Michael Benson
`U.S. Military Academy,
`West Point, NY 10966
`e mail: michael.benson@us.army.mil
`
`Sayuri D. Yapa
`e mail: yapasd@stanford.edu
`
`Chris Elkins
`e mail: celkins@stanford.edu
`
`John K. Eaton
`e mail: eatonj@stanford.edu
`
`Stanford University,
`Stanford, CA 94305
`
`Experimental-Based Redesigns
`for Trailing Edge Film Cooling
`of Gas Turbine Blades
`
`Magnetic resonance imaging experiments have provided the three dimensional mean
`concentration and three component mean velocity field for a typical trailing edge film
`cooling cutback geometry built into a conventional uncambered airfoil. This geometry is
`typical of modern aircraft engines and includes three dimensional slot jets separated by
`tapered lands. Previous analysis of these data identified the critical mean flow structures
`that contribute to rapid mixing and low effectiveness in the fully turbulent flow. Three
`new trailing edge geometries were designed to modify the large scale mean flow struc
`tures responsible for surface effectiveness degradation. One modification called the Dol
`phin Nose attempted to weaken strong vortex flows by reducing three dimensionality near
`the slot breakout. This design changed the flow structure but resulted in minimal
`improvement in the surface effectiveness. Two other designs called the Shield and
`Rounded Shield changed the land planform and added an overhanging land edge while
`maintaining the same breakout surface. These designs substantially modified the vortex
`structure and improved the surface effectiveness by as much as 30%. Improvements
`included superior coolant uniformity on the breakout surface which reduces potential
`thermal stresses. The utilization of the time averaged data from combined magnetic reso
`nance velocimetry (MRV) and concentration (MRC) experiments for designing improved
`trailing edge breakout film cooling is demonstrated. [DOI: 10.1115/1.4007601]
`
`Introduction
`
`Commercial turbofan engines typically use about 25% of the
`core air flow for cooling [1], and a large fraction of this protects
`the aft sections of the turbine blades and vanes. Blade trailing
`edges are too thin to cool internally, so film cooling is used. A
`common arrangement has slots cut into the airfoil pressure side.
`Cooling air discharging through these slots forms a set of wall jets
`which protect the final 10 15% of the blade chord. Rapid mixing
`of high temperature freestream gases with the coolant jets reduces
`the film cooling effectiveness and necessitates high flow rates of
`coolant air. Trailing edge film cooling improvements provide an
`opportunity for increasing the engine efficiencies. A reduction in
`the required coolant flow rate allows greater mass flow rates
`through the first stage turbine with no increase in compressor
`power, resulting in superior engine performance. Minimizing ther
`mal stresses requires relatively even cooling distributions along
`the blade surface, which can increase blade life.
`The performance of a film cooling system is measured by the
`adiabatic film cooling effectiveness, g, a nondimensional parame
`ter comparing surface temperatures for an idealized adiabatic
`boundary condition, Taw, with the coolant, Tc, and mainstream gas
`temperatures, Th.
`
`g
`
`Th
`Th
`
`Taw
`Tc
`
`(1)
`
`Values of this effectiveness of 100% indicate the surface and the
`coolant stream are the same temperature, whereas values of 0%
`indicate that
`the surface and hot mainstream are the same
`temperature.
`Advanced designs consider the balance of aerodynamic and
`thermal performance, which often are in competition [2 6]. In
`addition, practical manufacturing and material limitations must be
`
`Contributed by the International Gas Turbine Institute (IGTI) of ASME for publi-
`cation in the JOURNAL OF TURBOMACHINERY. Manuscript received July 16, 2012; final
`manuscript received August 7, 2012; published online June 5, 2013. Assoc. Editor:
`David Wisler.
`
`considered before final implementation. The extensive analysis
`and testing required, and the risk associated with completely new
`designs has limited the introduction of new approaches to trailing
`edge film cooling.
`Magnetic resonance imaging (MRI) based techniques have
`been developed in water flow experiments to provide time
`averaged full 3 D velocity and coolant concentration fields for
`complex trailing edge configurations [7 9]. The experiments are
`for incompressible flow at subscale Reynolds numbers, but they
`replicate the full geometry of realistic film cooled trailing edges.
