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A locally implicit TVD scheme on dynamic mixed meshes and an
improved dynamic mesh algorithm are developed to investigate
the transonic oscillating cascade flows. The unsteady Euler
and Navier-Stokes equations are solved in a Cartesian
coordinate system. To evaluate the accuracy of present TVD
scheme on mixed meshes, several steady inviscid and viscous
flow problems are investigated. From the numerical results,
the present scheme is accurate and efficient. To validate the
accuracy and reliability of present scheme on dynamic mixed
meshes, inviscid flow around single NACA 0012 airfoil pitching
harmonically about the quarter chord is computed. The
calculated instantaneous pressure coefficient distributions
during a cycle of motion compare well with the related
numerical and experimental data. To further evaluate the
present approach involving nonzero interblade phase angle,
Euler calculations of transonic flow around oscillating
cascade of two unstaggered NACA 0006 blades with interblade
phase angle equal to 180 deg are performed. From the
instantaneous pressure coefficient distributions and time
history of lift coefficient, the present approach, where a
simple spatial treatment is utilized on the periodic
boundaries, is reliable and robust. Transonic flows around
oscillating cascade of four biconvex blades with different
oscillation amplitudes, reduced frequencies and interblade
phase angles are investigated on two mesh systems. The leading
and trailing edges of each blade for the triangular mesh are
sharp, while the edges for mixed mesh are rounded to match the
experimental geometry. From the instantaneous pressure
coefficient distributions, the use of mixed mesh can avoid the
possible wiggles caused by using the triangular mesh.
Comparing the distributions of magnitude and
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