Modelling of the pressure tubes

For the purpose of this study, we modeled the pressure tubes covered by a sheet of metal as a simplified bump. This bump, modeled on a flat plate for clarity, is presented in Figure 2. The variables h and w denote the height and width of the bump, respectively, while r1 and r2 represent the radii. The radii r1 and r2 have been chosen so that all transitions of the bump boundary curve are tangential. The flat plate bump geometry is then scaled appropriately and transferred onto the curved surfaces of the blade (see Figure 3). These bumps extend across the full span of the blade with a width of 24% of the chord length and a height of 67% of the maximum blade thickness. The leading edge of the bumps is located at 30% of the streamwise surface length. All cascade blades have a fillet at the blade root and tip to dampen the formation of the corner vortex and maintain a two-dimensional flow over a large midspan region. When the bump is applied to the pressure side, we call this “pressure-sided bump” (PSB) and when added to the suction side, “suction-sided bump” (SSB).

Figure 2.

Simplified pressure tube geometry.

Figure 3.

Compressor blade with pressure tubes. (a) On the pressure side. (b) On the suction side.

Experimental setup

A high subsonic compressor cascade profile, which has already been used in previous investigations of our institute (Winter et al., 2013), was selected. The experiments were conducted at the linear cascade wind tunnel of the institute (see Figure 4). The air is supplied by a multistage radial compressor, which enables experiments in a Mach number range of 0.4 up to 0.85. Due to the closed-loop design, an engine-like Reynolds number between 650,000 and 1,250,000 can be adjusted independently of the Mach number. For the profile we selected, an inlet Mach number of about Ma≈0.5 and an isentropic Reynolds number of Re=790,000 were chosen as the operating point. Before entering the test section, the flow is homogenized and the turbulence is reduced in the settling chamber using honeycomb screens. With a passive turbulence grid located in the settling chamber, a turbulence level of approximately 2.5% is generated directly upstream of the blades. The flow is accelerated by a convergent nozzle and enters the rectangular cross section of the test section where the compressor cascade, consisting of nine blades, is located (see Figure 5). Adjustment of the operating point is achieved by measuring the total pressure in Measuring Plane 1 (MP1) with a pitot-probe and using static wall pressure taps. Measurements downstream of the three central blades (labeled as Blade −1, 0, 1 in Figure 5) were performed at midspan of the blade with a five-hole probe. The wake measurements were made at 60% of the axial chord length bax downstream of the trailing edge, referred to as Measuring Plane 2 (MP2), due to the occurrence of large separation bubbles, as will be shown later. Downstream of the test section, the discharge chamber is located.

Figure 4.

Linear cascade wind tunnel.

Figure 5.

Cascade test section with modified central blade (blade 0).

A cascade with only nominal blades is used as the reference case for this study. This configuration will be referred to as “clean blade” in the following. The periodicity of the flow is set for the clean blade cascade using the adjustable sidewalls and tailboards. To evaluate the influence of a spanwise bump, the central blade “Blade 0” is replaced by a modified blade with either a pressure-sided or a suction-sided bump, while all other blades remain nominal (see Figure 5). The additional losses generated by these bumps are found by comparing the modified cascade to the nominal cascade. The sidewall and the tailboard settings are not changed in relation to the clean blade cascade. All changes in the periodicity of the flow are therefore due to the influence of the bump. For the nominal cascade, only the wake of the central blade “Blade 0” is measured. In the case of the pressure-sided bump, the wake of the central modified blade is measured, while for the suction-sided bump, the pressure side-adjacent and suction side-adjacent blades (“Blade −1” and “Blade 1”) are measured as well. This configuration, in which there is only one modified blade surrounded by clean blades, is similar to a test rig which has only a few instrumented blades.

