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A micro steam turbine with a tip diameter of 15 mm was designed and experimentally characterized. At the nominal mass flow rate and total-to-total pressure ratio of 2.3 kgh−1 and 2, respectively, the turbine yields a power of 34 W and a total-tostatic isentropic efficiency of 37 %. The steam turbine is conceived as a radial-inflow, low-reaction (15 %), and partial admission (21 %) machine. Since the steam mass flow rate is limited by the heat provided by the system (solid oxide fuel cell), a low-reaction and high-power-density design is preferred. The partial-admission design allows for reduced losses: The turbine rotor and stator blades are prismatic, have a radial chord length of 1 mm and a height of 0.59 mm. Since the relative rotor blade tip clearance (0.184) is high, the blade tip leakage losses are significant. Considering a fixed steam supply, this design allows to increase the blade height, and thus reducing the losses. The steam turbine drives a fan, which operates at low Mach numbers. The rotor is supported on dynamic steam-lubricated bearings; the nominal rotational speed is 175 krpm. A numerical simulation of the steam turbine is in good agreement with the experimental results. Furthermore, a novel test rig setup, featuring extremely-thin thermocouples ( 0.15 mm) is investigated for an operation with ambient and hot air at 220 ◦C. Conventional zero and one-dimensional pre-design models correlate well to the experimental results, despite the micro size of the turbine blades. NOMENCLATURE A Area in m2 b (Channel) width in m d,D Diameter in m ds Specific diameter h Specific enthalpy in Jkg−1 H Blade height in m g Gravitational acceleration in ms−2 l Length in m ṁ Mass flow rate in kgs−1 M Torque in Nm ns Specific speed p Pressure in Pa P Power in W r,R Radius in m s Specific entropy in Jkg−1 K−1 Re Reynolds number Rg Specific gas constant in Jkg−1 K−1 S Clearance in m t (Blade) thickness in m T Temperature in K V̇ Volume flow rate in m3 s−1 z Number of blades α Absolute blade angle based on the circumference in rad β Relative blade angle based on the circumference in rad 1 Copyright c © 2020 by ASME δ Degree of reaction ζ Loss coefficient η Efficiency κ heat capacity raio Π Pressure ratio ρ Density in kgm−3 φ Flow factor ψ Stage loading factor ω Angular speed in rads−1 Subscript 1 machine inlet / inlet side test section 2 inlet nozzle inlet 3 inlet nozzle outlet 3.1 volute inlet 4 volute outlet / inducer inlet 5 inducer outlet / turbine stator leading edge 6 turbine stator trailing edge 7 turbine rotor leading edge 8 turbine rotor trailing edge 9 exducer outlet 10 diffuser inlet 11 diffuser outlet 12 machine outlet / outlet side test section amb ambient h hub hyd hydraulic is isentropic m meridional mech mechanical s shroud st static t total turb turbine Abbreviation CFD computational fluid dynamics FTU fan-turbine unit LE leading edge TC thermocouple TE trailing edge SOFC solid oxide fuel cell INTRODUCTION Within the last two decades, several researchers demonstrated small-scale turbines, mainly for the application in air-to-electrical-power and micro gas turbine generator systems. Epstein [1] suggested a “shirtbutton-sized” gas turbine, featuring a 6 mm radial-inflow turbine with prismatic blades and rotating up to 1200 krpm. The disc-shaped rotor was supported by static and dynamic gas bearings. Kang et al. [2] investigated a “fist-sized” gas turbine with a 12 mm compressor and a back-to-back mounted turbine impeller. The radial-inflow turbine had three-dimensional blades made of silicon nitride and was supported on a shaft with ball bearings. In preliminary tests with ambient air, Kang et al. operated the unit up to 420 krpm, corresponding to 53 % of the nominal speed. Since the compressor performance was the focus of this paper, no experimental results for the turbine were reported. In 2007, Tanaka et al. [3] realized the “worlds-smallest gas turbine” engine with a 17.4 mm radial-inflow turbine. At a rotational speed of 360 krpm and a combustor temperature of 800 ◦C to 900 ◦C, a self-sustained Brayton cycle was demonstrated. However, externally pressurized gas film bearings were used; hence, the entire system was cannot be considered as fully-self-sustained. In 2012, the Japenese IHI cooperation [4] added dynamic gas film bearings to the unit and demonstrated a fully autonomous operation with an electrical power of 60 W at a rotational speed of 330 krpm. Several other small-scale turbine systems can be found in the literature, some of which are listed in Table 1. The tip diameters are typically around 10 mm and rotational speeds of up to 500 krpm were reported. The experimentally measured power levels and maximum efficiencies range from one Watt, up to several 100 Watts and from 8 % up to 58 %, respectively. Note, that the rotational speeds in Table 1, correspond to the listed power and efficiency measurements and not to the nominal speed, since it was not reached due to technical limitations or the highest efficiency was reached at lower rotor speeds. The authors of this paper calculated and estimated several values with the data in the corresponding references (bold and underlined information, respectively). In 2003, Peirs et al. [5] presented a 9.9 mm axial impulse turbine with an optimal rotational speed of 420 krpm. Due to bearing challenges, the turbine was designed for 210 krpm. However, due to the limitations of the electrical generator, the highest overall efficiency (10.5 %) was reached at 100 krpm, yielding an isentropic efficiency of 18.4 % and a shaft power of 28 W. In a second step Peirs et al. implemented “better ball bearings”, adjusted the gap between the nozzle disc and rotor, and injected hot air (up to 360 ◦C) instead of ambient air. The turbine reached overall efficiencies of up to 16 %. Arnolds et al. [6] coupled an off-the-shelf dental drill to a magnetic generator. A maximum power of 1.1 W at a rotational speed of 200 krpm was reached. The exact turbine inlet mass flow rate was not measured, but it was estimated to 45 lmin−1 of ambient air, what leads to an estimated overall efficiency of 8 %. Krähenbühl et al. [7] tested a 9.5 mm axial impulse turbine, featuring prismatic blades with a height of 0.5 mm. The tip clearance was set to 0.1 mm. The power loss due to the generator and the ball-bearing-supported shaft were measured with coastdown tests (13 W at 500 krpm). This allowed to determine the turbine isentropic efficiency with the overall efficiency, based on the electrical power output. Krähenbühl et al. also intended 2 Copyright c © 2020 by ASME TABLE 1. Overview of micro turbines driven by ambient air (top) and steam with temperatures from 150 ◦C to 220 ◦C (bottom). Non-formatted numbers are directly stated in the reference (measurements), bold and underlined information is calculated and estimated, respectively, by the authors of this paper with the data available in the reference. A dash (-) indicates, that no information could be extracted from the reference. Year Authors Tip Rot. EffiPower Bearing Turbine Power Ref. of or diam. speed ciency type type meas. Ref. Company in mm in krpm in % in Watt methodg

Theoretical and Experimental Investigation of a 34 Watt Radial-Inflow Steam Turbine With Partial Admission