Recent advances in experimental methods have allowed researchers to study nozzle guide vane film cooling in the presence of combustor dilution ports and endwall films. The dilution injection creates nonuniformities in temperature, velocity, and turbulence, and an understanding of the vane film cooling performance is complicated by competing influences. In this study, dilution port temperature profiles have been measured in the absence of vane film cooling and compared to film effectiveness measurements in the presence of both films and dilution, illustrating the effects of the dilution port turbulence on film cooling performance. It is found that dilution port injection can create significant effectiveness benefits at the difficult-to-cool vane stagnation region, due to the more turbulent hot mainstream enhancing the mixing of film coolant jets that have left the airfoil surface. Also explored are the implications of endwall film cooling for infrared vane surface temperature measurements. The reduced endwall temperatures reduce the thermal emissions from this surface, so reducing the amount of extraneous radiation reflected from the vane surface where measurements are being made. The results of a detailed calibration show that the maximum local film effectiveness measurement error could be up to 0.05 if this effect were to go unaccounted for.

Overall cooling effectiveness was determined for a full-coverage effusion cooled surface which simulated a portion of a double wall cooling gas turbine blade. The overall cooling effectiveness was measured with high thermal-conductivity artificial marble using infra-red thermography. The Biot number of artificial marble was matched to real gas turbine blade conditions. Blowing ratio ranged from 0.5 to 2.5 with the density ratio of DR = 1.5. A variation of cooling arrangements, including impingement-only, film cooling-only, film cooling with impingement and film cooling with impingement and pins, as well as forward/backward film injection, were employed to provide a systematic understanding on their contribution to improve cooling efficiency. Also investigated was the effect of reducing wall thickness. Local, laterally-averaged, and area-averaged overall cooling effectiveness were shown to illustrate the effects of cooling arrangements and wall thickness. Results showed that adding impingement and pins to film cooling, and decreasing wall thickness increase the cooling efficiency significantly. Also observed was that adopting backward injection for thin full-coverage effusion plate improves the cooling efficiency.

In the internal cooling passages of the first stage turbine blade in the modern advanced gas turbines, the dense bleeding holes are arranged in order to supply the cold air for the external film cooling. The fluid extractions dramatically vary the flow field and convective heat transfer in the internal channels. In the current work, the flow and heat transfer in a high aspect ratio channel (AR = 4) with the side wall bleeding slots are investigated. Unlike the traditional single inlet channel, the cooling air is supplied into the channel from two entrances located at the both ends of the long straight channel. Therefore, a counteractive flow pattern is generated. The effects of the flow rate ratio of the two streams (MR = ṁ 2 /ṁ 1 ) on the flow and heat transfer inside the channel are investigated, where ṁ 1 and ṁ 2 , are the flow rate of the two streams at the two entrances. The local heat transfer is found to be zigzagging with an increase in the flow rate ratio. Interestingly, once a local flow ratio, MR x , is defined, which is based on the predicted local flow rate, all the data at different locations are converged to the same trend in the Nu/Nu 0 - MR x space, where Nu is the measured local Nusselt number normalized with the Dittus-Boelter correlation, Nu 0 . Based on the numerical simulations, the detailed flow structure is analyzed and reported. The thermal boundary conditions in the simulations mimic the heating scheme in the experiments, where the channel wall is segmented into a matrix of copper plates which are separated by the insulations. It shows that the segmental heating scheme influences the heat transfer significantly.

This paper presents extensive results of an ongoing study on internal blade cooling concepts. A new test rig has been designed, built and commissioned, allowing fast comparison of different cooling schemes as well as surface temperature measurements for different cooling concepts. By scaling the test specimen, full aerothermal similarity was achieved at high measurement accuracy and resolution. Surface temperature (and thus total cooling effectiveness) is measured using high resolution, high dynamic range infrared thermography with an improved data evaluation method. Results for a conventional multi-pass cooling design are presented as a baseline case. Several new internal cooling concepts are then assessed for their relative cooling performance to the conventional design as well as their absolute cooling effectiveness. Those designs include various internal swirl concepts (cyclone cooling). The results show that great care has to be taken when designing advanced internal cooling concepts with complex flow structures, since the effects of internal crossflow, internal pressure loss, internal heat transfer coefficient, and film cooling effectiveness strongly interact with each other and the hot gas flow and hence affect the resulting total cooling effectiveness.

