Computational and Experimental Study of Film-Cooling Effectiveness With and Without Downstream Vortex Generators

Film cooling protects turbine materials exposed to hot gases by forming an insulating layer of cooler air to separate the material from the hot gases [1–4]. When the insulating layer is formed by injecting cooler air into the hot gases through an inclined circular hole, the interactions between the cooling flow and the flow of the hot gases create a pair of counter-rotating vortices (CRVs) that always lift the cooling flow off the surface of the turbine material and entrains the surrounding hot gas to the surface [5,6]. Thus, the CRVs formed greatly reduce the effectiveness of film cooling.

Several methods have been developed to address the challenges created by CRVs. These methods can be classified into four categories [7]: (1) change the shape and/or orientation of film-cooling holes to minimize their effects (e.g., shaped holes [8–13], compound-angle holes [14–18], and slots instead of circular holes); (2) use CRVs to entrain cooler air instead of hot gases (e.g., two rows of film-cooling holes arranged in a staggered fashion [19] and flow-aligned blockers [20]); (3) modify how film-cooling and hot gas flows interact to eliminate the formation or minimize the strength of CRVs (e.g., trenches [21] and the upstream ramp [22,23]); and (4) create or enhance vortical structures that are anti-CRVs about the film-cooling flow to prevent lift off and to increase lateral spreading (e.g., struts [24], upstream and downstream tabs [25,26], side jets to create anti-kidney vortices [27], and vortex generators (VGs) [28–35]). With additive manufacturing, some of the aforementioned design concepts, previously considered not viable, are now possible. This study focuses on the use of vortex generators to create vortical structures and flow features to improve film cooling.

The use of VGs was first proposed by Rigby and Heidman [28]. They designed a VG that is a V-shaped tetrahedron with an isosceles triangle at the base and an apex that is perpendicular to that triangle. This VG, henceforth referred to as a delta ramp, is placed downstream of the film-cooling hole with the apex of the V-shaped tetrahedron facing the film-cooling hole. Their study based on Reynolds-averaged Navier–Stokes (RANS) showed the delta ramp to create a pair of anti-CRVs that entrains the film-cooling flow back to the surface and to increase its lateral spreading on the surface. In a later study, Zaman et al. [29] experimentally found the best height of the delta ramp to be 0.75D, where D is the diameter of the film-cooling hole; having sharp edges is better than having rounded ones; and the delta ramp should be placed between D to 3D downstream of the film-cooling hole. Song et al. [30] conducted an experimental study on the effects of the inclination angle of the delta ramp for different blowing ratios (BRs) on film-cooling effectiveness and found 20 deg inclination to be the best for the delta ramp in creating anti-CRVs.

Lee et al. [7] proposed a different type of VG. Instead of a single VG like the delta ramp, they proposed using a pair of rectangular plates arranged in a V-shape that is open on both ends of the V. Like the delta ramp, it is placed at a distance D downstream of a film-cooling hole. This VG increases film-cooling effectiveness by two mechanisms. First, the two rectangular plates—arranged in a V-shape (+45 deg for one plate and –45 deg for the other) and separated by 0.72D at x = D downstream of the film-cooling hole—serve as guide vanes that divert the cooling flow laterally. The delta ramp also has this feature—although the diversion is due to blockage instead of guide vanes and most of the diverted flow separates from the inclined portion of the delta ramp to form anti-CRVs. Second, instead of shedding vortices like in the delta ramp about its inclined surface, each plate’s leading edge induces the formation of horseshoe vortices that are counter rotating (CR) on the side of the plates that face each other and anti-CR on the sides of the plates that do not face each other. Figure 1 (taken from the study by Lee et al. [7]) illustrates this. The CRVs between the plates entrain the cooler flow back to the surface, and the anti-CRVs further increase lateral spreading. By using RANS, they examined the effects of height and aspect ratio of the rectangular plates on film-cooling effectiveness as a function of blowing ratio. Their study showed that the angled-plate VGs can increase film-cooling effectiveness by 50–100% and can outperform fan-shaped holes, W-shaped holes, flow-aligned blockers, and upstream ramps.

