ARTICLE IN PRESS JID: AMC [m3Gsc;August 4, 2017;21:44] Applied Mathematics and Computation 000 (2017) 1–14 Contents lists available at ScienceDirect Applied Mathematics and Computation journal homepage: www.elsevier.com/locate/amc Numerical simulation of flow through cascade in wind tunnel test section and stand-alone configurations J. Foˇ rt a,∗ , J. Fürst a , J. Halama a , V. Hric a , P. Louda a , M. Luxa b , D. Šimurda b a Faculty of Mechanical Engineering, Department of Technical Mathematics, Czech Technical University, Karlovo nam. 13, Praha 2 121 35, Czech Republic b Institute of Thermomechanics, v.v.i., AS ˇ CR, Dolejškova 5, Praha 8 182 00, Czech Republic a r t i c l e i n f o Article history: Available online xxx MSC: 65M08 76H05 Keywords: Numerical simulation Experimental investigation Transonic flow Turbine tip section blade cascades a b s t r a c t The paper deals with the numerical simulation of the flow field in a turbine cascade, which corresponds to the tip section of a last low-pressure steam turbine rotor. Considered cas- cade consists of very thin profiles with high stagger angle. The resulting flow field is com- plex with interactions of strong shock waves, shear layers and shock reflections. The paper proposes a proper numerical approximation of boundary conditions suitable for cases with supersonic inlet and outlet flow velocities and compares the flow field for two cascade configurations: the first one corresponding to real experiment (cascade with finite num- ber of blades located in the wind tunnel test section) and the second one corresponding to annular cascade. The experimental configuration includes the complicated geometry of wind tunnel. The annular configuration leads to blade to blade periodicity, which is not guaranteed for the experimental configuration. Numerical simulations are based on the Favre-averaged Navier–Stokes equations with SST k–ω turbulence model and the in-house implicit finite volume solver with AUSM-type discretization. This method considers struc- tured multi-block grid. Results are compared with experimental data. © 2017 Elsevier Inc. All rights reserved. 1. Introduction The overall demand for large output and high efficiency of steam turbines leads to design with enlarged turbine out- let area and consequently with very long last rotor blades. The most attention is currently aimed at the flow field around tip sections of these blades. The tip section profiles are very thin with large stagger angle and opposite bending of cen- tral line. The flow regimes are characterized by supersonic or high subsonic inlet flow and supersonic outlet flow with M out is ≈ 1.7–2.2. Therefore shock waves travel not only through outlet boundary, but they can cross also the inlet boundary. Moreover, the flow field is very sensitive on small variations of inlet flow angle. These issues together with a lack of exper- imental and simulation experiences make experimental as well as numerical investigations challenging, see e.g. [11,12] or [10]. Supersonic flow field in turbine cascades is nowadays in interest also for more compact turbines, see e.g. [13]. Presented paper is focused on implementation of outlet and inlet boundary conditions for numerical simulation, which allow shock waves traveling through outlet and inlet boundaries without generating spurious oscillations of solution. Nu- merous papers present these so called non-reflecting boundary conditions, see e.g. [1,14,16] or [15], which are based on ∗ Corresponding author. E-mail addresses: jaroslav.fort@fs.cvut.cz (J. Foˇ rt), jiri.furst@fs.cvut.cz (J. Fürst), jan.halama@fs.cvut.cz (J. Halama), vladimir.hric@fs.cvut.cz (V. Hric), petr.louda@fs.cvut.cz (P. Louda), luxa@it.cas.cz (M. Luxa), simurda@it.cas.cz (D. Šimurda). http://dx.doi.org/10.1016/j.amc.2017.07.040 0096-3003/© 2017 Elsevier Inc. All rights reserved. Please cite this article as: J. Foˇ rt et al., Numerical simulation of flow through cascade in wind tunnel test section and stand-alone configurations, Applied Mathematics and Computation (2017), http://dx.doi.org/10.1016/j.amc.2017.07.040