Experiments of Transpiration Cooling Inspired Panel Cooling on a Turbine Blade Yielding Film Effectiveness Levels Over 95% †

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International Journal of Turbomachinery Propulsion and Power

Article Experiments of Transpiration Cooling Inspired Panel Cooling on a Turbine Blade Yielding Film Effectiveness Levels over 95% †

Augustin Wambersie 1,*, Holt Wong 1 , Peter Ireland 1 and Ignacio Mayo 2

1 Department of Engineering Science, University of Oxford, Oxford OX1 3PJ, UK; [email protected] (H.W.); [email protected] (P.I.) 2 Rolls-Royce PLC, Derby DE24 8BJ, UK; [email protected] * Correspondence: [email protected] † This paper is an extended version of our meeting paper published in the 14th European Turbomachinery Conference, Gdansk, Poland, 12–16 April 2021.

Abstract: Panels were tested at different locations around the turbine blade, on both suction and pressure surfaces. Three different surface porosities were also tested. Results demonstrated that the approach can be very successful with high levels of film cooling effectiveness, exceeding 95%, achieved using low coolant mass flow rates. Increasing the surface porosity also proved to be an important parameter in the panel’s performance. Additionally, staggering the film holes lead to significant positive interactions between individual films, resulting in much improved panel performance.

Keywords: transpiration cooling; turbine blade; ﬁlm cooling; pressure sensitive paint

Citation: Wambersie, A.; Wong, H.; Ireland, P.; Mayo, I. Experiments of 1. Introduction Transpiration Cooling Inspired Panel The need to design turbine blades able to endure the ever increasing temperatures Cooling on a Turbine Blade Yielding found in the next generation of turbine engines has long motivated continuous improve- Film Effectiveness Levels over 95% . ment in cooling and material technology. However, despite the impressive progress made Int. J. Turbomach. Propuls. Power 2021, over the past 80 years, most gains have been slow, incremental improvements of existing 6, 16. https://doi.org/10.3390/ technology, with film cooling, thermal barrier coatings and ceramic matrix composites ijtpp6020016 being the few major significant innovations. While transpiration cooling is not a new concept, it has long been predicted to deliver Academic Editor: Giovanna Barigozzi a step change in cooling performance relative to conventional systems [1]. The very high internal surface area, positive effect on heat transfer coefficient and uniform distribution of Received: 16 May 2021 cooling films make it theoretically ideal for turbine blade applications. Recent advances in Accepted: 26 May 2021 Published: 4 June 2021 porous C/C-SiC and CMC have led to a revival in the field of transpiration in aerospace for uses such as rocket nozzle cooling [2], yet momentum in turbine blade technology has

Publisher’s Note: MDPI stays neutral lagged behind. While this may be due to the significant constraints in blade design arising with regard to jurisdictional claims in from the high thermal, mechanical and cyclical loading, a fundamental understanding of published maps and institutional affil- the true potential of transpiration cooling as applied to turbine blades remained mostly iations. unexplored before the present research. The development of high resolution, non-intrusive measurement techniques has facilitated the study of more complicated external cooling flows, allowing much greater understanding of cooling phenomena in representative conditions. By making use of Pressure Sensitive Paint (PSP) to measure the film effectiveness of transpiration cooling Copyright: © 2021 by the authors. features on turbine geometries, this paper will attempt to demonstrate how such cooling Licensee MDPI, Basel, Switzerland. This article is an open access article flows behave in engine-representative conditions. distributed under the terms and Two separate studies are considered in this paper. The first looks at the performance of conditions of the Creative Commons a transpiration panel over different locations around the blade, on both suction and pressure Attribution (CC BY-NC-ND) license surfaces. The second looks to compare several variants of the same panel at the same (https://creativecommons.org/ location. While transpiration cooling has benefits far beyond external film effectiveness, licenses/by-nc-nd/4.0/).

Int. J. Turbomach. Propuls. Power 2021, 6, 16. https://doi.org/10.3390/ijtpp6020016 https://www.mdpi.com/journal/ijtpp Int. J. Turbomach. Propuls. Power 2021, 6, 16 2 of 12

the simplicity of this type of experiment allows for a large number of geometries to be quickly sampled, making it a sensible starting point.

