Experimental

The SMURF rig 6 in the Whittle Laboratory, shown in Figure 2, has been used to conduct the sensitivity studies in this paper. The SMURF rig is a low-speed multi-stage compressor, representative of a modern high pressure compressor. Each stage has identical geometry, with shrouded stator hub endwalls. For use in this paper, experimental data has been collected from a 1% span shroud clearance build of the rig and a 3% span clearance build. The rotor tip gap for each stage is 1.75% span. The average stage Reynolds number is ~5 × 10⁵ based on chord, with blade aspect ratios of ~1 and stage reaction based on mid-span of 65%. The stage has been designed at a moderate flow and work coefficient, and contains 3D blading.

Figure 2.

SMURF multistage low speed compressor.

A five-hole probe, with a 2.5 mm head diameter was used to traverse downstream of stator 2. This is approximately 20% of the stator mid-span trailing edge thickness. A single straight hot-wire was used to traverse the rotor 3 exit wake.

Computational

The Computational fluid dynamics (CFD) modelling conducted in this paper uses Rolls-Royce’s in-house solver Hydra 8, operated in steady RANS mode with mixing planes. The computational results are all from simulations using Menter’s k-ω SST turbulence model 7 as it gave more accurate results that the Spalart-Allmaras model. Nonetheless, similar trends in the results were observed for both models. PADRAM 10 was used to generate the mesh, which was configured to provide a multi-block structured O-H grid topology throughout the domain with a y+ ~1 on all viscous surfaces. Shroud cavity wells are modelled using a stub cavity model and a knife-to-knife (k2k) cavity model which is based on an experimental study in the literature 12. The k2k model, which has been calibrated against rig test data, was found give more accurate results than fully meshing the cavities.

The computational studies in this paper are all performed on the embedded stator 2 of the SMURF rig. The operating point investigated in all of the sections corresponds to an off-design operating point, φ = 0.47 and ψ = 0.51. At this condition, the mid-span static pressure rise coefficient is 0.60 and diffusion factor is 0.55.

Transition and roughness modelling

In the CFD, the effect of transition on the suction surface is modelled by imposing the transition location on the stator suction surface. For the off-design operating point being considered, the transition from laminar to turbulent was estimated to finish by 15% chord length, based on a MISES 3 mid-span calculation. This transition location is specified between 5 to 95% span.

In the experiment, the effect of roughness typical of an end of life blade was modelled using the sand grain technique reported in the literature 5. The sand grain size was scaled to match the roughness Reynolds number of a real engine stator blade exposed to approximately 4,000 cycles, which was shown in the literature 2 to increase to around 34, with a roughness height of 2 μm. To match this roughness Reynolds number on the SMURF stator, the sand grain size was required to give a roughness height of 16 μm.

Validation of embedded “stage” model

The validity of the sensitivity study depends on the how well the CFD can capture the flow physics in the experimental test case. A specific embedded stage model was used in the study. The model is shown in Figure 3. The key elements are:

Figure 3.

Embedded “stage” CFD model.

The result of the model at the two clearance gaps studied is shown in Figure 4. The results show that at both clearances, if all of the conditions above are met that the embedded stage model is extremely accurate at predicting a blade row. Despite the simplification of using a steady RANS model with circumferentially uniform inlet conditions, the magnitude and size of the stator loss cores are remarkably well captured by the CFD. This comparison demonstrates that unsteady CFD is not required for this embedded stage study.

Figure 4.

Embedded stage model, stator 2 exit data compared with experiment, Top: 1% span hub clearance, Bottom: 3% span.

An understanding of why steady CFD is able to capture the main physical mechanisms of 3D separations can be learned from a study in the literature 9. Naylor performed hot-wire traverses downstream of a stator blade row and showed that the incoming rotor wakes only had a small effect on the size of the 3D separation. Similar insight is also gleaned from Goodhand and Miller who showed that by triggering a large 3D separation with a movable leading edge trip, the timescale of the growth of the separation is an order of magnitude larger than the blade passing frequency.

It should be noted that even two blade rows into a multistage CFD solution, the small errors shown in Figure 4 start to accumulate and large errors can occur. This effect was also seen in the literature 11.

Sensitivity to endwall and shroud modelling

Four endwall and shroud modelling methods were undertaken from the highest to the lowest fidelity. The cases include:

Note, due to subtle changes in blockage caused by the different modelling fidelity, the inlet mass flow was adjusted for each of the four models to ensure a consistent stator pressure rise.

Figure 6 shows the suction and endwall surface streamlines, and the downstream loss contours for the four cases. The first and surprising finding is that the suction surface streamlines are nearly identical for each of the four cases. This indicates that the “hub corner separation fraction” is nearly identical for each of the four cases, only changing by a couple of percentage points. The second finding is that the loss contours downstream of the trailing edge are nearly identical for the first three cases but slightly lower in magnitude in the fourth case. The lower value in the fourth case is simply due to the loss generated on the stator endwall being removed.

Figure 6.

