Heat Transfer Deterioration in Supercritical Water

For analytical studies assuming single-phase fluid dynamics, mixing length models are employed for turbulence. Since this type of model requires the distribution of turbulent viscosity in advance, a special assumption is used to incorporate effects of excessive change of thermophysical properties. In this case, validity of the special assumption is somewhat contentious even if the calculation results agree with the experimental values. In addition, change of density is not considered in the continuity and momentum equations, which implies that buoyancy force and fluid expansion are not incorporated. Therefore, these studies are applicable only to limited flow conditions. 

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. 

To obtain the deteriorated heat flux, calculations have been carried out with various combinations of flow rate G and heat flux q . Deterioration is assessed where the bulk temperature reaches the pseudocriticai temperature. The deterioration ratio a/ao is defined where ao is the ideal heat transfer coefficient. Some calculation results are shown in Fig. 2.5. The heat transfer coefficient monotonically decreases when the flow rate is large. On the other hand, it abraptly drops at a certain heat flux and maintains a constant value or increases with larger heat fluxes when the flow rate is small. The boundary is around 200 kg m s under the analyzed flow 

A map of deterioration is presented in Fig. 2.6. Occurrence of deterioration is judged when the deterioration ratio is smaller than 0.3 in the present analysis. A line obtained with the correlation of Yamagata et al. [8] is also provided in Fig. 2.6. This correlation was obtained when the heat transfer coefficient was deteriorated to about 1/3 to 1/2 of normal heat transfer predicted by their own correlation. The present calculation results agree with the correlation results by Yamagata et al. 

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