Design Guidelines for Radial Supersonic Stators

Abstract

Increasing concerns about the effects of freeing large quantities of greenhouse gases into the atmosphere have sparked interest in organic Rankine cycle for renewable power systems. Single-stage radial inflow turbines appear as suitable expansion devices for this type of application. However, supersonic conditions can be reached in the stator of these devices, causing non-ideal fluid-dynamic behavior. This makes it necessary to explore unconventional architectures, for which only a limited number of design methods have been proposed.
In this context, the principal activity of this study was to formulate guidelines, and thereby reduce the preliminary design space, of supersonic radial stator vanes. This was done by first identifying the relevant loss mechanism and design parameters through an examination of the available literature. This led to the formulation of a research hypothesis, which was studied by means of two-dimensional, steady computational fluid dynamic simulations.
To this end, a parametric study was devised, in which any design parameter can be varied to study its effect on the blade performance. This is done analyzing the trends resulting from the post-processing of simulation generated data. The data production is based on a workflow consisting of finding a condition-specific convergent-divergent nozzle, which is used to build a mean-line radial vane, for which a mesh grid is generated and utilized by a previously validated numerical solver to perform the simulations. The complete process was overseen by a semi-automated design chain constructed to manage and execute the necessary steps.
It was assumed that profile losses would be the most influential loss characteristic, given that two-dimensional flow is predominant in mean-line geometries. According to the literature, both its major components, viscous dissipation and mixing losses should have an impact on the stator’s efficiency. Likewise, the degree of expansion along the embedded nozzle present between adjacent blades, was identified as the main design specifications to be analyzed. A trade-off between the contribution of the main loss mechanisms based on the variation of this parameter was predicted to exist.
Applying the generalized research method on a candidate test case resulted in the generation of data from almost 500 different simulations. This led to several findings, including that it is not possible to vary the nozzle design Mach number without causing simultaneous changes to other relevant geometrical features, such as the throat width. This rendered invalid some of the initial assumptions used to set up the experiments.
Similarly, this finding was expected to be the reason behind large differences between the calculated and imposed pressure ratio on the boundary conditions, as well as large variations in the mass flow of each set of blades. Additional simulations were required to analyze these deviations, based on varying other relevant parameters, including the imposed pressure ratio and outflow boundary location. The results seem to suggest that, due to the supersonic nature of the flow, an additional geometrical constraint influences the expansion process.
Performance analyzes were then possible by adapting the definition of valid designs to blade configurations matching or exceeding the imposed pressure ratio. Based on these results, the relevance of the post-expansion ratio (defined as the ratio between the pressure level at the nozzle exit and the stator outflow) became apparent. This was also the case when this ratio was manipulated by changing the imposed back pressure on the system. Moreover, when quantified with respect to this parameter, the flow deviation showed a linear behavior and the losses exhibited a plateau of higher performance.
Finally, this project provides a foundation for this line of research, both in a theoretical and practical sense. Future studies should focus on validating claims made regarding the supersonic expansion process and extending the data to determine the generality of the found performance trends. Only then will it be possible to conclusively establish the dependence between design parameters and performance for this unconventional type of blade.