• 한국전산유체공학회:학술대회논문집
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• 2005.10a
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• pp.145-150
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• 2005

Generally, Compressible Navier-Stokes codes are used to solve high mach number flows. But, Most of high mach number flows embrace low mach number flows. This phenomenon results in low convergence rate and non-physical solution in CFD analysis. So Many researchers developed preconditioning technique to solve these problems. This Study presents how to modify previous compressible N-S computer code with little changes of structure into preconditioned compressible N-S code applying Roe's Approximate Riemann Solver. And this study show developed preconditioning code is very well operated at all mach number flows.

• 한국전산유체공학회:학술대회논문집
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• 2005.04a
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• pp.128-134
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• 2005

In the CFD area, the numerical analysis of high Mach number flow over a blunt-body poses many issues. Various numerical schemes have been developed to cover the issues, but the traditional schemes are still used widely due to the complexities of new schemes and intricacy of modifying the established codes. In the present study, the well-known Roe's FDS based on TVD-MUSCL scheme is used for the solution of very high Mach number three-dimensional flows posing carbuncle and non-physical phenomena in numerical analysis. A parametric study was carried out to account for the effects of the entropy fixing, grid configurations and initial condition. The carbuncle phenomena could be easily overcome by the entropy fixing, and the non-physical solution could be eliminated by the use of the modified initial condition regardless of entropy fixing and grid configurations.

• 한국전산유체공학회:학술대회논문집
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• 1998.05a
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• pp.35-42
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• 1998

Time marching algorithms applied to compressible Navier-Stokes equation have a convergence problem at low Mach number. It is mainly due to the eigenvalue stiffness and pressure singularity as Mach number approaches to zero. Among the several methods to overcome the shortcomings of time marching scheme, time derivative preconditioning method have been used successfully. In this numerical analysis, we adopted a preconditioner of K.H. Chen and developed a two-dimensional, axisymmetric Navier-Stokes program. The steady state driven cavity flow and backward facing step flow problems were computed to confirm the accuracy and the robustness of preconditioned algorithm for low Mach number flows. And the transonic and supersonic flows insice the JPL axisymmetric nozzle internal flow is exampled to investigate the effects of preconditioning at high Mach number flow regime. Test results showed excellent agreement with the experimental data.

• 한국전산유체공학회:학술대회논문집
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• 1996.05a
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• pp.40-45
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• 1996

This paper discribes the viscous interaction of Hypersonic Wedge Flows using Roe FDS and AUSM+. For this purpose we developed the frozen and the equilibrium code and numerically simulated the viscous interaction by changing the surface temperature and the mach number. We used curve fitting data in NASA Reference Publication 1181, 1260 to calculate equilibrium properties. We compare the equilibrium flow with the frozen flow. We conclude that the mach number and the surface temperature are significant parameters, as the surface temperature and the mach number increase the viscous interaction becomes stronger, and we must consider high-temperature effects in hypersonic flow

• Journal of computational fluids engineering
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• v.15 no.2
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• pp.55-61
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• 2010

A dependence of weighting parameter in preconditioning method for solving low Mach number flow with incompressible flow nature is investigated. The present preconditioning method employs a finite-difference method applied Roe‘s flux difference splitting approximation with the MUSCL-TVD scheme and 4th-order Runge-Kutta method in curvilinear coordinates. From the computational results of benchmark flows through a 2-D backward-facing step duct it is confirmed that there exists a suitable value of the weighting parameter for accurate and stable computation. A useful method to determine the weighting parameter is introduced. With this method, high accuracy and stable computational results were obtained for the flow with low Mach number in the range of Mach number less than 0.3.

• 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.

• Advances in aircraft and spacecraft science
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• v.9 no.2
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• pp.119-130
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• 2022

Supersonic projectiles like rockets, missiles, or aircraft find various applications in the field of defense. The shape of the wings is mainly designed as wedge shape or delta wings for supersonic vehicles. The study of supersonic flows over the wedges and flat plate delta wings around the large scale of incidence angle is considered in the supersonic projectile. In the present paper, the prime attention is to study the pressure at the nose of the plane wedge over the various Mach number and the various angles of incidence. Ghosh piston theory is used to obtain the pressure distribution analytically, and the results are compared with CFD analysis results. The wedge angle and Mach number are the parameters considered for the research work. The range of wedge angle is 50 to 250, and Mach number is 1.5 to 4.0 are considered for the current research work. The analytical results show excellent agreement with the CFD results. The results show that both the parameters wedge angle and Mach number are influential parameters to vary the static pressure. The static pressure increases with an increase in Mach number and wedge angle.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.34 no.6
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• pp.18-28
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• 2006

Numerical analysis of high Mach number flow over a blunt-body poses many difficulties and various numerical schemes have been suggested to overcome the problems. However, the new schemes were used in the limited fields of applications because of the lack of field experience compared to more than 20 years old numerical schemes and the intricacies of modifying the existing code for the special application. In this study, some tips to overcome the numerical difficulties in solving the 3D high-Mach number flows by using Roe's scheme, the most widely used for the past 25 years and adopted in many commercial codes, were examined without a correction of the algorithm or a modification of the CFD code. The well-known carbuncle phenomena of Riemann solvers could be remedied even for an extremely high Mach number by applying the entropy fixing function and a unphysical solution could be overcome by applying a simply modified initial condition regardless of the entropy fixing and grid configuration.

• 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.

• Journal of The Korean Astronomical Society
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• v.34 no.4
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• pp.321-323
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• 2001

Compressible, magnetohydrodynamic (MHD) turbulence in two dimension is studied through high-resolution, numerical simulations with the isothermal equation of state. First, hydrodynamic turbulence with Mach number $(M)_{rms}\;\~$1 is generated by enforcing a random force. Next, initial, uniform magnetic field of various strengths with Alfvenic Mach number Ma $\gg$ 1 is added. Then, the simulations are followed until MHD turbulence is fully developed. Such turbulence is expected to exist in a variety of astrophysical environments including clusters of galaxies. Although no dissipation is included explicitly in our simulations, truncation errors produce dissipation which induces numerical resistivity. It mimics a hyper-resistivity in our second-order accurate code. After saturation, the resulting flows are categorized as SF (strong field), WF (weak field), and VWF (very weak field) classes respectively, depending on the average magnetic field strength described with Alfvenic Mach number, $(Ma)_{rms}{\ge}1$, $(Ma)_{rms}{\~}1$, and $(Ma)_{rms}{\gg}1$. The characteristics of each class are discussed.