Effect of non-isothermality on film cooling effectiveness under partial blockage of coolant injection holes

Abstract

Modern gas turbine units (GTUs) operate at extremely high temperatures, with mainstream gas temperatures reaching 1700–1750 °C in transport and military applications, while heat-resistant blade materials are limited to approximately 1000–1100 °C. This necessitates advanced cooling techniques to ensure component durability and reliability. Film cooling, achieved by injecting coolant air through inclined holes to form a protective layer on the blade surface, is a widely adopted method. However, the effectiveness of film cooling is significantly influenced by the non-isothermality parameter Rₜ = Tf/Tc, which characterizes the temperature ratio between the mainstream and coolant flows. Real GTU operating conditions correspond to Rₜ = 2.0–2.2, while most experimental studies are conducted under low non-isothermality conditions (Rₜ ≈ 1.2), creating significant uncertainty when extrapolating laboratory data to actual turbine operating conditions.

An additional critical factor affecting cooling effectiveness is partial blockage of coolant injection holes caused by particle deposition (e.g., CaO–MgO–Al₂O₃–SiO₂) during operation in dusty or desert environments, which is particularly relevant for military GTU applications. Research shows that even after 50–200 hours of operation, sufficient deposits can accumulate to partially obstruct the hole cross-section. This study focuses on partial-load operation regimes characterized by reduced blowing ratios (m = 0.4–1.0), which are typical when the engine operates below maximum capacity. Such regimes require detailed investigation considering real temperature conditions, as reduced coolant mass flow can lead to changes in flow structure and thermal protection film redistribution.

Purpose of the Work. This study aims to numerically investigate the effect of flow non-isothermality (Rₜ = 1.8) on film cooling effectiveness of a flat surface under partial blockage of coolant injection holes in the blowing ratio range m = 0.4–1.0, characteristic of partial-load turbine operation. Particular attention is paid to comparative analysis with model conditions (Rₜ = 1.2) and assessment of transverse non-uniformity of coolant film formation in a four-hole configuration.

Research Methods. The investigation was conducted using numerical simulations in ANSYS CFX 2019 R2 with the Reynolds-Averaged Navier-Stokes (RANS) equations and SST turbulence model for closure. Three geometric configurations were created: a baseline without blockage and two configurations with partial blockage corresponding to 25% (h/d = 0.5) and 50% (h/d = 1.0) obstruction of the hole cross-sectional area. The blockage degree was characterized by the dimensionless parameter h/d, where h is the maximum transverse blockage height and d is the hole diameter (0.8 mm). Geometric dimensions were based on typical turbine blade cooling system parameters: hole diameter d = 0.8 mm, transverse pitch t = 2.4 mm (t/d = 3.0), and hole inclination angle of 30° relative to the surface. A hybrid unstructured mesh with approximately 1.1 million elements was employed, consisting of tetrahedral elements in the mainstream flow and prismatic layers near solid surfaces. Boundary conditions were set to achieve blowing ratios close to m = 0.4, 0.6, 0.8, and 1.0. The mainstream velocity was 400 m/s with a temperature of 1100 °C, while the coolant temperature was 500 °C, corresponding to Rₜ = 1.8 characteristic of real GTU operating conditions. Turbulence intensity was set to 1%, and adiabatic wall boundary conditions (δQ = 0) were applied to solid surfaces. Symmetry conditions were imposed on lateral surfaces of the computational domain. The model was verified against experimental data for the traditional configuration without blockage (h/d = 0) at m = 1.0, showing a deviation of 9.68%, which is acceptable for CFD simulations of film cooling.

Results and Conclusions. Analysis of local film cooling effectiveness distributions revealed that the character of coolant distribution maintains qualitative patterns typical of discrete film cooling with inclined holes, while absolute effectiveness values are significantly higher compared to model conditions (Rₜ = 1.2) due to the greater temperature difference between mainstream and coolant flows, providing more intensive thermal protection of the surface. The non-isothermality parameter plays a determining role in forming absolute values of film cooling effectiveness. Under high non-isothermality conditions (Rₜ = 1.8), characteristic of real operating regimes of transport and power GTUs, effectiveness is approximately twice as high as under model conditions (Rₜ = 1.2): at m = 0.4 for the baseline configuration without blockage, it increases from 16.8% to 33.6%. A similar trend is observed for all blockage configurations: at h/d = 0.5 and m = 0.4, effectiveness increases from 16.3% to 29.0%, and at h/d = 1.0 from 10.8% to 24.0%.

For high non-isothermality conditions (Rₜ = 1.8) at m = 0.4, partial hole blockage leads to a reduction in area-averaged effectiveness of 13.7% for h/d = 0.5 and 28.6% for h/d = 1.0 relative to the baseline configuration. The physical mechanism of this effect is complex: blockage at constant mass flow rate increases coolant exit velocity and effective blowing ratio, while also changing the jet discharge angle, causing early jet separation and intense turbulent mixing with the mainstream flow. As the blowing ratio increases to m = 1.0, characteristic of elevated partial-load regimes, effectiveness losses increase to 31.1% and 56.1%, respectively.

Importantly, the character of blockage influence is universal, but its intensity depends on temperature conditions. Comparative analysis showed that for low-temperature conditions (Rₜ = 1.2) at m = 0.4, the reduction in film cooling effectiveness was 3.0% for h/d = 0.5 and 35.7% for h/d = 1.0, whereas for real conditions (Rₜ = 1.8) it was 13.7% and 28.6%, respectively. This indicates that under high non-isothermality, the film cooling system demonstrates different sensitivity to geometric changes in holes, which must be considered when designing GTU blade cooling systems.

Analysis of spatial effectiveness distribution showed persistence of transverse non-uniformity of the coolant film for all investigated configurations and both temperature regimes. Local maxima form along hole axes corresponding to trajectories of the central portions of coolant jets, while zones with reduced effectiveness appear between holes where the surface remains inadequately protected from thermal exposure. This non-uniformity persists over a significant distance from the holes and does not disappear even with increasing blowing ratio, indicating the limited ability of discrete hole systems to provide continuous film coverage of the surface. Blockage intensifies this non-uniformity regardless of the non-isothermality level.

The obtained results emphasize the necessity of accounting for real temperature conditions when designing and optimizing film cooling systems for gas turbine blades. Extrapolation of data obtained under model conditions with low non-isothermality to real operating regimes can lead to significant errors in assessing cooling effectiveness and blade thermal state. The data obtained in this work can be used to improve calculation methods for the thermal state of turbine blades, accounting for non-isothermality effects and degradation of film cooling systems due to hole contamination.