Numerical Simulation of the Flow in the Row Labyrinth Seal of an Axial Turbine Using a Low-Mach Preconditioning Technique

Kurzfassung

Labyrinth seals on shrouded blades are an effective way for reducing efficiency penalties, as compared to free ended blades. Due to the difficulties of gaining optical access to cavity regions, mostly pressure measurements are available in the literature, from which the details of the flow must be inferred. The use of numerical tools can provide insight in the flow topology and therefore help obtaining a better understanding of the factors (geometric, thermodynamic and aerodynamic) which can affect the performance of the machine. Whilst in the main passage relatively high Mach numbers are to be found (0.3–1.3), the flow field in the cavities is dominated by extremely low flow speeds with strong recirculation patterns. The treatments of such flows, where large disparities between the acoustic and convective speed exist, are known to be highly problematic if density-based solution methods are employed. As the flow conditions approach the incompressibility limit a degradation of the convergence behaviour can be observed, leading, potentially to incorrect solutions. In order to overcome these problems preconditioning methods can be conveniently applied to the Navier-Stokes equations. In the current work the formulation of a fully implicit local preconditioning method with domain control of the Mach number dependency is presented. Numerical simulations of turbomachine components are generally performed on truncated domains. In order to prevent unphysical reflections at open boundaries and interfaces non-reflecting boundary conditions have been developed, e.g. [6, 8]. As reported in the available literature, low Mach preconditioning can cause stability problems and strongly impair the quality of the results especially in proximity of the domain’s boundaries. As shown in [14, 21] an appropriate scaling treatment of the boundary conditions is also required to alleviate such issues. In the current work non-reflecting boundary conditions, based on the formulation of Giles [6, 8], have been suitably modified to work reliably also in the limit of incompressible flows. To prove the robustness and accuracy of the algorithm implemented in the DLR’s CFD code TRACE, a canonical testcase representing an abstraction of the flow topology found in a labyrinth seal, such as a lid-driven cavity, is shown. Finally, the simulation of the steady flow in a multistage, shrouded low-pressure turbine is presented. For this, a classic RANS approach has been adopted using the k-ω model to illustrate the effectiveness of the developed method in a typical industrial application. Of particular significance and interest is the analysis of the mass conservation properties of the numerical scheme attained at mixing planes between rotor and stator and at non-matching grid interfaces, denoted as “zonal” and “zonal-mixed” interfaces.