2. Literature Review In previous work by Ngetich [3], the effectiveness of full coverage effusion cooling schemes on full turbine blade geometries was tested but with limited success. The introduction of large numbers of large holes across the entirety of the blade surface resulted in a significant flow migration towards the latter portion of the suction surface due to the high pressure gradient across the blade. Combined with the effects of secondary flows, this resulted in very low effectiveness on the pressure surface. Reducing the pitch and increasing the number of holes was seen to noticeably improve the external film effectiveness, though large mass coolant fractions of above 4% were required. Several studies have demonstrated the film effectiveness of arrays of more tightly packed holes and porous media, albeit on flat plates. In a study by Murray et al. [4], the effect of hole pitch of effusion cooled plates demonstrated that the for a given coolant output per unit area, reducing the pitch between coolant holes greatly improved the average film effectiveness of the studied plate. Reducing the pitch to hole diameter ratio from 5.75 to 3 more than doubled the effectiveness. When compared to results by Ling et al. [5] in which higher pitch to diameter ratios were used, the improvement in film effectiveness from a pitch of 10d to 3d was almost sevenfold for the same non dimensional mass flow. CFD modeling of the same domain remains a challenge, with so many interactions between closely spaced films proving difficult to predict. With each additional film row, divergence from experimental data as well as computing time was greatly increased. While simplified analytical approaches such as the one suggested by Sellers [6] can greatly reduce computing time, accuracy remains a challenge, leaving experimental data as the most reliable approach. In another flat plate study by Huang et al. [7] the metal effectiveness of perforated plates was compared to that of sintered porous media in a low speed wind tunnel. Here, it was shown that while perforated plates with higher porosities performed better those with lower porosities, the sintered plates did not have a noticeable improvement in performance despite being almost twice as porous. This suggests that downsizing cooling features is only beneficial up to a point, at which the individual cooling jets become smaller than the boundary layer characteristic length. While flat plate studies provide a level of insight into the behavior of transpired coolant flows, the nature of the flow around a turbine blade can lead to significant divergence from flat plate studies, particularly in the case of low blowing ratios. Schwarz et al. [8] examined the effect of the curvature to film hole size ratio 2 r/d on film effectiveness by studying high speed flows around a cylindrical section. It was observed that for highly convex surfaces at low film momentum ratios of 0.5, the measured film effectiveness was over twice as high as that measured on a flat plate and this increase was closely correlated to the 2 r/d ratio. The adverse effect of curvature on film effectiveness was found to be true on concave surfaces. El-Hady & Verma [9] argue that this is due to additional secondary flows, namely Taylor-Gortler vortices, which have a significant effect on the boundary layer stability and film effectiveness of concave surfaces, due to an increase in film to mainstream mixing. Winka et al. [10] took the study of convex surfaces further and examined how the non-uniform curvature of an airfoil affected film effectiveness. By comparing several different combinations of hole location and size, it was possible to deduce that the local curvature r, local curvature ratio 2 r/d and curvature of the entire downstream region play a significant role in the film to mainstream mixing. In this study, a momentum ratio of 0.2 was measured to be the most effective for convex surfaces. Another effect not considered by either of these studies is the effect of acceleration on the boundary layer. Vinton & Wright [11] subjected films to favorable pressure gradients resulting in a reduction in the boundary layer thickness, forcing the film core closer to the test surface and leading to improved film effectiveness. Int. J. Turbomach. Propuls. Power 2021, 6, 16 3 of 12

3. Experimental Facility Experiments were conducted at the Oxford Thermofluids Institute of The University of Oxford. A detailed description of the test apparatus and its operating conditions can be found in the work by Ngetich [3]. The airfoil profile used was a scaled up midsection profile of a high pressure turbine blade. The walls of the cascade are made of thick Perspex for optical access and were designed to achieve the periodic boundary conditions defined by the midpitch streamline in the engine. The facility was designed to match engine Reynolds numbers, as well as match the Mach number distribution predicted by a CFD infinite cascade simulation. The mainstream mass flow rate was calculated to be 1.43 kg/s. The test pieces were painted with PSP and monitored using three high resolution CCD cameras. Each was positioned so that their overlapping fields of view could be stitched into a single image covering the entirety of the blade surface. The data capture, processing and uncertainty measurements were carried out as described by Gurram et al. [12].

4. Blade Geometry and Test Regime The test pieces were fabricated in house by 3D additive manufacturing techniques. The interior of the blades were completely hollow and void of any features. The coolant inlet was a large simple cut into the side of the blade. For this experiment, only the middle 60 mm of the span was used in order to avoid end wall effects at either end the blade span. The default wall thickness of the blades were kept high, at 5 mm in order to reduce strain under aerodynamic loading, but was reduced at the panel location in order to produce representative blade wall thickness. Each test piece contained a panel formed by a large array of 0.5 mm diameter holes spanning an area of 60 mm × 18 mm. The spanwise pitch was equal to the streamwise pitch and the holes were always angled at 45◦ from the surface. The panel was tested at four different locations around the blade, indicated by Figure1. For the second part of the study, the film hole pitch was changed in order to vary the panel porosity. Lastly a final panel was tested with staggered rows. The full description of all geometries can be found in Table1 and a detail of Panel 1 can also be found in Figure1. Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 4 of 13 The test pieces were fitted with dedicated channels for thermocouples spaced at every 20 mm along the surface for PSP calculations as well as with pressure tappings to measure the internal plenum pressure.

(a) (b)

FigureFigure 1.1. ((aa)) DetailDetail ofof PanelPanel 11 geometrygeometry withwith ((bb)) crosscross sectionsection indicatingindicating locationslocations ofof Panels Panels 1–4. 1–4.

Table 1. Summary of geometries tested.