The profile loss is evaluated in terms of the local total pressure loss coefficient ω, which is defined as

The total inlet pressure pt1 is measured using a pitot-probe and the static inlet pressure ps1 is measured using pressure taps in MP1. The total outlet pressure pt2 is determined by means of the five-hole probe in MP2 using a look1up table approach. The measurement uncertainty is determined with linear Gaussian error propagation, resulting in a maximum uncertainty value of Δω/ωmax,clean,exp=0.52%. This value is given in relation to the experimentally determined maximum value of the clean blade total pressure loss coefficient ωmax,clean,exp. To characterize the flow losses by a single value, the integral total pressure loss coefficient ωint is calculated by

Here, pt2¯ denotes the mass flow averaged total outlet pressure in MP2 while pt1¯ stands for the mass flow averaged total inlet pressure in MP1. In order to eliminate the free stream loss of the flow from MP1 to MP2, a correction is applied to pt1¯. The mean static pressure at MP1 is expressed by ps1¯. A Monte-Carlo analysis was used to determine the measurement uncertainty of ωint, resulting in a value of Δωint/ωint,clean,exp=2.68%.

Since the blade geometry investigated is proprietary, all data on the total pressure loss coefficient ω is normalized. In the plots, ω is normalized with respect to the experimentally determined maximum value of the local total pressure loss coefficient for the clean blade ωmax,clean,exp. Integral values of ω for both experimental and numerical results are normalized with respect to the integral total pressure loss coefficient of the clean blade ωint,clean. The coordinate in pitchwise direction y, which is plotted on the x-axis of all wake plots, is normalized by the blade pitch t.

Numerical setup

To simulate the effects of the spanwise pressure tubes on the flow around the compressor blade, we used the code TRACE 9.4 (Turbomachinery Research Aerodynamic Computational Environment), which is developed by the German Aerospace Center (DLR) in cooperation with MTU Aero Engines. We solved the RANS equations with a finite volume scheme of second-order spatial accuracy by applying a MUSCL approach together with a central discretization of the viscous terms and Roe upwind-based convective flux difference splitting. In this study, the k−ω turbulence model by Wilcox (Wilcox, 1988) and the SST model by Menter et al. (2003) were used. The stagnation point correction by Kato and Launder (1993) was applied to both models. The transition was modelled by the γ−Reθ transition model by Menter et al. (2004) in the formulation from 2009 (Langtry and Menter, 2009) for both turbulence models. Additionally, we also conducted simulations using the k−ω model with activated Viscous Blending (VB) limiter, which limits the production of turbulent kinetic energy in the vicinity of the blade in order to improve the blade wake shape. Further details on this limiter can be found in the paper by Bode et al. (2014). All meshes were generated with AutoGrid 14.1 applying a structured meshing approach. Since the radii of the pressure tubes are comparatively small, a high mesh resolution was chosen to ensure a faithful reproduction of the smooth geometry by the mesh. A close-up of the mesh near the bump can be seen in Figure 6. For all models, the value of y+ was kept close to one to ensure an appropriate resolution of the boundary layer. All inlet boundary conditions were derived from experimental data acquired in MP1. The turbulent decay was adjusted via the specific turbulent dissipation rate so that the turbulent kinetic energy directly upstream of the leading edge matched the experimentally measured value.

Figure 6.

Close-up of the mesh near the bump.

Pressure-sided bump

In order to achieve mesh independence for every turbulence model, multiple mesh refinement studies were conducted. In the case of the pressure-sided bump, a single-passage approach (see Figure 7) was chosen, since the influence of the pressure-sided bump is mostly limited to the flow around the modified blade itself. Approximately 29 million cells were sufficient for the pressure-sided bump to achieve mesh independence with regard to the integral total pressure loss coefficient ωint when the k−ω turbulence model was used (see Table 1, first column). For the SST turbulence model, it was not possible to achieve full mesh convergence even with a mesh of 53 million cells (see Table 1, second column). However, since a continuation of the mesh independence study with even finer meshes was not feasible due to limited computational resources, the mesh with 53 million cells was considered to have a sufficiently fine resolution. The results of the k−ω model with activated VB limiter were almost identical to those of the SST model.

Figure 7.

Single-passage domain for the pressure-sided bump.

