Baseline compressor

The investigated TUDa-GLR-OpenStage is a single-stage high-speed axial compressor, representing a typical front stage of a high-pressure compressor in a commercial turbofan engine. The compressor stage, as shown in Figure 1, includes a blisk rotor with 16 radially stacked CDA-airfoils, an optimized 3D-shaped stator with 29 blades, and an outlet guide vane (OGV) that straightens the flow. The crucial design parameters of the investigated stage can be found in Klausmann et al. (2022). The rotor was initially designed and tested by MTU in 1994 and has been investigated extensively in a series of research (Hoeger et al., 1999; Bergner et al., 2006; Muller et al., 2011). The rotor blades are highly cambered near the hub and thin near the tip. At the design condition, the rotor running tip gap size is approximately 0.75 mm, and the rotor hub fillet radius is 5 mm. The stator is designed conjointly between GLR and German Aerospace Center (DLR). It was optimized via an automated multi-objective optimization process to suppress the separation size (Bakhtiari et al., 2015). The stator blades have a forward sweep feature near both endwalls and a bow feature towards the pressure surface near the casing. The shapes of the stator fillets at both endwalls are prescribed by a digitized geometry file.

Figure 1.

Illustration of TUDa-GLR-OpenStage test rig.

The TUDa-GLR-OpenStage was tested on the transonic compressor rig of GLR, which can measure the steady-state performance, the aerodynamic instabilities, and the blade vibration levels of the compressors. The schematic of the test facility is shown in Figure 1. Before reaching the compressor core, the inlet flow passes through an inlet throttle, a settling chamber and a mass flow measurement section. The pressure and temperature measured in the settling chamber reflect the incoming flow property. At the compressor core inlet section ME15, the total pressure profile of the incoming flow is measured by a boundary layer rake, and the total temperature profile is assumed to be uniform, with its value the same as that measured at the settling chamber (i.e., neglecting the heat transfer effect). The total pressure and total temperature measured at the settling chamber are used to correct the mass flow and the rotational speed to the International Standard Atmosphere (ISA) condition. A DC motor with a gearbox drives the compressor. Shaft input torque and rotor speed is measured using a torque meter. Further details of the experimental setup can be found in Klausmann et al. (2022).

The quantities of interest in the measurement campaign include the rotor exit profile at section ME21, the stator exit profile at section ME30 and the overall performance of the compressor. Among the overall performance quantities, the total pressure ratio π∗ and the total temperature ratio τ∗ are calculated by the area-averaged probe data at sections ME15 and ME30; the isentropic efficiency η∗ is calculated using the probe-based π∗ and the shaft power. For a fair comparison between the experiment and CFD, πCFD∗ and τCFD∗ are based on the area-averaged quantities, whereas ηCFD∗ is based on the area-averaged πCFD∗ and mass-averaged τCFD∗.

Endwall configuration

After a careful examination of the manufactured compressor geometry, the CAD geometry model and the CFD geometry model, the differences between the measured and the workshop geometries are summarized as follows:

CFD solver

The commercial three-dimensional Reynolds-Averaged Navier-Stokes flow solver, Ansys CFX (version 2021), is used to perform the steady simulations in this paper. Ansys CFX uses an element-based finite volume method to discretize the RANS equations based on unstructured meshes. It uses an implicit coupled solver that solves all the hydrodynamic equations as a single system. The linearized equations are solved by the Incomplete Lower Upper (ILU) factorization technique, accelerated by an algebraic multigrid method. A pseudo-time-stepping algorithm with an automatic time scale technique is used for steady-state calculations. For the best practice of turbomachinery simulation, the Menter k−ω Shear Stress Transport (SST-2003) turbulence model (Menter et al., 2003) and the second-order accurate high-resolution advection scheme (ANSYS, 2021) are recommended.

Grid topology and boundary conditions

In this work, Numeca AutoGrid5 is used to generate the grids. The main flow region of the rotor, the stator and the OGV are meshed using the O4H-type topology; the rotor tip clearance is meshed using the butterfly topology; the inlet duct, the outlet duct and the leakage path are meshed using the H-type topology. To achieve good resolution in the boundary layer, the area-average y+ values of the rotor grid and the stator grid are 1.05 and 1.28, respectively. Endwall features including clearances and fillets of the rotor and the stator are considered. The final grids for a periodic passage of the rotor, the stator, the OGV and the leakage path have 3.3, 1.8, 0.8 and 2.1 million grid points, respectively. Such a grid density is the same as that of the fine mesh in the previous work (He et al., 2023), which has met the grid independence requirement (i.e., discretization error of total pressure ratio below 0.7%).

