Methodology

In this section, the test facility is outlined. Furthermore, the measurement setup and the measurement principles are provided and the uncertainties are discussed.

Test section and measurement setup

The schematic setup of the test section and measurement setup used for the current investigation is displayed in Figure 1. The test section in Figure 1a was constructed for acquisition of adiabatic film cooling effectiveness ηa,W(=Trec,h−Taw/Trec,h−Tt,c) and ratio of heat transfer coefficients with and without film cooling hf/h0 on a flat plate. Uniformity of the inlet hot gas flow in terms of velocity and temperature field have been validated in previous works (Fraas et al., 2017). The test section consists of a hot gas and a coolant channel, where the latter can be oriented either in parallel or perpendicular to the hot gas channel, therefore facilitating realistic inflow conditions present in gas turbines and aero engines. The operating conditions for this study were derived from real-engine conditions and are summarised in Table 1 (Fraas et al., 2017).

Figure 1.

Schematics of test section and measurement setup including FOVs for IRT and SPIV measurements. (a) Schematic of test section containing hot gas and coolant channel including a turbulence grid ➀, boundary layer suction ➁, ejection module ➂, optical access for IRT ➃, thermal measurement plate ➄, IRT camera ➅ and FOV for SPIV ➆; adapted from (Fraas et al., 2017). (b) Schematic SPIV Setup as top view on test section including: ejection module ➀, camera lens ➁, Scheimpflug adapter ➂, camera ➃, light sheet optics ➄, ND:YLF laser ➅ and FOV for IRT ➆; adapted from (Stichling et al., 2021).

A turbulence grid (Roach, 1987) is placed downstream of the inlet nozzle ➀ and in combination with a subsequent boundary layer bleed ➁ is used to ensure well-defined and engine-like flow conditions at the coolant ejection. Coolant and hot gas channel are connected via the interchangeable ejection module ➂ containing three to five separate film cooling holes aligned laterally at a constant x/D-position. To prevent interaction between coolant jet and channel sidewalls a 50D wide hot gas channel is used. The ejection module is manufactured from polyetheretherketone (PEEK), a semi-crystalline high-temperature resistant thermoplastic with a low thermal conductivity of λth≈0.27W/(mK). The temperature change of the coolant during ejection is thus minimized. Five infrared-transmissive sapphire windows ➃ provide optical access through the top wall of the hot gas channel for temperature field acquisition on the thermal measurement plates ➄ using a camera sensitive for infrared radiation between 3…5μm ➅. For temperature calibration, a routine developed at ITS (Ochs et al., 2009) was used including adaptations for high dynamic range temperature data (Ochs et al., 2010). For calculating the thermal film cooling quantities, the superposition principle of film cooling (Choe et al. 1974) was used. Details regarding the test setup including the two thermal measurement plates and the calculation of the film cooling quantities can be found in Fraas et al. (2017).

The test section was adapted to accommodate stereoscopic Particle Image Velocimetry Measurements (SPIV) (Stichling et al., 2021) capturing the field of view (FOV) ➆ indicated by the green area in Figure 1a. The SPIV measurement setup is detailed in Figure 1b using a top view on the hot gas channel of the test section from Figure 1a. Optical access for the SPIV measurement is granted via two fused silica windows (not displayed), one on each lateral wall of the hot gas channel. A light sheet with a thickness of δz≈1.5mm is produced via the light sheet optics ➄ using a green (λ=527nm) dual pulse ND:YLF laser ➅ (Darwin-Duo by Quantronix). It is placed such that streamwise, wall-normal measurement planes can be investigated. Both cameras ➃ (Fastcam SA5 CMOS cameras by Photron) are equipped with a 100 mm focal length lens ➁ connected via a Scheimpflug adapter ➂ to compensate for the oblique viewing angle θ≈45∘. The Scheimpflug angle γ subtended by lens and image plane is adjusted to meet the Scheimpflug criterion.

Silicon oil particles with a mean diameter of d=1μm are seeded in both hot gas and coolant channel illuminating cropped camera frames with a resolution of each 1.024 px × 512 px. The double images are acquired at a frequency of f=2kHz in frame-straddling mode with a time delay of Δt=30μs at multiple lateral y/D positions. For camera and laser synchronization, a synchronizer by iLA5150 GmbH is used. For data evaluation, a multi-pass scheme with an overlap of 50% and a final interrogation window size of 16 px was used during evaluation with PIVview3C by PIVTEC GmbH, yielding approximately one velocity vector per millimetre.

