scholarly journals Theory of Non-Dimensional Groups in Film Effectiveness Studies

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
Francesco Ornano ◽  
Thomas Povey
Keyword(s):  
Heat Capacity ◽  
Physical Interpretation ◽  
Film Cooling ◽  
Gas Turbines ◽  
Momentum Flux ◽  
Density Ratio ◽  
Flux Ratio ◽  
Cooling Performance ◽  
Momentum Flux Ratio ◽  
Blowing Ratio

Abstract The desire to improve gas turbines has led to a significant body of research concerning film cooling optimization. The open literature contains many studies considering the impact on film cooling performance of both geometrical factors (hole shape, hole separation, hole inclination, row separation, etc.) and physical influences (effect of density ratio (DR), momentum flux ratio, etc.). Film cooling performance (typically film effectiveness, under either adiabatic or diabatic conditions) is almost universally presented as a function of one or more of three commonly used non-dimensional groups: blowing—or local mass flux—ratio, density ratio, and momentum flux ratio. Despite the abundance of papers in this field, there is some confusion in the literature about the best way of presenting such data. Indeed, the very existence of a discussion on this topic points to lack of clarity. In fact, the three non-dimensional groups in common use (blowing ratio (BR), density ratio, and momentum flux ratio) are not entirely independent of each other making aspects of this discussion rather meaningless, and there is at least one further independent group of significance that is rarely discussed in the literature (specific heat capacity flux ratio). The purpose of this paper is to bring clarity to this issue of correct scaling of film cooling data. We show that the film effectiveness is a function of 11 (additional) non-dimensional groups. Of these, seven can be regarded as boundary conditions for the main flow path and should be matched where complete similarity is required. The remaining four non-dimensional groups relate specifically to the introduction of film cooling. These can be cast in numerous ways, but we show that the following forms allow clear physical interpretation: the momentum flux ratio, the blowing ratio, the temperature ratio (TR), and the heat capacity flux ratio. Two of these parameters are in common use, a third is rarely discussed, and the fourth is not discussed in the literature. To understand the physical mechanisms that lead to each of these groups being independently important for scaling, we isolate the contribution of each to the overall thermal field with a parametric numerical study using 3D Reynolds-averaged Navier–Stokes (RANS) and large eddy simulations (LES). The results and physical interpretation are discussed.

Numerical Investigation of Coolant-to-Mainstream Scaling Parameters With Film Cooling on Pressure and Suction Side of a Gas Turbine Blade

2017 ◽  
Author(s):  
Lingyu Zeng ◽  
Xueying Li ◽  
Jing Ren ◽  
Hongde Jiang
Keyword(s):  
Gas Turbine ◽  
Film Cooling ◽  
Momentum Flux ◽  
Velocity Ratio ◽  
Density Ratio ◽  
Flux Ratio ◽  
Suction Side ◽  
Pressure Side ◽  
Blowing Ratio ◽  
Adiabatic Effectiveness

Most experiments of blade film cooling are conducted with density ratio lower than that of turbine conditions. In order to accurately model the performance of film cooling under a high density ratio, choosing an appropriate coolant to mainstream scaling parameter is necessary. The effect of density ratio on film cooling effectiveness on the surface of a gas turbine twisted blade is investigated from a numerical point of view. One row of film holes are arranged in the pressure side and two rows in the suction side. All the film holes are cylindrical holes with a pitch to diameter ratio P/d = 8.4. The inclined angle is 30°on the pressure side and 34° on the suction side. The steady solutions are obtained by solving Reynolds-Averaged-Navier-Stokes equations with a finite volume method. The SST turbulence model coupled with γ-θ transition model is applied for the present simulations. A film cooling experiment of a turbine vane was done to validate the turbulence model. Four different density ratios (DR) from 0.97 to 2.5 are studied. To independently vary the blowing ratio (M), momentum flux ratio (I) and velocity ratio (VR) of the coolant to the mainstream, seven conditions (M varying from 0.25 to 1.6 on the pressure side and from 0.25 to 1.4 on the suction side) are simulated for each density ratio. The results indicate that the adiabatic effectiveness increases with the increase of density ratio for a certain blowing ratio or a certain momentum flux ratio. Both on the pressure side and suction side, none of the three parameters listed above can serve as a scaling parameter independent of density ratio in the full range. The velocity ratio provides a relative better collapse of the adiabatic effectiveness than M and I for larger VRs. A new parameter describing the performance of film cooling is introduced. The new parameter is found to be scaled with VR for nearly the whole range.

