Experimental Investigation of Sweeping Jet Film Cooling in a Transonic Turbine Cascade

The hot section components of an advanced gas turbine experience an extreme thermal load that exceeds the material melting temperature. Turbine designers are still pushing the limit of the turbine inlet temperature to achieve higher engine efficiency. One of the critical components of the turbine hot section is the first stage nozzle guide vane (NGV) that experiences the maximum heat load. Many cooling strategies have been developed over the year to protect and improve the operating life of such components. One of the most widely adopted cooling strategies is external cooling that involves a comparably low temperature working fluid being extracted from the compressor and injected through discrete film cooling holes to protect the surface of the NGV from overheating. However, this adds a penalty to the thermal efficiency of the gas turbine, as the working fluid is being used for cooling instead of producing work. Therefore, turbine designers are constantly pursuing new methods to optimize the use of the coolant without sacrificing the existing engine efficiency.

One of the major developments in film cooling that has been widely adopted by the industry is the replacement of conventional cylindrical holes with shaped holes [1]. The diffusion shaped hole exhibits improved cooling by spreading the coolant in the lateral direction [2]. A number of studies are available in the open literature that showed the effect of the hole geometry such as hole shape [3], hole length [4], and injection angle [5] as well as the effect of coolant mass flow [6], coolant to freestream density ratio [7], freestream turbulence [8], and length scale [9] on cooling performance. These studies have documented details about the complex flow field associated with the film cooling hole. In addition, a number of research have been conducted to develop new film cooling hole geometries with complicated shapes to improve the cooling effectiveness. Among these, the laid-back fan-shaped hole [10], console hole [11], anti-vortex hole [12], and 777-shaped hole [13] are notable.

Preventing the formation of the counter-rotating vortex pair (CRVP) remains one of the major challenges for film cooling. Although the shaped hole reduces the strength of the CRVP, it is not eliminated completely [14]. The sweeping jet (SJ) film cooling hole is a recent innovation that has the potential to eliminate the detrimental CRVP completely by creating alternating streamwise vortices that interact with the freestream flow [15]. The working mechanism of such hole is explained in excellent detail in Ref. [16]. The concept of the SJ film cooling was pioneered by Thurman et al. [17] who conducted experiments with the SJ hole on a flat plate and showed superior cooling effectiveness in the lateral direction near the hole exit. Hossain et al. [18] later measured the convective heat transfer coefficient (HTC), adiabatic cooling effectiveness, and thermal field for the SJ hole on a flat plate. Their study covered a range of freestream turbulence and blowing ratios (BRs). Comparisons were made with the 777-shaped hole (baseline), and the SJ hole showed improved cooling performance over the shaped hole. Hossain et al. [18] also showed that the oscillating motion of the jet develops two alternating streamwise vortices and the direction of rotation of these alternating vortices is opposite to the conventional CRVP. Later, Hossain et al. [19] performed experiments in a low-speed linear cascade with the SJ hole on the suction surface of a nozzle guide vane geometry. Experiments were performed for a range of blowing ratios (0.5 ≤ BR ≤ 1.5) and freestream turbulence (Tu = 0.3% and 6.3%). The SJ hole showed superior cooling performance when compared with the 777-shaped hole at high blowing ratio (BR > 1).

Relatively fewer film cooling studies have been conducted at high Mach number. Luzeng and Hee [20] reported film cooling of a fan-shaped hole in a transonic linear cascade where they used thermochromic pressure-sensitive paint. Xue et al. [21] performed experiments on fan-shaped holes at the transonic condition with freestream turbulence of Tu = 12%. Carullo et al. [22] studied the turbine blade heat transfer in a transonic cascade and showed the effect of length scale, exit Reynolds number, and freestream turbulence. Although the sweeping jet hole showed improved cooling effectiveness in a low-speed large-scale turbine vane geometry, the effect of compressibility on the HTC and film cooling effectiveness of such unsteady jet is still unknown. The objective of the current work is to study the SJ hole on a nozzle guide vane geometry at an engine relevant Mach number (M_ex = 0.8) to determine the effect of compressibility. Experiments were performed for a range of blowing ratios. The freestream turbulence is also varied (Tu = 0.7% and 6%) in order to achieve a comprehensive understanding of the SJ hole at high-speed high Reynolds number conditions.

