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loss calculated in the RTGD code is the clearance loss, using the Dambach [13] equations, model that consider the axial and radial clearances influences. Trailing edge losses [14] arises due to mixing occurring, as the adjacent rows, of the two-blade surfaces exit the blade row. Moreover, at supersonic velocities shock losses also contribute. In the fourth step the RTGD code determine the trailing edge loss as a function of the exit Mach number, the exit pressure and temperature and relative pressure loss Ξp0 [5], as follows: 2 π₯π π₯h= 0πΎ (5) π‘ πΎ π2 5 π€2πΎβ1 π5(1+ 5 ) 2 π5 πΆπ Windage losses are frictional losses occurring on the back face of the turbine disk. The windage loss [14] is calculated as a function of the Reynolds number. The only external loss that is usually considered in radial turbine modelling is that of disk friction. This occurs because of the fluid leakage between the rotor disc and the stationary back plate, where the windage flow causes quite strong friction. Depending on the turbine, this leakage could also be recirculated into the turbine annulus or taken away. The back face of the impeller hub is an annular disk that spins with the impeller. Either this disc may mate with a fixed surface separated from it by a small clearance or it may spin freely far from other fixed surfaces. In either case, the fluid adjacent to the disc exerts a shear on the disc with result that the fluid does unproductive work. Finally, the rotor exit kinetic loss is expressed as: π₯h =1π2 (6) In conclusion, the turbine overall efficiency can be determined as a function of the different loss contributions: πts = Ξh0ββΞhloss (7) Ξh0 RTGD does not require the pressure ratio as input for the rotor exit pressure calculation, but the latter is calculated more accurately as a function of the efficiency and the total inlet pressure and temperature: πΎβ1 π π=π(1βπ )πΎ (8) π25 5 00 πππ π‘π π 00 RESULTS PRESENTATION The RTGD code has been validated considering two cases present in the literature, in order to demonstrate the effective validity of the implemented models. In the first case it was considered a real T-100 [9] turbine that uses Air as the working fluid, while in the second case RTGD was validated considering a radial turbine that uses Argon as working fluid, whose geometry is provided from RIFTUD code [5]. The purpose of RTGD is to simplify the radial turbine preliminary design in the absence of specific references and to optimize the turbine geometry in order to maximize performance while minimizing losses. The Table 1 shows the data of both turbines. TABLE 1. Working Fluid Input Data T-100 Argon Rotational Speed [rpm] Inlet Total Temperature [K] Inlet Total Pressure [Pa] Mass Flow Rate [kg/s] Power [kW] Pressure Ratio 5.73 106,588 38,500 1056.5 1083.33 580,400 91,011 0.33 0.2771 121 22.37 020097-6PDF Image | Radial turbine preliminary design and performance prediction
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