Experimental and Numerical Investigation of Sweeping Jet Film Cooling

Development of new film cooling technologies has played an important role in improving the efficiency of gas turbine engines. The temperature of the hot gas flow path is well above the material melting temperature in modern gas turbines. Thus, efficient cooling architecture is required to improve the engine efficiency. Film cooling is being used to reduce the heat load experienced by the turbine components where a relatively colder fluid is bled away from the compressor and injected through discrete holes onto the hot surface of the turbine components. In general, there are some penalties associated with the use of coolant since the fluid does not provide any potential work until after it is reinjected into the main gas path. Therefore, an effective use of coolant is required to maximize the engine performance.

In recent times, significant advances have been made in the design of the film cooling holes where conventional cylindrical holes are being replaced by compound-angle shaped diffused holes [1]. One of the primary benefits of the shaped hole is its superior cooling performance compared to the cylindrical hole. However, the interaction between the coolant and the freestream can vary significantly with holes of different shapes. A number of studies have reported on the effects of different shaped holes such as shaped holes with conical diffusers [2], laid-back fan-shaped holes [3,4], cusp-shaped holes [5], console holes [6], trenched holes [7,8], and dumbbell and bean shaped holes [9].

A major problem associated with any cooling hole is the formation of the counter-rotating vortex pair (CRVP) that assists the lift-off of the coolant. Research has been done to mitigate the detrimental effect of CRVP. Haven et al. [10] studied the interaction between the jet and freestream for shaped holes and concluded that breakout edges of shaped holes sometimes generate unsteady vortices that partially weaken the CRVP. Thole et al. [11] saw no sign of a strong CRVP in an aggressively expanded hole. Heidmann and Ekkad [12,13] introduced an “antivortex film cooling” concept which was later validated by Dhungel et al. [14]. Schulz et al. [15] reported a new vortex pair on either side of the main CRVP resulting in improved film effectiveness. LeBlanc et al. [16] used an antivortex hole embedded in a trench and found similar improvement in film effectiveness.

Thurman et al. [17] studied sweeping jet (SJ) film cooling with a hole spacing of P/D = 6 by implementing a fluidic oscillator with a $60deg$ exit fan angle and showed improved cooling performance in the lateral direction compared to the 777-shaped hole [18]. Thurman et al. concluded that improved performance in cooling effectiveness could be achieved by modifying the exit angle of the fluidic oscillator and optimizing the internal geometry of the hole. Since sweeping jet film cooling shows a marked increase in lateral film effectiveness, there is interest in exploring different fluidic oscillator hole exits and increased hole spacing to provide greater lateral coverage without additional coolant requirement.

The present study builds upon the result reported by Thurman et al. by introducing a new exit configuration of a sweeping jet film cooling hole and increasing the hole spacing to P/D = 8.5. In contrast with the previous study where the exit fan angle was $60deg$⁠, the current study utilized a larger exit sweeping angle of 70 deg in an effort to allow a larger lateral spreading of coolant.

Thurman et al. [17] reported adiabatic film effectiveness for a sweeping jet design over a range of blowing ratios $(1≤M≤2.5)$ at a single freestream turbulence level of 1.5%. No thermal field, convective heat transfer coefficient, or discharge coefficient data were reported. The objective of this study is to provide comprehensive adiabatic film effectiveness, thermal field, convective heat transfer coefficient, and discharge coefficient data for a new SJ film cooling hole design to determine their potential usefulness in gas turbine film cooling applications. Due to the elevated turbulence levels typical of turbine flowfield, data were acquired for two turbulence intensity levels $(Tu=0.4%and10.1%)$⁠. Film effectiveness, thermal field, and discharge coefficients are compared with the baseline 777-shaped hole [18] at P/D = 8.5. These comparisons will hopefully guide the design and implementation of sweeping jets in film cooling applications.

