• Journal of Energy Engineering
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• v.24 no.2
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• pp.110-114
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• 2015

A numerical investigation has been carried out on recirculation zone formed downstream of a compressible flow over a backward facing step. The study has been performed by solving Two-Dimensional Navier-Stokes equations. The system of governing equations has been solved, using an explicit Harten-Yee Non- MUSCL Modified flux type TVD scheme and a zero-equation algebraic turbulence model to calculate the eddy viscosity coefficient. The recirculation region dimensions are characterized over a range of Mach numbers of fixed step height 5mmThe detail of recirculation zone such as pressure, temperature, recirculation length, strength etc are reported. The variations of these characteristics due to change of Mach number are also presented.

• 한국가시화정보학회:학술대회논문집
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• 2004.04a
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• pp.29-36
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• 2004

A numerical study is carried out on the detonation wave propagation through a T-shaped flame tube, which represents a crucial part of the combustion wave ignition (CWI) system aimed for simultaneous ignition of multiple combustion chambers by delivering detonation waves. The formulation includes the Euler equations and an induction-parameter model. The reaction rate is treated based on a chemical kinetics database obtained from a detailed chemistry mechanism. A second-order implicit time integration and a third-order TVD algorithm are Implemented to solve the theoretical model numerically. A total of more than two-million grid points are used to provide direct insight into the dynamics of the detonation wave. Several important phenomena including detonation wave propagation, degeneration, and re-initiation are carefully examined. Information obtained can be effectively used to facilitate the design and optimization of the flame tubes of CWI systems.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.29 no.1 s.232
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• pp.80-86
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• 2005

This study presents numerical solutions of the two-dimensional Navier-Stokes equations for supersonic unsteady flow in a convergent-divergent nozzle with heat addition. The TVD scheme in generalized coordinates is employed in order to calculate the moving shock waves caused by thermal choking. We discuss on transient characteristics, start and unstart phenomena, fluctuations of specific thrust caused by thermal choking and viscous effects. We prove that the control of separation of boundary layer is the most important key problem to prevent the thermal choking.

• 한국전산유체공학회:학술대회논문집
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• 1999.05a
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• pp.85-89
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• 1999

Numerical Analysis has been done for the supersonic off-design jet flow due to the pressure difference between the jet and the ambient fluid. The difference of pressure generates an oblique shock or an expansion wave at the nozzle exit, The waves reflect repeatedly at the center axis and on the sonic surface in the shear layer, and the pressure difference is resolved across these waves interacted with the turbulence mixing layer. In this paper, the axi-symmetric Navier-Stokes equation has been used with two equation $k-{\varepsilon}$ turbulence closure model. The second order TVD scheme with flux limiters, based on the flux vector split by the smooth eigenvalue split, has been used to capture internal shocks and other discontinuities. The correction term for the compressible flow and the damping function are used in the turbulence model. Numerical calculations have been done to analyze the off-design jet flow due to the pressure difference. The variation of pressure along the flow axis is compared with an experimental result and other numerical result. The characteristics of the interaction between the shock cell and the turbulence mixing layer have been analyzed.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.31 no.2 s.257
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• pp.109-115
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• 2007

Airframe-integrated Scramjet engines of NASA Langley type consist of a compressor, a combustion chamber and a nozzle. When some disturbances occur in one module of the engine, its influences are propagated to other modules. In this study, it is investigated numerically how shock waves were caused by thermal choking in one module propagate upstream and how they influence adjacent modules. The calculations are carried out in 2-dimensional supersonic viscous flow model using explicit TVD scheme in generalized coordinates. The adverse pressure gradient caused by heat addition brings about separation of the wall boundary layers and formation of the oblique shock wave that proceed to upstream. This moving shock wave formed one module blocks the flow coming into the adjacent modules, which makes the modules unstarted.

• Journal of The Korean Astronomical Society
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• v.28 no.2
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• pp.223-243
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• 1995

We describe the implementation of a multi-dimensional numerical code to solve the equations for idea! magnetohydrodynamics (MHD) in cylindrical geometry. It is based on an explicit finite difference scheme on an Eulerian grid, called the Total Variation Diminishing (TVD) scheme, which is a second-order-accurate extension of the Roe-type upwind scheme. Multiple spatial dimensions are treated through a Strang-type operator splitting. Curvature and source terms are included in a way to insure the formal accuracy of the code to be second order. The constraint of a divergence-free magnetic field is enforced exactly by adding a correction, which involves solving a Poisson equation. The Fourier Analysis and Cyclic Reduction (FACR) method is employed to solve it. Results from a set of tests show that the code handles flows in cylindrical geometry successfully and resolves strong shocks within two to four computational cells. The advantages and limitations of the code are discussed.

• 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.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.30 no.3 s.246
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• pp.201-207
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• 2006

Transient radiative heat transfer is analyzed in a one-dimensional slab using finite volume method (FVM). In this study, the step, $2^{nd}$ order upwind, and QUICK schemes are used for incident diffuse radiation and collimated beam, respectively. The results fer diffuse radiation show that all schemes applied in this study give good agreements with available published results. In case of collimated beam however, the results show deviations from the analytical solutions. To successfully describe the propagations of collimated beam shock capturing schemes such as TVD scheme are need to be developed.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2008.03a
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• pp.597-601
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• 2008

Three-dimensional structures of detonation wave propagating in circular tube were investigated. Inviscid fluid dynamics equations coupled with a conservation equation of reaction progress variable were analyzed by a MUSCL-type TVD scheme and four stage Runge-Kutta time integration. Variable-$\gamma$ formulation was used to account for the variable properties between unburned and burned states and the chemical reaction was modeled by using a simplified one-step irreversible kinetics model. The computational code was parallelized based on domain decomposition technique using MPI-II message passing library. The computations were carried out using a home made Windows based PC cluster having 160 AMD AthloxXP and Athlon64 processor. The computational domain consisted of through a roundshaped tube with wall conditions. As an initial condition, analytical ZND solution was distributed over the computational domain with disturbances. The disturbances has circumferential large gradient. The unsteady computational results in three-dimension show the detailed mechanisms of multi-cell mode of detonation wave instabilities resulting diamond shape in smoked-foil record.

• Journal of Korea Water Resources Association
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• v.42 no.12
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• pp.1079-1089
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• 2009

The objective of this study is to develop the accurate, robust and high resolution two-dimensional numerical model that solves the computationally difficult hydraulic problems, including the wave front propagation over dry bed and abrupt change in bathymetry. The developed model in this study solves the conservative form of the two-dimensional shallow water equations using an unsplit finite volume scheme and HLLC approximate Riemann solvers to compute the interface fluxes. Bed-slope term is discretized by the divergence theorem in the framework of FVM for application of unsplit scheme. Accurate and stable SGM, in conjunction with the MUSCL which is second-order-accurate both in space and time, is adopted to balance with fluxes and source terms. The exact C-property is shown to be satisfied for balancing the fluxes and the source terms. Since the spurious oscillations in second-order schemes are inherent, an efficient slope limiting technique is used to supply TVD property. The accuracy, conservation property and application of developed model are verified by comparing numerical solution with analytical solution and experimental data through the simulations of one-dimensional dam break flow without bed slope, steady transcritical flow over a hump and two-dimensional dam break flow with a constriction.