• Journal of the Computational Structural Engineering Institute of Korea
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• v.13 no.4
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• pp.427-436
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• 2000

This study presents the nonlinear responses of a hinged-clamped beam under broadband random excitation. By using Galerkin's method the governing equation is reduced to a system or nonautonomous nonlinear ordinary differential equations. The Fokker-Planck equation is used to generate a general first-order differential equation in the joint moments of response coordinates. Gaussian and non-Gaussian closure schemes are used to close the infinite coupled moment equations. The closed equations are then solved for response statistics in terms of system and excitation parameters. The case of two mode interaction is considered in order to compare it with the case of three mode interaction. Monte Carlo simulation is used for numerical verification.

• Journal of the Korean Society of Environmental Restoration Technology
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• v.12 no.3
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• pp.98-105
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• 2009

The objective of this study is to develop numerical simulation model for analysing the wind speed reduction effect by coastal forest belts. The horizontally homogeneous turbulent flow equations, which are derived from the Reynolds-averaged Navier-Stokes method, both above the tree canopy and within the canopy were first formulated, and a first-order closure scheme with the capability of accounting the bulk momentum transport term within the canopy was employed. The averaged equations were solved numerically by finite difference method, FTCS (forward time centered space) scheme. The proposed model was also used to numerically investigate the effects of structural characteristic of forest belt on the wind speed. The effects of maximum leaf area density were evaluated, with the leaf area density of $1.0m^2/m^3$, $2.0m^2/m^3$, $3.0m^2/m^3$, and $4.0m^2/m^3$. Vertical distributions of leaf area, both uniform and varied distribution with a height, were also considered. A comparison of wind profile indicated that there was in good agreements between simulated and measured wind speed. Also, the results showed horizontal wind speed decreased under a height of the tree with increasing maximum leaf area density. In conclusion, in applications where computational efficiency and simplicity are desirable, the proposed numerical model has of great capability to determine the vertical turbulent momentum transport and wind profile in the costal forest belt.

• Structural Engineering and Mechanics
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• v.23 no.6
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• pp.599-613
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• 2006

A method for the dynamical analysis of FE discretized uncertain linear and nonlinear structures is presented. This method is based on the moment equation approach, for which the differential equations governing the response first and second-order statistical moments must be solved. It is shown that they require the cross-moments between the response and the random variables characterizing the structural uncertainties, whose governing equations determine an infinite hierarchy. As a consequence, a closure scheme must be applied even if the structure is linear. In this sense the proposed approach is approximated even for the linear system. For nonlinear systems the closure schemes are also necessary in order to treat the nonlinearities. The complete set of equations obtained by this procedure is shown to be linear if the structure is linear. The application of this procedure to some simple examples has shown its high level of accuracy, if compared with other classical approaches, such as the perturbation method, even for low levels of closures.

• Journal of Korean Society for Atmospheric Environment
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• v.12 no.5
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• pp.577-585
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• 1996

A screening study was performed in order to resolve the flow, combustion and emission characteristics of the gas furmace with co-axial diffusion flane burner. A control-valume based finite-difference method with the power-law scheme was employed for discretization. Numerical procedure for the differential equation was used by SIMPLEST to enclosute rapid converge. A k-.varepsilon. model was incorporated for the closure of turbulence. The mass fraction and mixture fraction were calculated by cinserved scalar method. An equilibrium analysis was employed to determine the concentration of radicals in the product stream and conserbation equations were them solved for N amd NO by Zelovich reaction scheme. The method was exercised in a simple one-dimensional case first, to determine the effects of air ratio, temperature and residence time on NO formation and applied to a furnace with co-axial diffusion flame burner.

• Journal of the Korean Society for Precision Engineering
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• v.18 no.3
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• pp.175-181
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• 2001

An investigation into the response statistics of a spring-pendulum system whose base oscillates randomly along vertical and horizontal line is made. The spring-pendulum system with internal resonance examined is known to be a good model for a variety of engineering systems, including ship motions with nonlinear coupling between pitching and rolling motions. The Fokker-Planck equation is used to generate a general first-order differential equations for the random responses of the system are reduced to a system of autonomous ordinary differential equations. In view of equilibrium solutions of this system and their stability, the response statistics is examined. It is seen that increase in horizontal excitation level leads to a decreased width of the internal resonance region.

