Slot cooling

Compared to discrete film cooling holes, it has been long recognised that slots can achieve higher effectiveness on blade sections (e.g., (Cunha and Chyu, 2006)). In practice their use on aerofoil sections has been limited because of the stress limitations, but they have been used to cool aerofoil TE sections, which are highly vulnerable to damage. Yang and Hu (2012) experimentally examined the aerothermal performance of a rectangular slot geometry, focusing on the detailed measurement of the flow field via particle image velocimetry and correlating the identified features to the measured Film Cooling Effectiveness (FCE). Further work on TE slot cooling includes that of Niharika et al. (2016) and Wong et al. (2016).

Slot cooling has also been examined for cooling the interior cavity of squealer tips. Zhang et al. (2022) examined slots with radially-outward flow, distributed across the tip cavities in a cascade. While Zhang et al. (2021) introduced streamwise slots into their cavity by integrating them into ribs inside the cavity design. However, neither of these examples targeted the pressure surface rim.

Squealer shelves

Another approach that has been seen in the patent literature, and some engines, is to place a small shelf into the exterior side of the PS rim and provide coolant using discrete, radially-aligned holes (Cherry et al., 2002; Leeke et al., 2003; Correia et al., 2008). In general, it is understood that a portion of the coolant tends to be trapped in the separation bubble generated as the OTL flow separates from the shelf edge, thus shielding the rim from hot flow. Further examples include the shelf at the TE of PS rim given in Crites et al. (2013). Another approach is shown in Lee et al. (1998), where a thin trench is cut into the tip of the squealer rim and fed with discrete cooling holes. The current study suggests that the inclined slots developed in this paper achieve significantly higher cooling effectiveness than these existing shelf designs.

New concept: inclined slots with steps

The new cooling concept is shown in Figure 1b, and consists of a step on the Pressure Side (PS) rim of the blade tip with an inclined protrusion containing a cooling slot. With respect to previous designs, the key features to note are:

Design parameters

Figure 2b shows an inclined slot applied to a squealer tip design. The cavity of this tip is open towards the trailing edge, but this feature is inconsequential for the slot performance. The slot exit is placed on an inclined step surface cut into the rim of the pressure surface, at around mid-chord in this example. A shelf cut into the pressure surface extends downstream of the slot and blends smoothly back into the blade. The following design parameters control the size and position of key features.

Figure 2.

Schematic of the dedicated pressure side rim cooling slot depicting the parametrisation of its main features: a recessed PS shelf and an inclined cooling slot.

The slot and inclined step surface can be geometrically characterised as shown in Figure 2a. The distance from the bottom of the shelf (h) and the offset from the external edge (dwall) were set to be 0.5% and 0.4% of axial chord (Cax) respectively to allow clearance for manufacturing. The width (w) of the recessed step was set to 50% of the total rim width for all studied geometries. The length (l) and diameter of the slot (dn) together control the slot aspect ratio and area, which is studied in detail in Section 3.2. For fixed mass flow, reducing slot area increases the Blowing Ratio (BR), thus increasing the streamwise momentum and spread of the coolant. Meanwhile, the higher flow gradients cause more mixing and effectiveness reduces more rapidly. Similar trade-offs are observed for fixed geometry with varying coolant flow rate.

The shelf length and height can be parametrized by three variables (Figure 2b). Longer shelf lengths (L) require greater modification of the rim geometry, but can improve manufacturability by improving drill access for the slot. The depth (d) sets the position of the slot in the spanwise direction. Together with the slot parameters, d sets the spanwise position of the slot and thus controls the coolant trajectory. The distance (dTE) controls the streamwise position of the shelf and slot.

The coolant ejection direction of the slot (Figure 2c) is defined by two angles: the vertical angle between the inclined surface and the shelf (α) and the pitch angle into the blade (β). Of the two, α has the largest impact on performance, since it defines the angle at which the coolant flow approaches the rim (see Section 3.3). Optimal coverage occurs at low values of α and β, such that the coolant is injected along the streamwise direction of the PS rim. These angles will also be limited by manufacturing constraints.

Nominal slot behaviour

Figure 3 shows a CFD prediction of the flow from a single slot at a tip gap size of 1.15% g/S - where the tip gap (g) is normalised by the blade span (S) - and a non-dimensionalised mass flow rate (m˙R) of 45% (i.e., 45% of the baseline conventional design). In general, the coolant ejected from the inclined slot has a much higher streamwise momentum than the local mainstream flow, which tends to pass almost straight over the tip at this location. As a result, the coolant tends to propagate along the tip, cooling a larger area.