Computational Fluid Dynamics Evaluations of Film Cooling Flow Scaling Between Engine and Experimental Conditions

2016 ◽  
Vol 139 (2) ◽  
Author(s):  
James L. Rutledge ◽  
Marc D. Polanka ◽  
Nathan J. Greiner
Keyword(s):  
Low Temperature ◽  
Film Cooling ◽  
Momentum Flux ◽  
Room Temperature ◽  
Density Ratio ◽  
Flux Ratio ◽  
Experimental Conditions ◽  
Cold Air ◽  
Momentum Flux Ratio ◽  
Adiabatic Effectiveness

The hostile turbine environment requires testing film cooling designs in wind tunnels that allow for appropriate instrumentation and optical access, but at temperatures much lower than in the hot section of an engine. Low-temperature experimental techniques may involve methods to elevate the coolant to freestream density ratio to match or approximately match engine conditions. These methods include the use of CO2 or cold air for the coolant while room temperature air is used for the freestream. However, the density is not the only fluid property to differ between typical wind tunnel experiments so uncertainty remains regarding which of these methods best provide scaled film cooling performance. Furthermore, matching of both the freestream and coolant Reynolds numbers is generally impossible when either mass flux ratio or momentum flux ratio is matched. A computational simulation of a film cooled leading edge geometry at high-temperature engine conditions was conducted to establish a baseline condition to be matched at simulated low-temperature experimental conditions with a 10× scale model. Matching was performed with three common coolants used in low-temperature film cooling experiments—room temperature air, CO2, and cold air. Results indicate that matched momentum flux ratio is the most appropriate for approximating adiabatic effectiveness for the case of room temperature air coolant, but matching the density ratio through either CO2 or cold coolant also has utility. Cold air was particularly beneficial, surpassing the ability of CO2 to match adiabatic effectiveness at the engine condition, even when CO2 perfectly matches the density ratio.

Influence of Coolant Density on Turbine Blade Film-Cooling With Compound-Angle Shaped Holes

2012 ◽  
Author(s):  
Kevin Liu ◽  
Shang-Feng Yang ◽  
Je-Chin Han
Keyword(s):  
Film Cooling ◽  
Momentum Flux ◽  
Density Ratio ◽  
Flux Ratio ◽  
Suction Side ◽  
Cooling Effectiveness ◽  
Film Cooling Effectiveness ◽  
Blowing Ratio ◽  
Shaped Hole ◽  
Compound Angle

Adiabatic film-cooling effectiveness is examined systematically on a typical high pressure turbine blade by varying three critical flow parameters: coolant blowing ratio, coolant-to-mainstream density ratio, and freestream turbulence intensity. Three average coolant blowing ratios 1.0, 1.5, and 2.0; three coolant density ratios 1.0, 1.5, and 2.0; two turbulence intensities 4.2% and 10.5%, are chosen for this study. Conduction-free pressure sensitive paint (PSP) technique is used to measure film-cooling effectiveness. Three foreign gases — N2 for low density, CO2 for medium density, and a mixture of SF6 and Argon for high density are selected to study the effect of coolant density. The test blade features 45° compound-angle shaped holes on the suction side and pressure side, and 3 rows of 30° radial-angle cylindrical holes around the leading edge region. The inlet and the exit Mach number are 0.27 and 0.44, respectively. Reynolds number based on the exit velocity and blade axial chord length is 750,000. Results reveal that the PSP is a powerful technique capable of producing clear and detailed film effectiveness contours with diverse foreign gases. As blowing ratio exceeds the optimum value, it induces more mixing of coolant and mainstream. Thus film-cooling effectiveness reduces. Greater coolant-to-mainstream density ratio results in lower coolant-to-mainstream momentum and prevents coolant to lift-off; as a result, film-cooling increases. Higher freestream turbulence causes effectiveness to drop everywhere except in the region downstream of suction side. Results are also correlated with momentum flux ratio and compared with previous studies. It shows that compound shaped hole has the greatest optimum momentum flux ratio, and then followed by axial shaped hole, compound cylindrical hole, and axial cylindrical hole.

