• Transactions of the Korean Society of Mechanical Engineers B
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• v.31 no.1 s.256
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• pp.29-39
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• 2007

A second-moment closure is applied to the prediction of a homogeneous turbulent shear flow laden with mono-size particles. The closure is curried out based on a 'two-fluid' methodology in which both carrier and dispersed phases are considered in the Eulerian frame. To reduce the number of coupled differential equations to be solved, Reynolds stress transport equations and algebraic stress models are judiciously combined to obtain the Reynolds stress of carrier and dispersed phases in the mean momentum equation. That is, the Reynolds stress components for carrier and dispersed phases are solved by modelled transport equations, but the fluid-particle velocity covariance tensors are treated by the algebraic models. The present predictions for all the components of Reynolds stresses are compared to the DNS data. Reasonable agreements are observed in all the components, and the effects of the coupling of carrier and dispersed phases are properly captured in every aspects.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.20 no.8
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• pp.2572-2592
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• 1996

A low-Reynolds-number second moment turbulence closure was developed with the aid of DNS data. Model coefficients of nonlinear return to isotropy term were derived by use of Cayley-Hamilton theorem and two component turbulence limit condition as the functions of invariances of anisotropy and turbulent Reynolds number. Launder and Tselepidakis' cubic mean pressure strain model was modified to fit the predicted pressure-strain components to the DNS data. Two component turbulence limit condition was the precondition to be satisfied in developing the second moment turbulence closure for the realizable Reynolds stress prediction. But the satisfactions of Reynolds stress level and pressure-strain level of each component were compromised because the satisfaction of both levels was impossible.

• Korean Journal of Air-Conditioning and Refrigeration Engineering
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• v.19 no.12
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• pp.831-841
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• 2007

This work is to extend the elliptic operator, which has been already adopted in turbulent stress model, to fully developed turbulent buoyant channel flows with changing the orientation of the buoyancy vector to be perpendicular to the channel walls. The turbulent heat flux models based on the elliptic concept are employed and closely linked to the elliptic blending second moment closure which is used for the prediction of Reynolds stresses. In order to reflect the stable or unstable stratification conditions, the present model introduces the gradient Richardson number into the thermal to mechanical time scale ratio and model coefficients. The present model has been applied for the computation of stably and unstably stratified turbulent channel flows and the prediction results are directly compared to the DNS data.

• Journal of the Korean Society for Precision Engineering
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• v.12 no.4
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• pp.127-134
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• 1995

The dynamic characteristics of a system can be critically influenced by system uncertainty, so the dynamic system must be analyzed stochastically in consideration of system uncertainty. This study presents a generalized stochastic model of dynamic system subjected to bot external and parametric nonstationary stochastic input. And this stochastic system is analyzed by a new stochastic process closure method and moment equation method. The first moment equation is numerically evaluated by Runge-Kutta method. But the second moment equation is founded to constitute an infinite coupled set of differential equations, so this equations are numerically evaluated by cumulant neglect closure method and Runge-Kutta method. Finally the accuracy of the present method is verified by Monte Carlo simulation.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.23 no.8
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• pp.1063-1071
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• 1999

Fine grid calculations are reported for the developing turbulent flow in a curved duct of square cross-section with a radius of curvature to hydraulic diameter ratio ${\delta}=Rc/D_H=3.357 $ and a bend angle of 720 deg. A sequence of modeling refinements is introduced; the replacement of wall function by a fine mesh across the sublayer and a low Reynolds number algebraic second moment closure up to the near wall sublayer in which the non-linear return to isotropy model and the cubic-quasi-isotropy model for the pressure strain are adopted; and the introduction of a multiple source model for the exact dissipation rate equation. Each refinement is shown to lead to an appreciable improvement in the agreement between measurement and computation.

• 한국연소학회:학술대회논문집
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• 2002.11a
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• pp.11-17
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• 2002

The first-order conditional moment closure (CMC) model is applied to $CH_4$/Air turbulent jet diffusion flames(Sandia Flame D, E and F). The flow and mixing fields are calculated by fast chemistry assumption and a beta function pdf for mixture fraction. Reacting scalar fields are calculated by elliptic CMC formulation. The results for Flame D show reasonable agreement with the measured conditional mean temperature and mass fractions of major species, although with discrepancy on the fuel rich side. The discrepancy tends to increase as the level of local extinction increases. Second-order CMC may be needed for better prediction of these near-extinction flames.

• Journal of the Korean Society of Industry Convergence
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• v.3 no.1
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• pp.43-51
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• 2000

The response statistics of a hinged-clamped beam under broad-band random excitation is investigated. The random excitation is applied at the nodal point of the second mode. By using Galerkin's method the governing equation is reduced to a system of nonautonomous nonlinear ordinary differential equations. A method based upon the Markov vector approach is used to generate a general first-order differential equation in the dynamic moment of response coordinates. By means of the Gaussian and non-Gaussian closure methods the dynamic moment equations for the random responses of the system are reduced to a system of autonomous ordinary differential equations. The case of two mode interaction is considered in order to compare it with the case of three mode interaction. The analytical results for two and three mode interactions are also compared with results obtained by Monte Carlo simulation.

• 한국전산유체공학회:학술대회논문집
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• 2007.04a
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• pp.171-176
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• 2007

A comparative study on the treatment of the turbulent heat flux with the elliptic mlending second moment closure for a natural convection is performed. Four cases of different treating the turbulent heat flux are considered. Those are the generalized gradient diffusion hypothesis (GGDH) the algebraic flux model (AFM) and the differential heat flux model (DFM). These models are implemented in the computer code specially designed for evaluation of turbulent models. Calculations are performed for a turbulent natural convection in the 1:5 rectangular cavity and the calculated results are compared with the experimental data. The results show that three models produce nearly the same accuracy of solutions.

• Wind and Structures
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• v.4 no.6
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• pp.469-480
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• 2001

The Leipzig Wind Profile is generally known as a typical neutral planetary boundary layer flow. But it became clear from the present research that it was not completely neutral but weakly stable. We examined whether we could simulate the Leipzig Wind Profile by using a ($k-{\varepsilon}$) turbulence model including the equation of potential temperature. By solving analytically the Second Moment Closure Model under the assumption of local equilibrium and under the condition of a stratified flow, we expressed the turbulent diffusion coefficients (both momentum and thermal) as functions of flux Richardson number. Our ($k-{\varepsilon}$) turbulence model which included the equation of potential temperature and the turbulent diffusion coefficients varying with flux Richardson number reproduced the Leipzig Wind Profile.

• 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.