**1. Introduction**

Film cooling has been widely applied to the highly-efficient thermal protection of guide vanes in modern gas turbines [1]. As the gas turbines advance, the turbine inlet temperature will be progressively elevated such that the thermal-protection requirement becomes more critical. To ensure the guide vanes work reliably under crucial aero-thermal conditions without significant deterioration, developing more efficient film cooling schemes is a necessity.

Researchers have devoted tremendous efforts to explore effective strategies for enhancing film cooling performance, either in passive or active mode [2,3]. The innovation of shaped holes is regarded as the most inspiring advancement [4]. Through shaped film cooling holes, the jet injection is modified and subsequently, the flow dynamics of jet-in-crossflow, which is attributed to the cancellation of the kidney vortex pair or counterrotating vortex pair (CVP) that originates from the mutual interaction of the ejecting jet with oncoming crossflow. It is well known that the earlier exploration of shaped holes was initialized in the middle of the 1970s. The preliminary investigation of Goldstein et al. [5]

**Citation:** Hang, J.; Zhang, J.; Wang, C.; Shan, Y. Numerical Investigation of Single-Row Double-Jet Film Cooling of a Turbine Guide Vane under High-Temperature and High-Pressure Conditions. *Energies* **2022**, *15*, 287. https://doi.org/ 10.3390/en15010287

Academic Editors: Roberto Alonso González Lezcano, Francesco Nocera and Rosa Giuseppina Caponetto

Received: 19 November 2021 Accepted: 27 December 2021 Published: 1 January 2022

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**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

demonstrated that a fan-shaped hole could produce a marked film cooling improvement on the immediate downstream surface. Following this acceptance, fan-shaped hole film cooling attracted much attention during the past decades. For instance, Thole et al. [6] presented a detailed flowfield measurement for the coolant injection from shaped holes with expanded exits. Gritsch et al. [7,8] experimentally investigated the geometric influence of fan-shaped holes on film cooling performances. Lee and Kim [9] conducted a singleobjective geometric optimization study of fan-shaped hole film cooling with the aim of increasing cooling effectiveness. Saumweber and Schulz [10] researched the effect of the geometric parameters of fan-shaped holes on the film cooling performance. These further investigations illustrated clearly the dominate dynamic flow features of fan-shaped hole film cooling, including less coolant-mainstream shear mixing, less coolant-jet penetration into the mainstream, and wider coolant-jet lateral spread relative to the conventional hole. Despite the widespread use in practical, the challenging subjects in multi-parameter influence and multi-objective optimization of fan-shaped hole film cooling remain unexamined so far. More recently, Huang et al. [11] performed a multi-objective optimization of the laidback fan-shaped hole as applied to the turbine guide suction surface by taking the film cooling effectiveness and the discharge coefficient into consideration. Lenzi et al. [12] revealed the unsteady flowfield characterization of a shaped-hole effusion system in the swirling mainstream from detailed experimental tests. Kim et al. [13] investigated the influence of fan-shaped hole position and jet-to-crossflow density ratio on the film cooling performance. Baek et al. [14] performed a numerical study to deeply reveal the inherent flow dynamics of fan-shaped hole film cooling by using the large eddy simulation methodology. Lee et al. [15] optimized the fan-shaped hole using experimental methods, wherein the influence of primary flow velocity on the optimization was examined. Based on the fan-shaped holes, many innovative film cooling holes were suggested in recent years (e.g., arrowhead hole [16], NEKOMIMI hole [17], crescent hole [18], dumbbell hole [19], ridge hole [20], tripod hole [21], slot-similar hole [22], etc.), aiming at the possible solutions to approach the ideal art of film cooling. Although these innovative shaped holes have been confirmed to indeed play positive roles in improving film cooling effectiveness, they generally face fabrication and feasibility problems in engineering application due to their complex geometries. From this viewpoint, apparently, developing more realistic film cooling enhancement configurations is of more practical significance.

