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rotors that are more vibration resistant and better suited for the high blade loadings and simpler overall system architectures to name a few [13]. These small turbines and sCO2 loops when com- bined with thermal storage and small modular heliostat fields2 are an enabler for solar base-load energy systems in rural settings. The design of radial turbines operating with steam or air has been well studied and detailed design procedures are available in the literature [14–17]. However, this design knowledge generally focuses on machines for low-density fluids and much larger in diameter compared to what is required for operation with sCO2. As preliminary design can be up to 50% of the total engineering time during radial turbine design [18], there is a need for effective tools and enhanced design space understanding. The aim of this work is to present an enhanced mean-line design tool for small-scale radial inflow sCO2 turbines and to present relevant design data in the 100–200 kW range, which is expected to be the focus of pilot studies in the near future. This paper is structured as an overview of the mean-line method and enhanced postprocessing tool, a design comparison to highlight effects of scale and speed, and finally, a discussion to elucidate the key aspects of small radial sCO2 turbine design. 2 Methodology Mean-line analysis is a well-established method for turbine design. Section 2.1 describes the mean-line tools and Secs. 2.2 and 2.3 describe the selection of the design point for the 100 kW and 200 kW turbine designs that will be compared. 2.1 Introduction to TOPGEN. TOPGEN [13] is a University of Queensland in-house quasi-one-dimensional design code for radial inflow turbines developed by Queensland Geothermal Energy Centre of Excellence, Brisbane, Australia. It uses the methodology presented by Moustapha et al. [14] for the rotor blade design calculations and performs separate calculations to establish a suitable stator design. In addition, the inclusion of detailed geometry modules provides the necessary information to construct turbine stage profiles, which allows the estimation of losses (using well-established loss models [19]) and allows the geometry to be assessed in regards to manufacturing and design constraints. For real gas cases, TOPGEN is coupled to the REFPROP database by NIST [20]. For sCO2, this provides access to the Span and Wagner equations of state [21]. Contrary to other design tools, TOPGEN performs a full design space exploration over a state space defined by a range of flow coefficient, u, and a range of head coefficient, w u1⁄4Cm6 1⁄4Cm4 (1) U4 nU4 w1⁄4Dh0 1⁄4Ch4 r6t Ch6 (2) U42 U4 r4U4 For each combination of coefficients, TOPGEN calculates the stator and rotor geometry and velocity triangles with the methods pro- vided by Moustapha et al. [14]. This is an iterative process as illustrated in Fig. 1, which uses well-established loss models to reach a point where overall efficiency and losses generated by the geometry match. The output from TOPGEN is a chart of u versus w, showing all the designs. This chart can be interrogated with respect to performance, geometry, or other characteristics. Based on empirical evidence, for example, data by Moustapha et al. [14] suggest that the optimum region for radial turbine design yielding maximum efficiency (gts) is defined as u1⁄4 0:1 0:4 and at w 1⁄4 0.71.1. A further input variable for TOPGEN is rotor speed, which indirectly influenced both u and w (U4 1⁄4 xr). In the current case, rotor speed is predefined to fixed levels of interest. 2For details see the website for Vast Solar Pty Ltd., http://www.vastsolar.com 081008-2 / Vol.139,AUGUST2017 Fig. 1 An overview of TOPGEN calculation process [19] In addition to analyzing the rotor, TOPGEN also incorporates a stator model to calculate the geometry of the nozzle guide vanes. Currently, this model assumes loss-free stator operation. This is a plausible assumption for sCO2 turbines due to the fact that the typical design pressure ratio (approximately 2.2) is only margin- ally above the critical pressure ratio for carbon dioxide. Similarly, for small geometries with high exit flow velocities, effects such as deviation have been identified to be small [22]. Finally, in contrast to the original version of TOPGEN [13] and many alternative mean-line codes, the ability to model rotor blade thickness as part of the design process has been added. Particu- larly with small turbines, blockage due to blades can have a nota- ble effect on rotor inlet flow area (up to 10%). 2.2 Feasibility Check Criteria. Only a subset of the designs generated in the u and w state space are feasible. The designs are filtered by a feasibility check considering both manufacturing and structural constraints and guideline performance constraints. The TransactionsoftheASME Downloaded From: http://turbomachinery.asmedigitalcollection.asme.org/pdfaccess.ashx?url=/data/journals/jotuei/936123/ on 04/05/2017 Terms of Use: http://www.asme.org/a bPDF Image | S CO2 Radial Turbine Design as a Function of Turbine Size
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