Preliminary Study of Stability of Flow From Two Ducts Discharging Into a Common Duct Page: 4 of 34
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NACA TN 2417
In some instances, such as the case of acoustic oscillations in a
simple duct system, the effect of R upon frequency is relatively
unimportant. Here, if V is the fluid velocity in the duct,
f = Ka2(l -2
where
K constant determined by geometry of system and mode
L characteristic duct length
For other problems, the Reynolds number is the determining variable for
the oscillation. An example of this occurs in pipe flow with a Reynolds
number in the critical region where the flow pulsates periodically
between a laminar and a turbulent state.
In the particular case of flow from two ducts discharging into a
common duct, oscillations, or surging of the fluid alternately in the
two ducts, as well as asymmetry in the flow for a symmetric setup have
been observed. The oscillations have been of relatively low frequency,
large amplitude, and, in some cases, of a destructive nature. This
suggests viscosity or turbulence rather than compressibility as the
cause of the phenomenon. Since compressible effects have been ruled
out, for experimental convenience water, rather than air, has been used
for the most part as the fluid.
The purpose of the experiments was to try to duplicate and to
observe the undesirable oscillations and instabilities and to determine
the effects of the various parameters. A potential solution that
approximates the physical picture was examined analytically to deter-
mine the form of the ideal flow and to see if the theoretical solution
is unique. It should be noted that for the related problem of two
impinging free streams the potential solution is not unique; evidently
in this case a stability condition is necessary to specify the "correct"
solution. (See reference 1.) Also, in a qualitative way, the phenomenon
has been considered in the light of turbulent mixing effects.
THEORETICAL ANALYSIS
The physical problem that is to be idealized is that of the flow
from two ducts that join and discharge into a single expanded duct as
shown in figure 1. Unless the velocity is extremely low, the flow3
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Bellin, Albert I.; Messina, D. Richard & Richards, Paul B. Preliminary Study of Stability of Flow From Two Ducts Discharging Into a Common Duct, report, July 1951; (https://digital.library.unt.edu/ark:/67531/metadc61880/m1/4/: accessed April 25, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.