He et al. [31] studied V-shaped and inverted V-shaped VGs that are placed upstream of a film-cooling hole, where the V-shape could be protruded like a rib or indented like a cavity. Their study based on RANS showed that both protrusions and indentations produce anti-CRVs and can significantly improve cooling effectiveness. Zhao et al. [32] also studied angle plates arranged in an “open” V-shape, except the plates were triangular instead of rectangular and placed upstream of the film-cooling hole instead of downstream. Via large-eddy simulation (LES), they showed their design to significantly improve film-cooling effectiveness. In a subsequent study, Zhao et al. [33] showed via LES that the upstream angled plates performed even better when the film-cooling flow is pulsated. Deng et al. [34] used RANS to examine how the shape of the upstream angled plates affect film-cooling effectiveness. Of the four shapes studied—triangular, rectangular, and two trapezoidal—the rectangular shape was found to be the best.

Zhao et al. [35] studied a configuration involving two nonstaggered rows of film-cooling holes and placed VGs between the two film-cooling holes. They used LES to study two types of VGs, one is a delta ramp and the other is made up of two “small” angled plates, like the ones studied by Lee et al. [7] except the plates are triangular in shape instead of rectangular to induce shedding like the delta ramp. They found the delta ramp to be superior.

The aforementioned studies clearly show the usefulness of VGs in improving film-cooling effectiveness. Although upstream VGs were shown to produce excellent results, they are exposed to the hot gases and need to be cooled, and this is a challenge that needs to be addressed. Downstream VGs, on the other hand, are embedded in the film-cooling flow and require no additional cooling. Thus, this study continues the work described in the study by Lee et al. [7] on downstream VGs that use a pair of angled plates arranged in an “open” V-shape. The objective is twofold. First, perform a computational study that is validated by experimental measurements to demonstrate the utility of downstream angled-plate VGs in improving film-cooling effectiveness. Second, further examine the usefulness of this class of downstream VGs and the flow mechanisms that these VGs create to enhance film cooling as a function of blowing ratio (BR) and temperature ratio (TR) with and without conjugate heat transfer.

The remainder of this article is organized as follows. First, the experimental component and the computational model of the experiment are described. Afterwards, the problem formulation, numerical method of solution, grid sensitivity, and solution validation connected to the computational study are given. The results generated in this study are then presented.

This section describes the downstream VG problem studied experimentally and computationally.

The experimental effort utilizes the steady-state conjugate aerothermal test facility at the US Department of Energy’s National Energy Technology Laboratory (NETL). This test facility has been described in detail by Ramesh et al. [36]. In this section, only the essence of the facility pertinent to this study is provided. For the tests described in this article, the hot gas temperature is kept constant at 650 K and the inlet cooling air temperature is controlled to approximately 342 K to produce a hot gas-to-coolant temperature ratio of 1.9. Table 1 presents the averages for the experimental process parameters that were kept constant in this study. The datasets used for these averages represent multiple replications of each test condition conducted over at least three different days of testing to measure (1) surface temperatures, (2) upstream velocity and temperature profiles, and (3) downstream velocity and temperature profiles.

Figure 2 shows a schematic of the experimental setup. The hot gas flow is conditioned to provide a uniform velocity and temperature profile to the 101.6 mm × 101.6 mm test section. The test section is capable of optical access on three of four walls. The fourth wall supports the film-cooled test coupon. The cooling air is supplied to a plenum (roughly 145 mm diameter) before it flows through film-cooling holes.

Figure 3 shows the two test coupons investigated. Both are fabricated from 316 stainless steel with a thermal conductivity of approximately 17 W/m-K at the operating temperature. Although the baseline test coupon does not have VGs, the same film-cooling hole geometry was used for both test coupons. The cylindrical-hole, film-cooling geometry can be summarized by the following parameters: hole diameter (D = 3.2 mm), hole spacing (P = 3D), hole length (5D), and angle of inclination (α = 30 deg). The baseline coupon was manufactured by using conventional machining processes, but the test coupon with VGs was additively manufactured using a laser powder bed fusion process. After fabrication, both test articles were painted with four coats of Krylon High Heat Max paint. This paint has a high emissivity that enables measurement of the surface temperature using an infrared (IR) camera. The surface roughness for the VG test coupon was measured before and after painting. The centerline average roughness height (Ra) before painting was approximately 5 µm, and after painting, the Ra was about 2.5 µm. For comparison, the baseline test coupon had an Ra of about 0.6 µm after painting.

