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Appl. Sci. 2020, 10, 4168 7 of 26 with the uncooled turbine gives a superior cycle efficiency compared to the cooled case, a 1.54% efficiency point gain. The heat transfer associated to preheating the turbine cooling flow within the regenerator (which also contributes to expansion losses) is removed and thus the detrimental efficiency penalty affiliated with this process is eliminated causing a beneficial impact on the cycle efficiency. In fact it is suggested that while turbine cooling allows an increase in turbine inlet temperature (TIT) which enhances cycle performance, it also increases energy losses in turbines and thus leads to a lower aerodynamic efficiency [28] that in turn would have a great negative impact on the net cycle efficiency [29]. Scaccabarozzi et al. [10] noted that the maximum net cycle efficiency is achieved at a relatively low turbine inlet temperature (lower than the maximum simulated TIT value) because of the substantial cooling mass flows required if a high combustor outlet temperature is implemented. Table 2. Comparison of optimised cycle between [10] and uncooled turbine model. Thermal energy of feedstock (LHV) Turbine power output Recycle flow compressors Natural gas compressor Air separation unit Storage compressor Net electric power output Turbine outlet temperature Turbine inlet flow rate Net electric efficiency (LHV) 3.1.2. Modified Cycle Unit Results of This Work MWth 768.21 MWe 610.55 MWe 88.00 MWe 3.97 MWe 85.51 MWe 0.25 MWe 432.82 ◦C 830.53 kg/s 1567.7 % 56.34 Results of [10] Optimised Cycle 768.31 609.74 97.81 - - - 421.06 783.81 1513.7 54.80 As discussed in Section 1, supercritical CO2 cycles, regardless of whether they employ cooling or not, have the beneficial characteristics of small turbomachinery components due to the high fluid density. Suggestions from literature limit the applicability of radial turbines to cycles of up to 30 MWe [30]. The criteria for that power level was proposed on the basis of closed sCO2 cycles with lower operating pressures and temperature compared to conditions witnessed in cycles similar to the Allam cycle. The numerical value of a turbine specific speed is used as an index of power output and passage size [31]; the dimensionless parameter is used by designers to determine turbine type and efficiency. ωQ ̇ Dixon shows that for a specific speed ns = 5 peak performance [31]. A larger-scale turbine—higher volumetric (Q ̇ ) or mass flow rate (m ̇ )—corresponds to a higher specific speed value for fixed ideal heat drops (∆hid) and rotational speeds (ω). Thus, taking a within-the-range recommended value of ns = 0.7 [18,31] and knowing the ideal enthalpy drop from the cycle model (∆hid = 284,370 J/kg), plus having performed some calculations on possible rotational speeds being in the range of 25,000 rpm, through initial turbine sizing (i.e., ω = 2618 rad/s) the corresponding maximum allowable mass flow rate is: m ̇max =Q ̇max·ρout = 0.7∆h0.75 2 in the narrow range of 0.3–1.0, where this (∆hid )0.75 span corresponds to small turbine passage areas, a 90◦ inward-flow radial (IFR) turbine can reach high efficiencies in contrast with the conventional axial turbines which have a much broader spectrum of where ρout is the density of the flow at turbine outlet and is around 33.2 kg/m3 from the cycle model. The limit obtained for the largest size of a radial turbine operating under the conditions of a dense working environment, at TIT = 900 ◦C, turbine inlet pressure (TIP) = 297 bar and pressure ratio ω id ·ρout ≈354kg/s (1)PDF Image | Radial Turbine Design for a Utility-Scale Supercritical CO2 Power
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