• Transactions of the Korean Society of Mechanical Engineers
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• v.10 no.1
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• pp.70-77
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• 1986

Turbulent mixing field with recirculating flow which is formed by injecting gaseous fuel on the main air stream is solved numerically by a finite difference method. The turbulence model for obtaining transport properties was k-.epsilon. model, which was obtained from turbulent kinetic energy and its dissipation rate. Considering the effects of streamline curvature, modified k-.epsilon model was used. Generally, Modified k-.epsilon. model makes better predictions than standard model, and from this result, it is recognized that standard model has deficiency when applied to turbulent recirculating flows, and that modified k-.epsilon. model takes into account of streamline curvature effects properly. Meanwhile, A more study will be necessary to find the reason why large differences between predicted and experimental turbulent kinetic energy exist.

• Transactions of the Korean Society of Mechanical Engineers
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• v.16 no.10
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• pp.1940-1954
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• 1992

Fine grid computations were attempted to analyze the turbulent flows in the near wall low Reynolds number region and the numerical analyses were incorporated by a finite-volume discretization with full find grid system and low Reynolds number k-.epsilon. model was employed in this region. For the improvement of low Reynolds number k-.epsilon. model, modification coefficient of eddy viscosity $f_{\mu}$ was derived as a function of turbulent Reynolds number $R_{+}$ and nondimensional length $y^{+}$ from the concept of two length scales of dissipation rate of turbulent kinetic energy. The modification coefficient $f_{\epsilon}$ in .epsilon. transport equation was also derived theoretically. In the turbulent kinetic energy equation, pressure diffusion term was added in order to consider low Reynolds number region effect. The main characteristics of this low Reynolds number k-.epsilon. model were founded as : (1) In high Reynolds number region, the present model has limiting behavior which approaches to the high Reynolds number model. (2) Present low Reynolds number k-.epsilon. model dose not need additional empirical constants for the transport equations of turbulent kinetic energy and dissipation of turbulent kinetic energy in order to consider wall effect. Present low Reynolds number turbulence model was tested in the pipe flow and obtained improved results in velocity profiles and Reynolds stress distributions compared with those from other k-.epsilon. models.s.s.

• Journal of Advanced Marine Engineering and Technology
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• v.20 no.5
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• pp.39-44
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• 1996

To overcome weak poinks of the standard k-${\varepsilon}$ turbulence model when applied to complex turbulent flows, various modified models were proposed. But their effects are confined to special flow fields. They have still some problems. Recently, an anisotropic k-${\varepsilon}$ turbulence model was also proposed to solve the drawback of the standard k-${\varepsilon}$ turbulence model. This study is concentrated on the evaluation of the anisotropic k-${\varepsilon}$ turbulence model by the analysis of axisymmetric swirling turbulent flow. Results show that the anisotropic k-${\varepsilon}$ turbulence model has scarecely the fundamentally physical mechanism of predicting the swirling structure of flow.

• Transactions of the Korean Society of Mechanical Engineers
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• v.9 no.1
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• pp.91-108
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• 1985

Turbulent flow and heat transfer in the 180.deg. bend with square cross section were analizied numerically by using k-.epsilon. 2 eqatiuon model with applications of QUICK scheme and PSL method. Results with PSL method show the more agreements with experimental data than those with wall function. However these results also show that it is very difficult to predict the 3-dimensional turbulent flow with strong secondary flow accuratly by standard k-.epsilon. equation model, and therefore it is necessary to introduce the higher order turbulent model or to correct the standard k-.epsilon. model for the more accurate predictions of these types of flow.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.23 no.5
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• pp.610-620
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• 1999

Recently, numerous modifications of low Reynolds number $k-{\epsilon}$ model have boon carried out with the aid of DNS data. However, the previous models made in this way are too intricate to be used practically. To overcome this shortcoming, a new low Reynolds number $k-{\epsilon}$ model has boon developed by considering the distribution of turbulent properties near the wall. This study proposes the revised a turbulence model for prediction of turbulent flow with adverse pressure gradient and separation. Nondimensional distance $y^+$ in damping functions is changed to $y^*$ and some terms modeled for one dimensional flow in $\epsilon$ equations are expanded into two or three dimensional form. Predicted results by the revised model show an acceptable agreement with DNS data and experimental results. However, for a turbulent flow with severe adverse pressure gradient, an additive term reflecting an adverse pressure gradient effect will have to be considered.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.22 no.5
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• pp.685-697
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• 1998