Measurements for each test condition given in Table 1 were taken over a 20-min, steady-state period. The temperatures, pressures, and flowrate data were sampled every second. The hot gas temperature and the coolant inlet temperature were measured using type-K thermocouples with uncertainties of 2–3 K for the conditions described in this article. The coolant mass flowrate was varied for each test coupon to achieve the blowing ratio conditions of 0.75 and 1.0. These blowing ratio conditions were chosen to reduce local jet lift-off conditions.

The temperature contours on the surface of the test coupons were measured by using an IR camera (FLIR Model A8300sc). Figure 4 shows the calibration curve of the IR camera. Since the IR measurements require a window with a high transmission coefficient in the 1–5 µm range, a sapphire window was used in this experiment with anti-reflective coatings on both (internal and external) surfaces of the window. The FLIR camera was bench calibrated by using a black body source. In addition, an in situ calibration was performed via an instrumented test coupon to account for other effects as described in the study by Ramesh et al. [36]. Based on the information from these tests, the infrared surface temperature measurements had a mean square error of 2.8 K for wall temperatures in the 475–600 K range. The mean square error for the IR temperature measurements is approximately the same (i.e., 0.4% of reading) as the type-K thermocouples used in the in situ calibration procedure.

To measure the temperature and velocity profiles, the infrared window in the test section is replaced by a stainless-steel plate that supports the boundary layer probe and translation stage. To measure the velocity in the momentum boundary layer, a (0.6 mm diameter) total pressure probe with a 0.08 mm sensing hole in the tip was used. The static pressure was also measured at the wall of the test section (same axial plane as the pressure probe). The uncertainty in the velocity measurements is less than 1% of the measured velocities (i.e., less than 1 m/s). The position of the total pressure probe was aligned with the center film-cooling hole, and the distance from the film-cooled surface was controlled by using a translation stage and a Raspberry Pi, programmed to collect data at 40–80 probe locations over a span of roughly 25 mm. At each location, the stage paused for 11 s before moving to the next location. This time interval for data collection was sufficient for the pressure and temperature data to plateau before moving to the next position. To produce the data points shown in the next section, approximately 10 data points were averaged at each location. The wall reference point was set when the test rig was “hot”, and this reference was repeatable to within 0.05 mm.

To measure temperature in the thermal boundary layer, two 0.8 mm diameter, type-K thermocouples were attached to the total pressure probe. These thermocouples were oriented parallel to the probe (see Fig. 5) and approximately mid-plane between adjacent upstream film-cooling holes. Minor corrections (<1 mm) were made to the thermocouple locations to align the center of the thermocouple with the sensing hole in the velocity probe. The tips of these thermocouples are approximately 3 mm downstream from the tip of the total pressure probe and spaced 4–5 mm in the transverse direction.

The spacing between data points decreased near the wall, and the variation in the process was assessed by replicating each test condition twice. So at least three velocity and temperature profiles were collected at each blowing ratio condition. Figure 6 shows all the experimental velocity and temperature data collected downstream of the film-cooling holes. Although the thermocouple diameters were large relative to the thickness of upstream boundary layer thickness, it was possible to measure differences in the temperature profile downstream of the film-cooling holes (see Fig. 6).

Figure 7 shows a schematic of the configuration used in the computational fluid dynamics (CFD) study, where all dimensions are given in terms of the diameter of the film-cooling hole, which is D = 0.125 in (3.2 mm). This configuration was designed to model the test section of the experiment so that the computational study is analyzing the same problem as the experiment. Thus, both test articles (i.e., the two coupons shown in Fig. 3 with the film-cooling holes and with and without the VGs, made of 316 stainless steel), were studied one at a time. The height of the computational domain was made sufficient so that the flow about the film-cooled flat plate can be captured correctly. For the plenum, the computational domain was made large enough so that the cooling flow through the film-cooling holes can be modeled correctly.

For the computational domain shown in Fig. 7, the one row of film-cooling holes is located at L₁ = 55.34D from the inflow boundary. The L₁ location was determined to ensure that the CFD study provided the same velocity and temperature profiles as the experimental study at a location upstream of the film-cooling holes (to be explained in the validation section)—a criterion needed to ensure that the CFD is solving the same problem as the experimental study.

On the film-cooling holes, each hole has a length-to-diameter ratio of 5 and an inclination angle of α = 30 deg relative to the flat plate. The spacing between the centers of the film-cooling holes in the spanwise direction is P/D = 3.

