## Abstract

Film cooling is a critical gas turbine technology to reduce heat loads on the combustion chamber and the turbine vanes and blades. To improve film cooling performance, trenched cooling configurations where the holes are connected by a cross-stream slot in the surface have been developed. In this study, for the first time, we experimentally examine the influence of mainstream turbulence and large vortices on trenched film cooling flows. We apply an imaging technique based on thermographic phosphor particles seeded into the flow to measure 2D time-resolved gas temperature and velocity distributions in film cooling flows established in a closed-loop heated wind tunnel. Two trenched configurations (straight and an optimized zigzag design) are compared with ordinary effusion holes at momentum ratios () relevant to gas turbine combustors. Furthermore, two turbulence generation methods were used to create realistic mainstream turbulence levels () and large vortices, so film cooling flows at typical wind tunnel turbulence ($Tu=5.3%$) can be compared with combustor-relevant conditions. By comparing the film position derived from the time-average temperature fields, the optimized trench performs best at low momentum ratios and turbulence levels but the performance rapidly drops when the momentum ratio rises or the turbulence level is increased. The straight trench performs best across all conditions studied and this configuration is therefore recommended for combustor liner cooling where main flow turbulence levels are high. In general, increased turbulence intensity reduces the effective length of the cooling film for all geometries. The straight trench, however, produces a more stable cooling film than typical effusion holes or the optimized trench configuration. Both phase-locked and time-resolved data indicate that, in the presence of a dominating frequency in the turbulent main flow field produced using a vortex generator, there are instances where the cooling films are strongly disturbed in the streamwise direction and hot gas is locally in contact with the surface.

## 1 Introduction

Film cooling is an essential technology to ensure maximum performance of modern gas turbine combustors, as it reduces heat loads on critical components of the combustion chamber and the turbine. The intention is to form a homogeneous film of cold air that protects the engine components from direct contact with the hot gas flow and removes surplus heat.

Typically, cooling films are formed by an array of inclined cylindrical holes. Films formed this way, however, usually do not yield a homogeneous distribution of the cold air and, furthermore, for a high momentum of the cold air flow, the cold air tends to lift off the surface when entering the cross flow. This leads to a reduced cooling performance which is the reason why new cooling configurations have been developed within the last decades [1,2]. One possibility to improve the efficiency of film cooling is trenches embedded in the surface that connect the hole exits of multiple cylindrical holes in the lateral (cross-stream) direction [3]. In this configuration, the cooling air is first fed into the trench which subsequently forms a cooling film downstream of the trench. Since the air flow impinges on the downstream edge of the trench when leaving the cooling hole, the jet flow momentum is reduced, which diminishes the detachment of the cooling film from the surface. Also, since part of the air spreads laterally before leaving the trench, the film homogeneity is increased.

Bunker [4] showed that the adiabatic film cooling effectiveness of a straight trench configuration outperforms the one of the standard cylindrical holes by up to 75%. The adiabatic film cooling effectiveness, however, only represents the adiabatic surface temperature, not the heat transfer coefficient, which is also important to determine the heat flux into the wall and thus quantify the benefit of the cooling method. Bogard and Thole [1] confirm this general principle, emphasizing that understanding film cooling performance requires consideration of film cooling effectiveness, heat transfer coefficients, and net heat flux reduction together. Lu et al. [5] indicate that the heat transfer coefficient in straight trench configurations is increased and, therefore, the setup does not always have a positive effect on the net heat flux reduction. To overcome the negative effect of the increased heat transfer coefficients, the film cooling effectiveness has to be further increased.

In the work of Waye and Bogard [6], the adiabatic film cooling effectiveness of nine trench configurations was investigated in comparison with a baseline geometry (30 deg inclined, round axial holes) with two-dimensional IR thermography. The flow parameters blowing ratio, density ratio, and turbulence intensity were independently varied, and the trench configurations differed in their width (wide trench/narrow trench) and the design of the walls (vertical or inclined). A narrow trench with a perpendicular wall at the downstream edge of the coolant holes showed the best adiabatic cooling effectiveness, while the geometry of the upstream trench wall only slightly affected the cooling performance. In addition, the narrow trench configuration showed a continuously increasing adiabatic cooling effectiveness when the blowing ratio was increased (M = 0.3−1.4), while the effectiveness passed a maximum and dropped at higher blowing ratios when axial holes without a trench were applied. The authors conclude that, in the case of the narrow trench, the ejected coolant hits the downstream trench wall which blocks the coolant and causes its distribution within the trench. Furthermore, the close upstream wall keeps the cooling flow inside the trench and reduces the entrainment of hot flow. Finally, the presented main flow turbulence conditions ($Tu=1.0%and3.9%$) did not reveal any influence of the main flow turbulence level on the cooling effectiveness of the studied configurations.

Kröss and Pfitzner [7,8] studied the flow field in the vicinity of trenched cooling holes using numerical simulations and found that hot air enters the trench in regions between the feeding holes, even though they were using the narrow trench design of Waye et al. which should minimize this effect. The entrainment of the hot air into the trench leads to mixing with the cold air and consequently reduces the adiabatic effectiveness downstream. This is why Schreivogel et al. [9] designed a contoured trench that counters this effect by reducing the trench width between the holes. Additionally, the contour was optimized to further improve the lateral distribution of the cold air. To verify the expected improvement, surface temperature measurements were carried out in a closed-loop wind tunnel facility. The resulting spatially averaged adiabatic film cooling effectiveness demonstrated that the new geometry raised the performance compared with the straight trench configuration by another 30% to 50%, depending on the selected momentum ratio. For the measurements, combustor-relevant density (DR = 1.6) and momentum ratios (I = 1 to 8) were chosen, but the main flow turbulence intensity was around 1%, which is not representative for realistic engine conditions.