High inlet temperature of turbine vane increases the demand of high film cooling effectiveness. Vane endwall region was extensively cooled due to the high and flat exit temperature distribution of combustor. Leakage flow from the combustor-turbine gap was used to cool the endwall region except for preventing hot gas ingestion. Numerical predictions were conducted to investigate the flow structure and adiabatic film cooling effectiveness of endwall region in a linear cascade with vane-endwall junction fillet. The simulations were completed by solving the three-dimensional Reynolds-Averaged Navier-Stokes(RANS) equations with shear stress transport(SST) k-ω turbulence model, meanwhile, the computational method and turbulence model were validated by comparing computational result with the experiment. Three types of linear fillet with the length-to-height ratio of 0.5, 1 and 2, named fillet A, fillet B and fillet C respectively, were studied. In addition, circular fillet with radius of 2mm was compared with linear fillet B. The interrupted slot, produced by changing the way of junction of combustor and turbine vane endwall, is introduced at X/Cax = −0.2 upstream of the vane leading edge. Results showed that fillet can significantly affect the cooling performance on the endwall due to suppressing the strength of the secondary flow. Fillet C presented the best cooling performance comparing to fillet A and fillet B because a portion of the coolant which climbs to the fillet was barely affected by secondary flow. Results also showed the effect of fillet on the total pressure loss. The result indicated that only fillet A slightly decreases endwall loss.

This paper presents a numerical investigation on the rationality and reliability of film cooling experiments, in which the realistic temperature ratio (TR) of mainstream to cooling air are substituted by the density ratio (DR) of ambient air to a foreign gas with high density. Today, advanced gas turbines operate at much higher temperatures than the allowable temperature of turbine component materials, which makes it very difficult to achieve real TR in the most of laboratory environments, because the real TRs are usually larger than 2.0. Therefore, the foreign gas (for example CO 2 ) with high density was widely used to obtain a proper density ratio for simulating the mixing process of cooling air with high temperature mainstream thereby. However, the TR effect on film cooling is not completely replaced by DR, because the influence factors of film cooling performances are not only DR, but also the thermal properties of cooling gas and mainstream, such as specific heat capacity, viscosity and conductivity. In this work, a film-cooled endwall is used as specimen, and DRs are controlled by two ways, i.e. changing mainstream temperatures, and using a foreign gas, respectively. The numerical results of film cooling performances at the same DR obtained by the two ways are analyzed and compared. The analysis reveals the difference of film cooling performances between TR and DR on the film-cooled endwall, and the comparison indicated that the errors caused by the substitution of foreign gas are acceptable, only when BR, DR, Re ∞ and T ∞ are all small, but when BR, DR or Re ∞ increases, the relative error cannot be neglected, and it may reach 30% in real running conditions.

Numerical simulations have been performed on the turbine shroud unsteady film cooling under the blade passing. There are many published experimental studies for turbine shroud heat transfer and a few computational fluid dynamics data. In this paper, unsteady RANS method has been performed to study the effect of the blade rotation speeds and the film blowing ratios on the behavior of film cooling effectiveness. And the sliding mesh in Fluent was used to achieve relative rotation between blade and shroud. These results are reported for blowing ratios of 1.0, 1.5, 2.0, blade rotation speeds of 1600 rpm, 1800rpm, 2089rpm, 2400rpm. The results show that the time instantaneous film cooling effectiveness on the shroud have a notable different distribution with the steady blade case. And at the rotation results, the film cooling effectiveness is even coverage with the blowing ratio increasing. The time-averaged film cooling effectiveness on the shroud increases by increasing the blowing ratio on all blade rotational velocities. And in this study, the blade at different rotation speeds, the distribution of time-averaged film cooling effectiveness has a significantly reduce on the shroud because of the relative movement of blade and shroud.