Approximate d L Streamwise Distance Hole Panel Surface Pitch (mm) Pitch/d L/d Porosity (mm) (mm) from LE over Chord Arrangement (%) 1 SS 1.05 0.5 2.1 3 6 0.1 25 Inline 2 SS 1.05 0.5 2.1 3 6 0.64 25 Inline 3 PS 1.05 0.5 2.1 3 6 0.1 25 Inline 4 PS 1.05 0.5 2.1 3 6 0.33 25 Inline 5 SS 1.20 0.5 2.4 3 6 0.1 20 Inline 6 SS 0.95 0.5 1.8 3 6 0.1 30 Inline 7 SS 1.05 0.5 2.1 3 6 0.1 25 Staggered

5. Results 5.1. Varying Panel Locations First, the film effectiveness map of Panels 1–4 across four different blowing rates are shown in Figures 2–5 respectively. The charts show the entire width of the blade surface from the start of the panel at x/d = 0 down to the trailing edge. The ratio Pr between the coolant and mainstream inlet total pressures is also shown. The plots are arranged so that the coolant is always being fed from the right side of the image. For all panels at low blowing rates, film distributions are uneven with coolant only being ejected from certain sections of the panels. This is mainly due to the significant external static pressure variation along the streamwise dimension of the panels. This favors flow towards the trailing edge of Panel 1, 2 and 4, and towards the leading edge of Panel 3, where a mild adverse pressure gradient occurs. The low internal pressure results in significant ingestion across the panels. Furthermore, variations in internal static pressure and coolant velocity within the blades lead to uneven spanwise distributions. As the coolant flow rate is increased, the distribution is first matched in the spanwise direction and, as the internal blade pressure is further increased, coolant is observed being ejected by every row. Due to the high resolution of the PSP, the films of the individual holes can be differentiated from the bulk of the coolant. These individual features mix out within a short distance of the end of the panels. On the other hand, the bulk of the panels form a much more robust sheet film.

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Table 1. Summary of geometries tested.

Approximate Pitch d L Streamwise Distance Hole Panel Surface Pitch/d L/d Porosity (mm) (mm) (mm) from LE over Chord Arrangement (%) 1 SS 1.05 0.5 2.1 3 6 0.1 25 Inline 2 SS 1.05 0.5 2.1 3 6 0.64 25 Inline 3 PS 1.05 0.5 2.1 3 6 0.1 25 Inline Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 5 of 13 4 PS 1.05 0.5 2.1 3 6 0.33 25 Inline 5 SS 1.20 0.5 2.4 3 6 0.1 20 Inline 6 SS 0.95 0.5 1.8 3 6 0.1 30 Inline 7 SS 1.05 0.5At the highest 2.1 mass 3 flows, 6Panel 1 demonstrates 0.1 an almost continuous 25 unbroken Staggered film, with the entire region downstream of the panel being of a similar film effectiveness. Once aboveEach 5 g/s, geometry the entire was span tested of the at panel eight is different fed with mass coolant, flow increasing rates covering the coolant the typical fraction range ofraises mass the coolant film effectiveness fractions representative uniformly across of engine the entire designs. area. This The is coolant a sharp mass contrast flow to rates testedPanel were2, where 5, 7.5, a higher 10, 12.5, film 15, effectiveness 17.5, 20 and 25is achieved g/s. This i equatesmmediately to a downstream coolant to mainstream of the masspanel fraction but quickly ranging falls fromoff. Increasing 0.58% to 2.91%.the cool Turbineant fraction blade slowly cooling extends requirements the film further can range fromdownstream, 2% to 6% requiring but most moderna higher firstcoolant stage fraction HP turbine in order blades to nowobtain require high alevels cooling of fractionfilm ofeffectiveness approximately at the 4.5% trailing [13]. edge. SensorThe difference data and in thefilms camera between inputs the two were pa averagednels can in over part a periodbe explained of 5 s by for the every measurementdifferences in local in order mainstream to obtain flow. a time-averaged Panel 1, shown result. in Figure 2, is located in a region of high convex curvature and a significant portion of the downstream region is also convex. 5.Furthermore, Results these films experience a very high favorable pressure gradient near the 5.1.panel Varying region. Panel These Locations two effects, combined with the low blowing ratio of the individual holes, result in the films remaining very close to the surface of the blade, with minimal First, the film effectiveness map of Panels 1–4 across four different blowing rates are decay. Any disturbances created by the small film jets are small enough to be stabilized shown in Figures2–5 respectively. The charts show the entire width of the blade surface by the larger dominant behavior of the mainstream flow. The rate of film decay only from the start of the panel at x/d = 0 down to the trailing edge. The ratio Pr between the begins to increase near the trailing edge region where the curvature flattens out and the coolant and mainstream inlet total pressures is also shown. The plots are arranged so that flow begins to slow down, increasing the boundary layer thickness as well as the turbulent the coolant is always being fed from the right side of the image. mixing, resulting in a loss of measured film effectiveness. Evidence of this can be seen in For all panels at low blowing rates, film distributions are uneven with coolant only both Panels 1 and 2; the films appear to narrow near the trailing edge as the boundary beinglayers ejectedof the sides from of certain the rig grow sections andof push the the panels. films toward This is the mainly middle. due to the significant externalAs Panel static 2 pressure is positioned variation further along back, the it can streamwise be seen from dimension Figure 3 of that the it panels. does not This favorsbenefit flow from towards the early the features trailing of the edge suction of Panel surface. 1, 2 andOn top 4, and of the towards reversal the of leadingthe pressure edge of Panelgradient, 3, where the Mach a mild number adverse at Panel pressure 2 approaches gradient occurs.0.8, resulting The low in much internal more pressure significant results infilm significant to mainstream ingestion interactions across the within panels. the Furthermore, panel itself. variations in internal static pressure and coolant velocity within the blades lead to uneven spanwise distributions.

FigureFigure 2. 2.Film Film effectivenesseffectiveness of Panel 1 1 at at different different coolant coolant mass mass flow ﬂow rates rates (mass (mass fraction). fraction).