Bogard and Thole [1] give an overview of multiple investigations and state that for a profound understanding of film cooling it is necessary to duplicate the real flow in the test bench as closely as possible, e.g., turbulence level, surface curvature and roughness, and shaping of the hole exit. They primarily show results from rows of discrete coolant holes which represent the dominant film cooling configuration used for cooling turbine airfoils and endwalls. Inside the combustion chamber of gas turbines, however, mixing processes, e.g., mixing of pressured air and fuel in the primary zone or exhaust gas and dilution air in the mixing zone, dominate the flow field and increase its turbulence level. For film cooling flows, the near-wall flow field is most relevant as it forms the specific inflow conditions for the cooling jets. Kakade et al. [10] measured turbulence intensities and turbulent length scales near the liner wall of an annular combustor and found values of $Tu=25%$ for the turbulence intensity and $lT/r=15%$ for the normalized turbulent length scale (normalized with the combustor radius). These data show that typical wind tunnel flow conditions with turbulence intensities of Tu = 1% to 5% are not representative for realistic film cooling applications and thus not sufficient to study the cooling performance at engine-like conditions. Consequently, experiments at particular high turbulence conditions are necessary to characterize the performance of common and new cooling geometries.

One example regarding the influence of main flow turbulence is a study by Schmidt and Bogard [11], who investigated a single row of film cooling holes with an injection angle of 30 deg. They found that the optimum momentum flux ratio for maximum film cooling effectiveness at high freestream turbulence levels is nearly an order of magnitude higher than for low freestream turbulence conditions. This finding underscores the importance of studying film cooling at realistic turbulence levels as they occur in real applications. However, only few studies were found considering higher turbulence levels with trenched geometries. Huang et al. [12] and He et al. [13] numerically investigated straight and contoured trench configurations with main flow turbulence of $Tu=8%$ and 10%, respectively. The flow conditions were chosen with respect to turbine vane cooling and therefore do not reach turbulence levels relevant to combustion liners. Furthermore, neither study examines the influence of the increased turbulence levels on the cooling film and since both studies applied steady-state Reynolds-averaged Navier–Stokes (RANS) methods to simulate the flow field, transient flow phenomena cannot be examined, too.

The cited studies show that the geometry of the cooling air inlet and turbulence of the main flow can have a tremendous influence on film cooling flows. Therefore, to obtain a better understanding of such flows, it is imperative to conduct studies under conditions close to those encountered in gas turbine combustors. In this work, our objective is to understand the effect of combustor-relevant flow conditions on film cooling flows emanating from cylindrical holes and from two different trench geometries (a typical straight trench and the aforementioned optimized trench from Schreivogel et al. [9]). Therefore, experimental investigations are applied in a closed-loop thermal wind tunnel facility. In order to investigate the influence of increased main flow turbulence on the film cooling, in addition to a flow without actively generated turbulence ($Tu=5.3%$), two variants of turbulence generators are employed which produce a turbulence intensity of $Tu=16.4%$ (active turbulence grid, ATG) and $Tu=22.7%$ (vortex generator, VG), respectively. The latter generates a phase frequency of 5.33 Hz, which simulates low-frequency main flow oscillations in combustors. The investigations are performed at a density ratio of DR = 1.6 and momentum ratios of $I=3.5,5.7,and8.3$. A nonintrusive time-resolved optical measurement technique for simultaneous acquisition of flow temperature and velocity fields thermographic particle image velocimetry (thermographic PIV) [14]) is used to study the film cooling flow, which allows the observation of the overall flow structure, determination of turbulent heat flux, and measurement of individual vortices and their influence on the cooling film. The focus of the investigations is on the turbulent mixing of cooling air and the main flow, with the aim of better understanding the fluid mechanical processes in these flows. Our prior experimental efforts using this measurement technique focused on two hole geometries at low mainstream turbulence levels of $Tu=1%$ [15], and straight cylindrical holes at high mainstream turbulence levels of $Tu=14%$ [16]. In this work, a central question is whether the turbulent main flow can penetrate into the cooling film and impair its cooling effect due to the reduction of the momentum of the cooling air flow specifically for the trench geometries. Overall, we evaluate which of the investigated film cooling geometries is best suited for use under realistic gas turbine combustor flow conditions.

## 2 Experiments

In this study, film cooling flows are investigated using an optical technique based on luminescent particles seeded into the flow allowing instantaneous two-dimensional velocity and temperature field measurements simultaneously. The simultaneous recording of these quantities allows evaluation of turbulent heat flux and the temporal resolution of 6 kHz reveals characteristics in the flow dynamics. The test facility, experimental setup, data acquisition, and flow conditions are described in the following sections.