The flow domain and boundary conditions are illustrated in Figure 3. The flow domain contains one blade passage for each blade row, with the periodic boundary condition applied to the side boundaries. The inlet plane is set at the stage inlet section ME15, whose boundary conditions are prescribed by the total pressure and temperature profiles from the experiment at the design speed¹ [1]. An outlet duct of 1.5 times the compressor axial length is attached to the OGV outlet. The radial equilibrium backpressure boundary condition is imposed at the outlet, and the difference in the average backpressure between the adjacent operating points is 100 Pa when approaching the stall limit. At the rotor-to-stator and stator-to-OGV interface, the mixing plane boundary condition is used. In the case of the stator hub cavity, the grids of the primary flow passage are the same as that without the cavity. At the rotor-to-cavity and stator-to-cavity interface, the frozen rotor boundary condition is used.

Figure 3.

Illustration of grid topology, flow domain and boundary conditions of TUDa-GLR-OpenStage.

Overall performance

The stage performance characteristics with and without the rotor casing pinch are presented in Figure 4. In these plots, the solid curves with open symbols represent simulation results; the solid squares denote the experimental data; the error bars represent the measurement uncertainty² [2]. Results show that the trapezoid-shaped pinch moves the π∗ and η∗ characteristics curves towards the low mass flow direction, which is due to a reduction in the rotor throat area. Such a translation effect becomes more evident when increasing the operating speed. Consequently, the case with the rotor casing pinch shows a better agreement with the measured data. Specifically at the design speed, the casing pinch reduces the total pressure ratio by 0.03 and 0.01 at the PE and the NS points; the casing pinch also reduces the efficiency by 0.2% at the PE point and increases it by 0.9% at the NS point.

Figure 4.

Effect of rotor casing pinch on predicting the TUDa-GLR-OpenStage performance characteristics. (a) total pressure ratio (b) isentropic efficiency.

Radial profiles

To examine the effect of rotor casing pinch in detail, the circumferentially area-averaged radial profiles downstream of the rotor and the stator are presented in Figure 5. In these plots, the hollow squares and circles denote the experimental results, and the curves represent the simulation results.

Figure 5.

Effect of rotor casing pinch on predicting the circumferentially mass-averaged radial profiles. (a) 100% speed, rotor exit (ME21). (b) 100% speed, stage exit (ME30). (c) 65% speed, rotor exit (ME21). (d) 65% speed, stage exit (ME30).

For the rotor exit profiles shown in Figure 5a, the rotor casing pinch reduces total pressure ratio π∗ and absolute flow angle α∗ especially at the upper 50% spans and at the PE condition. Note that the major effect of the pinch is a reduced throat area of the rotor. When comparing at the same mass flow, the case with the pinch will have a lower incidence at the upper spans and thus a reduced work input and π∗. Since the slope of the m−π∗ characteristic is steeper at the PE condition than the NS condition, as shown previously in Figure 4a, the performance quantities at the PE condition are more susceptible to the incidence change introduced by the pinch. Comparing both simulation results with the measured data, the pinch case matches better with the measured π∗ and α∗; in particular, α∗ is predicted with good accuracy, but minor deficiency of π∗ persists near 90% span. Such deficiency can be caused by the turbulence model deficiency or the asymmetric untwisting effect of the running geometry (Lu et al., 2019), which was observed during concurrent PIV measurements and needs further investigation.

For the stage exit profiles shown in Figure 5b, the pinch-induced reduction of π∗ and work input generally propagates from the rotor to the stator, leading to better agreement with the measured data. The pinch case shows good accuracy in predicting τ∗ at both PE and NS conditions, but it still over-predicts π∗ at the lower 20% spans of the PE condition and the lower 60% spans of the NS condition. Such an over-prediction is not observed in the rotor exit profile. Hence, it is likely caused by the stator hub geometric uncertainty and error (e.g., hub cavity).

To reveal the pinch effect at part speeds, the radial profiles at 65% speed are exhibited in Figure 5c and d. In general, the observations at 65% speed are similar to that at 100% speed: the pinch slightly reduces π∗, α∗ and τ∗ at the upper 50% spans at both the PE and NS conditions, leading to better agreement with the measured data. The differences are mainly twofold. Firstly, the pinch-induced reduction of π∗, α∗ and τ∗ at the PE condition of 65% speed is less significant than that of 100% speed. This is because the slope of the m−π∗ characteristic is steeper (i.e., more sensitive to the incidence change induced by the pinch) at the PE condition at 100% speed than that of 65% speed, as shown previously in Figure 4a. Secondly, the rotor exit π∗ and stage exit π∗ are over-predicted at all spans at 65% speed, whereas only the near-casing rotor exit π∗ and the near-hub stage exit are over-predicted at 100% speed. This can potentially be explained by the error in the inlet boundary condition and the rotor running tip clearance size, whose values are measured at the 100% speed. For future research, the values measured at the 65% speed need to be tested.