Two geometries are investigated and detailed in Figure 2. The first geometry (Figure 2a) constitutes a 10°-10°-10° laidback fan-shaped (LFH) hole with a cylindrical inlet segment. The cylindrical part of the cooling holes is scaled up by a factor of ≈14 to a diameter of D=10mm to facilitate a high spatial measurement resolution. Its length-to-diameter ratio is L/D=7.5, the area ratio AR=Aoutlet/Ainlet=3.71, and the coverage ratio (hole breakout width based on the pitch) is 0.93. The edges of the diffuser are rounded with redge=0.5D while inlet and breakout edges of the diffuser are sharp-edged. The ejection module contains a total of five LFH geometries with a pitch-to-diameter ratio of p/D=3 and an inclination angle of 35°. The coolant cross-flow is parallel to and in the same direction as the hot gas main stream flow. The second geometry is a slot geometry displayed in Figure 2b with an inclination angle and length-to-diameter ratio equivalent to that of the LFH geometry, where D is the diameter of the cylindrical part of the laidback fan-shaped geometry. The slot is bslot/D=0.4 thick with edges rounded with 0.4D at a spacing of p/D=5.45, resulting in a coverage ratio of 0.8. In total, the ejection module contains three slot geometries. On the coolant side, a plenum-like structure is added, and the coolant cross-flow is opposite to that in the measurements of the laidback fan-shaped geometry.

Figure 2.

Film cooling hole geometries considered in the current study. (a) 10°-10°-10° laidback fan-shaped hole; (Fraas et al., 2019a). (b) Slot geometry with coolant side plenum-like structure.

A strong interaction between the individual film cooling jets can be expected for the LFH geometry due to their lateral proximity (Baldauf, 2001) and can be anticipated for the slot geometry as well.

Measurement uncertainties

Detailed information regarding the measurement uncertainties of the flow parameters for both hot gas and coolant channel can be found in (Fraas et al., 2017). The measurement uncertainty, calculated according to (Kline, 1953), is below 12% for the heat transfer coefficient with film cooling hf in all regions where the adiabatic cooling effectiveness ηa,W≤0.7. The uncertainty for the adiabatic film cooling effectiveness ηa,W is globally ≤0.012.

For estimating the measurement uncertainty in the PIV experiments, a method based on correlation statistics (Wieneke, 2015) was used. In terms of absolute velocity, the spatially averaged relative local uncertainty was below 2.2%. The local relative uncertainty was found to be below 5% everywhere except in the close-wall region y/D<0.4 after which the local relative uncertainty increased locally towards the wall reaching up to 10%. Additionally, a slight decrease of uncertainty in streamwise direction of less than 1% was found.

Adiabatic film cooling effectiveness and heat transfer coefficient

In Figure 3 the spatial distribution of the adiabatic film cooling effectiveness ηa,W for both geometries is shown. For the LFH10, one can observe the expected trend of decreasing ηa,W along the streamwise direction x/D as well as from the streamwise centreline in both lateral directions ±y/D. The peak adiabatic effectiveness is slightly asymmetric and shifted towards positive y/D values. An increase in blowing ratio generally increases ηa,W for the investigated blowing ratios but, as well known in literature, the current data also indicates a certain optimum, as the beneficial effect of an increase in blowing ratio BR reduces towards the highest blowing ratio BR. This can be observed much better in the laterally averaged adiabatic film cooling effectiveness η¯a,W in Figure 4a. The legend for Figure 4a is equivalent to that in Figure 4b.

Figure 3.

Spatial adiabatic film cooling effectiveness ηa,W for both geometries and three blowing ratios each. (a) LFH10, p/D = 3, BR = 0.50, 1.00 and 1.50. (b) Slot, BR = 0.38, 0.76 and 1.14.

Figure 4.

Laterally averaged adiabatic film cooling effectiveness η¯_a,w (a) and ratio of heat transfer coefficients with and without film cooling hf=ho (b).

