Case study

As stated earlier, the objective of the work is to develop a methodology to predict the effects of multi-lobe rotating stall on blade vibration levels. Of particular importance is to link the variable vane scheduling to the number, size, distribution and speed of rotating stall cells so that the critical modes of vibration can be identified and avoided. Two vane settings, namely nominal and mal-scheduled, were used in the computations because of the availability of experimental data for these two conditions. The work was undertaken in two stages, first with a 3-bladerow model and then with a 6-bladerow model.

3-bladerow studies

As shown in Fig. 5, the case study was initially conducted for the first 3 bladerows of an aero-engine core compressor at some part-speed. The first bladerow consists of variable inlet guide vanes (VIGVs), while the next one is the first rotor bladerow (R1) and the last one is the first stator bladerow (S1). The nominal vane setting was used for all calculations reported in this section.

For this particular study, where the part-speed behavior is of primary inter­est, the compressor inlet boundary conditions were not available because of the very low fan speed. Therefore, it was decided to include the low pressure compression (LPC) domain in the model and to derive the required boundary conditions from a steady-state flow solution over the computational domain shown in Fig 5. A novel feature of the computational domain are two variable area nozzles (VANs), one upstream of the fan, labelled VANF in Fig. 5 , and one downstream of the compressor, labelled VANC in Fig. 5 . The VANF was used to control the by-pass mass flow and it was tuned until an appropri­ate working line point on the part-speed fan characteristic was obtained. The nozzle area was then kept constant for all remaining calculations. Therefore, it was implicitly assumed that the fan operating point would remain the same for the two compressor operating points that were being considered.

Once a steady-state solution was obtained, the computational domain was reduced by removing the LPC domain and the VANF. The reduced domain still included VANC which was used to control the core-compressor mass fbw as an alternative to prescribing a static pressure distribution at the compres­sor exit. The need for such an approach, described by Vahdati et al. (2003b), arises from the difficulties of defining accurate boundary conditions at the out­let compressor exit. Indeed, upstream downstream boundary conditions for most multi-bladerow computations use are derived from a 1D throughflow analysis calibrated by available experimental data. Such an approach is not suitable for stall and surge studies where the flow through the downstream bladerows undergoes significant temporal and spatial variations. When fixed conditions are imposed at the boundaries, the flow solution is stable at lower working lines but, higher working lines, which are of more interest here, are known to exhibit modeling difficulties because of potential inconsistencies be­tween the actual solution and the imposed boundary conditions. Rigid bound­ary conditions, based on imposing given exit pressure distributions, are not suitable for numerical studies because the bladerow exit pressure profiles are neither known nor fixed. Furthermore, at high working lines, the fbw becomes genuinely unsteady near the stall boundary, and the imposition of a fixed exit static pressure results in numerical instabilities, the so-called "numerical stall”. Therefore, the use of a downstream VAN alleviates some of the difficulties above by allowing the flow to develop naturally by providing a volume after the last bladerow included in the model. The ideal situation would be to include as many compressor bladerows as possible and to keep the LPC domain in the model so that atmospheric conditions can be used at either end. However, as will be discussed later, the rotating stall computations were conducted with the reduced-size model and keeping the VANC only because of computational considerations.

The rotating stall calculations were conducted in a time-accurate fashion using a viscous ft>w representation and by adjusting the VANC to obtain the required compressor operating point on the part-speed characteristic. A well – known difficulty is the initiation of rotating stall when using a numerical model since an initial perturbation is needed. Even if the ft>w structure is near insta­bility, a perturbation may still be needed for stall initiation. After some deliber­ation, it was decided to introduce a small amount of aerodynamic mistuning to Rotor 1 where each blade was given a random small geometric change in stag­ger (Fig. 5). Two different vane settings, listed in Table 1, were considered for two operating points, corresponding to two different VANC configurations, la­belled VANC1 and VANC2 in Fig. 5. Therefore four rotating stall simulations were undertaken using the 3-bladerow model (Table 2).

Stall behavior was examined by monitoring the mass ft>w at Rotor 1 exit for the VANC1 and VANC2 configurations for the nominal vane configura­tion. VANC1 corresponds to an operating point near stall and hence the sud­den drop in the mass ft>w rate persists, indicating that that there is no recovery from stall. On the other hand, VANC2 is on a lower working line and hence the compressor recovers from rotating stall after a short while. The effect of tem­perature was also investigated by lowering the inlet temperature by 15 degrees for the VANC1 configuration. No appreciable difference was noted.

It is best to visualize the rotating stall phenomenon by inspecting an ani­mation of the static pressure at Rotor 1 inlet, or negative mass flow at Rotor 1 exit. As discussed earlier, Configuration VANC1 yields persistent rotating stall, but the compressor recovers for Configuration VANC2. A typical snap­shot for VANC1 is given in Fig. 5 where about 13 rotating stall cells can be seen along the circumference. From a structural viewpoint, a 13-cell pattern is likely to excite a 13 nodal diameter/first fkp assembly mode provided there is also a frequency match between the natural frequency of the mode and the speed of the rotating stall pattern. The modal force for this particular mode is shown in Fig. 5. A Fourier transform of the modal force indicates an excitation frequency of about 910 Hz, suggesting that the stall pattern’s rotation occurs at about 910/13=70 Hz, the assembly speed being about 120 Hz. Therefore, it may be concluded that the speed of the rotating stall cells is 50Hz, a value that is consistent with previous experience of about half the rotational speed.

Experimental evidence suggested that the actual number of rotating stall cells was about 6, and not 13 as predicted here, for the nominal vane set-

ting. The calculations were repeated for the mal-scheduled vane setting but it was not possible to obtain a converged solution for this condition. It was thought that the inclusion of further downstream bladerows would improve the modeling accuracy by allowing the fbw to develop more naturally. As will be described in the next section, the stall calculations were repeated with a 6-bladerow model.