The fluidic oscillator is a promising device for many engineering applications due to its unique nature of producing an oscillating jet at high frequency with no moving parts. The unsteady nature of the jet and the distributed nature of momentum addition make it very attractive to the engineering community. Although the design of such devices varies depending on the application, all fluidic oscillators can be divided into two main types: wall-attachment type and jet interaction type [19].

A conventional wall-attachment type oscillator [20] was used in this study with an exit fan angle of $70deg$⁠. The aspect ratio (AR) of the oscillator is the ratio of the throat width (W_t) to the throat height (H_t). The power nozzle is the entrance aperture which is coupled to a source of fluid under pressure. Figures 1(a)–1(d) show the schematic of a typical wall-attachment type fluidic oscillator and its working sequence. The general working principle of such a device is quite simple and involves no moving parts [21]. A jet enters into the cavity from a pressurized plenum via the power nozzle. Then the power jet expands to fill the throat and the feedback channels. Two opposite vortices begin to form on both sides of the power jet. As the intensity of the vortices increases, one vortex becomes dominant. This causes the power stream to deflect against the opposite wall. When the power stream deflects to the side wall, it attaches to the wall due to the “Coanda effect.” This allows a portion of the fluid to enter into the feedback loop which flows back to the control port and causes the power stream to detach from the side wall. The power stream then switches to the opposite wall and the same process repeats, resulting in an oscillatory fluid motion at the exit of the throat.

Experiments were performed in an open-loop wind tunnel powered by a blower. The schematic of the wind tunnel is shown in Fig. 2. Downstream of the blower, an electric duct heater is used to heat the freestream flow temperature from ambient (293 K) to 333 K. The heated flow then enters into a conditioning plenum of diameter 0.6 m. This conditioning plenum consists of a single layer of perforated aluminum plate, 0.076 m of honeycomb straightener, and five layers of fine screen. A foam nozzle transitions the flow from the circular plenum to a 0.38 m square plexiglass test section. It is important to note that the tunnel has two identical test sections; freestream flow can be diverted from one test section to another with a butterfly valve. The freestream velocity was measured with a pitot static probe 1 m downstream of the test section entrance.

The freestream temperature was measured with two 0.5 mm bead diameter T-type thermocouples 1.42 m downstream of the test section entrance. A constant temperature anemometry hotwire was used to measure the turbulence level in the test section of the tunnel. With a nominal freestream velocity of 10 m/s and temperature of 308 K, a two-dimensional flow uniformity of ±0.4% in velocity and ±1 K in temperature were estimated at 1.42 m downstream of the test section entrance. A grid with vertical square bars (25.4 mm across at 58.4 mm intervals) was installed at 0.4 m downstream of the test section entrance. Each bar was rotated at an angle of 45 deg to make a “diamond shape” configuration with respect to the streamwise direction. With this bar configuration, the estimated turbulence intensity was 10.1% at 1.42 m downstream of the test section. At the floor of the test section, an acrylic (k = 0.2 W/m K) test plate 0.32 m long and 0.38 m wide was attached at 1.63 m downstream of the test section inlet. A rectangular slot was machined at the center of the plate to accommodate five fluidic oscillator film cooling test modules. These test modules were produced in a rapid prototype machine (polyjet) using a polyetherimide thermoplastic resin (RGD720, k = 0.216 W/m K).

Figure 3 shows the location of the fluidic oscillator test module and the exit configuration. A coolant conditioning box was placed at the bottom of the test plate. In order to reduce the thermal losses within the box, a layer of low thermal conductivity foam was used inside the box. Two fine screens were used to maintain a uniform coolant flow inside the box. A total pressure probe (Kiel probe) and a 0.54 mm bead diameter T-type thermocouple were installed inside the coolant box to measure the total pressure and temperature of the coolant. In addition, a 0.7 mm bead diameter J-type thermocouple was installed near the throat of one of the oscillator test modules to measure the coolant exit temperature at the throat.