`Previous work has shown that the geometry and blowing ratio are
`the major parameters controlling the film cooling effectiveness
`[7,8,10 18], while compressibility and Reynolds number (Re)
`have smaller effects [7,8,10,15,19]. The goal of the present study
`is to understand, design, and test new trailing edge configurations
`seeking improved average film cooling effectiveness and more
`uniform surface temperature distributions.
`Benson et al. [9] reviewed the extensive literature on trailing edge
`cooling. Much of the work focused on parameter adjustments, such
`as the effects of changes to the blowing ratio, defined in Eq. (2) as
`the ratio of coolant to freestream mass flux at the slot exit.
`quð Þc
`
`
`quð Þh
`
`BR
`
`(2)
`
`Other studies [11,12,14] modified the coolant feed conditions
`through internal blockages or varied the slot exit geometry. Com
`putational studies from Holloway et al. [20,21] and Martini et al.
`[11,22]
`showed time averaged models underestimating the
`coolant mainstream mixing and improved surface effectiveness
`calculations obtained with unsteady models. Joo and Durbin [23]
`demonstrated that
`these models require care in adjusting the
`unsteady coolant inlet conditions, which vary across turbine blade
`designs.
`The work most relevant to the present study was reported by
`Taslim et al. [10], who systematically studied the effect of cutback
`slot exit geometry on the surface effectiveness. Using letterbox
`style slot exits, they varied the slot injection angle, lip thickness,
`
`Journal of Turbomachinery
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`Copyright VC 2013 by ASME
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`JULY 2013, Vol. 135 / 041018-1
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`slot widths, and blowing ratio across a range from 0 to 1.3. Their
`work used a slot lip to slot height ratio (t/h) ranging from 0.5 to
`1.25, with thinner ratios yielding the highest surface effectiveness
`values. They identified this as the most
`important parameter
`impacting surface effectiveness of the ones studied.
`The specific objective of the present work is to leverage the
`detailed measurements reported by Benson et al. [9] for a baseline
`trailing edge configuration to redesign the breakout to improve
`surface effectiveness. The redesigns attempt to modify the geo
`metric sources of the primary mean flow structures responsible for
`local decreases in surface effectiveness. Surface concentration
`measurements are used to assess the performance of the redesigns.
`A common breakout surface was maintained among the designs to
`allow equitable comparisons. While optimization of film cooled
`turbine blades is of direct interest to manufacturers, the concept of
`leveraging experimental
`results
`to redesign and then re
`experiment becomes viable because of the detailed information
`available and the shortened time scale of the MRI based measure
`ment techniques. As such, it provides opportunities in a broad
`range of fields where turbulent mixing is an important characteris
`tic to either promote or limit.
`
`Overall Experiment Description
`
`The experimental setup, including the complete flow apparatus,
`is documented in Benson et al. [9], with Fig. 1 depicting only the
`1 m long test section without the upstream flow conditioning or
`channel exit geometry. A conventional uncambered 300 mm long
`NACA 0012 airfoil is used in the test section of the water channel
`and has a cutback film cooling geometry built into the interior and
`along the pressure side near the airfoil trailing edge. The final
`5.7% of the chord has been blunted, resulting in the net length of
`283 mm shown in Fig. 1, with a span of 76 mm. Because the flow
`around a real turbine blade trailing edge has a favorable pressure
`gradient and a thin boundary layer, the airfoil is mounted in a con
`tracting test section, which contracts from 152 mm to 62.3 mm at
`its narrowest.
`The cutback includes three rectangular shaped slots separated
`by lands that narrow in the spanwise direction as they approach
`the blunted trailing edge. The slots are fed by turbulent channel
`flow which splits around semicircular partitions on the upstream
`sides of the lands. The geometry is similar to that studied by Hol
`loway et al. [20,21]. A schematic is shown with top and plan
`views in Fig. 2 including dashed lines indicating internal features.
`A perspective view is depicted in Fig. 3 that includes the coordi
`nate system and describes the key features of the trailing edge
`geometry.
`The geometrical parameters of the baseline breakout are listed
`in Table 1. All of the present experiments were performed in
`water flow at Re below those typical of large propulsion gas tur
`bines. The airfoil chord length and the bulk averaged freestream
`velocity immediately above the slot breakout are used in the Re
`calculation. The blowing ratio for the liquids used in this study is
`essentially the velocity ratio, as the difference in densities is less
`than 1%. BR is the average velocity exiting a slot normalized by
`
`Fig. 2 Top and side views of the airfoil and its internal geometry.
