one-dimensional CFD results
to generate linear models for a number of different input variables.
Upstream input variables can be Mach number or static temperature.
Exit plane input variables can be Mach number, static pressure,
or corrected mass flow. Internal input variables can be the massflow
rate for bleed or bypass regions. Note that a linear model must
be generated for each input variable of interest. Superposition
can then be used to combine several linear models into a single
multi-input, multi-output linear model. Each linear model can
output the Mach number, static pressure, and total pressure for
any node in the CFD grid. Furthermore, bounds can be calculated
to describe the uncertainty of the model due to linearization
and order reduction.
The figure shows how the time response of a reduced-order linear
model with 20 states compares with the response of the original
nonlinear model with 123 states. The results shown here were generated
from a quasi-one-dimensional model of a mixed-compression inlet
being developed for the High Speed Civil Transport program. They
represent the pressure response at a point in the subsonic diffuser
to a 1-percent increase in exit plane corrected mass flow. The
strong agreement between the responses of the reduced-order model
and those of the nonlinear model increases confidence in the use
of the reduced-order model for control design. The linearization
process has been identified as the cause of the difference between
the transient response of the two models. Current research is
focused on improving this process.
Find out more about
this
research.
Lewis contact: Kevin J. Melcher, (216) 433-3743, kmelcher@grc.nasa.gov
Author: Kevin J. Melcher
Headquarters program office: OA (HPCCO)
Previous articleLast updated April 29, 1997
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