The VGs placed after each film-cooling hole are similar to the one proposed by Lee et al. [7], which consists of two rectangular plates arranged in an open V-shape. Each plate has a span of S = 0.5D and a chord of C = 0.4D. The thickness of each plate is t = 0.15D, and the leading and trailing edges of the plate are hemispherical with a radius of t/2. The thickness and the radii were changed from those reported in the study by Lee et al. [7] to improve the manufacturability of the VGs using additive manufacturing. The two plates are placed at a distance of 1D downstream of each film-cooling hole. At that location, the two plates are separated from each other by a distance of 0.72D. The angle of attack relative to the approaching film-cooling flow is + 45 deg for one plate and—45 deg for the other plate to create the “open” V-shape.

The conditions at the domain boundaries are as follows. At the inflow boundary (x = –L₁), the hot gas that enters is air with a uniform temperature of T_∞ = 650 K, a uniform velocity of V_∞ = 107.5 m/s that points in the x-direction, and 5% turbulent intensity. The cooling flow that enters the plenum is also air, and it enters with a uniform temperature of T_c. Two different temperatures were examined, and they are 343 K and 607.5 K, which give rise to two TRs: TR = 1.9 and 1.07. If the pressure of the hot gas and the pressure of the cooling flow are the same, then the density ratio (DR) is equal to the TR. The mass flowrate of the cooling flow that enters the plenum was adjusted to provide the desired BR. Two blowing ratios were examined: BR = 0.75 and 1.0. At the outflow boundary (x = L₂), the static pressure was fixed at P_b = 1.076 bar. On all solid surfaces, the no-slip condition was imposed. Since the test article (either of the coupons shown in Fig. 3) connects the hot air and the cooling flow, there is conduction heat transfer across it. At the air–solid interface, the temperature and heat flux of the air are equal to those of the coupon. At all other surfaces of the coupon, the heat flux is zero. Since the configuration and boundary conditions just described are symmetric about y = 0, only half of the computational domain was simulated.

A summary of all simulations performed is presented in Table 2. Note that eight cases were simulated with all walls being adiabatic to provide film-cooling adiabatic effectiveness, and eight cases were simulated to show how conjugate heat transfer affects the surface temperature on the hot side of the coupon.

The film-cooling problem described in the previous section involves air whose density varies appreciably throughout the flow field because of the large differences in temperature between the hot air and cooling air. Thus, even though the Mach number of the flow is quite low, the compressible formulation with temperature-dependent properties is needed for the gas phase. In this study, the governing equations employed for the gas phase are the Reynolds-averaged continuity, Navier–Stokes, and energy equations for a thermally perfect gas with temperature-dependent thermal conductivity, viscosity, and specific heats. The effect of turbulence was modeled by using the shear-stress transport (SST) model with curvature correction and production limiter [37]. The SST model was used because the simulation must resolve the flow induced by the downstream VGs about the film-cooled plate. Thus, wall functions, which model the velocity and the length scales of the turbulence at a distance from the plate instead of resolving the flow all the way to the wall, were not used. Also, the one-equation model, often used with the standard and the realizable k-ε models to resolve the low Reynolds-number turbulent flow next to the wall, were not used. This is because the one-equation model uses an algebraic equation for the length scales based on boundary layer flow without pressure gradients instead of resolving it and so cannot account for separated flows induced by the downstream VGs. Although the SST model has the same limitations that beset all RANS models, it can be useful in revealing flow mechanisms and understanding effects of design and operating parameters once validated by comparing them with experimental data. The validation study is described in the next section.

For the solid phase (i.e., the film-cooled plate with holes drilled through it and with downstream VGs) added, effects of thermal stresses were assumed to be negligible so that the shape of the solid phase does not change with the temperature. Thus, only the temperature distributions in the solid phase were simulated. The governing equation used was the balance of thermal energy closed by the Fourier law to account for conduction heat transfer. Since the temperature in the coupon can vary appreciably from the hot gas side to the cooled plenum side, temperature-dependent thermal conductivity was used. In this study, the thermal conductivity given in Ref. [38] was used. The solid phase is coupled to the gas by requiring the temperature and the heat fluxes at the gas–solid interfaces to be the same.

