• Journal of the Korean earth science society
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• v.38 no.3
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• pp.173-181
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• 2017

The stability of the steady Rossby-Haurwitz wave (R-H wave) in the nondivergent barotropic model (NBM) on the sphere was investigated with the normal mode method. The linearized NBM equation with respect to the R-H wave was formulated into the eigenvalue-eigenvector problem consisting of the huge sparse matrix by expanding the variables with the spherical harmonic functions. It was shown that the definite threshold R-H wave amplitude for instability could be obtained by the normal mode method. It was revealed that some unstable modes were stationary, which tend to amplify without the time change of the spatial structure. The maximum growth rate of the most unstable mode turned out to be in almost linear proportion to the R-H wave amplitude. As a whole, the growth rate of the unstable mode was found to increase with the zonal- and total-wavenumber. The most unstable mode turned out to consist of more-than-one zonal wavenumber, and in some cases, the mode exhibited a discontinuity over the local domain of weak or vanishing flow. The normal mode method developed here could be readily extended to the basic state comprised of multiple zonalwavenumber components as far as the same total wavenumber is given.

• Proceedings of the KSME Conference
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• 2001.11b
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• pp.481-486
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• 2001

The hydrodynamic instability of the three-dimensional boundary layer on a rotating disk introduces a periodic modulation of the mean flow in the form of stationary cross flow vortices. Detailed numerical values of the growth rates, neutral curves and other characteristics have been calculated for the Type II-instabilities. Presented are the neutral stability results concerning the two instability modes by solving new linear stability equations reformulated not only by considering whole convective terms but by correcting some errors in the previous stability equations. The present stability results are agree with the previously known ones within reasonable limit. The spatial amplification contours have been calculated for the moving disturbance wave, whose azimuth angle is between $\varepsilon=-10^{\circ}$ and $-20^{\circ}$. The transition flow of the moving disturbance wave will be developed at $\varepsilon=-15^{\circ}$ and Re=352 corresponding at the growth rates n = 5.8 from the spatial amplification contours.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 1996.11a
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• pp.119-133
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• 1996

A wave equation and a comprehensive linear combustion model are developed for ramjet and afterburner combustion instability predictions. Modal analysis is used to develop general results for frequencies and damping factors and examples of their applications are given.

• International Journal of Aeronautical and Space Sciences
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• v.17 no.4
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• pp.518-525
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• 2016

This paper presents the characteristics of non-fundamental multi-mode combustion instability and the effects of high-harmonic components on the Rayleigh criterion. Phenomenological observations of multi-harmonic-mode dynamic pressure waves regarding the intensity of harmonic components and the source of wave distortion have been explained by introducing examples of second- and third-order harmonics at various amplitudes. The amplitude and order of the harmonic components distorted the wave shapes, including the peak and the amplitude, of the dynamic pressure and heat release, and consequently the temporal Rayleigh index and its integrals. A cause-and-effect analysis was used to identify the root causes of the phase delay and the amplification of the Rayleigh index. From this analysis, the skewness of the dynamic pressure turned out to be a major source in determining whether multi-mode instability is driving or damping, as well as in optimizing the combustor design, such as the mixing length and the combustor length, to avoid unstable regions. The results can be used to minimize errors in predicting combustion instability in cases of high multi-mode combustion instability. In the future, the amount of research and the number of applications will increase because new fuels, such as fast-burning syngases, are prone to generating multi-mode instabilities.

• Journal of computational fluids engineering
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• v.16 no.1
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• pp.1-6
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• 2011

Flow instability is investigated in a two-dimensional channel with thin baffles placed symmetrically in the vertical direction and periodically in the streamwise dircetion. At low Reynolds numbers, the flow is steady and symmetric. Above a critical Reynolds number, the steady flow undergoes a Hopf bifurcation leading to unsteady periodic flow. As Reynolds number further increases, we observe the onset of secondary instability. At high Reynolds numbers, the two-dimensional periodic flow becomes three dimmensional. To identify the onset of secondary instability, we carry out Floquet stability analysis. We obseved the transition to 3D flow at a Reynolds number of about 125. Also, we computed dominant spanwise wavenumbers near the critical Reynolds number, and visualized vortical structures associated with the most unstable spanwise wave.

