## 4 Further Validation
### Design Point Performance Simulation  
Some available test results are used in this section to demonstrate the methodology applied to simulate the steady-state design point performance for a turbine stage. A further validation for the proposed loss model is provided from the stage efficiency measurements. The two tested units are single stage non-condensing steam turbines, partial admission design, applied to oil refinery service. The purpose of this project was to selectively apply this equipment concept to special purpose service, according to the API 612 standard [39], for which the multi-valve multi-stage design is traditionally specified. The mono-valve single stage units may present a satisfactory performance under favorable conditions of available steam enthalpy drop, speed and output power, with the benefit of a much lower acquisition cost. The performance tests were carried out at factory test bench, according to ASME PTC6 standard [40], as a contractual acceptance procedure. The turbine is tested coupled to a hydraulic brake through a reduction gearbox and a torque meter instrumented coupling. The output power and isentropic efficiency are calculated from the orifice plate flow meter and a set of pressure and temperature probes located at the turbine inlet, downstream of the governor valve and exit. The torque measurement is used to check and to validate the thermodynamic analysis results. Steady-state design point performance simulation of a steam turbine stage is assessed from certain geometric data and service conditions, and also involves real gas behavior. Stage geometry data needed for both stationary and rotating cascades are as follows: number of blades, solidity, aspect ratio, trailing edge blockage, blade flare angle and blade exit angle. Axial and radial clearances are also needed to evaluate leakage losses. Service data are given by the rotational speed, the inlet total pressure and temperature, and the exit static pressure. From the described input data the non-dimensionals specific speed and specific diameter are obtained. A size parameter [41] must be added in order to give the actual length scale to the non-dimensional geometric parameters. The problem of simulating a turbine stage performance consists in determining the degree of reaction which provides the better matching of both rotor blade exit angle and arc admission fraction to actual values. Service conditions and geometry data are shown in Table 3 for the two tested units. The performance simulation results are shown in Table 4 for the two tested units. Some relevant aero-thermal parameters are listed, as well the loss coefficients. Simulated total to static efficiencies are shown to be in agreement with factory test bench measurement results. Estimation of overexpression losses at supersonic nozzle blade exit flow were done according to [PERSON] [42]. Estimation of partial admission losses (filling and emptying loss, scavenge loss and leakage from the active flow to the inactive region) were done according to [PERSON] [43]. The simulated loss breakdown is shown in Table 5. In fact, commercial steam turbine design is not fully optimized to the specified service due to the utilization of standard-dimension components, like wheels and blades. Despite its advanced rotor blade profile, the detailed analysis clarifies that \begin{table}
\begin{tabular}{c c c c} \hline
**Rotor** & **_h/C_** & \(\mathbf{\xi_{tot}}\) **(Experiment)** & \(\mathbf{\xi_{tot}}\) **(Simulation)** \\ \hline \(a\) & 0.44 & 0.253 & 0.272 \\ \(b\) & 0.79 & 0.272 & 0.243 \\ \(c\) & 0.18 & 0.554 & 0.821 \\ \(d\) & 0.11 & 0.769 & — \\ \hline \end{tabular}
\end{table} 
Table 2: [PERSON] [37] rotors simulated and measured loss coefficients. of experimental data available. Computational implementation drives the use of analytical methods, in opposition to the traditional methods, based on a more empirical approach and turning to manual calculation through graphic information.