Unsteady Force Variation

The fuel injection in the turbine-combustor results in the modified the tan­gential forces in the turbine, as shown in Table 2. In situ reheat decreased tangential force Fy on the first blade row but increased tangential force on the subsequent rows. Since the tangential force decrease on the first stage is smaller than the increase on the subsequent stages, the power of the turbine – combustor increased for all cases with combustion. Although the variation of the averaged blade force Ftot is rather small, as shown in Table 2 and Fig. 4, the power increase of approximately 5% is significant.

Figure 4. Averaged force on rotors, Ftot

The time variation in of the rotor blade tangential forces, shown in Fig. 5, indicates that the largest amplitudes occur in the last rotor row and the small­est amplitudes occur in the first rotor row. This conclusion is valid for every combustion or no combustion case.

(d) Fourth rotor

Figure 5. Variation of tangential forces on the rotors

Table 2. Forces on blades No Combustion Case 1 Case 2 Case 3 Ftoti [kN] 18.28 18.21 18.71 18.67 a i [deg] 38.4 36.4 36.1 36.3 Fy і [kN] 11.36 10.81 11.03 11.05 Ftot2 [kN] 11.87 12.27 12.17 12.31 a2 [deg] 60.3 61.7 61.9 62.7 Fy 2 [kN] 10.31 10.81 10.74 10.94 Ftots [kN] 12.62 13.19 12.75 13.08 аз [deg] 62.2 65.0 63.9 63.8 Fy з [kN] 11.17 11.95 11.45 11.73 Ftot4 [kN] 11.41 13.03 12.31 12.58 a4 [deg] 65.5 65.5 65.7 66.1 Fy4 [kN] 10.38 11.85 11.21 11.51

Table 3. Power increase Case 1 Case 2 Case 3 Power increase [%] 5.1 2.8 4.6

A phase shift caused by fuel injection is visible for the first and second rotor blades. The larger unsteadiness within the second rotor makes this phe­nomenon more clearly distinguishable in Fig. 5(b). The patches of burning mixture and the reduced degree of mixedness are the probable causes for this tangential force phase shift in the upstream region.

Figure 6 shows the fast Fourier transform of the tangential forces. They have been nondimensionalized by the average tangential force obtained in the case without fuel injection. The blades of the fourth rotor are excited the most. This excitation occurs at the first blade passing frequency (BPF), which is 1920 Hz. For the rest of the blades, the excitation due to the second BPF is comparable in amplitude to the excitation of the first BPF. Except for first rotor in case 1 and third rotor in case 3, the fuel injection has the effect of increasing the excitation of the first BPF. The largest amplitude increase is 216% and occurs on the third row blades in case 2. The unsteady force, however, is approximately 50% of the maximum amplitude value that occurs on the fourth rotor blade at BPF.

3. Conclusions

The complexity of the transport phenomena in a multi-stage turbine-combustor makes it one of the most challenging numerical simulation problems. The large unsteadiness and straining of the fbw along with the wide range of velocity variation lead to a widely spread of local characteristic time scales for flow and combustion, which strongly impacted the on-going reactions. As a first step in the numerical simulation of the in situ reheat, a two-reaction chemistry mechanism has been considered.

The numerical simulation was used to predict the airfoil temperature vari­ation and the unsteady blade loading in a four-stage turbine-combustor. The in situ reheat decreased the power of the first stage, but increased more the power of the following stages. The power of the turbine increased between 2.8% and 5.1%, depending on the parameters of the fuel injection. The largest excitation of the four-stage turbine-combustor corresponded to the rotor of the fourth stage, with or without combustion. The highest excitation corresponded to the first blade passing frequency, for all cases analyzed.

TION