Experiments were conducted in a recently commissioned transonic cascade facility at the Ohio State University (OSU) Turbine Aero-thermodynamics Lab. The transonic cascade facility consists of a supply plenum and a test section shown in Fig. 1. The transonic tunnel operates in a blowdown mode using a high-pressure air supply reservoir (21 m³ at 16 MPa) and exhausts to ambient. The plenum section is made out of 37.5 mm aluminum plate. High-pressure supply air flows into a 155 mm × 500 mm calming section where it is conditioned for flow uniformity by honeycomb screens. The flow is then accelerated into the 100 mm × 250 mm test section through a 3:1 contraction. The tunnel is designed to run up to 1 min at a maximum mass flowrate of 3.25 kg/s. The test section side walls are made out of 25 mm aluminum plate, and the end walls are made out of 25 mm thick acrylic plate for maximum optical access. The test section includes a rectangular cascade inlet section (Fig. 1) and a vane passage section followed by an adjustable turning section.

The schematic of the test section and different instrumentation ports are shown in Fig. 2. A 0.5 mm bead diameter thermocouple (J-type) and a total pressure Kiel probe are used to measure the upstream stagnation temperature (T_o) and pressure (P_o). A turbulence grid was used two chords (2C) upstream of the test vane to generate freestream turbulence. The upstream static pressure and Mach number are measured by a row of static pressure taps at 1C upstream of the leading edge of the vane and five taps are used to check inlet flow uniformity. The vane passage section includes three vanes, two full passages, and two half passages. The curvature of the side walls in the vane passage section was determined using computational fluid dynamics (CFD) results performed for an infinite cascade. Three vanes are used to achieve a periodic flow at the middle vane section for the heat transfer study. Two IR viewports are utilized to measure the temperature of the central vane surface. The IR viewport at the turning section was used to observe the temperature of the suction surface of the central vane. The turning section consists of two tailboards that can be adjusted independently. To measure the exit Mach number, five static pressure taps are used at 0.25C (from the trailing edge of the vane) downstream of the exit plane. The tailboard can be adjusted by a set-screw that is attached to a connecting rod. Three connecting rods are used as a support structure and to adjust both tailboards. In addition, a slot was made to place a total pressure Kiel probe at 0.25C downstream of the test vane to measure the total pressure (Pt_ex) at the exit plane. This pressure measurement is used to estimate the total aerodynamic pressure loss caused by injecting the coolant through the film cooling hole.

The flow in the test section was characterized by the inlet and exit Mach number distribution. Two 16 channels Model 9116 Intelligent Pressure Scanners from NetScanner^TM were used to measure the pressure at the inlet and exit plane of the cascade test section. The same pressure scanner was also used to measure the surface pressures at the midspan of the vane geometry. The pressure scanners are rated for 45 psid with an accuracy of ±0.05%. Data were sampled at a 250 Hz frequency.

A mesh type turbulence grid was used at 2C upstream (shown in Fig. 2) of the test vane to generate freestream turbulence. The turbulence mesh grid has a bar width of 4.5 mm, and each bar is spaced 20.3 mm apart to form a 15.8 mm × 15.8 mm opening which is estimated by Baines and Peterson [23] correlation. The characteristics length scale and turbulence intensity were characterized by a constant temperature anemometry hot-film placed at 1C (10 cm) upstream of the test vane. The hot-film calibration was performed using a TSI Model 1127 air calibrator. An in situ calibration was also conducted to account for the temperature change during the transient blowdown test. Data were sampled at three discrete spanwise locations (spaced 84 mm apart) for 5 s at a sampling rate of 20 kHz, and the accuracy of the velocity measurement was within ±2.6%. The characteristics length scale and turbulence intensity were calculated by the method proposed by El-Gabry et al. [24]. Figure 3 shows the length scale and turbulence intensity of the tunnel. The measured turbulence level without the grids was 0.7%, and with the grids was 6% for an exit Mach number of M_ex = 0.8.