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Figure 3. Film effectiveness of Panel 2 at different coolant mass flow rates (mass fraction).

The two pressure surface panels share a similar trend and distribution with a few notable differences. Both significantly favor the left side, most likely due to the higher internal static pressure inside this half of the blade, opposite the coolant feed. At higher Int.Int. J. J. Turbomach. Turbomach. Propuls. Propuls. Power Power 20212021,, 66,, x 16 FOR PEER REVIEW 65 of of 13 12 mass fractions, the films start at very high levels but drastically fall off, particularly in Panel 3. This suggests the films follow a trend similar to the wall jet model, with a section of strong potential core in which the film remains mostly untouched by the mainstream, followed by a region of turbulent mixing, which typically dominates most conventional film behavior. Figure 4 of Panel 3 demonstrates high levels of lateral mixing as the film does not manifest any features reminiscent of the individual holes. In contrast, Figure 5 demonstrates that Panel 4 behaves more like the suction surface panels, with definitive streaks being visible, particularly at the higher mass fractions. This behavior is indicative of the high mainstream flow velocity and strong pressure gradient which dominates the flow. Beyond demonstrating a lack in lateral film spreading, the streaks are also indicative that the panels are not entirely successful in pushing the mainstream away from the surface of the blade as is typically expected in transpiration designs. The square arrangement of holes allows for streams of mainstream air to penetrate through the panels. This is best illustrated in Panel 4 at 15 and 20 g/s, where visible wakes of mainstream air can be seen compromising a large portion of the downstream film. FigureFigure 3. 3. FilmFilm effectiveness effectiveness of of Panel Panel 2 2 at at different different coolant coolant mass mass flow ﬂow rates rates (mass (mass fraction). fraction).

The two pressure surface panels share a similar trend and distribution with a few notable differences. Both significantly favor the left side, most likely due to the higher internal static pressure inside this half of the blade, opposite the coolant feed. At higher mass fractions, the films start at very high levels but drastically fall off, particularly in Panel 3. This suggests the films follow a trend similar to the wall jet model, with a section of strong potential core in which the film remains mostly untouched by the mainstream, followed by a region of turbulent mixing, which typically dominates most conventional film behavior. Figure 4 of Panel 3 demonstrates high levels of lateral mixing as the film does not manifest any features reminiscent of the individual holes. In contrast, Figure 5 demonstrates that Panel 4 behaves more like the suction surface panels, with definitive Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 7 of 13 streaks being visible, particularly at the higher mass fractions. This behavior is indicative Figure 4. Filmof the effectiveness high mainstream of Panel 3 flow at different velocity coolant and massstrong ﬂowflow pressure ratesrates (mass(mass gradient fraction).fraction). which dominates the flow. Beyond demonstrating a lack in lateral film spreading, the streaks are also indicative that the panels are not entirely successful in pushing the mainstream away from the surface of the blade as is typically expected in transpiration designs. The square arrangement of holes allows for streams of mainstream air to penetrate through the panels. This is best illustrated in Panel 4 at 15 and 20 g/s, where visible wakes of mainstream air can be seen compromising a large portion of the downstream film.

FigureFigure 5.5.Film Film effectivenesseffectiveness ofof PanelPanel 44 atat differentdifferent coolant coolant mass mass ﬂow flow rates rates (mass (mass fraction). fraction).

AsDespite the coolant these limitations, flow rate is increased,the overall the film distribution effectiveness is firstof all matched panels remains in the spanwise high for directioneven modest and, mass as the flow internal rates. blade Once pressure the bulk is fi furtherlm is established increased, over coolant theis entire observed span beingof the ejectedpanel, bya very every high row. average effectiveness is achieved by the spanwise uniformity of the film.Due This to differs the high from resolution typical film of the cooling PSP, thedesigns films that of the contain individual hot streaks holes canbetween be differ- film entiatedcooling holes, from thegreatly bulk increasing of the coolant. the film These to mainstream individual contact features area. mix out within a short

distanceThe of spatial the end data of thecan panels.be averaged On the out other laterally, hand, thepixel bulk by ofpixel, the panelsin order form to obtain a much a Figure 4. Film effectiveness of Panel 3 at different coolant mass flow rates (mass fraction). morespanwise robust average sheet film. of the films as shown by Figure 6. The averages are only performed overAt the the 120 highest z/d midspan mass flows, of the Panel blade 1 demonstrates containing anthe almost transpiration continuous panel. unbroken These film,plots withallow the for entire a greater region analysis downstream in the behavior of the panel of the being films. of In a similar these plots film the effectiveness. panel location Once is abovealso indicated 5 g/s, the by entire the shaded span of area. the panel is fed with coolant, increasing the coolant fraction raisesImmediately the film effectiveness downstream uniformly of the panels, across particularly the entire area. on the This suction is a sharp surface, contrast film lift- to Paneloff can 2, be where observed. a higher While film the effectiveness average blowing is achieved ratios of immediately either panel downstreamdoes not exceed of the0.3, panelthe rows but quicklyfurthest falls downstream off. Increasing have the acoolant higher fractionblowing slowly ratio extendsand the the films film furtherrequire approximately 15 d to recover. When compared to the other panels, Panel 1 undergoes a much lower rate of film decay, to the point at which the film effectiveness at the trailing edge is higher for Panel 1 than for Panel 2 for the same mass flow rates. Naturally, the blowing ratio of Panel 2 is lower than that of Panel 1 due to the higher mainstream velocity, yet the fact remains that the suction surface trailing edge is better served by Panel 1 than Panel 2, suggesting a fundamental difference in the structure and stability of the films. Panels 3 and 4 follow a similar pattern to Panel 2, with some notable differences. Panel 3 is seen to benefit from a much smaller streamwise pressure gradient resulting in no visible ingestion near the leading edge, even at the lowest blowing rates. Panel 4 is seen to perform better than Panel 3, possibly due to the high positive pressure gradient and larger radius of curvature, minimizing the relative effects of destabilizing secondary flows. The overall shape of the films is also not typically what is expected, with most analytical models predicting an exponential like decay. The results suggest more of a logarithmic decay, particularly in the case of higher blowing rates with the rate of film decay accelerating, instead of leveling off. One possible explanation is that the individual film rows reattach themselves one by one, rebuilding the film after a short period of film lift-off. On the other hand, the strong positive correlation between coolant mass flow rate and film effectiveness across all panels indicates that film lift-off is not yet the dominant mechanism at higher mass flows, as is often the case for conventional film holes.