Solutions to the aforementioned governing equations were obtained by using ansys fluent [39] on a discretized domain made up of a multiblock boundary-conforming structured grid. The details of the grid used are given in the section on verification. Since only the steady-state solutions or the long-term time-averaged solutions were of interest, the SIMPLE algorithm was used to generate solutions. The fluxes for density, momentum, and energy at the cell faces for the governing equations in the gas phase were interpolated by using the second-order upwind scheme. Pressure and all diffusion terms were approximated by using second-order accurate central formulas. For the solid phase, there are only diffusion terms, and they were also approximated by second-order accurate central formulas. For all computations, iterations were continued until all residuals for all equations plateau to ensure convergence to a steady state has been reached. At convergence, the scaled residuals were always less than 10⁻⁵ for continuity and the three components of the velocity, less than 10⁻⁷ for energy (including thermal energy for the solid phase), and less than 10⁻⁵ for the turbulence quantities.

Verification of this computational study was accomplished via a grid-sensitivity study. Figure 8 shows the typical grid used. The grid used is structured and consisted of a wrap-around grid about all solid surfaces, an H-H plus an O-H grid for the film-cooling hole, an H-H grid above the plate, and an H-H grid in the plenum, where H-H is generalized Cartesian and O-H is generalized cylindrical. Three grid sizes were examined, and they are as follows: mesh #1, the coarsest grid, with 13.3 million cells; mesh #2, the baseline grid, with 19.9 million cells; and mesh #3, the finest grid, with 25.7 million cells. Note that mesh #3 is a refinement of mesh #2, where the grid is refined only where most needed, namely, in regions where hot gas and the cooling flow interact and where CRVs entrain hot gas and anti-CRVs extend lateral spreading and in regions where the VGs divert the flow and create horseshoe vortices.

For all three grids, the first cell away from all solid surfaces has a y+ less than unity. The grid-sensitivity study was performed by using parameters from case 14 in Table 2 with BR = 1.0 and TR = 1.9, and the results are shown in Figs. 9 and 10. Figure 9 shows the pressure and friction coefficients at y = z = 0 and the centerline normalized temperature on the surface at z = 0 obtained by using the three grids. From this figure, it can be seen that the relative differences in the pressure and friction coefficients and centerline normalized temperature obtained by the baseline and the fine grids are extremely small, and they are within 0.7%, 1.8%, and 0.2%, respectively. Figure 10 shows the solution to converge as the grid is refined. Based on the grid-sensitivity study and the grid convergence study, the baseline grid was used to generate all solutions.

With the computed solution verified, Figs. 11–14 show results of the validation study, based on BR = 0.75 and 1.0, TR = 1.9, and with and without VGs. To ensure that the CFD is studying the same problem as the experimental study, simulations were performed for a wide range of L₁ until the velocity profile computed matched the experimentally measured values at x/D = −10.7, a location upstream of the film-cooling holes. From Fig. 11, the computed and measured velocity profile can be seen to match well at x/D = −10.7 if L₁ = 55.34D. However, Fig. 12 shows the computed and measured temperature profiles at x/D = −9.1 to match only in the freestream region but not in the thermal boundary layer. One reason for the mismatch of the temperature in the boundary layer is that the size of the thermocouple used is roughly 20% of the boundary layer thickness. Another reason is the heat transfer loss through the walls of the test section.

Figures 11 and 12 also show the computed and measured velocity and temperature profiles downstream of film-cooling holes with and without VGs at (x/D, y/D) = (11.6, 0) for velocity and at (x/D, y/D) = (13.2, 1.575) and (13.2, –1.575) for temperature. From Fig. 11, it can be seen that the computed and measured velocity profiles match in the freestream region but not in the boundary layer. However, the thicknesses of the boundary layer match reasonably well. This shows the limitation of the SST turbulence model used. The good match of the boundary layer thickness is important in capturing the extent of influence exerted by the film-cooling flow and their interactions with the VGs. From Fig. 12, the computed and measured temperature profiles can be seen to match reasonably well.

Figures 13 and 14 show computed and measured temperatures at several locations on the hot side and on the plenum side of the test coupons for BR = 0.75 and 1.0 and TR = 1.9. From these two figures, the maximum relative difference on the hot side is 4.9% without VGs and 8.4% with VGs. On the plenum side, the maximum relative difference is 2.0% without VGs on the hot side. Measurements of temperature on the coupon’s plenum side with VGs on the hot side were not made.

The reasonable match between the computed and the measured velocities and temperatures shown in Figs. 11–14 gives confidence to the validity of this computational study and the results presented in the next section.

