Nowadays, in the gas turbine industry, the engine combustion chamber operates at a very high capacity, creating a large amount of heat discharged into the turbine area. According to Dixon and Hall [1
], the material that makes the blades of the turbine cannot withstand this great amount of heat with a maximum temperature of 1000 °C. Therefore, the research on reducing the temperature on the turbine blades is a very active field of development. Turbine blade cooling plays an important role in increasing the thermal operating range of the gas turbine.
To obtain the highest FE, a variety of parameters must be considered; for example, the ratio between the length and diameter of the hole (L/D), the blowing ratio (M), the geometry of the hole, the ratio between the density coolant flow and hot gas, hot gas turbulent intensity, and coolant flow ejection angle. Lutum and Johnson [2
] and Burd et al. [3
] performed experimental studies on the influence of L/D of the hole on the FE with CH. The experimental results showed that the L/D ratio significantly affected FE. Lee and Kim [4
] numerically optimized a CH with the streamwise ejection angle and L/D ratio using the SST turbulence model.
improved by 3.6% compared to the reference geometry. Yuen and Martinez-Botas [5
] performed experimental studies on the effects of the ejection angle with streamwise angles of 30°, 60°, and 90° on the FE for single jets. They reported that the single 60° and 90° jets generated a smaller coefficient of heat transfer than the 30° jet.
Park et al. [6
] presented the control of vortex flows by using forward and backward injection jets with various vortex intensities and hole dispositions to increase FE. Li and Zhang [7
] numerically analyzed the effect of the geometry of the hole on the FE of a hole under trunk-branch shape with various M. The results showed that the FE is improved at M = 0.5. Li et al. [8
] numerically investigated the effect of the aperture ratios and injection angles of sister-shaped holes on FE. The results revealed that the FE was higher than that of the CH case at all M. Yao and Zhang [9
] conducted numerical and experimental studies on the FE on a flat plate with a converged slot-holes row. The results showed that the value of the heat transfer coefficient for the console case was slightly higher than that of the CH case.
Hyams and Leylek [10
] numerically presented a detailed assessment of FE with various M, density ratio (DR), and L/D. The results revealed that the laterally diffused hole and simple angle hole made the best FE. Saumweber et al. [11
] presented a study of the freestream turbulence influences on the FE with a variety of hole types. The results revealed that the FE is decreased with an increase in turbulence intensity at low M for CH. Silieti et al. [12
] presented the numerical research on the FE of gas turbine blades with three turbulence models: SST, realizable k-ε, and v2
-f models. The results revealed that hybrid and hexahedral grids are the same in FE. Gritsch et al. [13
] have carried out experimental research to assess the effect of fan-shaped hole variations on thermal efficiency. Among these parameters, most hole shapes only make a weak influence on FE. Goldstein et al. [14
] presented the influences of the hole’s shape and density on 3-D cooling efficiency using an experimental technique. The results showed that the FE was considerably increased with the shaped cooling holes. Liu et al. [15
] simultaneously carried out numerical simulations and experimental measurements for the FE of slot holes with waist shape. The FE of slot holes with waist shape was similar to that of the CH with a big divergence angle and the heat transfer coefficient in the zone near the hole centerline was higher to that in the downstream midspan zone. Yu et al. [16
] presented a study concentrating on the influences of diffusion hole-shape on the FE with three holes: shape A: CH, shape B: CH with a 10° forward diffusion, and shape C: same as shape B and a 10° lateral diffusion. The experimental results showed that both the FE and h of shape C were the highest among the tested shapes. Kim et al. [17
] experimentally analyzed the hole shape’s effects on the FE with CH, two laidback holes, and two tear-drop holes. According to the results, the CH case had a weak FE as compared to the shaped-hole cases, and the laidback hole had the best FE. Fu et al. [18
] investigated the effects of the inclination and diffusion angles of the chevron hole. The results revealed that a big inclination angle reduced the FE at M = 1.0 and 1.5, whereas the FE increased with the great diffusion angle at high M = 2.0. Liu et al. [19
] performed numerical simulations to examine the FE for a turbine inlet guide vane using fan-shaped holes. The results found that the FE increased significantly with the fan-shaped holes around the leading edge and up to 40% coolant mass flow was saved as compared to those of the CH case.
Kim et al. [20
] numerically analyzed the effect of converged-inlet hole shapes with the injection angle of coolant flow, streamwise and expanded angles in streamwise and pitchwise directions, and L/D. It was concluded that the FE increased by 46.5% in comparing with the CH case. Moreover,
reached the maximum at an injection angle of 40°. In the next research paper, Kim et al. [21
] continued the numerical analysis for a converging–diverging hole. With the diverged hole combination, the highest FE increased by 9.9% at M = 1.5 when compared to the fan-shaped hole case. For more complex hole shapes, Kim et al. [22
] also studied the FE of four shaped holes: louver, fan-shaped, dumbbell-shaped and crescent. The numerical results indicated that the dumbbell-shaped hole had the highest FE among all tested cases with M from 0.5 to 2. Kohli and Thole [23
] analyzed the influences of a cooling hole with an entrance angle of 35° in regard to the main-stream and an exit angle of 15°. Numerical results indicated that the FE was reduced with the orientation of the coolant flow. Gritsch et al. [24
] presented a comparison of the FE for the CH and two expanded holes. The experimental results indicated that both expanded holes in the exit part increased the FE, especially at a high M. Hay et al. [25
] experimentally studied the inclined holes at an injection angle of 30°. The results reported that the discharge coefficients at the hole inlet rounding was enhanced up to 15%.
An experiment from Afzal et al. [26
] studied the distance between the grooves on the plain tubes to maximize the Nusselt number. The study revealed that the Nusselt number will rise with a reduction in the tube surface temperature. Zhang et al. [27
] presented an unsteady research on the FE of a rotational turbine blade. The numerical results indicated that the main-stream swing had an impact on the FE and a higher FE in spanwise direction was achieved at a higher swing frequency. Du et al. [28
] presented a parametric study of a trenched-shaped hole on FE. The results indicated that the FE at the suction surface of the turbine blades in downstream zones was slightly changed when the trenched holes were modified.
From the above literature review, the shaped holes generally produce a high FE. Forward expanded holes have higher values of FE and lower values of heat transfer coefficient than that of the CH case. However, many of them are difficult to be manufactured. In addition, there are few studies that investigate in detail the expansion of the CH into converged and diverged holes or a combination of them. For that reason, this study proposes a design of a two-head flared hole to evaluate the FE between the hot and cool flows on a flat plate.