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downstream, requiring a higher coolant fraction in order to obtain high levels of film effectiveness at the trailing edge. The difference in films between the two panels can in part be explained by the differences in local mainstream flow. Panel 1, shown in Figure2, is located in a region of high convex curvature and a significant portion of the downstream region is also convex. Furthermore, these films experience a very high favorable pressure gradient near the panel region. These two effects, combined with the low blowing ratio of the individual holes, result in the films remaining very close to the surface of the blade, with minimal decay. Any disturbances created by the small film jets are small enough to be stabilized by the larger dominant behavior of the mainstream flow. The rate of film decay only begins to increase near the trailing edge region where the curvature flattens out and the flow begins to slow down, increasing the boundary layer thickness as well as the turbulent mixing, resulting in a loss of measured film effectiveness. Evidence of this can be seen in both Panels 1 and 2; the films appear to narrow near the trailing edge as the boundary layers of the sides of the rig grow and push the films toward the middle. As Panel 2 is positioned further back, it can be seen from Figure3 that it does not benefit from the early features of the suction surface. On top of the reversal of the pressure gradient, the Mach number at Panel 2 approaches 0.8, resulting in much more significant film to mainstream interactions within the panel itself. The two pressure surface panels share a similar trend and distribution with a few notable differences. Both significantly favor the left side, most likely due to the higher internal static pressure inside this half of the blade, opposite the coolant feed. At higher mass fractions, the films start at very high levels but drastically fall off, particularly in Panel 3. This suggests the films follow a trend similar to the wall jet model, with a section of strong potential core in which the film remains mostly untouched by the mainstream, followed by a region of turbulent mixing, which typically dominates most conventional film behavior. Figure4 of Panel 3 demonstrates high levels of lateral mixing as the film does not manifest any features reminiscent of the individual holes. In contrast, Figure5 demonstrates that Panel 4 behaves more like the suction surface panels, with definitive streaks being visible, particularly at the higher mass fractions. This behavior is indicative of the high mainstream flow velocity and strong pressure gradient which dominates the flow. Beyond demonstrating a lack in lateral film spreading, the streaks are also indicative that the panels are not entirely successful in pushing the mainstream away from the surface of the blade as is typically expected in transpiration designs. The square arrangement of holes allows for streams of mainstream air to penetrate through the panels. This is best illustrated in Panel 4 at 15 and 20 g/s, where visible wakes of mainstream air can be seen compromising a large portion of the downstream film. Despite these limitations, the overall film effectiveness of all panels remains high for even modest mass flow rates. Once the bulk film is established over the entire span of the panel, a very high average effectiveness is achieved by the spanwise uniformity of the film. This differs from typical film cooling designs that contain hot streaks between film cooling holes, greatly increasing the film to mainstream contact area. The spatial data can be averaged out laterally, pixel by pixel, in order to obtain a spanwise average of the films as shown by Figure6. The averages are only performed over the 120 z/d midspan of the blade containing the transpiration panel. These plots allow for a greater analysis in the behavior of the films. In these plots the panel location is also indicated by the shaded area. Immediately downstream of the panels, particularly on the suction surface, film lift-off can be observed. While the average blowing ratios of either panel does not exceed 0.3, the rows furthest downstream have a higher blowing ratio and the films require approximately 15 d to recover. When compared to the other panels, Panel 1 undergoes a much lower rate of film decay, to the point at which the film effectiveness at the trailing edge is higher for Panel 1 Int. J. Turbomach. Propuls. Power 2021, 6, 16 7 of 12

than for Panel 2 for the same mass ﬂow rates. Naturally, the blowing ratio of Panel 2 is lower than that of Panel 1 due to the higher mainstream velocity, yet the fact remains that Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 8 of 13 the suction surface trailing edge is better served by Panel 1 than Panel 2, suggesting a fundamental difference in the structure and stability of the ﬁlms.

Figure 6. Spanwise average ﬁlmfilm effectivenesseffectiveness ofof PanelsPanels 1,1, 2,2, 33 andand 44 atat differentdifferent coolantcoolant massmass ﬂowflow rates.rates.