Before leaving this section on verification and validation, one result in Figs. 12 and 13 needs to be highlighted. In Fig. 12, it can be seen that both the computations and the measurements show a lower temperature at the same distance from the wall when there are VGs, and this reduction in temperature is significant. This means that the use of these VGs could significantly reduce the cooling flow and still achieve the same cooling effectiveness. In Fig. 13, it can be seen that the temperature measured at probe D, which is located downstream of the film-cooling holes on the hot side of the test coupon, is cooler when VGs are added. It is cooler by 5.8 K when BR = 0.75 and TR = 1.9 and by 10.5 K when BR = 1.0 and TR = 1.9. Here, it is emphasized that this significant improvement in cooling—enabled by the angled plates VG studied—was predicted by the model and validated by experimental measurements.

As noted in the Introduction section, the objective of this study is twofold: (1) Perform a computational study that is validated by experimental measurements to demonstrate the utility of downstream VGs in improving film-cooling effectiveness. (2) Further examine the usefulness of the class of VGs made up of a pair of angled plates arranged in an open V-shape and the flow mechanisms that it creates to enhance film cooling as a function of blowing and temperature ratios with and without conjugate heat transfer.

The validation of the computational study and the demonstration of the utility of downstream VGs were presented in the previous section. In this section, results on how the flow mechanisms improve film-cooling effectiveness are presented through Figs. 15–23. Unless explicitly stated, all results presented are obtained by using conjugate analysis.

Figure 15 shows the normalized temperature (θ) and velocity vectors at two locations downstream of a film-cooling hole with and without VGs and with BR = 0.75 and TR = 1.9. From this figure, CRVs can be seen to be formed by the interactions between the film-cooling flow and the hot-gas flow at x/D = 1.2 and 2.0 when there are no VGs. These CRVs lift the film-cooling flow off the surface and entrain hot gas underneath it.

When there are VGs, each VG can be seen to create a pair of CRVs between the two plates of the VG and a pair of anti-CRVs on the external sides of the VG. In addition, the V-shape of the angled plates can be seen to serve as guide vanes that laterally spread the cooling flow. As noted in the Introduction section and shown in Fig. 1, these CRVs and anti-CRVs are parts of the two horseshoe vortices formed when the film-cooling flow flows past the two angled plates. From Fig. 15, CRVs between the two plates can be seen to entrain cooler air to the surface. When BR = 0.75 and TR = 1.9, the anti-CRVs formed along with the lateral deflection of the film-cooling flow by the angled plates completely eliminated the CRVs created by the interactions between the film-cooling flow and the hot-gas flow. Thus, adding these VGs greatly increased the effectiveness of film cooling.

Table 2 summarizes all parameters studied with BR = 0.75 and 1.0 and with TR = 1.07 and 1.9. Among the combinations of BR and TR studied, the following velocity ratios (VRs) result: 0.395, 0.526, 0.701, and 0.935. The corresponding momentum ratios (MR = BR x VR) are as follows: 0.296, 0.526, 0.525, and 0.935.

Figures 16 and 17 show the normalized magnitude of the velocity and velocity vectors in the x-z plane and two y-z planes downstream of a film-cooling hole with and without VGs and with the data arranged according to VR instead of BR or TR. From Fig. 16, it can be seen that when there are no VGs, the higher the VR or MR, the more intense and bigger the CRVs become. For example, the case with BR = 1.0 and TR = 1.9 corresponding to VR = 0.526 produced much smaller CRVs than the case with BR = 1.0 and TR = 1.07 corresponding to VR = 0.935. The reason why flow patterns for VR = 0.526 and VR = 0.701 are similar is because they both have essentially the same MR. Also, the film-cooling flow was found to separate upon exiting the film-cooling hole at the higher VRs. The role of VR on film-cooling structure was noted by Stratton and Shih [40]. In this study, VR was found to play a more important role than BR in the separation and reattachment of film-cooling flow upon exiting the hole.

From Fig. 17, it can be seen that when there are VGs, the higher the VR, the less effective is each VG in reducing the strength of the CRVs. This is because at higher VRs, the stronger are the CRVs. Also, at higher VRs, the film-cooling flow lifts off once exiting the film-cooling hole and may not reattach so that the two angle plates create much weaker horseshoe vortices and laterally deflect increasingly smaller portions of the film-cooling flow. For film-cooling flows with VRs greater than about 0.5, a taller set of angled plates (i.e., plates with larger values of S) would be needed.

Figure 18 shows the normalized temperature (θ) in the coupon with and without conjugate heat transfer, and Figs. 19 and 20 show the normalized temperature (θ) and velocity vectors in two planes downstream of the film-cooling hole with and without VGs and with and without conjugate heat transfer.

