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The purpose of this thesis is to study the steady and
unsteadyphenomena of subsonic and transonic turbine cascade
flows by using a new adaptive upwind finite-volume algorithm on
mixed type of meshes. For inviscid and viscous compressible
flows, the Euler and full Navier-Stokes equations are solved on
the unstructured triangular and/or mixed quadrilateral-
triangular meshes. To obtain the unstructured mesh system,
several adaptive mesh generation techniques, which includes the
concepts of single and dual background meshes, the error
indicators for evaluating remeshing parameters, the nodes-
clustering methods for generating interior nodes, and the
techniques for forming triangles and quadrilaterals, are
presented. In the present approach, the multi-step Runge-Kutta
time integration, Roe''s flux-difference-splitting Riemann
solver, MUSCL differencing with characteristic interpolation
variables, and appropriate treatments of boundary conditions
are included. For steady-state problems, the non-standard
weighting of Runge-Kutta stages, local time steps and residual
smoothing are introduced to accelerate the calculations. To
validate the current adaptive upwind approaches, the oblique
shock reflection at a wall, supersonic flow passing through a
channel with a 4% circular arc bump, transonic flows around
single and two-element airfoils, laminar boundary layer flow on
a flat plate, oblique shock/laminar boundary layer interaction,
and turbulent boundary layer flow on a flat plate are
investigated. By using the current adaptive approach, steady
and unsteady flows of subsonic and transonic turbine cascades
are studied. For the inviscid unsteady flows in the rotor
passages, the viscous-wake and potential-flow interactions are
modeled. These are achieved by prescribing a velocity defect
and a small pressure disturbance at the inlet plane of the
rotor blade row.
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