A Three-Regime Based Method for Correlating Film Cooling Effectiveness for Cylindrical and Shaped Holes

2015 ◽  
Author(s):  
Lieke Wang ◽  
Mats Kinell ◽  
Hossein N. Najafabadi ◽  
Matts Karlsson
Keyword(s):  
Experimental Data ◽  
Film Cooling ◽  
Gas Turbines ◽  
Density Ratio ◽  
Transition Regime ◽  
Cooling Effectiveness ◽  
Cooling Performance ◽  
Film Cooling Effectiveness ◽  
Blowing Ratio ◽  
Lift Off

To cope with high temperature of the gas from combustor, cooling is often used in the hot gas components in gas turbines. Film cooling is one of the effective methods used in this application. Both cylindrical and fan-shaped holes are used in film cooling. There have been a number of correlations published for both cylindrical and fan-shaped holes regarding film cooling effectiveness. Unfortunately there are no definitive correlations for either cylindrical or fan-shaped holes. This is due to the nature of the complexity of film cooling where many factors influence its performance, e.g., blowing ratio, density ratio, surface angle, downstream distance, expansion angle, hole length, turbulence level, etc. A test rig using infrared camera was built to test the film cooling performance for a scaled geometry from a real nozzle guide vane. Both cylindrical and fan-shaped holes were tested. To correlate the experimental data, a three-regime based method was developed for predicting the film cooling effectiveness. Based on the blowing ratio, the proposed method divides the film cooling performance in three regimes: fully attached (or no jet lift-off), fully jet lift-off, and the transition regime in between. Two separate correlations are developed for fully attached and full jet lift-off regimes, respectively. The method of interpolation from these two regimes is used to predict the film cooling effectiveness for the transition regime, based on the blowing ratio. It has been found this method can give a good correlation to match the experimental data, for both cylindrical and fan-shaped holes. A comparison with literature was also carried out, and it showed a good agreement.

Film-Cooling Effectiveness Downstream of a Single Row of Holes With Variable Density Ratio

1991 ◽  
Vol 113 (3) ◽  
pp. 442-449 ◽  
Author(s):  
A. K. Sinha ◽  
D. G. Bogard ◽  
M. E. Crawford
Keyword(s):  
Mass Flux ◽  
Film Cooling ◽  
Momentum Flux ◽  
Velocity Ratio ◽  
Density Ratio ◽  
Flux Ratio ◽  
General Distribution ◽  
Cooling Effectiveness ◽  
Film Cooling Effectiveness ◽  
Momentum Flux Ratio

Film-cooling effectiveness was studied using a row of inclined holes that injected cryogenically cooled air across a flat, adiabatic test plate. The density ratio of the coolant to mainstream varied from 1.2 to 2.0. Surface temperatures were measured using a unique surface thermocouple arrangement free of conduction errors. Temperatures were obtained along the jet centerline and across a number of lateral locations. By independently varying density ratio and blowing rate, scaling of adiabatic effectiveness with mass flux ratio, velocity ratio, and momentum ratio was determined. Depending on the momentum flux ratio, the jet either remains attached to the surface, detaches and then reattaches, or is fully detached. For attached jets, the centerline effectiveness scaled with the mass flux ratio. However, for detached-reattached jets, a consistent scaling was not found although the general distribution of the centerline effectiveness scaled with momentum flux ratio. Laterally averaged effectiveness was found to be dependent on density ratio and momentum flux ratio. Decreases in density ratio and increases in momentum flux ratio were found to reduce the spreading of the film cooling jet significantly and thereby reduce laterally averaged effectiveness.

CFD Evaluations of Film Cooling Flow Scaling Between Engine and Experimental Conditions

2016 ◽  
Author(s):  
James L. Rutledge ◽  
Marc D. Polanka ◽  
Nathan J. Greiner
Keyword(s):  
Low Temperature ◽  
Film Cooling ◽  
Momentum Flux ◽  
Room Temperature ◽  
Density Ratio ◽  
Flux Ratio ◽  
Experimental Conditions ◽  
Cold Air ◽  
Momentum Flux Ratio ◽  
Adiabatic Effectiveness