The double-jet film cooling configuration, referred as DJFC, is a simply constructed combined-hole configuration, wherein two film cooling holes with opposite orientation angles are integrated in a unit. On account of its realistic fabrication, DJFC gained much attention recently. Kusterer and his partners conducted a succession of investigations on the DJFC. Initially, they tried different spanwise spacings of the DJFC holes under a series of blowing ratios [23,24] and proved that the DJFC has the potential to produce an anti-kidney vortex pair. However, at this stage, some of the structures they tried were unsuccessful. For example, a "negative" spanwise spacing would significantly reduce the cooling effectiveness. Soon they discovered the reasonable double-jet structures and conducted further research with the use of these structures under both low and high blowing ratios [25,26]. They concluded that the DJFC with an appropriate design could form an anti-CVP structure to effectively alleviate the adverse CVP effect. As the double jets were arranged with opposite orientation angles, the compound injection angle was identified to be a crucial geometric parameter that affected the film cooling characteristics. Wang et al. [27] investigated the influence of streamwise spacing in a double-jet unit on film cooling performance. It was found that a larger streamwise spacing helps the formation of the anti-CVP structure and thus the improvement of film cooling effectiveness. Han et al. [28] studied the DJFC by using pressure sensitive paint technology and numerical simulation. It was demonstrated that the anti-CVP structure formed in the DJFC was tightly associated with the double-jet pitch and the compound injection angle, wherein the former affected the interaction and the latter affected the strength of each branch of the antikidney vortexes. Choi et al. [29] and Lee et al. [30] carried out an optimization of the DJFC

configurations by selecting four variables (spanwise and streamwise distances between film-hole centers, and respective spanwise injection angles) as design variables. The cooling performance was optimized with the increase in the spanwise injection angle, attributed to a wider spanwise spreading of coolant coverage. Khalatov et al. [31] experimentally studied the influence of primary flow turbulence and pressure gradient on the DJFC. From the test results, they concluded that the double-jet scheme is superior to the traditional two-row scheme. An increase of about 20% of the averaged cooling effectiveness could be achieved under low and moderate blowing ratios. In general, the primary flow turbulence had a weak influence on the average cooling effectiveness of the DJFC, but the favorable streamwise pressure gradient could reduce the average film cooling effectiveness by about 25%. Graf and Kleiser [32] performed an LES study to determine the influence of the coolant injection condition and yaw angle on the thermal and aerodynamic performances of the DJFC. They identified that the increase in the yaw angle helped to improve the spanwise spread of the coolant jet. However, the far downstream film cooling effectiveness was reduced and the mixing loss increased. It should be noted that their research was mainly carried out under the double-jet layout with zero spanwise spacing. Yao et al. [33,34] performed experimental studies to determine the influence of spanwise spacing and streamwise spacing of doublejet unit on the film cooling performance. They reported that the spanwise distance greatly influenced the range of lateral coverage. Under moderate spanwise distances, the antikidney vortex effect more clearly dominated, whereas this anti-kidney vortex effect was weaker under a larger spanwise distance. Furthermore, the influence of streamwise spacing on the DJFC was tightly associated with the spanwise spacing. He et al. [35] studied the influence of the primary flow attack angle on the DJFC. It was found that larger negative attack angles of primary flow generally had an adverse influence on doublejet film cooling because of the limited lateral coverage. Liao et al. [36] performed an investigation to determine the surface curvature influence on the DJFC. Compared to the flat surface, the film cooling effectiveness of the DJFC on a convex surface increased, but the situation was opposite on a concave surface under low blowing conditions. The appropriate blowing ratio varied in accordance with the surface curvature. In general, in the DJFC, the main geometric parameters that significantly affected film cooling performance were the compound injection angle and spanwise and streamwise pitches of the double-jet unit.

As far as we know, most of the previous investigations on the DJFC were performed on a flat surface. However, the film cooling performance is significantly influenced by the surface curvature and pressure gradient of the primary flow passage. Apparently, the assessment of shaped-hole film cooling on its potential use in real gas turbines is an obligatory issue. Although the effects of major variables in the DJFC have been extensively investigated, little attention has been paid to DJFC application in gas turbine vanes. Aiming at this issue, a numerical investigation is conducted in the current study to provide more detailed insight into the DJFC roles in the application of a turbine guide vane under the hightemperature and high-pressure conditions of gas turbines. From this work, the influence of the blowing ratio, spanwise injection angle, and spanwise spacing in a double-jet unit on film cooling performance is illustrated. Of particular, the different influential roles of the DJFC on the suction and pressure surfaces of a specific guide vane are identified.
