Effect and optimization of backward hole parameters on film cooling performance by Taguchi method
Introduction
Eternal themes for human being are problems of energy saving and sustainable development. In the past 30 years, gas turbines as a kind of power equipment with high thermal efficiency and low pollutant emission have been widely applied in many industrial fields such as aeronautical propulsion and land power generation [1]. Modern gas turbines operate at temperatures of above 2000 K, which is much higher than the metal melting point of the materials [2]. Park et al. [3] measured thermal load and cooling performance on the rim surface of the turbine blade. It was found that the rim surface bears the most severe thermal load. Chung et al. [4] indicated that excessively high thermal stress caused cracking on gas turbine blades. Film cooling can prevent high-temperature gas from thermal erosion to hot components of the gas turbine [5]. So improvements of film cooling technology can ensure stable and long-term operations for the gas turbines.
After the jet (coolant) flow is injected through discrete holes drilled on the metal wall, a low-temperature cooling layer is formed over the metal surface, which avoids direct contact between the metal wall and the hot mainstream [6]. However, considering that film cooling holes are inclined relative to the cooled wall, interaction between the jet flow and the mainstream results in a counter-rotating vortex pair, named as the kidney vortex [7]. This kidney vortex increases the mixing intensity between the jet flow and the hot mainstream, which causes lift-off of the jet flow from the wall surface. In order to improve the film cooling effectiveness, it is very important to weaken the effect of the kidney vortex. Nowadays, there are two main methods: one is to improve the film hole configuration, and the other one is to install flow control devices near the holes.
Among investigations of the hole configuration, Shine et al. [8] investigated the effect of tangential and azimuthal angles of cylindrical holes on film cooling. Results showed that with a tangential angle of 30° and an azimuth angle of 10°, the film cooling performance for the cylindrical hole increased as the blowing ratio increased. Al-Hamadi et al. [9] analyzed the effects of freestream turbulence on film cooling of two staggered rows of a compound angle hole. The results showed that an increase of the freestream turbulence intensity significantly decreased the local film cooling effectiveness at a blowing ratio of 0.5. Koç et al. [10] conducted numerical simulations of the film cooling effectiveness on five curved surfaces. It was found that the film cooling effectiveness along the downstream and lateral directions increased for blowing ratios in the range of 1.0–2.0. Asghar and Hyder [11] designed a novel semi-circular hole configuration. Compared with the cylindrical hole, the semi-circular hole showed weaker and smaller counter-rotating vortex pairs. Other researchers combined two or three cylindrical holes in some particular way to create a new hole configuration, such as double-jet hole [12], anti-vortex hole [13] and sister hole [14]. These combined hole configurations can effectively weaken harmful kidney vortices. Sun et al. [15] both experimentally and numerically conducted a comparison of various configurations on film cooling, including cylindrical hole, fan-shaped hole, double-jet hole and sister hole. Results showed that there was the strongest kidney vortex near the outlet of the cylindrical hole, which showed the worst film cooling effectiveness.
For research on flow control devices, Na et al. [16] placed a ramp upstream of the film hole, and An et al. [17] installed a crescent-shaped block downstream the film hole. Although applications of ramp and block configurations near the film hole can improve the film cooling effectiveness, the integrity of the blades is destroyed and manufacturing costs are significantly increased. Wang et al. [18] analyzed an effect of a bulge upstream the film hole on film cooling performance. It was concluded that the 0.3d-height bulge provided better film cooling effectiveness. Wang et al. [19] investigated the effect of different sizes of deposition on the wall film cooling, and the results showed that the coverage area of the jet flow decreased as the height of the deposition bulge increased. Moreover, Dai et al. [20] applied surface dielectric barrier discharge (SDBD) actuators to the film cooling, the results showed that these actuators could generate anti-kidney vortices to inhibit separation of the jet flow from the wall surface. Audier et al. [21] measured the effect of the surface plasma dielectric barrier discharge actuator on film cooling by particle image velocimetry (PIV) and infrared (IR) thermography. It was found that the actuator induced a deflection of the jet flow toward the wall at all blowing ratios, which delayed the jet flow diffusion into the mainstream.
