Design Guidelines for Supersonic Vanes Operating with Non-ideal Compressible Flows

orc2019 Tracking Number 22

Supersonic stator vanes of high temperature mini-ORC machines operating at high-expansion ratios account for two-thirds of the total losses of the turbine. Reducing these losses can substantially improve the turbine fluid-dynamic performance and eventually the economic viability of the ORC system. Although these vanes have predominant impact on the overall turbine performance, there is no established procedure for their optimal design. The usual design methodology involves a choice of the conceptual design parameter (e.g. solidity, degree of divergence) based on existing, non-tailored, correlations and the use of method of characteristics and CFD-based analysis to obtain the detailed blade profile. Therefore, there is need of best practices that can enable the rapid design of efficient vanes all along the entire turbine design phase. To the authors’ knowledge, the only existing model that can be employed to define the degree of divergence, i.e. the ratio between the nozzle throat section and the nozzle outlet section, at preliminary design level is the one proposed in [1]. The model provides the optimum degree of nozzle divergence as function of the averaged downstream Mach number for best vane efficiency. The model was exclusively derived for supersonic axial cascades operating with perfect gases, therefore its application to the design of supersonic vanes operating with non-ideal compressible flows is debatable. This work stems from these considerations and is focused on investigating the accuracy of such model for complex-fluids. To achieve the above-mentioned objective, the vane geometry generation method documented in [2] is adapted for axial configuration. The design procedure requires the flow-angle, the degree of divergence and the pitch as input. The baseline geometry is obtained using the optimum degree of divergence given by the model in [1] and variants to the baseline blade shape are generated by changing the degree of divergence, in a pre-defined range. The fluid-dynamic performance of the different blades is calculated using the open-source RANS solver SU2. The flow equations are complemented by the one-equation Spalart-Allmaras turbulence model. The results of the work show that the empirical model [1] is not accurate for the design of vanes operating with complex-fluids and thus highlight the need of a new unified design guideline for this type of vanes. [1] M. Y. Deych and M. Troyanovskiy, “Investigation and calculation of Axial-turbine stages”, Foreign Technology Division, Report No.: FTD-MT-65-409. [2] Anand N, Vitale S, Pini M, Otero GJ, Pecnik R. “Design Methodology for Supersonic Radial Vanes Operating in Non-ideal Flow Conditions.” ASME. J. Eng. Gas Turbines Power. 2018;141(2):022601-022601-9. doi:10.1115/1.4040182.