4.1. Adiabatic Effectiveness Measurements
shows the adiabatic effectiveness contour plots for all the tested configurations and blowing ratios. The different camera framings do not allow to cover the whole vane surface; nevertheless, the investigated areas are wide enough to characterize the behaviour of the film-cooling holes on the different surfaces. At a first sight it is possible to note, for the suction side results, a strong effect of the secondary flows, as the coolant traces are driven away from the endwalls towards the midspan; this well-known effect [10
] determines the presence of uncovered areas close to the endwalls, in the region between rows SS2 and SS3 and close to the trailing edge. In the latter location, this phenomenon also creates two areas (h/H = 65%–80% and 20%–35%) where the effectiveness is slightly higher than at midspan, due to the superposition of the converging coolant traces. On the pressure side the effects of secondary flows, that generally moves the traces towards endwalls, can be hardly noted on the maps.
An increase in blowing ratio determines important improvements, with longer coolant traces, in the film coverage on PS and FP results; for row PS1, at BR = 1, the local pressure ratio across the holes is very low and hence the performances near the exit of the hole is affected by the ingestion of mainstream. To better explain the behaviour, Figure 6
shows the 1D profiles of spanwise averaged effectiveness. The averaging areas, reported in Figure 5
with dotted red boxes, were selected far from the effects of secondary flows. The profiles confirm that an increase in the adiabatic effectiveness occurs for both PS and FP, as long as the
is enhanced: on the pressure side, in particular, the increase in the jets momentum is beneficial, as it works against the effect of the vane pressure gradient that tends to move the jets away from the surface. Regarding the suction side, the increase in
is detrimental for the film protection especially close to the holes break-out position where the surface curvature enhance the lift off phenomena. On the other hand, an increase of cooling flow helps the film coverage in the downstream areas where the higher amount of coolant injected reattach to the airfoil surface. For these phenomena, the SS averaged trends present a steep decay of adiabatic effectiveness close to the hole break-out, while the results get flatter downstream. This particular behaviour seems more emphasized by the blowing ratio and it strongly affects the shape of the averaged profiles downstream the row SS3.
In Figure 7
a direct comparison between FP, SS and PS results is reported varying the mean blowing ratio. The comparison has to be limited to the first two rows of cooling holes, as they are the only ones where the streamwise pitch is the same for all the configurations. It is worth to notice that, for the cascade rig, tests are setup imposing an averaged value of
: differences between the averaged values and real local
can occur especially at the lower coolant conditions. However, the intent of the Authors in this part of the data analysis is to emphasize the role of curvature and pressure gradient mainly on the shape of film effectiveness instead of comparing local values. The measured values are quite similar for SS and FP configurations. In particular, very similar peak values, are achieved while the decay rate slightly differs: for
and 2 the SS results show a steeper decay close to the hole exit, while they tend to recover downstream and their values are slightly higher respect to the flat plate. Increasing
, the FP configuration tends to provide the better results in the peak locations.
On the other hand, the PS results show significantly lower adiabatic effectiveness levels. Looking to the the full set of trends from to , the main difference between SS and PS can be found on the different shape of the film effectiveness downstream the hole exit: the PS trends have a strong drop off of film covering and just upstream the second row of holes the effectiveness is far below the set of data collected on the SS. At the difference is appreciable, even if the PS result is biased by the very low local of the first row. The differences between PS and the other two configurations tends to reduce as the BR is increased: at , the peak adiabatic effectiveness of the first cooling row is very similar between PS and SS.
Clearly, this comparison is affected by the local row-by-row values of that can not be precisely the same for FP and vane results since the mainstream conditions will induce a variation among the cooling rows of the vane configurations. In the next paragraph an attempt to scale this effect and achieve a more effective comparison will be provided, thanks to the adoption of a correlative approach.
4.2. Comparison with Correlations
Once the experimental results have been described and analysed, it is possible to provide a comparison with the values predicted by two correlations, developed for flat plate configurations (no effects of curvature and pressure gradient). The considered correlations were developed and described in the works of Colban et al. [2
] and Chen et al. [3
]; as described in the introduction, the second one provides little modification with respect to the first one, aimed at including the effect of the density ratio. The superposition effect between different rows is considered using Sellers’ superposition approach [18
]. Concerning the geometrical parameters, the cited correlations were developed within the following ranges of area ratio, hole spacing and coverage ratio:
The film cooling arrangements tested in this work actually present values outside of this ranges, or at the lower limit for , for FP, PS and for most of the SS configuration. Only the last row of the SS geometry presents values that fall within the correlations limits. For this reason it could be expected that some discrepancies could exist between the predicted values and the experimental findings. Despite that, the used correlations constitute, in the authors’ knowledge, the most accurate and comprehensive tools to describe the performance of shaped film-cooling holes, as well as the most adopted ones. The intent of the authors by comparing the experimental database with the outputs of these correlations is to asses their reliability in predicting the film performances of holes with an aggressive shaping () and to underline a possible under/over estimations when the pressure gradients and surface curvature are considered.
