EULER SOLUTIONS FOR TRANSONIC OSCILLATING CASCADE FLOWS USING DYNAMICTRIANGULAR MESHES

The modified total-variation-diminishing scheme and an improved dynami c triangular mesh algorithm are presented to investigate the transonic oscillating cascade flows. In a Cartesian coordinate system, the unst eady Euler equations are solved. To validate the accuracy of the prese nt approach, transonic flow around a single NACA 0012 airfoil pitching harmonically about the quarter chord is computed first. The calculate d instantaneous pressure coefficient distribution during a cycle of mo tion compare well with the related numerical and experimental data. To evaluate further the present approach involving nonzero interblade ph ase angle, the calculations of transonic flow around an oscillating ca scade of two unstaggered NACA 0006 blades with interblade phase angle equal to 180 deg are performed. From the instantaneous pressure coeffi cient distributions and time history of lift coefficient the present a pproach, where a simple spatial treatment is utilized on the periodic boundaries, gives satisfactory results. By using this solution procedu re, transonic flows around an oscillating cascade of four biconvex bla des with different oscillation amplitudes, reduced frequencies, and in terblade phase angles are investigated. From the distributions of magn itude and phase angle of the dynamic pressure difference coefficient, the present numerical results show better agreement with the experimen tal data than those from the linearized theory in most of the cases. F or every quarter of one cycle, the pressure contours repeat and procee d one pitch distance in the upward ol downward direction for interblad e phase angle equal to -90 deg or 90 deg, respectively. The unsteady p ressure wave and shock behaviors are observed From the lift coefficien t distributions, it is further confirmed that the oscillation amplitud e, interblade phase angle, and reduced frequency all have significant effects on the transonic oscillating cascade flows.