The temperature distribution in the coupon depends on the heat transfer coefficients on the coupon’s hot and plenum sides and in the film-cooling holes, which in turn depend on the fluid mechanics on those surfaces. For the conditions of this study, the magnitudes of the velocities, temperatures, and their gradients on the coupon’s plenum side are much lower than those on the hot side and in the film-cooling holes so the heat transfer coefficient is lowest on the coupon’s plenum side. Thus, most of the heat transfer through the coupon from the hot side is towards the film-cooling holes instead of the plenum. As a result, the temperature in the coupon is lowest about the film-cooling hole as shown in Fig. 18. If the heat transfer coefficient on the plenum side were comparable to that in the film-cooling holes, then the lowest temperatures would be about the film-cooling hole as well as about the coupon’s plenum side.

Figure 18 also shows the temperature distribution in the coupon to be a strong function of VR and TR. In particular, for a given TR, the coupon’s temperature on the hot side is lower when VR is lower. This is because at lower VRs, the film-cooling flow hugs the coupon’s surface but lifts off at higher VR as shown in Figs. 19 and 20.

From Fig. 18, it can also be seen that when downstream VGs are added, the temperature in the coupon is significantly reduced downstream of the film-cooling holes. This shows the utility of VGs in improving film-cooling effectiveness by increasing lateral spreading and re-entraining lifted cooling flow back to the surface of the coupon, which lowers the temperature of the coupon exposed to film cooling.

Figures 19 and 20 show conjugate heat transfer to increase the temperature of the film-cooling flow because it gets heated in the hole and that this increase in temperature reduces with increase in VR because higher VR reduces the resident time of the cooling flow in the hole. These figures also show the temperature of the hot gas and cooling flow on the hot side with conjugate heat transfer to differ considerably from those with adiabatic walls. Interestingly, these differences in temperature have little effect on the flow structure, at least not for the conditions of this study. Figures 19 and 20 show the flow patterns via velocity vectors for the conjugate and the adiabatic cases to be quite similar.

Figure 21 shows the adiabatic effectiveness (η) on the hot side of the coupon (z = 0 in Fig. 7) with and without VGs, where all solid surfaces are adiabatic. Figure 22 shows η along a line that passes through the center of the film-cooling hole (i.e., along x with y = z = 0) and η that is averaged along y from –P/2 to + P/2 (⁠$η¯$⁠). Figure 23 shows η with the adiabatic wall and normalized temperature (θ_w) on the hot side of the coupon with conjugate heat transfer. From Figs. 21 and 22, it can be seen that having VGs significantly improves adiabatic effectiveness, even when the film-cooling flow separates once exiting from the hole and do not reattach until much further downstream, which occurs when the VR exceeds about 0.5. From these figures, adding VGs can be seen to decrease η and $η¯$ from the film-cooling hole to the VGs because of the adverse pressure gradient induced by the VGs. However, once the film-cooling flow reaches the VGs, η and $η¯$ increase significantly because the VGs divert the cooling flow laterally and entrain lifted cooling flow to the coupon’s surface. With the VGs added, $η¯$ at 15D downstream of the film-cooling hole is increased by 145%, 94%, and 45% when (TR, VR) = (1.9, 0.395), (1.9, 0.526), and (1.07, 0.701), respectively. The only case, where adding VGs did not improve $η¯$ at 15D, is when (TR, VR) = (1.07, 0.935), where the temperatures of the cooling flow and the hot gas are nearly the same, and where the VGs were only able to deflect and entrain a small fraction of the lifted cooling flow back to the coupon’s surface. Although steady RANS based on the SST model is far from perfect in making accurate quantitative predictions, these results do show that adding downstream VGs can substantially improve adiabatic effectiveness.

