• 한국연소학회지
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• 제16권3호
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• pp.41-51
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• 2011

In this paper, we describe the behavior of two self-excitations in laminar attached free-jet flames under the influence of DC electric fields, one of buoyancy-driven and the other of diffusion-thermal instability, established from the horizontal and vertical injection. In the horizontal injection with removed buoyancy effect, oscillating flames with the frequency of 1.3 - 7.4 Hz were observed in a certain condition with Lewis number more than unity. On the other hand, it was appeared Lewis number induced self-excitation as well as buoyancy-driven self-excitation in the vertical upward injection with DC electric fields. This behavior had frequency range of 1.6 - 9.4 Hz and was exhibited to attribute the buoyancy effect. Finally, a well-defined division about two self-excitations having similar frequency range is briefly discussed.

• Korean Chemical Engineering Research
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• 제57권5호
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• pp.723-729
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• 2019

A theoretical analysis was conducted of convective instability driven by buoyancy forces under transient temperature fields in an annular porous medium bounded by coaxial vertical cylinders. Darcy's law and Boussinesq approximation are used to explain the characteristics of fluid motion and linear stability theory is employed to predict the onset of buoyancy-driven motion. The linear stability equations are derived in a global domain, and then cast into in a self-similar domain. Using a spectral expansion method, the stability equations are reformed as a system of ordinary differential equations and solved analytically and numerically. The critical Darcy-Rayleigh number is founded as a function of the radius ratio. Also, the onset time and corresponding wavelength are obtained for the various cases. The critical time becomes smaller with increasing the Darcy-Rayleigh number and follows the asymptotic relation derived in the infinite horizontal porous layer.

• Korean Chemical Engineering Research
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• 제57권1호
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• pp.142-147
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• 2019

The onset of buoyancy-driven convection in an initially isothermal and quiescent horizontal fluid layer was analyzed theoretically. It is well-known that at the critical Rayleigh number $Ra_c=669$ convective motion sets in with a constant-heat-flux cooling through the upper boundary. Here, based on the momentary instability concept, the dimensionless critical time ${\tau}_m$ to mark the onset of convective motion for Ra > 669 was analyzed theoretically. The energy method under the momentary stability concept was used to find the critical conditions as a function of the Rayleigh number Ra and the Prandtl number Pr. The predicted critical conditions were compared with the previous theoretical and experimental results. The momentary stability criterion gives more reasonable wavenumber than the conventional energy method.

• Korean Chemical Engineering Research
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• 제59권1호
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• pp.138-151
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• 2021

The effect of a reactant ratio on the growth of a buoyancy-driven instability in an irreversible A+B→C reaction system is analyzed theoretically and numerically. Taking a non-stoichiometric reactant ratio into account, new linear stability equations are derived without the quasi-steady state assumption (QSSA) and solved analytically. It is found that the main parameters to explain the present system are the Damköhler number, the dimensionless density difference of chemical species and the ratio of reactants. The present initial grow rate analysis without QSSA shows that the system is initially unconditionally stable regardless of the parameter values; however, the previous initial growth rate analysis based on the QSSA predicted the system is unstable if the system is physically unstable. For time evolving cases, the present growth rates obtained from the spectral analysis and pseudo-spectral method support each other, but quite differently from that obtained under the conventional QSSA. Adopting the result of the linear stability analysis as an initial condition, fully nonlinear direct numerical simulations are conducted. Both the linear analysis and the nonlinear simulation show that the reactant ratio plays an important role in the onset and the growth of the instability motion.

• 설비공학논문집
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• 제16권8호
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• pp.714-719
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• 2004

The objective of the present study is to investigate the convective instability driven by buoyancy and the heat transfer characteristics of nanofluids. Using the property relations of nanofluid expressed as a function of the volume fraction of nanoparticles, the ratio of nanofluid Rayleigh number to basefluid one, f is newly defined. The results show that the density and the heat capacity of nanoparticles act as a destabilizing factor. With an increase of ${\gamma}$ which is the ratio of thermal conductivity of nanoparticles to that of basefluid, the thermal instability of nanofluid decreases but the heat transfer rate increases.