The trailing edge of a vane is one of the most difficult areas to cool due to a narrowing flow path, high external heat transfer rates, and deteriorating external film cooling protection. Converging pedestal arrays are often used as a means to provide internal cooling in this region. The thermally induced stresses in the trailing edge region of these converging arrays have been known to cause failure in the pedestals of conventional solidity arrays. The present paper documents the heat transfer and pressure drop through two high solidity converging rounded diamond pedestal arrays. These arrays have a 45 percent pedestal solidity. One array which was tested has nine rows of pedestals with an exit area in the last row consistent with the convergence. The other array has eight rows with an expanded exit in the last row to enable a higher cooling air flow rate. The expanded exit of the eight row array allows a 30% increase in the coolant flow rate compared with the nine row array for the same pressure drop. Heat transfer levels correlate well based on local Reynolds numbers but fall slightly below non converging arrays. The pressure drop across the array naturally increases toward the trailing edge with the convergence of the flow passage. A portion of the cooling air pressure drop can be attributed to acceleration while a portion can be attributed to flow path losses. Detailed array static pressure measurements provide a means to develop a correlation for the prediction of pressure drop across the cooling channel. Measurements have been acquired over Reynolds numbers based on exit flow conditions and the characteristic pedestal length scale ranging from 5000 to over 70,000.

In modern gas turbines, film cooling technology is the most common and efficient way to provide thermal protection for hot parts. To improve film cooling effectiveness, different kinds of shaped holes have been designed, but most of them are complicated and difficult to machine. In this study, four cases of novel film cooling hole design, all based on cylindrical holes, are numerically studied. One is a single, two-stage cylindrical hole, whose downstreamhalf-length has a diameter D while the upstreamhalf-length has a diameter D/2. A second has a cylindrical primary hole with two smaller secondary holes located symmetrically about the centerline of the primary hole and downstream of the primary hole. The three holes of this second design are then combined to make a single shaped hole, constituting a third case, called the tri-circular shaped hole. The entry part of the third case is replaced by a cylindrical hole with a diameter of half the primary hole diameter, making a fourth case called the two-stage tri-circular shaped hole. Film cooling effectiveness and surrounding thermal and flow fields are numerically investigated for all four cases using various blowing ratios. It is shown from the simulation that the two-stage cylindrical hole cannot improve film cooling effectiveness. The primary hole with two secondary holes can enhance film cooling performance by creating anti-kidney vortex pairs, which will weaken jet lift-off, caused by the kidney vortex pairs, from the primary hole. The tri-circular shaped hole will provide better film cooling effectiveness near the hole area, and is not sensitive to blowing ratio. The two-stage structure for tri-circular shaped hole provides better film coverage because it changes the flow structure inside the channel and decreases jet penetration.

Simulating full-coverage film cooling remains an elusive task for aerodynamicists given the small scale of the holes relative to the duct size where the holes are applied. Source term models were developed to simulate the effect through a perforated surface; however, the documented approaches failed to adequately describe how source term locations within the computational domain were selected. This paper presents a continuous ‘checker-board’ surface function that enables a distributed selection of cells where the source terms are applied; furthermore, the source term strengths applied to cells within a given hole are weighted. A 3:1 aspect ratio S-duct with an 1.5 area ratio exhaust diffuser, and 4% porosity applied to the upstream convex bend was evaluated. Steady-RANS obtained with the realizable k-ε model and source terms derived based on the approach of Andreini et al. (2014) had good pressure distribution, outlet velocity, and coolant mass flow agreement with respect to experiment when the hole diameter was resolved with two nodes. Reducing the computational domain element count by 75% and simulating hole diameters 2.8-times larger with 4% surface porosity gave back pressure and outlet distortion coefficients within grid uncertainty of the finest grid solution; however, local-convex-surface-averaged quantities showed grid dependency.