### 2.1 Test Facility

#### 2.1.1 Wind Tunnel and Test Section.

The flow field measurements were carried out in a closed-loop thermal wind tunnel facility. The flow is driven by a radial blower and its temperature is regulated by an electrical heater. The flow passes through a settling chamber and a 5:1 contraction nozzle before entering the test section. The settling chamber is usually equipped with honeycombs and meshes to remove turbulence and prepare a homogeneous flow for the test section. Previous campaigns, however, showed that the meshes get blocked when the flow is seeded with thermographic phosphor particles and therefore all meshes were removed during this study. Thus, hot-wire measurements were carried out to characterize the provided flow at the test section inlet showing a homogeneous flow field with a turbulence intensity of about 4% in the relevant region upstream of the film cooling flow.

The test section (see Fig. 1) has a cross section of 400 mm × 150 mm (width × height) and contains a segmented test plate of 514 mm × 140 mm (total length × width). The blower and heater are controlled in such a way that the flow has a mean velocity of 10 m/s and a temperature of $100∘C$ inside the test section. These conditions were monitored using a Prandtl probe and a pt100 resistance thermometer that were located in an unaffected region of the test section. Upstream of the test plate, a boundary layer suction removes the near-wall flow so that a new boundary layer starts to develop above the first test plate segment (length: 140 mm). A trip wire ensures a turbulent boundary layer and a foil heater creates an adiabatic temperature profile in the wall-normal direction. The second segment (length: 79 mm) contains the film cooling geometry and the third segment (length: 295 mm) provides the wall to be cooled. Tanks provide pressured air, which is cooled down to $−40∘C$ using liquid nitrogen and a heat exchanger, and finally enters a plenum at the backside of the test plate, which feeds the cooling air into the main flow.

Fig. 1
Fig. 1
Close modal

The three applied film cooling geometries are depicted in Fig. 2. The standard effusion geometry consists of three evenly spaced cylindrical holes (D = 6 mm) that are inclined at an angle of $30deg$. The holes are extended with a tube on the inflow side to create a fully developed flow inside the holes. This is necessary as otherwise the cooling air flow cannot be homogeneously seeded with phosphor tracer particles due to flow separation inside the holes (see Ref. [17]). The two other geometries are the standard straight trench and the optimized trench developed by Schreivogel et al. [9], both fed by three evenly spaced and $30deg$ inclined cylindrical holes. In this study, the effusion hole geometry is provided as a baseline geometry while the focus is on the performance of the two trench geometries.

Fig. 2
Fig. 2
Close modal

#### 2.1.2 Turbulence Generation.

Between the contraction nozzle and the test section, turbulence generators can be installed to increase the turbulence level in the main flow. For this study, two turbulence generators—referred to as the active turbulence grid (ATG) and vortex generator (VG)—were used to produce different turbulence levels and specific flow characteristics inside the wind tunnel.

The ATG (Fig. 3) is based on the work of Makita [18,19]. It consists of 11 rotating axes that are equipped with diamond-shaped plates to swirl the air that is passing through the grid. Every axis is driven by an individually controlled motor which allows the operation of the grid with near-constant blockage of the wind tunnel cross section. Hot-wire and high-speed PIV measurements of Bakhtiari et al. [20] showed that in the region where the film cooling takes place, turbulence levels up to $Tu=20%$ can be produced.

Fig. 3
Fig. 3
Close modal

The VG, on the other hand, consists of a single rotating plate (see Fig. 4) that is 397 mm × 95 mm in size producing nominal turbulence levels up to $Tu=30%$. The characteristic of the turbulence, however, is different compared with the ATG. When rotating the plate, about 60% of the wind tunnel cross section is periodically blocked which chokes the flow and modulates the mean flow velocity. Therefore, using an overall mean for the calculation of the turbulence intensity leads to a higher deviation from this mean when looking at the instantaneous values and thus to higher values for the nominal turbulence intensity. The modulation frequency is twice the rotation rate of the plate as the setup is symmetrical. Fischer et al. [21] used triple decomposition to analyze this effect and showed that turbulence intensities up to $Tu=20%$ remain.

Fig. 4
Fig. 4
Close modal

In summary, the two turbulence generators produce turbulent flow fields with similar fluctuation levels but different overall flow characteristics. While the ATG creates mainly homogeneous turbulence, the VG produces a turbulent flow field with a dominant frequency modulating the average turbulent flow field. This allows the experimental simulation of two completely different and relevant turbulent inflow characteristics for the cooling film.

#### 2.1.3 Bypass Geometry.

In this study an optical measurement technique, thermographic PIV, was applied to investigate the flow field in the center plane of the film cooling flows. In our first attempt using this technique, we identified problems with multiple scattering from the seeded phosphor particles (see Ref. [15]). To overcome this issue we modified the experimental setup with a bypass geometry (see Fig. 5). As the new setup (including other modifications) showed good improvement regarding the reduction of multiple scattering (see Ref. [16]), we kept the bypass geometry inside the test section for the measurements that are presented in this study. The bypass splits the test section flow into three parts and lifts the flow on the observation side of the wind tunnel, reducing the number of particles between the optical detector and the film cooling area.

Fig. 5
Fig. 5
Close modal

### 2.2 Measurement Technique.

The optical diagnostics and the measurement uncertainty were previously described in Ref. [16] so here only a brief overview is provided.

