Non-linear gas oscillations in a pipe

Зарипов, Р. Г.; Ilhamov, M.A.

doi:10.1016/0022-460x(76)90441-7

Cited by 36 publications

(19 citation statements)

References 17 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(6) gives the Helmholtz-Kirchhoff wall-attenuation coefficient, TM for which the fluid is considered to be both viscous and heat-conducting, and the wall to be at a constant temperature: prl/2 (7) In this equation R is the dimensional radius of the chamber, which for convenience is assumed to be cylindrical, has also noted, bulk viscosity tends to smooth out shock discontinuities. So a should not be negligible relative to fl in the momentum equation at high nonlinearity.…”

Section: V2co 2 Po Cocomentioning

confidence: 99%

Nonlinear resonance and viscous dissipation in an acoustic chamber

Lee

Wang

1992

The Journal of the Acoustical Society of America

View full text Add to dashboard Cite

The nonlinear resonance of an air-filled acoustic chamber with rigid endwalls is studied numerically using the fully nonlinear Lagrangian wave equation. The effects of bulk viscous dissipation and external excitation are included. It has been found that at large excitation, the sound amplitude and the quality factor • of the chamber are independent of viscosity, and are inversely proportional to each other. The highlight of this work is the interpretation of these results in simple physical terms. These results are consistent with those from a previously developed analytical theory, although in the latter they have been overshadowed by algebra and have not been properly interpreted. It has been deduced that the free decay rate of a largeamplitude wave due to bulk dissipation is proportional to its acoustic Mach number, and is also independent of viscosity. Also considered was viscous dissipation on the side walls, but it was found that it is much less important than bulk dissipation at high nonlinearity, considering the typical dimension and boundary layer thickness in this type of system. The wave profiles excited at slightly off-resonance frequencies have also been calculated, and found to be similar to those in a piston-driven resonant tube.

show abstract

Section: V2co 2 Po Cocomentioning

confidence: 99%

Nonlinear resonance and viscous dissipation in an acoustic chamber

Lee

Wang

1992

The Journal of the Acoustical Society of America

View full text Add to dashboard Cite

show abstract

“…For more than 70 years, going back at least to the experiments of Lettau (1939) there has been significant interest in the forced nonlinear, resonant response of a gas in a container, see Betchov (1958), Gorkov (1963), Chester (1964), Seymour & Mortell (1973, 1980, Zaripov & Ilgamov (1976), Cox & Mortell (1983) and Ilgamov et al (1996). The majority of this work was focused on plane waves in a closed, straight tube and in understanding shock formation.…”

Section: Introductionmentioning

confidence: 99%

Resonant oscillations of an inhomogeneous gas between concentric spheres

2011

View full text Add to dashboard Cite

We investigate the effects of nonlinearity, geometry and stratification on the resonant motion of a gas contained between two concentric spheres. The emphasis is on whether the motion is continuous, and on how the inhomogeneity, geometry or nonlinearity can move the motion to a shocked state. Linear undamped theory yields a standing wave of arbitrary amplitude and an eigenvalue equation in which the higher eigenvalues are not integer multiples of the fundamental; the system is said to be dissonant. Higher modes, generated by the nonlinearity, are not resonant and consequently shocks may not form. When the output is shockless, the amplitude is two orders of magnitude greater than that of the input. When the eigenvalues for a homogeneous gas are not sufficiently dissonant and shocks form, the introduction of a stratification in the gas can restore dissonance and allow a continuous output. Similarly, the introduction of an inhomogeneity can change a continuous motion to a shocked one, as can an increase in the input Mach number, or an increase in the geometrical parameter. Various limits of the eigenvalue equation are considered and previous results for simpler geometries are recovered; e.g. a full sphere, a cone and a straight tube.

show abstract

“…The resonance of plane standing waves in a closed tube continues to attract particular attention, [1][2][3][4][5][6][7][8][9] leading to the development of the corresponding part of nonlinear wave theory. Of primary concern in the nonlinear plane wave resonance is, from both theoretical and application points of view, the formation of shock waves, which causes the energy dissipation at a shock front and restrains the growth of wave amplitude.…”

Section: Introductionmentioning

confidence: 99%

“…Of primary concern in the nonlinear plane wave resonance is, from both theoretical and application points of view, the formation of shock waves, which causes the energy dissipation at a shock front and restrains the growth of wave amplitude. In the plane wave resonance with shock waves, therefore, the maximum wave amplitude in the quasisteady state oscillation is limited to O͑ ͱ M͒, [1][2][3][4][5][6][7][8][9] where M is the acoustic Mach number defined at the sound source and usually rather small compared with unity ͑typically M Շ 10 −3 ͒.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear analysis of periodic modulation in resonances of cylindrical and spherical acoustic standing waves

Kurihara

Yano

2006

Physics of Fluids

View full text Add to dashboard Cite

The nonlinear resonance of cylindrical acoustic standing waves of an ideal gas contained between two coaxial cylinders is theoretically investigated by the method of multiple scales. The wave motion concerned is excited by a small-amplitude harmonic oscillation of the radius of the outer cylinder, and the formulation of the problem includes the wave phenomenon in a hollow cylinder without the inner one as a limiting case. The spherical standing wave in two concentric spheres is also studied in parallel. The resonance occurs if the driving frequency falls in a narrow band around the linear resonance frequency, and in the weakly nonlinear regime, no shock wave is formed in contrast to the plane wave resonance. A cubic nonlinear equation for complex wave amplitude can then be derived by the method of multiple scales. Using a first integral of the cubic nonlinear equation, we shall demonstrate that the resonant oscillation is accompanied by a periodic modulation of amplitude and phase when the dissipation effect due to viscosity and thermal conductivity is negligible. The period of the modulation varies as the minus two-thirds power of the acoustic Mach number defined at the outer cylinder or sphere and decreases with an increase in the radius ratio of the inner and outer cylinders or spheres. When the dissipation effect is small but not negligible, the modulation is slowly weakened and the resonant oscillation approaches a steady state oscillation, which corresponds to the steady solution examined in earlier works.

show abstract

Non-linear gas oscillations in a pipe

Cited by 36 publications

References 17 publications

Nonlinear resonance and viscous dissipation in an acoustic chamber

Nonlinear resonance and viscous dissipation in an acoustic chamber

Resonant oscillations of an inhomogeneous gas between concentric spheres

Nonlinear analysis of periodic modulation in resonances of cylindrical and spherical acoustic standing waves

Contact Info

Product

Resources

About