7.3 Numerical studies
7.3.2 Studies with blunt leading edge plate for R-SWBLI
Studies with blunt leading edge plate for R-SWBLI 133 that the present studies belong to the strong interaction case.
FIGURE 7.5: Comparison of wall pressure distribution on the plate portion of the model with viscous interaction theories
Studies with blunt leading edge plate for R-SWBLI 134 an optimum grid level that offer grid independent solution. Such mesh independent results are considered for analysis of R-SWBLI. Similar mesh refinement and mesh independence studies are carried out for all the radii under consideration. Different levels of quadrilateral meshes are employed for these studies as well. The details of the computational domains employed for blunt leading edge studies are also given in table7.2
FIGURE 7.6: Computational domain of representative blunt leading edge (Rn=0.5 mm) case marked with boundary conditions
Grid independent Mach number contours for the reference case and leading edge bluntness of 0.5 mm are as shown in figure 7.8. Completely different aerodynamics can be noticed with leading edge radius, even at upstream of the ramp. The foremost change that can be evidenced is the replacement of attached weak leading edge shock for the reference test case by the strong detached bow shock ahead of the blunt plate. Such a shock pattern alters the flow properties where Mach number and flow velocity decrease while temperature and pressure increase in the shock layer. Presence of entropy layer is also inevitable for such blunted configurations. The characteristic features of the shock layer are thus largely dependent on interaction of boundary layer with this entropy layer. These changes affect the downstream viscous-inviscid interaction.
The variation of pressure along the wall, for different leading edge radii, is shown in figure 7.9.
Increase in favorable pressure gradient along the plate, with increase in leading edge radius, is evident from this figure. Besides, increase in upstream influence pressure and decrease in peak
Studies with blunt leading edge plate for R-SWBLI 135
FIGURE7.7: Skin friction distribution for various mesh sizes in case ofRn=0.5 mm
FIGURE7.8: Comparison of Mach contours for (a) blunt leading edge case and (b) sharp leading edge reference case
pressure on the ramp, with increased leading edge bluntness, is also clear here. Distribution of skin friction coefficient (Cf) and Stanton number (St) along the wall, shown in figure 7.10 and figure 7.11 respectively, confirms the observations of pressure plot. Sudden decrease in surface heat flux beyond the upstream influence location is evident from figure 7.11 for all
Studies with blunt leading edge plate for R-SWBLI 136 bluntness radii. It can as well be observed that the reduction in peak heat flux on the ramp portion of the model exhibits same trend as that of the peak pressure with increase in leading edge radius. Furthermore, separation point and reattachment point can be located from figure 7.10 as the points where distribution of skin friction coefficient crosses zero line. Variation of these two locations for different leading edge radii is plotted in figure 7.12. It can be noticed here that, the separation point moves upstream with initially increase in leading edge radii, whereas reattachment point shifts downstream for the initial change in radius. However, this trend reverses betweenRn=0.3 mm and 0.6 mm of leading edge bluntness. Length of separation bubble can be evaluated from these locations since it is defined as the stream-wise distance between separation and reattachment point. Thus obtained separation bubble size, for all the radii under consideration, is plotted in figure 7.13.
0.02 0.04 0.06 0.08 0.1 0.12
1 2 3 4 5 6 7 8
x (m)
p/p ∞
0.020.040.060.080.1 2 4 68
X (m) P/P inf
Sharp Rn=0.1mm Rn=0.3mm Rn=0.5mm Rn=1.0mm Rn=1.5mm Rn=2.0mm
FIGURE7.9: Comparison of surface pressure distributions for various leading edge radii
In this figure, separation bubble size is non-dimensionalised using the reference length scale as the distance between leading edge and upstream influence start location (x0). Choice of this length scale is mainly due to its direct correlation with the boundary layer thickness at upstream influence location [20]. Here the separation bubble size is first seen to increase with increase in
Studies with blunt leading edge plate for R-SWBLI 137
0.02 0.04 0.06 0.08 0.1 0.12
−2 0 2 4 6 8 10 12 14x 10−3
x (m)
C f
0 0.050.1 0
5 10
x 10Sharp−3 Rn=0.1mm Rn=0.3mm Rn=0.5mm Rn=1.0mm Rn=1.5mm Rn=2.0mm
FIGURE7.10: Comparison of skin friction distributions for various leading edge radii
0.02 0.04 0.06 0.08 0.1 0.12 0
0.002 0.004 0.006 0.008 0.01 0.012 0.014
x (m)
St
0.020.040.060.080.1 0 0.01 0.02
X (m) Sharp Rn=0.1mm Rn=0.3mm Rn=0.5mm Rn=1.0mm Rn=1.5mm Rn=2.0mm
FIGURE7.11: Comparison of Stanton number distributions for various leading edge radii
Effect of governing parameters on R-SWBLI with leading edge bluntness 138 leading edge radius till the first critical radius. This radius can be termed as ’inversion radius’, since it represents the maximum separation bubble size for given geometry and freestream con- ditions. Although separation bubble size decreases beyond the inversion radius, its magnitude is still greater than the reference separation bubble size till the leading edge radius reaches to a second critical value. This critical radius can be termed as ’equivalent radius’ for which sepa- ration bubble size is same as that of the reference case of sharp leading edge plate. A smaller separation zone in comparison with the reference case is observed for leading edge radii greater than the equivalent radius and hence this range of radii must be chosen for implementation of separation control.
FIGURE7.12: Variation of Separation and reattachment locations for various leading edge radii (BL is boundary layer and HEL is high entropy layer)