PanelsAnother 3 possible and 4 follow reason a for similar the behavior pattern tois contained Panel 2, with within some the notabletangential differences. injection Panelmodel 3 for is seen films to by benefit Seban from and a Back much [14]. smaller This streamwise comparison pressure is not unreasonable gradient resulting given in the no visiblesimilarity ingestion in performance near the leading in flat plate edge, tests even between at the lowest tangential blowing injection rates. and Panel transpiration 4 is seen to performfilms as highlighted better than Panelby Goldstein 3, possibly [15]. due According to the high to this positive model, pressure the films gradient first form and largera wall radiusjet region of curvature,in which the minimizing films remain the intact relative and effects only mix of destabilizing with the mainstream secondary flow flows. through diffusionThe overallmechanisms. shape of This the filmsregion is is also then not fo typicallyllowed by what a region is expected, of turbulent with most boundary analyti- callayer models mixing predicting where film an effectiveness exponential like is expected decay. The to resultsdrop off suggest dramatically. more of a logarithmic decay,Further particularly justification in the can case be of found higher when blowing considering rates with the the secondary rate of film flows decay within acceler- the ating,panel films. instead Conventional of leveling off. films One are possible typically explanation dominated isby that strong the individualcoupled vortex film rowspairs reattachwhich lift themselves off and then one dissipate by one, rebuildinginto the mainstream, the film after as well a short as allow period hot of filmmainstream lift-off. Onair theto be other pulled hand, underneath the strong the positive film. correlationThe quasi between2D behavior coolant of massthe panel flow ratefilms and delays film effectivenessmainstream gas across from all being panels pulled indicates in from that filmthe si lift-offdes, resulting is not yet in the a tangential dominant mechanismjet like film ateffectiveness higher mass distribution, flows, as is particularly often the case when for conventional good spanwise film distribu holes. tion is achieved. Another possible reason for the behavior is contained within the tangential injection model5.2. Varying for films Panel by Configuration Seban and Back [14]. This comparison is not unreasonable given the similarity in performance in flat plate tests between tangential injection and transpiration In the second part of the study, different permutations of panel designs were tested films as highlighted by Goldstein [15]. According to this model, the films first form a wall in the same location as Panel 1. By changing the hole pitch within the panel, the effective jet region in which the films remain intact and only mix with the mainstream flow through porosity was varied. The effectiveness data of these panels is shown in Figures 7 and 8. diffusion mechanisms. This region is then followed by a region of turbulent boundary layer mixing where film effectiveness is expected to drop off dramatically. Further justification can be found when considering the secondary flows within the panel films. Conventional films are typically dominated by strong coupled vortex pairs which lift off and then dissipate into the mainstream, as well as allow hot mainstream air to be pulled underneath the film. The quasi 2D behavior of the panel films delays mainstream

Int. J. Turbomach. Propuls. Power 2021, 6, x FOR PEER REVIEW 9 of 13

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gas from being pulled in from the sides, resulting in a tangential jet like ﬁlm effectiveness distribution, particularly when good spanwise distribution is achieved.

5.2. Varying Panel Conﬁguration

Int. J. Turbomach. Propuls. Power 2021, 6, x FORIn thePEER second REVIEW part of the study, different permutations of panel designs were tested9 of 13 in the same location as Panel 1. By changing the hole pitch within the panel, the effective porosity was varied. The effectiveness data of these panels is shown in Figures7 and8.

Figure 7. Film effectiveness of Panel 5 at different coolant mass flow rates (mass fraction).

Increasing the pitch, as is the case for Panel 5 reduces the number of holes in the panel. This leads to a more uniform film distribution at a coolant mass flow of 5 g/s. As coolant mass fraction is increased, the film effectiveness plateaus at a relatively low value. The film is also dominated by significant variations in spanwise effectiveness, which appears as very predominant streaks. With greater spacing in between holes, there is more space for mainstream gas to push its way between the coolant jets and mix with the coolant. This effect is magnified as more coolant is added, with the right side of the panel performing worse at 15 and 20 g/s than at 10 g/s, with defined lines of film effectiveness below 0.4 visible. Figure 7. Film effectiveness of Panel 5 at different coolantcoolant massmass ﬂowflow ratesrates (mass(mass fraction).fraction).

Figure 8. FilmFilm effectiveness effectiveness of Panel 6 at different coolant mass flow ﬂow rates (mass fraction).

ReducingIncreasing the the hole pitch, pitches as is thehas casethe opposite for Panel effect, 5 reduces with thePanel number 6 reaching of holes a higher in the maximumpanel. This film leads effectiveness to a more than uniform Panel film1. It is distribution worth noting at that a coolant the improvement mass flow ofof 5Panel g/s. 6As over coolant Panel mass 1 is much fraction less isthan increased, that of Panel the film 1 over effectiveness Panel 5, indicating plateaus diminishing at a relatively returns low asvalue. the Theporosity film isis alsoincreased dominated and bythe significant near wall variationsboundary in layer spanwise becomes effectiveness, saturated which with coolant.appears as very predominant streaks. With greater spacing in between holes, there is moreThe space final for panel mainstream tested was gas Panel to push 7, and its way is shown between in Figure the coolant 9. Here jets the and pitch mix was with kept the thecoolant. same This as Panel effect is1 magnifiedbut every asother more row coolant was isshifted added, by with half the a rightpitch. side Here of thethe panel film effectivenessperforming worse rate was at 15 measured and 20 g/s to thanbe highes at 10t g/s, across with all defined panels, linesdespite of filmhaving effectiveness the same below 0.4 visible. Figure 8. Film effectiveness of Panel 6 at different coolant mass flow rates (mass fraction). Reducing the hole pitches has the opposite effect, with Panel 6 reaching a higher maximum film effectiveness than Panel 1. It is worth noting that the improvement of Reducing the hole pitches has the opposite effect, with Panel 6 reaching a higher maximum film effectiveness than Panel 1. It is worth noting that the improvement of Panel 6 over Panel 1 is much less than that of Panel 1 over Panel 5, indicating diminishing returns as the porosity is increased and the near wall boundary layer becomes saturated with coolant. The final panel tested was Panel 7, and is shown in Figure 9. Here the pitch was kept the same as Panel 1 but every other row was shifted by half a pitch. Here the film effectiveness rate was measured to be highest across all panels, despite having the same