One of the state-of-the-art system for turbine blade trailing edge cooling consists in blowing air, coming from the internal cooling system of the blade, through slots over a cutback on the pressure side. To increase the stiffness, this cutback is commonly equipped with internal ribs. The classical RANS method is widely used in industry to design such a system. However, it has been shown that the accuracy of such a stationary formalism is limited for the prediction of the adiabatic effectiveness due to the fact that the flow is driven by large-scale unsteadiness. In this context, Large Eddy Simulation (LES) appears as a good alternative to improve the quality of the predictions. However, the LES formalism has been scarcely used for trailing edge cooling configuration mainly because of the computational effort associated with such a problem as well as the need to deal with real complex geometries. To reduce costs, most of the time LES studies assume a periodic flow in the spanwise direction. Using this hypothesis, only one cooling passage is simulated making use of a lateral periodic boundary condition. The flow is however likely to be forced by this assumption while the side effects due to the end walls are neglected. In practice, the applicability of this periodic boundary condition has been rarely investigated in past studies. In the case of a trailing edge cutback equipped with internal ribs, there are several phenomena, e.g. coalescence of adjacent jets, which should be considered before using a lateral periodic boundary condition. In the present study, the relevance of such a periodic boundary condition is investigated. To do so, a transonic vane trailing edge equipped with a pressure side cutback and internal ribs is simulated using LES. The chosen setup was studied experimentally at DLR within the framework of the European project AITEB-2. The cooling air is blown through a channel, which is equipped with 2 rows of ribs in an inline arrangement to increase the stiffness of the thin trailing edge region. From the experimental results, it is reasonable to assume that several jets merge if looking at the adiabatic effectiveness results. Therefore, this configuration appears as a good candidate to investigate the relevance of lateral periodic boundary condition for trailing edge cutback flows. To achieve this, two LES are performed for two different computational domain sizes using lateral periodic boundary conditions. Merging of adjacent jets, expected from the experimental results, is highlighted in the simulations. This regrouping mechanism is shown to be dependent on the size of the computational domain. A strong sensitivity of the local adiabatic effectiveness to the computational domain size is highlighted while the global adiabatic effectiveness shows little sensitivity. Finally, it is shown that state-of-the-art RANS modeling is unable to reproduce correctly the local distribution of the adiabatic film effectiveness as well as the decrease of the laterally averaged effectiveness.

This paper describes the numerical investigations on the aerodynamic and thermal performance of a rotor blade cascade with multiple film cooling rows in the passage. First, the experimental data on an annular cascade with upstream film cooling was compared with the numerical results to validate the numerical method. The CFD simulations of the models with a row of film holes at four different locations on the hub endwall were performed respectively. The aerodynamic and thermal performance under the interaction of the secondary flow and endwall film cooling are analyzed based on the CFD predicted streamlines of mainstream flow and film injection, the contours of total pressure loss on the sections located in the passage and at the blade exit, the pitch-averaged film cooling effectiveness and film cooling effectiveness contours. The results show that film holes placed at low level of iso-Mach line tends to provide a better cooling with a smaller amount of coolant.

The tip clearance between turbine blade and stationary casing leads to the exposure of blade tip to high temperature gas and contributes to a high thermal load in this region. Then it is necessary to perform cooling on the blade tip. Moreover, the tip leakage flow in a high speed brings complex aerothermal conditions to the blade tip. The blade tip film cooling on the transonic squealer tip is investigated in this research. The effects of tip and pressure-side coolant injections on the blade tip heat transfer are discussed. And the influences of total pressure ratio of coolant to main flow and endwall moving on the film cooling are considered. Firstly, the reliability of a commercial CFD code with different turbulence models was first validated by contrasting with the experimental results. The heat flux and isentropic Ma number predicted with the BSL k-ω model shows a better agreement with the test data. Then the mesh independency study was performed. The mesh with tip and pressure-side injection hole is generated by in-house code. For the tip without film cooling at outlet Mach number of 0.96, the squealer tip shows a high heat transfer at front of the tip cavity floor caused by the impingement of tip leakage flow, besides the suction-side rim has high heat transfer coefficient. With the tip coolant injection, the tip coolant is pushed towards the cavity pressure-side and provides better coverage in this region. At the front of cavity floor near suction-side, there is almost no coolant coverage then it shows little cooling effects. The coolant discharges from the tip over the suction-side rim thereby the heat transfer near the trailing edge is less affected by the tip coolant injection. With the pressure-side near tip film cooling, the coolant injection shows high film-cooling effectiveness at low coolant stagnation pressure and lift off blade surface at high coolant stagnation pressure. The endwall motion increases the total heat load of the blade tip by increase heat load at cavity floor and suction-side near tip region and the reduces film-cooling effectiveness.

