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LOSS GENERATION IN RADIAL OUTFLOW STEAM TURBINE CASCADES

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LOSS GENERATION IN RADIAL OUTFLOW STEAM TURBINE CASCADES ( loss-generation-in-radial-outflow-steam-turbine-cascades )

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Ysec = √ 0.038 + 0.41tanh(1.20δ∗/h) . (7) cosΓ(CR)(h/C)0.55(Ccosα2 )0.55 Cx For the calculation of one-dimensional off-design primary losses, the correlation of Benner et al. (1997) is employed relative to the primary losses from CFD simulations at zero incidence. BLADE GEOMETRY AND STUDIED CASES The examined geometry is a non-scaled model of the first-stage rotor (Fig. 1 (b)) used in a four-stage turbine protype. Table 1 shows the main design parameters of the blade cascade. The basic design is characterised by an ultra-low aspect ratio and relatively low Mach number. Overall, five aspect ratios were studied, in the range 0.26 ≤ h/c ≤ 1.58. When the aspect ratio was varied, the number of spanwise cells was kept comparable between different cases. This means that e.g. when the aspect ratio and also the blade height was doubled the number of spanwise cells was doubled as well and the same node distribution function was used for both cases. The Reynolds number and Mach number were also kept constant between the modelled cases to keep the simulations comparable. Although it is known from the work of Persico et al. (2015) that the rotation of the rotor can greatly influence the flow in a ROT, this work is closely connected to stationary cascade experiments and the capability of axial turbine loss models to predict the performance in an early design phase, and the influence of rotation is therefore not included in this work. Table 1: Blade cascade design parameters. Aspect ratio [-] Pitch to chord ratio [-] Reynolds number [-] Total-to-static pressure ratio [-] GRID DEPENDENCY 0.26 Blade inlet Mach number [-] 0.23 0.71 Blade outlet Mach number [-] 0.40 575000 Blade inlet metal angle [◦] 47.5 1.15 Blade outlet flow angle [◦] -67.3 A total of six grids (three grids for both 2D and 3D) were built to examine how the grid affects the results. The case with the lowest aspect ratio h/c = 0.26 was used in the study. The grid convergence index method by Celik et al. (2008) was used to evaluate the discretisation error. As shown in Table 2, the average non-dimensional wall distance y+ was kept below unity at every 2D grid and slightly higher, but still acceptable, values are noticed when changing to 3D geometries. Since the height of the first cell is constant between all two and three dimensional cases, the slightly higher y+ values are due to three dimensional effects. The grid refinement factor r is suggested to be greater than 1.3 by Celik et al. (2008). All 2D grids satisfy this value, and the 3D grids are just below the limit. This is still acceptable, since the general idea was to first find a reasonably grid-independent 2D grid, which was then modified to 3D by only changing the number of spanwise cells by doubling the cell number. Figure 2 (a) shows the effect of the grid on the total mixed out loss coefficient in 2D. It is noticeable that by almost doubling the number of cells from the medium grid, the loss coeffi- cient does not change significantly. Also, the isentropic Mach number distribution in Fig. 2 (c) 5

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