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Panel 6 over Panel 1 is much less than that of Panel 1 over Panel 5, indicating diminishing Int. J. Turbomach. Propuls. Power 2021, 6returns, x FOR PEER as the REVIEW porosity is increased and the near wall boundary layer becomes saturated10 of 13

with coolant. The final panel tested was Panel 7, and is shown in Figure9. Here the pitch was numberkept the of same holes as and Panel blowing 1 but everyratio as other Panel row 1. Here was shiftedthe effect by of half individual a pitch. Hereholes thecan film no effectiveness rate was measured to be highest across all panels, despite having the same longer be discriminated and the film appears much more uniform, as there is no path for number of holes and blowing ratio as Panel 1. Here the effect of individual holes can no the mainstream gas to push through the panel. Higher film effectiveness values are also longer be discriminated and the film appears much more uniform, as there is no path achieved in between the holes of the panel, with the downstream region of the panel for the mainstream gas to push through the panel. Higher film effectiveness values are essentially obscured from view and saturated at the higher mass fractions. The significant also achieved in between the holes of the panel, with the downstream region of the panel improvement of Panel 7 over the others can also be attributed to the fact that the films are essentially obscured from view and saturated at the higher mass fractions. The significant interacting more constructively. With the streamwise pitch essentially doubled, the film improvement of Panel 7 over the others can also be attributed to the fact that the films are jets do not push each other off the surface as is the case with the non-staggered interacting more constructively. With the streamwise pitch essentially doubled, the film jets arrangement. do not push each other off the surface as is the case with the non-staggered arrangement.

FigureFigure 9. 9. FilmFilm effectiveness effectiveness of of Panel Panel 7 7 at at different different coolant coolant mass mass flow ﬂow rates rates (mass (mass fraction). fraction).

FigureFigure 1010 comparescompares the the film film effectiveness effectiveness of of these panels at x/d = = 75 75 against against the the calculatedcalculated average average blowing blowing ratio ratio of of each each panel. panel. AA clear clear correlation correlation between between pitch pitch and and film film effectiveness effectiveness can be can observed. be observed. While WhilePanel 5Panel has a 5 higherhas a film higher effectiveness film effectiveness than Panel than 1 at Panel mean 1 atblowing mean blowingratios below ratios 0.1 below due to 0.1 a betterdue to spanwise a better spanwisedistribution, distribution, the maximum the maximum film effectiveness film effectiveness achieved achieved does not does exceed not 0.65.exceed 0.65. TheThe effectiveness effectiveness of of all all panels panels is is observed observed to to level level off off at at a a mean mean blowing blowing ratio ratio of of approximatelyapproximately 0.2. 0.2. This This is is significantly significantly lower lower to to most most conventional conventional film film geometries, geometries, which which tendtend to to reachreach maximummaximum effectivenesseffectiveness at at a blowinga blowing of aboutof about 0.8. Additionally,0.8. Additionally, this effec-this effectivenesstiveness does does not dropnot drop back back down down as blowing as blowing ratio ratio continues continues to increase to increase indicating indicating that, that,overall, overall, film film lift-off lift-off does does not yetnot dominate yet dominate the coolant the coolant flow. flow. While not necessarily lifting off, it still can be assumed that the films have reached a sat- uration point at higher mass flows and that additional coolant would not lead to an improvement in film effectiveness. Therefore the discriminating factor between Panels 1, 5, 6 and 7, is not the ability to add coolant to the boundary layer, but the ability to push the mainstream off of the blade surface. In conventional film theory, this would be equivalent to reducing the mass fraction of mainstream gas within the near wall boundary layer at the end of the panel.

