• The Pure and Applied Mathematics
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• v.24 no.4
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• pp.201-209
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• 2017

We prove convergence properties of the global solutions to the cooperative cross-diffusion system with the intra-specific cooperative pressures dominated by the inter-specific competition pressures and the inter-specific cooperative pressures dominated by intra-specific competition pressures. Under these conditions the $W^1_2-bound$ and the time global existence of the solution for the cooperative cross-diffusion system have been obtained in [10]. In the present paper the convergence of the global solution is established for the cooperative cross-diffusion system with large diffusion coefficients.

• 한국연소학회:학술대회논문집
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• 1999.10a
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• pp.11-20
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• 1999

Acoustic pressure response and NO formation of hydrogen-air diffusion flames at various pressures are numerically studied by employing counterflow diffusion flame as a model flame let in turbulent flames in combustion chambers. The numerical results show that extinction strain rate increases linearly with pressure and then decreases, and increases again at high pressures. Thus, flames are classified into three pressure regimes. Such non-monotonic behavior is caused by the change in chemical kinetic behavior as pressure rises. Acoustic pressure response in each regime is investigated based on the Rayleigh criterion. At low pressures, pressure-rise causes the increase in flame temperature and chain branching/recombination reaction rates, resulting in increased heat release. Therefore, amplification in pressure oscillation is predicted. Similar phenomena are predicted at high pressures. At moderate pressures, weak amplification is predicted. Emission index of NO shows similar behaviors as to the peak-temperature variation with pressure.

• Journal of Mechanical Science and Technology
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• v.18 no.2
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• pp.325-334
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• 2004

Computational experiments on fundamental un stretched laminar burning velocities and flame response to stretch (represented by the Markstein number) of hydrogen-air flames at high temperatures and pressures were conducted in order to understand the dynamics of the flames including hydrogen as an attractive energy carrier in conditions encountered in practical applications such as internal combustion engines. Outwardly propagating spherical premixed flames were considered for a fuel-equivalence ratio of 0.6, pressures of 5 to 50 atm, and temperatures of 298 to 1000 K. For these conditions, ratios of unstretched-to-stretched laminar burning velocities varied linearly with flame stretch (represented by the Karlovitz number), similar to the flames at normal temperature and normal to moderately elevated pressures, implying that the "local conditions" hypothesis can be extended to the practical conditions. Increasing temperatures tended to reduce tendencies toward preferential-diffusion instability behavior (increasing the Markstein number) whereas increasing pressures tended to increase tendencies toward preferential-diffusion instability behavior (decreasing the Markstein number).

• Transactions of the Korean Society of Mechanical Engineers B
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• v.21 no.11
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• pp.1527-1537
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• 1997

Extinction characteristics and acoustic response of hydrogen-air diffusion flames at various pressures are numerically studied by employing counterflow diffusion flame as a model flamelet in turbulent flames in combustion chambers. The numerical results show that extinction strain rate increases linearly with pressure and then decreases, and increases again at high pressures. Thus, flames are classified into three pressure regimes. Such nonmonotonic behavior is caused by the change in chemical kinetic behavior as pressure rises. The investigation of acoustic-pressure response in each regime, for better understanding of combustion instability, shows different characteristics depending on pressure. At low pressures, pressure-rise causes the increase in flame temperature and chain branching/recombination reaction rates, resulting in increased heat release. Therefore, amplification in pressure oscillation is predicted. Similar phenomena are predicted at high pressures. At moderate pressures, weak amplification is predicted since flame temperature and chain branching reaction rate decreases as pressure rises. This acoustic response can be predicted properly only with detailed chemistry or proper reduced chemistry.

• Journal of the Korean Crystal Growth and Crystal Technology
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• v.31 no.3
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• pp.127-136
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• 2021

This paper is dedicated to numerical simulation for diffusion-advective convection in a square cavity during physical vapor transport of Hg₂Br₂. Flow characteristics of the temperature difference between the source and crystal regions, 50℃ (300℃ → 250℃), partial pressures of component argon of 20 Torr and 100 Torr are investigated and presented as velocity vectors and streamlines, isotherms and iso-mass concentrations contours. Moreover, alterations of average Nusselt and average Sherwood numbers with (a) the source and crystal regions, (b) the pressures of component argon of 20 Torr and 100 Torr are analyzed and addressed in details. Both average Nusselt and average Sherwood numbers are seen to decrease with the increasing values of the partial pressures of component argon. Also, it is found that for the two different partial pressures of component argon, average Nusselt numbers at the source region are greater than at the crystal region, and inversely, average Sherwood numbers at the crystal region are greater than the source region by a factor of 3.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.21 no.9
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• pp.1174-1184
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• 1997

Extinction characteristics of pure hydrogen-oxygen diffusion flames, at high pressures in the neighborhood of the critical pressure of oxygen, is numerically studied by employing counterflow diffusion flame as a model flame let in turbulent flames in rocket engines. The numerical results show that extinction strain rate increases almost linearly with pressure up to 100 atm, which can be explained by comparison of the chain-branching-reaction rate with the recombination-reaction rate. Since contributions of the chain-branching reactions, two-body reactions, are found to be much greater than those of the recombination reactions, three-body reactions, extinction is controlled by two-body reactions, thereby resulting in the linearity of extinction strain rate to pressure. Therefore, it is found that the chemical kinetic behaviors don't change up to 100 atm. Consideration of the pressure fall-off reactions shows a slight increase in extinction strain rate, but does not modify its linearity to pressure. The reduced kinetic mechanisms, which were verified at low pressures, are found to be still valid at high pressures and show good qualitative agreement in prediction of extinction strain rates. Effect of real gas is negligible on chemical kinetic behaviors of the flames.