The transonic nozzle guide vane geometry was designed and manufactured at OSU. The vane has a true chord of 10.16 cm (4 in.) with a span of 10.16 cm (4 in.). Table 1 shows the geometric details and Fig. 4 shows the vane schematic and its internal cooling architecture. Although the entire turbine vane consists of three cooling schemes—film cooling on the suction surface, impingement cooling on the leading edge, and trailing edge cooling, the focus of this paper is solely film cooling on the suction surface. A detailed schematic of the SJ hole is also shown in Fig. 4(c). It is noteworthy that the separate coolant supply plenum was designed for each cooling scheme so that experiments can be performed for each cooling scheme independently. High-resolution stereolithography (SLA) was adopted to build the test vane with the Accura ABS Black (k = 0.175 W/m² K) material. The external surfaces were processed with 320 grit sandpaper, and internal channels were cleaned with water honing (150 grit white sand).

To characterize the surface pressure distribution of the vane, a separate solid vane geometry was manufactured that consists of 15 0.3 mm diameter pressure taps on the suction side and eight pressure taps on the pressure side. The surface pressure was also measured with a Model 9116 Intelligent Pressure Scanners from NetScanner^TM to estimate the isentropic Mach number (M_is) distribution at the midspan of the vane. Figure 5 shows the surface Mach number distribution at the vane midspan. The location of the throat and the film cooling holes are also identified by two dashed lines, respectively. Data are presented for the tunnel flow with an exit Mach number of M_ex = 0.7 and 0.8. Tests were performed at the same exit condition at different days to confirm data repeatability. In addition, the commercial software package fluent was used to estimate the M_is distribution for an infinite cascade to verify the experimentally measured Mach number distribution. The experimental measurement agrees well with the CFD result for an infinite cascade, demonstrating the flow periodicity of the vane passage. It is believed that the discrepancy between the experiment and CFD at x/C_ax = 0.55 on the suction surface is caused by a partially blocked pressure tap.

In this study, a single row of six SJ holes was used on the suction surface of the test vane at x/C_ax = 0.5 from the leading edge which is shown in Fig. 4(b). The hole has a square metering section with a hydraulic diameter (D) of 1.71 mm and a hole spacing (P/D) of 6. The fan angle of the exit of the hole is 70 deg, and the coolant exits with 45 deg injection angle with the streamwise direction. A detailed description of the SJ hole geometry can be found in Ref. [19]. One of the characteristics of the SJ hole is to generate oscillating jets and the frequency of the jet oscillation was measured by a (1/4 in.) microphone (DeltaTron type 4954B), and the microphone has a bandwidth of 30–3000 Hz with an accuracy of ±5% of the mean frequency. The frequency of the oscillating jet emanating from the SJ hole was measured at 5D downstream of the hole exit. Separate frequency measurements were performed for each hole to ensure manufacturing consistency. Adhesive tape was used to block the other holes.

The peak frequency was extracted from the power-spectral analysis of the microphone signal. Figure 6 shows the peak frequency of the oscillating jet emanating from each SJ hole as a function of mass flowrate. It is evident that the oscillation frequency is a strong function of mass flowrate and each jet shows a very similar but not identical peak frequency at a corresponding mass flowrate. Previous results show that the manufacturing roughness of the internal channels of such a device can cause this deviation [25]. Additional flow visualization confirmed no synchronized oscillation of two adjacent holes which is also reported in the previous large scale studies [19].

A separate vane geometry was manufactured with a single row of the 777-shaped holes (shown in Fig. 4(b)) for a direct comparison. The geometry of the 777-shaped hole has been described in excellent detail in Ref. [13]. The metering section diameter (D = 1.71 mm) of the 777-shaped hole was matched with the throat hydraulic diameter of the SJ hole. However, due to the curvature of the vane geometry, the exit breakout section of the 777-hole has been modified slightly.

