Film Hole Diameter Research Articles

A comprehensive investigation of the effect of hole diameter and number on film cooling performance of rotating blade leading edge

The combined effect of film hole number and diameter on the film cooling were investigated on the rotating blade leading edge by using experimental and numerical methods. The film cooling performance was obtained by pressure sensitive paint technique under rotational condition. To better understand the experimental results, the flow fields obtained from numerical simulation were also analyzed. The effects of hole length-to-diameter ratio (L/d = 2.5/5/7.5), hole number (N = 7/9/10/11/13), hole diameter(d = 0.64∼1.26 mm), Hole to hole pitch, (P/d = 6.3∼9.2) and hole exit area (Ahole/ALE=4 %-14 %) on the film cooling performance are investigated. Five blowing ratios are also employed (M = 0.5 to 2.0). The results indicate that the hole length-to-diameter ratios (L/d = 2.5∼7.5) have a negligible influence on the film cooling effectiveness. Both the film hole number (N = 10/13) and the hole diameter (d = 0.64/0.75 mm) monotonically affect the film cooling performance under each blowing ratios. However, a comprehensive study indicates that there is a significant quadratic correlation between the area-averaged cooling effectiveness and the total film hole exit area for different combinations of hole number and diameter. Meanwhile, there is an optimal film hole exit area on the leading edge and it increases as the blowing ratio or mass flow rate increases.

The investigation of double wall cooling configuration with spherical cavity

Double wall cooling is an efficient cooling method for turbine blade. Commonly used double wall cooling configurations contains a cubic cavity between two walls. Chaos flow flied in the cavity impedes heat transfer. In this research, a new spherical cavity was proposed, traditional cubic cavity was replaced by several spherical cavities, film hole located on the top of spherical cavity, and impact hole located at the button of spherical cavity. Adjacent spherical cavities were connected by channel. Different spherical cavities were established and numerical simulation was used to check their performance. The influence of blowing ratio, channel, film hole diameter, spherical cavity diameter was analyzed. The performance of cavities was also compared with common double wall cooling configurations. According to the result, when blowing ratio was 0.3, spherical cavity increased cooling effectiveness by 45.6% maximumly compared to common configurations. As for coolant consumption, spherical cavity needs less coolant than common configurations to achieve the same cooling effectiveness. What's more, film hole located at −45° position was benefit for cooling, and cooling effectiveness would increase further when spherical cavity diameter was enlarged.

Effects of film hole spanwise angle and diameter on flow and heat transfer of impingement/effusion cooling with crossflow diverters

This paper studies the blade cooling under the co-effect of external film extraction and internal impingement cooling with crossflow diverters. The influence of spanwise angle (α) and diameter (Df) of film hole on flow and cooling performance are analyzed when the impingement jet Reynolds number ranges (Rei) from 15,000 to 45,000. From the results, if a row of film holes is set on the target surface of an impingement cooling with crossflow diverters, the overall cooling effectiveness will be greatly improved, especially the pressure side. When the α ranges from 35° to 115°, no matter pressure side or suction side, the film jet injection towards blade hub is more beneficial to cooling, and the smaller the α, the more beneficial. When the Df ranges from 0.25 mm to 1.00 mm, at suction side, as Df increases, overall cooling effectiveness gradually increases; at pressure side, when the Df ranges from 0.25 mm to 0.75 mm, overall cooling effectiveness increases, but if the Df continues to increase, it will decrease, which means the Df of 0.75 mm can obtain the most excellent cooling performance. This study provides a theoretical basis for the comprehensive application of film extraction, impingement cooling, and crossflow diverters in blade cooling design.

Effect of film hole diameter and attack angle on the film cooling performance of leading edge with double swirl chamber under crossflow condition