Table 1.

Integral total pressure loss coefficients resulting from the mesh independence.

Pressure-sided bump			Suction-sided bump
Cells [*106]	ωint/ωint,clean,exp		Cells [*106]	ωint,3/ωint,clean,exp,3
	k−ω	SST		k−ω	SST
3.97	2.82	2.27	35.06	4.65	3.84
22.12	2.77	1.85	52.70	3.69	3.85
29.48	2.85	2.14
53.03	2.89	1.93

In the experiment performed, only the central blade of the cascade was modified, while all other blades were identical to the nominal blade. In the numerical simulations, however, this setup cannot be implemented due to the periodic boundary conditions in the pitch direction. A single-passage simulation here is equivalent to an infinite cascade where each blade is modified. In the case of large-scale flow separation, however, this approach is of limited value because the modified blade can influence the adjacent nominal blades. In order to verify whether there is influence from the neighboring blades and, if so, how large their influence is, simulations containing several passages were performed. In these multi-passage simulations, periodic boundary conditions were still used, but only the central blade was modified, so that the numerical model is equivalent to an infinite cascade in which only every n-th blade is modified. Since the adjacent nominal blades could be resolved using a much coarser mesh, they were connected to the mesh of the modified blade via non-matching zonal interfaces (see Figure 8 for the five-passage model).

Figure 8.

Five-passage domain for the suction-sided bump.

For the pressure-sided bump, four setups were investigated using 1, 3, 5 and 7 blades respectively. In these setups, only the central blade was modified. Figure 9a shows the resulting total pressure loss coefficient distribution in MP2, normalized by ωmax,exp,clean. The analysis of ωint of the central blade revealed that the single-passage model deviates less than 0.01 in relation to the seven-passage model for both the k−ω model and the SST model (see Table 2). Therefore, the single-passage model was considered appropriate for the investigation of the pressure-sided bump. By comparing the y/t-coordinate of the total pressure loss coefficient maxima, the changes in the flow turning depending on the number of passages can be seen. If only one passage is included in the numerical model, the resulting wake exhibits less flow turning than the models with 3, 5 or 7 passages. When comparing these multi-passage models, no significant difference can be found. This deviation in the flow turning by the single-passage model is a drawback. However, since we are mainly interested in the losses generated by the bump, this deviation is considered to be acceptable when considering the computation time.

Figure 9.

Total pressure loss coefficients in MP2 for a varying number of blades, calculated with the k−ω turbulence model. (a) Pressure-sided bump. (b) Suction-sided bump.

Table 2.

Integral total pressure loss coefficient for varying number of simulated blades.

Pressure-sided bump			Suction-sided bump
Blades	ωint/ωint,clean,exp		Blades	ωint,3/ωint,clean,exp,3
	k−ω	SST		k−ω	SST
1	2.77	1.85	3	3.87	4.25
3	2.74	1.81	5	3.69	3.85
5	2.74	1.84	7	3.65	3.89
7	2.74	1.85	9	3.66	3.88

Clean blade

Before discussing the results of the modified blades, we first evaluate the performance of the CFD solver in the case of the clean blade by comparing the local and the integral total pressure loss coefficient to the experimental data. Figure 10 shows the normalized local total pressure loss coefficient for the experiment as well as the simulation results using the k−ω turbulence model both with and without VB limiter and the SST turbulence model for one pitch. All wakes were centered with regard to the experimentally determined wake center, which makes it easier to identify the shift in the turning of the flow. The k−ω model with activated VB limiter as well as the SST model are able to predict the shape of the wake flanks with very good accuracy. The peak value is overpredicted by ca. 35%. The simulation without VB limiter predicts the wake as being much wider than the experimental data due to an overproduction of turbulent kinetic energy around the blade. This overproduction leads to a wrong prediction of the transition location on the suction side, which is now located close to the leading edge, resulting essentially in a fully turbulent flow around the blade. The overestimation of the peak is similar to that simulated by the activated VB limiter. Table 3 indicates the integral pressure loss coefficients, normalized relative to the value of the experimental data of the clean blade. The setups with the k−ω model and VB limiter as well as the SST model are able to reproduce the experimental value with deviations of 0.1 and 0.07, respectively. Without the VB limiter, the larger wake leads to a 1.85 times larger integral total pressure loss coefficient compared to the experimental value.

