Investigation of Film Cooling Using Time-Resolved Stereo Particle Image Velocimetry

Enhancing the understanding of the interaction between cooling air jet and hot gas is indispensable for further advancements in film cooling. It will enable the development of more efficient sustainable gas turbines and aero-engines. Numerous experimental investigations predominantly determining the film cooling effectiveness dependent on parameters such as blowing ratio (M), density ratio (DR), velocity ratio (VR), and momentum flux ratio (IR) have been conducted in the past. Furthermore, high cost of experimentation has encouraged putting more effort into conducting numerical investigations. Although simulations provide three-dimensional field information, due to the complex flow field, the vast amount of numerical simulations have only been able to correctly reproduce laterally averaged values of adiabatic film cooling effectiveness η_aw when compared to experimental studies. Also, there are little means of validating the complex flow field in and around the film cooling hole to further improve modeling in numerical simulations. Extensive flow field measurements are required to improve the understanding of mixing between hot gas and coolant and vortical structures in film cooling. However, only few studies present flow field measurements, most of which showing time-averaged and only two-dimensional data. Pietrzyk et al. [1] focused on the streamwise wall-normal centerplane investigating the effect of DR at different blowing ratios using laser-Doppler velocimetry. While comparing dense to unit-density jets, they found the dense jet’s velocity field to vary significantly from the unit-density case. Fric and Roshko [2] postulated the presence of four different vortical structures, namely, the jet shear layer vortices, a system of horseshoe vortices, the counter-rotating vortex pair, as well as wake vortices mainly by means of flow visualization using smoke streaklines and smoke-filled jets. According to Gogineni et al. [3], an increase in turbulence intensity of the hot gas can be directly translated to an increase in lateral jet spreading for low blowing ratios.

The 3D time-averaged velocity field was studied by Bernsdorf et al. [4] for cylindrical holes fed by a plenum. The effect of freestream turbulence intensity on film cooling ejection at low blowing ratios and unity DR was investigated using 2D particle image velocimetry (PIV) by Wright et al. [5,6] for cylindrical and fan-shaped holes, respectively. Similarly, Johnson et al. [7] studied the effects of DR on cylindrical holes using 2D PIV employed at the streamwise wall-normal centerplane. They showed the beneficial effects to reduction of film cooling jet detachment towards elevated DRs. Two-dimensional PIV of the streamwise wall-normal centerplane at low and high DRs was conducted by Eberly and Thole [8]. Snapshots of vorticity contours were shown indicating the shear layer for different parameter configurations. However, the freestream turbulence intensity in the flow facility was close to zero and therefore not representative of realistic engine conditions. Böttger et al. [9] investigated the flow around the inlet of a cylindrical film cooling hole under the influence of different turbulators using 2D PIV.

Aside from the film cooling community, the more generic jet in crossflow configuration has been studied extensively in the past. An overview of the findings can be found in Refs. [10,11]. In Ref. [12], a thorough investigation of the jet in crossflow using the proper orthogonal decomposition (POD) was conducted with detailed analysis of the spatial modes based on stereoscopic particle image velocimetry (SPIV) data. A complementary numerical study was conducted by Cavar and Meyer [13] showing qualitatively similar results for the first few spatial modes. Biden et al. [14,15] used POD to investigate unforced and forced film cooling jets in terms of vortical structure. However, only qualitative experimental techniques were applied while the modal analysis was conducted based on large eddy simulations.

None of the previously mentioned studies considered coolant crossflow at the hole inlet and only Bernsdorf et al. [4] applied DRs close to real-engine conditions. The flow field around an exiting film cooling jet in hot gas, however, clearly contains three-dimensional and transient flow phenomena [12] that are amongst others highly dependent on DR, freestream turbulence intensity, and coolant flow supply configuration. Therefore, SPIV measurements are of interest in particular due to their ability of capturing instantaneous three-dimensional velocity information. Employed at high frequencies, this technique has the capability to provide high-fidelity data to improve understanding of the interaction of all parameters influencing the film cooling effectiveness. Furthermore, it provides a basis for validation of numerical investigations and may allow further improvement of the numerical models. The current study employs time-resolved stereo particle image velocimetry (TRDSPIV) on an experimental facility capable of providing engine-realistic operating parameters by keeping dimensionless parameters constant. Post-processing of the averaged velocity information as well as the snapshots in time using data-driven processing is conducted. For the latter, POD is used to analyze coherent structures in terms of spatial modes.