The film cooling characteristics of the blade leading edge with a double swirl chamber are studied experimentally under crossflow(CF) conditions. Aerodynamic and structural parameters such as CF intensity, blowing ratio(BR, 0.5–1.5), film hole diameter(df, 2–4 mm), and attack angle(αa, 0-16°) are considered comprehensively in the experiment. The computational simulation method was introduced to reveal the mechanism of CF affecting the cooling performance. The results present that introducing the CF condition at the same BR condition led to BR redistribution in the film holes, significantly improving the cooling protection near the C1 film holes for the df=3 mm and df=4 mm cases. Unlike the adverse effects of CF on the heat transfer in previous studies, the results present that CF under low BR conditions can help avoid the mainstream intrusion of the film holes. In the case of αa=8° and 16°, The film cooling effectiveness performs the highest in the CF0-BR1.0 condition at s/df>8, and the equivalent film coverage can be obtained under the CF1-BR0.5 condition. CF at αa=8° similarly avoids the mainstream intrusion under the small BR, but the CF reduces η near the C2– film holes. In contrast, the CF has little effect on the cooling performance around the C2– film holes in the case of αa=16° under BR=0.5. The area-averaged film cooling effectiveness of CF2-BR0.5 improves by 85 % relative to CF0-BR0.5 at df=3 mm case. When df=4 mm, the area-averaged film cooling effectiveness enhancement of the CF1-BR1.0 condition is about 87.43 % higher than that of CF0-BR1.0.

Investigation on the influence of the film hole diameters on the cooling performance of the film and vortex composite cooling under rotating conditions

This article numerically explores the effects of the film hole diameter on the performance of the film and vortex composite cooling. The vortex cooling structure is set in the leading edge of a GE E3 airfoil, connecting with the mainstream flow by the film holes and the blade material to achieve mass transfer and heat transfer, respectively. Five cooling structures with the film diameter d equal to 0.12 mm, 0.20 mm, 0.28 mm, 0.36 mm, and 0.44 mm are involved. Simulations are carried out under the rotating speed of 0 rpm, 1000 rpm, 2000 rpm, 2500 rpm, and 3000 rpm for all structures. The dimensionless temperature θ of the blade leading edge surface is defined to evaluate the cooling performance. The higher θ represents the lower temperature. Results show the different rotational effects on the different structures. First, the value of θ increases with the increasing film hole diameter under the same rotating speed. The value of θ in the case of 0.44 mm is around 5 times that in the case of 0.12 mm. Second, the peak value of θ is observed under the rotating speed higher than 2500 rpm when d is lower than 0.28 mm. While the peak value of θ is observed under 1000 rpm when d is higher or equal to 0.28 mm. The peak value of θ represents an increase of 11.23% and 2.76%, as compared to the lowest value of θ when d is equal to 0.12 mm and 0.44 mm, respectively. Because the dominating cooling methods are different in the cases with different film hole diameters.

Stress Characteristics and Structural Optimization of Spacecraft Multilayer Insulation Components

Multilayer insulation (MLI) components are important parts of spacecraft, in which thin films are the core elements. The film thicknesses are generally small, between 10 and 30 μm, to reduce the weight of the spacecraft. During the launch of a spacecraft, there is a rapid drop in the internal pressure, which causes the internal gas to flow out rapidly through the component. The resulting fluid force may cause film damage and failure, thereby directly affecting the normal operation of the spacecraft. Therefore, the mechanical characteristics of the thin films under rapid decompression conditions were investigated during this study. Considering the effects of the flow field stress distributions on the films during the rapid decompression, a fluid–structure interaction (FSI) model for a component was first constructed. The results show that the stress is largest in the outlet film, which is the part of the overall structure most vulnerable to failure. Furthermore, the effects of the structural parameters of the component on the stresses in the different film layers were analyzed using the orthogonal experimental method. The results show that the film thickness had the largest influence, followed by the film hole diameter, the number of component layers, and finally the staggered hole distance. Finally, a structurally optimized design scheme for the component is proposed based on a parameter range analysis with respect to the maximum film stress. After optimization, the maximum stress of the thin film decreased by 97.6%. This research has practical engineering value for the structural design and optimization of MLI components.

Multi-objective design of laminated cooling configuration applied in gas turbine based on fuzzy grey relational analysis