#### 2.2.1 Thermographic PIV.

The basic principle of the measurement technique is as follows. Micron-sized thermographic phosphor particles are seeded at low concentrations ($∼1011particles/m3$) into the main and cooling air flows as a tracer. The particles are electronically excited in a thin plane of the flow defined by a laser light sheet. The ensuing temperature-sensitive luminescence emission is captured by two cameras and the 2D temperature field is determined by a two-color ratio-based approach [14]. Simultaneously, velocity measurements are conducted based on the same tracer particles using conventional PIV. In these experiments, the phosphor zinc oxide was used (Sigma-Aldrich 96479). ZnO was found to offer the following benefits: (1) the inherent spectral temperature sensitivity of ZnO is quite high relative to the previously employed BAM:Eu phosphor, which improves the single-shot single-pixel temperature precision to ±5 K; (2) the small (600 nm) size and agglomerate morphology of the ZnO particles lead to improved flow tracing (the tracing response time is ∼5 μs allowing accurate tracking of turbulent fluctuations approaching 10 kHz); and (3) no influence of multiple scattering was observed with ZnO particles in this geometry at an average seeding density of $3×1011particles/m3$.

#### 2.2.2 Optical Setup and Data Acquisition.

The optical setup is depicted in Fig. 6 with the test plate in the center and the field of view (FOV) just above the central cooling air hole. The seeded particles are excited by a high-speed Nd:YAG laser (355 nm) operating at 6 kHz. Luminescence is detected using two high-speed CMOS cameras equipped with objective lenses and interference filters to isolate the temperature-dependent redshift and broadening of the ZnO emission. Image pairs are background subtracted, mapped using an image dewarping algorithm, binned and smoothed to a final nominal in-plane resolution of 1 mm. Then, the two images are divided by one another to generate intensity ratio fields. In the last step, intensity ratios are converted to temperature using a calibration curve derived from in-situ measurements of the intensity ratio in gas flows at known temperatures as measured using a thermocouple. For PIV, a double pulse high-speed Nd:YAG laser (532 nm) illuminates the particles at the same time and in the same plane as the UV laser. Green scattered light is detected by a third CMOS camera using a standard high-speed PIV frame straddling technique. Image pairs are used to determine the velocity field using a commercial PIV algorithm (Davis, LaVision). In this way, simultaneous temperature and velocity measurements are conducted at a 6 kHz rate during a 3 s recording time, which are then used to calculate time-average, root-mean-square (RMS) fluctuations, and turbulent heat flux fields. All specifics of this experiment are described in complete detail in the aforementioned paper [16]. For ease of reference, the single-shot single-pixel temperature precision is ±5 K, the overall systematic absolute temperature error is ±6 K, and the random error in the velocity measurement is ∼0.5 m/s. Owing to the finite response time of the particles, the turbulent heat flux is underestimated by 6% at 7 kHz. All these uncertainties are quoted at a 1σ confidence interval.

Fig. 6
Fig. 6
Close modal

### 2.3 Flow Conditions.

During this campaign, measurements were carried out for three combustor-relevant momentum ratios, $I=3.5,5.7,and8.3$, and three main flow turbulence conditions. The momentum ratios were controlled based on sensor data of temperature and velocity/volume flow constantly recorded during the experiment. To avoid periodically changing flow conditions due to the main flow oscillations, a 60 s floating average main flow velocity was calculated for controlling the test rig. The comparison of the resulting flow conditions throughout the series of measurements showed a variation in the average momentum ratio between 1% (at $I=3.5$) and 3% (at $I=8.3$). The actual turbulence levels were derived from the 2D PIV data in an unaffected region upstream of the film cooling inlet. The turbulence intensity without a turbulence generator was $Tu=5.3%$ and varied within 5% (relative deviation) between the different test cases. The ATG was operated with a motor rotation rate of 60 rpm, resulting in a turbulence intensity of $Tu=16.4%$ and the rotation rate of the VG plate was 160 rpm, resulting in a nominal turbulence intensity of $Tu=22.7%$ and a modulation frequency of 5.33 Hz. The variation of the turbulence level in the case of operation of any of the turbulence generators was 1.5% (relative deviation). All test cases of the present campaign are listed in Table 1.

Table 1

Test cases

ITu
Effusion hole3.5/5.7/8.3$5.3%/16.4%/22.7%$
Straight trench3.5/5.7/8.3$5.3%/16.4%/22.7%$
Optimized trench3.5/5.7/8.3$5.3%/16.4%$
ITu
Effusion hole3.5/5.7/8.3$5.3%/16.4%/22.7%$
Straight trench3.5/5.7/8.3$5.3%/16.4%/22.7%$
Optimized trench3.5/5.7/8.3$5.3%/16.4%$

## 3 Results

The following results are derived from sets of 6000 consecutive images. This corresponds to 1 s recording time which means that in the case of the vortex generator 5 full periods are part of the processed dataset. In the case of the active turbulence grid 1 s recording time corresponds to 2 full periods which is enough as no dominant frequency is produced. The data reduction was necessary because processing of the full 3 s-dataset raises computational time and storage excessively. Comparison of the results from multiple 1 s-datasets as well as longer datasets containing up to 3 s showed only small variations in the average flow field and therefore the data reduction was deemed a valid approach.