Figure 10.

Comparison of experimental data for the clean blade with results from numerical simulations using the k−ω turbulence model both with and without VB limiter and the SST model.

Pressure-sided bump

To evaluate the additional total pressure losses caused by the pressure-sided bump, we investigated the total pressure loss coefficient in the wake of the modified blade. As the CFD results indicate that most of the additional total pressure losses are generated in the wake of the modified blade, the wakes of the adjacent blades have not been investigated further in this study. To improve the comparability of the wakes and to eliminate the influence of the single-passage model on the flow turning, all wakes were centered with regard to their loss maxima. Figure 11 shows the experimental local total pressure loss coefficient for both the modified and the clean blade, as well as the numerical results of a single-passage simulation with a pressure-sided bump for the different turbulence model settings mentioned previously. When comparing the two experimental data, we find that the wake of the modified blade is wider than that of the clean blade and the peak is approx. 12% higher. By calculating the integral total pressure loss coefficient, we can observe that the PSB leads to an increase in ωint by a factor of 1.9 in the experiment by widening the wake (see Table 4).

Figure 11.

Total pressure loss coefficient for the PSB blade.

The k−ω model, regardless of the VB limiter and the SST model overpredict the maximum local total pressure loss coefficient. Without activated VB limiter, the wake predicted by the k−ω model is too wide on both the suction side and pressure side. Again, like the in the case of the clean blade (see Figure 10), this setup leads to an overproduction of turbulent kinetic energy, which results in a fully turbulent boundary layer on the suction side. This, together with the overproduction of turbulent kinetic energy on the pressure side, leads to a wake which is much wider than measured in the experiment. For the k−ω model with activated VB limiter and the SST model, the transition on the suction side is correctly simulated and therefore the right wake flank matches the experimental data better. As a result, the setup “k−ω model” overpredicts ωint by 1.5 (see Table 4, second column). Using both the k−ω model with activated VB limiter and the SST model, ωint, normalized with regard to the experimental value, is calculated much more accurately with a value of 1.04 and 1.02, respectively (see Table 4, second column). When comparing the wakes calculated with k−ω VB and SST to their corresponding “clean” wakes in Figure 10, a clear widening of the wake especially at the left flank, which is associated with the pressure-sided bump, can be observed. In order to evaluate the performance of the turbulence models further, we normalized each integral total pressure loss coefficient by the corresponding integral total pressure loss coefficient of the clean blade for each turbulence model (see Table 4, first column). This analysis shows that the k−ω model with VB limiter and the SST model are able to closely match the trend shown by the experimental data. The k−ω model, however, predicts a loss increase of only 1.54 times the loss of the clean blade also simulated with the k−ω model. This is a result of the integral loss calculated by this model for the clean blade already being much larger than for the other turbulence models.

Using surface oil flow visualization, we further analyzed the flow distortions caused by the PSB on the surface of the pressure side. The resulting oil flow pattern was then compared to the numerically obtained wall stream lines for the k−ω model (see Figure 12a) and for the SST model (see Figure 12b). The wall stream lines for the k−ω model with VB were basically identical to those of the SST model and are therefore not shown here. Early transition via a separation bubble is evident from the accumulation of paint near the leading edge, followed by a coarse streamline pattern due to turbulent flow. The same flow behavior was observed for the clean blade near the leading edge by Hoesgen (2019), who conducted surface hot-film measurements, as well as oil flow visualization. Upstream of the rising flank of the bump, the flow detaches again, forming a separation bubble. The flow then reattaches on top of the bump. This flow behavior is similar to the flow over a forward-facing step. At the falling flank of the bump, the flow once again detaches and then reattaches downstream on the pressure side, forming a closed separation bubble. The formation of a closed bubble is favored by the concave surface of the pressure side. The lines perpendicular to the flow direction, which are visible downstream of the bump, are caused by the application of the paint with brush strokes in this direction. In this area, the paint did not follow the flow because the velocity in the separation bubble was too low. This flow behavior is correctly reproduced by all numerical setups used, which is illustrated by the overlying wall stream lines in Figure 12. Compared to the k−ω model, the SST model predicts a slightly larger separation bubble on top of the bump. Apart from this, both numerical results are in good agreement with the oil flow visualization, considering the rather qualitative nature of oil flow visualization. One further insight is given by the Mach number distribution in the midspan of the PSB blade normalized by the inlet Mach number in Figure 13. The previously described separation upstream, and downstream as well as on top of the bump, are visible.