• Wind and Structures
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• v.5 no.2_3_4
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• pp.141-150
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• 2002

Numerical simulations based on the ALE finite element method are carried out to examine the aerodynamics of an oscillating circular cylinder when the separated shear flows around the cylinder are stimulated by periodic jet excitation with a shear layer instability frequency. The excitation is applied to the flows from two points on the cylinder surface. The numerical results showed that the excitation with a shear layer instability frequency can reduce the negative damping and thereby stabilize the aerodynamics of the oscillating cylinder. The change of the lift phase seems important in stabilizing the cylinder aerodynamics. The change of lift phase is caused by the merger of the vortices induced by the periodic excitation with a shear layer instability frequency, and the vortex merging comes from the high growth rate, the rapid increase of wave number and decrease of phase velocity for the periodic excitation in the separated shear flows.

• The Transactions of the Korean Institute of Electrical Engineers C
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• v.53 no.6
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• pp.337-341
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• 2004

In this paper the effect of chaos induced instability in Brillouin-active fiber-ring sensor is described. The inherent optical feedback by the backscattered Stokes wave in optical fiber leads to instabilities in the form of optical chaos. The paradigm of optical chaos in fiber serves as a test for fundamental study of chaos and its suppression and exploitation in practical application in communication and sensing. At weak power, the nature of the Brillouin instability can occur at before threshold. At strong power, the temporal evolution above threshold is periodic and at higher intensity can become chaotic. The threshold for the Brillouin instability in fiber-ring sensor is much lower than the threshold of the normal Brillouin instability process.

• International Journal of Aeronautical and Space Sciences
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• v.7 no.2
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• pp.26-32
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• 2006

This paper targets a direct and quantitative prediction of characteristics of unstable waves in a combustion chamber, which employs the governing equations derived in terms of amplification factors of flow variables. A freshly formulated nonlinear acoustic equation is obtained and the analysis of unsteady waves in a rocket engine is attempted. In the present formalism, perturbation method decomposes the variables into time-averaged part that can be obtained easily and accurately and time-varying part which is assumed to be harmonic. Excluding the use of conventional spatially sinusoidal eigenfunctions, a direct numerical solution of wave equation replaces the initial spatial distribution of standing waves and forms the nonlinear space-averaged terms. Amplification factor is also calculated independently by the time rate of changes of fluctuating variables, and is no longer an explicit function for compulsory representation. Employing only the numerical computation, major assumptions inevitably inherent, and in erroneous manner, in up to date analytical methods could be avoided. With two definitions of amplification factor, 1-D stable wave and 3-D unstable wave are examined, and clearly demonstrated the potentiality of a suggested theoretical-numerical method of combustion instability.

• Journal of the Korean Society of Propulsion Engineers
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• v.20 no.1
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• pp.20-27
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• 2016

The prediction of combustion instability is important to avoid an obvious threat to the structural safety and the motor performance because it affects the apparent response function of the propellant, the burning rate, and a mean flow Mach number at the local surface. The combustion instability occurs in case acoustic waves were coupled with the combustion/flow dynamic frequency. In this paper, an acoustic instability model is derived from the nonlinear wave equation for analysing acoustic dynamics in solid rocket motors. The chamber pressure and burning rate effects on combustion instability have been investigated.

• 한국해양학회지
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• v.15 no.1
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• pp.1-7
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• 1980

The results of measurements of shear current induced in water by wind in wind wave tunnel are presented briefly. The shear current distributions are found to fit reasonably well an exponentiall form. This form was used to estimate surface velocity and boundary layer thickness used in stability analysis. An analysis of hydrodynamic stability of the shear current was carried out, using a broken line as an approximate profile, to see the stability as a possible mechanism of wind wave generation. Comparison between experimental results and theoretical ones shows that there exists a large discrepancy particularly in phase velocity and hydrodynamic instability of the shear current seems not to be the basic mechanism of wind wave generation.