• 한국전산유체공학회:학술대회논문집
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• 1999.05a
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• pp.155-161
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• 1999

The three-dimensional turbulent cascade flows with and without endwall fences are numerically investigated by solving the incompressible Navier-Stokes equations with a high-Reynolds number $k-{\varepsilon}$ turbulence closure model. A projection method based algorithm is used in the finite-volume formulation, with the second order upwind-differencing scheme for the convective terms. First, assessments on accuracy of the present method are made by comparing the static pressure distributions at the mid-span of the cascade with measured data, and also by confirming the experimental observations on the choice of an optimal fence height for the secondary flow control. In understanding the three-dimensional nature of the secondary flow in turbine cascade, the limiting streamline patterns and the static pressure contours at the suction surface of the blade as well as on the cascade endwall are employed to visualize the effectiveness of the endwall fence for the secondary flow control. Analysis on the streamwise vorticity contour maps along the cascade with the three-dimensional representation of their iso-surfaces reveals the strucuture of the complicated vortical flow in the turbine cascade with endwall fence, and also leads to an understanding on formation of the counter-rotating streamwise vortex over the endwall fence, in explaining the mechanisms of controlling the secondary flow and also for the proper selection of an optimal fence height.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2003.05a
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• pp.91-93
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• 2003

A comprehensive numerical study is carried out to investigate for the understanding of the flow evolution and flame development in a supersonic combustor with normal injection of ncumally injecting hydrogen in airsupersonic flows. The formulation treats the complete conservation equations of mass, momentum, energy, and species concentration for a multi-component chemically reacting system. For the numerical simulation of supersonic combustion, multi-species Navier-Stokes equations and detailed chemistry of H2-Air is considered. It also accommodates a finite-rate chemical kinetics mechanism of hydrogen-air combustion GRI-Mech. 2.11[1], which consists of nine species and twenty-five reaction steps. Turbulence closure is achieved by means of a k-two-equation model (2). The governing equations are spatially discretized using a finite-volume approach, and temporally integrated by means of a second-order accurate implicit scheme (3-5).The supersonic combustor consists of a flat channel of 10 cm height and a fuel-injection slit of 0.1 cm width located at 10 cm downstream of the inlet. A cavity of 5 cm height and 20 cm width is installed at 15 cm downstream of the injection slit. A total of 936160 grids are used for the main-combustor flow passage, and 159161 grids for the cavity. The grids are clustered in the flow direction near the fuel injector and cavity, as well as in the vertical direction near the bottom wall. The no-slip and adiabatic conditions are assumed throughout the entire wall boundary. As a specific example, the inflow Mach number is assumed to be 3, and the temperature and pressure are 600 K and 0.1 MPa, respectively. Gaseous hydrogen at a temperature of 151.5 K is injected normal to the wall from a choked injector.A series of calculations were carried out by varying the fuel injection pressure from 0.5 to 1.5MPa. This amounts to changing the fuel mass flow rate or the overall equivalence ratio for different operating regimes. Figure 1 shows the instantaneous temperature fields in the supersonic combustor at four different conditions. The dark blue region represents the hot burned gases. At the fuel injection pressure of 0.5 MPa, the flame is stably anchored, but the flow field exhibits a high-amplitude oscillation. At the fuel injection pressure of 1.0 MPa, the Mach reflection occurs ahead of the injector. The interaction between the incoming air and the injection flow becomes much more complex, and the fuel/air mixing is strongly enhanced. The Mach reflection oscillates and results in a strong fluctuation in the combustor wall pressure. At the fuel injection pressure of 1.5MPa, the flow inside the combustor becomes nearly choked and the Mach reflection is displaced forward. The leading shock wave moves slowly toward the inlet, and eventually causes the combustor-upstart due to the thermal choking. The cavity appears to play a secondary role in driving the flow unsteadiness, in spite of its influence on the fuel/air mixing and flame evolution. Further investigation is necessary on this issue. The present study features detailed resolution of the flow and flame dynamics in the combustor, which was not typically available in most of the previous works. In particular, the oscillatory flow characteristics are captured at a scale sufficient to identify the underlying physical mechanisms. Much of the flow unsteadiness is not related to the cavity, but rather to the intrinsic unsteadiness in the flowfield, as also shown experimentally by Ben-Yakar et al. [6], The interactions between the unsteady flow and flame evolution may cause a large excursion of flow oscillation. The work appears to be the first of its kind in the numerical study of combustion oscillations in a supersonic combustor, although a similar phenomenon was previously reported experimentally. A more comprehensive discussion will be given in the final paper presented at the colloquium.