Figure 23 shows how conjugate heat transfer affects the temperature on the coupon’s hot side as a function of TR and VR. Here, it is noted that the normalized temperature shown in this figure is not adiabatic effectiveness and should not be compared with Fig. 21. This is because once there is conjugate heat transfer, the temperature on the coupon’s surface depends on the heat transfer coefficients on all surfaces of the coupon exposed to the cooling flow and the hot gas. If a superior film-cooling strategy is selected (e.g., adding downstream VGs), then the coupon should be cooler if the heat transfer coefficients on the plenum side and in the film-cooling holes are unchanged. Figures 18 and 23 show that this is indeed the case; namely, the coupon’s surface temperature on the hot side is substantially cooler with VGs added. This again shows the effectiveness of the downstream VGs proposed. In addition, it is noted that though adding downstream VGs reduce η and $η¯$ from just after the film-cooling hole to just before the VGs, conjugate heat transfer from the film-cooling hole cools that region so that this reduction in η and $η¯$ does not cause a problem. Once again, it is emphasized that the downstream VG proposed is embedded in the cooling flow so that it does not require additional cooling.

A combined computational and experimental study was performed to examine “how” and “how well” a class of VGs made up of a pair of angled plates arranged in an open V-shape that are placed at a short distance downstream of the film-cooling hole can improve the effectiveness of film cooling a flat plate as a function of BR and TR with and without VGs and with and without conjugate heat transfer. Results obtained show that if the TR is not near unity (e.g., 1.9 vs 1.07), then it is the VR and not the BR that determines whether a film-cooling flow will separate or not once exiting the film-cooling hole. In addition, the higher the VR, the more intense the CRVs formed by the interactions between the cooling flow and the hot-gas flow, where the MR plays a role as well. When a VG is placed downstream of a film-cooling hole, the lateral deflection of the film-cooling flow by the angled plates can completely eliminate the effects of CRVs next to the surface. The anti-CRVs generated by the horseshoe vortices about the two plates further reinforce this. The CRVs formed between the two angled plates improve film-cooling effectiveness by entraining even lifted film-cooling flow back to the surface. The VG examined was found to be ideal in enhancing film cooling with low VRs, where the film-cooling flow does not separate appreciably after exiting the film-cooling hole. The results of this study show that with downstream VGs added, the laterally averaged adiabatic effectiveness at 15D downstream of the film-cooling hole is increased by 145%, 94%, and 45% when (TR, VR) = (1.9, 0.395), (1.9, 0.526), and (1.07, 0.701), respectively. Also, by being placed downstream of the film-cooling hole, VGs are embedded in the cooling flow and so require no additional cooling.

This research at Purdue University was supported by the US Department of Energy-Office of Fossil Energy, Advanced Turbines Program under contract no. DE-AC02-07CH11358 through the Ames Laboratory agreement no. 26,110-AMES-CMI. The authors are grateful to Rich Dennis, Richard Dalton, and Mark Bryden for this support and their guidance on the research. The authors are also grateful for the helpful discussions with Jim Black, Sridharan Ramesh, Matthew Searle, and Joseph Yip of DOE NETL.

There are no conflicts of interest.

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

y =

normal distance from wall

C =

chord of the vortex generator

D =

diameter of film-cooling hole

L =

length of film-cooling hole

P =

static pressure

S =

span of the vortex generator

T =

temperature

|V| =

velocity magnitude

C_f =

skin friction coefficient: C_f = τ_w/(0.5ρ_∞V_∞²)

C_p =

pressure coefficient: C_p = (P–P_∞)/(0.5ρ_∞V_∞²)

P_b =

static pressure at hot-gas outflow boundary

T_ad =

adiabatic wall temperature

T_c =

temperature of cooling flow entering the plenum

T_w =

wall temperature at z = 0 plane

T_∞ =

temperature of hot gas at inflow boundary

U_τ =

friction velocity: U_τ = (τ_w/ρ_w)^0.5

V_c =

cooling flow velocity

V_∞ =

hot gas velocity at inflow boundary

y⁺ =

normalized distance from wall: y⁺ = ρU_τy/μ

x-y-z =

coordinate system

BR =

ρ_cV_c/ρ_∞V_∞

DR =

ρ_c/ρ_∞ = TR if P of cooling and hot air are the same

MR =

(BR)(VR)

Pr =

Prandtl number: Pr = Pr(T)

TR =

T_∞/T_c

VR =

V_c/V_∞

V_x, V_y, V_z =

x-, y-, and z-component velocity

β =

angle of attack of the vortex generator

η =

film-cooling adiabatic effectiveness: η = (T_∞–T_ad)/(T_∞–T_c)

µ =

dynamic viscosity

θ =

normalized temperature: θ = (T_∞–T)/(T_∞–T_c)

ρ =

density

ρ_c =

density of cooling flow based on T_c

ρ_∞ =

density of hot gas flow based on T_∞

  τ_w =

wall shear stress (z = 0)