Figure 4 shows the schematic of the fluidic oscillator test module. The area ratio between the exit opening to the throat is 5.5. The hydraulic diameter (D) is 4.1 mm with an AR of unity, and the axis of the hole is inclined at an angle of 30 deg with the plate surface in the streamwise direction. The pitch-to-diameter ratio is P/D = 8.5, and the distance between two feedback channels is 6.9D. The exit hole has a 1.5D leading edge and a 4D trailing edge, and the distance between the leading edge and the trailing edge is 2D with an exit fan angle of $70deg$⁠.

In this study, the baseline-shaped hole considered for comparison has a laidback fan-shaped geometry, which is commonly known as 777-shaped hole. The hole consists of a cylindrical metering section which transitions to a diffused outlet that expands in the forward and lateral directions from the circular end of the metering section. The diameter of the circular end of the metering section is matched with the hydraulic diameter at the throat of the SJ hole. Figure 5 shows the detailed schematic of the 777-shaped hole, and the geometric parameters are listed in Table 1. A detailed description of the 777-shaped hole geometry can be found in Ref. [18].

The surface temperature of the test plate was measured by an Electrophysics Silver 420 shortwave infrared (IR) camera which has a 320 × 256 pixel resolution indium antimonide (InSb) detector with a 20 deg × 16 deg field of view and a 3.6–5.1 μm spectral range. The camera has a sensitivity of 0.02 K with a maximum frame rate of 270 Hz. The test plate was painted black to keep the emissivity close to unity. The camera was installed 0.5 m above the test plate and was focused on a 145 mm (cross stream) × 181 mm (streamwise) field of view which is shown in Fig. 6 by a dark region.

Here, $Tw$ was obtained from the IR recordings by averaging all 500 images to estimate a time-averaged adiabatic wall temperature $(Tw)$⁠.

Here, q corresponds to the heat flux with film cooling, and q_o is the heat flux without film cooling. A typical value of $Φ$ is 0.6. The heat flux ratio (q/q_o < 1) corresponds to an overall cooling benefit for any given cooling configuration.

where $T$ is the local temperature measured with the thermocouple rake.

The incoming boundary layer upstream of the holes was measured with a 0.635 mm head diameter boundary layer probe. Differential pressure data measured with the probe were sampled at a frequency of 1000 Hz for 20 s at each location. The probe was traversed 30 mm vertically from the wall with an initial step height of 0.1 mm. The key parameters of the boundary layer profile are listed in Table 2.

In order to assess the repeatability of the experimental measures, an uncertainty analysis was performed on the measurement system by the method described by Coleman and Steele [25]. The freestream velocity was estimated by a pitot static probe and a differential pressure transducer with an accuracy of ±1.6%. A 0.5 mm bead diameter T-type thermocouple was used to measure the freestream and the coolant temperature with an accuracy of ±1 °C. The IR temperature measurement was compared with the thermocouple measurement, and an accuracy of ±0.5 °C was estimated. The coolant massflow was measured with a FMA-2600 series massflow controller with an accuracy of ±1%. The overall uncertainty for the blowing ratio (M), film effectiveness (⁠$η$⁠), thermal field (⁠$θ$⁠), convective heat transfer coefficient (h), and discharge coefficient (C_D) is tabulated in Table 3.

An SJ film cooling hole was evaluated by measuring the adiabatic film effectiveness, heat transfer coefficient, thermal field, and discharge coefficient. Comparative discussions of the aforementioned parameters are presented and compared with the baseline 777-shaped hole in the Adiabatic Effectiveness, Thermal Field, Convective Heat Transfer Coefficient, Discharge Coefficient and Computational Study sections.

The oscillation of the jet was characterized by the frequency of the acoustic wave generated by the device. A microphone (1/4 in DeltaTron type 4954B) was used to measure the fluctuating pressure wave caused by the unsteady motion of the oscillator jet. The microphone was placed 5D downstream in the streamwise direction of the oscillator exit. The raw voltage data of the microphone were then transmitted to a signal conditioner and displayed on a LabVIEW interface by a NI 9215 DAQ card as a power spectrum. The bandwidth of the microphone sensor was 30–3000 Hz, which limits the frequency measurement at very low flow rates. The overall uncertainty of the frequency measurement was within ±5% of the mean frequency.

