Impact of Blowing and Density Ratio on the Film Cooling and Heat Transfer in an Aggressive Turbine Center Frame

The continuous increase in turbine inlet temperature to fulfill the stringent environmental goals in aviation [1,2] has also brought the turbine center frame (TCF) more and more into the focus of thermal investigations. The TCF, shown in Fig. 1, is a duct that connects the high-pressure turbine (HPT) to the low-pressure turbine (LPT). It is commonly used in modern high-bypass ungeared turbofan engine architectures, such as the GE9X, GEnX, and GP7000, for long-range aircraft. The TCF belongs to the superordinate family of intermediate turbine ducts and can be differentiated from the turning vane frame by a larger radial offset between the inlet and outlet and vanes that are nonturning. These nonturning vanes are called struts and are usually thick, symmetrical, and airfoil shaped. The struts accommodate supply lines and carry the rear bearing load of the HPT shaft. The TCF is the first engine component in the hot gas path without film cooling. In current engines, the TCF inlet temperature already exceeds 1000 °C [4]. Additionally, a patent already exists to introduce ceramic matrix composites in TCFs [5], which underlines the increasing thermal stress and importance of thermal investigations on these ducts.

In the past, the TCF was primarily the focus of aerodynamic investigations with the scope to minimize its total pressure loss and optimize the outflow for the downstream LPT. These efforts, undertaken by several research groups, are thoroughly reviewed by Göttlich [6]. An important step forward in the research of TCFs was made by Zerobin et al. [7,8] by investigating the influence of HPT purge flows on TCF performance. They found that increasing the purge mass flows enhanced the HPT stator and rotor passage vortices and, consequently, increased the pressure loss in the downstream TCF. In addition, they reported that the HPT aft hub purge is entrained by counterrotating vortex pairs into longitudinal purge streaks. These purge streaks were found to be located along the TCF hub surface. The existence of these purge streaks was later confirmed by Patinios et al. [9] by tracing the purge migration in a TCF using the seed gas concentration technique. Also, Patinios et al. [9] showed that the HPT aft hub and aft tip purge flows are still confined in high-concentration boundary layers on both endwalls at the TCF inlet plane, indicating a significant cooling potential for the TCF. This purge cooling potential, sometimes referred to as “phantom cooling,” was never investigated before this series of studies in open literature.

Engine-relevant full surface coverage data on the thermal behavior of TCFs is very sparse. Arroyo Osso et al. [10] were the only team to publish 2D heat transfer measurements of a TCF's whole hub, strut, and shroud surfaces where an HPT was operating upstream. However, their test setup did not include purge flows and, therefore, did not shed light on the HPT purge cooling potential for the TCF.

To fill this gap, the Opti-TCF project was founded with the aim of thorough heat transfer and purge film cooling measurements in an aerodynamically aggressive TCF. All investigations were conducted at the Institute of Thermal Turbomachinery and Machine Dynamics (ITTM) at Graz University of Technology. As part of the Opti-TCF project, a sector cascade of the aggressive TCF was first 3D printed [11] to develop the thermal measurement technique, which is also used in this article, and to carry out the first fundamental measurements. These first heat transfer and purge film cooling measurements were conducted with a “clean inflow” condition (no rotor upstream) and proved a purge cooling potential on the hub of up to η = 0.4 for nominal purge rates. Then, a purge flow parameter study [12] was conducted in this sector rig, where the purge film cooling along the TCF hub was found to scale with the blowing ratio, and a nonlinear scaling function was developed. After maturing the measurement technique [12] in the sector cascade rig, it was transferred to the Mach-similar Transonic Test Turbine Facility (TTTF), the facility with the highest technology readiness level of the institute. There, a fully purged HPT was operated upstream of the TCF, and the heat transfer and the purge film cooling effectiveness were measured at the aero design point (ADP) [13]. These first combined heat transfer and film cooling measurements of an aggressive TCF gave valuable insights into the aerothermal flow physics of TCFs under engine-representative conditions. The existence of the longitudinal purge streaks was confirmed as the film cooling distribution on the TCF hub showed longitudinal streaks of increased effectiveness. Furthermore, the heat transfer coefficient distribution on the hub also showed longitudinal streaks of increased heat transfer. However, the high heat transfer streaks were alternately arranged with the high film cooling streaks. In other words, poor film cooling coincided with high heat transfer and vice versa. This disadvantageous combination was traced back to the effect of the HPT stator wake and a counterrotating vortex pair that emanates from the interaction of the lower passage vortices of the HPT rotor and the HPT stator. The same high heat transfer streaks were also reported by Arroyo Osso et al. [10] for a less-aggressive TCF.

Furthermore, in this first series of TTTF measurements [13], it was shown that the blowing ratio is the dominant film cooling parameter at ADP and nominal purge flowrates. A change of approximately 20% in density ratio (DR) did not change the heat transfer or film cooling results at all. The reason is the very low blowing ratio of HPT purge flows. For blowing ratios, M, below 0.5, and attached cooling films, Goldstein [14] has already reported that a density ratio insensitive regime exists. In the review of Bogard and Thole [15], this regime is stated to exist until M ≤ 0.2. In contrast to turbine film cooling with rows of holes, the purge film cooling in TCFs is a slot film cooling problem. The flow physics behind slot film cooling is simpler and more straightforward than for hole film cooling, and, therefore, a multitude of correlations was already available in the sixties as reviewed by Goldstein [14]. Despite the low purge blowing ratios in the previous study [13], the purge injection still led to heat transfer intensification on the TCF hub of approximately 10% close to the cavity exit. This is only a mild increase compared to the heat transfer intensification of turbine film cooling. For instance, Hummel et al. [16] reported for a turbine endwall with several rows of cooling holes and a blowing ratio around one a heat transfer intensification of up to +100%.