For the slot, two lateral peaks in film cooling effectiveness can be observed for all blowing ratios. Towards higher blowing ratios and in streamwise direction x/D the double peak converges to a single maximum in lateral direction for each x/D. Directly downstream of the slot exit, the lateral extent of the film cooling imprint reduces for an increase in blowing ratio. This effect propagates and amplifies in streamwise direction, especially for the highest blowing ratio.

Comparing both geometries, much higher values of adiabatic cooling effectiveness ηa,W are evident for the slot and reflect strongly in the laterally averaged adiabatic cooling effectiveness η¯a,W as shown in Figure 4a along the streamwise direction x/D. Since the coolant mass flow per area is equivalent for both geometries, it can be concluded that the coolant is used much more efficiently in case of the slot. For the investigated blowing ratios and geometries, an increase in η¯a,W for increasing blowing ratios is observed with a decrease in rate of change in η¯a,W towards the highest blowing ratio while the global maximum is achieved by the highest blowing ratio of the LFH10 geometry. However, for all blowing ratios the η¯a,W decays much more quickly for the LFH10 as compared to the slot geometry which can maintain relatively high values of η¯a,W along the entire investigated streamwise section. Only in case of the lowest blowing ratio of the slot geometry a nearly identical rate of change in streamwise direction is present.

Nearly no significant increase in η¯a,W can be achieved downstream of the slot cooling hole exit by increasing the blowing ratio from BR=0.76 to BR=1.14. This is due to a potential coolant lift-off at this blowing ratio as will be discussed later in the flow field analysis. Further downstream, a more significant difference in η¯a,W can be observed, which can be attributed simply to the higher available coolant mass flow and the reattachment of parts of the coolant jet to the wall.

The laterally averaged ratio of heat transfer coefficients with and without film cooling hf/h0 is displayed in Figure 4b and shows the expected behaviour for the LFH10: A decrease in hf/h0 with decreasing blowing ratio and increasing streamwise position x/D. In case of the slot geometry, hf/h0 also decreases with decreasing blowing ratio. For an increase in x/D the values of hf/h0 do not follow a clear trend. For the lowest and highest blowing ratio, very similar hf/h0 are observed at x/D=12 after which hf/h0 for the highest blowing ratio drops below that of the lowest blowing ratio likely due to a coolant lift-off. The middle bowing ratio yields overall higher values of hf/h0 compared to all other cases and maintains them at a relatively constant value for x/D≥18. Downstream of x/D=25 hf/h0 increases again for the highest blowing ratio and reaches the same level as that of the middle blowing ratio which indicates a reattachment of the coolant jet. For the slot geometry, this indicates that he coolant jet stays well-attached to the surface for the two lower blowing ratios. As long as the coolant film is attached, an increase in blowing ratio yields and increase in hf/h0. For the highest blowing ratio BR, the coolant film seems to get close to a detachment and the vortex structures of the jet in cross-flow have a less severe influence on the heat transfer coefficient. Comparing the LFH10 and slot geometry for the middle blowing ratio downstream of x/D=20 an average of ≈25% increase in hf/h0 for the slot geometry is observed.

Flow field analysis

While assumptions about the underlying aerodynamics of film cooling jets are often based on thermal film cooling parameters, measurements of the velocity field around the coolant-hot gas interaction are required to fully understand the competing effects causing the observations presented so far.

In Figure 5, velocity profiles normalised by the hot gas main flow velocity uref along the wall-normal direction are depicted for the absolute velocity uabs and the velocity component in wall-normal direction w at the streamwise positions x/D=0,3,6and9 for central plane at y/D=0. While the coolant mass flow per surface area is equivalent for respective blowing ratios in both geometries, the effective blowing ratio BR and momentum ratio IR are lower for the slot geometry. In case of the LFH10, these quantities are calculated for the cylindrical section of the cooling hole and depending on the diffusion achieved in the diffuser section of the hole a lower effective blowing ratio BR or momentum ratio IR is intended compared to the slot. The position of the LFH10 and slot exit geometries are indicated by the black lines below the x-axis with the line styles matching those in Figure 5 for the respective geometry.

Figure 5.