`External flow is from left to right. Internal flow enters from top and
`exits through three slots near the trailing edge.
`
`Fig. 3 Key features of the trailing edge region
`
`Table 1 Key dimensions for the trailing edge region. All values
`normalized by the slot height h.
`
`Trailing Edge Component
`
`Slot Height (h
`5 mm)
`Slot Lip Thickness (t)
`Slot Lip Thickness (Dolphin Nose Only)
`Cutback length (Slot to TE)
`Straight Cutback Length (Shield Designs)
`Slot Width at Slot (w)
`Land Width at Slot
`Land Width at TE
`Slot Spacing
`
`Size/h
`
`1
`0.76
`0.14
`8.4
`5.5
`2.0
`2.8
`0.4
`4.8
`
`the bulk averaged freestream velocity on the pressure side above
`the slot exit.
`
`Methods
`
`The MRI apparatus and procedure are described in detail in
`Benson [8,9]. The experiments were conducted in the same GE
`1.5T whole body scanner model SE utilized previously, including
`use of the standard transmit and receive head coil for both velocity
`and concentration measurements.
`The time averaged velocity field was measured using phase
`contrast magnetic resonance velocimetry (MRV) as described in
`Elkins et al. [24]. Encoding velocities for the MRV scans were set
`at 1.25 m/s (x, streamwise), 0.9 m/s (y), and 0.65 m/s (z). The fluid
`
`041018-2 / Vol. 135, JULY 2013
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`Transactions of the ASME
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`Fig. 1 Channel test section, with dimensions in mm
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`flow. The data from each run were scaled as necessary to ensure
`regional magnitude averages were consistent and not influenced
`by temporal variations in the MRI hardware. Then the data from
`each of the four run types were averaged.
`Concentration was then calculated from the four run types using
`Eq. (3), where N refers to the number of runs for each subscripted
`run type.
`
`
`
`S BS
`R BS
`
`C ¼
`
`
`
`
` NS þ 1
`NS þ NIð
`
`
`
`
`
`
`
`
` NI
`
`BI
`I
`R BI
`
`Þ
`
`(3)
`
`was a dilute solution of 0.04 Mol/Liter of copper sulfate in de
`aerated water, which had a very small impact (< 1%) on fluid pa
`rameters such as density and viscosity. Each scan took six minutes
`to conduct, with flow off scans preceding and following sets of
`three flow on scans. The two flow off data sets were averaged and
`subtracted from the average of the three flow on scans to elimi
`nate eddy current and temporal drift effects. This entire process
`was repeated five times so the final presented velocity field is an
`average of 15 flow on scans for a total averaging time of 90 min.
`All measurements were isothermally conducted at T¼ 20 C,
`with Re¼ 110,000. The main flow rate (123 L/min) was con
`trolled with a diaphragm valve and metered by a Model 515
`Rotor X paddlewheel flowmeter connected to a GF Signet 8550 1
`4 20 mA ProcessPro Flow Transmitter with calibrated uncertainty
`of 1.6%. The coolant flow rate (4.4 L/min) was controlled with a
`needle valve and metered by a Blue/White Industries F 1000RB
`paddlewheel flow meter with a calibrated uncertainty of 2.0%.
`The total velocity uncertainty was estimated to be between 6.9
`and 8% of the bulk averaged velocity above the slot exit using
`techniques described in Elkins et al. [24]. The uncertainty esti
`mates include contributions from the variability of the main and
`coolant flow rates which is typically about 61%. As a check on
`the velocity measurements, the volumetric flow rates were calcu
`lated by integrating the velocity data across the mainstream and
`coolant flow fields at each streamwise plane. The results agreed
`with the meter readings well within the stated uncertainty bands.
`Magnetic resonance concentration measurements (MRC) were
`conducted separately from the MRV to measure the time
`averaged coolant concentration distribution on a uniform Carte
`sian array of 3D voxels. Using the heat/mass transfer analogy, the
`coolant concentration is analogous to the nondimensional temper
`ature for the case of adiabatic surfaces. During the concentration
`measurements, one fluid stream, either main or coolant, consisted
`of a dilute solution of copper sulfate pentahydrate in de aerated
`water, while the other contained only plain de aerated water.