Figure 7(a) shows the frequency response of the fluidic oscillator as a function of massflow rate. Each vertical slice represents an individual power spectrum at a single massflow rate. In addition, the contour scale represents the relative magnitude of the signal intensity of the power spectrum. The oscillator shows strong frequency response as the massflow increases. As the internal feedback path was fixed for this particular device, the oscillating frequency increases with massflow rate and eventually plateaus. A sudden increase in intensity level of the noise floor of the frequency map at 1 g/s implies a transition from laminar to turbulent flow inside the oscillator [26,27]. Two additional harmonics (second and third) were observed, and the prominent frequency peaks with maximum signal intensity of the primary oscillation frequency were marked by black dots in Fig. 7(a).

The jet spreading angle is then estimated by taking two points on U/U_t = 0.1 contour line at x/D = 2 and 10. The estimated spreading angle for the SJ hole is approximately 47 deg.

Figure 8 shows the adiabatic film effectiveness contours for the SJ and 777-shaped holes at four different blowing ratios $(0.97≤M≤3.96)$ at a low freestream turbulence intensity of Tu = 0.4%. Since the sweeping motion of the jet is unsteady, the time-averaged effectiveness contours are shown here. In addition, the contours are plotted from the trailing edge of the hole to 30D downstream of the hole exit and for a single pitch (P/D = 8.5). Good periodicity was observed for both the SJ and 777 holes at all blowing ratios. At the lowest blowing ratio (M = 0.97), the SJ hole exhibited a concentrated coolant streak downstream of the hole. This is due to the weak oscillation that occurs at low massflow rates for this fluidic device. As the blowing ratio increases, the SJ hole showed stronger oscillation and larger spreading of the coolant in the lateral direction compared to the 777-hole. It is interesting to note that as the blowing ratio increases, the film effectiveness decreases along the centerline of the SJ hole. This happens due to a strong oscillation of the jet which allows the coolant to deflect further from the centerline. Similar observations have been reported by Thurman et al. [17] where the fan angle was $60deg$⁠. As described earlier, the fan angle of the SJ hole is 70 deg, this implies that the dwell time of the jet on the exterior attachment walls is longer, leading to increased cooling at the edges of the fan pattern. The residence time of the jet on the inner portion of the sweep is less, so the film effectiveness there is lower.

Figure 9 shows the adiabatic film effectiveness contours for the SJ and 777-shaped holes at four different blowing ratios at a high freestream turbulence intensity of Tu = 10.1%. As one might expect, freestream turbulence increases mixing resulting in an overall decrease in effectiveness at all blowing ratios. No significant change in lateral spreading was observed for the SJ and 777 holes. However, the SJ hole still showed higher lateral film effectiveness compared to the 777-hole at all blowing ratios. In addition, 777-hole shows a decreasing trend as blowing ratio increases. Schroeder and Thole [18] reported a similar trend for a baseline 777-shaped hole at a freestream turbulence level of 5%.

Figure 10 shows the span-averaged effectiveness $(η¯)$ for the SJ hole and 777-shaped holes at three blowing ratios $(0.98≤M≤2.94)$ and at low freestream turbulence (Tu = 0.4%). The SJ hole exhibits higher span-averaged effectiveness at the near hole region (x/D < 15) compared to the 777-hole at all blowing ratios. With the increase of blowing ratio, the span-averaged effectiveness $(η¯)$ decreases for the SJ hole while the film effectiveness value remains higher at x/D > 15 for 777-hole. The highest span-averaged effectiveness for both the SJ and 777-hole was obtained at M = 0.97. At this blowing ratio, the SJ hole exhibited a slower decay in $η¯$ at the near hole region. A faster decay in $η¯$ was observed at higher blowing ratios (M = 1.97 and 2.96) since the large M corresponds to a higher oscillation frequency for the SJ holes. Effectiveness data were not shown at the interface (Fig. 3) region (x/D = 6) for SJ hole and (x/D = 10) for 777-hole between the plate and the test module in Figs. 10 and 11.