The hostile turbine environment requires that film cooling designs are tested in wind tunnels that allow for appropriate instrumentation and optical access, but at temperatures much lower than in the hot section of an engine. Low temperature experimental techniques may involve methods to elevate the coolant to freestream density ratio to match or approximately match engine conditions. These methods include the use of CO2 or cold air for the coolant while room temperature air is used for the freestream. However, density is not the only fluid property to differ between typical wind tunnel experiments so uncertainty remains regarding which of these methods is best suited to provide scaled film cooling performance. Furthermore, precise matching of both the freestream and coolant Reynolds numbers is generally impossible when either mass flux ratio or momentum flux ratio is matched. A computational simulation of an engine scale film cooled leading edge geometry at high temperature engine conditions was conducted to establish a baseline condition to be matched at simulated low temperature experimental conditions with a 10x scale model. Matching was performed with three common coolant types used in low temperature film cooling experiments — room temperature air, CO2, and cold air to match density ratio. Results indicate that matched momentum flux ratio is the most appropriate for matching adiabatic effectiveness for the case of room temperature air coolant, but also matching density ratio through either CO2 or cold coolant has utility. Cold air was particularly beneficial, surpassing the ability of CO2 to match adiabatic effectiveness at the engine condition, even when CO2 perfectly matches density ratio.

Volumetric Velocimetry Measurements of Film Cooling Jets

2018 ◽  
Vol 141 (3) ◽  
Author(s):  
Artur Joao Carvalho Figueiredo ◽  
Robin Jones ◽  
Oliver J. Pountney ◽  
James A. Scobie ◽  
Gary D. Lock ◽  
...  
Keyword(s):  
Film Cooling ◽  
Momentum Flux ◽  
Three Dimensional ◽  
Flux Ratio ◽  
Quality Data ◽  
Data Set ◽  
Momentum Flux Ratio ◽  
Jet In Crossflow ◽  
Lift Off ◽  
Induced Velocity

This paper presents volumetric velocimetry (VV) measurements for a jet in crossflow that is representative of film cooling. VV employs particle tracking to nonintrusively extract all three components of velocity in a three-dimensional volume. This is its first use in a film-cooling context. The primary research objective was to develop this novel measurement technique for turbomachinery applications, while collecting a high-quality data set that can improve the understanding of the flow structure of the cooling jet. A new facility was designed and manufactured for this study with emphasis on optical access and controlled boundary conditions. For a range of momentum flux ratios from 0.65 to 6.5, the measurements clearly show the penetration of the cooling jet into the freestream, the formation of kidney-shaped vortices, and entrainment of main flow into the jet. The results are compared to published studies using different experimental techniques, with good agreement. Further quantitative analysis of the location of the kidney vortices demonstrates their lift off from the wall and increasing lateral separation with increasing momentum flux ratio. The lateral divergence correlates very well with the self-induced velocity created by the wall–vortex interaction. Circulation measurements quantify the initial roll up and decay of the kidney vortices and show that the point of maximum circulation moves downstream with increasing momentum flux ratio. The potential for nonintrusive VV measurements in turbomachinery flow has been clearly demonstrated.

Experimental Study of the Effects of an Oscillating Approach Flow on Overall Cooling Performance of a Simulated Turbine Blade Leading Edge

2009 ◽  
Author(s):  
Ross Johnson ◽  
Jonathan Maikell ◽  
David Bogard ◽  
Justin Piggush ◽  
Atul Kohli ◽  
...  
Keyword(s):  
Turbine Blade ◽  
Film Cooling ◽  
Density Ratio ◽  
Leading Edge ◽  
Stagnation Line ◽  
Cooling Performance ◽  
Blowing Ratio ◽  
Oscillation Frequencies ◽  
Overall Effectiveness ◽  
Blade Leading Edge

When a turbine blade passes through wakes from upstream vanes it is subjected to an oscillation of the direction of the approach flow resulting in the oscillation of the position of the stagnation line on the leading edge of the blade. In this study an experimental facility was developed that induced a similar oscillation of the stagnation line position on a simulated turbine blade leading edge. The overall effectiveness was evaluated at various blowing ratios and stagnation line oscillation frequencies. The location of the stagnation line on the leading edge was oscillated to simulate a change in angle of attack between α = ± 5° at a range of frequencies from 2 to 20 Hz. These frequencies were chosen based on matching a range of Strouhal numbers typically seen in an engine due to oscillations caused by passing wakes. The blowing ratio was varied between M = 1, M = 2, and M = 3. These experiments were carried out at a density ratio of DR = 1.5 and mainstream turbulence levels of Tu ≈ 6%. The leading edge model was made of high conductivity epoxy in order to match the Biot number of an actual engine airfoil. Results of these tests showed that the film cooling performance with an oscillating stagnation line was degraded by as much as 25% compared to the performance of a steady flow with the stagnation line aligned with the row of holes at the leading edge.

