8.3 Results and discussions
8.3.1 Effect of freestream stagnation enthalpy
In order to investigate the influence freestream stagnation enthalpy on critical radii of R-SWBLI, two freestream total enthalpy conditions have been considered. A flowfield with freestream en- thalpy corresponding to stagnation temperature of 1080 K, which is referred as low enthalpy conditions (Case 1), and an other flowfield of 1800 K total temperature, referred as high en- thalpy condition (Case 2), are considered for this study. The simulations are carried out for all leading edge radii cases with these two freestream conditions. Earlier studies of R-SWBLI with sharp leading edge geometry have showed that, the separation bubble size and extent of upstream influence decrease with increase in freestream stagnation enthalpy. Therefore the objective of present study is to understand the effect of same on separation bubble dynamics for blunt lead- ing edge geometry. It has been observed that, the presence of leading edge bluntness offers increased boundary layer edge static enthalpy for a given freestream total enthalpy. Hence it is interesting to study the combined effect of freestream total enthalpy and leading edge bluntness on downstream R-SWBLI.
The Mach contours of 0.5 mm blunt leading edge domain obtained with two freestream stag- nation enthalpies of present considerations are compared in figure 8.1. This figure shows that, the separation zone is wider for low enthalpy freestream as compared to high enthalpy case. This again points towards the observation that has been made with sharp leading edge case. Higher freestream enthalpy seems to be offering more stability to the boundary layer, thus delaying the separation. Figure 8.2 shows normal variation of various flow properties at representative loca- tions for better understanding of separation dynamics in case of 0.5 mm leading edge bluntness.
Sharp leading edge case profiles are also been analyzed in figure 8.2 to explore the relative ef- fect of freestream enthalpy on blunt and sharp geometries. All these profile comparisons are performed for a location of 32 mm away from the leading edge, which is the most upstream location of undisturbed boundary layer for all radii of present consideration.
Effect of freestream stagnation enthalpy 158
FIGURE8.1: Comparison of Mach contours 0.5 mm leading edge case for different freestream total enthalpies
FIGURE8.2: Comparison of boundary layer profiles for different freestream total enthalpies
The boundary layer profile comparison clearly demonstrates the influence of freestream stag- nation enthalpy on both hydrodynamic and thermal boundary layer. The streamwise velocity profiles give qualitative picture of the boundary layer thickness obtained with different stagna- tion enthalpies. It is very much clear from the velocity and temperature profiles that, thickness of thermal and hydrodynamic boundary layers decrease with increase in stagnation enthalpy for sharp leading edge case. Besides, the temperature values of both inside and outside the bound- ary layer are observed to be higher for high enthalpy flowfield as compared to low enthalpy flow. Interestingly, maximum temperature in the thermal boundary layer for blunted geometries
Effect of freestream stagnation enthalpy 159
FIGURE8.3: Effect of freestream total enthalpy on critical radii of R-SWBLI
is higher in comparison with sharp leading edge case for both enthalpies. This difference in maximum temperature of sharp and blunt leading edge cases is more prominent in case of high enthalpy flowfield. The Mach number profile comparison for sharp and bluntness cases clearly displays the significant reduction of inside and edge Mach numbers of the boundary layer with leading edge bluntness. This decrease in Mach number is mainly due to increase in static tem- perature owing to blunt leading edge. However no significant difference in the Mach profiles of low and high enthalpy flowfields has been noticed in either cases, being same freestream Mach number in both the flowfields. The bluntness based temperature boost also leads to reduction in boundary layer density. In the presence of such low density fluid particles, the boundary layer thickens and separates early.
Separation bubble size obtained for different leading edge radii for two enthalpy conditions are plotted against leading edge radius in figure 8.3. As it has been mentioned earlier, the separation zone widening can be noticed from this figure as well for all the leading edge radii cases with reduction in freestream stagnation enthalpy. Moreover the difference between the separation bubble sizes of higher and lower enthalpy flowfields is observed to be increasing with increase in leading edge radius till a radius just higher than the inversion radius. Beyond
Effect of wall temperature 160 this radius margin, the separation zone sizes of high and low enthalpy flowfield are seen to be approaching close to each other. This observation is more prominent beyond the equivalent radius zone. Interestingly the inversion and equivalent radii are also noticed to be different for two enthalpy cases. The inversion radius for high enthalpy flowfield can be seen to be lower as compared to that of low enthalpy flowfield. The equivalent radius also found to be increased to higher value with reduction in freestream stagnation enthalpy. This observation can again be correlated to boundary layer entropy layer interaction. Since both the freestream have same Mach number, the entropy layer generated for a given degree of bluntness will have almost same structure and size for any stagnation enthalpy. However the boundary layer size at all locations of the forward flat plate is higher for low enthalpy flowstream as compared to high enthalpy.
Hence complete swallowing of the entropy layer by the boundary layer would happen with slightly higher leading edge bluntness for lower freestream enthalpy case. This is the reason for the delayed reach of inversion radius in case of low enthalpy freestream. Hence on the same line, equivalent radius also increases in magnitude with decrease in stagnation enthalpy.
Therefore increase in freestream total enthalpy effect can be summarized as the lowering of both inversion and equivalent radii for a given flowfield of constant Mach number and for a given flow deflection angle. Therefore the magnitude of leading edge bluntness required for the successful implementation of this passive technique as a R-SWBLI control method reduces with increase in freestream stagnation enthalpy.