• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.9
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• pp.2283-2296
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• 1995

Experiments of normal shock wave/turbulent boundary layer interaction were conducted in a supersonic diffuser. The flow Mach number just upstream of the normal shock wave was in the range of 1.10 to 1.70 and Reynolds number based upon the turbulent boundary layer thickness was varied in the range of 2.2*10$^{[-994]}$ -4.4*10$^{[-994]}$ . The wall pressures in streamwise and spanwise directions were measured for two test cases, in which the turbulent boundary layer thickness incoming into the supersonic diffuser was changed. The results show that the interactions of normal shock wave with turbulent boundary layer in the supersonic diffuser can be divided into three patterns, i.e., transonic interaction, weak interaction and strong interaction, depending on Mach number. The weak interactions generate the post-shock expansion which its strength is strong as the Mach number increases and the strong interactions form the pseudo-shock waves. From the spanwise measurements of wall pressure, it is known that if the flow Mach number is low, the interacting flow fields essentially appear two-dimensional, but they have an apparent 3-dimensionality for the higher Mach numbers.

• 한국전산유체공학회:학술대회논문집
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• 1995.10a
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• pp.241-245
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• 1995

This paper presents the studies on the variation of shape and thickness of a normal shock wave with Mach number and density by using the most useful numerical technique in rarefied gas regime, DSMC(Direct Simulation Monte Carlo). Calculations are peformed for the three different Mach numbers and for one Mach number with different densities. From the obtained results, we find that the shock thickness is decreasing with increasing Mach number, and there are much variations in thickness and shape with decreasing density. Also, there is a noticeable overshoot of the translational temperature near the shock center in the case of a large Mach number.

• 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.

• Bulletin of the Korean Chemical Society
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• v.17 no.4
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• pp.385-390
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• 1996

It has been well known that the Grad thirteen-moment equations have solutions only when the Mach number is less than a limiting value for the stationary plane shock-waves. The limit of Mach number has been re-examined by including successive terms in the series expansion of distribution function. The method employed is the linear analysis of moment equations near up-streaming and down-streaming flows. For the thirteen moment case, it has been confirmed that equations have solutions only when the Mach number is less than 1.6503, which is consistent with the literature value. For the case of twenty moments, the limit of Mach number is decreased to 1.3416.

• 한국가시화정보학회:학술대회논문집
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• 2002.11a
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• pp.113-116
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• 2002

The shock wave discharged from an annular duct leads to very complicated flow features, such as Mach stem, spherical waves, and vortex rings. In the current study, the merging phenomenon and propagation characteristics of the shock wave are numerically investigated using a CFD method. The Harten-Yee's total variation diminishing (TVD) scheme is used to the unsteady, axisymmetric, two-dimensional, compressible Euler equations. The Mach number of incident shock wave $M_s$ is varied in the range below 2.0. The computational results are visualized to observe the major features of the annular shock waves discharged from the tube. On the symmetric axis, the peak pressure produced by the shock wave and its location depend upon strongly the radius of the annular tubes. A Mach stem is generated along the symmetric axis of the annular tubes.

• 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.

• 한국가시화정보학회:학술대회논문집
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• 2004.11a
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• pp.72-75
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• 2004

The present study describes a computational work to investigate detailed behaviors of the twin shock waves discharged from the exits of two-parallel ducts. In computations, the Yee-Roe-Davis's TVD scheme was used to solve the unsteady, three-dimensional, inviscid, compressible, Euler equations. The distance between two ducts is varied and the Mach number of the incident shock wave is changed below 2.0. The results obtained show that on the symmetric axis between two-parallel ducts, the maximum pressure achieved by the merge of twin shock waves and its location strongly depend upon the distance between two-parallel ducts and the Mach number of the incident shock wave. It is also found that the twin shock waves discharged from the exits of two-parallel ducts leads to the complicated flow fields, such as Mach stem, spherical waves, and vertical structures.

• Proceedings of the KSME Conference
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• 2001.11b
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• pp.417-422
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• 2001

The shock structure of supersonic, dual, coaxial jet is experimentally investigated. Eight different kinds of coaxial, dual nozzles are employed to observe the major features of the near field shock structure of the supersonic, coaxial, dual jets. Four convergent-divergent supersonic nozzles having the Mach number of 2.0 and 3.0, and are used to compare the coaxial jet flows discharging from two sonic nozzles. The primary pressure ratio is changed in the range between 4.0 and 10.0 and the assistant jet pressure ratio from 1.0 to 4.0. The results obtained show that the impinging angle, nozzle geometry and pressure ratio significantly affect the near field shock structure, Mach disk location and Mach disk diameter. The annular shock system is found depending the assistant and primary jet pressure ratios.

• Proceedings of the Korea Institute of Applied Superconductivity and Cryogenics Conference
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• 2002.02a
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• pp.23-26
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• 2002

Two modes of shock waves propagating in He II (superfluid helium), this is a compression and a thermal shock waves, were studied experimentally by using superconductive temperature sensors, piezo pressure transducers and Schlieren visualization method with an ultra-high-speed video camera (40,500 pictures/sec). The shock waves are induced by a gas dynamic shock wave impingement upon a He II free surface. It is found that the shock Mach number of a transmitted compression shock wave is up to 1.16, and the shock Mach number of a thermal shock wave coincides well with the second sound velocity under each compressed He II state condition. The temperature rise ratio of an induced thermal shock wave to that of an incident gas dynamic shock wave was found to be very small, as small as 0.003 at 1.80K.