## 3 Operating Conditions  
Two sets of operating conditions were considered for the present investigation. The first group of conditions, denoted as OP in the following, is composed by four configurations tested to characterize the effect of the expansion ratio, ranging from an almost incompressible (OP4) to a transonic one (OP1) including two intermediates (OP3 and OP2) classified according to the expansion ratio. It has to be noted that OP3 is the reference condition for this stage. The second group of conditions, denoted OPL in the following, includes three further configurations close to OP3 and tested to investigate the effects of rotor loading only at constant expansion ratio, namely almost eliminating the Mach and Reynolds effects: these OPLs are reference as OPLU for the unloaded case, OPLR for the reference and OPLL for the loaded one.  
As discussed in the Introduction, the pair of expansion ratio and rotational speed in OP1-4 were chosen in order to have the same absolute flow angle at the stage outlet. Notably, as this turbine has a fully three-dimensional geometry and the secondary flows alter the flow pattern at the endwalls, the constraint was imposed on the midspan region, as shown in Figure 2, which reports about measured flow angle distributions at the stage exit.  
In order to change the rotor loading, the rotational speed was modified for the same expansion ratio, thus modifying the incidence angle on the rotor and the rotor outlet flow angle, but not significantly the Reynolds and Mach number levels. Due to constraints in the rig operation, the stage inlet temperature was set in the range of 300-325 K with a constant outlet pressure, close to the atmospheric one; Table 3 summarizes the main stage features for the several OP and OPL tested. As the different expansion ratios are achieved by pressurizing the turbine incoming flow, the inlet Mach number weakly varies ranging from \(M\) = 0.12 to 0.145; the inlet direction is always axial (thanks to the straightener) and the non-dimensional inlet velocity profile as well as the inflow turbulence intensity do not change. By applying the similarity concepts, the OP1-4 can be expressed in terms of non-dimensional flow rate, peripheral Mach number and expansion ratio, as well as flow and load coefficients, as reported in Table 4.  
Figure 2: Absolute flow angle downstream of the stage for the different Operating condition (OP).  
As clearly visible from the tabular data, the non-dimensional parameters indicate that these OP are not in a fully similarity condition even though a similarity in the outlet velocity directions imposed. The obvious reason lies in the change of the Mach number that cannot be kept constant as this constraint would have required a very high change in the inlet temperature [\(T/T_{\text{ref}}=(\textit{rps}/\textit{rps}_{\text{ref}})^{2}\)], not feasible in the LFM facility nor in a real gas turbine operation. As a result, the inter blade row region has to deal with the change in the kinematic similarity; in other words, the effect of the compressibility is to introduce a deviation in the \(U/V_{1}\) ratio. The following Sections discuss the impact of these deviations on the flow configuration as well as on the overall stage performance.