Figure 3.

Film cooling effectiveness contour of the single cooling slot geometry at nominal conditions with superimposed streamlines showing the two modes of coolant propagation.

It is seen that most of the coolant follows the ejection direction of the slot for some distance, before being drawn over the top of the PS rim (pink streamlines in the figure). This behaviour provides relatively high η values for a section of the rim roughly equal to the shelf length in this case. After the high effectiveness region, the strong OTL flow causes the coolant to dissipate, which results in relatively low film effectiveness downstream of the shelf. In addition, Figure 3 also demonstrates that a portion of the coolant flow seeps into the separation region created by the shelf, where it propagates along the pressure surface to the blade trailing edge (blue streamlines).

Paper aims and approach

The key aims of this paper are to develop the inclined slot concept, to understand the flow behaviour and to quantify its performance compared to conventional cooling designs.

To this end, Computational Fluid Dynamics (CFD) simulations are used to rapidly explore the design space and understand the sensitivities. The most promising designs were then tested experimentally on a transonic cascade representative of HP turbines, which demonstrates the significant improvement in cooling effectiveness.

The paper is organised as follows: Section 2 describes the CFD procedure, including the detailing of a mesh sensitivity study and the film cooling effectiveness calculation methodology. Section 3 details the CFD studies of the design space, whilst the validation experiments are presented in Section 4. The data are complemented in Section 5 by simulating additional engine-representative conditions.

Meshing and CFD

To model the cascade, a single periodic passage is simulated, with the inlet plane located two axial chords upstream of the blade Leading Edge (LE) and the outlet one axial chord downstream of the TE. A distribution of total pressure matching the cascade is specified at the inlet, together with constant total temperature and flow angle. The slot inlet feed is setup as a constant mass inflow, with fixed inlet angles and temperature. A constant static pressure is specified at the outlet. The hub, casing and the entirety of the blade are no-slip walls.

An unstructured mesh was generated using BoxerMesh, combining an octree freestream mesh with body-fitted viscous layers (Figure 4). Surface y⁺ values in the order of 0.5 were obtained for the entirety of the tip region. The mesh resolution at the tip is particularly high, with a refinement focus in the region downstream of the slot, which is the principal area of interest for the study. Total mesh size depends on the geometry, but is typically between 20 and 22 million nodes, in accordance to the mesh independence study presented below (Section 2.3).

Figure 4.

Details of the numerical mesh for an example inclined slot geometry.

Reynolds-Averaged-Navier-Stokes (RANS) calculations are performed using the Rolls-Royce in-house Hydra solver (Moinier, 1999). Spatial discretisation is performed with a 2nd order upwind edge-based finite volume method and time stepping employs a 5th order Runge-Kutta explicit scheme with Jacobi preconditioning. The turbulence model used in this study was k−ω with Shear-Stress Transport scheme (Menter, 1994).

Film cooling effectiveness calculation and associated performance metrics

A two-temperature approach was used to calculate the surface FCE of the CFD simulations, by comparing the surface temperature data of two simulations with coolant temperatures set 10 degrees apart:

where Tg and Tc are the total temperatures of the mainstream (285 K) and of the coolant (275 K), respectively. The blade tip surface temperatures of the “reference” case (Tref) represent the nominal condition with the coolant inlet set to the same temperature as the mainstream (285 K), whilst the temperatures in the cooled “test” simulation (Ttest) portray the impact of the coolant stream, with the coolant set to 275 K.

While the pointwise η over the surface of the tips is an useful comparison metric on its own, it is also useful to establish the following integrated parameters:

Figure 5.

Averaging regions for the cooling evaluation parameters. Numbered positions are the probing points implemented in the mesh independence study.

Mesh sensitivity

Mesh independence was evaluated on a single case. A total of five meshes with identical mesh refinement settings with increasing grid density were examined, ranging from 7.4 to 39 million nodes. Grid sensitivity is assessed first by considering area-averaged FCE over the two regions denoted in Figure 5, and second by considering local FCE at four points downstream of the slot exit. The data in Figure 6 evidences that suitable convergence occurs at mesh sizes of 20 million nodes, where the variation in global FCE is only 0.25% compared to the case with the highest mesh density. Expectedly, larger variations are observed in the localised FCE data present in high-dissipation regions, which is the case for points 2, 3 and 4. Nevertheless, the η values at these points converge convincingly with the increase of mesh density. Accordingly, the meshes for all the CFD cases in this publication were generated with the same refinement settings as the 20 million node grid.

