• Journal of the Korean Society of Combustion
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• v.18 no.2
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• pp.42-50
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• 2013

Linear stability analysis of radiating counterflow diffusion flames is numerically conducted to examine the instability characteristics of cellular patterns. Lewis number is assumed to be 0.5 to consider diffusional-thermal instability. Near kinetic limit extinction regime, growth rates of disturbances always have real eigen-values and neutral stability condition of planar disturbances perfectly falls into quasi-steady extinction. Cellular instability of disturbance with transverse direction occurs just before steady extinction. However, near radiative limit extinction regime, the eigenvalues are complex and pulsating instability of planar disturbances appears prior to steady extinction. Cellular instability occurs before the onset of planar pulsating instability, which means the extension of flammability.

• Journal of The Korean Astronomical Society
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• v.37 no.4
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• pp.249-255
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• 2004

Here we present a linear stability analysis and an MHD 2D model for the Parker-Jeans instability in the Galactic gaseous disk. The magnetic field is assumed parallel to a Galactic spiral arm, and the gaseous disk is modelled as a multi-component, magnetized, and isothermal gas layer. The model employs the observed vertical stratifications for the gas density and the gravitational acceleration in the Solar neighborhood, and the self-gravity of the gas is also included. By solving Poisson's equation for the gas density stratification, we determine the vertical acceleration due to self-gravity as a function of z. Subtracting it from the observed gravitational acceleration, we separate the total acceleration into self and external gravities. The linear stability analysis provides the corresponding dispersion relations. The time and length scales of the fastest growing mode of the Parker-Jeans instability are about 40 Myr and 3.3 kpc, respectively. In order to confirm the linear stability analysis, we have performed two-dimensional MHD simulations. These show that the Parker-Jeans instability under the self and external gravities evolves into a quasi-equilibrium state, creating condensations on the northern and southern sides of the plane, in an alternate manner.

• 한국연소학회:학술대회논문집
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• 2015.12a
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• pp.247-250
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• 2015

The characteristics of opposed nonpremixed tubular flames with radiation heat loss are investigated using linear stability analysis and 2-D numerical simulations. Two extinction limits, as the $Damk{\ddot{o}}hler$ number is small or large, are confirmed using finite difference method with a simple continuation method. It is verified that the results of linear stability analysis predict the number of flame cells and the critical Da starting cellular instability or amplification of temperature near both extinction limits with good resolution.

• Journal of the Korean Society of Propulsion Engineers
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• v.16 no.6
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• pp.32-40
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• 2012

For predicting eigenfrequency and initial growth rate of combustion instabilities in lean premixed gas turbine combustor, linear thermoacoustic analysis model was developed in the current paper. A model combustor was selected for the model validation, which has well-defined inlet and outlet conditions and a relatively simple geometry, compared to the combustor in the previous works. Analytical linear equations for thermoacoustic waves were derived for a given combustion system. It was found that the prediction results showed a good agreement with the measurements, even though there was underestimation for instability frequencies. This underestimation was more obvious for a longer flame (i.e. wider temperature distribution) than for a shorter flame.

• Steel and Composite Structures
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• v.31 no.2
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• pp.187-199
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• 2019

This paper presents the semi-analytical development of the dynamic instability behavior and the dynamic response of functionally graded (FG) cylindrical shallow shell panel subjected to different type of periodic axial compression. First, in prebuckling analysis, the stresses distribution within the panels are determined for respective loading type and these stresses are used to study the dynamic instability behavior and the dynamic response. The prebuckling stresses within the shell panel are the same as applied in-plane edge loading for the case of uniform and linearly varying loadings. However, this is not true for the case of parabolic loadings. The parabolic edge loading produces all the stresses (${\sigma}_{xx}$, ${\sigma}_{yy}$ and ${\tau}_{xy}$) within the FG cylindrical panel. These stresses are evaluated by minimizing the membrane energy via Ritz method. Using these stresses the partial differential equations of FG cylindrical panel are formulated by applying Hamilton's principal assuming higher order shear deformation theory (HSDT) and von-$K{\acute{a}}rm{\acute{a}}n$ non-linearity. The non-linear governing partial differential equations are converted into a set of Mathieu-Hill equations via Galerkin's method. Bolotin method is adopted to trace the boundaries of instability regions. The linear and non-linear dynamic responses in stable and unstable region are plotted to know the characteristics of instability regions of FG cylindrical panel. Moreover, the non-linear frequency-amplitude responses are obtained using Incremental Harmonic Balance (IHB) method.

