• Journal of the Korean Society of Combustion
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• v.17 no.4
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• pp.44-50
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• 2012

The present study was conducted to investigate the flame instability(evaluated by Markstein length and cellular instability) and laminar burning velocity in a constant volume combustion chamber at room temperature and elevated pressure up to 0.3 MPa to suggest the possibility of utilizing mixtures of syngas added DME-air premixed flames in internal combustion engines. The experimentally measured laminar burning velocities were compared to predictions calculated the PREMIX code with Zhao reaction mechanism. Discussions were made on effects of syngas addition into DME-Air premixed flames through evaluating laminar burning velocity, Markstein length, and cellular instability. Particular concerns are focused on cellular instability caused by hydrodynamic instability and diffusive-thermal instability.

• 한국연소학회:학술대회논문집
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• 2003.05a
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• pp.209-214
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• 2003

The Saffman-Taylor instability mechanisms in laminar premixed flames in a Hele-Shaw cell are investigated using two-dimensional numerical simulations with Poiseuille assumption for the viscous effect. The baseline calculations considering the Darrieus-Landau and diffusive-thermal instability modes show the results consistent with the classical linear instability theory. With the Saffrnan-Taylor instability mechanism. the overall effect is to enhance the destabilizing mechanism by providing an increased viscous force in the product gas. The linear instability behavior is found to qualitatively similar to the Darrieus-Landau mechanism. However, the results in the nonlinear range demonstrate that there may exist distinct characteristic time scales associated with Darrieus-Landau and Saffman-Taylor mechanisms, such that the latter effect sustains longer in time, contributing to a higher overall flame speed.

• 한국연소학회:학술대회논문집
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• 2005.10a
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• pp.281-286
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• 2005

To understand fundamental characteristics of combustion in a small scale device, the effects of the momentum and heat loss on the stability of laminar premixed flames in a narrow channel are investigated by two-dimensional high-fidelity numerical simulation. A general finding is that momentum loss promotes the Saffman-Taylor (S-T) instability which is additive to the Darrieus-Landau (D-L) instabilities, while the heat loss effects result in an enhancement of the diffusive-thermal (D-T) instability. These effects are also valid in nonlinear behavior of the premixed flame. The simulations of multiple cell interactions are also conducted with heat and momentum loss effects.

• Journal of the Korean Society of Combustion
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• v.10 no.3
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• pp.25-33
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• 2005

Fast-time instability is investigated for diffusion flames with Lewis numbers greater than unity by employing the numerical technique called the Evans function method. Since the time and length scales are those of the inner reactive-diffusive layer, the problem is equivalent to the instability problem for the $Li\tilde{n}\acute{a}n#s$ diffusion flame regime. The instability is primarily oscillatory, as seen from complex solution branches and can emerge prior to reaching the upper turning point of the S-curve, known as the $Li\tilde{n}\acute{a}n#s$ extinction condition. Depending on the Lewis number, the instability characteristics is found to be somewhat different. Below the critical Lewis number, $L_C$, the instability possesses primarily a pulsating nature in that the two real solution branches, existing for small wave numbers, merges at a finite wave number, at which a pair of complex conjugate solution branches bifurcate. For Lewis numbers greater than $L_C$, the solution branch for small reactant leakage is found to be purely complex with the maximum growth rate found at a finite wave number, thereby exhibiting a traveling nature. As the reactant leakage parameter is further increased, the instability characteristics turns into a pulsating type, similar to that for L < $L_C$.

