Simulation of a 3D unsteady flow in an axial turbine stage

Abstract

The contribution deals with a numerical simulation of an unsteady flow in an axial turbine stage. The solution is performed using an in-house numerical code developed in the Aeronautical and Test Institute, Plc. in Prague. The numerical code is based on a finite volume discretization of governing equations (Favre aver- aged Navier-Stokes equations) and a two-equations turbulence model. The temporal integration is based on the implicit second-order backward Euler formula, which is realized through the iteration process in dual time. The proposed numerical method is used for solution of the 3D, unsteady, viscous turbulent flow of a perfect gas in the axial turbine stage. The flow path consists of an input nozzle, stator blade-wheel, blade-wheel, a shroud-seal gap and a diffuser. Attention is paid to the influence of a secondary flow structures, such as generated vortices and flow in shroud-seal gap. 1I NTRODUCTION The aim of this study is to investigate some properties of flow field in the axial turbine stage. At first the flow in the turbine stage was modeled in the middle section of the turbine stage as the two-dimensional turbulent unsteady flow. Furthermore, a calculation of the three-dimensional unsteady inviscid flow was performed. Boundary phenomena - secondary flow - have been studied using model of the three- dimensional steady turbulent flow, using the frozen rotor technique. Effect of the secondary flow through the seal of the was studied in a simplified model of a prismatic blade cascade using model of the three-dimensional steady turbulent flow. The turbine stage consists of the stator and wheels. The stator wheel contains 70 and the wheel 90 blades. Therefor it was possible consider only periodic field of seven stator and nine blades for the calculation. The hub diameter of the stage is 0.506 m, the tip diameter is 0.597 m (blades span is 0.0455 m), the axial chord of the stator is 0.01955 m, the axial chord of the is 0.025 m (both at the hub), the gap between stator and is 0.005 m. The shape of the blades is shown in Figure 1. The angular speed of the is 455.11 rad s −1 . The inlet total pressure is 1.311 · 10 5 Pa, the inlet total temperature is 55.81 ◦ C, the angle of attac is 0 ◦ and the outlet static pressure is 0.9538 · 10 5 Pa. The in-house URANS numerical code was developed for calculation of flow in the turbine stage.