• 대한기계학회논문집B
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• 제21권1호
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• pp.153-164
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• 1997

Flame oscillation phenomena in a co-flow diffusion flame was experimentally studied with periodic fuel supply using a solenoid valve. The degree of excitation was controlled by changing the volume flux of fuel passing through the valve. Flame oscillation frequencies were measured utilizing a photodiode, a spectrum analyzer, video and high speed movies. Laser planar visualization was employed to study the correlation between the flame oscillation and the toroidal vortices. Observed are three regimes of flame oscillation, where the oscillation frequencies are for the multiples of excitation, the excitation itself and the flame natural oscillation. Both periods of natural oscillation and of excitation induced oscillation exist over one cycle of the excitation in the frequency multiplied regime. It is considered as an effect of balancing the influence of buoyancy driven vortex with that of excitation induced vortex near the excitation rate of 0.2. Flame shapes are become monotonous as increasing the excitation frequency to the range of over two fold of the natural oscillation. The flame oscillation can be modulated to the frequency of either multiples of excitation or excitation itself under certain conditions. This implies that the flame oscillation could be modulated to avoid the resonance frequency of the combustor, and shows the possibility of active control of the flame oscillation.

• Journal of Mechanical Science and Technology
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• 제15권10호
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• pp.1451-1460
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• 2001

The critical condition of the onset of buoyancy-driven convective motion of uniformly heated horizontal fluid layer was analysed by the propagation theory which transforms the disturbance quantities similarly. The dimensionless critical time, $\tau$$\sub$c/, is obtained as a function of the Rayleigh number and the Prandtl number. Based on the stability criteria and the boundary-layer instability model, a new heat transfer correlation which can cover whole range of Rayleigh number was derived. Our theoretical results predict the experimental results quite reasonably.

• 천문학회지
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• 제33권2호
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• pp.111-121
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• 2000

Many models of globular cluster formation assume the presence of cold dense clouds in early universe. Here we re-examine the Fall & Rees (1985) model for formation of proto-globular cluster clouds (PGCCs) via thermal instabilities in a protogalactic halo. We first argue, based on the previous study of two-dimensional numerical simulations of thermally unstable clouds in a stratified halo of galaxy clusters by Real et al. (1991), that under the protogalactic environments only nonlinear (${\delta}{\ge}1$) density inhomogeneities can condense into PGCCs without being disrupted by the buoyancy-driven dynamical instabilities. We then carry out numerical simulations of the collapse of overdense douds in one-dimensional spherical geometry, including self-gravity and radiative cooling down to T = $10^4$ K. Since imprinting of Jeans mass at $10^4$ K is essential to this model, here we focus on the cases where external UV background radiation prevents the formation of $H_2$ molecules and so prevent the cloud from cooling below $10^4$ K. The quantitative results from these simulations can be summarized as follows: 1) Perturbations smaller than $M_{min}\~(10^{5.6}\;M{\bigodot})(nh/0.05cm^{-3})^{-2}$ cool isobarically, where nh is the unperturbed halo density, while perturbations larger than $M_{min}\~(10^8\;M{\bigodot})(nh/0.05cm^{-3})^{-2}$ cool isochorically and thermal instabilities do not operate. On the other hand, intermediate size perturbations ($M_{min} < M_{pgcc} < M_{max}$) are compressed supersonically, accompanied by strong accretion shocks. 2) For supersonically collapsing clouds, the density compression factor after they cool to $T_c = 10^4$ K range $10^{2.5} - 10^6$, while the isobaric compression factor is only $10^{2.5}$. 3) Isobarically collapsed clouds ($M < M_{min}$) are too small to be gravitationally bound. For supersonically collapsing clouds, however, the Jeans mass can be reduced to as small as $10^{5.5}\;M_{\bigodot}(nh/0.05cm^{-3})^{-1/2}$ at the maximum compression owing to the increased density compression. 4) The density profile of simulated PGCCs can be approximated by a constant core with a halo of $p{\infty} r^{-2}$ rather than a singular isothermal sphere.