Figure 11 shows the span-averaged film effectiveness $(η¯)$ for the SJ and 777-shaped holes at three different blowing ratios and at a high freestream turbulence intensity of Tu = 10.1%. Freestream turbulence increases dilution of the coolant resulting in an overall decrease in effectiveness at all blowing ratios. In the near hole region (x/D < 5), a higher decay in $η¯$ was observed at all blowing ratios. The SJ hole showed higher effectiveness at the highest blowing ratio (M = 2.94). A stronger oscillation of the jet at this high blowing ratio augments lateral spreading resulting in an overall increase in film effectiveness in this region. No significant effect of blowing ratios was observed far downstream (6 < x/D < 30). However, 777-hole shows better cooling performance in this region because the coolant remains attached to the plate surface for a longer period of time.

Figure 12 shows the lateral distribution of film effectiveness $(η)$ along a single pitch at x/D = 10 for the SJ and 777-shaped holes at three blowing ratios (M = 0.98, 1.97, and 2.94) and at a freestream turbulence of Tu = 0.4%. As one might expect, the centerline film effectiveness for 777-hole is higher at all blowing ratios compared to the SJ hole and drops quickly in the lateral direction due to slower spreading of coolant through diffusion. In contrast, the lateral spreading of the coolant increases as blowing ratio increases for the SJ holes. This shows the benefit of using sweeping jets. Although the 777-hole shows higher film effectiveness in the centerline, it shows poor performance in the midpitch region compared to the uniform film effectiveness of the sweeping jet film cooling hole. The coolant spreading increases laterally at high freestream turbulence (Tu = 10.1%) for the SJ hole, which is shown in Fig. 13.

Figure 14 shows the area-averaged film effectiveness $(η¯¯)$ for the SJ hole over a streamwise distance between 2.5 < x/D < 30 over one pitch (8.5D) and compared with the 777-shaped hole. At low freestream turbulence, the SJ hole shows better cooling performance compared to the 777-hole. A decreasing area-averaged effectiveness pattern with increasing M was observed for the SJ and 777-hole. At high freestream turbulence, the area-averaged film effectiveness for both holes did not vary significantly at high blowing ratios (M = 2.94 and 3.96).

Figure 15 shows the time-averaged thermal field normal to the plate at x/D = 6 for the SJ and 777-shaped holes in terms of a nondimensional temperature $(θ)$ contour. The thermal fields are shown over a single pitch (8.5D) in the lateral direction and 4D in the direction normal to the plate for four different blowing ratios and for a low freestream turbulence (Tu = 0.4%). The contours in the left column of Fig. 15 show the thermal field for the SJ hole, and the contours in the right column show the thermal field for the 777-hole. At the lowest blowing ratio (M = 0.97), the core region of the coolant remains attached near the wall for both holes.

The coolant penetration height is approximately 1.75D for the SJ hole, and the lateral spreading of coolant is approximately ±2D from the centerline of the hole. As the blowing ratio increases, the lateral spreading for both holes also increases. Coolant from the SJ hole shows larger spreading than the 777-hole. At M = 2.94, the coolant from the SJ hole spreads almost a hole pitch (8.5D or ±4.25D from the centerline). At the highest blowing (M = 3.96), the maximum penetration is roughly 2.5D for the SJ hole. Interestingly, the core region of the coolant remains attached near the wall for the 777 holes at all blowing ratios. However, the jet penetration height increases from 1.25D to 2D as blowing ratio increases from $0.98≤M≤3.96$⁠. In addition, the lateral jet spreading increases from ±1D to only ±1.75D as the blowing ratio varies from $0.98≤M≤3.96$ for the 777-hole. This clearly indicates the benefit of using fluidic oscillators to achieve larger lateral spreading for better cooling coverage. The spreading of the core region of the coolant for the SJ hole is much wider, and it remains closer to the wall compared to the 777-hole. At blowing ratio of M = 3.96, two distinct lobes of coolant fluid are observed in the thermal field of the SJ hole. The oscillation of the sweeping jet is responsible for this cold region as will be discussed later.