The local values of
, for the different rows, to be used in the correlations, were calculated knowing the mainstream local conditions, by CFD results, and an average holes discharge coefficient value, through the results of a preliminary flow check. The local, row-by-row, values of
is provided in Table 2
As it can be noted from the table, some consistent discrepancies between the local values and the nominal occur, especially concerning the PS. Row PS1 shows the maximum variation of with very low values at the average , due to the very low pressure ratio across the holes, and very high values at , due to the fairly limited mainstream velocity. Consequently the downstream rows show opposite behaviours in order to reach the nominal average value, while the suction side holes are much closer to the nominal one. Since these differences, not present in the flat plate configuration, can not be considered through the simple analysis of the experimental results, the comparison with the correlations assumes mandatory importance as it allows to account for the actual local values of . Summarizing, the comparison with these correlations is useful to complement the presented experimental data for the following reasons:
Compare correlation predictions to a baseline flat plate configuration, in the case of film-cooling holes with aggressive shaping, so to assess their prediction capability.
Remove the effect of the variations of fluid-dynamic and geometric parameters, from row to row and between different configurations, that could bias the FP-vane comparisons reported in Figure 7
, since they are accounted for in the adopted correlations.
Assess how the actual performance on the vane can deviate from what would be calculated through common correlations.
The comparisons are reported in Figure 8
for all the configurations and test points. It is worth to underline that the correlations locate the peak values at the hole break-out position; its intensity only depends on the coverage ratio of the holes, assuming
over the whole spanwise length of the hole t
. These hypothesis clearly represent an approximation of the coolant behaviour since in the experiment the adiabatic effectiveness starts to increase upstream of the break-out and the peak value can be lower if the hole is overly diffused and jet separation occurs inside it. Analysing the results of Figure 8
, the hypothesis of the correlative approach must be considered especially looking to the film values near the rows of holes.
Starting from the FP configuration, the correlations tend to predict slightly higher peak values and a reduced decay rate, with respect to the measurements. In the authors’ opinion this is due to the effect of the area ratio since the correlations have been developed using experimental data collected on configurations whose AR ranged from 2.5 to 4.7; according to this data, an increase in the adiabatic effectiveness with the AR is predicted by the correlations. On the other hand, Gritsch et al. [19
], showed that the effect of AR was marginal beyond 3.5. For these reasons it is reasonable to assume that the extrapolation of the correlations predictions at a higher AR (more than 7 for the tested configurations) could provide an overestimation of the adiabatic effectiveness. The hole spacing could also play a role, if the correlations underestimated the decrease in effectiveness, increasing
beyond their limits (
), but, in the authors’ knowledge, there is no proof of this in the open literature. A slightly better prediction of the decay rate is provided by the correlation that accounts for the actual
value, but the impact of this parameter is very limited. Despite these difference, the matching between correlations and experiments is acceptable, pointing out at the reliability of the correlative model to quantify the effectiveness generated by the tested hole pattern and flow conditions. Therefore, an effective comparison between the vane experimental results and a flat plate configuration, described through the correlation-predicted values, accounting for the actual and local fluid dynamic conditions of the vane configurations, can be carried out in the following.
The correlations always over predict the PS results in a significant way. Even if the increase in is beneficial to the pressure side behaviour, as showed previously, it doesn’t actually result in an improvement in the comparison and the plots remain quite far from each other. The correlative approach seems not able to predict effectiveness peaks and decay shape. The strong differences in the peak values of effectiveness is ascribable to the behaviour of the holes on the vane surface which present values below in hole traces due to a strong interaction with the mainstream.
Concerning the SS, experiments and correlations are in a good agreement especially at lower conditions. In addition, the different trend of the adiabatic effectiveness decay downstream of the holes is confirmed: the decay is steeper for the experiments, close to the break-out position, while the trend is flatter moving downstream. This behaviour well highlights the tendency of the coolant to lift off from a convex surface, while, downstream, the vane pressure gradient counteracts this effect pushing the cooling flow towards the surface. As a result, flat plate correlations reveals inaccuracy near the SS1 and SS2 holes, while downstream the agreement with experiments is acceptable (see for example the region upstream the SS3). The biggest differences between experiments and correlations are located downstream the last row of holes and they are enhanced increasing the value. Since SS3 presents some differences in the coverage ratio and in the area ratio, with respect to the other rows, it could be thought that this is the reason of the mismatch. However, SS3 geometrical parameters values fall well within the range of the experimental data used for developing the correlations: therefore, it should not be expected to be the cause of the detected differences. For these reasons the behaviour of SS3 should be expected to be caused by the suction side configuration itself: it is worth to notice, in fact, that in the final part of the suction side the pressure gradient (i.e., pressure different between pressure and suction side), which generally help the film protection increasing the , is significantly lower than in the upstream region. Therefore, it is reasonable to conclude that the reduction of this beneficial effect is responsible for the drop of performance with respect to the predicted values of correlations.