• Transactions of the Korean Society of Mechanical Engineers B
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• v.38 no.3
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• pp.219-225
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• 2014

In this study, to find the characteristics of the oscillation of a terminating shock wave in a transonic airfoil flow with non-equilibrium condensation, a NACA00-12,14,15 airfoil flow with non-equilibrium condensation is investigated through numerical analysis of TVD scheme. Transonic free stream Mach number of 0.81-0.90 with the variation of stagnation relative humidity and airfoil thickness is tested. For the free stream Mach number 0.87 and attack angle of ${\alpha}=0^{\circ}$, the increase in stagnation relative humidity attenuates the strength of the terminating shock wave and inactivates the oscillation of the terminating shock wave. For the case of $M_{\infty}=0.87$ and ${\phi}_0=60%$, the decreasing rate in the frequency of the shock oscillation caused by non-equilibrium condensation to that of ${\phi}_0=30%$ amounts to 5%. Also, as the stagnation relative humidity gets larger, the maximum coefficient of drag and the difference between the maximum and minimum in $C_D$ become smaller. On the other hand, as the thickness of the airfoil gets larger, the supersonic bubble size becomes bigger and the oscillation of the shock wave becomes higher.

• Journal of Mechanical Science and Technology
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• v.16 no.11
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• pp.1511-1521
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• 2002

High-speed moist air or steam flow has long been of important subject in engineering and industrial applications. Of many complicated gas dynamics problems involved in moist air flows, the most challenging task is to understand the nonequilibrium condensation phenomenon when the moist air rapidly expands through a flow device. Many theoretical and experimental studies using supersonic wind tunnels have devoted to the understanding of the nonequilibrium condensation flow physics so far. However, the nonequilibrium condensation can be also generated in the subsonic flows induced by the unsteady expansion waves in shock tube. The major flow physics of the nonequilibrium condensation in this application may be different from those obtained in the supersonic wind tunnels. In the current study, the nonequilibrium condensation phenomenon caused by the unsteady expansion waves in a shock tube is analyzed by using the two-dimensional, unsteady, Navier-Stokes equations, which are fully coupled with a droplet growth equation. The third-order TVD MUSCL scheme is applied to solve the governing equation systems. The computational results are compared with the previous experimental data. The time-dependent behavior of nonequilibrium condensation of moist air in shock tube is investigated in details. The results show that the major characteristics of the nonequilibrium condensation phenomenon in shock tube are very different from those in the supersonic wind tunnels.

• Journal of Mechanical Science and Technology
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• v.16 no.11
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• pp.1448-1456
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• 2002

The present study addresses the flow characteristics involved in the self-induced oscillations of the underexpanded jet impinging upon a cylindrical body. Both experiment and computational analysis are carried out to elucidate the shock motions of the self-induced oscillations and to find the associated major flow factors. The underexpanded sonic jet is made from a nozzle and a cylindrical body is placed downstream to simulate the impinging jet upon an obstacle. The computational analysis using TVD scheme is applied to solve the axisymmetric, unsteady, inviscid governing equations. A Schlieren system is employed to visualize the self-induced oscillations generated in flow field. The data of the shock motions are obtained from a high-speed video system. The detailed characteristics of the Mach disk oscillations and the resulting pressure variations are expatiated using the time dependent data of the Mach disk positions. The mechanisms of the self-induced oscillations are discussed in details based upon the experimental and computational results.

• The Bulletin of The Korean Astronomical Society
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• v.40 no.1
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• pp.65.2-65.2
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• 2015

We developed a three-dimensional magnetohydrodynamic (MHD) code to reproduce the structure of a solar wind, the properties of a coronal mass ejection (CME) and the interaction between them. This MHD code is based on the finite volume method incorporating total variation diminishing (TVD) scheme with an unstructured grid system. In particular, this grid system can avoid the singularity at the north and south poles and relax tight CFL conditions around the poles, both of which would arise in a spherical coordinate system (Tanaka 1994). In this model, we first apply an MHD tomographic method (Hayashi et al. 2003) to interplanetary scintillation (IPS) observational data and derive a solar wind from the physical values obtained at 50 solar radii away from the Sun. By comparing the properties of this solar wind to observational data obtained near the Earth orbit, we confirmed that our model captures the velocity, temperature and density profiles of a solar wind near the Earth orbit. We then insert a spheromak-type CME (Kataoka et al. 2009) into the solar wind to reproduce an actual CME event. This has been done by introducing a time-dependent boundary condition to the inner boundary of our simulation domain. On the basis of a comparison between a simulated CME and observations near the Earth, we discuss the physics involved in an ICME interacting with a solar wind.