This article investigates the impact of varying HPT purge blowing and density ratios on heat transfer and purge film cooling in a TCF. For this purpose, higher and lower than nominal purge flowrates are investigated, and CO₂ is used to increase the density ratio artificially. Not only is the purge film cooling effectiveness investigated for varying purge flow parameters but also the corresponding heat transfer intensification is measured. The insensitivity of heat transfer and film cooling to changes in the density ratio, as found in the preceding study [13], is now assessed for higher than nominal purge blowing ratios. Finally, an attempt is made to scale the film cooling results with correlations for slot film cooling.

As this is a purge flow parameter study based on the nominal measurements of the previous work [13], the identical test facility, test vehicle, and measurement technique were used here, and this section is therefore kept short.

All measurements were again performed in the TTTF at Graz University of Technology. In short, the TTTF is a continuously operating, open-circuit, cold-flow, and Mach-similar test facility, thoroughly explained in the studies by Erhard and Gehrer [17] and Neumayer et al. [18]. The purge flow conditioning system used to supply the four HPT purge flows is described in the study by Steiner et al. [19]. In essence, every purge flow is individually mixed from a hot and a cold supply tank using two needle valves.

The test vehicle is a 1.5-stage HPT-TCF-LPT vane setup illustrated in Fig. 2. The HPT is uncooled, i.e., it has no cooling holes or trailing edge cooling, but it is fully purged with four individually adjustable purge flows. The unshrouded HPT is aerodynamically engine-representative of the second stage of a state-of-the-art turbofan HPT. The two hub purge flows are fed into the forward (FWD) and aft (AFT) wheelspace cavities and, from there, injected into the main flow through engine-representative rim seal geometries. The two tip purge flows are fed into the FWD and AFT tip cavities and are then injected perpendicularly into the main flow through axial slots. The HPT is followed by the investigated TCF, where the film cooling effectiveness of all four HPT purge flows is measured on the hub, strut, and shroud. The HPT vane count per TCF strut is exactly four, making the flow field in the TCF periodic (and the same in every TCF passage). After the TCF, a row of LPT vanes completes the 1.5-stage setup and sets an engine-representative outlet flow condition for the TCF.

The test vehicle was operated under Mach-similarity and with matching Strouhal number by matching the corrected HPT speed. As a result, the velocity triangles are similar to the real engine. The corrected mass flow is automatically consistent between different test runs by setting a constant rig outlet pressure with a 0.6 MW suction blower. The effect of rotation on the film cooling results in this study is limited to the fact that the flow field at the TCF inlet and the swirl of the AFT hub purge flow are engine representatives. There is a rotational effect on the FWD purge flows, but the cooling potential of the FWD purge flows for the TCF is negligible, as will be shown.

All measurements in this study were conducted at the ADP of the test vehicle, given in Table 1. The respective uncertainty of each operating parameter is given in the bracket next to the value. While the ADP was always maintained, altogether six test cases with different purge flow conditions were investigated, given in Table 2. Here, the 0% purge case corresponds to the no purge case and the 100% purge case corresponds to the nominal purge case in the previous study [13]. Starting from the 100% purge (nominal purge) case, all four HPT purge mass flows were either reduced or increased simultaneously to hold the HPT tip gap constant. An isolated increase or a decrease of one single purge would have led to either a tighter or looser HPT tip gap and, consequently, to a significant operating point deviation.

The 0% purge case is the uncooled baseline case for the infrared (IR) film cooling measurements. With the increasing purge mass flow (50%–100%–200% purge case), the purge blowing ratios increase accordingly, but the purge density ratios also increase because, at higher purge mass flows, the purge flows heat up less in the pipes and cavities. In the CO₂ purge cases, the AFT hub purge flow was supplied with as much CO₂ from the seed gas system as possible to artificially increase the AFT hub purge density. While this was done, the AFT hub blowing ratio and all other purge flows were held constant. The 100% CO₂ purge case here corresponds to the CO₂ purge case in the previous study [13]. The CO₂ purge cases are intended to demonstrate the insensitivity of the heat transfer and the film cooling in the TCF to variations in the density ratio for the given operating and purge parameters.

The TCF geometry shown in Fig. 2 is aerodynamically more aggressive than current state-of-the-art TCFs in modern direct-drive two-spool turbofans. Figure 2 is, therefore, distorted for confidentiality reasons. The radial offset to axial length ratio (Δr/L), a typical aggressiveness metric for TCFs, is significantly higher than 0.5. Typical for all TCFs, the outlet-to-inlet area ratio is greater than 1, which means that the TCF is a diffuser. The chord-to-axial duct length ratio (c/L) of the struts is 0.822. These design parameters result in pronounced concave and convex bends on the TCF endwalls and, consequently, quite an intricate pressure distribution throughout the TCF that is prone to separation.