Figure 7 displays the average flow field in the film cooling flow center plane for the effusion hole geometry. Normalized temperature (upper subplot) is presented as a contour plot while the velocity field (lower subplot) is displayed in two ways, a contour plot to show the velocity magnitude and an overlaying vector field to visualize its direction. These and all the following figures displaying the average flow field in a similar way indicate the location of the film cooling geometry in the lower left corner. The momentum ratio in Fig. 7 is I = 5.7 and the main flow turbulence intensity is $Tu=5.3%$. The average cooling air flow is lifted off the surface and forms two shear layers: (1) between the main flow and the cooling air jet and (2) between the jet and the wall. This means that hot air can enter the wake region between the cold air flow and the wall, and thus reduces the cooling efficiency. This setup is selected as a basis for comparison with the studied trench geometries. A detailed discussion of the flow characteristics with the effusion hole and the effect of mainstream turbulence is given in Straußwald et al. [16]. A range of additional results from the present measurement campaign are also presented in an upcoming dissertation of the first author.

Fig. 7
Fig. 7
Close modal

### 3.1 Trenched Holes Geometries – Flow Structure and Turbulent Heat Flux.

Similar to the effusion hole case, measurements with the two trench geometries were carried out in the center plane of the middle cooling hole (y/D = 0). For the discussion of the basic flow structure of the two trench geometries and the comparison of the different geometries, test cases with a momentum ratio of I = 5.7 and a main flow turbulence intensity of $Tu=5.3%$ were chosen. Resulting plots of the average flow field (normalized temperature and velocity), the turbulent heat flux and the turbulent momentum are presented in Fig. 8 for both geometries. The top two rows show the normalized average temperature and the velocity field plotted similar as for the effusion hole geometry (Fig. 7). The plots in the third to the fifth row display the corresponding turbulent heat fluxes (x-direction: $ux′T′¯$, z-direction: $uz′T′¯$) and momentum ratios ($ux′uz′¯$), which were calculated from the instantaneous temperature and velocity fields.

Fig. 8
Fig. 8
Close modal

#### 3.1.1 Straight Trench.

The left column of Fig. 8 displays the results for the straight trench geometry. From the average flow field, it can be observed that the average film cooling flow is mostly attached to the surface between x/D = 0 and the end of the field of view. Just downstream of the cooling air injection a separation bubble can be observed which, however, can only be seen in the velocity field but not in the temperature field. This indicates that, even though the cooling air flow slightly separates from the surface, hot air cannot enter this region and the cooling effect is hardly disrupted.

The turbulent heat flux and the turbulent momentum reveal further characteristics of the straight trench flow. While in the case of the effusion hole configuration two equivalent shear layers are present, the trench produces a dominant (upper) shear layer and a less pronounced shear layer between the cooling air flow and the separation bubble. Furthermore, the turbulent heat flux in the x-direction shows a change of sign along the x-coordinate in the dominant upper shear layer. While the negative turbulent heat flux can be explained by relatively fast and cold air from the cooling holes mixing with relatively hot but slow air from the main flow, the positive turbulent heat flux is unexpected. Kröss and Pfitzner [7,8] showed that hot air enters the trench, which might be an explanation for the positive heat flux as the hot air is accelerated while the cold air is blocked and therefore decelerated. Moreover, since the cold air is blocked by the downstream edge of the trench, the x-component of the velocity is almost zero. Therefore, when considering just the x-component of the turbulent heat flux, the blockage of the cooling air results in relatively fast hot air and relatively slow cold air and consequently produces a positive heat flux. After leaving the trench the cooling air flow changes its main direction as it stays attached close to the wall. This leads to a rising x-component of the velocity vector which finally results in a negative turbulent heat flux in the x-direction. The z-component of the turbulent heat flux is always negative in the upper shear layer and does not show any change in sign. This can be explained by the z-component of the main flow velocity which is almost zero, while the z-component of the cooling air flow is continuously positive. In combination with the relatively low temperature compared with the main flow, the turbulent heat flux in the z-direction becomes negative.

#### 3.1.2 Optimized Trench.

Figure 8 right shows the corresponding plots for the optimized trench geometry. Again, the momentum ratio is I = 5.7 and the main flow turbulence intensity is $Tu=5.3%$. The flow field (normalized temperature and velocity) shows that the average cooling air flow is thinner than in the straight trench case. A separation bubble is not visible either in the velocity or in the temperature field, and relatively cold air ($θ¯=0.6$) stays right next to the wall until x/D ≈ 7.5. This suggests that the optimized trench geometry improves the adiabatic film cooling effectiveness compared with the straight trench which is consistent with the findings of Schreivogel et al. [9] using surface measurements.

The turbulent heat flux and turbulent momentum generally support these findings. Still, the turbulent momentum indicates a small separation bubble between the cooling air and the wall. However, the (upper) shear layer is well pronounced and closer to the surface compared with the straight trench results. This confirms that the optimized trench cooling flow is thinner than the straight trench cooling flow, which might be due to the improved lateral distribution in the optimized trench case. Again, the x-component of the turbulent heat flux shows a change of sign in the upper shear layer, while the positive part is less pronounced than in the straight trench case. This can be explained with the trench contour that is inclined toward the main flow direction and narrows between two feeding holes, preventing hot air from entering the trench and at the same time not completely eliminating the x-component of the cooling air flow. Therefore, the x-component of the cooling air flow velocity exceeds the main flow velocity at shorter streamwise distances compared with the straight trench and thus the sign change in the turbulent heat flux occurs at shorter distances after leaving the trench.