Figure 16 shows the time-averaged thermal field normal to the plate only for the SJ hole at x/D = 10 for both low and high freestream turbulence (Tu = 0.4% and 10.1%). It is evident that the freestream turbulence increases the lateral spreading and dilution of coolant over the surface. Furthermore, a hot region along the centerline of the hole (z/D = 0) confirms a low concentration of coolant at high blowing ratio (M = 3.96) for both low and high freestream turbulence cases. A strong oscillation at this high blowing ratio allows the coolant to sweep aggressively across the centerline of the hole resulting in a low film effectiveness there. However, the lateral coverage due to the sweeping action improves overall film effectiveness in the spanwise direction.

Heat transfer measurement was performed for both SJ and 777-shaped holes only over a range of blowing ratios $(0.98≤M≤2.94)$⁠. The convective heat transfer coefficient and heat flux ratio data are presented for high Tu condition only because the high Tu (10.1%) case exhibits a more realistic engine condition where the turbulence intensity (Tu) can be above 20% [28]. Figure 17 shows the area-averaged convective heat transfer coefficient and wall heat flux ratio for the SJ hole and 777-shaped hole at three different blowing ratios and high freestream turbulence (Tu = 10.1%). Data were averaged over an area of 20D (5 < x/D < 25) in the streamwise direction and over one hole pitch in the lateral direction. The convective heat transfer coefficient was measured by the transient IR technique described earlier. This technique was used to measure heat transfer coefficient with film cooling (h) and without film cooling (h_o) by Eq. (2). Because of the oscillation of the jet, an augmentation of heat transfer coefficient (h/h_o > 1) is not unexpected. However, this augmentation did not show monotonic behavior with increasing blowing ratios. The highest augmentation (16%) of h was found at M = 2.94, while the lowest augmentation (5.1%) was at M = 1.97. In contrast, the area-averaged heat transfer coefficient augmentation for 777-shaped hole was close to unity at M = 0.98, and as the blowing ratio was increased, the area-averaged heat transfer coefficient augmentation increased up to 1.18 at M = 2.94. The heat flux ratio (q/q_o) indicates the overall benefit of the film cooling which is shown in Fig. 17.

Values of $q/qo$ lower than unity have a net positive cooling effect. Although 777-shaped hole shows cooling benefit at M = 0.98 and 1.97, the sweeping jet performed comparable at M = 1.97 with a uniform coolant distribution in the lateral direction. It is important to note that the unsteady sweeping action of the jet augments the heat transfer near the hole exit, and the heat transfer augmentation decreases along the centerline of the hole at farther downstream of the hole exit.

Figure 18 shows the discharge coefficient C_D for the SJ and 777-shaped holes as a function of blowing ratio $(0.98≤M≤2.94)$⁠. The C_D value was estimated by Eq. (5). It is important to note that the measurement was taken without internal crossflow. With an external crossflow applied $(U∞=10m/s)$⁠, the C_D value increases for both the SJ and 777 holes as the blowing ratio increases. It was also observed that the 777-hole shows higher C_D value compared to the SJ hole at a corresponding blowing ratio. At M = 1.97, the C_D value for the SJ hole is dropped by 6%, while at M = 2.94, the C_D value for the SJ hole is dropped by 8.2%. This drop in C_D value implies a larger pressure drop across the hole inlet and exit of the SJ hole compared to the 777-shaped hole.

Numerical simulation was performed for both the SJ and 777-shaped holes to better understand the flow field near the holes. Figure 19 shows the computational domain and the grid for both holes. The domain was extended 35D along the streamwise direction, 8.5D (±4.25D from the centerline) along the spanwise direction, and 9D in the wall normal direction. The main flow inlet is located 5D upstream of the hole leading edge. An experimentally measured boundary layer profile was used as a freestream inlet velocity boundary condition, while a massflow inlet condition was set for the coolant inlet. The turbulence level was set as 0.4% for both inlets. In addition, a slip wall boundary condition was applied to the top boundary of the domain based on the assumption that the boundary is far away from the adiabatic wall.

