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2.3.2.3 Influence of aerodynamic parameters on wall heat transfer
“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).
“Experimental aerothermal characterization of a pulsating jet issuing in a crossflow:
Influence of Strouhal number excitation on film cooling” -32- penetrated more into the mainstream. However, further downstream the effectiveness tended to increase with the blowing ratio in some cases, where the coolant jets have been reattached to the surface.
( )
(
∞)
∞
−
= −
T T
T T
i ad
ηc ...(2. 2)
Where,
T∞ Mainstream temperature, Ti Injection temperature Tad Adiabatic wall temperature
Density Ratio
The adiabatic wall measurements by Goldstein et al. (1974) and Sinha et al. (1991a) showed that the film-cooling effectiveness strongly depends on the density ratio. For constant momentum flux ratio, jets with higher density ratio will have higher mass flux ratio, which results in greater centerline effectiveness ‘ηc’. Jessen et al. (2007) studied 30° jets of air and CO2 emanating from a pipe into a cross-stream boundary layer at different velocity ratio by using PIV technique. They examine the effects of density ratio between coolant and mainstream on the mixing behavior, as well as on cooling efficiency. Their results show that a higher velocity ratio enlarges the size of the recirculation region leading to a more pronounced entrainment of cross-flow fluid into the wake of the jet. Velocity effects dominate the flow field in the vicinity of the jet hole. However, the lateral spreading of the coolant downstream, which is crucial for the cooling efficiency, is strongly increased at a higher density ratio.
(a) (b)
Figure (2. 15): Centerline effectiveness at different density ratio, (a) M=0.5, (b) M=1.0; Sinha et al.
(1991a).
“Experimental aerothermal characterization of a pulsating jet issuing in a crossflow:
Influence of Strouhal number excitation on film cooling” -33- Figure (2.15a) and (2.15b) present some results from Sinha et al. (1991a), it is clear that at high blowing ratio ‘M ’ the phenomena of detachment and reattachment occurs.
Moreover, higher levels of centerline effectiveness ‘ηc’ seem to occur at higher density ratio.
Ratio of momentum flux
Sinha et al. (1991a) deduced from their study of a single row of holes with variable density and blowing ratios, that the flow characteristics downstream of the jet primarily depends on the momentum flux ratio ‘I’, as the jet either remains attached to the surface, detaches and then reattaches, or to become fully detached. Their studies were composed of a row of 35 degree jet with a length to diameter ratio ‘L/d’ of 3.5 and hole spacing of 3d. At I=0.2, as shown in figure (2.16a), the jet remain attached and the distribution of ‘ηc’ is nearly similar in the initial region of x/d=10, for density ratio ‘DR’ of 1.2 and 1.6. At I=0.3, figure (2.16b) shows that the jet have barely detached. Moreover, the trends of the ηcdistributions for DR=1.2 and DR=2.0 seem very similar, but ηcfor DR=1.2 is slightly lower than for DR=2.0. For I=0.5, figure (2.16c) demonstrates a clear detachment and reattachment that occurs for all density ratios. The level of ηcis consistently lower for DR=1.2 compared to the higher density ratios. They proposed that the reduced levels of ηcfor lower density ratios may be attributed to the lower blowing ratio at same momentum flux ratio.
Figure (2. 16): Centerline effectiveness in different cases of constant momentum flux ratio, (a) I=0.2, (b) I=1.3, (c) I=0.5; Sinha et al. (1991a)
Schmidt et al. (1996) have examined the film cooling effectiveness for different hole geometries as a function of momentum flux ratio ‘I’. They studied the behavior of the row of round hole with compound angle ‘CA’ at zero degree and 60 degree, and the holes with 15 degree forward expansion and a compound angle at 60°. The injection angle with respect to the test surface was 35 degree in all configurations. The intermediate space between two
“Experimental aerothermal characterization of a pulsating jet issuing in a crossflow:
Influence of Strouhal number excitation on film cooling” -34- holes ‘P’ and length to diameter ratio ‘L/d’ were 3d and 4 respectively. Figure (2.17) shows that the spatially average effectiveness η (effectiveness averaged over a particular area, Eq.
(2.3)) at low ‘I’ is quite similar for the different geometries.
