###### Abstract  
This paper presents the design procedure and analysis of a radial turbine design for a mid-scale supercritical CO\({}_{2}\) power cycle. Firstly, thermodynamic analysis of a mid-range utility-scale cycle, similar to that proposed by NET Power, is established while lowering the turbine inlet temperature to 900 \({}^{\circ}\)C in order to remove cooling complexities within the radial turbine passages. The cycle conditions are then considered for the design of a 100 MW\({}_{th}\) power scale turbine by using lower and higher fidelity methods. A 510 mm diameter radial turbine, running at 21,409 rpm, capable of operating within a 5% range of the required cycle conditions, is designed and presented. Results from computational fluid dynamics simulations indicate the loss mechanisms responsible for the low-end value of the turbine total-to-total efficiency which is 69.87%. Those include shock losses at stator outlet, incidence losses at rotor inlet, and various mixing zones within the passage. Mechanical stress calculations show that the current blade design flow path of the rotor experiences tolerable stress values, however a more detailed re-visitation of disc design is necessitated to ensure an adequate safety margin for given materials. A discussion of the enabling technologies needed for the adoption of a mid-size radial turbine is given based on current advancements in seals, bearings, and materials for supercritical CO\({}_{2}\) cycles. supercritical carbon dioxide; radial turbine; utility-scale; turbomachinery design; NET Power 20202010 10.3390/app1024168 10. * High cycle efficiencies are also obtained, attributed to lower pumping power requirements and the non-ideal gas properties of sCO\({}_{2}\) which translate into lower fuel consumption and lower capital and operating costs. Targeted efficiencies of large-scale, closed supercritical CO\({}_{2}\) Brayton cycles approach 50%
* The suitability of the cycle for waste heat recovery from a variety of heat sources (e.g., nuclear, solar, fossil, geothermal, etc.) * The application of these high-efficiency cycles reduces greenhouse gas effects because a CO\({}_{2}\) emission is used as a working fluid or as a recycle stream (i.e., not emitted)
* The suitability of sCO\({}_{2}\) cycle systems for use in arid climates because of their ability to use dry cooling (thus saving water) [7]
* Low purification requirements for fluid leakages because the cycle operates above the critical pressure of CO\({}_{2}\)  
The NET Power (Allam) cycle combines both originalities of oxy-combustion and supercritical CO\({}_{2}\) fluids in one system which is aimed at high power generation efficiencies coupled with high levels of CO\({}_{2}\) capture [8]. A review of oxy-combustion cycles has been reported by the International Energy Agency (IEA) identifying the main cycle configurations, requirements, benefits, complications and future developments by presenting cycle modelling and techno-economic study results [9]. The NET Power is one of the most attractive of the listed oxy-combustion cycles in terms of efficiency reaching 55% on lower heating value of fuel (LHV). Natural gas fuel or coal and oxygen from an air separation unit are combusted at high temperatures reaching 1200 \({}^{\circ}\)C at high pressures (\(\approx\)30 MPa) with the recirculated CO\({}_{2}\); due to the absence of N\({}_{2}\) in the combustion process, the flue gases are mostly composed of CO\({}_{2}\) and H\({}_{2}\)O with no formation of NO\({}_{x}\) (for a natural gas based cycle). The combustion products are then expanded in the CO\({}_{2}\) turbine with a pressure ratio between 6 and 12 before entering a multi-flow economizer heat exchanger where the turbine cooling flow and the recycled CO\({}_{2}\) and O\({}_{2}\) streams to the combustor are pre-heated using the residual flue gas heat [10]. The exhaust stream is also cooled for condensation and separation of water from the mixture.