### 3.2 Influence of Main Flow Turbulence on Film Cooling Flows.

Figure 9 displays temperature and velocity fields at a momentum ratio I = 5.7 and a main flow turbulence intensity of $Tu=16.4%$ for the effusion hole, the straight trench, and the optimized trench geometry, respectively. Comparing the data to the corresponding plots in Figs. 7 and 8 reveals the effect of an increased main flow turbulence intensity on the cooling film.

Fig. 9
Fig. 9
Close modal

The length of the average cooling film is reduced which becomes apparent when comparing the maximum x-positions of corresponding $θ¯$ contour lines at low and high turbulence. The negative effect of increased main flow turbulence is the strongest in the case of the optimized trench geometry. The maximum x/D-value of the $θ¯=0.5$ contour line, for example, is reduced from beyond the end of the field of view to immediately downstream of the trench. These results imply that the cooling film that emanates from the optimized trench geometry is less resistant to main flow turbulence than the one emanating from the effusion hole or the straight trench geometry. Therefore, we can conclude that the positive effect of the optimized trench, which was found by Schreivogel et al. at low turbulence conditions [9], is reversed at high main flow turbulence levels.

#### 3.2.1 Influence of Cooling Hole Geometry.

For direct comparison of the three geometries, z-profiles of the averaged temperature at two locations ($x/D=0and5$) normal to the wall are plotted for $Tu=5.3%$ and $Tu=16.4%$ in Fig. 10. Due to the angled contour of the optimized trench, its downstream edge in the center plane is shifted by x/D = −1 compared with the other geometries. Therefore, z-profiles of the corresponding locations are additionally plotted with separate markers.

Fig. 10
Fig. 10
Close modal

At low main flow turbulence (Fig. 10, left), the data show that the optimized trench cooling flow stays closest to the surface while the straight trench flow is thicker. This can be explained with the increased lateral distribution which reduces the amount of cooling air in the center plane in the case of the optimized trench. Both geometries indicate a well-attached cooling film, while the effusion hole jet is clearly lifted off the surface at x/D = 5.

Increasing main flow turbulence (Fig. 10, right) does not change this basic characteristic. The optimized trench flow is closest to the wall while the effusion hole jet lifts off the surface at downstream locations. However, the effect of the cooling film from the optimized trench tends toward zero at x/D = 5. Of the three geometries, the straight trench cooling film penetrates the furthest downstream and therefore is considered to perform best in terms of cooling efficiency.

#### 3.2.2 Influence of Momentum Ratio.

Typical film cooling parameters, such as the momentum ratio I, scale the resulting flow field downstream of the cooling air inlet on the basis of the density and the velocity of the main flow and the cooling air flow. The momentum ratio ($I=(ρcuc2)/(ρmum2$)) in particular is a good parameter to characterize the dynamic interaction between the two flows [1], and the cooling air lift off in the case of the effusion hole geometry [22]. Thus, the cooling performance will be analyzed together with the effect of the chosen geometry and the main flow turbulence by varying the momentum ratio between $I=3.5and8.3$.

The measured flow fields cannot be used to calculate the absolute film cooling effectiveness nor the net heat flux reduction, but they do allow comparison of the relative performance of the different configurations. As an indicator for the cooling performance in a specific test case, the distribution of the cold air in the average temperature field is quantified by the location of the $θ¯=0.5$ contour line. This contour line was chosen as it represents the mean between pure main flow and pure cooling air, and therefore provides an optimal threshold to distinguish between hot and cold regions. The comparison of the behavior of this contour line indicates the cooling performance in the manner that (1) the further downstream the contour line ends the longer the cooling effect of the cold air is maintained and (2) the closer the contour line stays to the surface, the better the flow attaches to the wall that has to be cooled.

These conditions are represented by the maximum x-position $xmaxθ¯$ and the maximum z-position $zmaxθ¯$ of the $θ¯=0.5$ contour line, respectively (see Fig. 11). To allow simple comparison of different test cases, the conditions are merged into a single measure by dividing $xmaxθ¯$ by $zmaxθ¯$. This approach eventually forms a measure that can be simply evaluated in the following way: the higher the measure, the better the test case performs as the cold air stays close to the surface (small $zmaxθ¯$) and does not mix with the surrounding hot air for an extended distance (high $xmaxθ¯$).

Fig. 11
Fig. 11
Close modal

In Fig. 12, the results are plotted against the momentum ratio for the three geometries and the two main flow turbulence levels $Tu=5.3%and16.4%$. For low main flow turbulence (blue datasets) the effusion hole and straight trench show relatively constant performance for the full range of measured momentum ratios. This means that raising the cooling air volume flow certainly increases cooling flow propagation in the x-direction but also in the z-direction. In the case of the effusion hole geometry, increasing z-expansion means increasing cooling air lift off and hot air can easily enter the wake region downstream of the cooling air inlet. In the case of the straight trench, increased z-expansion does not necessarily imply flow lift off. Actually, mean flow fields show that the cooling air flow stays attached to the surface for all momentum ratios. The cooling film, however, thickens up and consequently surplus air is not fully distributed in the lateral direction. Therefore, it has to be assumed that the cold air is not evenly spread across the surface, forming a cooling film that is not fully homogeneous. The optimized trench shows a higher performance in the case of low main flow turbulence and momentum ratios. Furthermore, data show a rise in performance from $I=3.5to5.7$. This means that increasing the cooling air volume flow results in a longer cooling film that does not thicken up by the same percentage. Consequently, most of the surplus cooling air is used for a longer cooling film and better homogeneity in the lateral direction. However, in the case of I = 8.3, the performance of the optimized trench drops close to zero. This can be explained with the average flow field data that show a flow lift off, indicating a transition in the average flow field from “trench flow” to “effusion hole flow”. This means that the momentum of the cooling air flow is too high so the majority of the cold air leaves the trench without being deflected at its downstream edge. This ends in an effusion-hole-like flow field with less air being distributed in the lateral direction and flow lift off in the center plane. Comparing the low turbulence data (blue datasets) with the increased turbulence data (red datasets), a consequent reduction in performance can be observed. This is true for all geometries but in the case of the optimized trench the drop in performance is such that the geometry has lower $xmaxθ¯/zmaxθ¯$ values than both the effusion hole and the straight trench geometries. This can be explained with the reduction in flow momentum that is the reason for the excellent performance at low turbulence ($I=3.5and5.7$) but allows increased mixing in the case of rising main flow turbulence.

