Throughflow Theory for Nonaxisymmetric Turbomachinery Flow: Part I—Formulation

Throughflow theory has been limited in its applicability and in its accuracy by the fact that it has not historically been cast in a form that can account for the non-axisymmetries that naturally arise in turbomachinery flow due to the presence of finite numbers of rotor and stator airfoils. The attempt to circumvent this limitation by the introduction of an aerodynamic blockage factor has been demonstrated in earlier work to produce fundamental inconsistencies in the calculation, which lead to significant errors in the regions of the flow where the nonaxisymmetries are severe. The formulation in Part I of the present work is a derivation of a system of through-flow equations for nonaxisymmetric flow. A benchmark database is used in Part II to provide input to the calculation and to help identify the dominant terms. It is demonstrated that the dominant effect of nonaxisymmetry is contained in two terms that relate the total pressure of the averaged flow to the mass-averaged total pressure. It also is demonstrated that the present formulation produces a result that is more accurate than that obtained with the historical blockage-based formulation.