The key experimental parameter that has been shown to be a significant factor in ascertaining that flow aerodynamics are adequately captured in the cooling short holes, is the pressure loss, ∆P (Equation (1)). It provides that if ∆P is successfully predicted, then the hole inlet flow separation and reattachment are also correctly predicted, hence the vena contracta effects [3] [13] . Therefore, work here concentrate on resolving and predicting the hole flow characteristics, in order to compare measured data with CFD predictions. The correctness of the ∆P (Equation (1)), is also the perfection of the flow velocities, turbulence kinetic energy (TKE), k (m²/s²) and the heat transfer coefficient (HTC), h (W/m²∙K) [9] [13] [16] [17] [18] [19] [20] as Equations (1) - (5) shows, which this CFD CHT work is expected to reveal. Similar analysis (CFD CHT), can also be applied to other cooling techniques with short holes and 90˚ entrance region.

Work here, predominantly concentrate on the hole in the cooling wall with small thickness, in order to understand the effects of the geometrical design parameters alongside mass flux, G (kg/s∙m²). The equivalent of the cooling wall thickness, is the short hole where cooling air as ambient or sea temperatures of 25˚C or 15˚C [5] [7] [21] , respectively with a range of inlet velocities are used. This results into the hole Reynolds number, hence the CFD simulation is enabled for the predictions of the flow fields that characterize cooling efficiently [19] [22] [23] [24] [25] . Work here, ignores the impact of the airflow on the impingement target plate and does not consider the flow resolutions in the impingement gap and effects of the reversed flow jets, but the visual outlook will be shown using Equation (5), for a better understanding of its impacts. Worth noting is that the CHT is the influence of combined fluid and solid interactions, whereby conduction inside a solid wall and convection of fluid along the wall surface coexists, as shown in Equation (3). This relationship is based on the wall boundary layer concept where at the surface, energy transfer is only by conduction as fluid motion is at zero velocity with thermal conductivity, k = kf. Hence, Equation 3 is from the combined concepts of heat transfer laws: Fourier’s Equation and Newton’s law of cooling [6] [26] [27] , where fluid thermal effects and temperature differences characterized the HTC.

V j = G ρ A = 4 G π ρ ( X D ) 2 = C d ( 2 R T Δ P P ) 0.5 (1)

h = q ″ T s − T ∞ (2)

h = − k f ∂ T / ∂ y | y = 0 T w − T ∞ (3)

N u = h D k f (4)

T * = T − T ∞ T w − T ∞ (5)

Protecting the life of the GT hot walls, significantly satisfy the requirements for high power output and low fuel consumption, which are better achieved using cooling techniques [1] [2] . The GT cycle thermal efficiency, which is controlled by the turbine entry temperature (>2800 K for aero engines [28] in the near future), is also a significant factor that must be adequately managed. This is in order to keep the walls of the GT combustor and turbine blades within a safe operating temperature and would not be above the melting point of the metal walls. To effectively cool the walls, the geometrical design and heat transfer analysis must be correctly carried out, hence Equations (2) and (4) are applied in the CFD code in order to conduct the predictions. With metallurgical limitations of the metal materials, cooling the walls of the GT component, is a reliable method of protecting the GT engine from the hot gas core flow or stream, as Figure 2(a) show.

Reliably, GT hot metal walls cooling helps in controlling [15] [29] [30] [31] the effects of increased turbine inlet temperature alongside the associated pollutant emissions [32] [33] that also affects the air mass flow rate, as in Figure 3. Optimizing the GT cooling design in order to overcome material deterioration and minimized emissions, the solution is the application of CFD CHT tool. The dimensional wall convective cooling heat transfer coefficient (HTC), h (W/m²∙K) of Equation (2), is defined in the CFD code to ascertain cooling effectiveness, which is normalized as dimensionless Nusselt number, Nu and is based on the geometry and thermal effects, as in Equation 4. Both Equations (2) and (4) are used in the present CFD research work, to validate the CFD predictions. Also the temperature differences that indicates influence of heat transfer are normalized in Equation (5), which is in order to show the reversed heating of air jets will be revealed here, as this is rarely shown experimentally.

Grid sensitivity test using ICEM meshing combined with ANSYS Fluent tools was previously carried out by El-jummah et al. [34] , which work here also adopts. This work implored the same grid refinement techniques in the hole with grid size (~60 cells/plane) varying based on X/D or G values using hexahedral structured grid [9] [27] [35] [36] [37] . Table 1 show the parameters that were used to transformed the computational diagram of Figure 4 into the grid modelled geometry of Figure 5, where the half short hole with smooth surface was also shown. Experimentally [3] , the hole wall typical of Nimonic-75 material [38] [39] , cannot be smooth and is based on roughness effects that is due to certain inaccuracies caused by the porosity of material or drilling equipment. Figure 4 show that application of symmetry was imposed at the centre line of hole and plane between rows of 10 × 10 holes, which is a replica of the experimental rig shown in Figure 2. Table 2 shows that the percentage of grid size in the holes with varied X/D, indicates that higher X/D gives larger percentage of grids in the holes. Also worth noting is that decreasing G decreases the number of cells in the hole, hence for every X/D and with changes in G, grid size is also altered accordingly.