• Proceedings of the KSME Conference
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• 2001.06e
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• pp.355-360
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• 2001

This study addresses a computational work of the impulsive wave which is discharged from the open end of a pipe. An initial compression wave inside the pipe is assumed to propagate toward atmosphere. The over pressure and wave-length of the initial compression wave are changed to investigate the characteristic values of the impulsive wave. The second order total variation diminishing (TVD) scheme is employed to solve the axisymmetric, compressible, unsteady Euler equations. The relationship between the initial compression wave form and impulsive wave is characterized in terms of the peak pressure of the impulsive wave and its directivity. The results obtained show that for the initial compression wave of a large wave-length the peak pressure of the impulsive wave does not depend on the over pressure of the initial compression wave, but for the initial compression wave of a very short wave-length, like a shock wave, the peak pressure of the impulsive wave is increased with an increase in the over pressure of the initial compression wave. The directivity of the impulsive wave to the pipe axis becomes significant with a decrease in the wave-length of the initial compression wave.

• Proceedings of the KSME Conference
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• 2001.06e
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• pp.299-304
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• 2001

The current study describes experimental and computational work on the passive control of the steady and unsteady condensation shock waves, which are generated in a transonic nozzle. The bleed slots are installed on the contoured wall of the transonic nozzle in order to control the magnitude of the condensation shock wave and its oscillations. For computations, a droplet growth equation is incorporated into the two-dimensional Navier-Stokes equation systems. Computations are carried out using a third-order MUSCL type TVD finite-difference scheme with a second-order tractional time step. Baldwin-Lomax turbulence model is employed to close the governing equations. An experiment using an indraft transonic wind tunnel is made to validate the computational results. The current computations represented well the experimental flows. From both the experimental and computational results it is found that the magnitude of the condensation shock wave in the bleed slotted nozzle is significantly reduced, compared with no passive control of solid wall. The oscillations of the condensation shock wave are successfully suppressed by a bleed slot system.

• Journal of computational fluids engineering
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• v.21 no.2
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• pp.1-11
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• 2016

Considerable efforts are required to develop a monotone, robust and stable high-order numerical scheme for solving the hyperbolic system. The discontinuous Galerkin(DG) method is a natural choice, but elimination of the spurious oscillations from the high-order solutions demands a new development of proper limiters for the DG method. There are several available limiters for controlling or removing unphysical oscillations from the high-order approximate solution; however, very few studies were directed to analyze the exact role of the limiters in the hyperbolic systems. In this study, the performance of the several well-known limiters is examined by comparing the high-order($p^1$, $p^2$, and $p^3$) approximate solutions with the exact solutions. It is shown that the accuracy of the limiter is in general problem-dependent, although the Hermite WENO limiter and maximum principle limiter perform better than the TVD and generalized moment limiters for most of the test cases. It is also shown that application of the troubled cell indicators may improve the accuracy of the limiters under some specific conditions.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.20 no.7
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• pp.2315-2325
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• 1996

A compression wave is attenuated or distorted as it propagates in a tube. The present study investigated the propagation characteristics of the compression waves which are generated by a train in a high-speed railway tunnel. A Total Variation Diminishing (TVD) difference scheme was applied to one-dimensional, unsteady viscous compressible flow. The numerical calculation involved the effects of wall friction, heat transfer and energy loss due to the friction heat in the boundary layer behind the propagating compression wave, and compared with the measurement results of a shock tube and a real tunnel. The present results show that attenuation of the compression wave in turbulent boundary layer is stronger than in laminar boundary layer, but nonlinear effect of the compression wave is greater in the laminar boundary layer. The energy loss due to the frictional heat had not influence on attenuation and distortion of the propagating compression waves.

• Journal of computational fluids engineering
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• v.8 no.4
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• pp.16-25
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• 2003

The design method for transonic turbine blades has been developed based on Wavier-Stokes equations. The present computing process is done on the four separate steps, i.e., determination of the blade profile, generation of the computational grids, cascade flow simulation and analysis of the computed results in the sense of the aerodynamic performance. The blade shapes are designed using the cubic polynomials under the control of the design parameters. Numerical methods for the flow equations are based on Van-Leer's FVS with an upwind TVD scheme on the finite volume. In the present study, numerical simulation has been done to investigate the effects of the design parameters on the aerodynamic peformance of the axial-flow turbine blades. Applications are made to the VKI transonic rotor blades. Computed results are analyzed with respect to four parameters and compared with the experimental data.

• Journal of computational fluids engineering
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• v.3 no.1
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• pp.11-21
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• 1998

A vorticity-based method for the numerical solution of the two-dimensional incompressible Navier-Stokes equations is presented. The governing equations for vorticity, velocity and pressure variables are expressed in an integro-differential form. The global coupling between the vorticity and the pressure boundary conditions is fully considered in an iterative procedure when numerical schemes are employed. The finite volume method of the second order TVD scheme is implemented to integrate the vorticity transport equation with the dynamic vorticity boundary condition. The velocity field is obtained by using the Biot-Savart integral. The Green's scalar identity is used to solve the total pressure in an integral approach similar to the surface panel methods which have been well established for potential flow analysis. The present formulation is validated by comparison with data from the literature for the two-dimensional cavity flow driven by shear in a square cavity. We take two types of the cavity now: (ⅰ) driven by non-uniform shear on top lid and body forces for which the exact solution exists, and (ⅱ) driven only by uniform shear (of the classical type).