Loss mechanism analysis

The rotor casing pinch is expected to change the rotor near-casing flow field and therefore the local entropy production. In this section, the mechanism by which the pinch changes the compressor efficiency is analyzed in detail. The analysis is based on the streamwise efficiency deviation Δη(m) and the spanwise efficiency deviation Δη(n) (Appendix A), which measure the difference of the dimensionless entropy between the smooth casing case and the pinched casing case. In other words, Δη(m) and Δη(n) represent the efficiency gain from the pinched casing at the given streamwise coordinate m or spanwise coordinate n.

The streamwise efficiency deviation is plotted against the normalized axial location in Figure 6a. In this plot, solid curves and dashed curves represent the PE condition and the NS condition, respectively. Each of these curves is composed of 58 points in the axial direction, with the Δη value of each point calculated from Equation 3 in Appendix A. The horizontal axis represents the axial location normalized by the axial distance between the stage inlet and the exit (bottom axis) or by the rotor axial tip chord (top axis). In general, the change of Δη for all the cases occurs mainly in the rotor passage; the net change of Δη at the stage exit is about 0.1% for the PE conditions and 0.7% for the NS conditions at both 65% and 100% speed, which is consistent with the data presented in Figure 4. For the PE condition at 100% speed, Δη increases initially between −1.0 and 0.5 Ct and then drops between 0.5 and 1.5 Ct, which indicates two competing flow mechanisms change the rotor efficiency simultaneously. For the NS condition at 100% speed, Δη not only increases between −1.0 and 0.5 Ct but between 2.2 and 3.3 Ct, implying the rotor casing pinch reduces loss in the stator. For the other conditions at 65% speed, Δη increases before 0.5 Ct and then stays at a similar level in the downstream locations, indicating the rotor casing pinch has a neutral effect on the downstream stator.

Figure 6.

Distribution of efficiency deviation between cases with and without the rotor casing pinch. (a) Streamwise distribution. (b) Spanwise distribution.

To help pinpoint the change of efficiency further, the spanwise efficiency deviation at the stage exit is illustrated in Figure 6b, where the Δη value is calculated from Equation 4 in Appendix A. For the PE condition at 100% speed, the pinch increases efficiency between 75% and 95% span but reduces it between 10% and 75% span. For the other conditions, the pinch generally increases the efficiency in the upper 50% span.

Based on the observations in Figure 6, the following regions of flow have evident effects on the compressor efficiency and hence need investigation:

Regarding the PE and NS conditions at 100% speed, the static pressure contours and the limiting streamlines on the rotor suction surface and the rotor hub surface are presented in Figure 7. For all the cases presented, a hub corner separation and a shock-induced tip separation are observed. At the PE condition, the pinch pushes the shock front to a further downstream location, reduces the spanwise regions affected by the tip separation (from 36% to 31% span) and thus reduces the loss near the casing: on the other hand, the pinch also enlarges the hub corner separation size (from 46% to 48% span), which increases the loss near the hub. These competing flow mechanisms are responsible for the bump shape of Δη shown in Figure 6a. At the NS condition, the pinch also reduces the spanwise location affected by the tip separation (from 52% to 51% span), but it has an almost neutral effect on the hub corner separation. Therefore, the net contribution to efficiency is higher in the NS condition than in the PE condition.

Figure 7.

Meridional view of static pressure contour and surface streamlines on the hub surface and the suction surface of the rotor; ➀: corner separation; ➁: shock-induced separation; ➂: shock front.

Regarding the NS condition of 65% speed, the relative Mach number contours and the relative streamlines are compared in Figure 8. In both cases, a tip leakage vortex is formed due to the shear between the tip leakage flow and the main flow. The difference is that the blockage cell featured by the low Mach number is smaller in the case with the pinch. Therefore, the pinch reduces the mixing loss associated with the tip blockage cell.

Figure 8.

Relative Mach number contour and relative streamlines in the rotor passage with and without the rotor casing pinch.

Overall performance

The stage performance characteristics with and without the stator hub cavity are presented in Figure 9, where the simulation results are represented by the solid curves with open symbols and the measured data are represented by the solid squares. From the first glance of Figure 9, there are no visible changes in the global performance characteristics with or without the cavity. Further examinations of the characteristic values of the compressor performance quantities show that the cavity does not change π∗ and mc, but it reduces η∗ by 0.5% and 0.4% at 100% and 65% speeds, respectively. Such an effect slightly improves the agreement with the experiment.

Figure 9.

