Velocity and concentration field measurements and large eddy simulation of a shaped film cooling hole

Highlights

• MRC provides an accurate measure of film cooling adiabatic effectiveness.

• Separated flow inside shaped film cooling holes is likely geometrically sensitive.

• The time-averaged position of separated regions is difficult to predict using LES.

Abstract

The 3D velocity and scalar concentration fields from a laidback fan-shaped film cooling hole are measured using Magnetic Resonance Velocimetry (MRV) and Magnetic Resonance Concentration (MRC). The velocity and scalar concentration fields of the same geometry are also obtained using Large Eddy Simulation (LES). The geometry under consideration features a single film cooling hole with a 30° inclination angle and 7° forward and lateral expansion angles. The results are compared to an existing adiabatic effectiveness experiment using infrared imaging of an identical geometry (Schroeder and Thole, 2014). Flow separation is observed inside the hole in the LES and MRV. The separated region in the LES is symmetrically located, but it is offset to a lateral side in the MRV which slightly skews the scalar concentration field to one side. Comparisons of the LES with the MRV and MRC experiments show good agreement in the velocity and scalar concentration field elsewhere throughout the 3D domain. Despite some disagreement in the adiabatic effectiveness values with the IR experiment immediately after injection, there is good agreement downstream of injection between the IR experiment and the LES and MRC. Differences in the concentration field can be attributed to differences in the in–hole velocity field. The results suggest that the mean position of the region of separation inside the hole is geometrically sensitive.

Introduction

A variant of the canonical jet in crossflow, the inclined jet in crossflow, is commonly used in gas turbines to release coolant flow onto the surface of turbine blades, protecting them from hot combustion gases in a technique called film cooling (Bogard and Thole, 2006). Hole shape is an important parameter governing the flow and can lead to dramatic changes in flow structures, mixing, and film cooling effectiveness. The most prevalent shaped hole found in film cooling literature is the laidback fan-shaped diffuser hole, which is defined by the forward and lateral expansion angles. Diffuser holes are favored over cylindrical holes because they slow down the coolant flow and thus mitigate the negative effects of the counter-rotating vortex pair and reduce or eliminate jet blow-off. A thorough review of the literature in the field of shaped hole film cooling is given by Bunker (2005).

Laidback fan-shaped diffuser exits are prone to separation within the diffuser if the expansion angles are too large. Thole et al. (1998) found evidence of separation inside shaped holes with large expansion angles based on turbulence levels. Gunady et al. (2019) measured the velocity field of a laidback fan-shaped hole with forward and lateral expansion angles of 12° using Magnetic Resonance Velocimetry (MRV) and observed separated flow at the inlet of the metering section of the hole as well as in the diffuser. Gritsch et al. (1998) measured adiabatic effectiveness of a similar hole with 15° forward expansion and 14° lateral expansion. In both studies of holes with large expansion angles by Gunady et al., 2019, Gritsch et al., 1998, the flow separated on one side of the laidback diffuser portion of the hole due to the large expansion angles.

The present study focuses on a specific hole geometry known as the “7-7-7 shaped hole,” a laidback fan-shaped diffuser hole designed by Schroeder and Thole (2014) with forward and lateral expansion angles of 7°. The smaller expansion angle compared to some other holes is intended to reduce flow separation inside the diffuser section of the hole. Schroeder and Thole (2014) used an infrared camera to measure the adiabatic effectiveness of the 7-7-7 shaped hole at density ratios of 1.2 and 1.5, blowing ratios between 1 and 3, and various freestream turbulence intensities. In addition to flowfield and adiabatic effectiveness measurements, Schroeder and Thole (2017b) used a thermal rake to collect thermal field measurements for different blowing ratios and freestream turbulence intensities. Haydt and Lynch, 2018b, Schroeder and Thole, 2017a measured the flowfield of the 7-7-7 shaped hole using particle image velocimetry (PIV) for varying compound angles, freestream turbulence intensities, in–hole roughness, and blowing ratios.

The 7-7-7 geometry is important because it is used as a benchmark to which the performance of new hole geometries are compared (Hossain et al., 2020, Thurman et al., 2016, Snyder and Thole, 2020). Numerous other studies have been conducted using the 7-7-7 shaped hole geometry or other similar geometries. However, many of these studies use laser based techniques or hot-wire anemometry, both of which have limitations on where data can be taken due to optical or physical access requirements. Separated flow in the metering section of the hole or in the diffuser can be inferred based on downstream turbulence intensity or adiabatic effectiveness contours, but the existence or absence of separated flow is seldom directly observed. Detailed experimental data of 3D velocity fields, especially inside of the hole, are needed to gain a more complete understanding of the flow resulting from the 7-7-7 hole geometry.

The 7-7-7 shaped hole has also been studied using simulations. In addition to adiabatic effectiveness measurements, Haydt and Lynch (2018a) conducted RANS CFD predictions of the 7-7-7 hole at various compound angles. Oliver et al. (2019) performed compressible high fidelity simulations of the 7-7-7 geometry to study Mach number sensitivity; they observed in–hole separation in all cases, and flow asymmetry only in their high Mach number simulation.

Although diffuser holes mitigate the counter-rotating vortex pair, jet lift off, and excessive mixing with the freestream, complex in–hole flows, such as separation, can still negatively impact performance. Separated flow can create a jetting effect inside the hole, reducing the effective area ratio of the diffuser.

Conventional CFD does not consistently capture the detailed flow features of real film cooling flows. There is a glaring need for fully 3D data to inform the development of improved models. Many experimental methods exist for measuring 3D velocity and concentration fields. Some of these methods can result in time-resolved data. However, laser based techniques can be complex and are limited by geometry and optical access. Magnetic Resonance Velocimetry (MRV) and Magnetic Resonance Concentration (MRC) can be used to acquire the 3D mean velocity and scalar concentration field, respectively, of an arbitrarily complex geometry. When applied to film cooling, flow structures and the resulting adiabatic effectiveness can be studied in three dimensions. Large Eddy Simulation (LES) can compliment MRV and MRC results by providing near-wall results and turbulent statistics. Milani et al. (2019) studied an inclined round hole using 3D data from MRI and LES. Effects of asymmetry caused by the plenum conditions and persisting through the metering section are observed in the flow. Flow inside the diffuser section of shaped diffuser holes could be affected by asymmetric flow in the metering section of such holes.

In this study, MRV and MRC experiments as well as a LES of the 7-7-7 shaped hole geometry are conducted. The MRV and MRC are used to validate the LES, and adiabatic effectiveness results from the MRC and LES are compared with data from Schroeder and Thole (2014).