Figure 6.

Percentage deviation of the mesh independence criteria from the values obtained at the highest density grid, plotted against number of nodes.

Overall performance of the studied geometries

The overall performance of various slot designs are compared to the conventional cooling design from Figure 1a. Figure 7 charts the average film effectiveness in the region-of-interest: ηav¯ (see Section 2.2), against the non-dimensionalised mass flow rate for cases at 1.15% g/S tip clearance. The diamond marker is the baseline reference value, the circles show single slot configurations, and the dashed lines link cases that were examined at multiple coolant mass flow rates. The square symbols indicate the dual slot design, discussed in detail in Section 3.4. The conventional baseline tip is on the bottom-right, having the lowest ηav¯ value (0.11) and the highest coolant expenditure. On the left, the range of single slot variants are distributed between ηav¯ values of 0.18 and 0.34. The dual slot geometry matches the highest performing single slot cases at m˙R=45% and then proceeds to significantly improve upon that as the coolant mass flow increases, with the m˙R=91% case having the highest ηav¯ of the studied cases, at a value of 0.45.

Figure 7.

Average film cooling effectiveness (ηav¯) plotted against total coolant mass flow. Single slot geometries are shown as circles, dual slot design as squares and the baseline tip as a diamond.

The following two subsections will examine the impact of key slot design parameters on the cooling performance, arranged from highest to lowest relative importance: slot flow area (3.2) and slot angles (3.3). Dual slot designs are then discussed in Section 3.4. Table 1 shows the parametrisation of the test geometries for each study.

Sensitivity to slot flow area

The first case study is that of the slot coolant ejection area. The slot flow area is defined by the slot length (l) and nominal diameter (d_n). As shown in the first row of Table 1, dn was kept constant at 1.6% Cax, while l was varied between 5.5 and 11.1% Cax to give a ±33% variation in area from the nominal slot design. The three cases were simulated at a tip gap size of 1.15% g/S.

Figure 8 charts the average effectiveness values on the top and side surfaces against the coolant ejection area. Black markers refer to ηtop¯ and red markers to ηside¯, while the diamond markers are reference values for the baseline tip. The relationship between coolant coverage and slot BR is evidenced in the slot data where it is seen that both averages peak at nominal slot flow area (A_i = 1).

Figure 8.

Area-averaged ηtop and ηside for the cases with varying slot flow area (Ai).

Slot blowing ratio is defined as:

Where the numerator refers to the velocity and density of the coolant, whilst the denominator refers to the mainstream gas. Thus - for fixed mass flow rates - decreasing the slot area increases jet velocity, causing the slot BR to increase, whilst the reverse occurs when the area is increased. The effects of decreasing slot area on the cooling distribution can be seen in the 2/3Ai case (leftmost insert plot). The smaller area increases the blowing ratio of the slot, causing the coolant to be projected further along the PS rim, at the detriment of effectiveness in the near-slot region. This change leads to an increase of ηtop in the latter 10% Cax of the rim (label A in the figure), but significantly lowers the values in the 60 to 85% Cax region (label B). In addition, the higher velocity jet undergoes greater dissipation, lowering average η values. A similar effect occurs on the side of the rim, where this case achieves slightly more coverage after the 80% Cax point, while having lower upstream values.

Inversely, the larger slot flow area case (rightmost insert plot) causes a decrease in slot BR, shifting the coolant coverage and associated peak η values upstream. This factor leads to a large improvement in near-slot ηtop, but penalises ηside on the latter 20% Cax of the rim. A similar effect is observed when BR is changed by varying mass flow rate for a given design (clear circle markers in Figure 8), which highlights the dependency of the coolant distribution on slot blowing ratio. It is also seen that the nominal flow area slot case is less affected by the decrease in coolant mass flow rate than the larger area case, which underwent a reduction of ∼30% in both performance metrics. This difference is largely due to the slot BR in each of the cases, which at nominal slot area results in jets that have a higher resilience to the change in coolant mass flow.

Overall, compared to the baseline tip (diamond markers in the figure), it is shown that the single slot geometries greatly outperform the reference conventional design in both ηtop¯ and ηside¯ for most of the examined region, with the conventional tip only achieving superior ηtop coverage at the last 10% Cax of the rim. Average values for the nominal flow area case show a 44% improvement over the reference for ηtop¯ and of 250% for ηside¯, with a coolant expenditure of less than half that of the reference case.

