Abstract
We consider dissipative mechanisms involved in resonance vibrations of gas in a closed pipe. Using analysis of a resonance curve as an example, we show the existence of four regimes differing in the mechanism of dissipation. We determine their boundaries, as well as lay a foundation for the procedures used to calculate the amplitude of vibrations within these intervals. Comparison of calculating formulas with experiments conducted by various authors is made.
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Abbreviations
- L :
-
length of the pipe
- R :
-
radius of the pipe
- d :
-
diameter of the pipe
- ν:
-
coefficient of kinematic viscosity
- c 0 :
-
speed of sound in an unperturbed gas
- ɛ=(κ+1)/2:
-
parameter of nonlinearity
- κ=c p /c ν :
-
wherec p andc ν are the specific heats at a constant pressure and constant volume, respectively
- ω:
-
cyclic frequency
- k=ω/c 0 :
-
wave number
- l :
-
amplitude of the vibrations of piston
- M=ωl/c 0 :
-
mach number
- Re:
-
Reynolds number
- ν:
-
amplitude of the speed of the piston
- U :
-
dimensionless rate of vibrations
- U 1m :
-
maximum value of the amplitude of the 1st harmonic
- U A :
-
amplitude of speed oscillations
- \(\bar U\) :
-
pipe cross-section-averaged speed
- \(H = R\sqrt {\omega /2\nu }\) :
-
frequency parameter
- A C=2U A /(ων)1/2 :
-
the Sergeev number
- τw :
-
shear stress on the wall
- λ s :
-
coefficient of hydraulic resistance
- β t :
-
turbulent coefficient of absorption
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Additional information
Kazan State University. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 68, No. 3, pp. 408–415, May–June, 1995.
Subscripts 1 and 2 relate to the 1st and 2nd harmonics, respectively
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Galiullin, R.G., Galiullina, É.R. & Permyakov, E.I. Influence of absorption on nonlinear vibrations of gas in a closed pipe. J Eng Phys Thermophys 68, 346–352 (1995). https://doi.org/10.1007/BF00859047
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DOI: https://doi.org/10.1007/BF00859047