Hybrid grid was used in this study which consists of a cluster of ten prism layers near the adiabatic wall, and the rest of the domain was discretized into a polyhedral mesh. Table 4 shows the properties of each grid in terms of a nondimensional wall distance, $y+$⁠. Previously, a detailed model validation was performed by Hossain et al. [29] for a similar sweeping jet injecting normal to a crossflow. Oscillation frequency and cross-plane velocity vector field at x/D = 15 were compared with experimental data and found to be in excellent agreement [30]. Since the objective of the current computational study is to investigate the flowfield only, a similar approach was considered in this case where the oscillation frequency predicted by CFD was compared with experimental frequency. Figure 20 shows the oscillation frequency from CFD and experiment as a function of blowing ratio (and massflow). CFD predicted frequency was approximately 10% higher than the experimental frequency which is in line with other studies of fluidic oscillators [31]. In addition, the frequency from CFD was well within the experimental uncertainty range.

Since the flow at the exit of a fluidic oscillator is inherently unstable, a unsteady Reynolds-averaged Navier–Stokes (URANS) simulation was performed in this study using commercial code fluent to estimate the time-averaged and time-accurate flow fields. Three massflow rates were considered for coolant inlet condition. The time-step was estimated by keeping the Courant (CFL) number close to unity. It is important to note that the throat velocity was used to calculate the CFL number. The flow equations were discretized by a second-order upwind scheme, and spatial gradients were reconstructed by a least-square cell-based method. k–ω shear stress transport model by Menter [32] was employed for the turbulent flow prediction. A second-order implicit discretization in time has been adopted for the unsteady calculation.

Figure 21 shows the time-averaged cross-plane velocity vectors colored by average streamwise vorticity for both SJ and 777-shaped holes. A pair of counter-rotating vortices is evident in both cases. However, the sense of rotation of these vortex pair is exactly opposite for the SJ hole compared to the 777-shaped hole which is indicated by a pair of red arrows in Fig. 21. Because of the sense of the 777-hole CRVP, the vortices mutually induce each other away from the wall. Also, their mirror vortices keep them from spreading laterally.

By contrast, the opposite sense of the SJ vortices allows them to be moved laterally by their mirror vortices. Also note that the steady-state picture is deceiving since it would suggest that the SJ vortices mutually induce each other to the wall. This is clarified in the time-accurate image. Figure 22 shows the time-accurate flowfield over a half-oscillation for the SJ hole. In plane velocity vectors at x/D = 6 are shown at four different phase angles (⁠$∅$⁠) of the sweeping jet colored by streamwise vorticity. Here, $∅=0$ implies the phase when the jet is attached to one of the side walls of the hole exit, the jet acts as a vortex generator as it interacts with the freestream. From vortex dynamics, it is well established that this single streamwise vortex will induce a fictitious image vortex of equal strength below the wall [33]. As the vortex pair (actual vortex and fictitious image vortex) approaches the wall, the velocity field associated with the vortex pair moves outward from the center of the hole resulting in a strong jetting action directing outward, which makes the coolant spread in the lateral direction. Although there is a CRVP in the time-averaged flowfield for SJ hole, it is important to note that they never exist simultaneously at the same x/D. This allows the mirror vortex to induce the desired lateral motion.

Experiments have been conducted to investigate the performance of an SJ film cooling hole to determine its suitability for gas turbine film cooling application. Film effectiveness, thermal field, convective heat transfer coefficient, and discharge coefficient were measured at a range of blowing ratios under low and high freestream turbulence and compared with the baseline 777-shaped hole. IR thermography was used to measure the wall surface temperature; thus, the film effectiveness and a transient IR technique were implemented to estimate the convective heat transfer coefficient, thus the heat flux at the wall. The overall performance of the holes was evaluated by investigating heat flux ratio with and without film cooling. The flow fields of both the SJ and 777-shaped holes were also examined using a URANS simulation. The key findings are listed as follows:

1. (1)

   The SJ configuration shows uniform lateral spreading of coolant at all blowing ratios compared to the 777-hole.

