• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.35 no.12
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• pp.1075-1081
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• 2007

The temperature preconditioning is applied to the Navier-Stokes equations. Also, a new concept of diffusion Mach numbers is introduced to modify the reference Mach number for the Navier-Stokes equations. Flows over a circular cylinder were calculated at different Reynolds numbers. It is shown that the temperature preconditioning improves the convergence characteristics of Navier-Stokes equations. Also, it is shown that the modified reference Mach number alleviates the convergence problems at locally low speed regions.

• Journal of The Korean Astronomical Society
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• v.37 no.5
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• pp.405-412
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• 2004

Cosmological shocks form as an inevitable consequence of gravitational collapse during the large scale structure formation and cosmic-rays (CRs) are known to be accelerated at collisionless shocks via diffusive shock acceleration (DSA). We have calculated the evolution of CR modified shocks for a wide range of shock Mach numbers and shock speeds through numerical simulations of DSA in 1D quasi-parallel plane shocks. The simulations include thermal leakage injection of seed CRs, as well as pre-existing, upstream CR populations. Bohm-like diffusion is assumed. We show that CR modified shocks evolve to time-asymptotic states by the time injected particles are accelerated to moderately relativistic energies (p/mc $\ge$ 1), and that two shocks with the same Mach number, but with different shock speeds, evolve qualitatively similarly when the results are presented in terms of a characteristic diffusion length and diffusion time. We find that $10^{-4} - 10^{-3}$ of the particles passed through the shock are accelerated to form the CR population, and the injection rate is higher for shocks with higher Mach number. The CR acceleration efficiency increases with shock Mach number, but it asymptotes to ${\~}50\%$ in high Mach number shocks, regardless of the injection rate and upstream CR pressure. On the other hand, in moderate strength shocks ($M_s {\le} 5$), the pre-existing CRs increase the overall CR energy. We conclude that the CR acceleration at cosmological shocks is efficient enough to lead to significant nonlinear modifications to the shock structures.

• Journal of The Korean Astronomical Society
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• v.37 no.4
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• pp.225-232
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• 2004

Shocks are ubiquitous in astrophysical environments and cosmic-rays (CRs) are known to be accelerated at collisionless shocks via diffusive shock acceleration. It is believed that the CR pressure is important in the evolution of the interstellar medium of our galaxy and most of galactic CRs with energies up to ${\~}\;10^{15}$ eV are accelerated by supernova remnant shocks. In this contribution we have studied the CR acceleration at shocks through numerical simulation of 1D, quasi-parallel shocks for a wide range of shock Mach numbers and shock speeds. We show that CR modified shocks evolve to time-asymptotic states by the time injected particles are accelerated to moderately relativistic energies, and that two shocks with the same Mach number, but with different shock speeds, evolve qualitatively similarly when the results are presented in terms of a characteristic diffusion length and diffusion time. We find that $10^{-4} - 10^{-3}$ of the particles passed through the shock are accelerated to form the CR population, and the injection rate is higher for shocks with higher Mach number. The time asymptotic value for the CR acceleration efficiency is controlled mainly by shock Mach number, and high Mach number shocks all evolve towards efficiencies ${\~}50\%$, regardless of the injection rate and upstream CR pressure. We conclude that the injection rates in strong quasi-parallel shocks are sufficient to lead to significant nonlinear modifications to the shock structures, implying the importance of the CR acceleration at astrophysical shocks.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.25 no.7
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• pp.989-996
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• 2001

High-speed and low-speed flows are simulated numerically by flowfield-dependent mixed explicit-implicit (FDMEI) method. This algorithm depends on implicitness parameters of convection, diffusion, diffusion gradients, and source terms which are calculated from the changes of local Mach, Reynolds, Peclet, and Damkohler numbers between adjacent nodes. Convection phenomena or shock waves are resolved from Mach number-dependent implicitness parameters whereas diffusion or viscous actions are simulated by Reynolds number or Peclet number-dependent implicitness parameters. Fluctuation components of all variables are properly accommodated spatially and temporally in the FDMEI procedure. To illustrate, some benchmark example problems are presented for comparisons of the FDMEI results with other available data. These results appear to be encouraging and point toward the need for further investigations of the FDMEI theory.

• Journal of The Korean Astronomical Society
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• v.36 no.1
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• pp.1-12
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• 2003

Nonthermal particles can be produced due to incomplete thermalization at collisionless shocks and further accelerated to very high energies via diffusive shock acceleration. In a previous study we explored the cosmic ray (CR) acceleration at cosmic shocks through numerical simulations of CR modified, quasi-parallel shocks in 1D plane-parallel geometry with the physical parameters relevant for the shocks emerging in the large scale structure formation of the universe (Kang & Jones 2002). Specifically we considered pancake shocks driven by accretion flows with $U_o = 1500 km\;s^{-l}$ and the preshock gas temperature of $T_o = 10^4 - 10^8K$. In order to consider the CR acceleration at shocks with a broader range of physical properties, in this contribution we present additional simulations with accretion flows with $U_o = 75 - 1500 km\;s^{-l}$ and $T_o = 10^4K$. We also compare the new simulation results with those reported in the previous study. For a given Mach number, shocks with higher speeds accelerate CRs faster with a greater number of particles, since the acceleration time scale is $t_{acc}\;{\propto}\;U_o^{-2}$. However, two shocks with a same Mach number but with different shock speeds evolve qualitatively similarly when the results are presented in terms of diffusion length and time scales. Therefore, the time asymptotic value for the fraction of shock kinetic energy transferred to CRs is mainly controlled by shock Mach number rather than shock speed. Although the CR acceleration efficiency depends weakly on a well-constrained injection parameter, $\epsilon$, and on shock speed for low shock Mach numbers, the dependence disappears for high shock Mach numbers. We present the 'CR energy ratio', ${\phi}(M_s)$, for a wide range of shock parameters and for $\epsilon$ = 0.2 - 0.3 at terminal time of our simulations. We suggest that these values can be considered as time-asymptotic values for the CR acceleration efficiency, since the time-dependent evolution of CR modified shocks has become approximately self-similar before the terminal time.

