Computer program based on an equation for the velocity gradient along an arbitrary quasi- orthogonal analyzes flow through a turbomachine. The program obtains meridional solutions for a hub-to-shroud analysis and blade-to-blade analysis at the hub, mean, and shroud surfaces in a single computer run

Katsanis, T.

English

NASA Technical Reports Server

November 1966	 Brief 66-10496 
NASA TECH BRIEF 
NASA Tech Briefs are issued to summarize specific innovations derived from the U. S. space 
program and to encourage their commercial application. Copies are available to the public from 
the Clearinghouse for Federal Scientific and Technical Information, Springfield, Virginia 22151. 
Computer Program Performs Flow Analysis Through Turbines 
The problem: 
To devise a method of analyzing flow through a 
turbomachine (turbine, compressor, or pump) that is 
readily adaptable to computer programming. Previous 
methods obtained a two-dimensional solution based 
on an equation for the velocity gradient along the 
normal to the projection of the streamlines on a plane 
containing the axis of rotation (the meridional plane). 
The meridional streamlines and their normals are 
used to establish a grid for a meridional-plane solu-
tion. In cases where the distance between the hub and 
shroud is great and there is a large change in flow 
direction within the rotor, the normals vary con-
siderably in length and in direction during the course 
of the calculations. Therefore, it is difficult to obtain 
a direct solution on the computer without resorting 
to intermediate graphical steps. 
The solution: 
A new method and computer program based on an 
equation for the velocity gradient along an arbitrary 
quasi-orthogonal rather than the normal to the 
streamline as used in previous methods. The program 
(in the Fortran programming language) obtains 
meridional solutions for a hub-to-shroud analysis and 
blade-to-blade analysis at the hub, mean, and shroud 
surfaces in a single computer run. 
How it's done: 
This method obtains a direct solution by the use 
of arbitrary curves (called quasi-orthogonals) from 
hub to shroud instead of streamline normals. The 
quasi-orthogonals are not necessarily orthogonal to 
each streamline but intersect every streamline once 
across the width of the passage. The quasi-orthog-
onals remain fixed regardless of any change in 
streamlines.Using this technique, a computer program
is developed that calculates a streamline solution in 
the meridional plane without any intermediate graphi-
cal procedures, even for turbomachines with wide 
passages and a change in direction from radial to 
axial within the rotor blade. 
From the meridional solution, it is possible to 
obtain blade-surface velocities by several methods. 
However, the basic concept used to obtain the merid-
ional solution can also be applied to obtain a blade-
to-blade solution. In this case, the quasi-orthogonals 
run from blade to blade on a stream surface deter-
mined by the meridional solution. By extending the 
solution upstream and downstream, a good solution 
throughout the rotor is obtained. 
Notes: 
1. This program will be useful in the design of any 
type of turbomachines (turbines, compressors, or 
pumps) and for either compressible or incompressi-
ble fluids. 
2. Further information concerning this innovation is 
presented in NASA TN D-2546, "Use of Arbitrary 
Quasi-Orthogonals for Calculating Flow Distribu-
tion in the Meridional Plane of a Turbomachine" 
by Theodore Katsanis, December 1964; and in TN 
D-2809, "Use of Arbitrary Quasi-Orthogonals for 
Calculating Flow Distribution on a Blade-to-Blade 
Surface in a ,Turbomachine" by Theodore Kat-
sanis, May 1965, available from the Clearinghouse 
for Federal Scientific and Technical Information, 
Springfield, Virginia 22151. Inquiries may also be 
directed to: 
Technology Utilization Officer 
Lewis Research Center 
21000 Brookpark Road 
Cleveland, Ohio 44135 
Reference: B66-10496
(continued overleaf) 
This document was prepared under the sponsorship of the National	 Government assumes any liability resulting from the use of the 
Aeronautics and Space Administration. Neither the United States 	 information contained in this document, or warrants that such use 
Government nor any person acting on behalf of the United States 	 will be free from privately owned rights.
https://ntrs.nasa.gov/search.jsp?R=19660000494 2020-03-11T17:37:53+00:00Z
Patent status: 
No patent action is contemplated by NASA. 
Source: Theodore Katsanis 
Lewis Research Center 
(Lewis-236)
. 
S 
Brief 66-10496 Category 01


Computer program performs flow analysis through turbines

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