Use of Arbitrary Quasi-Orthogonals for Calculating Flow Distribution in a Turbomachine

Abstract

A method of analyzing flow through a turbomachine i s summarized which i s r l s u i t a b l e f o r computer programming. The method, which has been reported i n NASA t r a r y quasi-orthogonal r a t h e r than t h e normal t o t h e streamline as used i n previous methods. A quasi-orthogonal is defined t o be any curve that i n t e r s e c t s every streamline between t h e flow boundaries e x a c t l y once, as does an orthogonal t o t h e streamlines. With t h i s method a streamline a n a l y s i s can be made on any given stream surface. A quasi-three-dimensional s o l u t i o n can be obtained by using t h e method f o r a hub-to-shroud analysis, followed by blade-to-blade analyses at hub, mean, and shroud. As an example, t h e method was applied t o a radial inflow t u r b i n e w i t h s p l i t t e r blades. The complete quasi-three-dimensional SOYutioii was o'uiained i n a s i n g l e computer run.

Cooled radial turbine for high power-to-weight applications

“…4, assuming a linear velocity distribution in the blade-to-blade direction. Using the calculated velocity distribution on an earlier UACL rotor of known performance as a guide, the rotor was designed to minimize local blade surface diffusion.…”

Quasi-Three-Dimensional Flow Solution by Meridional Plane Analysis

“…After the stream function is obtained, the velocity distribution is obtained by numerical partial differentiation of the stream function and by using equation (2). The details of the numerical procedure and programming technique are described in reference (4).…”

“…A solution on the mid-channel surface will show this variation. The solution can be obtained either by the quasi-oirthogonal method, which solves the velocity-gradient equation from hub to shroud on the mid-channel flow surface (2), or by a finite-difference method, which solves a finite-difference equation for stream function on the same flow surface. The quasi-orthogonal method is efficient in many cases and can obtain solutions into the transonic regime.…”

A Cooled Laminated Radial Turbine Technology Demonstration

“…Rotor stresses limit the achievable tip speeds to nonoptimum levels due to excessive bore stresses, Presented as Paper 80-0300 at the AIAA 18th Aerospace Sciences Meeting, Pasadena, Calif., Jan. [14][15][16]1980; submitted April 24, 1980; revision received March 2, 1981. Copyright © American Institute of Aeronautics and Astronautics, Inc., 1980.…”