6-bladerow studies

As shown in Fig. 5, the computational domain was extended by three bladerows, namely Rotor 2 (R2), Stator 2 (S2) and Rotor 3 (R3). The VANC was placed after the R3 bladerow. As before, a single-passage mixed-plane steady state-solution was obtained (Fig. 5). The two different vane settings, listed in 1, were considered. The computations were performed for an operat­ing point near stall, corresponding to VNAC1 configuration.

A comparison of the overall compressor characteristic is shown in Fig. 5 for the two vane settings while the corresponding individual rotor characteristics are given in Fig 5. As expected, there is a performance degradation with the mal-scheduled case. Of some interest is the individual rotor characteristic for the datum case when using steady-state and averaged unsteady fbw results. It is seen that there are significant differences, indicating that there is significant unsteadiness, a result that can also be seen from the separation zones of Fig. 5.

The instantaneous rotating stall patterns are shown in Fig. 5 for the nomi­nal and mal-scheduled vane settings by plotting the static pressure at R1 inlet. In agreement with measured data, there are 5-6 stall cells for the nominal set­ting while the number of cells switches to 11 for the mal-scheduled setting. A summary of all rotating stall calculations is given in 3. The modal force time histories are plotted in Fig. 5 for the same two configurations where 5, 6, 7, 10 & 12 nodal diameter modes have been included for the nominal vane set­ting, and the 11 nodal diameter mode for the mal-scheduled setting. As can be from the Fourier transforms, the main excitation is at about 430 Hz for the former and 770 Hz for the latter, corresponding to stall pattern rotation speeds of 34 Hz and 50 Hz respectively. Although there is good agreement with the number of stall cells in both cases, the measured rotating stall speed is about 60% higher for both settings. However, as can be seen from the static pressure plots of Fig. 5, the distribution of the rotating stall cells along the circum­ference is not uniform and hence several harmonics with different frequencies can be assumed to be present in the measured signal. Therefore, it is difficult to compare the measured and predicted peak excitation frequencies. Indeed, it is possible that the number of rotating stall cells might change by one or two between successive rotations. Furthermore, it is likely that the detail of the rotating stall pattern may be infhenced by the downstream bladerows which are not included in the model. Finally, the rotation stall excitation may interact with the dynamic characteristics of a bladerow and even lock into a mode of vibration.

Table 3. summary of rotating stall calculations Vane setting VANC setting No of cells in test No of cells predicted by 3- bladerow calculations No of cells predicted by 6- bladerow calculations Nominal High working line 6 13 5-6 Mal-scheduled High working line 13 No convergence 11

2. Concluding Remarks

The most important conclusion is the feasibility of simulating rotating stall with a large scale numerical model. Although the computational effort is significant, parallel processing on inexpensive PC clusters al­lows the runs to be undertaken in “advanced design” timescales. For instance, the 6-bladerow model has about 30 million grid points and a typical run taking about 3 weeks on a 32-CPU cluster, each node con­sisting of a 2 GHz Intel Xeon CPU. Given Moore’s law for single-CPU speed increases, which is acceptable in industrial environments.

From a numerical viewpoint, numerical stall initiation can be achieved by aerodynamically mistuning the rotor blade. Ideally, a systematic study needs to be undertaken to see if the obtained stall pattern and speed are independent of the initial stagger angle perturbation. Also, stall ini­tiation is still relatively slow, requiring the simulation of 5-6 full engine revolutions. Further work is needed to see if white noise excitation can be used to represent ft>w randomness as an alternative to rotor blade mistuning.

It has been confirmed that the most important parameter for rotating stall pattern and speed is the stator vane setting. Inlet temperature effects were seen to be of secondary importance.

It appears that the inclusion of further bladerows downstream improves modeling accuracy in the sense that the correct number of rotating stall cells was obtained with the 6-bladerow model only. Furthermore, it was not possible to obtain a solution for the mal-scheduled vane setting using the 3-bladerow model.

■ From a design viewpoint, both the exact pattern and the speed of the ro­tating stall cells must be determined so that the critical vibration modes can be identified and avoided. However, such a requirement may not only be beyond the available modeling accuracy but it also relies on both the pattern and speed to remain constant between successive rotations. The latter issue needs to be studied by undertaking long rotating stall simulations, say over 100 engine rotations, with representative inlet per­turbations to see the stability or otherwise of the rotating stall structure.

Acknowledgments

The authors thank Rolls-Royce plc for both sponsoring the work and allow­ing its publication.

References

Greitzner, E. M. (1978) “Surge and rotating stall in axial flaw compressors. Parts 1 & 2” ASME J. of Engineering for Power 98, 190-217.

Longley, J. and Hynes, T. P. (1990) “Stability of fbw through multi-stage axial compressors”, ASME J of Turbomachinery 112, 126-132.

Weigl, H. J., Paduano, J. D., Frechette, L. G., Epstein, A. H., Greitzer, E. M., Bright, M. M. and Strazisar, A. J. (1998) “Active Stabilization of Rotating Stall and Surge in a Transonic Single-Stage Compressor” Journal of Turbomachinery 120, 625-636.

Moore, F. and Greitzer, E. M. (1986) “A theory of post-stall transients in axial compressors”. ASME J. of Eng for Gas Turbines & Power 108, 371-379.

Paduano, J., Epstein, A. H., Greitzner, E. M. and Guenette, G. (1994) “Modelling for control of rotating stall” Automatica 30, 1357-1373.

Niazi, S. (2000) Numerical simulation of rotating stall and surge alleviation in axial compres­sors. PhD thesis, Georgia Institute of Technology, Dept of Aerospace Engineering, Atlanta, USA

He, L., (1997) “Computational study of rotating stall inception in axial compressors”, AIAA Journal of Power and Propulsion 13(1), 31-38.

Sayma, A. I, Vahdati, M., Sbardella, L. and Imregun, M. (2000) “Modelling of 3D viscous compressible turbomachinery flaws using unstructured hybrid grids”. AIAA Journal, 38(6), 945-954.

Sbardella, L. Sayma, A. and Imregun, M. (2000) “Semi-structured meshes for axial turboma­chinery blades”. International Journal for Numerical Methods in Fluids 32(5), 569-584.

Rai, M. M. (1986) “Implicit conservative zonal boundary scheme for Euler equation calcula­tions” Computers & Fluids 14, 295-319.

Sayma, A. I., Vahdati, M. and Imregun, M. (2000) “Multi-bladerow fan forced response predic­tions using an integrated 3D time-domain aeroelasticity model” J of Mechanical Engineering Science, Part C, 214(12), 1467-1483.

Vahdati, M., Breard, C., Sayma, A. and Imregun, M. (2003) “An integrated time-domain aero­elasticity model for the prediction of fan forced response due to inlet distortiona” ASME Journal of Engineering for Gas Turbines & Power 124(1), 196-208.

Vahdati, M., Sayma, A., Freeman, C. and Imregun, M. (2003) “On the use of atmospheric boundary conditions for axial-flow compressor stall simulations”. Submitted to the ASME J of Turbomachinery

Figure 1. omputational domain for steady-state computations (top) 3-bladerow model (bot­tom)

Figure 7. Steady-state solution for 6-bladerow model

Figure 8. Comparison of the overall characteristic

Mass flow

Figure 9. Individual rotor characteristics for datum scheduling

Figure 11. Instantaneous stall bands. Nominal condition (top) and mal-scheduled condition (bottom)