Description of aerodynamic and heat transfer of an inclined Jet in crossflow applied to film cooling

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

Influence of Strouhal number excitation on film cooling” -23- accelerate at the downstream side. Temperature fluctuations ϑ² at the hole exit were indicated to reduce from the upstream side to the downstream side, and were shown to hold higher values for the low Reynolds number condition, figure (2.7a).

(a) (b)

Figure (2. 7): Streamwise distribution at the exit plane of pipe at different Reynolds number, R=0.5, (a) Temperature fluctuation ϑ² , (b) Turbulent heat flux in normal direction ^vϑand longitudinal

direction ^uϑ. Opened symbols: Re=20500, filled symbols: Re=41000, (Andreopoulos 1983).

The second-order temperature-velocity correlations or turbulent heat fluxes were reported to contain higher fluxes in normal direction ^vϑ, whereas the fluxes in the longitudinal direction ^uϑ has featured low values almost everywhere on the exit plane, and seemed to change sign close to the upstream edge of the pipe, figure (2.7b). Further it was mentioned that, up to 4 diameters downstream for the case of R=0.5, the temperature fluctuations and longitudinal and normal turbulence heat fluxes reached a higher values, and further downstream they decay considerably.

2.3. Description of aerodynamic and heat transfer of an inclined

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

Influence of Strouhal number excitation on film cooling” -24- o The formation of counter rotating vortex pair

o The horseshoe vortex system

o The wake region and the reverse flow o The wall vortex

In case of the inclined jet the strength of the vortex systems is comparatively low. It is to be noted that the cases of film cooling usually require the flow field inspection at lower velocity ratios compared to the normal injection, due to the variety of their practical applications.

The flow field aerodynamics due to the interaction of the two flow streams with oblique injection were studied by (Foucault et al. 1992; Pietrzyk et al. 1989; Dorignac et al.

1992; Lee et al. 1994; Walters and Leylek 2000; Guo et al. 2006; ). Pietrzyk et al (1989) used a short delivery tube (L/D=3.5) for the injectant flow and explained the evolution of the downstream flow along with the skewing of the jet exit profile, which settles towards the downstream side at low blowing ratio and moves towards the upstream side at high blowing ratio. Foucault et al. (1992) described the existence of the CVP (Counter Rotating Vortex Pair) for a 45° inclined jet and its influence on both velocity and temperature fields. Dorignac et al. (1992) studied the injectant flow dynamics downstream of a row of holes as a function of blowing ratio for a slightly heated jet flow. The computational results of Walters and Leylek (2000) traced back to the origin of vorticity leading to the CVP for an inclined jet. They also reported the appearance of small reverse flow zones immediately downstream of the trailing edge for a blowing ratio of 1 and a density ratio of 2. They nominated the streamwise vorticity originating from the lateral edges of the hole and the shearing between the jet and the mainstream flow as being the primary sources for developing the counter-rotating–

vertex pair (CVP).

Mendez and Nicoud (2006) performed the LES on effusive cooling or full-coverage film cooling, employing a model of multi-perforated wall that contained 30° cylindrical holes of a length of 4d. The descriptions of flow structures given for a blowing ratio of 1.17 have shown the presence of the number of features at different magnitudes of employed Q criterion.

Figure (2.8a) and (2.8b) shows two different views of the flow field, which indicate the following flow structures.

(1) The pair of counter-rotating vortices (CVP). The two vortices were described to originate from the lateral edges of the hole outlet and their direction of rotation is such that the fluid is pulled away from the wall at the centreline and entrained towards the wall when coming from the sides of the jet.

(2) The two counter-rotating vortices aligned with the jet were shown to present in the hole itself, which were much less intense than the earlier one.

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

Influence of Strouhal number excitation on film cooling” -25- (3) A horseshoe vortex much weaker than the one found in case of a normal jet was also shown. Consistently with the fact that the adverse pressure gradient experienced by the primary stream flow is smaller when the jet is inclined.

(4) A pair of small downstream spiral separation node vortices locating immediately downstream of the hole exit were reported to originate from the wall, where they were almost vertical, and they rapidly reoriented in the direction of the jet.

(5) A pair of suction vortices was shown near the inlet, originating as the flow enters through the sharp inlet.

(6) A small streamwise vortices lying beneath the CVP were reported to have a direction of rotation opposite to that of the CVP.

Figure (2.8c) shows author’s Q criterion results indicating the flow field dominated by shear layer vortices formed at the upstream face of the jet and also inside the hole.

(a)

(b)

(c)

Figure (2. 8): Q-criterion showing flow structures present in the time-averaged field (a) and (b), instantaneous field (c), (Mendez and Nicoud 2006)

Lee et al. (1994) studied both normal and inclined jet cases and reported the disappearance of reverse flow, lesser crossflow entrainment and stronger secondary motion

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

Influence of Strouhal number excitation on film cooling” -26- due to larger pressure gradient in wake region in the case of an inclined jet, compared to a normal jet. They mentioned that the bound vortex region lies much closer to the wall and the induced flow into the wake is much stronger in the inclined injection case than in the normal injection case. The large eddy simulations of an inclined and a normal jet issuing in the cross-stream flow were conducted by Guo et al. (2006). They noticed that the interaction between the mainstream and the jet flow is considerably reduced and the first occurrence of the vortex pair is shifted downstream for inclined jet. Figure (2.9a) and (2.9b) show the distribution of the velocity vector at the lateral plane of x/d=0.75 for a normal jet and an inclined jet respectively. The strength of the streamwise vortex is much higher for the case of a normal jet (the portion of jet flow near the tube exit was not shown for normal jet). In case of streamwise inclined jet, they observed that the separation at the leading edge of the jet hole is suppressed, which follows the vortex formation due to the streamline rollup of the freestream boundary layer due to the initial blockage from the upstream edge of the jet.

They also examined the anisotropy of the flow by using the invariant technique, and concluded that the JICF problem possesses a complicated anisotropic turbulence characterises, which is hard to be described by standard one- or two-equation models, especially for the flow field in the separation area downstream of the jet exit.

(a) (b)

Figure (2. 9): Development of counter rotating vortex pair, M=1 and x/d=0.75, (a) perpendicular jet, (b) inclined jet; Guo et al. (2006).

2.3.2 Thermal description

2.3.2.1 Fundamental parameters of film cooling analysis

Sinha & al. (1991a) provided a brief overview of the parameters that influences the film cooling performance of the coolant jet issuing in a crossflow. These include the parameters of the hole geometry and their placement on the injection wall, properties of interacting flows and the parameters of the fluid dynamics. Author summarized these parameters or the

“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