Spanwise Averaged Data

Figures 112 to 117 show plots of spanwise averaged film effectiveness acquired through both experiment and simulation for each of the six geometries at the same conditions described in the previous section. Solid lines represent experimental data while dashed lines indicate data obtained through CFD simulations.

As suggested by the 2D surface contour data in Figure 105, the simulation does not match the experimental results for the Cylindrical hole case. Instead, as shown in Figure 112, the spanwise averaged film effectiveness is under-predicted by as much as 0.4. The only condition that could be considered to approximate the experimental data is at the 𝑇𝑇𝑇𝑇 = 20% and 𝑀𝑀𝑀𝑀 = 3.32 condition but even this shows poor agreement after the 5th _{row of cooling holes. As these tests} represent single skin type geometries, the pressure drop over the plate and hence blowing ratio is into the detached jet region for a cylindrical hole with flow generally remaining attached up to 𝐵𝐵𝑀𝑀 = 0.7 before becoming fully detached at 𝐵𝐵𝑀𝑀 = 1 as reported by Martin (57). While increasing freestream turbulence intensity increases the blowing ratios at which transition and detachment occur, the conditions considered in this study (the minimum blowing ratio considered is 1.75) are firmly in the detached jet regime. Therefore it is expected that the realisable 𝑘𝑘 − 𝜀𝜀 turbulence model used in this study is unable to capture the flow physics leading to the coolant pattern seen in the experimental data, however, the reasons behind this shortcoming in modelling detached jets is unexplained (66).

By fanning the exit region of the hole the exit velocity is reduced, resulting in a coolant flow that remains attached to the surface even at the highest blowing ratios applied here. The computational code is much better at modelling attached flows and hence the simulated spanwise averaged data for the remaining geometries provides a more favourable comparison to the experimental data. This is immediately apparent for the Spey fan case displayed in Figure 113. Here the data are generally similar with spanwise averaged adiabatic film effectiveness slightly over predicted at the higher momentum ratio conditions and slightly under-predicted at the lower momentum ratio condition. However, while the experimental data show little sensitivity to freestream turbulence level at the higher momentum ratios, the computational data indicate a mean difference of around 0.04. Conversely, the simulation indicates little sensitivity to freestream turbulence intensity at the lowest momentum ratio condition while the

spanwise averaged experimental data, and indeed the simulated 2D surface contours, both show a notable difference.

Figure 114 shows the spanwise averaged adiabatic film effectiveness plots for the Modified fan geometry. Here the simulations show an increased sensitivity to the freestream turbulence levels when compared with the experimental data. This is due to the increased turbulent mixing at higher turbulence intensity increasing the spread of the coolant. This brings the spanwise mixing of the coolant film more in line with that seen through the PSP experiment. However it is it should be noted again that the asymmetric nature of the physical plate caused by the DLD build direction, results in geometry which departs from that used for the computational domain. A rigorous and detailed comparison of the experiments and predictions performed for this geometry is therefore difficult.

With the exception of the 𝑇𝑇𝑇𝑇 = 20% and 𝑀𝑀𝑀𝑀 = 3.32 case, Figure 115 shows that while initially under-predicting the film performance by a large margin (up to 67%), the Slotted simulation agrees more closely with the experimental data in the downstream direction as more rows of coolant are introduced. At the low turbulence, high momentum ratio condition the 𝑘𝑘 − 𝜀𝜀 turbulence model is unable to properly simulate the jet in crossflow interaction at the high momentum ratio resulting from the small area ratio of the fan. In this case the jet appears to be mostly detached similar to the cylindrical hole geometry.

Simulated data for the two helical designs is presented in Figures 116 and 117 for the circular and rectilinear cross sections respectively. Again the different flow conditions are largely similar with the exception of the high turbulence intensity, low momentum ratio condition. Both geometries show under-predicted film effectiveness performance compared to the experimental data at this condition of around 0.07-0.1. The film performance is over-predicted at the higher momentum ratio and lower turbulence intensity conditions. This over-prediction is large, with differences up to 0.14 seen in some areas due to the decreased lateral mixing caused in part by the isotropic turbulence model.

This inability to predict the absolute performance of the various geometries is expected when using a simple 2-equation RANS based turbulence model, partially because they treat turbulence as an isotropic property. One of the principal objectives of this study however is to determine if numerical modelling can be used to rank candidate cooling designs in order to

quickly down select geometries for further, more comprehensive investigation through either more complex simulations or experimental testing. In this case, the ability to capture the relative performance of many candidate designs becomes an important and desirable goal for the aerothermal engineer. This particular attribute is shown in Figure 118 which displays the relative ranking predicted for each of the geometries described here. This plot indicates that the best performance is given by the two helical geometries with the Circular cross section performing very slightly better than the Rectilinear case with a difference of around 0.02. The Spey fan geometry then falls 0.11 below with the Modified fan around 0.1 below that. The Slotted design lies around the same level as the Spey and Modified fanned designs due to the increased spacing between subsequent cooling rows and the Cylindrical design is then placed around 0.45 below the rest. While the differences between the performance levels are smaller in the experimental data, as can be seen in Figure 86, the ranking of the six geometries is the same. On this basis the computational method is useful as a tool to provide a first approximation of potential new effusion cooling designs.

Figure 112 - Cylindrical hole spanwise averaged overall effectiveness comparison between experiment and CFD

Figure 114 – Modified fan spanwise averaged overall effectiveness comparison between experiment and CFD

Figure 116 – Circular helix spanwise averaged overall effectiveness comparison between experiment and CFD