A number of experiments were performed in the transonic blowdown facility, including measurement of adiabatic cooling effectiveness (η), heat transfer augmentation, hole discharge coefficient (C_d), and aerodynamic loss. Each experiment starts with opening two valves (connected to the 16 MPa supply tank) instantaneously to set the desired Mach number (M_ex = 0.8). A total pressure Kiel probe (located 2C upstream of the test vane) and a row of five static pressure taps (located at 1C upstream) were used to estimate the inlet Mach number (M_in). The Mach number at the exit (M_ex) was estimated at 0.25C_ax downstream of the test vane with a row of five downstream static pressure taps and the upstream total pressure (Pt_in). A 0.5 mm bead thermocouple (J-type) was used to record the upstream total temperature (T_o), and the secondary coolant temperature (T_c) inside the coolant supply plenum was measured with the T-type (0.2 mm bead diameter) thermocouple. The accuracy of the thermocouple temperature measurements was well within ±0.5 K. It is important to note that all experiments were performed using a hot secondary flow though it is referred to as “coolant” in this paper.

Figure 7 shows the Mach number and temperature response of a typical test. The run time of each test is approximately 40 s, and it takes about 5 s to set the desired exit Mach number (M_ex = 0.8). After the transition period of the tunnel startup, a portion of the time window (approximately 12 s) was considered for the heat transfer analysis which is shown in Fig. 7 by a dotted region.

In this study, the temperature of the freestream dropped from 290 K to 275 K during each test, while the temperature of the “hot coolant” and the “cold coolant” were approximately 325 K and 300 K, respectively. Each test begins with setting the coolant mass flowrate for a specific blowing ratio. The suction surface temperature of the vane is monitored until it reaches an isothermal surface condition. Once the coolant temperature and the surface temperature reach steady-state, the tunnel starts to run and the surface temperature (T_w) is recorded with the IR camera at a frequency of 15 Hz. The freestream total temperature (T_o) and the coolant temperature (T_c) are also recorded simultaneously.

Figure 8 shows the raw IR images of two typical tests with the SJ hole and the 777-shaped hole. The data reduction area is also marked by a white rectangular region. First, the heat flux is calculated from the transient temperature history for each pixel within the data reduction area for both hot and cold coolant cases using Eq. (7). It is quite clear from Eq. (5) that the heat transfer coefficient (slope of Eq. (5)) and the adiabatic cooling effectiveness (η) will remain the same regardless of the coolant temperature if the freestream condition (Mach number and Reynolds number) remains the same. Therefore, an iterative method was adopted to predict the correct recovery temperature (T_r) so that the slope of the cold coolant case and the hot coolant case line up perfectly. Xue et al. [26] recommended the freestream total temperature as an initial guess for the T_r searching method. An in house root-finding algorithm was employed to search for the correct T_r. Figure 9 shows a few steps of the iteration process where the convergence criteria were set by the coefficient of determination (R² ≥ 0.98). Once the solution converges, the slope corresponds to the convective heat transfer coefficient and the adiabatic film effectiveness was estimated using Eq. (6) for each pixel of the data reduction area shown in Fig. 8.

Here, q_o is the uncooled heat flux of the vane surface and q is the heat flux of the cooled vane surface. The net positive cooling benefit (NPCB) can be achieved when q/q_o < 1 and considered as a positive cooling benefit.

Here, Pt_in and Ps_in are the upstream total pressure and static pressure measured at 1C upstream of the test vane. A total pressure Kiel probe was traversed at 0.25C_ax downstream (shown in Fig. 2) of the test vane to measure the wake total pressure (Pt_ex). First, the measurement was performed for the uncooled case and considered as the baseline loss coefficient (γ_o). Then, the same measurement was performed with the film cooling at several blowing ratios for both SJ and 777-holes. The aerodynamic loss was then estimated and presented in terms of a loss coefficient (γ). In order to determine the relative contribution of the total pressure loss due to film cooling, γ was compared with the baseline γ_o.

A number of experiments were conducted at varying blowing ratios and freestream turbulence (Tu) to determine the effect on heat transfer (h/h_o), cooling effectiveness (η), and aerodynamic loss (γ) for the SJ hole. All experiments were performed at an engine relevant exit Mach number (M_ex = 0.8). Key operating parameters for a modern turbine engine and the OSU tunnel are compared in Table 2.

Here, the coolant cavity pressure (Pt_c) and temperature (Tt_c) were monitored during each test to calculate the jet velocity (U_c) and density (ρ_c) using the static pressure measurement at the hole exit. A summary of test conditions is listed in Table 3.

