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between the inlet and outlet, and the mass flow is considered to be converged when the differ- ence is stabilised. In addition, the L2 norms of density, momentum in all three directions, and energy residuals are important convergence parameters. Loss evaluation methods The losses in CFD simulations are divided into primary and secondary losses where the total mixed out losses are defined as the sum of primary and secondary losses Ytotal = Yprim + Ysec, (1) where the total mixed out losses are defined as Ytotal = pt1 − pt2 . (2) pt2 − p2 In Equation 1, the primary losses are calculated with the penetration depth correlation of Benner et al. (2006a) to include the effect of passage vortex separation lines on the primary loss as follows: Yprim = Ymid(1 − Zte ). (3) h Where Zte is the separation line height and is defined as the height of the secondary region at the blade trailing edge and Ymid is the total mixed out loss from two dimensional CFD. Benner et al. (2006a) states that the maximum realizable value of Zte/h=0.5 occurs when the passage vortex separation lines from each end-wall meet at midspan. As is later shown in Fig. 3 (b) the maximum realizable value is reached at the lowest aspect ratio or even earlier as predicted by CFD. To keep the cases in Fig. 3 (a) comparable to each other the penetration depth correlation is applied even if the maximum value is exceeded. However, at the off-design incidence it is assumed that the maximum realizable value has been exceeded and Yprim = Ymid. The penetration depth Zte/h is defined as Z 0.1F0.79 t δ∗ +32.70( )2. (4) te=√ h h Where the tangential loading parameter Ft is defined as C R(h/C )0.55 Ft = 2Cs cos2αm(tanα1 − tanα2), (5) x and the mean mean vector angle αm may be solved from tanαm = 21(tanα1 + tanα2). (6) In the one-dimensional loss calculations, the Ymid is evaluated based on the prediction method by Kacker and Okapuu (1981), and the secondary loss correlation of Benner et al. (2006b) is used to predict the secondary losses in blade cascade as follows 4PDF Image | LOSS GENERATION IN RADIAL OUTFLOW STEAM TURBINE CASCADES
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