In the subsequent section, the test rig and cooling hole geometry investigated in this study are introduced. The optical setup for PIV is described, and an overview of the data processing is given. More details to the test rig and flow parameters can be found in Ref. [16]. Previously conducted infrared thermography measurements yielding film cooling parameters can be found in Ref. [17].

A detailed schematic of the test rig utilized for the current investigations is depicted in Fig. 1. Unless stated specifically, all further considerations will refer to the coordinate system shown in Fig. 1. It is a right-handed trihedron with its origin at the start of the test plate ⑤. The test rig consists of two wind tunnels, the upper one constituting the hot gas and the bottom one the coolant channel. The test rig was first introduced by Fraas et al. [16], and uniformity of the inlet hot gas flow in terms of velocity and temperature field have been validated. A turbulence grid designed according to Roach [18] downstream of the inlet nozzle ① in combination with a further downstream boundary layer bleed ② is used to ensure well-defined and engine-like flow conditions at the position where coolant is ejected into the main stream. The interchangeable ejection module ③ connects coolant and hot gas channel via five separate film cooling holes aligned laterally at a constant x-position. It is manufactured from polyether ether ketone, a high-temperature-resistant plastic to ensure a low thermal conductivity (λ_th = 0.27 W/m/K). A change in coolant temperature between the cooling hole inlet and outlet is thus minimized. Coolant exits the ejection module at $35deg$ with no compound angle. Periodicity is assured due to the amount of holes. The interaction between single film cooling jets is dependent on the pitch to diameter ratio P/D. For the current study, a P/D = 8 is used, wherefore interaction between the film cooling jets is expected to be negligible as stated in Ref. [19].

To ensure thorough analysis of jet-mainstream interaction with a high measurement resolution, cooling holes are scaled up to a diameter of D = 10 mm. A 50D wide hot gas channel is used to prevent interaction between coolant jet and channel sidewalls. The coolant channel can be oriented either parallel or orthogonal to the hot gas channel. For the current study, the coolant channel is setup in parallel configuration with coolant flow in a positive x-direction. Optical access is provided through infrared-transmissive sapphire windows ④ at the top wall of the hot gas channel for infrared measurements and through fused silica ⑥ (dotted line) at both sidewalls. The latter are used in the current study as optical access for the cameras as part of the PIV system. The test conditions for this study were derived from real-engine conditions as shown in Ref. [16]. Hence, the test rig in this study combines all previously mentioned criterion for investigating film cooling under engine-realistic conditions insuring transferability of the results.

The aim of this study is the aerodynamic analysis of a baseline cooling hole geometry supplementary to infrared measurements presented by Fraas et al. [17]. The investigated geometry as shown in Fig. 2 constitutes a $10deg$–$10deg$–$10deg$ laidback fan-shaped hole with a cylindrical inlet segment. The length-to-diameter ratio is L/D = 7.5, the area ratio = 3.71, and the coverage ratio (hole breakout width based on the pitch) is 0.35. The corners of the diffuser are rounded with 0.5D while inlet and breakout edges of the diffuser are sharp edged.

The test rig operating conditions are summarized in Table 1.