Although the improved film hole configuration and installation of flow control devices in the vicinity of the film hole enhance cooling protection for turbine blades, serious problems can be found in practical engineering applications, such as destruction of blade integrity, complexity of processing, complicated structure, and high manufacturing costs. Therefore, it is necessary to further optimize the existing hole configuration by some low-cost and reliable ways, such as the Taguchi method. In addition, for conventional film cooling holes, the coolant flow is injected in the same direction as the mainstream, and this configuration is named as the forward injection hole. The backward injection hole means that the jet flow is in the opposite direction to the mainstream. The application of the backward injection hole shows the advantages of easy processing and significant increases in film cooling effectiveness. Subbusward et al. [22] numerically revealed the aerodynamic principle of a backward injection. Results showed that kidney vortices can be suppressed using a backward injection. Li et al. [23] investigated the effect of the backward injection numerically, and the results showed that the backward injection significantly improved the film cooling effectiveness compared to the conventional injection direction. Singh et al. [24] carried out both experimental and numerical studies on an injection angle of a backward hole. It was found that the film cooling effectiveness for the case of the backward hole was less sensitive to the injection angle.
The film cooling effectiveness of the backward hole is affected by many parameters, including hole dimensions, inclination angle of hole, and blowing ratio. It is very important to optimize the structure of the backward hole to obtain the best cooling performance. For numerical optimization of film hole configurations, present studies are mainly involved with surrogate models, such as radial basis function neural network (RBF-NN) [25], Kriging model [26], response surface methodology (RSM) [27], etc. The reliability and accuracy of these methods depend on the quantity and selection of the input samples. If the number of the input data is very small, these models cannot reflect the actual situation correctly. However, the Taguchi method can accurately predict the results by testing special combinations based on an orthogonal array and statistical analysis. This design method was proposed by the Japanese scholar Genichi Taguchi in the 1950s to improve the quality of the manufactured products [28]. Compared with the surrogate model, the Taguchi method not only provides most information of all the experiments, but also avoids getting the wrong results generated from random combination of various factors. However, in order to investigate the effects of various parameters of the hole configurations on the film cooling, it is found that only few references about film cooling mentioned the Taguchi method.
In addition, most studies on the hole configurations are mainly focused on the forward injection hole, and there are very few research findings concerning the backward injection hole. Studies on the backward hole in the open literature show that the backward hole can weaken the kidney vortex, which improves the film cooling effectiveness. Moreover, only few investigations on the cooling performance include many of the impact factors. This paper includes two parts. The first part reveals the mechanism of improving the film cooling performance, the flow characteristics and the film cooling performance of the backward hole and the forward hole based on a comparison of numerical results under various blowing ratios. In order to select the optimal hole configuration parameters, the Taguchi method was applied in the second part to analyze the cooling performance under the interaction of three important factors, i.e., hole length, inclination angle and blowing ratio.
Section snippets
Numerical method and validation
Fig. 1 exhibits schematic diagrams of three-dimensional computational domain and two hole configurations for the present study. From Fig. 1(a), it is observed that the computational domain is symmetrical about the X-axis, and the coordinate origin is located at the trailing edge of the film hole outlet. The film cooling hole with a diameter (D) of 12.7 mm has a length-to-diameter ratio (L/D) of 1.75. Flow channel has a length of 59D and a height of 10D. Both the length and width of the coolant
Results and discussion
Studies of the backward hole in the open literature show that the backward hole can weaken the kidney vortex, which improves the film cooling effectiveness.
Conclusions
In this work, a three-dimensional computational model was used to analyze film cooling performance and flow characteristics of backward injection holes. Comparison with the traditional forward injection hole revealed that the mechanism of the cooling performance improvement of the backward injection hole. In addition, according to the Taguchi method, the orthogonal table L16 (34) was designed to investigate the coupled influence of hole length, inclination angle and blowing ratio on the cooling
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgement
This work is supported by the National Natural Science Foundation of China [Grant No. 51606059].
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