• 한국연소학회:학술대회논문집
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• 2002.06a
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• pp.68-75
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• 2002

The dynamic behaviors of the single vortex and flame-vortex interaction in a $CH_4/Air$ diffusion flame with addition of $CO_2$ were investigated numerically. The numerical method was based on a predictor-corrector for low Mach number flow. A two-step global reaction mechanism was adopted as a combustion model. Through comparison of results by effect of $CO_2$ added either on the fuel or oxidizer side, it was found that the growth of single vortex and entrainment of surrounding fluid by $CO_2$addition on the fuel side are larger than those by $CO_2$ addition on oxidizer side. Also, when $CO_2$ is added on fuel side, flame-vortex interaction becomes more significant than on air side.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.20 no.2
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• pp.616-623
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• 1996

This paper investigates the linear stability of reacting mixing layers with special emphasis on the existence of multiple unstable modes. The governing equations for laminar flows are from two-dimensional compressible boundary-layer equations. The chemistry is a finite rate single step irreversible reaction with Arrhenius kinetics. For the incompressible reacintg mixing layer with variable density. A necessary condition for instability has been derived. The condition requires that the angular momentum, not the vorticity, to have a maximum in the flow domain. New inflectional modes of instability are found to exist in the outer part of the mixing layer. For the compressible reacting mixing layer, supersonic unstable modes may exist in the abscence of a generalized inflection point. The outer modes at high Mach numbers in the reacting mixing layer are continuations of the inflectional modes of low Mach number flows. However, the generalized inflection point is less important at supersonic flows.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.25 no.8
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• pp.1087-1096
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• 2001

The dynamic structures of unsteady CH$_4$/Air jet diffusion flame with a flame-vortex interaction were numerically investigated. A timed-dependent, axisymmetric computational model and a low mach number approximation were employed in the present calculation. A two-step global reaction mechanism which considers 6 species, was used to calculate the reaction rates. The predicted results including the gravitational effect show that the large outer vortices and the small inner vortices can be well simulated without any additional disturbances near nozzle tip. It was found that the temperature and species concentrations have deviated values even for the same mixture fraction in the flame-vortex interaction region. It was also shown that the flame surface is not deformed by the inner vortex in upstream region, while in downstream region, the flame surface is compressed or stretched by the outer vortex roll-up. The present unsteady jet flame configuration accompanying a flame-vortex interaction is expected to give good implications for the unsteady structures of turbulent flames.

• Journal of The Korean Astronomical Society
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• v.45 no.5
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• pp.127-138
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• 2012

We explore how wave-particle interactions affect diffusive shock acceleration (DSA) at astrophysical shocks by performing time-dependent kinetic simulations, in which phenomenological models for magnetic field amplification (MFA), Alfv$\acute{e}$nic drift, thermal leakage injection, Bohm-like diffusion, and a free escape boundary are implemented. If the injection fraction of cosmic-ray (CR) particles is ${\xi}$ > $2{\times}10^{-4}$, for the shock parameters relevant for young supernova remnants, DSA is efficient enough to develop a significant shock precursor due to CR feedback, and magnetic field can be amplified up to a factor of 20 via CR streaming instability in the upstream region. If scattering centers drift with Alfv$\acute{e}$n speed in the amplified magnetic field, the CR energy spectrum can be steepened significantly and the acceleration efficiency is reduced. Nonlinear DSA with self-consistent MFA and Alfv$\acute{e}$nic drift predicts that the postshock CR pressure saturates roughly at ~10 % of the shock ram pressure for strong shocks with a sonic Mach number ranging $20{\leq}M_s{\leq}100$. Since the amplified magnetic field follows the flow modification in the precursor, the low energy end of the particle spectrum is softened much more than the high energy end. As a result, the concave curvature in the energy spectra does not disappear entirely even with the help of Alfv$\acute{e}$nic drift. For shocks with a moderate Alfv$\acute{e}$n Mach number ($M_A$ < 10), the accelerated CR spectrum can become as steep as $E^{-2.1}$ - $E^{-2.3}$, which is more consistent with the observed CR spectrum and gamma-ray photon spectrum of several young supernova remnants.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.27 no.9
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• pp.1209-1219
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• 2003

The dynamic behaviors of the single vortex interacting with $CH_4-Air$ jet diffusion flame are investigated numerically. The numerical method is based on a predict-corrector scheme for a low Mach number flow. A two-step global reaction mechanism is adopted as a combustion model. Studies are conducted in fixed initial velocities for the three cases according as where $CO_2$ is added; (1) without dilution, (2) dilution in fuel stream and (3) dilution in oxidizer stream. A single vortex is generated by an axisymmetric jet, which is made by an impulse of a cold fuel when a flame is developed entirely in a computational domain. The simulation shows that $CO_2$ dilution in fuel stream results in somewhat larger vortex radius, and greater amount of entrainment of surrounding fluid than in other cases. Thus, the dilution of $CO_2$ in fuel stream enhances the mixing in single vortex and increases the stretching of the flame surface. The budgets of the vorticity transport equation are examined to reveal the mechanism of vortex formation when $CO_2$ is added. It is found that, in the case of $CO_2$ dilution in fuel stream, the vortex destruction due to volumetric expansion and the vortex production due to baroclinic torque are more dominant than in other cases.