• Journal of the Korean Society of Propulsion Engineers
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• v.17 no.5
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• pp.27-36
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• 2013

Linear stability analysis for combustion instability within a cylindrical port of solid rocket motor has been conducted. The analysis of acoustic energy has been performed by a commercial COMSOL code to obtain the mode function associated to each acoustic mode prior to the calculation of stability alpha. An instability diagnosis based on the linear stability analysis of Culick is performed where special interests have been focused on 5 stability factors(alpha) such as pressure coupling, nozzle damping, particle damping and additionally, flow turning effect and viscous damping to take into account the flow and viscosity effect near the fuel surface. The instability decay characteristics depending on the particle size is also analyzed.

• Structural Engineering and Mechanics
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• v.65 no.1
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• pp.121-128
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• 2018

Three structure-dependent integration methods with no numerical dissipation have been successfully developed for time integration. Although these three integration methods generally have the same numerical properties, such as unconditional stability, second-order accuracy, explicit formulation, no overshoot and no numerical damping, there still exist some different numerical properties. It is found that TLM can only have unconditional stability for linear elastic and stiffness softening systems for zero viscous damping while for nonzero viscous damping it only has unconditional stability for linear elastic systems. Whereas, both CEM and CRM can have unconditional stability for linear elastic and stiffness softening systems for both zero and nonzero viscous damping. However, the most significantly different property among the three integration methods is a weak instability. In fact, both CRM and TLM have a weak instability, which will lead to an adverse overshoot or even a numerical instability in the high frequency responses to nonzero initial conditions. Whereas, CEM possesses no such an adverse weak instability. As a result, the performance of CEM is much better than for CRM and TLM. Notice that a weak instability property of CRM and TLM might severely limit its practical applications.

• The Bulletin of The Korean Astronomical Society
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• v.39 no.1
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• pp.37.2-37.2
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• 2014

Gas in disk galaxies interacts nonlinearly with a underlying stellar spiral potential to form galactic spiral shocks. Numerical simulations typically show that these shocks are unstable to the wiggle instability, forming non-axisymmetric structures with high vorticity. While previous studies suggested that the wiggle instability may arise from the Kelvin-Helmholtz instability or orbit crowding of gas elements near the shock, its physical nature remains uncertain. It was even argued that the wiggle instability is of numerical origin, caused by the inability of a numerical code to resolve a shock that is inclined to numerical grids. In this work, we perform a normal-mode linear stability analysis of galactic spiral shocks as a boundary-value problem. We find that the wiggle instability originates physically from the potential vorticity generation at a distorted shock front. As the gas follows galaxy rotation, it periodically passes through multiple shocks, successively increasing its potential vorticity. This sets up a normal-mode that grows exponentially, with a growth rate comparable to the orbital angular frequency. We show that the results of our linear stability analysis are in good agreement with the those of local hydrodynamic simulations of the wiggle instability.

• Journal of The Korean Astronomical Society
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• v.37 no.5
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• pp.601-603
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• 2004

We present the results of the linear analysis for the Parker-Jeans instability in the magnetized gas disks including the effect of cosmic-ray diffusion along the magnetic field lines. We adopted an uni-formly rotating two temperature layered disk with a horizontal magnetic fields and solved the perturbed equations numerically. Fragmentation of gases takes place and filamentary structures are formed by the growth of the instability. Nagai et al. (1998) showed that the direction of filaments being formed by the Parker-Jeans instability depends on the strength of pressure outside the unperturbed gas disk. We found that at some range of external pressures the direction of filaments is also governed by the value of the diffusion coefficient of CR along the magnetic field lines k.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.22 no.7
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• pp.899-904
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• 1998

Surface motion of a magnetic fluid is studied by a linear stability analysis. When a thin horizontal magnetic-fluid layer is placed on a nonmagnetic substrate, with a vertical magnetic field applied, the surface of the ferrofluid layer can be severely corrugated, due to the normal-field instability. Based on conservation laws, it is shown that the normal-field instability of thin ferrofluid layers is a long-wave instability and that it is analogous to the interfacial mode of the thermocapillary instability in a thin horizontal layer heated from below.