This thesis presents the formulation and validation of a novel time-accurate
method for the computation of forced response and flutter in multiple blade row
turbomachinery.

Advanced gas turbine and aeroengine designs require unsteady computational
methods to predict aeroelastic behaviour and prevent the occurrence of flutter
or forced response which could ultimately lead to engine failure. Currently,
time-accurate schemes can successfully represent unsteady flows across multiple
blade rows if the domain encompasses the full circumference. However, the large
domain size and range of time scales involved make this approach very expensive
and unfeasible during the design cycle. More efficient methods take advantage of
the inherent time-space periodicity in turbomachines to reduce the computational
domain to a single bladed passage per row. These single-passage multi-row
methods successfully model unsteadiness due to rotor-stator interaction or blade
vibration by applying phase-lagged boundary conditions. However, they are
limited to assemblies without passage-to-passage variations in the time-averaged
flow field. In multi-stage turbomachinery, where the interaction of rows with
unequal blade counts in the same frame of reference creates steady
circumferential variations, single-passage methods cannot be applied as no
phase-shifted temporal periodicity exists between adjacent passages. Similarly,
it is not possible to represent non-axisymmetries such as inlet distortions or
stagger profiles using a single passage approach. The time-domain Fourier
method presented in this thesis models multi-row non-axisymmetric flows on a
reduced number of passages. In order to capture stationary variations, the flow
inside several discrete passages, which are located at different circumferential
positions, is solved using a time-accurate scheme. Boundary conditions at the
azimuthal and inter-row surfaces are approximated from a time-space Fourier
series and couple the individual passages.

The method is validated for several applications including low engine order
forcing in an aerodynamically mistuned assembly and rotor-rotor interaction. It
is demonstrated that, within the limit of the Fourier approximation, the
resulting solution is equivalent to the full circumference solution and requires
only a fraction of the computational resources.