The objective of this study was to investigate the effects of oscillations in the main flow on film cooling at various single frequencies at a low average blowing ratio of M = 0.5. The oscillations in the main flow could be a result of combustion instabilities that have been one of the major concerns for gas turbine industry. Understanding the effect of the instabilities on film cooling is important for better design of the gas turbine engines. The frequencies from 268 to 2144 Hz were identified as the dominant frequencies from a Fourier analysis of a combustor instability data on pressure oscillations. Lastly, the experimental data on gas turbine combustor instabilities is applied to the main flow using Fourier Series and the results are compared to those at single frequencies. Numerical simulations are carried out using LES Smagorinsky-Lilly and URANS k-epsilon models. This study is focused on film cooling effectiveness and heat transfer coefficient which are very important in calculation of the blade temperatures. The results show that as the frequency of the main flow goes from 0 to 180 Hz, the film cooling effectiveness is decreased due to enhancement of jet lift off with increasing frequency. However, when the frequency goes from 180 to 268 Hz, the film cooling effectiveness climbs up sharply because a thin coolant film near the wall is overlapped by large vortices containing the coolant. If the frequency changes from 268 to 1072 Hz, the effectiveness drops because the large vortices generated catch up with each other and they start overlapping and they are moved away from the wall. Main flow frequencies from 1072 to 2144 Hz cause an increase of the film cooling effectiveness since the coolant jet could not respond to these very high frequencies and the coolant behavior starts to return to that at 0 Hz gradually along with the effectiveness. In terms of heat transfer coefficients, when the oscillation frequency climbs from 0 to 536 Hz, the spanwise-averaged Stanton number ratio (St m /St o ) increases due to growing disturbances in the flow. If the frequency is increased from 536 to 2144, the spanwise-averaged Stanton number ratio is decreased. When the oscillation frequency exceeds 536 Hz, the mixing between the hot mainstream and the coolant is reduced because jets do not respond to the flow oscillations as quickly by very short period.

Current turbulent heat flux models fail to predict accurate temperature distributions in film cooling flows. The present paper focuses on a machine learning approach to this problem, in which the Gradient Diffusion Hypothesis (GDH) is used in conjunction with a data-driven prediction for the turbulent diffusivity field α t . An overview of the model is presented, followed by validation against two film cooling datasets. Despite insufficiencies, the model shows some improvement in the near-injection region. The present work also attempts to interpret the complex machine learning decision process, by analyzing the model features and determining their importance. These results show that the model is heavily reliant of distance to the wall d and eddy viscosity v t , while other features display localized prominence.

This paper is based on a combined experimental and numerical investigation on pressure side film cooling in a high pressure turbine vane. The pressure side cooling geometry exhibits two staggered rows of cylindrical holes and a trailing edge cutback, fed by the same plenum chamber. The investigated conditions refer to low speed (exit isentropic Mach number of Ma 2is = 0.2) and low turbulence intensity data. The choice of one only coolant-to-mainstream mass flow ratio equal to MFR = 1.5% was dictated by the hole discharge: on the one side, mainstream injection into the cooling holes and, on the other side, jet liftoff were avoided to get an effective thermal coverage downstream of the holes. Stress-Blended Eddy Simulation (SBES) model has been used to capture the unsteady physics of cooling jet-mainstream interaction downstream of each cooling row and cutback slot. The focus is on SBES capability of developing vortical structures at the interface between coolant and mainstream, as a function of local coolant-to-mainstream velocity ratio, because of their ultimate effect on vane surface temperature. Special attention has been paid to the shape and dynamics of coherent unsteadiness: SBES provided evidence of shear layer Kelvin-Helmholtz instability and hairpin vortices, downstream of cooling holes, with a Strouhal number ( St ) of 1.3 and 0.3–0.4, respectively. Simulated vortex shedding in the cutback region was characterized by St of 0.32, to be compared against the measured St value of 0.40.

Modern film cooling is an essential method to protect the turbine blade from the hot gas, and the issue about how to improve the film cooling performance has attracted much attention. In this study, a tree-shaped film cooling structure is carried out to improve the overall effectiveness and better decrease the metal temperature of the blade at the same time. To validate the superiority of the proposed structure, a series of numerical simulation cases are conducted under a typical blowing ratio of M = 0.764. The first case is a film cooling channel with a single film hole which with a diameter of 5 mm and is inclined by α = 45° relative to the mainstream direction. The other three cases are tree-shaped structures with one level, two levels and three levels of bifurcations. For all cases, the same boundary conditions and turbulence model (Realizable k- ε ) are adopted, and three-dimensional numerical simulations are used as well to test the thermal performance of the models. It is found from the computing results that the overall effectiveness of the tree-shaped structure is improved more than 50% compared to the case with a single film hole, and the results also demonstrate that the more levels of the structure the lower the metal temperatures. Therefore, it is indicated that this research will make a contribution to a higher performance gas turbine.