Sensitivity to endwall and shroud modelling fidelity for the “design intent” geometry.

The results show that for a modern 3D compressor stator the topology of the 3D corner separation is not very sensitive to the local blade modelling fidelity of the endwall and shroud.

Sensitivity to transition modelling

Two cases were undertaken: a fully turbulent case and an imposed transition case, where point transition is imposed along a spanwise line on the blade surface, based on MISES 2D calculations of individual sections. The endwalls in both cases were fully turbulent. Figure 7 shows the two cases and the experimental flow visualisation.

Figure 7.

Sensitivity to surface transition (taken from the 3% hub clearance case).

The first thing to note is that when transition is modelled the suction surface boundary is not separated at the trailing edge over a small portion of the span (from 60 to 70% span). The fully turbulent case however shows separation across the whole span, with the “hub corner separation fraction” increasing by 8 percentage points. The experimental flow visualisation agrees closely with the case where transition is modelled, as shown by the suction surface boundary layer similarly not separated at the trailing edge over a small portion of the span (60–70% span). The downstream loss contours show that the change in separation size has changed the size of the downstream loss contours.

The sensitivity to transition modelling, though significant, is much smaller than the effect reported on 2D compressor blades in the literature 5. This implies that though transition modelling is important, its importance on 3D blades is much weaker than in 2D blades.

Sensitivity to modelling in the multi-stage environment

The way in which the multi-stage environment communicates with the 3D corner separation in a particular blade row is through the blade inlet profile. The inlet profile develops over multiple stages and is notoriously difficult to predict using RANS CFD. The result is that many gas turbine manufacturers predict stage matching using low order methods tuned to experimental levels of blockage, deviation and loss.

The aim of this section is to investigate the sensitivity of the 3D corner separation to errors in different regions of a blade’s inlet profile. The measured “repeating stage” inlet profile to the stator is shown in red in Figure 8. The profile is made up of three regions. From 40–60% span, the freestream region, the profile is close to that of the design intent. From 5–40% and 60–100% span, the profile is dominated by the “repeating stage” endwall boundary layers. These are the regions that develop over multiple blade rows and are difficult to predict accurately with RANS CFD. From 0–5% span, very close to the hub endwall, the profile is dominated by the highly skewed boundary layer caused by the change in frame of reference of the upstream rotor hub platform boundary layer. The blue inlet profile in Figure 8 has the radial profile from 5–40% and 60–100% replaced with a scaled “design intent” profile. The green profile in Figure 8 is the same as the blue profile but also has the 0–5% span region replaced with the scaled “design intent” profile.

Figure 8.

Different inlet profiles studied in embedded stage CFD model.

The effect of the three inlet profiles on the 3D corner separations is shown in Figure 9. The first and most important thing to note is that replacing 5–40% and 60–100% of the span, the “repeating stage” endwall boundary layer region, with the scaled “design intent” profile has a very large effect on the topology and size of the 3D corner separation. Comparing the LHS and centre of Figure 9 shows that there has been a dramatic reduction in the “hub corner separation fraction” of 13 percentage points. This can also be seen from the downstream loss contours, which show that the size of the 3D corner separation has been significantly reduced.

Figure 9.

Sensitivity to inlet profile modelling fidelity for the “design intent” geometry.

The second thing to note is the effect of the highly skewed endwall boundary layer region due to the frame of reference change, 0–5% span. Comparing the centre and RHS of Figure 9 shows that the effect of the skewed boundary layer, though modest, is not insignificant. It is clear that the presence of the skewed boundary layer is acting to reduce the size of the hub corner separation by 6 percentage points.

Conclusions of “design intent” geometry sensitivity study

The results of all the design intent geometry investigations are summarised in Figure 10. The study clearly shows that for a modern 3D compressor blade, with the “design intent” geometry, the size of the 3D corner separations was only a weakly sensitive to the modelling fidelity within the blade row. However, the size of the 3D corner separations was strongly sensitive to the modelling fidelity within the multi-stage environment. Of course, multi-stage modelling fidelity also derives from the cumulative sum of the modelling fidelity within individual blade passages, however, it is the effect of inaccuracies built up over several blade rows which is important and not the modelling accuracy in the particular blade row being studied.

Figure 10.

Effect of modelling on hub corner separation fraction for “design intent geometry.”

This explains why many gas turbine manufacturers develop complex low order models tuned to experimental levels of blockage, deviation and loss. These models are used to predict radial profiles which are then fed into “embedded stage” CFD models such as the one described in this paper.

This work also explains why the findings on multi-stage endwall design in the literature 1 were so powerful. The authors showed that to really influence a design you need to design in the multi-stage environment, exploiting the inlet profile sensitivity identified in this study. However, this presents the designer with a dilemma. The designer must use low order models to predict the multi-stage matching accurately, but those low-order methods prevent the designer exploiting the true power of sensitivity to multi-stage design. Developing new compressor design systems that exploit this sensitivity whilst accurately predicting multi-stage matching will be one of the most important challenges facing compressor designers.

