Effect of suction and cooling on the stability of subsonic and supersonic boundary layers
An investigation is conducted into the effect of cooling and suction on the stability of subsonic flows over two-dimensional roughness elements and supersonic flows over flat plates. First, the effect of wall cooling on the two-dimensional linear stability of subsonic flows over two-dimensional surface imperfections is investigated. Results are presented for flows over smooth humps and backward-facing steps with Mach numbers up to 0.8. The results show that, whereas cooling decreases the viscous instability, it increases the shear-layer instability and hence it increases the growth rates in the separation region. The coexistence of more than one instability mechanism makes a certain degree of wall cooling most effective. For the Mach numbers 0.5 and 0.8, the optimum wall temperatures are about 80% and 60% of the adiabatic wall temperature, respectively. Increasing the Mach number decreases the effectiveness of cooling slightly and reduces the optimum wall temperature.
Second, the effect of suction on the stability of compressible flows over backward-facing steps is investigated. Mach numbers up to 0.8 are considered. As expected, suction considerably reduces the separation region. The results show that continuous suction stabilizes the flow outside the separation bubble, as expected, but it destabilizes the flow inside it. Nevertheless, the overall N factor decreases as the suction level increases. This is due to the considerable reduction in the separation bubble. For the same suction flow rate, properly distributed suction strips are more effective in stabilizing the flow than continuous-suction distributions. Furthermore, the size of the separation bubble, and hence its effect on the instability, can be considerably reduced by placing strips with high suction velocities in the separation region
Third, the effect of suction on the stability of supersonic and hypersonic boundary layers is investigated. Calculations are performed for non-similar and self-similar boundary layers. The variation of the maximum growth rate with Mach number at low levels of suction is different from that at high levels of suction. This is due to the coexistence of viscous and inviscid instability mechanisms in supersonic and hypersonic boundary layers. Suction is more effective in stabilizing the viscous instability, and hence it is more effective at low Mach numbers. Although suction decreases the maximum growth rate of second-mode waves, small levels of suction increase the growth rates of disturbances having certain frequencies. On the other hand, first-mode waves are stabilized by suction at all frequencies. Constant-suction distributions considerably move the critical Reynolds numbers of second-mode waves to higher values while the critical Reynolds numbers of first-mode waves are not sensitive to suction.