`MRC scans generate a 3D distribution of signal intensity using a
`T1 weighted fast spoiled gradient sequence. Specific parameters
`of the scans are given in Table 2. Calibrations conducted previ
`ously showed that the signal intensity is linearly related to the
`local concentration of CuSO4 [8,9]. A maximum concentration of
`0.015 mol/L of CuSO4 was utilized. Measurements were obtained
`with 1 mm spanwise and streamwise resolution and 0.5 mm reso
`lution in the wall normal direction, yielding 100 measurement
`points for the coolant flow at the exit plane of each slot and
`1.44 106 data points in the flow field.
`The data were processed in each case precisely in the manner
`described in Ref. [9]. For each experiment, there were 21 scans
`conducted for the background (water in both mainstream and
`coolant feed), standard (copper sulfate in the coolant feed, water
`in the mainstream), and inverted (water in the coolant feed and
`copper sulfate in the mainstream) runs. Twenty four reference
`runs (copper sulfate in both streams) were conducted with half the
`runs conducted before the inverted scans and half after to account
`for any changes in the concentration of the reference reservoir
`during the inverted scans. The signal magnitude to noise ratio for
`the raw data had an average of 36:1 in the unmixed regions of the
`
`Table 2 Experimental parameters
`
`Parameter
`
`Bulk velocity at slot exit plane
`Re
`Blowing ratio*
`Fluid Temperature
`De aerated water density
`Copper sulfate (0.015 Mol/L solution) density
`
`Value
`
`0.39 m/s
`110,000
`1.30
`20 C
`998 kg/m3
`1007 kg/m3
`
`Note: Limited test results from BR 1.0 and BR 1.5 are also presented
`in the discussion section.
`
`The film cooling effectiveness was calculated by extrapolating
`the field measurements of the coolant concentration to the wall
`following the procedures laid out in Benson et al. [7,8], as in Eq.
`(4). A major advantage of using the concentration instead of tem
`perature measurements is that the zero mass flux boundary condi
`tion analogous to an adiabatic wall condition is exactly realized
`[18,20,25]. Thermal measurements require corrections to account
`for nonzero conduction and radiation heat transfer to the surface
`[3,8 12,16].
`
`gaw ¼ Ch Cw
`Ch Cc
`
`¼ Cw
`
`(4)
`
`The MRC uncertainty was estimated following the procedures
`outlined fully in Benson et al. [8,9]. Surface uncertainties are 6%
`in concentration whereas concentration measurements away from
`surfaces have an uncertainty of 5.1%. The slightly higher uncer
`tainty near surfaces is a result of the technique utilized to infer
`the surface values from the values immediately above the surface
`and discriminating from measurements partially or fully within
`the solid surface of the airfoil. The reported uncertainty is a root
`sum of squares combination of pointwise variation of the signal
`magnitudes by run type, the uncertainty of assessing the near wall
`gradient, and a small streamwise correction factor employed to
`ensure mass conservation of the coolant at all measurement
`planes.
`
`Redesigned Trailing Edge Breakout Geometries. The first
`redesign, termed the Dolphin Nose, focuses primarily on reducing
`the three dimensionality associated with separation bubbles that
`are present behind the slot lip for the baseline case, Fig. 4(a). Fig
`ure 4(b) depicts an isometric view of the Dolphin Nose geometry.
`As with each of the redesigns, the slot feed channels and the
`breakout floor area remain unchanged from the baseline case. In
`this case, the slot exit is also unchanged. The slot lip has been sub
`stantially thinned in hopes of reducing the strength of the vortices
`shed from the slot lip. These vortices have been identified as one
`of the primary sources for mixing [5,7 9,17,20 23,26]. In the
`design, the tapered slot lip feature extends spanwise across the
`pressure side of the airfoil resulting in thinner lands and reducing
`the corner between the lip and the land at the slot exit. While the
`lands are thinner at the slot exit than in the baseline case, they
`taper to the same height just upstream of the trailing edge where
`they end as in the baseline configuration.