Laminated cooling is a compound system consisting of different cooling units that can provide effective protection to the hot components in next generation gas turbines. In the present work, using validated numerical simulations, the influential levels of geometrical parameters in laminated cooling configuration (film hole diameter, pin-fin diameter, impingement hole diameter and film hole inclined angle) on multi-objective functions (overall cooling effectiveness, friction loss and temperature uniformity) are calculated and ranked by fuzzy grey relational analysis (FGRA). The FGRA results indicate that the film hole diameter is the primary influence factor on the overall cooling effectiveness and temperature uniformity, but insensitive to the friction loss. Based on this finding, two novel laminated cooling configurations with revised film-hole shapes, i.e., fan-shaped film holes and discrete rectangular film slots, are proposed to meet the multi-objective requirement. Through calculations, it is proved that the overall cooling effectiveness of the discrete film slots with a width of 0.5 mm can be increased by approximately 20%, whereas the additional friction loss is negligible (the increase of flow resistance coefficient is only 0.06 at mass flow ratio equals to 1.19%). Meanwhile, the acceptable temperature uniformity along with high overall cooling effectiveness, low friction loss can be obtained with the design of the fan-shaped film holes. The present work provides a novel analytical method for the multi-influence-factor problem and multi-objective design of complex laminated cooling system in gas turbine application.

Cooling and Flow Characteristics of Multi-Channel Wall Jet Structure With Film Holes at Blade Leading Edge

Abstract Efficient cooling is imperative for gas turbine blades that suffer from hot gas erosion. Cooling and flow characteristics of multi-channel wall jet structure combined with film holes for blade leading edge are numerically investigated through the Reynolds-averaged Navier–Stokes method in this paper. Several geometrical schemes with different rows and diameters of film holes were conducted, and the influences of the cooling air mass flow ratio of the first coolant supply cavity were also considered, which presented the detailed flow and cooling characteristics of wall jet and film composite cooling on conjugate heat transfer. The results implied that film extraction improves the overall cooling effectiveness compared with pure wall jet cooling. And the mainstream intrusion happens in some film holes at the bottom of blades, especially on the pressure side. The film-hole diameter can raise the mass flow ratio and enhance external thermal protection produced by cooling air, and it also affects the uniformity of film flow and the temperature gradient of some regions for turbine blades. Furthermore, the cooling performance and pressure loss are significantly influenced by the coolant mass flowrate of the first cooling air supply cavity. This study will offer a consultation for the design of film-hole structures for multi-channel wall jet cooling.

Numerical Investigation of Single-Row Double-Jet Film Cooling of a Turbine Guide Vane under High-Temperature and High-Pressure Conditions

Single-row double-jet film cooling (DJFC) of a turbine guide vane is numerically investigated in the present study, under a realistic aero-thermal condition. The double-jet units are positioned at specific locations, with 57% axial chord length (Cx) on the suction side or 28% Cx on the pressure side with respect to the leading edge of the guide vane. Three spanwise spacings (Z) in double-jet unit (Z = 0, 0.5d, and 1.0d, here d is the film hole diameter) and four spanwise injection angles (β = 11°, 17°, 23°, and 29°) are considered in the layout design of double jets. The results show that the layout of double jets affects the coupling of adjacent jets and thus subsequently changes the jet-in-crossflow dynamics. Relative to the spanwise injection angle, the spanwise spacing in a double-jet unit is a more important geometric parameter that affects the jet-in-crossflow dynamics in the downstream flowfield. With the increase in the spanwise injection angle and spanwise spacing in the double-jet unit, the film cooling effectiveness is generally improved. On the suction surface, DJFC does not show any benefit on film cooling improvement under smaller blowing ratios. Only under larger blowing ratios does its positive potential for film cooling enhancement start to show. Compared to the suction surface, the positive potential of the DJFC on enhancing film cooling effectiveness behaves more obviously on the pressure surface. In particular, under large blowing ratios, the DJFC plays dual roles in suppressing jet detachment and broadening the coolant jet spread in a spanwise direction. With regard to the DJFC on the suction surface, its main role in film cooling enhancement relies on the improvement of the spanwise film layer coverage on the film-cooled surface.

Effects of Holes Arrangement on the Superposition Characteristics of Film Cooling Effectiveness

The purpose of the current research is to test and analyze the applicability of the Sellers model in different arrangements and configurations of film cooling holes and then to modify the Sellers model to improve the accuracy of the superposition prediction. The film cooling effectiveness distributions at different blowing ratios are obtained using the infrared thermometry technology. The flat plate experiments are completed in a low-speed closed-loop wind tunnel facility. The mainstream Reynolds number based on the film hole diameter is 6300, and the blowing ratios range from 0.8 to 1.8. The superposition characteristics are described in three different cases: double rows of cylindrical holes in an inline arrangement, double rows of cylindrical holes in a staggered arrangement, and double rows of compound angle holes in an inline arrangement. The results indicate that the Sellers model cannot accurately predict the film cooling effectiveness in certain conditions, which is mainly attributed to the interaction between counter-rotating vortex pairs of the adjacent rows and the increasing momentum of mainstream near the wall surface. For all cases, the corresponding modified superposition prediction methods are given in this paper.