Series of recent k-.epsilon. model modification have been carried out with the aid of DNS data to include the effect of near wall. Though these methods opened new way of turbulence modelings, newly developed turbulence models of its kind had yet shortcomings in prediction for the turbulent flows with various Reynolds numbers and various geometric conditions. As a remedy for these shortcomings, a new k-.epsilon. model proposed here by improving the dissipation rate equation and the damping function for eddy viscosity model. The new dissipation rate equation was modeled based on the energy spectrum and magnitude analysis. The damping function for eddy viscosity was also formulated on the ground of distribution of dissipation rate length scales near a wall and the DNS data. The new k-.epsilon. model was applied to the fully developed turbulent flows in a channel and a pipe with a wide range of Reynolds numbers. Prediction results showed that the present model represents properly the turbulence properties in all turbulent regions over a wide range of Reynolds numbers.

• Transactions of the Korean Society of Mechanical Engineers
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• v.19 no.8
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• pp.2039-2050
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• 1995

The nonlinear low-Reynolds-number k..epsilon. model of park and Sung is extended to predict the turbulent heat transports in separated and reattaching flows. The equations of the temperature variance( $k_{\theta}$ and its dissipation rate(.epsilon.$_{\theta}$ are solved, in concert with the equations of the turbulent kinetic energy(k) and its dissiation rate(.epsilon). In the present model, the near-wall effect and the non-equilibrium effect are fully taken into consideration. The validation of the model is then applied to the turbulent flow behind a backward-facing step and the flow over a blunt body. The predicted results of the present model are compared and evaluated with the relevant experiments.

• Proceedings of the KSME Conference
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• 2001.06e
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• pp.783-788
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• 2001

Choosing the most suitable mathematical model and relating this to turbulent tangential tensions model are very important in the investigations of turbulent two-phase flow. This paper considers two-fluid scheme. According to it, two phases have their own densities, velocities, and temperatures at any spatial point and at any moment. The equations of motion and heat transfer for each phase are linked with the forces of interaction between two phases. These forces are considered as predominant for the flow. As a closure in the system of motion equations, one modification of $K - {\epsilon}$ turbulent model is worked out. The modification uses two equations for turbulent kinetic energy of the phases and one - for the turbulent energy loss of main phase. This model can be set as a $K_g - K_p -{\epsilon}$ model. The modified model has been tested for both a two-phase non-isothermal flat jet and axially symmetrical jet. The numerical results are compared with the reference data revealing a good agreement between them.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.21 no.9
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• pp.1149-1164
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• 1997

In this study, the applicability of the RNG k-.epsilon. model to the analysis of the complex flows is studied. The governing equations based on a non-orthogonal coordinate formulation with Cartesian velocity components are used and discretized by the finite volume method with non-staggered variable arrangements. The predicted results using the RNG k-.epsilon. model of three complex flows, i.e., the flow over a backward-facing step and a blunt flat plate, the flow around a 2D model car are compared to these from the standard k-.epsilon. model and experimental data. That of the unsteady axisymmetric turbulent flow within a cylinder of reciprocating model engine including port/valve assembly and the spray characteristics within a chamber of direct injection model engine are compared to these from the standard k-.epsilon. model and experimental data. The results of reattachment length, separated eddy size, average surface pressure distribution using the RNG k-.epsilon. model show more reasonable trends comparing with the experimental data than those using the modified k-.epsilon. model. Although the predicted rms velocity using the modified k-.epsilon. model is lower considerably than the experimental data in incylinder flow with poppet valve, predicted axial and radial velocity distributions at the valve exit and in-cylinder region show good agreements with the experimental data. The spray tip penetration predicted using the RNG k-.epsilon. model is more close to the experimental data than that using the modified k-.epsilon. model. The application of the RNG k-.epsilon. model seems to have some potential for the simulations of the unsteady turbulent flow within a port/valve-cylinder assembly and the spray characteristics over the modified k-.epsilon. model.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.2
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• pp.668-676
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• 1991

Turbulent flows around tube banks and in the diffuser were studied using a non-orthogonal boundary fitted coordinate system and the modified K-.epsilon. turbulence model. In these cases, many problems emerge which stem from the geometrical complexity of the flow domain and the physical complexity of turbulent flow itself. To treat the complex geometry, governing equations were reformulated in a non-orthogonal coordinate system with Cartesian velocity components and discretised by the finite volume method with a non-staggered variable arrangement. The modified K-.epsilon. model of Hanjalic and Launer was applied to solve above two cases under the condition of strong and mild pressure gradient. The results using the modified K-.epsilon. model results in both test cases.