Figure (2. 17): Spatially average effectiveness ηas a function of Momentum flux ratio for P/D=3;
Schmidt et al. (1996).
For the case with compound angle ‘CA’ holes at 60°, the η is higher compared with the simple angle hole and the region over which high ηexisted is also increased. The forward expanded exit holes with CA=60° maintained essentially the same level of η over the full range tested, with 0.25<I<3.9, and were significantly better than the round CA=60°
holes at the larger I. For the round CA=60 holes, ηdecreased slightly with increasing I, but still had reasonably good effectiveness at I=3.9.
(
−)(
−) ∫ ∫ ( )
= 2
1 2
1
1 ,
1 2 1 2
z
z x
x
dxdz z z x
z x
x η
η ...(2. 3)
Free-stream turbulent intensity of cross-stream flow
The effect of free-stream turbulence on the film cooling was studied by Mayhew et al.
(2003), Burd et al. (1996), Lebedev et al. (1995), Bons et al. (1995) and Marek et al. (1975).
Bons et al. (1995) studied the effects of free stream turbulence intensity along with jet pulsation to mimic the unsteadiness of real gas turbine units. High Free-stream turbulent intensity (FSTI) cases are more influenced by the freestream flow and are characterized by increased mixing downstream of the edges of the film cooling holes, which reduces the film cooling effectiveness (Burd etal. 1996).
“Experimental aerothermal characterization of a pulsating jet issuing in a crossflow:
Influence of Strouhal number excitation on film cooling” -35- Figure (2. 18): Raw images of model at various blowing rates and low and high freestream turbulence levels: (a) M=0.5, Tu=0.1%, (b) M=1.0, Tu=0.1%, (c) M=1.5, Tu=0.1%, (d) M=0.5, Tu=10%, (e) M=1.0,
Tu=10%, and (f) M=1.5, Tu=10%; Mayhew et al. (2003)
Figure (2.18a-f) shows the raw images of the color pattern achieved with the blowing ratio of M=0.5, 1 and 1.5, where free-stream flow held the turbulent intensity of Tu=0.1% and 10%
in different test configurations (Mayhew et al. 2003). In the array of subfigures given below, M varies row-wise and Tu varies column-wise. In low turbulent intensity cases (Tu=0.1%) shown in figure (2.18a-c), a thin black region between the hole are essentially unprotected.
This unprotected region increased for M=1 and 1.5 as the liftoff occurs. In high turbulent intensity cases (Tu=10%) shown in figure (2.18d-f), the injectant spreading in the lateral direction increases, which shortened the distance that the cooling air had traveled downstream in the low turbulent intensity case. It was concluded that the high freestream turbulence affects the film cooling effectiveness only slightly for a blowing ratio of M=1.5, but has significantly detrimental effects for the blowing ratios of M=0.5 and 1.0.
Boundary layer thickness of cross-stream flow
Goldstein et al. (1974) observed that the film cooling effectiveness decreases when the ratio of boundary layer thickness to injection hole diameter ‘δ/D’ increases, although the trend is diminished at large δ/D, figure (2.19).
“Experimental aerothermal characterization of a pulsating jet issuing in a crossflow:
Influence of Strouhal number excitation on film cooling” -36-
(a) (b)
Figure (2. 19): Effect of upstream boundary layer thickness on centerline film cooling effectiveness for air injecting through cylindrical holes (symbols with a mark at the centre stands for single hole, empty
symbol stands for a single row of holes) (a) M=0.5, (b) M=1.0; Goldstein et al. (1974).
The decreased in effectiveness has been attributed to the lower mainstream velocity inside the boundary layer, which permits greater penetration of the jet. Author has suggested that at a large distance downstream there should be a greater difference between the results for a single hole and a row of holes due to the merging of the jets from the row of holes. Eriksen et al. (1974) noticed that there were no significant difference between centerline film cooling effectiveness as a function of Reynolds number (using free stream velocity and injection tube diameter (ReD =ρ∞U∞D/µ∞) and the boundary layer thickness δ /D within the limit of M ≤1.0, when secondary flow is injected through a single hole or through the row of holes at 35 degree. Moreover, the physical mechanism responsible for the variation of centerline effectiveness was found to be similar as suggested by Goldstein et al. (1974).