`The second redesigned trailing edge focuses on protecting the
`breakout surface from longitudinal vortices that shed from the
`edges of the tapered lands. To do this, the land edges are straight
`ened to be streamwise for the first 66% of the breakout geometry,
`and the sides of the lands are undercut to preserve the breakout
`surface area. Figure 4(c) shows an isometric view for this redesign
`termed the Shield. This rendering highlights the 3D nature of
`the undercut surface. The upper land surface rapidly returns to the
`baseline configuration at its tip after the straight section, while the
`lower land surface follows the spanwise taper of the baseline case.
`To highlight the changes to the lands, a top view is also presented
`of the Shield in Fig. 4(d).
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`The final redesign, called the Rounded Shield (Fig. 4(e)),
`reduces the slot exit area by 10% through the filleting of the upper
`corners of the slot exit on both sides. The goal of the filleting was
`to limit surplus coolant flow observed near the lands in the Shield
`geometry while sustaining the behavior of the coolant near the
`slot centerline. All other aspects of this design are identical to the
`Shield. Since each of the redesigns was tested at the same blowing
`ratio, the 10% reduction in flow area corresponds to a 10% reduc
`tion in the coolant flow rate. The internal fillets originate just
`downstream of the teardrop shaped partitions within the slot feed
`channel, so that they smoothly fill in the corner.
`
`Results
`
`MRC and MRV measurements are reported here for three
`modified trailing edge designs and compared to the baseline case
`which was previously reported. All designs were tested at
`BR¼ 1.3, with some additional tests conducted at BR¼ 1.0 and
`reported only in terms of a performance metric. Table 2 presents
`the key experimental parameters used in both MRV and MRC
`experiments for the test cases.
`The features of the baseline case that are important in rapid
`mixing of coolant with the mainstream flow include the slot lip
`separation region, mean streamwise vortices that originate on the
`teardrop shaped lands within the slot feed channel, and mean
`streamwise vortices produced at the intersection of the slot lip and
`land.
`
`Slot Lip Separation. The slot lip separation region is identi
`fied as critically important because of its 3D impact on the flow,
`especially with regards to its role in strengthening spanwise pres
`sure gradients and transverse velocity components. Figure 5(b)
`shows isosurfaces representing the separated flow regions for the
`Dolphin Nose along with 3D streamlines originating near the air
`foil surface one slot height upstream of the slot exit. The separated
`flow regions are depicted where the flow reverses on average
`(negative streamwise velocity values). The reverse flow regions at
`the slot exit change substantially from the baseline case, shown in
`Fig. 5(a). Small regions of reverse flow exist everywhere behind
`the spanwise uniform curved feature including large regions on
`top of each land surface. This is different from the baseline case
`in which there was only separation behind the slot lips. Streamline
`curvature over the land surface is slight, and the separation bub
`bles close slowly. Because the curvature remains different
`between streamlines over the lands and slots, spanwise pressure
`gradients may not have been significantly diminished in this modi
`fication. The streamlines also suggest a second important feature
`that is new in this redesign. Several streamlines initially on the
`land surface move off the lands and appear to move onto the
`breakout surface, indicating that the reduction in the upstream
`height of the lands has an important impact on the spanwise
`motion and penetration of the mainstream flow. The separated
`region at the trailing edge appears similar to that of the baseline
`case.
`Isosurfaces outlining regions of reverse flow and velocity
`streamlines are shown for the Shield in Fig. 5(c). In this depiction,
`the separation bubbles both at the slot lip and at the trailing edge
`closely resemble those in the baseline case. However, the stream
`lines show an interesting feature that differs from the baseline
`data. The lands are straight for 2/3 of the distance downstream
`from the slot exits so streamlines originating near the slot exit stay
`approximately straight. The mainstream fluid does not appear to
`have significant interaction with the coolant fluid beneath this
`upper land surface.
`The slot exit modification in the Rounded Shield case changes
`the slot lip separation bubble relative to the Shield and baseline
`cases. Figure 5(d) depicts the reverse flow regions for this rede
`sign, and the separation bubble appears to have a more 3D nature.
`The downstream legs of the separation bubble on both sides of the
`slot are thickened, reflecting the increase in the slot lip thickness
`
`Fig. 4 Isometric views of the (a) Baseline, (b) Dolphin Nose, (c)
`Shield, and (e) Rounded Shield. A top view (d) of the Shield
`shows the regions of the lands that are overhung.