Normalised absolute and wall-normal velocities along wall normal direction for multiple x/D positions. Solid and dotted lines below the x-axes indicate the film cooling hole exits of the LFH10 and slot geometry, respectively. (a) Normalised velocity magnitude u_abs for x/D = 0, 3, 6 and 9. (b) Normalised wall-normal velocity w for x/D = 0, 3, 6 and 9.

For the absolute velocity in Figure 5a at x/D=0 very similar velocity profiles can be observed for all geometries and blowing ratios. The slot geometry leads to a slightly larger velocity gradient towards the wall and a slightly increased deceleration of the main flow for 0.2≤z/D≤1.0. The wall-normal velocity component w at x/D=0, shown in Figure 5b, increases with increasing blowing ratios for both geometries and is ≠0 even at y/D=3. For LFH10 at the highest blowing ratio a near-wall regime with very high wall-normal velocities w can be observed. For the slot geometry, the overall wall-normal velocities are much larger compared to those of the LFH10 geometry at this streamwise position.

Further downstream at x/D=3 near-zero and negative wall-normal velocities can be observed in case of the slot, indicating the deflection of the coolant jet back towards the wall with increasing magnitude for increasing blowing ratios. In case of the LFH10, a further increase in wall-normal velocities can be observed at x/D=3 compared to the upstream position. Similarly as for the high blowing ratio at x/D=0, the wall-normal velocity w peaks again towards the wall for the highest and even more so for the lowest blowing ratio. This indicates that the location, at which the coolant is ejected from the hole shifts depending on the blowing ratio due to a flow separation occurring in the laidback portion of the coolant hole. It partially blocks the coolant hole exit reducing the effective cross section and shifting the mean exit location of the coolant. Downstream of x/D≥6 the wall-normal velocities for all cases are very uniform and approach zero at x/D=9 with only slight deviations in case of the slot geometry for BR=1.14.

The absolute velocity profiles at x/D=3 for the LFH10 are still relatively similar for all blowing ratios, but the gradient is smaller compared to x/D=0. For x/D=6and9 the differences with blowing ratio become more enhanced with decreasing velocities towards higher blowing ratios for 0.2≤z/D≤1.2.

For the slot geometry a strong decrease in velocity towards increasing blowing ratios can be observed at x/D=3, with the wall velocity gradient tending towards zero for BR=1.14, potentially allowing a flow separation. At x/D=6 the coolant jet’s wall-normal momentum is fully deflected in streamwise direction, so that the jet is attached to the wall producing near-wall velocity gradients ≥0 and a region with velocities higher than the reference velocity for 0.5≤z/D≤1.0. Further downstream the velocity peak shifts towards the wall as seen for x/D=9.

To understand the volumetric flow field, measurements were conducted at multiple lateral positions for the highest blowing ratio of each geometry by shifting the SPIV setup in Figure 1b in y-direction. This data was then interpolated laterally resulting in the velocity fields displayed in the y,z-plane in Figure 6 for x/D=1 and x/D=9. The contour in the background encodes the absolute velocity uabs and is overlaid by vectors showing the direction and magnitude of the in-plane components v and w. A reference vector indicating the correspondence between vector length and velocity is shown at the top right of each figure.

Figure 6.

Velocity fields in the y,z-plane for the LFH10 geometry at BR = 1.50 and the slot geometry at BR = 1.14 for multiple x/D positions. (a) LFH10, p/D=3, x/D=1. (b) Slot, x/D=1. (c) LFH10, p/D=3, x/D=9. (d) Slot, x/D=9.

At x/D=1 (Figure 6a and b) the in-plane velocities are dominated by the wall-normal component w for both geometries which is expected as this streamwise position is within the hole breakout for both geometries. Nevertheless, secondary flow structures appear for both geometries mostly towards the lateral ends of the hole pitch. In both cases, the rotational direction corresponds to that expected for the two legs of the counter rotating vortex pair (CVP) which is found in many configurations of jets in cross-flow.

In generic jet in cross-flow (JIC) studies its origin is frequently associated with the effect of the jet’s impulse on the cross-flow boundary layer, which would classify the CVP as a far-field phenomenon. Near-field studies indicate a different or at least additionally contributing formation process connected to a tilting and folding of the jet shear layer (Fric and Roshko, 1994; Karagozian, 2014). Numerical studies related to the JIC application in film cooling suggest a vortex pair formation already in the hole which at least contributes to the CVP (Baldauf and Scheurlen, 1996).