The (red) circles in Fig. 2 illustrate thermocouples, and the (green) squares illustrate pressure taps. At least three thermocouples and pressure taps are evenly distributed around the circumference in all four cavities to monitor the purge flows.

As in the previous article [13], a thermal technique and a mass transfer measurement technique were used. The thermal measurement technique combines IR thermography and heating foils and is thoroughly explained in the open-access publication by Jagerhofer et al. [12]. The thermally instrumented TCF sector is shown in Fig. 2, and the thermal technique is described in the following: A FLIR T650sc microbolometer IR camera observes the hub and strut surfaces through a broad-band antireflection-coated germanium window. The camera is moved with a five-axis traversing system to 21 different positions to capture the whole hub and both strut surfaces. These thermally investigated surfaces are re-made in this sector from a quasi-adiabatic polymethacrylimide foam (Rohacell Hero 200) with a thermal conductivity of 0.043 W/mK. On top of this quasi-adiabatic surface, tailor-made and flexible heating foils, carefully designed to deliver constant heat flux, are glued. The heating foils are made up of multiple layers. From the bottom, the first layer is a 75 µm thick Kapton isolation layer, followed by the 35 µm thick active layer of etched copper conductor tracks. Then, a 50 µm thick Kapton layer follows. Next, a full sheet of 35 µm copper is added on top to laterally distribute the heat between the hot copper conductor tracks and the cold interstitial gaps. The final layer on top is once more a 75 µm Kapton layer. Without glue, the total thickness of the heating foil is 270 µm. On top of the heating foils, 15 flat, tailor-made and single calibrated surface thermocouples are placed at strategic positions for in situ calibrating the IR temperature readings. The five in situ thermocouples along the hub centerline are shown in Fig. 2. The surface thermocouples were then, together with the heating foils, spray painted with the high emissivity paint Nextel Velvet 811-21. A gold mirror was necessary to optically access the hub surface close to the AFT hub cavity exit, as illustrated in Fig. 2.

The mass transfer technique used in this study is the seed gas concentration technique, which was initially established in the TTTF and described by Patinios et al. [20]. Here, it is used to improve the purge film cooling effectiveness measurement accuracy on the hub, reveal the individual cooling share of each purge flow, and measure the purge film cooling effectiveness on the optically inaccessible TCF shroud surface. In short, the technique works by seeding the FWD and AFT purge flows with different foreign gases (here CO₂ and N₂O) and analyzing gas samples drawn from overall 60 hub, 54 strut, and 43 shroud static wall pressure taps. The wall tap diameter was 0.6 mm, and the sampling flowrate was less than 0.2 l/min, leading to a maximum suction velocity of ∼12 m/s. In comparison, Clark et al. [21] used virtually the same seed gas equipment for studies on rim seals and cavities. They concluded that their combination of taps with a diameter of 0.5 mm and a sampling flowrate of 0.12 l/min, which results in a suction velocity of ∼10 m/s, led to isokinetic flow conditions and thus no influence of the sampling method on the results. The samples were always drawn one by one from the wall pressure taps, ensuring that sampling from an upstream tap did not influence a sample drawn from a downstream tap. The wall tap locations are shown later in Sec. 3.1. The gas samples were analyzed using a two-channel Siemens Ultramat 6E gas analyzer. The wall pressure taps were situated in another TCF passage than the thermal instrumentation. This is no impediment, as the flow is identical in each TCF passage due to the periodicity of the flow (exactly 4 HPT vanes per TCF strut). The gas sampling points of the purge flows were situated far upstream in the supply pipes, and the sampling point of the main flow was upstream of the HPT, as illustrated with (blue) diamonds in Fig. 2. The seed gas concentration technique delivers more accurate and robust results than the IR technique; however, the data are only available pointwise at the wall tap locations.

The data reduction in this study is only briefly summarized here, as it is identical to the previous study [13].

The definition of T_P for the η_IR measurements bears some ambiguity for three reasons: First, all four purge flows have to be simultaneously switched off when measuring $TS,ad′$ to hold the tip gap constant. Therefore, η_IR on the hub represents the combined film cooling effectiveness of both hub purge flows. For T_P, the assumption must be made that the AFT hub purge significantly dominates the cooling effect over the FWD hub purge. Second, the hub purge flows heat up due to viscous dissipation in the rotating wheelspace cavities. As a result, T_P becomes a function of the radius where it is measured, and so does η_IR. This is illustrated in Fig. 3, where η_IR was evaluated with T_P taken from different radial measurement positions, shown as (red) circles, that were available in the test setup. Third, the AFT hub cavity is not entirely sealed at nominal purge mass flows, as is normally the case in turbines. The radially uppermost T_P measurement position is influenced by ingress, while in the two lower positions, ingress is negligible. In the end, the definition of T_P decides where the system boundaries for the film cooling problem are drawn, and which phenomena (ingress, viscous dissipation) are considered part of the problem. Here, the radially middle position is defined as the T_P measurement. This means that ingress is included, and most of the viscous dissipation heating is excluded from the film cooling problem.

To combine the film cooling share of the FWD and AFT purge of Eq. (3), the well-known formula of Sellers [23] is used. Please note that the film cooling contribution of the FWD purge flows is so small that the difference between using the Sellers superposition principle and the simple addition of the FWD, and AFT film cooling effectiveness values is less than 0.01 in all investigated cases. Therefore, the choice of the combination method of η_SG,FWD and η_SG,AFT is practically insignificant here.

