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Research Papers

# Geometrical Uncertainty and Film Cooling: Fillet Radii

[+] Author and Article Information
Francesco Montomoli, Michela Massini

Whittle Laboratory, University of Cambridge, 1 JJ Thomson Avenue, CB3 0DY, Cambridge, UK

Department of Energy Engineering, University of Florence, via S. Marta 3, 51036, Firenze, Italy

J. Turbomach 134(1), 011019 (May 31, 2011) (8 pages) doi:10.1115/1.4003287 History: Received July 06, 2010; Revised July 07, 2010; Published May 31, 2011; Online May 31, 2011

## Abstract

This study presents an investigation of the impact of filleted edge variations on heat transfer. In real gas turbines, sharp edges are an approximation because of manufacturing tolerances and/or geometrical modifications occurring during operation. The value of fillet radius is not exactly known a priori. It can be assumed that a specific radius occurs with a probability following a probabilistic distribution. For this reason, the effect of variation of the filleted edge on internal channel of a film cooling configuration has been studied numerically using an in house solver. The hole exit is fanshaped and the feeding duct axis and the main stream are perpendicular to each other. A response surface has been generated, varying the internal Mach number of coolant and the pressure ratio range between coolant and main gas. Four fillet radii for the internal duct have been analyzed, $r/D=0.0–5%$. A Gaussian distribution for the fillet radius has been assumed. Using the overmentioned distributions, it is possible to obtain the probabilistic functions of corresponding discharge coefficient Cd and adiabatic effectiveness $η$. The overall variation of Cd and $η$ can be more than 10% the value without fillet. Furthermore, the differences on Cd due to the uncertainties on fillet radius are bigger than those obtained due to modifying the exit duct shape (i.e., from cylindrical to fanshaped). This paper shows that the effect of variation of fillet radii must be included in numerical simulations. This has direct consequences on LES and DNS simulations, which normally include sharp corners or mean radii. A probabilistic approach must be included in the analysis of the results and the equivalent fillet radius must be assumed instead.

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## Figures

Figure 2

Schematic of coolant channel with fillets

Figure 3

Computational mesh and boundary conditions

Figure 4

Computational matrix, 64 CFD simulations

Figure 5

Discharge coefficient with r/D=0%

Figure 6

Comparison of η, Ptc/Pm=1.4, Mac=0.6, and Mam=0.55

Figure 7

Streamlines r/D=0% and Mac=0.15,0.30,0.45

Figure 8

Vorticity in the coolant duct

Figure 9

Isocontours of Mach number

Figure 10

Discharge coefficient for Mac=0.3 and r/D=0.0%,1.25%,2.5%,5%

Figure 11

Variations of discharge coefficient: 1.4<Ptc/Pm<2.0, 0.15<Mac<0.6, Mam=0.55, and 0<r/D<5%

Figure 12

Cd, Ptc/Pm=1.4, and Mac=0.3

Figure 13

Equivalent r/D and Cd errors with deterministic approach

Figure 14

Discharge coefficient for a mean value of r/D=0.5% and σ=1%

Figure 15

Adiabatic effectiveness for r/D=0.0% and 4.0%, Mac=0.45, Mam=0.55, and Ptc/Pm=1.4

Figure 16

Adiabatic effectiveness due to manufacturing uncertainty, Ptc/Pm=1.4 and Ptc/Pm=1.6

Figure 1

Experimental arrangement of coolant channels

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