The position of the vortices for the current investigation suggest a formation outside the hole but very close to it’s exit in the near-field. For x/D=9 further downstream of the coolant ejection (Figure 6c and d), the in-plane velocities are distinctively different for both geometries. It has to be pointed out that the vector scaling is different in Figure 6a and b as compared to Figure 6c and d. In the first case, the unit vector at the top right of each figure represents a velocity magnitude of 20% of uref, whilst for the latter case it represents just 10% of uref, increasing the displayed length of each vector by a factor of two.

In case of the LFH10 geometry, no secondary motion related to the CVP can be observed at x/D=9. Although not shown here, no secondary motions related to the CVP were found anywhere downstream of x/D≈1.5. The proximity of the neighbouring film cooling holes seems to suppress the CVP before it fully forms at all, which is expected and the intention for hole configurations with such a small pitch (Baldauf et al., 1999a,b).

For the slot geometry a complex vortex system can be observed at x/D=9. The CVP-like vortex legs at the lateral ends at x/D=1 are now larger and have moved towards the centre by ≈0.5D. The increase in wall-normal distance of the vortex cores to the wall in streamwise direction frequently observed for the CVP is nearly negligible. This supports the conclusions by Brittingham and Leylek (1997), who state that the lift typically produced by the two legs of the CVP is reduced by spreading them apart. An additional vortex pair with identical rotational direction can be observed closer to the centre of the jet. Both CVP-like vortex pairs suggest cross-flow entrainment in and below the coolant jet, which is typically associated with a reduction in adiabatic film cooling effectiveness and an increase in heat transfer coefficient. Obliterating the CVP is often the main goal of geometry studies. The current study, however, shows that amongst two geometries at comparable blowing ratios the one with the weaker CVP and lower momentum ratio IR is not necessarily achieving a lower ηa,W. Despite of the absence of the CVP and a theoretically lower momentum ratio for the LFH10, the adiabatic film cooling effectiveness is lower than that of the slot and also decreases much more quickly compared to the slot. Since the slot does show significant CVP-like vortex structures, it raises the question what else the effectiveness is influenced by to cause the observed results. For this purpose, a flow visualisation using enhanced PIV coolant seeding is used. In Figure 7, representative dewarped instantaneous PIV raw images are presented in the streamwise, wall-normal centre plane for the highest blowing ratio BR of both geometries. Brighter areas thereby correspond to coolant present in the flow. By “representative”, the authors refer to an instant in time, which shows a characteristic behaviour, which repeats itself at least qualitatively in many instants over the recorded time series.

Figure 7.

Dewarped instantaneous PIV raw images with enhanced coolant seeding for the streamwise, wall-normal centre plane; blowing ratio BR=1.50 for the LFH10 and blowing ratio BR=1.14 for the slot.

In Figure 7, a clear qualitative difference between the coolant distribution for the different geometries can be observed. Coolant “chunks” are present for the LFH10 geometry, whose streamwise locations vary dependent on the chosen instant in time, whereas a uniform and relatively time-independent coolant distribution can be observed for the slot geometry. While both geometries are subjected to the same turbulent fluctuations in the main flow, the slot geometry seems to be much more robust towards local changes in the main flow velocity close to the hole exit. The instability of the exiting coolant for the LFH10 geometry is likely connected to a flow separation in the laidback section of the diffuser, which strongly responds to the instantaneous main flow boundary condition. The separation of these coolant “chunks” from the coolant jet into the main flow carries coolant away from the wall and effectively reduces the near-wall coolant mass flow drastically. It also indicates a flapping of the jet, which is responsible for creating the coolant “chunks” in the first place. Even if those merge back into the coolant jet again, their temperature would have increased due to the enhanced hot gas main flow exposure and mixing. This further detriments the cooling potential provided by a certain coolant mass flow. This also explains the more rapidly decreasing adiabatic film cooling effectiveness in case of the LFH10 geometry. The stability of the generated coolant jet or coolant film therefore plays an important role in how efficiently a provided coolant mass flow is used.

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