`
`041018-4 / Vol. 135, JULY 2013
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`
`vortex pair is now prevented from directly interacting with cool
`ant near the surface due to the sloped land sides in this design.
`This reduces the effect of the upper vortices on the surface effec
`tiveness. The lower vortices are similar to the baseline case. The
`goal of this design was to utilize the lower vortex pair for circulat
`ing high concentration coolant from each slot towards the sides of
`the land walls along the breakout surface while reducing the mix
`ing from the upper vortex pair.
`the
`for
`The normalized streamwise vorticity contour plot
`Rounded Shield in Fig. 6(d) depicts a set of vortex interactions
`similar to the Shield design. The upper and lower pairs of vortices
`at the slot exit still exist. The vortices against the land sides have
`higher peak magnitudes than in the Shield design and cover a
`larger region of the flow. Additionally, the upper vortex pair
`extends on top of the land slightly, although this is not sustained
`downstream. It is likely that the change in the upper vortex pair
`occurs as a result of the fillet within the slot feed creating a larger
`slot lip in the corner between the slot exit and land. Due to the na
`ture of the undercut land sides, its impact is relatively slight at the
`surface although there is some impact in the distribution of cool
`ant as will be seen below.
`
`Concentration Distribution. Figure 7(b) shows in plane ve
`locity vectors overlaid on contours of concentration at (x
`xs)/
`h¼ 5.5 for
`the Dolphin Nose design. At
`this position,
`the
`mounded coolant field and relatively thick shear layer in the cen
`ter are evident. The coolant field is essentially symmetric about
`the centerline with nearly zero in plane velocities at that location.
`Stronger velocity vectors near the land sides highlight the stream
`wise vorticity present in this region as well as their proximate
`location compared to the breakout surface and land sides. Because
`the lands in this redesign are shorter than in the baseline configu
`ration depicted in Fig. 7(a), these vortices actively mix fluid
`located closer to the breakout surface than in the original design.
`Figure 7(c) shows concentration contours with overlaid in
`plane velocity vectors for the Shield at the same streamwise loca
`tion. The coolant is more uniformly distributed across the span of
`the slot than in either the baseline or dolphin nose cases. In con
`trast to the other cases, the secondary velocities above the lands
`are very small, indicating that the flow is passing straight over the
`lands. This is clearly an effect of the straight land planform.
`Streamwise vortices are evident near the edge of the lands, but
`they appear weaker than in the other cases. The overhang feature
`prevents the vortices from sweeping freestream fluid into the cor
`ner at the breakout surface. The coolant concentration near the
`lands is very close to 100% indicating that no freestream fluid
`penetrates beneath the overhang. This high coolant concentration
`will help to prevent high temperature oxidation of this seemingly
`vulnerable feature of the shield design.
`Figure 7(d) shows in plane velocity vectors overlaid on con
`tours of concentration for the Rounded Shield. The coolant distri
`bution is somewhat wavy across the span indicating the effects of
`stronger secondary flows than in the original Shield design. The
`vortex motion near the upper land corners is clearly stronger in
`this case as well. As hypothesized before, these vortices likely are
`strengthened by the thickened slot lip in the near land regions at
`the slot exit. Above the lands, the secondary velocities remain
`very small. This is an effect of the straight land planform and is
`nearly independent of the slot configuration.
`
`Surface Effectiveness. The surface effectiveness for the center
`slot of the baseline case is shown in Fig. 8(a) for comparison with
`the redesigns. These data are quantitative in nature and represent
`the concentration extrapolated to the wall surface. The corre
`sponding Dolphin Nose surface effectiveness is depicted in Fig.
`8(b). In this image, the core region where the effectiveness is at
`least 90% extends essentially to the trailing edge within a long
`narrow tongue near the slot centerline. However, as a result of this
`narrow high effectiveness region bordered by lower effectiveness
`
`Fig. 5 Isometric views of the (a) Baseline, (b) Dolphin Nose, (c)
`Shield, and (d) Rounded Shield geometries with reverse flow
`regions (purple) and streamlines (black)
`
`across the slot exit plane. Streamlines along the sides of the slot
`lip separation bubble show increased curvature over those in the
`Shield, but the remaining streamlines are similar. As with each of
`the cases, the trailing edge separation region appears similar to the
`baseline case.