Figure 12.

Oil flow visualization with overlaid wall streamlines for the PSB blade. ①: leading edge, ②: rising flank, ③: falling flank, ④: trailing edge. (a) Wall streamlines of k−ω model. (b) Wall streamlines of SST model.

Figure 13.

Normalized Mach number distribution in midspan of the PSB blade. (a) k−ω model. (b) SST model.

In conclusion, the numerical simulations are able to capture the trends of the experiments quite well. All turbulence models lead to a considerable increase in the integral total pressure loss coefficient, ranging from an increase by a factor of 1.54 to 1.81 caused by the PSB. The comparison between the oil flow visualizations and the numerically determined wall stream lines further demonstrates that the general flow physics is satisfactorily reproduced. Only the local distributions of ω reveal the weaknesses of the numerical simulations as they are unable to match the experimental distribution. This is to be expected however, since RANS models rarely perform well for flow cases with large separations. Overall, this study demonstrates that a PSB has a significant effect on the losses generated by a blade and that this effect can be reproduced with RANS simulations by application of a single-passage model.

Suction-sided bump

Analogous to the pressure-sided bump, Figure 14 shows the local total pressure loss coefficient for the blade modified with a suction-sided bump (SSB) and the clean blade for both the experimental and numerical results. As previously discussed, a domain with five blades was used to simulate the flow. As the SSB only significantly influences the losses generated in the central three passages, those results are shown in Figure 14. Again, all wakes were centered with regard to the experimentally determined wake center. The k−ω model with VB limiter did not converge for the suction-sided bump and is therefore not shown.

Figure 14.

Total pressure loss coefficient of the SSB blade.

From Figure 14, it is immediately apparent that the losses caused by the SSB are much larger than those caused by the PSB. Compared to the clean blade, the peak value of the suction-sided bump is 2.2 times larger. The flow deflection is reduced, as shown by the positive y-shift of the wake. Furthermore, the wake is much wider and extends into the wake of the adjacent blade, which can be seen by the fact that ω does not reach the freestream loss level of close to zero at y/t=0.9, resulting in the merging of both wakes. This once again confirms that a single-passage numerical model is not sufficient for the suction-sided bump. In the wake of the suction side-adjacent blade, additional losses are generated as indicated by a higher peak value of 15% and a wider wake compared to the clean blade. This is caused by a local positive incidence in the inflow of this blade due to the bump blocking the passage and the associated redistribution of the mass flow. Compared to the clean blade, the flow deflection is reduced. The influence on the wake adjacent to the pressure side is negligible. To account for the influence of the suction-sided bump on the adjacent blades, the integral loss coefficient is calculated for three wakes. The suction-sided bump increases the loss of the three blades by a factor of 4.10, as given in the first column of Table 5.