Optical measurements were conducted employing TRDSPIV. A schematic of the optical setup is shown in Fig. 3. A green (λ = 527 nm) dual pulse Neodymium-doped yttrium lithium fluoride (ND:YLF) laser (Darwin-Duo by Quantronix) was used to illuminate d = 1 μm silicon oil particles seeded in both the hot gas and the cooling air channel. The scattered light was captured by two complementary metal-oxide semiconductor cameras with a resolution of 1024 px × 888 px. The double images were acquired in a frame-straddling mode with a time delay of Δt = 10 μs. For camera and laser synchronization, a synchronizer by ILA5150 GmbH was used. A laser light sheet with a thickness of δ_z = 1.5 mm was established orthogonal to the test plate and in opposite direction to the main stream through a fused silica window at the downstream end of the test rig. Double images were gathered at a frequency of 2000 Hz at multiple lateral locations (z-direction). To keep the measurement resolution high, two fields of view (FOV1 and FOV2) were recorded for every lateral position. FOV1 spans along −5.5 < x/D < 0.5 and FOV2 along 0 < x/D < 5.5. Each FOV was covering roughly 60 mm × 50 mm in terms of in plane dimensions with an overlap in x-direction of 5 mm. The separate FOVs—each constituting a measurement volume—will be referred to as measurement plane FOV1 and FOV2 in the following. The measurement plane can therefore be considered as the centerplane of the light sheet in z-direction for each FOV.

For data evaluation, a multi-pass scheme with an overlap of $50%$ and a final interrogation window size of 16 px in combination with a background subtraction were employed using PIVview3C by PIVTEC GmbH, yielding one velocity vector per millimeter.

For estimating the measurement uncertainty in the PIV experiments, a method based on correlation statistics introduced by Wieneke [20] 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 $3.7%$ 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 $8.0%$⁠. Additionally, a slight decrease of uncertainty in the streamwise direction of less than $1.0%$ was found. Detailed information regarding the measurement uncertainties of the flow parameters for both hot gas and coolant channel can be found in Ref. [16].

The flow field around the exit of a $10deg$–$10deg$–$10deg$ laidback fan-shaped hole (see Fig. 2) is analyzed for three different blowing ratios in the streamwise wall-normal centerplane (z/D = 0) and in a parallel plane in the lateral direction (z/D = −1). In the first part of this section, results of the PIV measurements are presented discussing general features of the flow. The instantaneous field data acquired through PIV are averaged generating a mean velocity field. Velocity profiles are extracted and compared for three different blowing ratios at different streamwise positions x/D. Additionally, the lateral spreading is analyzed for one blowing ratio by comparison of velocity profiles of different lateral planes.

In the second part, the POD is applied to the instantaneous field data and the resulting spatial POD modes are presented and analyzed.

All results shown in the following sections were obtained at a constant Reynolds number of Re_D,h = 13,000 for hot gas with a turbulence intensity of $8.2%$ and Re_D,cc = 30,000 for coolant flow parallel to the x-direction. Both Reynolds numbers are based on the cooling hole diameter D. For all further references, the position of the hole exit relative to the coordinate axis is shown in Fig. 4 for the streamwise wall-normal centerplane z/D = 0.

In Fig. 5, the contours at the blowing ratio M = 1.0 of all three velocity components are shown for the streamwise wall-normal centerplane z/D = 0 (Fig. 5(a)) and the parallel plane z/D = −1 (Fig. 5(b)). For the given blowing ratio, the ejected coolant causes a reduction in streamwise velocity component for both planes; however, the effect is more pronounced on the centerplane. Similarly, the imposed wall-normal velocity is larger in the centerplane compared to the laterally shifted plane. The fan-shaped outlet transports fluid towards its sidewalls causing the lateral velocity component to deviate from zero for the z/D = −1 plane. In Fig. 6, velocity profiles around the film cooling hole exit for a blowing ratio of M = 1.0 are depicted at different x/D positions as indicated in Fig. 4 for z/D = 0. All profiles converge to a common far-field velocity of U_∞ ≈ 46 m/s.

In Figs. 6(a), 6(c), and 6(e), the velocity profiles split up in all three components at different streamwise positions and are compared, while in Figs. 6(b), 6(d), and 6(f), the velocity profiles of two lateral positions are shown. At the upstream end of the first measurement plane (x/D = −5, z/D = 0), the flow appears indifferent of the ejection of coolant. At x/D = −4 just upstream, the upstream edge of the film cooling hole outlet (see Fig. 4) and a reduction of $2%$ in the streamwise velocity component can be observed (Fig. 6(a)). The wall-normal and lateral component remain constant as expected for the streamwise wall-normal centerplane (Figs. 6(c) and 6(e)). Towards the streamwise center of the cooling hole diffuser (x/D = −2), the streamwise velocity decreases further and a reasonable effect on the wall-normal velocity component can be observed in Fig. 6(c). This trend remains and the peak wall-normal velocity is reached at x/D = 0 right after the downstream edge of the fan-shaped hole. At the position furthest downstream within the measured FOV, the wall-normal velocity is back to its original profile upstream of the hole while the streamwise velocity converges to the profile shown in Fig. 6(a) for x/D = 5. For all x/D positions on the streamwise wall-normal centerplane, the lateral velocity component remains unchanged and close to zero (Fig. 6(e)) as expected for a symmetric ejection.

