The primary mechanism for generation of acoustic waves in a centrifugal pump, due to the rotor/stator interaction, is an unsteady source at the entrance of the blade row as represented by the unsteady velocity field. The amplitudes of wave generated by pressure loading on the blades and by velocity boundary condition are compared

Jackson, E. D.

English

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July 1968	 Brief 68-10265 
NASA TECH BRIEF 
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from the Clearinghouse for Federal Scientific and Technical Information, Springfield, Virginia 22151. 
Acoustic Wave Analysis 
A study has been made of the mechanism of genera-
tion of acoustic waves in a rotor/stator combination 
with a comparison of the relative strengths of waves 
generated by different sources in a centrifugal pump. 
The velocity leaving a blade row is nonuniform due 
to both the gradients in the region designated as the 
potential flow and the viscous boundary layers along 
the blade surfaces, but is periodic in the mean, the 
period extending from blade to blade. This nonuni-
form velocity would appear to a downstream blade 
row in relative motion to the upstream blade row as a 
periodic unsteady velocity field which produces un-
steady pressures on the downstream blades. Acoustic 
waves are generated by both the unsteady velocity field 
at the entrance of the blade row, and the unsteady 
blade pressure loads on the downstream blades due to 
the unsteady velocity field. 
A primary effort was made to indicate the relative 
importance of the acoustic waves generated by these 
two related mechanisms. Before this could be done, the 
amplitude of the unsteady pressures on the down-
stream blade row had to be calculated. In the litera-
ture, these unsteady pressures have been investigated 
as a function of four effects which have been desig-
nated as the circulation, blade thickness, wake, and 
wake distortion effects. The analytical development of 
each is based primarily on the two-dimensional theory 
of the unsteady flow about a thin airfoil. Only the 
viscous wake effect was adopted for use in the current 
program, a computer program being written to calcu-
late the unsteady pressures on a blade due to an ap-
proaching arbitrary wake velocity. 
The generation of waves into a medium surrounding 
a plate, by unsteady forces on the plate surface, is a
coupled problem requiring solution of the equation of 
motion for transverse displacement of the plate, as well 
as solution of the wave equation in the medium. The 
two solutions are coupled by the boundary conditions 
which require continuity of both the normal velocity 
and pressure across the fluid-plate interface. To esti-
mate the order of magnitude of the wave amplitude 
generated by this coupled motion, a simpler example 
problem was considered. This example problem con-
sisted of a plate of infinite extent and uniform thick-
ness. The fluid medium above the plate was assumed 
to be coupled to the plate motion, but the fluid below 
the plate was not. The coupled equations were solved, 
yielding for this example problem an expression for 
the amplitude of the waves generated by an unsteady 
force on the plate. 
To estimate the order of magnitude of the amplitude 
of the waves generated by an unsteady velocity bound-
ary condition at the inlet of a blade row (or duct), a 
second simple example was assumed. This example 
consisted of a straight, infinite, rectangular duct with a 
simple harmonic velocity at its inlet boundary, which 
velocity was uniform in the plane of the duct. The 
wave equation was solved to yield the generated wave 
amplitude. 
Using data for a standard centrifugal pump, the 
amplitudes of the oscillations generated by these two 
mechanisms were computed and compared. This com-
parison indicated that the amplitude of the waves gen-
erated by the pressure loading on the blades (which in 
this case were volute tongues), were less by a factor of 
101 to 105
 than those generated by the velocity bound-
ary condition. Thus, the primary mechanism for gener-
ation of acoustic waves in the centrifugal pump, due to 
(continued overleaf) 
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https://ntrs.nasa.gov/search.jsp?R=19680000265 2020-03-12T06:10:36+00:00Z
the rotor/stator interaction, is seen to be that of an 
unsteady source at the entrance of the blade row as 
represented by the unsteady velocity field. 
Note: 
Inquiries concerning this study may be directed to:
Technology Utilization Officer 
Marshall Space Flight Center 
Huntsville, Alabama 35812 
Reference: B68-10265
Patent status: 
No patent action is contemplated by NASA. 
Source: E. D. Jackson 
of North American Rockwell Corporation 
under contract to 
Marshall Space Flight Center 
(MFS-18076) 
Brief 68-10265	 Category 02


Acoustic wave analysis

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