Jones Launder

As mentioned above, numerical computations were carried out [5, 6] based on a k-e model by Jones-Launder. This model has a more general description for turbulence than the mixing length models. Effects of buoyancy force and fluid expansion on the heat transfer to normal fluids are successfully analyzed by the k-e model. Thermophysical properties are treated as variables in the governing equations and evaluated from a steam table library. Thus, extremely nonlinear thermophysical properties of supercritical water are evaluated directly and correctly. This approach is applicable to a wide range of flow conditions of supercritical water. Many cases of different inlet temperatures can be calculated and the relation between the heat transfer coefficient and the bulk enthalpy can be obtained in a wide range. 

Prandtl numbers. Thus, the coefficient near the pseudocriticai temperature, where the Prandtl number becomes large, may be smaller. The ideal coefficient calculated by the Jones-Launder k-e model at the pseudocriticai temperature is plotted in Fig. 2.4. It is calculated by fixing the thermophysical properties at the pseudocriticai temperature. This value is higher than that shown by the curve of 2.33 x 10 W m . When the Jones-Launder k-e model is used, it is known that the wall shear stress is relatively large and the heat transfer coefficient is also large with a constant turbulent Prandtl number. As indicated by Jackson and Hall [4], the heat transfer coefficient is the maximum when the heat flux is zero and it monotonically decreases as the heat flux increases. The calculation supports their assertion. 

The axial distributions of the enthalpy, temperature, density, and velocity of the coolant and the moderator are determined for a given core power, feedwater temperature, feedwater flow rate, and the pressure. The calculation is carried out iteratively until the temperature distributions are convergent to steady-state values. The fuel and cladding temperatures are calculated for each axial mesh with onedimensional radial heat transfer equations using the coolant and moderator temperature distribution. Steady-state temperature distributions are assumed in the fuel pellet, fuel cladding, and the gap. The heat transfer between fuel pellet and the coolant, as well as the heat transfer between the fuel channel and the water rods is considered. The heat transfer coefficients are calculated by the Oka-Koshizuka correlation, which was developed by using the Jones-Launder k-e turbulence model. 

Although numerous turbulence models are reported in the literature,1113 by far the most popular is the two-equation k-e model, first proposed by Jones and Launder.14 In this model, the turbulent stresses are recast in a form similar to the molecular stress tensor with mean velocity gradients, an assumption generally known as the Boussinesq hypothesis ... 

Jones, W. P. and Launder, B. E., The prediction of laminarisation with a two-equation turbulence model, Int. J. Heat Mass Transfer, 15, 301, 1972. 

Examination of several two-equation models reveals that there is only very small differences between the various models of this t3q>e [106]. This may be expected since all proposals for formulating the 2nd equation are closely related, though they differ in the forms of diffusion and near wall terms employed [95]. However, as mentioned above, the k-e model of Jones and Launder [78] has been predominant in the literature, and this model also determine the basis for most multi-phase turbulence models adopted in the more fundamental (CFD) reactor modeling approaches. 

Jones WP, Launder BE (1972) The Prediction of Laminarization with a Two-Equation Model of Turbulence. Int J Heat Mass Transfer 15 301-314 Jones WP (1980) Models for Turbulent Plows with Variable Density and Combustion. In Kollman W (ed) Prediction Methods for Turbulent Plow, Hemisphere Publishing Company... 

Compared with (a) and (c) in Fig. 9, adding two low-speed zones in the front of the first baffle, which is called dead zone in engineering, dead zone isn t beneficial to separate gas and solid (Jones, W.P. Launder, B.C. 1972), can t use space of precipitator effectively, reduce the efficiency of collection. Compared with (b) and (d), dead zone affect the dust size of 30 pm little, dust was trapped fully after the third baffle, in general, part dust in model three move disorder, but dust in model one move regularly. 

Jones, W.P. Launder, B.C. 1972. The Prediction of lam-inarization with a two-equation model of turbulence. bit. J. Heat and mass transfer, (15) 301-314. 

The k—E model has been pioneered by various researchers including Harlow and Nakayama [21], Jones and Launder [26], Launder and Spalding [29, 31] and others. The standard form of the k—E two-equation model for an incompressible flow is given by (cf. Refs. [26, 30])... 

W. P. Jones and B. E. Launder. The prediction of laminarization with a two-equation model of turbulence. International Journal of Heat Mass Transfer, 15 301-314, 1972. 

Two additional transport equations, respectively for k and for , are then to be solved [Jones and Launder, 1972 Launder and Spalding, 1972 Launder and Sharma, 1974],... 

Transport equations for the turbulent kinetic energy, k, and its rate of dissipation, , are solved according to Jones and Launder [48]. The model constants of Launder and Sharma [49] are used to close the system. 

Jones WP, Launder BE (1970) The calculation of Low-Raynolds-number phenomena with a two-equation model of turbulence. Int J Heat Mass Transfer 16 1119-1130... 

The transport equations for the A — model proposed by Jones and Launder [59] for the turbulence kinetic energy and turbulence energy dissipation in transient form... 

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