When compared to the measurement plane at z/D = −1 (Figs. 6(b), 6(d), and 6(f)), the streamwise and wall-normal velocity components are less affected by the coolant ejection while the lateral velocity component is increased. The diffuser shape of the film cooling hole outlet carries fluid in the lateral direction thereby decreasing the ejection’s influence in streamwise and wall-normal direction as observed in Fig. 5(b). While the lateral velocity component approaches zero again for the downstream position x/D = 5, the widening of the jet due to the diffuser is not yet fully completed.

In Fig. 7, the velocity profiles around the film cooling hole exit are shown for z/D = 0 (Fig. 7(a)) and z/D = −1 (Fig. 7(b)). For both lateral positions, the velocities for blowing ratios M = 0.5, 1.0, and 1.5 are shown.

Comparing M = 0.5 to M = 1.0, the influence of the ejected coolant causes a change in the gradient of the streamwise velocity component for both the centerplane and z/D = −1. In case of comparing the blowing ratios M = 1.0 and M = 1.5 at z/D = 0, the gradient of the streamwise velocity component is close to identical except close to the near-wall region where they diverge slightly. For the lateral z/D = −1 plane, a change in velocity gradient is still observable. This indicates a changed mixing behavior between coolant and hot gas for M = 1.0 towards M = 1.5 compared to M = 0.5 potentially due to the changed VR. The depth of aforementioned influence on the streamwise velocity profile is independent of the blowing ratio and increases downstream of the ejection until assimilation is reached at x/D = 5. A similar “saturation” effect at x/D = 5 can be observed in adiabatic film cooling effectiveness data shown in Ref. [17] for z/D = 0. However, this effect occurs between blowing ratios M = 1.5 and M = 2.0 as shown in Fig. 8. The same can be observed in the lateral distribution of the film cooling effectiveness at x/D = 5 as shown in Fig. 8. In both Figs. 8 and 9, the additional operating points M = 2.0, 2.5, and 3.0 are shown to clarify the aforementioned “saturation” effect. No difference in centerline adiabatic film cooling effectiveness can be observed when comparing M = 1.0 and M = 1.5. For judging the penetration depth of the coolant jet, temperature contours would be required additionally. However, due to the increase in VR from low to high blowing ratios, the wall-normal velocity increases in the vicinity of the hole exit for both lateral positions (not shown). The lateral velocity component is close to zero for all blowing ratios at z/D = 0 and increases as shown in Fig. 6(f) with a larger magnitude towards higher blowing ratios.

This method has the ability to produce a lower order model of a system by reconstructing a (flow) phenomenon using only a certain number of modes. Applied to fluid dynamics problems, the spatial modes represent coherent structures in the flow while the respective time coefficients contain information of the frequency of occurrence of the spatial modes.

In the current study, the POD was conducted for the fluctuating vector field on the x–y plane, corresponding to z/D = 0 at blowing ratios M = 0.5, 1.0, and 1.5. The percentage of the cumulative POD modes energy for the first 100 modes is shown in Fig. 10 for FOV1 (Fig. 10(a)) and downstream of the coolant ejection for FOV2 (Fig. 10(b)) at the streamwise wall-normal centerplane z/D = 0. The horizontal dashed lines denote $50%$ and $80%$ of the cumulative energy while the vertical dashed-dotted line marks mode 10. Modes one to six and further modes 10, 20, 30, etc. are marked additionally. Roughly, $50%$ of the total energy is cumulated after mode 20 for FOV 1 and after mode 10 for FOV2. While for both streamwise measurement planes the energy is largest for the lowest blowing ratio M = 0.5 and smallest for the highest blowing ratio M = 1.5, the difference in energy cumulated along the first few modes is more distinct for the downstream measurement plane. For both planes, the effect can be mainly attributed to the energy content of the first mode for each blowing ratio as it increases most significantly for the lowest blowing ratio.