In summary, it is seen that the cooling performance of the dedicated slot geometry is highly dependent on slot blowing ratio, with the data suggesting that blowing ratio increases are less penalising to the overall performance than blowing ratio decreases. For this dedicated slot configuration, at the identified optimal conditions, there is an optimal area of coverage consisting of roughly 20% Cax downstream of the slot. This area can be increased by increasing slot blowing ratio, at the cost of having more diffuse coolant. Alternatively, one can also increase the number of slot features along the rim, which maximises both coverage and performance. This hypothesis is explored in Section 3.4.

Sensitivity to slot angles α and β

The orientation of the cooling slot in relation to the shelf plays an important role on jet direction and coolant propagation. This section details the study of the impact of the vertical angle α and the pitchwise angle β (Figure 2c) on the cooling performance. In total, five variations to the baseline geometry were examined, three with incremental α angles: 4°, 30° and 45°; and two with incremental β angles: 0° and 16°, as shown in the middle two rows of Table 1. The lower α and upper β bounds of these distributions were established by the geometrical limitations of the underlying tip geometry, thus exploring the full range of allowable values. The nominal slot flow area case is also included as a sixth case, with the angles α = 18° and β = 8°. All cases were simulated at a tip gap size of 1.15% g/S and a coolant mass flow of m˙R=45%.

It is immediately apparent from the datapoints in Figure 9a that lower α angles improve: (1) the η magnitude on the top surface of the rim and (2) the overall coverage on the side surface. This increase in performance is expected, as lower α angles improve the alignment of the cooling jet with the shelf, which allows the jet to more effectively fill the shelf and enhances the shielding of the coolant against the dissipative action of the OTL flow. Additionally, the larger amount of coolant inside the shelf is greatly beneficial to ηside, as it not only improves the coverage on the side rim surface inside the shelf, but also increases downstream propagation along the side of the blade (Figure 3). In overall terms, this behaviour results in an essentially linear decrease of ηside¯ with the angle α, as is shown by the red circular markers in Figure 9.

Figure 9.

Area-averaged ηtop and ηside for the cases with varying α and β slot angles. Dashed lines are the reference values for the conventionally cooled baseline tip.

The impact of α on the top surface is more subtle. Black markers in the figure show that the most significant change occurs between the 30° and 45° cases, where the extreme slot inclinations cause the coolant to be mostly convected directly into the tip gap rather than propagating along the rim, considerably reducing coverage. Contrastingly, the two other α cases are mostly identical, except for the near-slot region, with the difference between the α=4∘ and the α=18∘ cases being just 2.3%, which implies that reducing α below 20° has diminishing benefits on the coverage of the top of the rim.

Sensitivity to β is shown in Figure 9b. The pitchwise angle has an overall smaller impact on cooling performance compared to α, partly due to the smaller feasible range of values (limited by blade thickness). Expectedly, the β=0∘ case achieves the highest performance values, as this is the condition in which the coolant stream is parallel to the shelf surface and, thus, can more easily propagate along the rim surfaces. As the β angle increases, the coolant flow is gradually redirected away from the blade and into the ascending OTL flow, decreasing the amount of coolant available inside the shelf. On the side surface, this change results in a consistent, albeit small, reduction of ηside¯, with the β=16∘ having an overall value 11% lower than the β=0∘ case. In contrast, the only major difference at the top rim surface is the near-slot region in the β=0∘ case, resulting in a 7% increase over the nominal conditions (β=8∘), which performs almost identically to the β=16∘ case. Designs with higher β values would be expected to have worse cooling performance, but these are impractical unless thicker blade profiles were to be adopted.

In summary, it is apparent from these two studies that the dedicated PS slot geometry functions optimally at low slot α and β angles, so that the cooling jet is directed approximately parallel to the PS rim.

Dual slots

The single slot designs achieved promising results in relation to conventional cooling schemes and were shown to be capable of cooling a region of up to 20% Cax downstream of the slot. As depicted in Figures 8 and 9, this effective range resulted in undesirably low coolant coverage on the last 10% Cax section of the PS rim. Increasing blowing ratio can increase coverage far downstream of the slot, but this results in greater near-field mixing, leading to a substantial reduction in overall cooling performance.