scholarly journals Film Cooling From Spanwise Oriented Holes in Two Staggered Rows

1995 ◽  
Author(s):  
Phillip M. Ligrani ◽  
Anthony E. Ramsey
Keyword(s):  
Film Cooling ◽  
Density Ratio ◽  
Flux Ratio ◽  
Test Surface ◽  
Spanwise Direction ◽  
Transfer Coefficients ◽  
Blowing Ratio ◽  
Streamwise Location ◽  
Adiabatic Effectiveness ◽  
Lift Off

Adiabatic effectiveness and iso-energetic heat transfer coefficients are presented from measurements downstream of film-cooling holes inclined at 30 degrees with respect to the test surface in spanwise/normal planes. With this configuration, holes are spaced 3d apart in the spanwise direction and 4d in the streamwise direction in two staggered rows. Results are presented for an injectant to freestream density ratio near 1.0, and injection blowing ratios from 0.5 to 1.5. Spanwise-averaged adiabatic effectiveness values downstream of the spanwise/normal plane holes are significantly higher than values measured downstream of simple angle holes for x/d<25–70 (depending on blowing ratio) when compared for the same normalized streamwise location, blowing ratio, and spanwise and streamwise hole spacings. Differences are principally due to different coalescence of injectant accumulations from the two different rows of holes, as well as significantly different lift-off dependence on momentum flux ratio. Spanwise-averaged iso-energetic Stanton number ratios are somewhat higher than ones measured downstream of other simple and compound angle configurations studied. Values range between 1.0 and 1.41, increase with blowing ratio at each streamwise station, and show little variation with streamwise location for each value of blowing ratio tested.

Liquid Jets in Subsonic Air Crossflow at Elevated Pressure

2014 ◽  
Vol 137 (4) ◽  
Author(s):  
Jinkwan Song ◽  
Charles Cary Cain ◽  
Jong Guen Lee
Keyword(s):  
Weber Number ◽  
Momentum Flux ◽  
Drop Size ◽  
Density Ratio ◽  
Flux Ratio ◽  
Mie Scattering ◽  
Air Pressure ◽  
Scattering Intensity ◽  
Nozzle Orifice ◽  
Momentum Flux Ratio

The breakup, penetration, droplet size, and size distribution of a Jet A-1 fuel in air crossflow has been investigated with focus given to the impact of surrounding air pressure. Data have been collected by particle Doppler phased analyzer (PDPA), Mie-scattering with high speed photography augmented by laser sheet, and Mie-scattering with intensified charge-coupled device (ICCD) camera augmented by nanopulse lamp. Nozzle orifice diameter, do, was 0.508 mm and nozzle orifice length to diameter ratio, lo/do, was 5.5. Air crossflow velocities ranged from 29.57 to 137.15 m/s, air pressures from 2.07 to 9.65 bar, and temperature held constant at 294.26 K. Fuel flow provides a range of fuel/air momentum flux ratio (q) from 5 to 25 and Weber number from 250 to 1000. From the results, adjusted correlation of the mean drop size has been proposed using drop size data measured by PDPA as follows: (D0/D32)=0.267Wea0.44q0.08(ρl/ρa)0.30(μl/μa)-0.16. This correlation agrees well and shows roles of aerodynamic Weber number, Wea, momentum flux ratio, q, and density ratio, ρl/ρa. Change of the breakup regime map with respect to surrounding air pressure has been observed and revealed that the boundary between each breakup modes can be predicted by a transformed correlation obtained from above correlation. In addition, the spray trajectory for the maximum Mie-scattering intensity at each axial location downstream of injector is extracted from averaged Mie-scattering images. From these results, correlations with the relevant parameters including q, x/do, density ratio, viscosity ratio, and Weber number are made over a range of conditions. According to spray trajectory at the maximum Mie-scattering intensity, the effect of surrounding air pressure becomes more important in the farfield. On the other hand, effect of aerodynamic Weber number is more important in the nearfield.

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