Effect of stator hub leakage flow on predicting the TUDa-GLR-OpenStage performance characteristics. (a) total pressure ratio. (b) isentropic efficiency.

The stator hub cavity effect is proportional to the cavity leakage flow rate. In Figure 10, the simulated leakage-to-inlet mass flow ratio is plotted against the inlet mass flow rate. It shows that the investigated cavity seal only allows between 0.15% to 0.25% of leakage-to-inlet mass flow ratio at the PE and NS conditions. According to the previous research (Wellborn and Okiishi, 1999), a leakage mass flow ratio of 0.25% only leads to an efficiency penalty between 0.2% and 0.6% in a multistage compressor, which is consistent with the observations in this work. Although the stator hub cavity investigated in this work does not have an evident effect on the global performance, its effects on the local flow fields still need further check.

Figure 10.

Proportion curve of leakage flow to mainstream under different rotational speed conditions.

Radial profiles

To examine the effect of the stator hub cavity in detail, the circumferentially area-averaged radial profiles downstream of the stator are presented in Figure 11, where the hollow scatters denote the experimental results and the curves represent the simulation results. Results show that the cavity does not affect the distribution of τ∗, which is expected because τ∗ is mainly dependent on the rotor work input. The effect of the cavity is mainly on the near-hub π∗ prediction: at the PE condition of 100% speed, the NS condition of 100% speed and the NS condition of 65% speed, the largest reduction of π∗ by the cavity is 2.1%, 2.2% and 1.3%, respectively. According to the previous research on an earlier version of the TUDa-GLR-OpenStage compressor (Zhu et al., 2019), a leakage mass flow ratio of 0.3% can lead to a 1% to 2% reduction in total pressure ratio below the 20% span, which is consistent with the current research. Although the inclusion of the stator hub cavity slightly improves the agreement with the measured data, deficiency persists especially at the NS condition at 100% speed. This is likely caused by the under-estimation of the seal throat area in the current simulation. Further parametric study of the seal throat area is needed to confirm this hypothesis.

Figure 11.

Effect of stator hub cavity on predicting the circumferentially mass-averaged radial profiles. (a) 100% speed, stage exit (ME30). (b) 65% speed, stage exit (ME30).

Loss mechanism analysis

The stator hub cavity is expected to change the stator near-hub flow fields and therefore, the local entropy production. In this section, the mechanism by which the cavity changes the compressor efficiency is analyzed via the streamwise efficiency deviation Δη(m) and the spanwise efficiency deviation Δη(n) (Appendix A). In this context, Δη(m) and Δη(n) represent the efficiency change due to the stator hub cavity leakage at the given streamwise coordinate m or spanwise coordinate n.

For the streamwise development of efficiency deviation shown in Figure 12a, Δη for all cases stays at almost the same value in the rotor passage, indicating the stator hub cavity has limited effects on the upstream rotor: at the front end of the stator hub cavity, Δη suddenly drops due to the mixing with the injected high-entropy leakage flow: at the rear end of the cavity, Δη immediately increases due to the bleeding of the high-entropy leakage flow. For the spanwise distribution of efficiency deviation shown in Figure 12b, the efficiency penalty due to the stator hub cavity is at the lower 30% spans. The observations above suggest that the flow field of the stator near the hub has a noticeable effect on the compressor efficiency. Since the results of 65% speed are similar but less evident than that of 100% speed, only the PE and NS conditions at 100% speed will be presented for brevity.

Figure 12.

Distribution of efficiency deviation between cases with and without the stator hub cavity. (a) Streamwise distribution. (b) Spanwise distribution.

The static pressure contours and the limiting streamlines on the stator suction surface and the stator hub surface are presented in Figure 13. For the PE condition of 100% speed, a hub corner separation and a near-tip trailing edge separation are observed. When considering the stator hub cavity, the hub corner separation size is enlarged (from 10% to 24% span), but the near-tip trailing edge separation is not affected. For the NS condition of 100% speed, a hub corner separation, a mid-span trailing edge separation and a tip corner separation are observed. The cavity again increases the size of hub corner separation (from 18% to 55% span), but the mid-span separation and near-tip separation are barely affected (slightly reduced from 38% to 32% span). The increment of corner separation size at the NS condition is larger than that at the PE condition, which is due to a higher leakage mass flow rate shown in Figure 10. Therefore, it can be concluded that the stator hub cavity leakage enhances the hub corner separation and hence reduces the compressor efficiency and total pressure ratio. Such an effect will become more prominent if the leakage flow ratio increases (i.e., larger seal throat area).

Figure 13.

Meridional view of static pressure contour and surface streamlines on the hub surface and the suction surface of the stator; ➀: corner separation; ➁: trailing edge separation.