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Figure 10. Film effectiveness of Panels 1, 5, 6 and 7 at x/d = 75 at different average blowing ratios. Figure 10. Film effectiveness of Panels 1, 5, 6 and 7 at x/d = 75 at different average blowing ratios. While not necessarily lifting off, it still can be assumed that the films have reached a The consequencesaturation of this is thatpoint insteadat higher of mass diluting flows and the entrainedthat additional hot coolant air in thewould boundary not lead to an layer with ever increasingimprovement mass flows in film of effectiveness. coolant, a highTherefore coolant the discriminating to mainstream factor ratio between can Panels be 1, achieved with much lower5, 6 and mass 7, is not flows. the ability to add coolant to the boundary layer, but the ability to push the mainstream off of the blade surface. In conventional film theory, this would be When comparing all of the different Panels at a mass flow for which the film is fully equivalent to reducing the mass fraction of mainstream gas within the near wall boundary developed, further similaritieslayer at theand end of differences the panel. can be established. As shown by Figure 11, all inline Panels with pitchThe to consequence diameter ratiosof this is of that 2.1 instead share approximatelyof diluting the entrained the same hot filmair in the effectiveness at x/d =boundary 40. At this layer stage with ever the increasing film effectiveness mass flows of is coolant, dominated a high coolant by the to Panels mainstream ability to add coolantratio to the can boundary be achieved layerwith much and lower fend mass off theflows. mainstream gas. Once past When comparing all of the different Panels at a mass flow for which the film is fully this point, behavior becomesdeveloped, dominated further similarities by the and particularities differences can of be the establis localhed. mainstream As shown by flow Figure 11, such as the rate of boundaryall inline layer Panels mixing with pitch and to mainstream diameter ratios turbulence, of 2.1 share with approximately the film coolingthe same film geometry having onlyeffectiveness a minor effect at x/d due = 40. to At the this very stagelow the fi blowinglm effectiveness ratios is used. dominated This by is bestthe Panels Int. J. Turbomach. Propuls. Powerexemplified 2021, 6, x FOR PEER by REVIEW the near ability parallel to add behavior coolant to of the Panels boundary 1 and layer 5–7, and showing fend off the that mainstream each12 of 13 is affectedgas. Once past this point, behavior becomes dominated by the particularities of the local mainstream flow by the mainstream flowsuch equally. as the rate of boundary layer mixing and mainstream turbulence, with the film cooling geometry having only a minor effect due to the very low blowing ratios used. This is best exemplified by the near parallel behavior of Panels 1 and 5–7, showing that each is affected by the mainstream flow equally.

FigureFigure 11. Spanwise11. Spanwise average average of all Panels Panels at at15 15g/s g/s(1.75%). (1.75%).

6. Conclusions Very high cooling effectiveness was achieved around the entire blade at very low mass coolant fractions. Films perform particularly well on the early suction surface, which benefits from the effects of curvature and acceleration, resulting in very constant film coverage downstream of the panel. The ability to cool the entire suction side of the blade almost uniformly with a modest coolant fraction is a significant achievement which could warrant diverting additional coolant and attention to this area. While performance on the pressure surface is more modest, particularly around Panel 3, large regions of high film effectiveness were still attained. Divergence from conventional film hole cooling models also implies that the behavior of a large array of small holes cannot be simply extrapolated from single hole studies. Comparisons between different pitches and hole arrangements confirmed that minimizing the spacing between holes can greatly improve the film effectiveness, and suggests that both interactions between individual films and the influence on the mainstream may have a significant impact on film performance. However, it has also been established that the nature of the mainstream flow around a turbine still dominates film cooling behavior once beyond the immediate region of the cooling geometry, particularly on the pressure surface. The relative simplicity of the designs used leads to a hopeful assumption that transpiration-inspired cooling features are not as remote a concept as previously imagined, though practicalities of implementing transpiration cooling will remain a challenge with issues such as uniform distribution and ingestion still to be solved. Nonetheless, a clear demonstration of its potential has been achieved.

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6. Conclusions Very high cooling effectiveness was achieved around the entire blade at very low mass coolant fractions. Films perform particularly well on the early suction surface, which benefits from the effects of curvature and acceleration, resulting in very constant film coverage downstream of the panel. The ability to cool the entire suction side of the blade almost uniformly with a modest coolant fraction is a significant achievement which could warrant diverting additional coolant and attention to this area. While performance on the pressure surface is more modest, particularly around Panel 3, large regions of high film effectiveness were still attained. Divergence from conventional film hole cooling models also implies that the behavior of a large array of small holes cannot be simply extrapolated from single hole studies. Comparisons between different pitches and hole arrangements confirmed that minimizing the spacing between holes can greatly improve the film effectiveness, and suggests that both interactions between individual films and the influence on the mainstream may have a significant impact on film performance. However, it has also been established that the nature of the mainstream flow around a turbine still dominates film cooling behavior once beyond the immediate region of the cooling geometry, particularly on the pressure surface. The relative simplicity of the designs used leads to a hopeful assumption that transpiration-inspired cooling features are not as remote a concept as previously imagined, though practicalities of implementing transpiration cooling will remain a challenge with issues such as uniform distribution and ingestion still to be solved. Nonetheless, a clear demonstration of its potential has been achieved.

Author Contributions: Conceptualization, A.W. and P.I.; methodology, H.W.; investigation, A.W. and H.W.; writing—original draft preparation, A.W..; writing—review and editing, P.I. and I.M.; supervision, P.I. and I.M. All authors have read and agreed to the published version of the manuscript. Funding: This work is supported by Rolls Royce plc. and the Transpiration Cooling Systems for Jet Engine Turbines and Hypersonic Flight Programme Grant (EP/P000878/1). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: Not applicable. Acknowledgments: The authors wish to thank the technicians at the Oxford Thermoﬂuids Institute for their contributions in running experiments, as well as Peter Walters for his contributions in improving the additive manufacturing process. Conﬂicts of Interest: Rolls-Royce PLC as the funding sponsor provided input to the general scope of interest in the study and the decision to publish the results. They had no direct role in the collection, analyses or interpretation.

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