Infiltration reduction characteristics and a simplified calculation model of film hole irrigation during interference infiltration*

AbstractThe infiltration types of film hole irrigation (FHI) can be divided into film hole free infiltration (FHFI) and film hole interference infiltration (FHII). Numerical simulations were carried out with HYDRUS to investigate the influence of soil texture (ST), film hole diameter (D), film hole spacing (S) and water depth above the film hole (H) on the cumulative infiltration under two infiltration types of FHFI and FHII. The results showed that the amount of FHII was reduced significantly compared to that of FHFI. ST, D and S are the dominant factors affecting the infiltration reduction volume (ΔI). The relationship between ΔI and the time after interference (t − t0) is a proportional function (R2 ≥ 0.96), and its proportional coefficient has a good power function relationship with D and S. The power function coefficients have large differences for different ST, and the range of variation is 0.1–191, whereas there is little difference between the power function index of D and S; the average values were 2.6 and −2.5, respectively. A simplified calculation model of infiltration reduction was established, and the estimation accuracy was high (RMSE = 0.017 L, EF = 0.980). This research can provide a reference for the calculation of the irrigation water volume of the FHI.

Effects of Cooling Configurations on the Aerothermal Performance of a Turbine Endwall With Jet Impingement and Film Cooling

Abstract With the increase of turbine inlet temperature and the application of premixed combustion, turbine components, particularly the turbine endwall, work in a harsh environment and must be effectively cooled to ensure the component durability. Recently, new cooling schemes that employ both external film cooling and internal jet impingement cooling have drawn much attention due to their extraordinary performance. In this study, a numerical model of turbine endwall with jet impingement and film cooling was established and validated against the experiment. To investigate the effects of geometric parameters related to this cooling scheme, four parameters including impingement hole-to-hole pitch Pi, impingement hole diameter Di, impingement channel height H, and film hole diameter Df were selected to adjust within a reasonable range. The uniform design method was used to collect a database that represented the design space formed by the four parameters. Performance criteria including area-averaged overall cooling effectiveness, standard deviation of overall cooling effectiveness, and total pressure drop coefficient of the cooling system were evaluated through computational fluid dynamics (CFD) calculations. To explore and exploit the design space, a Kriging model was built from the database. Analysis of variance (ANOVA) was conducted afterward to investigate the main effect of each parameter and the correlation between parameters. Finally, based upon the knowledge obtained from ANOVA, typical designs were selected which yielded either best or poorest performances. Through detailed analysis of flow and heat transfer mechanisms of these designs, the influence of each parameter was illustrated clearly and suggestions for the design of similar cooling schemes were drawn.

Enhancement in Film Cooling Effectiveness Using Delta Winglet Pair

Abstract A simulation study has been carried out to investigate the influence of delta winglet pair (DWP) for improving the film cooling effectiveness of a gas turbine blade. Incompressible continuity, momentum, energy, and two equations k − ω SST model have been used for investigating the nature of flow field, temperature field, and turbulent statistics. The Reynolds number based on the jet velocity and the diameter of the film cooling hole is set at a constant value equal to 4232. The jet to the crossflow blowing ratio has been varied as 0.5, 1.0, and 1.5. The corresponding Reynolds numbers based on the crossflow inlet velocity and film hole diameter are equal to 6462, 4229, and 3231, respectively. It is observed that common-flow-down (CFD) DWP configuration augments the film cooling effectiveness due to generation of secondary longitudinal vortices, which annihilates the counter-rotating vortex structures present in the baseline flow. The generation of hairpin vortices and the growth of shear layer vortices are modified due to the implementation of DWP. The overall turbulence intensity and vorticity get reduced due to the presence of DWP. A maximum of 97.46% and a minimum of 61.50% enhancement in film cooling effectiveness have been observed at blowing ratio of M = 1.5 and M = 0.5, respectively. The wake region of the film cooling jet is modified due to DWP leading to formation of stagnation region and lower mixing resulting in higher film cooling effectiveness. The strength of horseshoe vortices is reduced due to the presence of DWP, resulting in lower mixing between the jet with the cross flows and stable film formation. Lower thermal boundary layer thickness is observed in DWP configuration compared to that of the baseline case confirming lower mixing due to the implementation of DWP. Overall, the present study explains the effectiveness of DWP configuration for enhancement of film cooling effectiveness of a DWP.