In Figs. 11 and 12, the spatial POD modes including information about their energetic contribution to the total kinetic energy are shown as vector plots with a contour of the streamwise component of the according spatial mode for a blowing ratio of M = 1.0 in FOV1 and FOV2, respectively.The POD modes for M = 0.5 are shown in Fig. 13 for FOV2. For FOV1, the first six spatial modes are fairly similar for all investigated blowing ratios varying only in their exact energy content (not their order) and the precise location of vortex cores in the spatial modes domain. Hence, for FOV1, the POD modes are representatively shown for blowing ratio M = 1.0 (Fig. 11). For FOV2, the first six modes are structurally equivalent for blowing ratios M = 1.0 and M = 1.5. For blowing ratio M = 0.5 in FOV2, however, some modes differ from the other investigated blowing ratios. Therefore, the spatial modes in FOV2 are shown for blowing ratios M = 1.0 (Fig. 12) and M = 0.5 (Fig. 13). While the first mode is equivalent for M = 0.5 and M = 1.0 in FOV2, the second and third modes are interchanged. The flow structures signified by the third spatial mode for blowing ratio M = 0.5 become more relevant for higher blowing ratios shown by the larger mode energy. It therefore reappears as the second mode for blowing ratio M = 1.0. The second mode of blowing ratio M = 0.5 switches to third mode for blowing ratios M = 1.0 and M = 1.5. Modes four to six appear structurally similar despite differences in the exact locations of singularities. Comparing FOV1 and FOV2 for blowing ratio M = 1.0, the first three modes appear to match given the offset in x-direction. Modes four to six for FOV1 seem to be connected to the ejection of coolant rather than the jet shear layer as for FOV2. Within the scope of this study, only the first mode will be discussed thoroughly.

For all FOVs and blowing ratios, the first mode indicates a fluctuating behavior of the jet while exiting the hole. This becomes specifically evident when the first mode of FOV1 and FOV2 are compared for blowing ratio M = 1.0. The structure of large coherent motion at y/D < 1 starts in the region where coolant is ejected. Reconstruction of the velocity field using just the first mode (not shown) yields either a deceleration of the hot gas flow or leaves it almost unaffected to slightly accelerated. This suggests a pulsating behavior caused by the film cooling hole likely due to instationary flow separations in the diffuser or at the hole inlet. The energy content of the first mode varies largely between the different blowing ratios and FOVs (see also Fig. 10). The variation in the first mode’s energy content when comparing the different FOVs can be explained by the fact that the first FOV is only partially affected by the coolant ejection. In combination with the wall-normal and streamwise velocity contours shown in Fig. 5(a), this also shows that coolant is ejected majorly via the second half of the diffuser.

Additionally, the first modes energy content reduces with increasing blowing ratios: from M = 0.5 to M = 1.0, the energy reduces by $42%$ relative to blowing ratio M = 0.5 and by another $30%$ from M = 1.0 to M = 1.5 relative to M = 1.0 for FOV2. For blowing ratio M = 1.0, the second POD mode as shown in Fig. 12 contains roughly $20%$ of the total kinetic energy. The reasons for the significant change in energy content are twofold: first, a pulsation during coolant ejection would affect lower blowing ratios more strongly as the relative change in terms of ejected mass flow would be larger.

Second, a larger blowing ratio would enhance other secondary structures or even cause additional structures that would take up portions of the total kinetic energy. The time coefficient signifies the temporal behavior of the spatial modes. The combination of spatial mode and respective time coefficient allows the reconstruction of velocity fields from the spatial modes reintroducing the temporal information. Conducting a fast Fourier transformation on the time coefficient belonging to the first mode of FOV2 as shown in Fig. 14 reveals increasing amplitudes towards lower frequencies. Hence, the results indicate a fluctuation of the coolant ejection with increasing magnitudes when occurring with lower frequencies. However, no definite conclusion should be drawn until all significant coherent structures and their influence are fully comprehended. It has to be pointed out that the depicted modes (one to six) resemble only a portion of the total kinetic energy contained in all modes and therefore in the flow field (⁠$≈40%$ for FOV1 and $≈50%$ for FOV2). Many of the lower-energy modes are caused due to the complexity of the flow including the freestream turbulence. Therefore, the interpretation of the modes is far from trivial and will be discussed in more detail in future studies.

