A General Though-Flow Theory of Fluid Flow With Subsonic or Supersonic Velocity in Turbomachines of Arbitrary Hub and Casing Shapes
Abstract
A general steady through-flow theory of nonviscous fluid in turbomachines: of arbitrary hub- and casing-wall shapes with subsonic or supersonic velocity is presented. The theory is applicable to both direct and inverse problems and is derived primarily for use in turbomachines having thin blades of high solidity with a simple approximate correction factor for blade-thickness effect. Through the use of the stream function, the continuity equation and the equation of motion in the radial direction are combined to form a principal equation for the present problem. The principal equation contains some terms that are either prescribed or to be determined by other equations defining the problem. Two forms of the principal equation are obtained for the two main groups of current compressor and turbine design in which the variation of tangential velocity and the variation of the ratio of tangential to axial velocity throughout the blade region are given. When the tangential velocity is given, the principal equation is elliptic or hyperbolic, depending on whether the meridional velocity is subsonic or supersonic, respectively. When a relation between the tangential and the axial velocity is given, however, the principal equation becomes hyperbolic when the relative-velocity is supersonic. A general method of solution for both the elliptic and the hyperbolic case is outlined. Specific applications of the theory to several common types of compressor and turbine employing free-vortex, symmetrical-velocity-diagram, solid-rotation-type, nontwisted-blade, and radial-blade - element designs are discussed.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1951
- Accession Number
- ADA382106
Entities
People
- Chung-hua Wu
Organizations
- National Aeronautics and Space Administration