Fig. 12
Fig. 12
Close modal

Summarizing the results for the three geometries shows that the optimized trench geometry performs best in a certain range of momentum ratios and at low turbulence levels. Outside this range or at higher turbulence levels, the performance rapidly drops. The straight trench, however, not only outperforms the effusion hole geometry at all investigated momentum ratios but also performs best in the case of increased main flow turbulence. Therefore, the authors recommend the use of straight trench geometries for combustor liner cooling where increased main flow turbulence is always present.

#### 3.2.3 The Influence of Large Main Flow Vortices on Cooling Film Structure and Dynamics.

In this section, the effects of a dominant frequency in the turbulent mainstream on film cooling flows are investigated. Figures 13 and 14 display average temperature and velocity fields at different phase angles ϕ for the effusion hole and the straight trench geometry, respectively. The phase angles are $0deg$ (upper subplot), $45deg$ (middle subplot), and $90deg$ (lower subplot) and the phase frequency f = 5.33 Hz is the modulating frequency introduced by the VG plate. The average images are calculated from the 1 s recording time which means that the same phase angles are extracted from five consecutive periods.

Fig. 13
Fig. 13
Close modal
Fig. 14
Fig. 14
Close modal

A schematic of the phase lock average calculation method is depicted in Fig. 15 for a single pixel and a generic measure. The value tϕ of $ϕ=0deg$ was manually chosen from the time-resolved data by identifying maximum deviation from the mean in the instantaneous flow field. Then, the points in time t2ϕ···5ϕ representing the same phase angle in the other periods were calculated. Equivalent points in time for $ϕ=45deg$ and $90deg$ were then derived relative to the $ϕ=0deg$ data. Finally, the phase lock average images are calculated from the respective points in time determined in every period while for every tϕ···5ϕ a range of tϕ···5ϕ ± 2 ms was selected for averaging. This procedure smooths the resulting average flow field without loosing the main flow characteristics, highlighting the application of kHz-rate measurements to extract meaningful averages during short run times.

Fig. 15
Fig. 15
Close modal

Processing of all relevant datasets ($Tu=22.7%$, see Table 1) shows that the resulting influence on the cooling air flow, which is described in the following paragraph, is true for all investigated geometries and flow conditions. Therefore, the presented results for the effusion hole and the straight trench are displayed for I = 3.5 and I = 5.7, respectively.

In both test cases, the phase lock average shows a strong variation in the characteristic flow field over time. At $0deg$, the influence of the cooling air on the average flow temperature ends after a shorter distance downstream of the hole exit, than at $90deg$, where the cooling film shows maximum expansion (see the left column in Figs. 13 and 14). Two effects might explain this behavior: (1) variable turbulence intensities vary the mixing rate between hot and cold air and (2) the amount of cold air leaving the plenum is not constant over time. A change in turbulence intensity is reasonable as the rotating plate of the vortex generator certainly does not produce homogeneous turbulence. The second explanation, furthermore, is consistent with findings of Sperling et al. [23] that the cooling air plenum can work as a Helmholtz resonator when pressure oscillations occur in the main flow. A consequence of the Helmholtz resonator is the modulation of the instantaneous cooling air volume flow which would result in a variation of the cooling film length. In the present setup, the operation of the VG periodically blocks the wind tunnel cross section which produces pressure oscillations in the main flow. Thus, preconditions for the Helmholtz resonator are given. Furthermore, the phase lock average velocity fields (see the right column in Figs. 13 and 14) display a rise of the maximum velocity in the region of the cooling air flow, supporting the assumption of an oscillating cooling air volume flow. The token in the upper right corner of every subplot symbolizes the relative position of the VG plate which might be associated with the current flow behavior. Note this is not the actual plate position, as there is a time shift between the plate position and the effect on the cooling air flow because the blockage has to propagate through the test section before reaching the cooling air inlet. However, the tokens are used to indicate the VG-flow phase relationship: the horizontal plate position (upper subplot) releases the main flow that was previously blocked, increasing the pressure in the test section and pushing back the cooling air flow. A vertical plate position (lower subplot) blocks the wind tunnel flow, resulting in a low main flow pressure and an increased cooling air flow and therefore jet penetration.

