• 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.

• 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.

• 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.

• 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.

• 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.

• 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.

• 한국연소학회:학술대회논문집
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• 2007.05a
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• pp.118-125
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• 2007

The firtst-order conditional moment closure (CMC) model is applied to CH4/air swirl diffusion flame in a gas turbine model combustor. The flow and mixing fields are calculated by fast chemistry assumption with SLFM library and a beta function pdf for mixture fraction. RNG k-e model is used to consider the swirl flame in a confined wall. Reacting scalar fields are calculated by elliptic CMC formulation with chemical kinetic mechanism, GRI Mech 3.0. Validation is done against measurement data for mean flow and scalar fields in the model combustor [1]. Results show reasonable agreement with the mean mixture fraction and its variance, while temperature is overpredicted as the level of local extinction increases. The second-order CMC model is needed to consider local extinction with considerable conditional fluctuations near the nozzle.

• Journal of computational fluids engineering
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• v.12 no.2
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• pp.26-31
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• 2007

A comparative study on the treatment of the turbulent heat flux with the elliptic blending second-moment closure for a natural convection flow is performed. Three 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 flux model (DFM). The constants in the models are adjusted with a primary emphasis placed on the accuracy of predicting the local Nusselt number. These models are implemented in a 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 available experimental data. The results show that the three models produce nearly the same accuracy of solutions. These results show that the GGDH, AFM and DFM models for treating the turbulent heat flux are sufficient for this simple shear flow where the shear production is dominant. It is observed that, in the weakly stratified region at the center zone of the cavity, the vertical velocity fluctuation is nearly zero in the GGDH solutions, which shows that the GGDH model may not be suitable for the strongly stratified flow. Thus, further study on the strongly stratified flow should be followed.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.28 no.5
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• pp.526-534
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• 2004

A new second-moment closure model for turbulent heat fluxes is proposed on the basis of the elliptic equation. The new model satisfies the near-wall balance between viscous diffusion, viscous dissipation and temperature-pressure gradient correlation, and also has the characteristics of approaching its respective conventional high Reynolds number model far away from the wall. The predictions of turbulent heat transfer in a channel flow have been carried out with constant wall heat flux and constant wall temperature difference boundary conditions respectively. The velocity field variables are supplied from the DNS data and the differential equations only fur the mean temperature and the scalar flux are solved by the present calculations. The present model is tested by direct comparisons with the DNS to validate the performance of the model predictions. The prediction results show that the behavior of the turbulent heat fluxes in the whole region is well captured by the present model.