As seen for the pressure-sided bump, both the k−ω model and the SST model overpredict the maximum local total pressure loss coefficient. Again, the k−ω model manages to predict the left side of the wake more effective than the SST model, which shows better agreement with the right side of the wake. In contrast to the experimental data, both models predict that the wake reaches the freestream loss level. According to the k−ω model, this is the case at y/t=0.65 whereas the wake of the SST model is wider and reaches the freestream level at y/t=0.8 and thus closer to the experiment. For the adjacent blades, the SST model performs significantly better than the k−ω model since it is better able to predict the losses of the clean blade. A further difference is the prediction of the turning of the flow, which is underestimated by the k−ω model whereas the SST model shows an overprediction. As both turbulence models predict a smaller wake compared to the experimental data, they both underestimate the increase in the integral total pressure loss coefficient ωint,3. The SST model performs slightly better than the k−ω model by deviating only 6% from the experimental value instead of 10%. Like for the PSB blade, we can normalize ωint,3 with the corresponding value for each turbulence model for the clean blade. This will enable us to assess whether the turbulence models can predict the relative loss increase correctly (see Table 5, first column). From this evaluation, we conclude that the SST model underpredicts the loss increase with a factor of 3.55 compared to the experiment (factor of 4.10). The relatively poor agreement with the experiment, that is a loss increase of only a factor of 1.97 for the k−ω model, is mainly due to the higher clean blade loss when the VB limiter is not being used (see Table 3).

To analyze the reason for the large difference between the two models and to quantify which of these describes the flow physics more accurately, we again performed an oil flow visualization. The results for the suction side with the bump are depicted in Figure 15, with overlaid wall streamlines for both turbulence models. On the suction side, there is no transition with a laminar separation bubble at the leading edge due to a favorable pressure gradient. Hoesgen (2019) determined that the transition occurs between 30% and 50% of the axial chord length, which in this case coincides with the location of the bump. The separation bubble upstream of the bump therefore triggers the transition from laminar to turbulent. At the top of the bump, the streamlines are curved toward the midspan and are not parallel to the inflow and the channel walls. Downstream of the bump, the backward-facing step again causes a separation bubble. Unlike for the pressure-sided bump, there is no reattachment line, indicating a fully separated flow with an open separation bubble extending beyond the trailing edge. In the vicinity of the bump, large amounts of paint accumulate near the cascade walls.

Figure 15.

Oil flow visualization with overlaid wall streamlines for the SSB blade. ①: leading edge, ②: rising flank, ③: falling flank, ④: trailing edge. (a) Wall streamlines of k−ω model. (b) Wall streamlines of SST model.

The area upstream of the bump is predicted similarly by both models, correctly predicting the separation bubble at the forward-facing step. However, the results for the surface of the bump and downstream of the bump differ significantly. A small closed separation bubble is present for the k−ω model, resulting in a reattached flow on the bump surface with inflow parallel streamlines. In contrast, the SST model shows that the flow does not reattach at the bump surface, as indicated by the curved wall streamlines which are similar to the oil flow streamlines. While both models predict a fully separated flow downstream of the bump, the SST model exhibits two vortices that correspond to the accumulation of paint near the cascade walls. In these two areas, paint accumulates and is then entrained by the flow and carried away from the blade surface. In conclusion, this oil flow visualization shows that the occurring flow phenomena are much more effectively modeled by the SST model. The results of the k−ω model can be regared as physically incorrect.

The difference between the k−ω model and the SST model can again be seen by comparing the Mach number distribution in the blade midspan as presented in Figure 16. The wake and the separation bubble are smaller for the k−ω model because the flow reattaches at the bump surface, whereas for the SST model the separation at the beginning of the bump merges with the separation downstream of the bump to form a large separation bubble. This results in a wider wake, as indicated by the local total pressure loss coefficient in Figure 14. Due to the larger separation bubble, the turning of the flow is lower, resulting in the shift of the wake in a positive y-direction.

Figure 16.

Normalized Mach number distribution in midspan of the SSB blade. (a) k−ω model. (b) SST model.

Overall, these experiments show that the addition of a bump to the suction side of a blade leads to an increase in the total pressure loss of factor 4.1 over three passages. This drastic increase is only reproduced by the SST turbulence model, which is likewise the only model able to simulate the detached flow over the bump correctly. Considering the challenging flow physics present in this case, the numerical simulation is able to reproduce the experimental results with good accuracy.