Z/D is important but is not part of this work and is meant to show that the exit air is also flown out.

The Table excludes other parts of the geometry, as work here only deals with short holes.

ANSYS Fluent CFD code is the numerical software used in this work and the calculations (using flow parameters in Table 3) for all the geometries modelled, were carried out using standard wall function approach and standard k - ε turbulence model. The range of y⁺ values increases [6] [9] with increased X/D and G of 1.93 kg/s∙m² (Table 2), which was based on the uniformity of the cells down through the holes, it also indicates resolution of air flow fields in the holes. The values of the y⁺ (operates within near wall law 30 < y⁺ < 300) [40] [41] [42] in all cases have been shown by El-jummah et al. [9] [20] to captured high or low Reynolds number flow approach in the short holes, hence L/D effects [15] . The initial and boundary conditions (BC) imposed includes: fixed inlet coolant and hot-side temperatures, T_∞ of 288˚C and 353˚C, respectively, density, ρ of 1.225 kg/m³, velocity inlet (G/ρ)/outflow, walls (hole, sides, coupled thermal and temperature) symmetry. Turbulence intensity of ~5% calculated from the plenum

Target wall temperature applied in this work is 353 K.

inlet Reynolds number and hydraulic diameter. The criteria that were sets for convergence includes: 10⁻⁵ for continuity, 10⁻⁸ for energy and 10⁻⁷ for k, ε, ω and momentum (x, y and z velocities), respectively. Iterations were run and converges using steady state solutions at flow time ~0.05 s and in order to stabilized the computations, transient simulations were also carried out. An industrial and upgraded generation type of high performance computer (HPC) was used, which is in order to adequately calculate regions of flow and heat transfer with large number of grids and regions with refined grids and cell growth downstream the hole exits.

Figure 6 and Figure 7 show typical description of flows as depicted by work of Cho and Goldstein [3] of Figure 6 that vena contracta effects, results into flow separation and reattachment, which also increases the flow velocity with flow reduced area. Their work was compared with this CFD predictions in Figure 6, it reveals that the regions that were described by Cho and Goldstein [3] are correctly predicted by the velocity pathlines and TKE, k results. It shows from the TKE predictions that flow reattachment also creates vortices that possibly have consequential effects on the air mass flow, G for X/D = 4.66, as in Figure 7. Figure 7 indicates that if G is less than 0.35 kg/s m², the effects of the contracta could affect the reattaching flow and increases the downstream air jets velocity, while other Gs are not affected as the flows are within the vena contracta regions, implying that the ∆P is expected to be valid, as in Figure 8. This implies

that the CFD predictions with the application of the refined hexahedral structured grid, wall function and standard k - ε turbulence model, captured well the flow aerodynamics in the hole and the use of high performance computer (HPC) is adequate for the CFD calculations.

Comparison of measured data and CFD predictions were made in Figure 8 and Figure 9, whereby pressure loss and heat transfer coefficient for the hole wall boundaries are correctly predicted. Figure 8 shows that ∆P increases with increased X/D and there is perfect agreement with work by Andrews and Mpadi [5] , as both the geometrical and flow parameters are similar to that simulated in this work. Also predicted correctly with the experimental data [5] and within the 10% experimental error bar, is the surface average HTC of Figure 9. It shows similar trend with that predicted in Figure 8, which indicates that ∆P influences HTC, hence the aerodynamics in the short holes that captured the flow separation and reattachment (Figure 6 and Figure 10).

Figure 11 is the comparison of Nusselts number per measured data of work by Mills [12] with this CFD prediction. It shows reasonable agreement and with insufficient influence on L/D. The disparity in agreement could be based on the fact that the experimental parameters vary with the computational one but are closely similar and the differences are insignificant, hence comparisons are possible. Figure 8, Figure 9 and Figure 11 show that the experimental results validate the CFD predictions, which implies that the use of the present CFD code and techniques are adequate in optimising the design procedures used here. Figure 10 shows that conjugate heat transfer can also be combined with CFD tools in order to predict the complex mechanisms in the short hole that experimentally are either not possible or are costly.

Figure 10 shows that the predicted heat transfer is clearly the influenced of the TKE aerodynamics prediction of Figure 12, with a similar trend of prediction for the Nusselts number result in Figure 12. This further demonstrates the predicted results shown in Figure 6 and the consequences associated with aerodynamics, whereby largely the Reynolds number, Re in Table 3 are turbulence in nature and hence resulted into jets flow. The used of Equation (5) (T^*) reveals that the exit hole sides are associated with reversed air jets flow as in Figure 12, which also affects the conjugate heat transfer in the hole wall surfaces and is the reason why high X/D with high Re of Figure 10 gave high transfer. Also shown in Figure 13 is T^*, which indicates that upstream holes extract heat higher with

X/D, while downstream holes gave lower heat transfer as a result of crossflow effects [9] [13] [19] [20] .