Matrix and Relaxation Solutions That Determine Subsonic through Flow in an Axial-Flow Gas Turbine
Abstract
A method recently developed for determining the steady flow of a nonviscous compressible fluid along a relative stream surface between adjacent blades in a turbomachine was applied to investigate the subsonic through flow in a single-stage axial-flow gas turbine. A free-vortex type of variation in tangential velocity was prescribed along the stream surface. Cylindrical bounding walls were specified in order to avoid radial flow at the walls. The flow variations on the stream surface for incompressible and compressible flows were obtained by using the relaxation method with hand computation and the matrix method on both an IBM Card Programmed Electronic Calculator and a UNIVAC. In all solutions considered in this investigation, convergence was obtained without difficulty. A comparison between the relaxation and the matrix methods showed that more accurate results were obtained with the matrix method in a shorter interval of time. The results of these accurate calculations provide a basis for evaluation of simpler, more approximate methods for computing subsonic through flow in turbines. Considerable radial flow was obtained for both incompressible and compressible flows because of the radial twist of the stream surface required by the prescribed velocity diagram and the compressibility of the gas; the radial twist of the stream surface and the compressibility of the gas had equally important effects, and the nonlinear nature of the equations defining the flow was quite evident. The shape of the stream surface was found to be sensitive to the axial position of the radial element of the stream surface in the stator. When the radial element of the stream surface in the rotor was near the midaxial position in the rotor, a large negative gradient of axial velocity was observed in all cases ahead of the rotor.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1952
- Accession Number
- ADA377096
Entities
People
- Chung-hua Wu
Organizations
- National Aeronautics and Space Administration