The uncertainty of the experimental measurement was estimated by multiple methods [31,32]. The freestream Mach number was measured by a 0.31 MPa differential pressure scanners (NetScanner^TM) with an accuracy of ±0.05%. The same pressure scanner was also used to measure the surface pressure to estimate the vane Mach number (M_is) distribution and the wake total pressure loss. The freestream and the coolant temperature were measured by a J-type thermocouple (0.5 mm bead diameter) and a T-type thermocouple (0.2 mm bead diameter), respectively. The accuracy of the thermocouple temperature measurements was well within ±0.5 K. The accuracy of the temperature measurement of the IR measurement was ±0.5 K according to the manufacturer specification. The coolant massflow was measured by an Alicat massflow controller (Model FMA-2600) with an accuracy of ±1%.

The uncertainty analysis of the DLRT was carried out through the method recommended by Xue [33]. The error propagation for the heat flux reconstruction (DLRT-step 1) by the finite difference code was analyzed by Moffat’s perturbation method [31]. In addition, the error estimation for the linear regression (DLRT-step 2) was carried out by the method proposed by Coleman and Steele [32]. Since the searching method of the recovery temperature was an iterative process, the error estimation was not carried out during each iteration. However, the uncertainty of the recovery temperature was estimated for the final recovery temperature. The overall uncertainty for different measurement is listed in Table 4.

The contours of adiabatic cooling effectiveness for the SJ hole and 777-shaped hole are shown in Fig. 10. Results are shown for a mainstream turbulence level of Tu = 0.7% and a range of blowing ratios (0.55 ≤ BR ≤ 1.85). The contours are plotted for three hole pitches extending 30D (streamwise) and 18D (spanwise) from the hole exit.

Both holes show good periodicity in coolant distribution. At BR = 0.55, the coolant remains in a concentrated streak along the centerline of the SJ hole. The cooling effectiveness drops quickly far downstream of the hole exit. This happens due to an inferior oscillation of the jet at this low blowing ratio. Previously, the large scale flat plate study [17,18] also showed similar behavior for the SJ hole. With increasing blowing ratio, the strength (jet momentum) and the oscillation frequency of the jet oscillation also increase thus promoting the spanwise coolant spreading. Accordingly, the adiabatic effectiveness increases for the SJ hole, as the blowing ratio increases from BR = 0.55 to 0.95. The 777-shaped hole also shows higher film effectiveness at the centerline of the hole at this blowing ratio (BR = 0.95).

The coolant distribution changes dramatically at higher blowing ratios (BR > 0.95). At BR = 1.45, the 777-hole shows a significant drop in cooling effectiveness compared to the BR = 0.95 case. The coolant distribution also narrows down implying jet liftoff. This causes a lack of cooling in the region between two adjacent holes. By contrast, the SJ hole shows improved coolant spreading in the spanwise direction at this blowing ratio (BR = 1.45) such that it covers almost the full hole pitch far downstream of the hole exit. At BR = 1.85, the centerline effectiveness for the 777-shaped hole drops even more indicating severe jet liftoff. This causes a lack of cooling in the spanwise direction that ultimately results in a non-uniform wall temperature and the potential for severe thermal stresses. In contrast, no significant change in coolant distribution can be seen for the SJ hole at BR = 1.85 compared to the BR = 1.45 case. Although the centerline effectiveness drops slightly, the near hole effectiveness in the lateral direction is much higher than the 777-shaped hole. This also confirms that the jet does not liftoff from the vane surface at this high blowing ratio. Since the oscillatory motion of the jet creates a fluctuating jet velocity [18] at the hole exit, the effective jet momentum remains much smaller than the steady jet at a similar blowing ratio. Thus, the low momentum jet is immediately pushed toward the wall as it interacts with the freestream.