`
`Streamwise Vorticity. A streamwise vorticity contour plot at
`xs)/h¼ 3.0 is shown for the Dolphin Nose in Fig. 6(b). The
`(x
`vorticity is normalized by the bulk velocity at the slot exit and the
`slot height. It is calculated in a discretized sense from the three
`components of velocity from the MRV measurements. The black
`lines show approximate solid boundaries associated with the
`structural lands and overlap vorticity contours showing the dis
`crete nature of the data and its impact on the calculated vorticity.
`The key feature of this plot is the single vortex pair that emerges
`from each slot. This is in contrast to the baseline case, Fig. 6(a),
`where two vortex pairs emerge adjacent to the land sides. In the
`baseline case, the upper pair of vortices at the intersection of the
`slot lip and the land is responsible for mixing mainstream and
`coolant fluid and generating a wavy coolant distribution in the
`shear layer. In the Dolphin Nose geometry, these are much less
`evident with the implication that the mixing of the fluid streams
`by mean streamwise vorticity structures is no longer a primary
`cause of reduced surface effectiveness. The reduction of these
`vortices was a goal in this redesign.
`Figure 6(c) shows the same normalized contour plot of stream
`wise vorticity for the Shield. There are two counter rotating vorti
`ces at the slot exit as in the baseline case. However, the upper
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`JULY 2013, Vol. 135 / 041018-5
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`Fig. 6 Normalized streamwise vorticity contours in a vertical and spanwise cross plane for the
`(a) Baseline, (b) Dolphin Nose, (c) Shield, and (d) Rounded Shield at (x – xs)/h 5 3.0
`
`adjacent to the land sides, strong concentration gradients exist in
`the spanwise direction, especially at the trailing edge. Moreover,
`distinct from the baseline case, there is evidence that coolant is
`present on the surface of the lands beginning one slot height
`downstream of the slot exit. This occurs in the region where the
`land separation bubbles close and concentrations as high as 40%
`exist on top of the lands. The height of the lands is clearly an im
`portant geometrical factor to consider since the reduction of that
`height has contributed to the degradation of the coolant field near
`the land edges.
`Figure 8(c) shows the surface effectiveness for the center slot
`of the Shield redesign. High effectiveness is maintained adjacent
`to the lands all the way to the trailing edge, a major improvement
`over the other designs. This improvement is accomplished without
`a loss to the length of the core region in the center of the slot. The
`concentration is above 80% over the entire breakout surface
`except for a very small region near the trailing edge. Gradients in
`the surface effectiveness are significantly smaller than in the other
`cases. No coolant is present on top of the lands similar to the base
`line configuration.
`Note that in the Shield case, there is a surplus of coolant near
`the lands since the region of 95 100% coolant extends all the way
`to the trailing edge. In addition, this region of maximum surface
`effectiveness adjacent to the lands extends well beyond the center
`line core region and imposes spanwise concentration gradients.
`
`This suggests that the amount of coolant injected adjacent to the
`lands could be reduced thereby motivating the Rounded Shield
`redesign.
`The surface effectiveness along the middle slot for the Rounded
`Shield design is shown in Fig. 8(d). The impact of the coolant
`flow reduction in the present case appears to have decreased the
`near land effectiveness. This case has the smallest spanwise effec
`tiveness gradients of any of the designs. The effectiveness is still
`significantly larger than the baseline case, even though the coolant
`flow rate is reduced. There is only a small region near the trailing
`edge where the effectiveness falls below 80%.
`
`Discussion
`
`Figure 9 shows the spanwise averaged surface effectiveness for
`the baseline case and each of the three redesigns. For this plot, the
`averaging is taken across the breakout surface and does not
`include the lands. The Shield design has the best performance in
`terms of the average surface effectiveness of any of the trailing
`edge configurations, with local values of the averaged effective
`ness in excess of 10% higher than the baseline performance. The
`baseline and the Dolphin Nose are the most similar, with a slight
`performance increase for the Dolphin Nose near the trailing edge.
`The Rounded Shield design, which uses 10% less coolant flow
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`Transactions of the ASME
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`Fig. 7 Concent