This Sellers-combined film cooling effectiveness from seed gas is the final film cooling result, η_SG, on the TCF shroud. On the TCF hub, the Sellers-combined film cooling effectiveness is used to calibrate the IR film cooling results. The working principle of this in situ calibration is as follows: The results of Eq. (3) only exist at the pointwise locations of the wall pressure taps. Due to the aforementioned reasons, η_SG delivers more robust results and is, therefore, now used as an in situ calibration ground truth for η_IR. First, the difference between η_IR and η_SG is calculated at the pressure tap locations (=calibration offset). Second, this pointwise calibration offset is interpolated to obtain a spatially continuous offset field covering the hub and strut surfaces using the natural neighbor interpolation [24]. Third, this continuous offset field is now subtracted from the continuous η_IR field. The result is the final η field, which equals the value of η_SG at the pressure tap locations, but also contains the variations of η_IR between the taps [13]. In this way, the high spatial resolution of the IR technique is maintained in the final results, while the accuracy and robustness are inherited from the seed gas technique. The outcome of this in situ calibration is the final η field on the hub, and it represents the combined film cooling effectiveness of the FWD and AFT hub purge flows.

The uncertainties presented herein are given as 95% confidence intervals and were calculated using the guide to the expression of uncertainty in measurement [25]. A detailed breakdown of the different uncertainty sources for h and η_IR is given by Bogard and Thole [15] and for η_SG by Patinios et al. [9].

Figure 4 shows the uncertainty in h as a circumferential average along the TCF hub and along the strut midspan as an average of strut sides I and II.

Figure 5 shows the uncertainty in η_IR and η_SG as a function of its value. The uncertainty of the infrared film cooling measurements depends on the purge flow ratio because the purge flow temperature is colder at higher purge flowrates, and therefore, the available delta T are also higher. As can be seen, the uncertainty of η_SG is significantly lower, which again justifies using the seed gas technique to in situ calibrate the IR measurements. The uncertainty of the final η on the TCF hub is close to the uncertainty of η_SG. The uncertainties of η_IR can be regarded as pessimistic upper limits.

It must be noted here that these uncertainties refer to the absolute values. The uncertainties in the differences between the investigated test cases are significantly smaller because the same test facility, test vehicle, and measurement technique were used.

In this section, the purge film cooling results are presented first, then the associated intensification of the heat transfer by the purge injection is discussed, and finally, the combination of these results into the heat flux reduction is presented. The 100% purge case corresponds to the nominal purge case, and the 100% CO₂ purge case corresponds to the CO₂ purge case in the previous study [13] and is reprinted here for comparison. Five-hole probe measurements of the 100% purge case at the TCF inlet and outlet plane can be found open access in the previous study.

In this section, the purge film cooling effectiveness results are presented first as full surface coverage measurements, then condensed into circumferentially averaged lines, and, finally, compared to conventional slot film cooling correlations.

Figure 6 presents full surface coverage distributions of η on the TCF hub and shroud surfaces. At the hub, η is the Sellers-combined film cooling effectiveness of the FWD and AFT hub purge flows, and at the shroud, η is the Sellers-combined effectiveness of the FWD and AFT tip purge flows. The top views of the hub and shroud are shown for the 50%, 100%, and 200% purge cases, whereas the cavity exit is situated at the bottom and the flow direction is from bottom to top. Always one TCF passage is shown, which is bordered on the left and right by a strut. As described earlier, the η results on the hub of the 100% and 200% purge cases stem from the in situ calibration of η_IR with η_SG. The η results on the hub of the 50% purge case stem solely from the seed gas measurements, η_SG, as IR temperature measurements were not possible in this case. In this test case, the AFT hub purge temperature was too hot and, consequently, too close to the main flow temperature to obtain a useful temperature difference for IR measurements. Since the seed gas data were only available pointwise, the η_SG distribution on the hub of the 50% purge case was obtained by using the natural neighbor interpolation [24] between the wall taps, shown as black dots. The exact same procedure was conducted for all shroud film cooling distributions (50%, 100%, and 200% purge case), as the shroud was optically inaccessible and only seed gas data were available there. Areas on the shroud, where the distances between the wall taps were too far for a trustworthy interpolation, are shaded white. The unwound running lengths over the hub and shroud s/L_Hub and s/L_Shroud are also shown as ruler left of the plots and as white dashes in the plots to aid the following discussion.

On the hub, shown on the top in Fig. 6, the cooling film forms, in all three cases, four longitudinal streaks in every TCF passage. As explained in the previous publication [13], these streaks have the same count as the HPT stator vanes and are driven by two mechanisms. First, each HPT stator wake locally causes a small static pressure deficit at the hub cavity exit, which causes the AFT hub purge flow to exit the cavity preferentially in this wake region. Second, four counterrotating vortex pairs exist at the inlet of every TCF passage, which emanates from the interaction of the HPT stator and rotor lower passage vortices. These vortex pairs collect the purge flow into even more distinct streaks along the TCF hub surface. It can now evidently be seen that these mechanisms and, consequently, these high η streaks exist in all shown cases and over the whole range of investigated blowing ratios. The relative peak to trough strength of these streaks (max η in streaks divided by min η in the trough toward the next streak at the same axial position) equals approximately 1.5 for all three cases.