In the case of the straight trench geometry (Fig. 14), the separation bubble increases with rising cooling air velocity from $ϕ=0deg$ to $90deg$. This, however, only has a small effect on the z-expansion of the cooling film as shown in the temperature fields, which supports the assumption that the straight trench produces a cooling film that is less vulnerable to large oscillations in the main flow.

Figure 16 shows instantaneous temperature and velocity fields for both geometries extracted from the subsampled 6 kHz recording such that the series covers a full phase from $Φ=0deg$ to $180deg$. These images reveal the interaction of large-scale coherent main flow fluctuations with the cooling films. For the standard effusion holes (Fig. 16, left), in the first image one can see evidence of a large vortex with an instantaneous velocity fluctuation pointing upstream which acts against the flow direction of the cooling film. As the VG plate rotates, instants with a relatively low mainstream fluctuation velocity show an extended cooling jet. Where the mainstream fluctuation velocity is high, the jet is typically contorted and reduced in length. Similar dynamics can be observed for the straight trench cooling films. In the first image, the film is reduced in length to x/D = 2, instantaneously even shorter than indicated by the phase lock average temperature images. Here, either the film is disturbed in the lateral direction (which is not accessible by these measurements), or pushed back into the trench. As the plate rotates, the jet length recovers but there are moments where large vortices in the main flow drive hot gas through the cooling film and into local contact with the surface.

Fig. 16
Fig. 16
Close modal

## 4 Conclusions

Thermographic PIV measurements have been performed to study the cooling air flow emanating from three different film cooling geometries at various turbulence main flow conditions and momentum ratios relevant to gas turbine combustors. The turbulence conditions have been varied using an active turbulence grid and a single-rotating plate vortex generator. Without any of these devices, the closed-loop wind tunnel facility provides a turbulence intensity of $Tu=5.3%$. When the ATG was installed it was operated in such a way that the turbulence intensity was increased to $Tu=16.4%$ and in the case of the VG being installed $Tu=22.7%$ was reached. In addition, the latter flow condition shows a dominant frequency that is related to the plate rotation rate of the VG and thus simulates strong perturbations inside the combustor liner.

Results for a standard effusion hole configuration were shown as a baseline in our study of the effects of a straight trench and an optimized trench geometry on the flow field. At low main flow turbulence levels, the normalized temperature and velocity fields show attached cooling films for the two trench geometries while in the case of the effusion hole at the same momentum ratio, the jet is lifted off the surface.

Average turbulent heat flux and turbulent momentum data identify only a single (upper) shear layer for the trench configurations which verifies that the cooling films emanating from the trenches are attached to the surface. In the case of the straight trench, a separation bubble is visible that almost disappears for the optimized trench geometry. The turbulent heat flux in the x-direction displays a change of sign in the shear layer. This can be explained by the cold air from the feeding holes being blocked by hot air entering the trench and the downstream trench wall that reduces the x-component of the velocity vector. Therefore, when cooling flow is leaving the trench the turbulent heat flux is positive. Later, once the flow propagates parallel to the wall the x-component increases and the turbulent heat flux turns negative.

Increased turbulence intensity reduces the effective length of the cooling film for all geometries. This can be explained with increased mixing intensity due to increased velocity fluctuations. By comparing the film position derived from the time-average temperature fields, the optimized trench performs best at low momentum ratios and turbulence levels but the performance rapidly drops when the momentum ratio rises or the turbulence level is increased and thus is not suitable for applications with increased main flow turbulence. Both phase-locked and time-resolved data indicate that, in the presence of a dominating frequency in the turbulent main flow field produced using the vortex generator, there are instances where the cooling films are strongly disturbed in the streamwise direction and hot gas is locally in contact with the surface. In terms of cooling film position and stability with regard to main flow turbulence, the straight trench performs best across all conditions studied and this configuration is therefore recommended for combustor liner cooling where main flow turbulence levels are high and strong oscillations can occur.

To finally verify this conclusion, however, it is necessary to measure the adiabatic film cooling effectiveness and the heat transfer coefficient in future work, as the flow field data can only indicate the cooling performance without providing any quantification on the resulting heat transfer into the wall.

## Acknowledgment

The work was financially supported by Deutsche Forschungsgemeinschaft (DFG, PF 443/7-1) and Universität der Bundeswehr München (FORscience Research Fund). The support is gratefully acknowledged.

## Conflict of Interest

There are no conflicts of interest.

## Data Availability Statement

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

## Nomenclature

• f =

frequency, Hz

•
• r =

•
• t =

time, s

•
• v =

velocity, m/s

•
• D =

hole diameter, m

•
• I =

momentum ratio, $(ρcuc2)/(ρmum2)$, –

•
• M =

blowing ratio, (ρcuc)/(ρmum), –

•
• T =

temperature, K

•
• lT =

turbulent length scale, m

•
• x, y, z =

coordinate system, m

•
• DR =

density ratio, ρc/ρm, –

•
• Tu =

turbulence intensity, –

•
• α =

hole inclination, $deg$

•
• θ =

normalized temperature, (TmT)/(TmTc), –

•
• σ =

standard deviation, –

•
• ϕ =

phase angle, $deg$

### Subscripts and Superscripts

• c =

cooling air

•
• m =

main flow

•
• max =

maximum

•
• x, y, z =

coordinate system

•
• ϕ…5ϕ =

nth period of phase angle ϕ

•
• $θ¯$ =

specific contour line of the average temperature field

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