One further point is worth making. The study described above is for a shrouded stator. A similar study has been undertaken for a rotor. Despite the suction surface flow topology being very different to the stator, the same conclusions can be drawn as shown in Appendix A. The 3D separation is shown to be insensitive to local changes in endwall modelling and again, only the inter-blade row profile has any significant influence.

Sensitivity to endwall and shroud modelling

The four endwall and shroud modelling methods were again used but this time the clearance on the shroud was raised to 3% of span. The three key cases, the full cavity model, the dead cavity and the no cavity model are shown in Figure 11. The 3% clearance was found to have a leakage mass flow rate, which is 1.1% of the inlet mass flow.

Figure 11.

Endwall geometry sensitivity surface streamlines and loss contours, 3% clearance.

Figure 9 shows that for the 3% clearance, modelling the full cavity results in a large increase in the size of the hub corner separation (~13 percentage points). This shows that at very high clearances, the hub corner separation starts to become sensitive to the leakage flow in that blade row.

The reason for this can be observed from the dynamic pressure and tangential velocity profiles just upstream of the stator leading edge for the 1% and the 3% clearance, shown in Figure 12. As leakage flow rate is increased, the shorter residence time of the flow in the cavity results in it picking up less tangential momentum from the rotating cavity walls, hence the leakage flow exits the cavity with a lower tangential velocity and dynamic pressure.

Figure 12.

Influence of shroud leakage flow on incoming hub platform boundary layer.

To illustrate the importance of the tangential velocity component of the leakage flow on the hub corner separation, the 3% clearance case was modelled again with double the cavity rotational speed. This acts to increase the tangential velocity of the leakage jet by 60% and eliminates most of the dynamic pressure deficit caused by the increased leakage flow rate, as shown in the radial profiles Figure 13.

Figure 13.

Influence of cavity rotation speed on incoming hub platform boundary layer.

The importance of the leakage jet’s tangential velocity is shown in Figure 14. For the double cavity wall speed case, the increased tangential velocity of the leakage jet reduces the corner separation size significantly, to a size similar to that of the dead cavity case in Figure 11. This is because the increased inlet tangential velocity allows the endwall flow to overturn later in a similar way to the dead cavity case, which results in significantly less disruption to the suction surface flow.

Figure 14.

The effect of tangential leakage velocity, 3% clearance.

This leakage flow tangential velocity study also explains why the removal of the 1% clearance shroud model had very little impact on the corner separation size. As evident from Figure 12, the tangential velocity of the leakage flow just upstream of the stator is virtually identical to the flow in the dead cavity case, meaning very similar endwall flow develops. Interestingly, the same leakage flow study on an equivalent 2D stacked stator blade, as shown in Figure 17 in Appendix B, gives the same insensitivity, proving that it is the leakage tangential velocity that is key to determining the sensitivity of corner separations to leakage flow.

Figure 17.

Leakage flow sensitivity on a 2D stacked SMURF stator blade.

Sensitivity to surface roughness

Two experimental roughness cases were tested. These, along with the baseline case are shown in Figure 15. Only two stators in the blades row, labelled on the contour plots, had roughness added. This was due to only having access to two removable stator blades in the multi-stage rig.

Figure 15.

Experimental roughness sensitivity study on SMURF rig stator 2.

The first case has roughness located over the entire hub endwall between the two removable stators. The was done because in the computational endwall and shroud sensitivity studies earlier in the paper, it was found that making the endwall inviscid had relatively little effect on size of the hub corner separation. In this case, the opposite is done and the endwall is made extremely rough. Once again, it can be seen from Figure 15 that changes to the endwall have little effect on the size of the corner separation.

The second case has 5–95% span roughness located on leading edges of the two removable stators (2% chord along pressure surface, around the leading edge to 5% chord along the suction surface). The aim of this test was to investigate the effect of large levels of leading edge roughness on the 3D corner separation. Work in the literature 4, 5, showed that on 2D compressor blades 3D corner separation are extremely sensitive to leading edge roughness. Figure 15 shows that the effect of roughness on the 3D compressor blade in this study was extremely large, larger than the effects reported in the literature 4, 5.

The high sensitivity of the blade to leading edge roughness in the current study is very surprising. Previous tests which exhibited sensitivity 4, 5 were undertaken on two dimensional compressors blades which were designed without lean or sweep. In such blades, leading edge roughness “weakens” the blade surface boundary layer and results in a significant rise in the size of the 3D corner separation.

The design of the lean and sweep on the current blade was undertaken by “balancing” the two aerodynamic failure mechanisms (3D corner separation and trailing edge separation). This method of 3D design is described in the literature 11. Such a design is normally very insensitive to leading edge roughness. However, Figure 15 shows that above a critical roughness the “balance” design approach results in the boundary layer separating, “unzipping” across the whole span.

This finding is important because it shows that whilst 3D blades are more resistant to leading edge transition and roughness, once the leading edge roughness reaches a critical value the blade suffers from a catastrophic aerodynamic failure across the whole span.