Experimental investigation on the effect of hole diameter on the leading edge region film cooling of a twist turbine blade under rotation conditions

Film cooling performance on the twist turbine blade leading edge (LE) model has been experimentally investigated employing the thermochromic liquid crystal (TLC) technology under rotation conditions. The novelty of this paper is the earlier study on the effect of film hole diameter (d = 0.4 mm and 0.5 mm) on the LE region of a rotating twist blade. The effects of blowing ratio (M) and density ratio (DR) were also considered. M ranged from 0.5 to 2.0 when DR = 1.56 and M ranged from 0.5 to 1.25 when DR = 1.04. The whole experiment was conducted at the rotating speed of 574 r/min with the Reynolds number of 63,400. Results show that the film hole diameter of leading edge has a significant effect on the spanwise average film cooling effectiveness. The spanwise effectiveness provided by the larger DR (1.56) increases with increasing hole diameter in the whole range of −4.3d to 3.75d at M = 0.5, 1.0 and 1.5. When DR = 1.56, the spanwise effectiveness increases monotonically with increasing blowing ratio in the whole range of −4.3d to 3.75d under the condition of d = 0.4 mm case, and it increases first and then descends with increasing blowing ratio in the whole range except −3.3d to −0.5d with the best M = 1.5 under the condition of d = 0.5 mm case. The area average film cooling effectiveness provided by the larger DR (1.56) is higher than that provided by the smaller DR (1.04) when M = 0.5 and 1.0 for the d = 0.5 mm case. More results on the influence of hole diameter, blowing ratio and density ratio are shown in this paper.

Multi-optimization of a specific laminated cooling structure for overall cooling effectiveness and pressure drop

The structural optimization of a specific laminated cooling structure is conducted under gas turbine combustor representative aero-thermal conditions, with the aim at improving its overall cooling effectiveness. The optimization procedure is realized by using conjugate heat transfer CFD analysis and radial basis function neural network (RBFNN) surrogated model. For this specific laminated cooling structure, both the thickness of impinging plate (ti) and the thickness of film cooling plate (tf) are all fixed as 0.5 mm. The other geometric parameters including impinging-hole diameter(di), pin-fin diameter(dp), film-hole diameter (df), inner height of double walls (H), streamwise hole-to-hole pitch (S) and spanwise hole-to-hole pitch (P) are selected as the design variables. Two geometric constrains are considered that the total thickness of laminated cooling structure is not bigger than 2 mm, and the minimum clearance between adjacent fins should be bigger than 0.5 mm. By using the current CFD-based optimization methodology, the optimized laminated cooling structures are presented from the given range of possible geometric variables. An optimized laminated cooling structures makes the maximum spatially-averaged overall cooling effectiveness approach to 0.9, and the other for minimum relative total pressure drop can reach 0.17%. Moreover, it is found that the thermal stress has a regularity with the overall cooling effectiveness.

Nonlinear Optimization of Turbine Conjugate Heat Transfer with Iterative Machine Learning and Training Sample Replacement

A simple yet effective optimization technique is developed to solve nonlinear conjugate heat transfer. The proposed Nonlinear Optimization with Replacement Strategy (NORS) is a mutation of several existing optimization processes. With the improvements of 3D metal printing of turbine components, it is feasible to have film holes with unconventional diameters, as these holes are created while printing the component. This paper seeks to optimize each film hole diameter at the leading edge of a turbine vane to satisfy several optimum thermal design objectives with given design constraints. The design technique developed uses linear regression-based machine learning model and further optimizes with strategic improvement of the training dataset. Optimization needs cost and benefit criteria are used to base its decision of success, and cost is minimized with maximum benefit within given constraints. This study minimizes the coolant flow (cost) while satisfying the constraints on average metal temperature and metal temperature variations (benefits) that limit the useful life of turbine components. The proposed NORS methodology provides a scientific basis for selecting design parameters in a nonlinear design space. This model is also a potential academic tool to be used in thesis works without demanding extensive computing resources.