A dual slot configuration can be adopted to achieve greater coverage with high FCE. As shown in Figure 7, the design consists of two smaller shelves - with lengths of 20% Cax - distributed along the TE of the PS rim. Location-wise, the dTE of the fwr. shelf is 62% Cax, while for the aft. shelf it is 24% Cax. All other parameters of the two features are the same as those of the single slot design with nominal area (last row in Table 1). This dual slot geometry was simulated at four coolant mass flows, split equally between the two cooling orifices: from m˙R=45% to m˙R=91% total coolant feed.

The η distributions are shown in the insert plots of Figure 10, a stark contrast exists between the dual slot and the single slot results (shown in Figures 8 and 9). Particularly, there is a more complete cooling of the top of the rim, where the coverage provided by the fwr. slot is succeeded by that of the aft. slot, resulting in a substantially more consistent coverage of the target region. It should be noted that a low η patch is present between the shelves in the cases with lower m˙R, which is completely eliminated in the higher m˙R cases, as demonstrated in the right-hand insert plot in Figure 10.

Figure 10.

Area-averaged ηtop and ηside for the double slot cases with varying coolant mass flow rate and tip gap size. Note that the y-axis limits differ from previous η¯ plots.

In regards to the general trends, data shows that increasing m˙R is beneficial for the size and concentration of the coolant distribution on the downstream tip surfaces, causing a consistent increase in ηtop¯ and ηside¯ up to m˙R=76%. However, little performance gains are present between the m˙R=76% and m˙R=91% cases, with an increase in performance metrics of only 2.5%, at the cost of 20% added coolant. These factors evidence a performance plateau of the dedicated PS slots, with the limiting coolant mass flow rate at the tested conditions being roughly m˙R=45% per slot.

In comparison to the reference values of the baseline tip (diamond markers in the figure), the double slot m˙R=91% case further develops on the benefits of the single slot configurations, achieving improvements of 185% and 455% over the ηtop¯ and ηside¯ of the baseline, respectively, whilst using 9% less coolant. Moreover, since the performance of the m˙R=76% case is similar to that of the m˙R=91% case, these large improvements are achievable whilst saving roughly 25% of the coolant budget.

The impact of tip clearance was also examined in this study, with the clear circle markers representing the cases with smaller tip clearance (0.65% g/S). The data for the small tip gap cases show a substantial increase of ηtop¯ and ηside¯, likely due to the smaller OTL mass flow causing less dissipation of the cooling jets and increasing overall coolant residency time. Thus, it is seen that the tip clearance reduction has a positive impact on the cooling performance of the dedicated PS slot over both rim surfaces.

In summary, the dual dedicated PS slot geometry demonstrates a substantial increase in cooling effectiveness over the conventional cooling schemes. The following section presents an experimental validation of this concept.

High speed linear cascade

The Oxford HSLC is a 5-blade cascade with variable tip gap, which operates as a blowdown facility with around 90 s of run time (Vieira et al., 2021). The experiments are run at transonic exit Mach number (0.99) and a Reynolds number based on true chord and exit conditions of 1.24 × 10⁶. Further details can be found in Zhang et al. (2011) and O’Dowd et al. (2013).

Film cooling is delivered to the blade tips using dedicated cooling feeds, while cooling effectiveness distributions are measured using dual-component Pressure Sensitive Paint (PSP). This optical measurement method employs a mass transfer analogy to obtain adiabatic film cooling effectiveness, with the calculation evaluating the phosphorescent excitation of the PSP coat applied to the test pieces, the emissivity of which is dependent on the local partial pressure of Oxygen. This property is exploited to calculate local partial pressures using a filtered color-corrected camera (Han and Rallabandi, 2010). For each measurement, ambient temperature Air and Nitrogen are sequentially used as coolant to generate a comparative evaluation, in which Nitrogen functions as an effective tracer gas for the distribution of coolant over the surface of the blade. Dual-component PSP includes a second, temperature-dependent paint that allows corrections for temperature variation, leading to greater accuracy in the calculated effectiveness. Linear perturbation analysis demonstrates that the experimental uncertainties depend on the signal level, giving local uncertainties of approximately ±0.045 for η < 0.2 and ±0.015 for 0.2 < η < 1.0, at a 95% confidence level.

Though not the focus of this paper, aerodynamic measurements are also performed 0.5 Cax downstream of the cascade trailing edge using a 4-hole probe with 1.2 mm head diameter. Traverses consist of a grid of 26 pitchwise locations by 10 spanwise locations. Total pitchwise length is one blade pitch, while spanwise length is 25% of blade span.

