Abstract:
PART I The Mechanism of Damping Factor. PART II Meridional Flow Calculations. PART III Blade-to-Blade Flow Calculations. Part I of the report exposes the dependence of asymptotic numerical convergence upon the eigenvalues of a perturbation matrix which is a function of the principal equation of motion for the calculation of two-dimensional flows in turbomachines. The mechanism of damping factor and its limitations are thereby exposed and presented graphically. The interpretation of convergence criterion is discussed and proposals made to improve the numerical solution by extrapolation. Part II discusses the convergence of solutions for prescribed S2 surface flows and axi-symmetric flows and shows that these are strongly influenced by the density-streamfunction relationship, leading to a Mach number limitation but being also dependent upon streamsurface twist. The principles of Part I and the theory of Part II are illustrated by numerical examples. Part III applies and illustrates the principles of Part I to prescribed S1 streamsurfaces of revolution. It is demonstrated that a density-streamfunction relationship similar to that of Part II controls convergence behaviour of these flows but that lack of streamsurface twist conveys superior properties which are only Mach number limited. In all cases the Mach number limitation coincides with the elliptic-hyperbolic boundary of the analytic problem.