The contours of the adiabatic cooling effectiveness at Tu = 6% are shown in Fig. 11. At low blowing ratio (0.55 < BR < 1), the coolant distribution remains very similar to the low turbulence (Tu = 0.7%) case. However, the coolant spreading in the spanwise direction increases slightly at high blowing ratio (notably at BR = 1.85) for the 777-shaped hole. It is believed that this interaction of the coolant with the mainstream flow at high freestream turbulence causes this spanwise spreading. Similar trends have been observed for the 777-hole by other researchers at a similar freestream turbulence level [13]. In contrast, the spanwise spreading of the coolant does not change significantly for the SJ hole. Although the cooling effectiveness value drops due to enhanced mixing of the coolant with the freestream, the near hole cooling effectiveness is significantly higher for the SJ hole. In addition, the SJ hole distributes the coolant more uniformly, which could reduce the thermal stress development on the vane surface, thus improving the operating life of the turbine component.

The span averaged cooling effectiveness $(η¯)$ for the SJ hole and 777-shaped hole is shown in Fig. 12 for a range of blowing ratios (0.55 ≤ BR ≤ 1.85) and freestream turbulence of Tu = 6%. Effectiveness data were averaged over three hole pitches (18D) in the lateral direction. Note that the error bar has been shown for one case since the uncertainty of the other case is very similar. As seen in the effectiveness contour, the SJ hole shows a lower span averaged effectiveness than the 777-shaped hole at M = 0.55. Previous studies also showed that the SJ hole has deteriorating cooling effectiveness compared to the 777-shaped hole at low blowing ratio (0.5 ≤ BR ≤ 1) [19]. A weak jet oscillation at the low coolant mass flowrate causes this to happen. However, with increasing blowing ratio, the span averaged cooling effectiveness improves significantly at the near hole region for the SJ hole

The difference in $η¯$ between the SJ and 777-hole becomes much more pronounced as the blowing ratio increases. Of note, the span averaged film effectiveness at high blowing ratios (1.45 ≤ BR ≤ 1.85) increases in the far field (x/D > 15) for the 777-hole. This implies the classic jet liftoff and reattachment phenomena for the shaped hole. This is not present for the unsteady SJ hole as the $η¯$ value drops continuously. Although the oscillatory motion of the coolant emanating from the SJ hole augments the local mixing as it moves downstream, the lateral spreading improves the average cooling effectiveness near the hole exit at high blowing ratios. This underscores the benefit of using the SJ hole over the conventional steady shaped hole.

The area-averaged cooling effectiveness $(η¯¯)$ for the SJ hole and the 777-shaped hole is shown in Fig. 13. The cooling effectiveness data were averaged over three hole pitches extending 30D (streamwise) and 18D (spanwise) from the hole exit. Results are presented for two freestream turbulence (Tu = 0.7%, 6%). Note that the error bars have been shown for one case (SJ hole, Tu = 0.7%) since the uncertainty of the other cases is very similar. Both holes exhibit the highest $η¯¯$ at BR = 0.95. For the low blowing ratio range (0.25 ≤ BR ≤ 0.95), the area-averaged effectiveness for the 777-shaped hole is higher than the SJ hole. However, the $η¯¯$ value for the SJ hole changes notably at high blowing ratios (1.45 ≤ BR ≤ 2.23) compared to the 777-hole. A significant improvement in the $η¯¯$ value can be seen for the SJ hole for both turbulence cases. Similar trends have also been observed and reported by the same authors in a low-speed cascade study [19]. The effect of mainstream turbulence on the average film effectiveness is also shown in Fig. 13. Due to enhanced turbulence mixing at high freestream turbulence, the area-average effectiveness drops for the SJ hole. In contrast, the 777-hole exhibits higher $η¯¯$ at BR ≥1.85 and Tu = 6%. As seen in Fig. 11, the spanwise spreading of the coolant increases with high mainstream turbulence for the 777 hole that result in a higher $η¯¯$ value.

Previous sections show that the SJ hole has improved cooling effectiveness at the engine relevant Mach number (M_ex = 0.8) compared to the shaped hole at high blowing ratio (0.95 ≤ BR ≤ 2.23). However, the measurement of the convective heat transfer coefficient is also required to accurately quantify the overall cooling benefit or the net heat flux reduction due to film cooling. In this study, the transient heat transfer experiment in conjunction with the DLRT provides the adiabatic cooling effectiveness (η) and the convective heat transfer coefficient (h) simultaneously for a range of blowing ratios. Separate experiments were performed for the uncooled case for both holes to determine the convective heat transfer coefficient without film cooling (h_o). The contours of the heat flux ratio (h/h_o) for the SJ hole and the 777-hole are shown in Fig. 14 at two blowing ratios (BR = 0.95 and 1.85) and Tu = 6%.

