Geometrical parameters

“Experimental aerothermal characterization of a pulsating jet issuing in a crossflow:

Influence of Strouhal number excitation on film cooling” -27- ratio of parameters as follow; coolant to mainstream density ratio (D.R.), velocity ratio (R.), mass flux ratio (M), and momentum flux ratio (I).

∞

= ρ ρi

R

D. ;

∞

=U R Uⁱ ;

∞

∞

= U

“Experimental aerothermal characterization of a pulsating jet issuing in a crossflow:

Influence of Strouhal number excitation on film cooling” -28- Figure (2. 10): Range of holes studied; Sargison & al. (2002a)

Sargison et al. (2002) compared the cooling performance of a single row of consoles with the typical 35 degree cylindrical, fan-shaped holes and slot, by employing equal throat area per unit width for each type of hole shape. In Figure (2.11a), the laterally averaged adiabatic effectiveness demonstrates that the console approaches towards the slot effectiveness, as does the fan-shaped hole effectiveness. The console laterally averaged heat transfer coefficient is similar to the slot, and higher than the cylindrical and fan-shaped holes, Figure (2.11b). The slot and console do not significantly change the boundary layer flow compared with the case of no film cooling, and hence the heat transfer coefficient is similar. The fan- shaped and cylindrical film-cooling holes appear to thicken the boundary layer and reduce the heat transfer coefficient compared with no film cooling. Author has mentioned that there is an aerodynamic penalty associated with this thickening. While, the aerodynamic loss due to a console is significantly less than for the fan-shaped or cylindrical film cooling holes.

(a) (b)

Figure (2. 11): Laterally average adiabatic effectiveness and heat transfer; Sargison et al. (2002)

Angle of injection

The effect of angle of injection on film cooling is an issue, which is by far the most studied parameter, for various hole shapes and the pattern of their placement. For a simple cylindrical type injection hole or slot, it is widely known through open literature that at the

“Experimental aerothermal characterization of a pulsating jet issuing in a crossflow:

Influence of Strouhal number excitation on film cooling” -29- higher angles the flow tends to lift off from the surface and the wall protection is significantly reduced. For every angle of injection, there exists an optimum blowing ratio (Yuen et al. 2003a). Various investigations on film cooling that employed ‘α’ as low as 0°

(tangential surface) up to high values of 90° (normal to surface) have been studied, Volchkov et al (1967), Aly (1999), Yuen et al.(3003a, b), Yuen et al.(3005a, b). It may be concluded that a lower angle jet losses a good fraction of momentum during its flow in the vicinity of the wall, while a higher injection angle lifts the jet off the surface and thus reduces the wall coverage.

Aly (1999) observed a general trend for a jet emanating from a thin slot and observed that the ratio of displacement thickness to the slot thickness (δ1/t) increases by increasing

‘α’, and its sign changes from negative to positive somewhere between α=45° to 60°. The negative (δ1/t) indicates that the jet did, not only make up for the displacement created by the boundary layer upstream of the slot, but also bring more fluid to the wall vicinity compared with the main stream. This behavior is increased by increasing blowing ratio ‘M’

for 30° and 45°, especially in the near downstream of the slot and starts to level towards the far end of the test surface, figure (2.12a) and (2.12b). In the case of higher ‘α’ (i.e, 60° and 90°), (δ1/t) acquires positive values which increases by increasing ‘α’ and/or ‘M’, figure (2.12c) and (2.12d). The shown distributions indicate that the jet could not make up for the flow deficiency in the wall region. The incoming main stream pushed the jet towards the surface, which brings more fluid to the wall vicinity, and accordingly (δ1/t) decreases gradually, until we see that the curve changes its sign in some case, which implies to the reattachment of injectant fluid towards the wall.

“Experimental aerothermal characterization of a pulsating jet issuing in a crossflow:

Influence of Strouhal number excitation on film cooling” -30- Figure (2. 12): Variation of boundary layer displacement thickness in case of different velocity ratios

(a) 0 deg, (b) 45deg, (c) 60 deg, (d) 90 degree; Aly (1999).

Effect of length to diameter ratio

The form of exit velocity profile of the secondary jet significantly depends upon the hole length-to-diameter ratios ‘L/d’, which generally are responsible for important consequences on film cooling performance. Short length-to-diameter ratios are more representative of turbine actual configurations, such as employed by Pietrzyk et al. (1989) and Walters and Leylek (2000) to an order of (L/d=3.5). With short L/d, the additional vorticities leaving the hole due to the flow separation inside the pipe plays an essential role in the formation of jet structure in the near-field.

Figure (2. 13): Centerline mean velocity profiles at the hole-exit plane with FSTI=12%; Burd et al.

(1996).

Burd et al. (1996) studied the influence of free stream turbulence intensity and hole length-to-diameter ratio on film cooling, with a streamwise injection of 35° and velocity and

“Experimental aerothermal characterization of a pulsating jet issuing in a crossflow:

Influence of Strouhal number excitation on film cooling” -31- density ratio equal to 1.0. They suggested that film cooling with low free stream turbulence intensity (FSTI) is more affected to the changes in L/d than that with high FSTI. Short-hole injection leads to the phenomena of “jetting”, where the coolant ejects further into the freestream and spreads more in the spanwise direction than with long L/d injection. With jetting, the jet velocity profile is not uniformly distributed across the majority of the plane at which it exits, but is skewed with substantially higher velocities upstream as shown in figure (2.13).