In the 50% purge case, the film cooling effectiveness on the hub is almost negligible, as η drops below 0.1 already around s/L_Hub = 0.1. In the 100% purge case, the cooling film becomes nonsymmetric after the struts and extends until s/L_Hub = 0.15 toward the right strut and s/L_Hub = 0.30 toward the left strut before η drops below 0.1. In the 200% purge case, the cooling film extends until approximately s/L_Hub = 0.65, and its asymmetry is less pronounced than in the 100% purge case. However, even in this case, with double the nominal blowing ratio, no significant film cooling effectiveness is found on the struts. Even close to the strut leading edge, η drops below 0.1 right above the fillet on both strut sides. It can be concluded that the TCF struts cannot be sufficiently film cooled by HPT hub purge flows. The same applies to the HPT tip purge flows, as their cooling films do not reach the struts on the shroud side either.

On the shroud, shown at the bottom in Fig. 6, the film cooling coverage is more even and symmetric than on the hub for all investigated blowing ratios. There is no evidence of longitudinal streaks or the like for the 50% and 100% purge cases. In the 200% purge case, however, a small circumferential variation is visible directly at the TCF inlet. In contrast to the hub, the flow field below the shroud surface is more uniform in the circumferential direction, as this is where the HPT's underturned high-energy tip leakage flow is located [13]. This tip leakage flow is a thin circumferential band characterized by high velocity and smaller circumferential variations. It is hypothesized that a higher AFT tip purge flow pushes this tip leakage band radially downward and into the upper passage vortices of the HPT vanes. This could lead to a modulation of the tip gap band by the circumferentially fixed (four per passage) upper passage vortices, which could result in weak longitudinal streaks in the film cooling data on the shroud. In any case, investing in further research in this area would be worthwhile.

The upstream blockage effect of the struts is clearly visible in the shroud film cooling data in all cases, as the film cooling effectiveness is lower upstream of the strut leading edges. In the 50% purge case, the cooling film extends on the shroud until approximately s/L_Shroud = 0.22 before dropping below 0.1. For the 100% and 200% purge cases, the η = 0.1 limit is reached approximately at s/L_Shroud = 0.42 and s/L_Shroud = 0.7, respectively.

Figure 7 shows the circumferentially averaged film cooling effectiveness along the TCF hub of the same cases presented in Fig. 6. The averaging region is illustrated in the insert and excludes the struts and their fillets. In this diagram, $η¯$ is, as always, the Sellers-combined film cooling effectiveness of the FWD and AFT purge flows, and $η¯SG,FWD$ is the film cooling share of the FWD hub purge flow alone.

The FWD hub purge flow is thermally negligible for the TCF. The highest film cooling effectiveness generated by the FWD hub purge flow is 0.03 in the 200% purge test case. Consequently, the AFT hub purge flow contributes the overwhelming majority to the combined film cooling effectiveness, $η¯$⁠, on the TCF hub. For this reason, only the AFT hub purge blowing ratios are shown in Fig. 7.

The typical film cooling behavior of ever lower film cooling gains for ever higher blowing ratios is also observed here. Doubling the purge flow ratio (and with that, the blowing ratio) does not double the achieved film cooling effectiveness. For instance, at s/L_Hub = 0.1, the 50% purge case has an average total film cooling effectiveness of $η¯=0.11$⁠, the 100% purge case has $η¯=0.18$⁠, and the 200% purge case has $η¯=0.28$⁠. This can be seen as a degressive saturation process that is likely to continue until a critical momentum ratio is exceeded and the cooling film separates. Even at double the nominal purge flowrate (200% purge case), no indication of cooling film separation is found in the η distribution in Fig. 6 and in the $η¯$ curve in Fig. 7. All $η¯$ curves are monotonously decreasing with s/L_Hub.

Figure 8 is analogous to Fig. 7, but now with film cooling data along the TCF shroud. The FWD tip purge flow is, as the FWD hub purge flow, thermally negligible for the TCF as its film cooling effectiveness is everywhere below 0.025, even for the 200% purge case. Again, no indication of cooling film separation can be found for any of the blowing ratios investigated. The typically very low blowing ratios of HPT purge flows make a cooling film separation very unlikely, even in the case of the perpendicular injection of the tip purge flows.

Figure 9 shows the difference in film cooling effectiveness between the CO₂ purge cases and the corresponding normal purge cases with the same blowing ratio. As mentioned earlier, no seed gas measurements were possible in the CO₂ purge cases. Therefore, the film cooling effectiveness measured solely with IR thermography, $η¯IR$⁠, is used in Fig. 9. The data are again presented as the circumferential average along the hub. For both blowing ratios, nominal and doubled, no significant differences can be observed when the density ratio is increased. The differences are always within ±0.025. The area close to the hub cavity exit (s/L_Hub < 0.2) was the most challenging region to capture with the IR camera and, therefore, shows stronger fluctuations in the differences between the CO₂ and the normal purge cases. To capture this region, very shallow surface and window viewing angles had to be dealt with, and the gold mirror had to be used as well. For the investigated range of density ratios, it can be concluded that the herein investigated HPT AFT hub purge flow operates in the density ratio insensitive regime. This statement was already reported in the previous study [13] for 100% purge, but can now be extended to twice the nominal purge blowing ratio of M = 0.22. The differences in Fig. 9 could rather be seen as a repeatability metric of the IR measurements. Since this insensitivity was demonstrated on the purge flow with the most complex flow behavior (longitudinal streaks, rotating wheelspace cavity, etc.), it might be reasonable to assume that this insensitivity also applies to the other three HPT purge flows.