It is evident that the heat transfer augmentation (h/h_o > 1) is notably higher for the SJ hole in the near hole region (2 ≤ x/D ≤ 15). The unsteady sweeping motion of the jet enhances the local velocity fluctuation, thus augmenting the local heat transfer. Figure 14 also shows that the heat transfer augmentation is the highest along the centerline near the hole exit. The sweeping motion of the jet causes local velocity fluctuation at the centerline which is responsible for this augmentation. In addition, the sweeping frequency and jet spreading increases with blowing ratio, and the heat transfer augmentation covers a much wider area in the lateral direction.

Figure 15 shows the net heat flux ratio (q/q_o) contours for the SJ hole (left column) and the 777-hole (right column). Here, q and q_o represent the heat flux of the cooled and uncooled surface. The heat flux ratio was estimated using Eq. (8), and results are presented for two blowing ratios (BR = 0.95 and 1.85) and freestream turbulence of Tu = 6%. A net positive cooling benefit can be achieved where q/q_o < 1. The region with q/q_o < 1 representes the location where the film cooling has a positive effect. Thus, a cooling benefit has achieved. The white region corresponds to no cooling benefit, and the region with q/q_o >1 represents a negative cooling effect or a loss of coolant. It is evident that the 777-shaped hole has a significantly negative cooling effect at high blowing ratio (BR = 1.85), while the SJ hole shows a reasonably high benefit at the same blowing ratio (BR = 1.85).

The overall heat transfer augmentation and the net positive cooling benefit are shown in Fig. 16 for all blowing ratios and for high freestream turbulence. It is evident that the SJ hole has a higher heat transfer augmentation (h/h_o > 1) than the 777-hole at almost all blowing ratios. However, the net positive cooling benefit (q/q_o < 1) can be achieved by the SJ hole at high blowing ratio (1.45 ≤ BR ≤ 2.23) whereas the 777-hole failed to provide a positive cooling benefit.

Figure 17 shows the coefficient of discharge (C_d) for the SJ hole and 777 hole for a range of pressure ratios (1 ≤ PR ≤ 2.2). The discharge coefficient is estimated using Eq. (9). The C_d value for the SJ hole shows an increasing trend with pressure ratio. At low pressure ratio (PR ≤ 1.6), the C_d value for the SJ hole is slightly lower than the 777-hole. The pressure loss in the internal channels dominates at low mass flowrate due to internal roughness for the channel that results in a lower C_d value. However, at higher pressure ratio (PR > 1.6), the loss across the internal channels is less dominant compared to the overall loss across the device. The C_d values for the SJ hole are also compared with the smooth (electrical discharge machining) 777-shaped hole, additively manufactured (direct metal laser sintering) 777-shaped hole, and the fan-shaped hole reported by Stimpson et al. [34]. It is evident that the SJ hole has a comparable C_d value which is indicative of no additional pressure penalty for the unsteady device compared to a steady shaped hole.

The aerodynamic loss caused by film cooling was characterized by measuring the total pressure loss coefficient (γ). A total pressure Kiel probe was traversed along the pitchwise direction of the cascade passage at 0.25C_ax downstream of the test vane. The downstream total pressure (Pt_ex) in conjunction with the inlet total pressure (Pt_in) and inlet static pressure (Ps_in) were used to estimate the aerodynamic loss coefficient (γ) described in Eq. (10). The loss coefficient for the no cooling case was considered as the baseline (γ_o). Then, the loss coefficient was estimated for the film cooling cases (γ) for both hole types at several blowing ratios. The loss coefficient (γ) was integrated along the entire pitch P to estimate the average loss coefficient $(γ¯)$⁠.