2. (2)

   High freestream turbulence enhances mixing resulting in an overall reduction in cooling effectiveness and greater lateral spreading of coolant for both the SJ and 777-shaped holes. However, the lateral spreading of coolant from the SJ hole is significantly higher than the 777-hole.

3. (3)

   The coolant jet penetration height increases from 1.75D to 2.5D for the SJ holes over a range of blowing ratios $(0.98≤M≤3.96)$⁠. However, high freestream turbulence has no significant effect on jet penetration height.

4. (4)

   Sweeping action of the jet augments the heat transfer coefficient at all blowing ratios. However, the overall cooling performance improves for the SJ at low blowing ratios (M = 1.97) which is comparable to 777-shaped hole.

5. (5)

   The discharge coefficient C_D for the SJ hole is comparable to the baseline 777-hole and remains within 8.2% of the C_D for 777-hole over a range of blowing ratios $0.98≤M≤2.94.$

6. (6)

   Time-resolved flow fields revealed two alternating streamwise vortices for the SJ hole at all blowing ratios. The sense of rotation of these alternating vortices is opposite to the traditional CRVP found in 777-hole exit and serves to spread the film coolant laterally.

Computational resources were provided by the Ohio Supercomputer Center (OSC).

• U.S. Department of Energy (DOE-NETL), Project Manager: Robin Ames (Award No. DE-FE0025320).

A_t =

throat area

AR =

aspect ratio (⁠$Wt/Ht)$

c_p =

specific heat at constant pressure, J/kg K

CFL =

Courant–Friedrichs–Lewy condition

D =

throat hydraulic diameter

DR =

density ratio (⁠$ρc/ρ∞$⁠)

h =

convective heat transfer coefficient with film cooling, W/m² K

H =

shape factor

h_n =

convective heat transfer coefficient at nth time-step, W/m² K

h_o =

convective heat transfer coefficient without film cooling, W/m² K

H_t =

throat height

$h/ho¯$ =

ratio of the area-averaged heat transfer coefficient

L_faw =

length of forward expansion (777-shaped hole)

L_lat =

length of lateral expansion (777-shaped hole)

L_m =

length of metering section (777-shaped hole)

M =

blowing ratio, (⁠$ρU)c/(ρU)∞$

$m˙c$ =

coolant massflow rate, kg/s

P =

pitch

$Ps$ =

static pressure at 20D upstream of the hole, Pa

$Pt$ =

total pressure, Pa

$Ptc$ =

total pressure at the coolant plenum, Pa

q =

convective heat flux with film cooling, W/m²

q_o =

convective heat flux without film cooling, W/m²

$q/qo¯$ =

area-averaged heat flux ratio

R =

specific gas constant, 287 J/kg K

Re_D =

hole Reynolds number (U_∞D/ ν)

$Reθ$ =

Reynolds number based on momentum thickness

SJ =

sweeping jet

T_c =

coolant temperature, $K$

T_tc =

coolant total temperature, $K$

T_w =

adiabatic wall temperature, $K$

T_∞ =

freestream temperature, $K$

Tu =

freestream turbulence intensity

$uτ$ =

friction velocity

U_t =

throat velocity, m/s

U_∞ =

freestream velocity, m/s

W_t =

throat width

x =

streamwise direction

y =

surface normal direction

z =

cross stream direction along the span

Greek Symbols

$α$ =

thermal diffusivity (κ/ρc_p)

$βfaw$ =

forward expansion angle (777-shaped hole)

$βlat$ =

lateral expansion angle (777-shaped hole)

$∅$ =

phase angle of the oscillating jet

$ϕ$ =

hole injection angle