Figure 10 shows a traditional scaling approach for film cooling data, where the abscissa is scaled with the blowing ratio, M, times the cavity slot width, d. This factor, M·d, can be interpreted as the purge mass flow per circumferential unit span, and it is a decisive parameter when different film cooling configurations shall be compared [15]. Here, the $η¯$ curves along the hub and shroud were taken from Figs. 7 and 8 and were scaled with the AFT hub or AFT tip M·d values, respectively. The diagram is double logarithmic, and the hub curves are shown again as solid lines and the shroud curves as dashed lines.

The three hub and shroud film cooling curves collapse relatively well into curve bundles using the above-described scaling method. The shroud film cooling data seem to scale slightly better with s/Md than the hub curves. It is hypothesized that the more complex flow field over the hub with the counterrotating vortex pairs is the reason for this. Zerobin et al. [7] found that these counterrotating vortex pairs are intensified and radially moved when the purge mass flows increased. This means that there is a flow-physical feedback from the blowing ratio onto the vortices that, in turn, again interact with the cooling film. This retroactive effect might explain why the hub film cooling data scales slightly worse.

Since the data are scaled with the purge mass flow per circumferential unit span, M·d, in Fig. 10, it can now easily be seen that the shroud purge film cooling outperforms the hub purge film cooling. For the same purge mass flowrate, $η¯$ is always higher along the shroud than $η¯$ along the hub. This applies over the whole range of investigated blowing ratios. There were two mechanisms identified in the previous study [13] that explain the better film cooling performance on the shroud. First, the aforementioned counterrotating vortex pairs enhance the dilution of the purge cooling film along the hub. Second, purge flows are low momentum flows, which form a more stable cooling film on a convex wall (shroud) than on a concave wall (hub) [26].

This correlation predicts the decay of the hub cooling film downstream of the purge injection very well, as the inclinations of the hub curve bundle and the correlation are identical for s/Md > 100. However, the Hartnett correlation heavily overpredicts the magnitude of $η¯$⁠.

The Seban correlation (Eq. (5)) tangents the shroud curve bundle and shows good agreement with the shroud film cooling data between 20 < s/Md < 100.

The constant was lowered from 16.9 to 6 because it was found that the AFT hub purge flow premixes with the main flow in the rim seal. The purge is leaving the cavity already with η < 1. This premixing was confirmed with a computational fluid dynamics (CFD) simulation shown in Fig. 11 and taken from Jagerhofer [29]. Two vortices exist in the rim seal, whereas the upper vortex rotates clockwise and dilutes the purge flow with mainstream fluid before the purge flow exits the rim seal. The adapted Hartnett correlation (Eq. (6)) is now able to fit the hub film cooling bundle for s/MD > 100 very well.

It can be concluded that the film cooling behavior of HPT purge flows in a TCF is very similar to traditional slot film cooling. The hub film cooling data behave like slot film cooling with tangential injection, which leaves the slot in an already premixed state. The strong tangential velocity component of the AFT hub purge can also be seen in the CFD stream traces in Fig. 11. The shroud film cooling data behave like traditional slot film cooling with perpendicular injection, which is plausible since the AFT tip purge flow is injected perpendicularly into the main flow through a thin axial slot. This axial slot is illustrated in Fig. 2. The downstream decay of the purge cooling films can be predicted with satisfying accuracy using traditional slot film cooling correlations.

This section presents the heat transfer coefficient, h, results on the TCF hub and struts, focusing on the heat transfer intensification, Δh, caused by the purge injection. In Sec. 3.1, full surface coverage measurements are presented first and then condensed into circumferentially averaged lines. For reasons of confidentiality agreements with the industrial collaborators, all h and Δh values are nondimensionalized with the max heat transfer coefficient of the 0% purge case, $hmax′$⁠.

Figure 12 shows the h distribution of the 0% purge case at the top and the heat transfer intensification distributions of the 100% purge and 200% purge cases at the bottom. As mentioned earlier, the top views of the TCF hub and struts are shown, where the hub cavity exit is situated at the bottom, and the flow direction is from bottom to top. Additionally, side views of the left and right strut are shown next to their top views. Five small spots with locally increased heat transfer can be seen along the hub centerline. These are thermal signatures of the flat in situ thermocouples. The heat transfer intensification, Δh, is simply the difference of h from a purged case minus the h value of the 0% purge case.

The h distribution of the 0% purge case shows four longitudinal high h streaks along the hub surface, marked with black dashed lines. As explained in the previous publication [13], these high h streaks are alternately arranged with the high η streaks, meaning that high heat transfer meets poor cooling and vice versa. The high h streaks are driven by a surplus of velocity in the undisturbed core flow region of the HPT vanes and by the aforementioned counterrotating vortex pairs. The h field in general, as well as the formation and behavior of these streaks, is thoroughly explained with five-hole probe measurements in the previous study [13]. The position with the highest h in the dataset is found on the right strut and marked with a black plus.