A measurement setup using TRDSPIV on film cooling hole ejection was introduced. The adopted experimental facility satisfies engine-realistic dimensionless parameters for the investigation of the aerodynamics of film cooling with crossflow in the coolant channel either parallel or perpendicular to the hot gas flow. Specifically, the realistic DR of 1.7 and a high turbulence intensity in the hot gas flow of $8.2%$ provide unique conditions considering all influencing parameters. The influence of coolant ejection on the hot gas flow is visualized and shows the significance of VR when investigating film cooling. Given a constant DR, the VR increases towards higher blowing ratios and the influence on the near-wall streamwise velocity component due to coolant ejection seems to “saturate” from blowing ratio M = 1.0 to blowing ratio M = 1.5. Marginal differences in streamwise velocity gradient are found at the position furthest downstream of the hole in the measurement area. This suggests a local VR close to unity due to the diffusion at the hole exit. The results agree with film cooling effectiveness data shown in Ref. [17], as they also show no difference in adiabatic film cooling effectiveness on the centerline just downstream of the ejection between blowing ratios M = 1.5 and M = 2.0. A thorough comparison of aerothermal measurements will be treated in future publications.

Applying POD on the time-resolved PIV data, the most energetic coherent structure indicates a pulsation of the coolant ejection potentially due to instationary effects in the hole. Flow separations at the hole inlet and specifically in the diffuser outlet may partially block the coolant from ejecting. The kinetic energy content of the respective first mode is largest for small blowing ratios and decreases with increasing blowing ratios. The blockage may affect low blowing ratios more drastically due to the relatively lower total mass ejected. Furthermore, larger blowing ratios may cause additional flow structures taking up portions of the energy. Additionally, changes in significance of specific flow structures in film cooling jet interaction based on their relative energy content are implied by the ranking of the spatial modes dependent for different blowing ratios.

The investigations were conducted as part of the joint research program COOREFLEX-turbo in the frame of AG Turbo. The work was supported by the Bundesministerium für Wirtschaft und Energie (BMWi) as per resolution of the German Federal Parliament under grant no. 03ET7091O. The authors gratefully acknowledge AG Turbo and Siemens AG for the support. Thanks to Olivier Mersch and Tristan Römer. The responsibility for the content lies solely with its authors.

There are no conflicts of interest.

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

k =

number of velocity snapshot

n =

number of gridpoint in evaluated velocity field

p =

pressure

r =

radius

u =

streamwise velocity component (x-direction)

v =

wall-normal velocity component (y-direction)

w =

lateral velocity component (z-direction)

x =

streamwise coordinate

y =

wall-normal coordinate

z =

lateral coordinate

A =

area

D =

cooling hole diameter

H =

height

K =

total number of velocity snapshots

L =

cooling hole length

M =

blowing ratio (=(ρ_cu_c)/(ρ_hu_h))

N =

total number of gridpoint in evaluated velocity field

P =

cooling hole pitch

T =

temperature

V =

freestream velocity

l_ε =

turbulent length scale

DR =

density ratio (=ρ_c/ρ_h)

IR =

momentum ratio (⁠$=(ρcuc2)/(ρhuh2$⁠))

Re =

Reynolds number

Tu =

turbulence intensity

VR =

velocity ratio (=u_c/u_h)

aw =

adiabatic wall

c =

coolant

cc =

cooling channel

cyl =

cylindrical

h =

hot gas

α =

inclination angle

Δt =

time between double images

δ_z =

light sheet thickness

δ₁ =

displacement thickness

η =

film cooling effectiveness

λ_th =

thermal conductivity

λ =

eigenvalue

ρ =

density

$Φ~$ =

eigenvector

Φ =

spatial POD mode