Abstract
PurposeTo assess how effectively two‐layer and low‐Reynolds‐number models of turbulence, at effective viscosity and second‐moment closure level, can predict the flow and thermal development through orthogonally rotating U‐bends.Design/methodology/approachHeat and fluid flow computations through a square‐ended U‐bend that rotates about an axis normal to both the main flow direction and also the axis of curvature have been carried out. Two‐layer and low‐Reynolds‐number mathematical models of turbulence are used at effective viscosity (EVM) level and also at second‐moment‐closure (DSM) level. In the two‐layer models the dissipation rate of turbulence in the new‐wall regions is obtained from the wall distance, while in the low‐Re models the transport equation for the dissipation rate is extended right up to the walls. Moreover, two length‐scale correction terms to the dissipation rate of turbulence are used with the low‐Re models, and original Yap term and a differential form that does not require the wall distance (NYap). The resulting predictions are compared with available flow measurements at a Reynolds number of 100,000 and a rotation number (ΩD/Ubl) of 0.2 and also with heat transfer measurements at a Reynolds number of 36,000, rotation number of 0.2 and Prandtl number of 5.9 (water).FindingsWhile the main flow features are well reproduced by all models, the development of the mean flow within the just after the bend in better reproduced by the low‐Re models. Turbulence levels within the rotation U‐bend are under‐predicted, but DSM models produce a more realistic distribution. Along the leading side all models over‐predict heat transfer levels just after the bend. Along the trailing side, the heat transfer predictions of the fully low‐Re DSM with the differential length‐scale correction term NYap are close to the measurements, with an average error of around 10 per cent, though at the bend exit it rises to 25 per cent. The introduction of a differential form of the length‐scale correction term to improve the heat transfer predictions of both low‐Re models.Research/limitations/implicationsThe numerical models assumed that the flow remains steady and is not affected by large‐scale, low frequency fluctuations. Unsteady RANS computations or LES must also be tested in the future.Originality/valueThis work has expanded the range of complex turbulent flow over which the effectiveness of RANS models has been tested, to internal cooling flows simultaneously affected by orthogonal rotation and strong curvature.
Highlights
Tight square-ended U-bends, shown in Figure 1, can be consideredas an idealised representation of the tight turns present in internal cooling passages of gas-turbine blades
The axis of rotation is normal to the main flow direction, known as orthogonal rotation, and in relation to the U-bend, its orientation tends to be closer to that shown in Figure 1a where it is normal to the axis of curvature
As the main flow direction becomes parallel to the axis of rotation, the Coriolis force disappears, which removes the difference in pressure between the leading and trailing sides
Summary
Tight square-ended U-bends, shown in Figure 1, can be consideredas an idealised representation of the tight turns present in internal cooling passages of gas-turbine blades. In the authors’ group, previous numerical investigations and most earlier experimental studies focused on round-ended U-bends, shown, see Bo et al [3] and Iacovides et al [4] These studies employed low-Reynolds-number models at both effective-viscosity and second-moment closure levels. The objective is to use the same models of turbulence employed in our earlier studies of flows through round- and square-ended U-bends and through ribbed passages, see Iacovides and Raisee [7], in order to assess their effectiveness in predicting the flow and thermal development in rotating square-ended U-bends These models include two-layer and low-Re models at both effective-viscosity and secondmoment closure level
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