Steam filament solution determines velocity distribution due to potential flow in the blade-to-blade plane of the radial impeller. This is used to determine the mass-averaged relative fluid angle, which is in turn used in an axisymmetric program to obtain steam surfaces of the assumed axisymmetric flow

Jackson, E. D.

English

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June 1970	 Brief 70-10124 
NASA TECH BRIEF H 
NASA Tech Briefs announce new technology derived from the U .S. space program. They are issued to encourage commercial 
application. Tech-Briefs are available on a subscription basis from the Clearinghouse for Federal Scientific and Technical 
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be directed to the Technology Utilization Division, NASA, Code UT, Washington, D.C. 20546. 
Method of Calculating Blade-to-Blade Plane Flow in Centrifugal Pump 
A simple stream-filament solution has been devised 
for determining the velocity distribution due to poten-
tial flow in the blade-to-blade plane of a radial im-
peller in a centrifugal pump. 
The blade-to-blade flow is first assumed to take 
place on an axisymmetric stream surface. Given the 
blade geometry on this surface, the problem is re-
duced to finding the two-dimensional potential flow 
through the resulting cascade. The passage between 
adjacent blades is divided into three regions separated 
along lines normal to the blade surfaces. These regions 
are the channel-flow region (where the blades over-
lap), the entrance region, and the exit region. A stream 
filament method (essentially the method of Flugel) 
is used to determine the flow in the channel region 
of the passage. Because the streamlines downstream of 
the channel-flow region are not known without the 
use of an "exact" (e.g., relaxation) solution, the in-
discriminate use of the stream-filament method would 
not correctly indicate the fluid "slip" (or deviation 
from blade direction) that occurs in the channel. The 
procedure used to circumvent this problem is to fix 
the streamline curvature and velocity distribution at 
the exit of the channel-flow region based on an accept-
able slip correlation (such as Pfleiderer's). This essen-
tially fixes a boundary condition for the stream-fila-
ment solution obtained further upstream in the chan-
nel, and appears to give a good prediction of the way 
in which the fluid slip or deviation is distributed in 
the passage. Thus, the procedure allows a determina-
tion of the flow distribution in the channel-flow por-
tion of the passage. The velocity distribution on the 
blades in the other two regions is approximated 
through application of the Kutta condition and a 
circulation balance over these regions. The resulting 
velocity distribution is then used to determine the 
mass-averaged relative fluid angle, which is in turn 
used in an existing axisymmetric program to obtain 
improved stream surfaces of the assumed axisym-
metric flow. 
Note: 
The following documentation may be obtained 
from:
Clearinghouse for Federal Scientific 
and Technical Information 
Springfield, Virginia 22151 
Single document. price $3.00 
(or microfiche $0.65) 
Reference: 
NASA-CR-80153 (N67-12915), Study 
of Pump Discharge Pressure Oscillations, 
Final Report. 
Patent status: 
No patent action is contemplated by NASA. 
Source: E. D. Jackson of 
North American Rockwell Corp. 
under contract to 
Marshall Space Flight Center 
(MFS-18087) 
Category 06 
This document was prepared under the sponsorship of the National 
Aeronautics and Space Administration. Neither the United States 
Government nor any person acting on behalf of the United States
Government assumes any liability resulting from the use of the 
information contained in this document, or warrants that such use 
will be free from privately owned rights.
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Method of calculating blade-to-blade plane flow in centrifugal pump

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