Computational fluid dynamics (CFD) is nowadays central to modern industrial design and optimization of turbomachinery components. In the context of low-pressure steam turbines, real gas flow and non-equilibrium condensation, with the resulting presence of a second phase, pose particular challenges. The inherent unsteady nature of the condensation process and its interaction with other unsteady flow phenomena is not yet fully understood and simple steady state computations cannot adequately address this issue. However, at the relatively moderate Reynolds numbers in the low-pressure turbine and in the light of the continuously increasing computational power, high-fidelity, unsteady, scale-resolving simulation techniques such as Large Eddy Simulations (LES) hold the potential to address this research need and to improve future designs.  
With this goal, we have devised a turbomachinery-optimized, density-based CFD solver, which accounts for complex thermodynamics, including non-equilibrium condensation and two-phase flow based on tabulation techniques. The two-phase flow is treated for now by means of the mono-dispersed Source-Term Euler-Euler model and the non-equilibrium condensation effects are modeled based on the classical theory of droplet nucleation and droplet growth. To improve computational efficiency, the thermodynamic properties of steam and water are computed using the Spline Based Table Lookup method \[1\]. The solver has been validated in different, well-documented flow configurations, including decaying homogeneous isotropic turbulence, nozzle configurations and a low-pressure turbine cascade \[2\].  
The energy transfer process in LES is strongly affected by dissipation properties of the numerical scheme. In presence of strong discontinuities caused by shock waves and spontaneous condensation, shock-capturing capabilities with minimal damping at the subgrid-scale level must be realized. This is achieved by a hybrid flux switching between a baseline non-dissipative central flux in energy consistent split form and a shock-capturing upwind flux in shocked regions based on a shock sensor. The temporal integration is 4th-order accurate. This numerical scheme for Large Eddy Simulations of shocked flows is validated showing results of compressible homogeneous isotropic turbulence containing eddy shocklets.  
On this basis, a Large Eddy Simulation of the well-known White Cascade \[3\] test case is presented. The original blade profile including a blunt trailing edge is considered. The parameters of the non-equilibrium condensation model are optimized by means of preliminary RANS computations based on the measured blade pressure distribution. The RANS results are also used to construct an adequately refined mesh for the wall-resolving LES, in terms of boundary layer resolution and the position of sensitive features such as the wake, the trailing edge shock wave system and the condensation zone. As no information about the inlet turbulence is known \[3\], a laminar inflow is assumed. Within the condensing wet steam cascade, transition and strong unsteady effects are observed in the LES results which are not detectable with RANS. As the porous tailboards adopted in the experimental setup prevent interactions with the adjacent blades’ wakes, a direct quantitative comparison between numerical results and measurement is not possible. However, it is show that these are very well captured by the low dissipation scale resolving unsteady LES in contrast to the conventional RANS approach.

 

\[1\]    M. Kunick, H.-J. Kretzschmar, F. di Mare and U. Gampe ”CFD Analysis of steam turbines with the IAPWS standard on the spline-based table look-up method (SBTL) for the fast calculation of real fluid properties,” ASME Paper GT2015-43984, Proceedings of ASME Turbo Expo 2015: Turbine Technical Conference and Exposition GT2015, June 15 – 19, 2015, Montreal, Canada  
\[2\]    P. Post, M. Sembritzky, F. di Mare “Towards scale resolving computations of condensing wet steam flows,” ASME Paper GT2019-91269, Proceedings of ASME Turbo Expo 2019: Turbine Technical Conference and Exposition GT2019, June 17 – 21, 2019, Phoenix, Arizona, USA  
\[3\]    A. J. White, J. B. Young, and P. T. Walters, “Experimental Validation of Condensing Flow Theory for a Stationary Cascade of Steam Turbine Blades,” Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, vol. 354, no. 1704, pp. 59–88, Jan. 1996


Large Eddy Simulation of a Condensing Wet Steam Turbine Cascade

Division / Sponsor:
International Gas Turbine Institute (IGTI)

Paper Proceedings: https://asmedigitalcollection.asme.org/GT/GT2020/volume/84058

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