|
Unsteady transonic channel flow solutions have long been
recognized as useful in understanding the stability problems of
operating aircraft engines. The primary purpose of this thesis
is to study unsteady transonic flows in inflexible or flexible
channels with various expansion ratios. To accurately calculate
transonic flow solutions with shock waves, a fast, high-
resolution Total Variation Diminishing (TVD) scheme is
considered for flow simulations. To implement the fast TVD
scheme, the concept of a correct weighting function on initial
data for analyzing numerical schemes used for solving
hyperbolic equations is introduced. The concept can be used to
understand quantitatively the wave propagation behavior for
different schemes. The weighting functions of some basic
spatial difference schemes are presented based on the linear
convection equation. From the viewpoint of weighting on initial
data, the accuracy and stability of a scheme, either implicit
or explicit, can be made clear. This weighting concept on
initial data is further applied to nonlinear schemes. Thus, the
weighting functions of three second-order implicit TVD schemes,
including the Harten scheme, the Yee scheme, and the present
scheme, are compared, leading to the suggestion of a robust
flux limiter for the TVD scheme. To verify the present scheme,
several test problems are simulated. The present scheme is
found to be efficient and accurate. In this study, quasi-one-
dimensional and two-dimensional transonic channel flow problems
are simulated to assess the effect of channel expansion ratio
using Euler equations model. From the numerical data obtained,
the characteristics of flow unsteadiness, such as phase lag,
amplitude, and average position of shock oscillation, that are
related to flow disturbances, such as frequency and amplitude
of back pressure, are investigated. The range of channel
expansion ratio is enlarged in the present work rather than
limited to a small value as in the assumption of
|