• Geomechanics and Engineering
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• v.37 no.2
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• pp.97-107
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• 2024

The accurate prediction of grouting upward diffusion height is crucial for estimating the bearing capacity of tip-grouted piles. Borehole construction during the installation of bored piles induces soil unloading, resulting in both radial stress loss in the surrounding soil and an impact on grouting fluid diffusion. In this study, a modified model is developed for predicting grout diffusion height. This model incorporates the classical rheological equation of power-law cement grout and the cavity reverse expansion model to account for different degrees of unloading. A series of single-pile tip grouting and static load tests are conducted with varying initial grouting pressures. The test results demonstrate a significant effect of vertical grout diffusion on improving pile lateral friction resistance and bearing capacity. Increasing the grouting pressure leads to an increase in the vertical height of the grout. A comparison between the predicted values using the proposed model and the actual measured results reveals a model error ranging from -12.3% to 8.0%. Parametric analysis shows that grout diffusion height increases with an increase in the degree of unloading, with a more pronounced effect observed at higher grouting pressures. Two case studies are presented to verify the applicability of the proposed model. Field measurements of grout diffusion height correspond to unloading ratios of 0.68 and 0.71, respectively, as predicted by the model. Neglecting the unloading effect would result in a conservative estimate.

• Bulletin of the Korean Mathematical Society
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• v.38 no.4
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• pp.643-655
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• 2001

We discuss the existence of positive solutions to a certain nonlinear elliptic system representing a competition interaction with self-diffusion. The method used here is a fixed point index theory in a positive cone. We give a sufficient condition for the existence of positive solutions.

• Journal of the Korean institute of surface engineering
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• v.31 no.1
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• pp.54-62
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• 1998

In this study, the behaviorof ion nitriding of AISI 304 stainless steel was investigated using plasma ion nitriding system. The characteristics of ion nitriding, and their micsoctrucyures, and physical properties were investigated as a function of process parmeteds. important conclusions can be summarzied as follows. Firstly, it was found that growth of nitride layer in ion nitriding are mainly affected by N2 partial pressures and nitriding temperatures for AISI 304 stainless steel. The $N_2$<\TEX> partial pressure plays on important role in ion nitriding since it determiness the incoming flux of nitrogen species onto specimen surface. Nitriding thmprrature is also important besauseit determines the diffusion rates of nitrogen through nitride layers. While both parameters affects the characteristics rateding are controlled by nitridingen diffusion nitration profiles of N and alloying elements such as Cr and Ni are observed through niride layers. Secondly, nitride layer consists of the upper white laywe having various nitride phases and the underneath diffusion layers. The thickness of white layer increases with $N_2$<\TEX> partial pressures and nitriding temperatures. The thinkness of diffusion layer is increasting nitriding temperatures. Finally, nitriding of stainless steels steel show slighly low their corrsionce prorerties. However, passivation properties, which is normally observed in stainless steels, were still observed aftre ion nitriding.

• Bulletin of the Korean Chemical Society
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• v.23 no.3
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• pp.447-453
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• 2002

In this paper we have presented the results of thermodynamic, structural, and dynamic properties of model systems for liquid benzene, toluene and p-xylene in an isobaric-isothermal (NpT) ensemble at 283.15, 303.15, 323.15, and 343.15 K using molecular dynamics (MD) simulation. This work is initiated to compensate for our previous canonical (NVT) ensemble MD simulations [Bull. Kor. Chem. Soc. 2001, 23, 441] for the same systems in which the calculated pressures were too low. The calculated pressures in the NpT ensemble MD simulations are close to 1 atm and the volume of each system increases with increasing temperature. The first and second peaks in the center of mass g(r) diminish gradually and the minima increase as usual for the three liquids as the temperature increases. The three peaks of the site-site gC-C(r) at 283.15 K support the perpendicular structure of nearest neighbors in liquid benzene. Two self-diffusion coefficients of liquid benzene via the Einstein equation and via the Green-Kubo relation are in excellent agreement with the experimental measures. The self-diffusion coefficients of liquid toluene and p-xylene are in accord with the trend that the self-diffusion coefficient decreases with increasing number of methyl group. The friction constants calculated from the force auto-correlation (FAC) function with the assumption that the fast random force correlation ends at time which the FAC has the first negative value give a correct qualitative trends: decrease with increase of temperature and increase with the number of methyl group. The friction constants calculated from the FAC's are always less than those obtained from the friction-diffusion relation which reflects that the random FAC decays slower than the total FAC as described by Kubo [Rep. Prog. Phys. 1966, 29, 255].