An increasingly common experimental method allows determination of the overall effectiveness of a film cooled turbine component. This method requires the Biot number of the experimental model to match that of the engine component such that the nondimensional surface temperature, ϕ, is matched to that of the engine component. The matched Biot number requirement effectively places a requirement on the thermal conductivity of the model and the traditional implementation places no requirement on the model’s density or specific heat. However, such is not the case if such a model is exposed to unsteadiness in the flow such as with film cooling unsteadiness. In this paper, we develop an additional nondimensional parameter that must also be theoretically matched to conduct overall effectiveness experiments with unsteady film cooling. Since finding suitable materials with an acceptable combination of thermodynamic properties for a typical low temperature experiment can be difficult, simulations were conducted to determine the impact of imperfectly matched parameters achievable with common materials. Because the disparity between the diffusion and unsteadiness time scales can hinder numerical simulation, a novel analytical solution to the heat equation with relevant unsteady Robin type boundary conditions is developed. Particular solutions are examined to determine the sensitivity of the temperature response of a turbine blade (or a model of one) to its material properties and the form of the unsteady variation in the convection parameters. It is shown that it is possible to obtain useful experimental results even with imperfectly matched parameters.

The present study provides new effusion cooling data for both surfaces of full coverage effusion cooling plate. For the effusion cooled surface, presented are spatially-resolved distributions of surface adiabatic film cooling effectiveness, and surface heat transfer coefficients (measured using transient techniques and infrared thermography). For the impingement cooled surface, presented are spatially-resolved distributions of surface Nusselt numbers (measured using steady-state liquid crystal thermography). To produce this cool side augmentation, impingement jet arrays at different jet Reynolds numbers, from 2720 to 11100, are employed. Experimental data are given for a sparse effusion hole array, with spanwise and streamwise impingement hole spacing such that coolant jet hole centerlines are located midway between individual effusion hole entrances. Considered are initial effusion blowing ratios from 3.3 to 7.5, with subsonic, incompressible flow. The velocity of the freestream flow which is adjacent to the effusion cooled boundary layer is increasing with streamwise distance, due to a favorable streamwise pressure gradient. Such variations are provided by a main flow passage contraction ratio CR of 4. Of particular interest are effects of impingement jet Reynolds number, effusion blowing ratio, and streamwise development. Also included are comparisons of impingement jet array cooling results with: (i) results associated with cross flow supply cooling with CR = 1 and CR = 4, and (ii) results associated with impingement supply cooling with CR = 1, when the mainstream pressure gradient is near zero. Overall, the present results show that, for the same main flow Reynolds number, approximate initial blowing ratio, and streamwise location, significantly increased thermal protection is generally provided when the effusion coolant is provided by an array of impingement cooling jets, compared to a cross flow coolant supply.

Film cooling performance of the compound hole and the Y-shaped hole configurations with the cross-flow coolant channel is investigated experimentally and numerically in this paper. The Reynolds numbers of coolant flow are fixed as 50000 and 100000 respectively. The film cooling effectiveness and heat transfer coefficient were measured by the transient liquid crystal measurement technique under three blowing ratios of 0.5, 1.0 and 2.0 respectively. And flow resistance measurements were also performed to obtain the discharge coefficient of the two film hole configurations. Numerical simulations with Reynolds-averaged Navier-Stokes (RANS) method were performed to explain the experiment results. The results show that the distribution feature of film cooling effectiveness for the compound hole and Y-shaped hole configurations is different. The film cooling effectiveness of the Y-shaped hole configuration is higher than that of the compound hole, and the film spanwise coverage is larger than that of the compound hole under all cases. For two film hole configurations, the heat transfer coefficient increases with the increase of the cross-flow Reynolds number and the blowing ratio. The heat transfer coefficient of the compound hole and Y-shaped hole configurations is close to each other under small cross-flow Reynolds number. However, under large cross-flow Reynolds number, the compound hole configuration has much higher heat transfer coefficient. The discharge coefficient increases gradually with the rising blowing ratio, then tend to a fixed value. Under the condition of the small cross-flow Reynolds number, the discharge coefficient of two film hole configurations is high. The discharge coefficient of the Y-shaped hole configuration is a little higher than that of the compound hole configuration under the condition of the large blowing ratio.