• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.5
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• pp.1203-1217
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• 1994

In the present study, in order to analyze a turbulent flow in a square sectiond 180.deg. bend, Kim's low Reynolds number second moment turbulence closure is adopted. In this model, turbulence model constants in the wall region are modified as functions of turbulent Reynolds number by use of near wall turbulent universal properties based on Laufer's experimental results of Reynolds stress distriburions. Algebraic stress model and Reynolds stress equation model are used to verify the low Reynolds number second moment closure. The application of the present low Reynolds number algebraic stress model to the prediction of a square sectioned 180.deg. bend flow gives improved velocities and Reynolds stresses profiles compared with those obtained by using the van Driest mixing length model and present low Reynolds number Reynolds stress equation model.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.24 no.4
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• pp.578-588
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• 2000

A low-Reynolds-number second moment turbulence closure is improved with the aid of DNS data. For the model coefficients of pressure-strain terms, we adopted Shima's model with some modification. Shin and Choi's new dissipation-rate equation is employed to simulate accurately the turbulence energy dissipation rate distribution in the near wall sublayer. The results of computations are compared with DNS, LES data and experimental data for turbulent plane channel flow with rotation about spanwise axis. The present second moment closure achieves a level of agreement similar to that for the non-rotating. In particular, it accurately captures the distribution of turbulence energy dissipation rate in the near wall region.

• 한국전산유체공학회:학술대회논문집
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• 2008.03a
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• pp.111-117
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• 2008

This paper reports briefly on the computational results of a turbulent Rayleigh-Benard convection with the elliptic-blending second-moment closure (EBM). The primary emphasis of the study is placed on an investigation of accuracy and numerical stability of the elliptic-blending second-moment closure for the turbulent Rayleigh-Benard convection. The turbulent heat fluxes in this study are treated by the algebraic flux model with the temperature variance and molecular dissipation rate of turbulent heat flux. The model is applied to the prediction of the turbulent Rayleigh-Benard convection for Rayleigh numbers ranging from $Ra=2{\times}10^6$ to $Ra=10^9$, and the computed results are compared with the previous experimental correlations, T-RANS and LES results. The predicted cell-averaged Nusselt number follows the correlation by Peng et al.(2006) ($Nu=0.162Ra^{0.286}$) in the 'soft' convective turbulence region ($2{\times}10^6{\leq}Ra{\leq}4{\times}10^7$) and it follows the experimental correlation by Niemela et al. (2000) ($Nu=0.124Ra^{0.309}$) in the 'hard' convective tubulence region ($10^8{\leq}Ra{\leq}10^9$) within 5% accuracy. This results show that the elliptic-blending second-moment closure with an algebraic flux model predicts very accurately the Rayleigh Benard convection.

• Journal of computational fluids engineering
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• v.13 no.3
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• pp.62-68
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• 2008

This paper reports briefly on the computational results of a turbulent Rayleigh-Benard convection with the elliptic-blending second-moment closure (EBM). The primary emphasis of the study is placed on an investigation of accuracy and numerical stability of the elliptic-blending second-moment closure for the turbulent Rayleigh-Benard convection. The turbulent heat fluxes in this study are treated by the algebraic flux model with the temperature variance and molecular dissipation rate of turbulent heat flux. The model is applied to the prediction of the turbulent Rayleigh-Benard convection for Rayleigh numbers ranging from Ra=$2{\times}10^6$ to Ra=$10^9$ and the computed results are compared with the previous experimental correlations, T-RANS and LES results. The predicted cell-averaged Nusselt number follows the correlation by Peng et al.(2006) (Nu=$0.162Ra^{0.286}$) in the 'soft' convective turbulence region ($2{\times}10^6{\leq}Ra{\leq}4{\times}10^7$) and it follows the experimental correlation by Niemela et al. (2000) (N=$0.124Ra^{0.309}$) in the 'hard' convective turbulence region ($10^8{\leq}Ra{\leq}10^9$) within 5% accuracy. This results show that the elliptic-blending second-moment closure with an algebraic flux model predicts very accurately the Rayleigh-Benard convection.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.6
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• pp.1596-1608
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• 1993

Low Reynolds number second moment turbulence model which be applicable to the fine gird near the wall region was developed. In this model, turbulence model coefficients in the pressure strain model of the Reynolds stress equation was expressed as functions of turbulence Reynolds number $R_{t}\equivk^{2}/(\nu\varepsilon)).$ In the derivation procedure of the present low Reynolds number algebraic stress model, Laufer's near wall experimental data on Reynolds stresses were curve fitted as functions of R$_{t}$ and the resulting simultaneous equations of the model coefficients were solved by using the boundary conditions at wall and high Reynolds number limiting conditions. Predicted Reynolds stresses and dissipation rate of turbulent kinetic energy etc. in the 2 dimensional parallel, plane channel flow and pipe flow were compared with the preditions obtained by employing the Launder-Shima model, standard algebraic stress model and several experimental data. Results show that all the Reynolds stresses and dissipation rate of turbulent kinetic energy predicted by the present low Reynolds number algebraic stress model agree better with the experimental data than those predicted by other algebraic stress models.

• 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.20 no.8
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• pp.2650-2669
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• 1996

A new low Reynolds number nonlinear second moment turbulence closure was introduced to analyze a square sectioned 180.deg. bend flow. Inclusion of nonlinear return to isotropy term and cubic mean pressure strain term has brought out a marked improvement in the level of agreement with measured velocity profiles. Optimization of present closure was performed by comparison of computed velocity profiles with the experimental ones with variation of nonlinear return to isotropy term and quadratic and cubic pressure-strain model. Progressive vortex breakdown due to the interaction of primary and secondary flows was well captured by using the optimized second moment turbulence closure.

• 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.

• Journal of computational fluids engineering
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• v.12 no.3
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• pp.55-61
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• 2007

A computational study on a strongly stratified natural convection is performed with the elliptic blending second-moment closure. The turbulent heat flux is treated by both the algebraic flux model (AFM) and the differential flux model (DFM). Calculations are performed for a turbulent natural convection in a square cavity with conducting top and bottom walls and the calculated results are compared with the available experimental data. The results show that both the AFM and DFM models produce very accurate solutions with the elliptic-blending second-moment closure without invoking any numerical stability problems. These results show that the AFM and DFM models for treating the turbulent heat flux are sufficient for this strongly stratified flow. However, a slight difference between two models is observed for some variables.

• 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.