Figure 18 shows the ratio of the average loss coefficient with $(γ¯)$ and without $(γo¯)$ the film cooling. This ratio is indicative of film cooling’s contribution to the total aerodynamic loss. Figure 18 implies that the aerodynamic loss for the unsteady SJ hole is slightly higher than the steady shaped hole. At Tu = 6%, the total aerodynamic loss is approximately 4.5% and 8% at a blowing ratio of 0.95 and 1.85, respectively. In contrast, the estimated aerodynamic loss for the 777-shaped hole is 3% at BR = 0.95 and 7.8% at BR = 1.85.

In this study, experiments were conducted in a transonic cascade facility to determine the performance of the unsteady SJ holes. A near engine scale transonic nozzle guide vane was designed that utilizes a row of the SJ hole on the suction surface. A transient heat transfer analysis was conducted in conjunction with a dual linear regression technique (DLRT) to estimate the convective heat transfer coefficient (h) and the adiabatic film effectiveness (η) simultaneously. Experiments were performed for a range of blowing ratios (0.25 ≤ BR ≤ 2.23) with varying mainstream turbulence intensity (Tu = 0.7% and 6%). The heat transfer augmentation and net positive cooling benefit were estimated. The hole discharge coefficient and aerodynamic loss coefficient were also measured. Results were compared with a baseline 777-hole. Some concluding remarks are listed below:

1. The SJ hole exhibits higher adiabatic cooling effectiveness in the near hole region at high blowing ratio (1.45 ≤ BR ≤ 2.23).

2. The lateral spreading of the coolant is attributed to the sweeping motion of the jet that creates a non-uniform jet velocity at the SJ hole exit. This non-uniform jet velocity results in a lower effective jet momentum that prevents jet liftoff at high blowing ratio.

3. The effectiveness drops slightly for the SJ hole at high blowing ratios. In contrast, the cooling effectiveness improves slightly for the 777-hole due to increased spanwise coolant spreading at high blowing ratio and a high level of mainstream turbulence.

4. The heat transfer augmentation for the SJ hole is higher than the 777-hole. The heat transfer augmentation (h/h_o) is maximum at the near hole region due to the enhanced lateral motion of the jet emanating from the SJ hole.

5. The net positive cooling benefit (q/q_o < 1) can be achieved by the SJ hole at high blowing ratio (1.45 ≤ BR ≤ 2.23) where the 777-hole failed to provide a positive cooling benefit.

6. The SJ hole has a comparable C_d value which is indicative of no additional pressure penalty for the unsteady device compared to the conventional steady shaped hole.

7. The total aerodynamic loss for the SJ hole is approximately 4.5% and 8% at a blowing ratio of 0.95 and 1.85, respectively. In contrast, the estimated aerodynamic loss for the 777-shaped hole is 3% at BR = 0.95 and 7.8% at BR = 1.85.

The authors would like to acknowledge the financial support from the US Department of Energy (DOE-NETL, Award No. DE-FE0025320, Program Manager: Robin Ames). The authors would also like to acknowledge the Ohio Supercomputer Center (OSC) for the computational resources.

h =

convective heat transfer coefficient, W/m² K

q =

convective heat flux, W/m²

C =

true chord

D =

throat hydraulic diameter

P =

pressure/vane pitch

R =

universal gas constant

T =

temperature

U =

velocity

$m˙c$ =

coolant mass flowrate, kg/s

c_p =

specific heat at constant pressure, J/kg K

A_t =

throat area

C_ax =

axial chord

C_d =

discharge coefficient

M_ex =

exit Mach number

P_D =

hole pitch, 6D

R² =

coefficient of determination

BR =

blowing ratio, (ρU)_c/(ρU)_∞

Re_ex =

exit Reynolds number (U_∞C_ax/υ)

Tu =

turbulence intensity

α =

thermal diffusivity (k/ρC_p)

γ =

total pressure loss coefficient/ ratio of specific heat

η =

cooling effectiveness

k =

thermal conductivity, W/m K

ρ =

density, kg/m³

ρ_c =

density of the coolant, kg/m³

υ =

kinematic viscosity, m²/s

Λ =

integral length scale

Φ =

overall cooling effectiveness

c =

coolant

ex =

exit

in =

inlet

is =

isentropic

o =

reference (no cooling)

r =

recovery

s =

static

t =

total or throat

w =

wall

∞ =

freestream

^– =

overbar average

⁼ =

double overbar area average