Published: 2012
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A one-dimensional model for a radial inflow turbine has been developed for super-critical carbon dioxide (S-CO2) Brayton cycle applications. The model accounts for the main phenomena present in the volute, nozzle, and impeller of a single-stage turbine. These phenomena include internal losses due to friction, blade loading, and angle of incidence and parasitic losses due to windage and blade-housing leakage. The model has been added as a component to the G-PASS plant systems code. The model was developed to support the analysis of S-CO2 cycles in conjunction with small-scale loop experiments. Such loops operate at less than a MWt thermal input. Their size permits components to be reconfigured in new arrangements relatively easily and economically. However, the small thermal input combined with the properties of carbon dioxide lead to turbomachines with impeller diameters of only one to two inches. At these sizes the dominant phenomena differ from those in larger more typical machines. There is almost no treatment in the literature of turbomachines at these sizes. The present work therefore is aimed at developing turbomachine models that support the task of S-CO2 cycle analysis using small-scale tests. Model predictions were compared against data from an experiment performed for Sandia National Laboratories in the split-flow Brayton cycle loop currently located at Barber-Nichols Inc. The split-flow loop incorporates two turbo-alternator-compressor (TAC) units each incorporating a radial inflow turbine and a radial flow compressor on a common shaft. The predicted thermodynamic conditions at the outlet of the turbine on the main compressor shaft were compared with measured values at different shaft speeds. Two modifications to the original model were needed to better match the experiment data. First, a representation of the heat loss from the volute downstream of the sensed inlet temperature was added. Second, an empirical multiplicative factor was applied to the Euler head and another to the head loss to bring the predicted outlet pressure into better agreement with the experiment. These changes also brought the overall efficiency of the turbine into agreement with values cited by Barber Nichols for small turbines. More generally, the quality of measurement set data can in the future be improved by additional steps taken in the design and operation of the experimental apparatus. First, a thermocouple mounted at the nozzle inlet would provide a better indication of temperature at this key point. Second, heat losses from the turbine should be measured directly. Allowing the impeller to free wheel at inlet conditions and measuring the temperature drop between inlet and outlet would provide a more accurate measure of heat loss. Finally, the enthalpy change during operation is more accurately obtained by measuring the torque on the stator using strain gauges rather than by measuring pressure and temperature at inlet and outlet to infer thermodynamic states.