Study of utilizing double lateral sub holes at different spanwise angles on blade film cooling effectiveness

A numerical study of the effect of using double lateral sub-holes at different span-wise angles on flow structure and film-cooling performance is performed. The lateral angles for each sub-hole change from 10° to 20° at the same film-hole diameter (12.7 mm) and jet angle (35°). The flow-field analysis and the performance of film-cooling for the double lateral sub-hole models are investigated comparing with the basic single-hole model. There are high augmentations in the overall effectiveness of film-cooling by 14.2%, 26.5%, and 37.2% for the first, the second, and the third double lateral sub-hole models, respectively when the blowing ratio increases from 0.5 to 1.0. By evaluating the film-cooling performance for the third double lateral sub-hole model compared to the basic model, there is an increasing ratio in the overall effectiveness by 54.2% and 149.5% for the low and high ratio of blowing, respectively. Consequently, the third double lateral sub-hole model can be selected as the best model among the other models and by further operating at a broad range of blowing ratios from 0.25 to 3.5, the model achieves a maximum value of overall film-cooling effectiveness of 44% at an optimum value of blowing ratio 2.5.

INFILTRATION CHARACTERISTICS OF FILM HOLE IRRIGATION UNDER THE INFLUENCE OF MULTIPLE FACTORS

AbstractFilm hole irrigation is a new type of film‐mulched irrigation technology. To investigate the influences of five factors—bulk density, initial soil water content, irrigation depth, film hole diameter and infiltration time—on the infiltration characteristics of film hole irrigation, 12 experiments were conducted. The infiltration characteristics considered were the cumulative infiltration (I), infiltration rate (i) and average increment of soil water content (∆θ). Two empirical models were established that describe the relationship of I with ∆θ and various influential factors. The proposed models of I and ∆θ had a root mean square error of 5.82 ml and 0.003 cm3 cm−3, respectively. The results revealed that the effects of initial soil water content and irrigation depth on I were not significant (P > 0.05) and that the ranking of factors according to degree of influence, from large to small, was infiltration time, soil bulk density and film hole diameter. Soil bulk density, initial soil moisture, irrigation depth and film hole diameter had highly significant effects on ∆θ (P < 0.01), and their ranking according to degree of influence, from large to small, was initial moisture content, soil bulk density, irrigation depth and film hole diameter. © 2020 John Wiley & Sons, Ltd.

Multi-objective optimization of round-to-slot film cooling holes on a flat surface

This paper describes a multi-objective optimization method for round-to-slot shaped film-holes (RTSH) using computational fluid dynamic analysis and surrogate model approximation. The physical model is a single-row of film cooling holes on a flat surface. Three design variables relating to the main RTSH geometric parameters are investigated: the film-hole inclination angle (θ), slot width (s), and film-hole height (t). The slot length (l) and hole-to-hole pitch (P) are fixed as 2d and 2.4d, respectively, where d is the film-hole diameter. The optimal model is constructed by selecting the discharge coefficient (Cd) and spatially-averaged adiabatic film cooling effectiveness (ηad,av) as independent objective functions. From the Pareto front of optimal solutions, the optimized round-to-slot holes are obtained under blowing ratios of M=0.5 and 1.5. Numerical assessments corresponding to the maximum ηad,av (Opt-A), maximum Cd (Opt-B), and a compromise between the two objective functions (Opt-C) are performed, and the mechanisms influencing the optimal film-hole shapes in terms of film cooling performance are analyzed in depth.

Experimental investigation of geometrical effect on flow and heat transfer performance of lamilloy cooling structure

Effect of film hole diameter to discharge coefficients and film cooling effectiveness of the lamilloy were experimentally investigated at the blowing ratios ranging from 0.6 to 2.5. Generally, the cooling effectiveness on the test surface is increased with the film hole diameters and blowing ratios increasing, and the variation tendency along the streamwise through the centerline of film holes also keeps consistent. In the upstream, all configurations have a relatively lower cooling effectiveness, however, with the flows to the downstream, cooling effectiveness grows gradually, and the peak values of effectiveness appeared periodically, the position matches the film hole positions. Besides, between the film holes, fluctuation exists simultaneously. By comparison, the cooling effectiveness and discharge coefficients are both increased with the blowing ratio with same film hole diameters, Moreover, under the same blowing ratios, the cooling effectiveness and discharge coefficients are getting higher when hole diameters increase.