The purge injection clearly leads to pronounced heat transfer intensification close to the hub cavity exit, which increases with the purge flowrate. The maximum heat transfer intensification was found for both shown cases in this region and equals 12% for the 100% purge case and 22% for the 200% purge case. In the 200% purge case, four spots of enhanced heat transfer exist over the circumference close to the cavity exit. The circumferential position of these spots coincides with the high η streaks, shown in Fig. 6. Further downstream into the TCF passage, the heat transfer intensification reduces and forms longitudinal streak-like patterns. These streak-like patterns are caused by the so-called purge clocking effect, initially described by Zerobin et al. [7]. In short, purge clocking is an effect that causes a slight circumferential shift of flow features with increasing hub purge flowrates. Increasing the hub purge flowrates affects the incidence angle at the TCF inlet and, thus, slightly moves the high h and high η streaks to the side. When high h streaks of the 0% purge case are subtracted from the slightly shifted high h streaks of a purged case, such streaky patterns appear in the Δh distributions. Interestingly, there is a region in the middle of the passage where the heat transfer is slightly reduced due to purge injection in both shown cases. This heat transfer reduction, albeit small, is surprising because the preliminary tests without an HPT upstream of the TCF [30] did not show such behavior. There, the same TCF was tested with the same blowing ratios, and the heat transfer was always and everywhere along the hub increased by purge injection. It is, therefore, hypothesized that the herein observed local heat transfer reduction is due to the interaction of the hub purge flows with the HPT flow field.

As mentioned in the film cooling results in Sec. 3.1, the purge flows never reach the strut surfaces beyond the fillets. Still, the heat transfer is enhanced locally on both strut sides in the 100% purge case and almost on the whole strut in the 200% purge case. By injecting the purge flows, the effective flow cross section for the main flow is reduced, which slightly accelerates the main flow and enhances the heat transfer on the struts. Most importantly, the point of maximum heat transfer of the whole dataset, marked with the black plus on the right strut, is further intensified by purge injection by 4% in the 100% purge case and by 15% in the 200% purge case.

Figure 13 shows the circumferential average of the heat transfer intensification, $Δh¯$⁠, for all investigated cases along the hub. The normal purge flow cases are shown as solid lines, and the corresponding CO₂ purge cases are shown as dashed lines.

Varying the DR does not affect the heat transfer coefficient, as the normal and corresponding CO₂ cases always agree within ±2.5%. This also includes the region close to the hub cavity exit, which posed the greatest challenge for the measurement technique. It can be concluded that the herein investigated variation in DR affects neither the film cooling nor the heat transfer in the TCF. The differences between the same colored dashed and solid lines can be interpreted as the repeatability of the experiment.

Varying the blowing ratio, M, leads to a heat transfer intensification that is highest right at the AFT hub cavity exit at s/L_Hub = 0 and then gradually fades out until s/L_Hub = 0.3. From there, the aforementioned heat transfer reduction due to purge injections sets on and lasts, depending on the blowing ratio, until s/L_Hub = 0.5–0.8. With the increasing blowing ratio, the circumferentially averaged heat transfer intensification near the cavity exit increases and equals in the 200% purge case +17%. As for the film cooling effectiveness, doubling the purge blowing ratio does not double the associated heat transfer intensification. The slight heat transfer reduction after s/L_Hub = 0.3 is also more pronounced with the increasing blowing ratio, but it is significantly weaker, with the highest reduction in the 200% purge case equaling −2.5%. Toward the TCF exit at s/L_Hub = 1, the heat transfer intensification fades out, and all cases approach the 0% purge case.

Here, h is the purged, $h′$ is the nonpurged heat transfer coefficient, and $ϑ$ is the ratio of internal heat transfer (including conduction through the wall) over the external heat transfer. As the coolant/purge flows inside the TCF are compared to the main flow very slow and unguided, $ϑ$ is assumed to equal 0.01. A positive Θ means that the purge injection reduces the net heat flux into the surface. In other words, the gain in film cooling outweighs the heat transfer intensification. A negative Θ means that the film cooling has a negative effect, as it increases the heat flux into the wall.

Figure 14 shows the circumferential average of Θ along the hub surface. Since $Θ¯$ is positive for all investigated blowing ratios, the film cooling benefit always outweighs the heat transfer intensification along the hub. The CO₂ purge cases are not shown here but would collapse with their corresponding normal purge case with the same blowing ratio. The heat flux reduction curves have a similar shape as the η curves in Fig. 7, whereas the maximum is expectedly located at the AFT hub cavity exit, followed by an asymptotic decrease toward the TCF exit. Also here, doubling the blowing ratio does not double the heat flux reduction. Changing the value of $ϑ$ changes the shape of the $Θ¯$ curves slightly but does not affect the qualitative message of Fig. 14. Such a $ϑ$ variation can be found in the previous study [13].

On surfaces where the h is enhanced due to purge injection but η is zero, Θ becomes negative. Although not shown here, this is the case on the struts in Fig. 12, where Δh > 0 and includes the point with the highest heat transfer coefficient of the whole dataset. This point is marked with a black plus in Fig. 12, and Θ equals −0.07. If this point is the thermally most critical, the TCF could even be damaged by increasing the purge flows.