Experimental results

The film cooling effectiveness of the dual slot design was measured on the HSLC via a test tip manufactured with stereolithography additive manufacturing using ABS plastic, with the rims edges and cooling orifices being machined to match geometrical specifications. Test conditions for this geometry were the smaller tip gap setting (0.65% g/S) and the four coolant mass flow rates from the CFD study, which range from m˙R=45% to m˙R=91%, with the coolant being equally distributed between the two slots. Results are shown in Figure 11. In addition, some optimisation of the coolant balance between the two slots was attempted, with the most successful case being a m˙R=76% configuration with a 3:2 split, resulting on 60% of the coolant being routed to the fwr. slot and the remaining 40% to the aft. slot (clear circle marker).

Figure 11.

Plot of ηtop¯ experimental averages against coolant mass flow rate for the double slot and baseline tip geometries at small tip gap.

The η insert plots presented in the figure demonstrate that the excellent coolant coverage of the top rim surface generated by the dual slot design is successfully replicated in an experimental setting, corroborating the performance predicted in the CFD study. Impressively, the coolant distribution over the target TE portion of the rim is already exemplary in the m˙R=45% case (left insert plot) and improves further as additional coolant is added, with near perfect coverage of the rim being achieved in the m˙R=91% case (right insert plot).

In comparison to the experimental ηtop¯ value for the baseline tip at small tip gap, the dual slot design is shown to comfortably surpass the performance of the conventional cooling scheme throughout the trailing edge region of the rim, representing a coolant savings of 9% in the m˙R=91% case, while improving ηtop¯ by 46%. Optimising the split of coolant flow between the two slots maintained performance while saving approximately a quarter of the coolant mass flow rate. Furthermore, the experimental data do not include the improvements on the side of the rim, where the CFD predicts that the double slot configuration should greatly outperform the conventional cooling scheme. Thus, it is expected that the overall cooling advantage is greater than the value quoted above. The aerodynamic loss of the dual slot, as measured by the 4-hole probe, showed no significant differences in performance to that of the baseline tip.

In comparison to the CFD data from Section 3.4, the dual slot cases exhibited a ηtop¯ progression that is very similar to that predicted by the simulations. For reference, the red square markers in Figure 11 denote the CFD cases at the same tip clearance as the experimental data (0.65% g/S). As can be seen, CFD overpredicted the experimental effectiveness for the two higher m˙R cases by approximately 20%, which shows a significant magnitude mismatch, but still represents a relatively close agreement for RANS simulations of film cooling effectiveness performance.

Relative casing motion

The previously described simulations and experiments were realised in a purely stationary frame. To address the impact of rotor rotation on the cooling performance of the slot features, the baseline version of the single slot geometry from Section 1.5 was simulated with engine-representative casing motion. All other aspects of the setup are identical to those described in Section 2.1. The η distributions with and without casing motion are shown in Figure 12, and show only very minor differences. Both ηtop¯ and ηside¯ are within 1% for the two cases. This resilience to the scraping flow is consistent with similar calculations performed by Virdi et al. (2015), Ma et al. (2017) and Saul et al. (2019), as well as the model of Dambach et al. (1999). The OTL flow at the rear of the rims is dominated by pressure differentials and not casing motion, thus the cascade setup is representative of the engine.

Figure 12.

Film cooling effectiveness contours for the single slot geometry with flow nominal area and 1.15% g/S tip clearance. Case on the left has stationary casing, while the case on the right is setup with engine-representative casing motion.

Coolant density

One limitation of the experimental setup is that the coolant-to-mainstream density ratio is approximately unity (ρ_ratio = 1). For the dual-slot geometry, CFD predictions in Figure 13 show the sensitivity to density ratio: Figure 13a shows the effectiveness for unity density ratio. For higher coolant density and matching mass flow rate, Figure 13b shows that the near-slot effectivness remains very high but the downstream effectiveness reduces. This effect is caused by a reduction in the blowing ratio, as per the results in Figure 8. Without changing the slot geometry, the original performance can be restored by increasing the mass flow rate by approximately 30% (Figure 13c), so that the cooling jet Mach numbers match the unity-density case in 13.a. In practice, one can achieve similar performance by reducing the slot width dn to preserve blowing ratio while maintaining the mass flow rate.

Figure 13.

Film cooling effectiveness contours for the double slot geometry. On the left, nominal case discussed in Sections 3.4 and 4. On the middle, case with the same coolant mass flow rate but with an engine-representative density ratio. On the right, case with engine-representative density ratio and matching jet Mach number to that of the nominal condition.

Abbreviations

Symbols

Subscripts