• Journal of the Korean Society of Combustion
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• v.12 no.2
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• pp.34-41
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• 2007

The dynamic behaviors of counterflow non-premixed flame have been investigated experimentally to study effects of heat losses and Lewis number on edge flame oscillation, which result from the advancing and retreating edge flame motion of outer flame edge at low strain rate flame. For low strain rate flame, lateral conduction heat loss in addition to radiation heat loss could be more remarkable than the others. Oscillatory instabilities appear at fuel Lewis number greater than unity. But excessive lateral conduction heat loss causes edge flame instability even at fuel Lewis number less than unity. The excessive heat loss caused by the smaller burner diameter in which the flame length is an indicator of lateral conduction heat loss extends the region of flame oscillation and accelerates oscillatory instability in comparison to the previous study with the burner diameter of 26mm. Extinction behaviors quite different from the previous study are also addressed.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.34 no.4
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• pp.399-408
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• 2010

The characteristics of lifted laminar propane flames diluted with nitrogen have been investigated experimentally to elucidate self-excitation and the effects of flame curvature. Flame oscillation modes are classified as follows: oscillation induced by heat loss, a combination of oscillations induced by heat loss and buoyancy, and a combination of the oscillations induced by heat loss and diffusive thermal instability. It is shown that the oscillation induced only by heat loss is not relevant to the diffusive thermal instability and hydrodynamic instability caused by buoyancy; this oscillation is observed under all lift-off flame conditions irrespective of the fuel Lewis number. These experimental evidences are displayed through the analysis of the power spectrum for the temporal variation of lift-off height. The possible mechanism of the oscillation induced by heat loss is also discussed.

• Journal of applied mathematics & informatics
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• v.41 no.1
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• pp.11-31
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• 2023

The paper presents a critical analysis of selected topics related to the modeling of interacting species in which prey has nonlinear reproduction, which is in competition with predator. The mathematical model's stochastic stability is investigated. The method of designing appropriate Lyapunov functions is used to identify permanence conditions among the parameters of the model and conditions for the structure to no longer be extinct. The system's two-dimensional diffusive stability is regarded and studied. The system experiences the process of saddle-node bifurcation by varying the death rate of predator parameter. Further effects of parameters that undergo inherent oscillations are numerically investigated, revealing that as the intensity of predation parameter b is increased, the device encounters non-periodic and damped oscillations.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.385-400
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• 2009

The adverse effect of harmful plankton on the marine ecosystem is a topic of deep concern. To investigate the role of such phytoplankton, a mathematical model containing distinct dynamical equations for toxic and non-toxic phytoplankton is analyzed. Stability analysis of the resulting three equation model is carried out. A continuous time variation in toxin liberation process is incorporated into the model and a stability analysis of the resulting delay model is performed. The distributed delay model is then extended to include the spatial distribution of plankton and the delay-diffusion model is analyzed with spatial and spatiotemporal kernels. Conditions for diffusion-driven instability in both the cases are derived and compared to explore the significance of these kernels. Numerical studies are performed to justify analytical findings.

• 한국연소학회:학술대회논문집
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• 2007.05a
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• pp.145-152
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• 2007

The dynamic behaviors of counterflow non-premixed flame have been investigated experimentally to study effects of heat losses on edge flame oscillation, which result from the advancing and retreating edge flame motion of outer flame edge at low strain rate flame. For low strain rate flame, lateral conduction heat loss in addition to radiation heat loss could be more remarkable than the others. Oscillatory instabilities appear at fuel Lewis number greater than unity. But excessive lateral conduction heat loss causes edge flame instability even at fuel Lewis number less than unity. The dramatic change of burner diameters in which flame length is an indicator of lateral conduction heat loss was applied to examine the onset condition of edge flame oscillation and flame oscillation modes. Especially, extinction behaviors quite different from the previous study were observed.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.17 no.2
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• pp.129-138
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• 2013

A spatio-temporal models as systems of ODE which describe two-species Beddington - DeAngelis type predator-prey system living in a habitat of two identical patches linked by migration is investigated. It is assumed in the model that the per capita migration rate of each species is influenced not only by its own but also by the other one's density, i.e. there is cross diffusion present. We show that a standard (self-diffusion) system may be either stable or unstable, a cross-diffusion response can stabilize an unstable standard system and destabilize a stable standard system. For the diffusively stable model, numerical studies show that at a critical value of the bifurcation parameter the system undergoes a Turing bifurcation and the cross migration response is an important factor that should not be ignored when pattern emerges.