This study deals with the thermal impact of HPT purge flows on the downstream TCF. The purge film cooling effectiveness, as well as the associated heat transfer intensification due to the purge injection, are measured for varying purge blowing ratios and density ratios. The investigated 1.5-stage test vehicle was tested under Mach-similarity and consisted of a fully purged HPT, an aerodynamically aggressive TCF, and a row of LPT vanes. The unshrouded HPT has four purge flow injections, two on the hub through engine-representative rim seal geometries and two from the tip through axial slots. These purge flows are the source of film cooling for the TCF surfaces in this study. A thermal and a mass transfer measurement technique were used in this work. The thermal technique is a combination of infrared thermography and heating foils. This technique was used on the TCF hub and struts to measure the film cooling effectiveness and the heat transfer coefficient. The mass transfer technique was the seed gas concentration method, which was used on all TCF surfaces to measure the purge film cooling effectiveness more accurately and also to split the combined film cooling effectiveness into the individual share of each purge flow. Three purge blowing ratios were investigated, namely, nominal (100% purge), 50% of nominal, and 200% of nominal. The density ratio of the AFT hub purge flow was also varied to some extent by replacing a larger fraction of purge air with CO₂. This purge flow was chosen as it exhibited the most complex film cooling behavior.

The blowing ratio was found to be the dominant parameter for thermal investigations of purge flows in a TCF. There were no significant differences in the film cooling or heat transfer results within the varied range of density ratios. The cooling films remained attached to the TCF hub and shroud for all investigated cases. Even at double the nominal blowing ratios, purge flows can be regarded as low momentum flows, whereas the blowing ratio is the most important parameter for studies.

On the hub, the cooling film forms longitudinal streaks for all investigated blowing ratios. These streaks are driven by the HPT flow field and have the same count as the HPT vanes. The heat transfer intensification due to purge injection is highest at the cavity exit and increases with the blowing ratio. The FWD hub purge flow is thermally negligible for the TCF, even in the 200% purge case. The AFT hub purge flow, however, is a significant source of film cooling for the TCF. In the 200% purge case, the cooling film extends over more than 60% of the hub length and exceeds η = 0.5 close to the hub cavity exit.

On the shroud, the cooling film is more even and symmetric than on the hub. Also there, the FWD tip purge flow was found to be thermally negligible for the TCF, and virtually the whole cooling effect can be attributed to the AFT tip purge flow. In the 200% purge case, the cooling film extends over more than 70% of the shroud length and exceeds η = 0.6 close to the tip cavity exit.

The circumferentially averaged purge film cooling effectiveness along the TCF hub and shroud was found to scale with the traditional approach of dividing the streamwise coordinate with the purge mass flow per unit span, Md. There, it was shown that the shroud film cooling outperforms the hub film cooling over the whole range of investigated blowing ratios. The shroud film cooling effectiveness was found to fit best to the traditional slot film cooling correlation for perpendicular injection of Seban et al. [28]. The downstream decay of the hub film cooling effectiveness was captured by the conventional correlation of Hartnett et al. [27] for tangential injection. By tuning the constant of the Hartnett correlation to correct for ingress-induced premixing in the AFT hub cavity, a good fit for the hub film cooling data in the downstream region was obtained.

From the engine designer's perspective, the cooling potential of the HPT AFT purge flows is significant on the hub and shroud. The heat flux reduction (Baldauf et al. [31]) is positive for all investigated blowing ratios along the hub. Care should be taken on the struts, as no purge flow reaches them, but purge injection tends to increase the heat transfer there. For roughly predicting the film cooling behavior of purge flows in a TCF, the traditional scaling approach with s/Md in combination with well-established slot film cooling correlations may be sufficient, especially for the downstream region.

This work has been carried out in collaboration with GE Aviation Munich and MTU Aero Engines AG as part of the research project LuFo V-3 Opti-TCF (contract no. FKZ 20T1705B) funded by the German Ministry of Industry BMWi.

There are no conflicts of interest.

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.

c =

strut chord length (m)

d =

cavity exit slot width (m)

h =

heat transfer coefficient (W/m²K)

s =

unwound streamwise length (m)

ṁ =

mass flowrate (kg/s)

$q˙$ =

heat flux (W/m²)

L =

axial length of TCF (m)

M =

blowing ratio (=ρ_P V_P/ρ_M V_M)

T =

temperature (K)

V =

absolute velocity (m/s)

c_P =

specific isobaric heat capacity (J/kgK)

L_Hub =

unwound hub length (m)

Re_c =

Reynolds number based on strut chord length (=V_∞c/ν)

U_F =

uncertainty in parameter F

conc. =

seed gas concentration (CO₂ or N₂O)

Ma =

Mach number

ACR =

advective capacity ratio (=c_p,Pρ_P V_P/c_p,Mρ_M V_M)

DR =

density ratio (=ρ_P/ρ_M)

Δr =

radius difference (Δr = r_out − r_in) (m)

η =

adiabatic film cooling effectiveness

Θ =

heat transfer reduction, Baldauf et al. [31]

ν =

kinematic viscosity (m²/s)

π =

total pressure ratio

ρ =

density (kg/m³)

ω_sw =

streamwise vorticity (1/s)

ad =

(quasi) adiabatic

in =

inlet

IR =

from infrared

M =

mainstream

out =

outlet

P =

purge

S =

surface

SG =

from seed gas

0 =

total

∞ =

freestream

′ =

0% purge case