PSE as applied to problems of secondary instability in supersonic boundary layers
- 48 Downloads
Parabolized stability equations (PSE) approach is used to investigate problems of secondary instability in supersonic boundary layers. The results show that the mechanism of secondary instability does work, whether the 2-D fundamental disturbance is of the first mode or second mode T-S wave. The variation of the growth rates of the 3-D sub-harmonic wave against its span-wise wave number and the amplitude of the 2-D fundamental wave is found to be similar to those found in incompressible boundary layers. But even as the amplitude of the 2-D wave is as large as the order 2%, the maximum growth rate of the 3-D sub-harmonic is still much smaller than the growth rate of the most unstable second mode 2-D T-S wave. Consequently, secondary instability is unlikely the main cause leading to transition in supersonic boundary layers.
Key wordsparabolized stability equations secondary instability fundamental disturbances sub-harmonic waves
Chinese Library ClassificationO357.41
2000 Mathematics Subject Classification76E09
Unable to display preview. Download preview PDF.
- Herbert Th. Subharmonic three-dimensional disturbances in unstable plane Poiseuille flows[R]. AIAA Paper 83-1759, 1983.Google Scholar
- Herbert Th. Analysis of subharmonic route to transition in boundary layer[R]. AIAA Paper 84-0009, 1984.Google Scholar
- Saric W S, Kozlov V V, Levchenko V Ya. Forced and unforced sub-harmonic resonance in boundary layer transition[R]. AIAA Paper 84-0007, 1984.Google Scholar
- Thomas A S W. Experiments on secondary instability in boundary layers[C]. In: Proc 10th US Natl Congr Appl Mech, Austin, Texas, US, 1987, 436–444.Google Scholar
- Spalart P R, Yang K S. Numerical simulation of boundary layers: part 2. ribbon-induced transition in Blasius flow[R]. NASA TM 88221, 1986, 24.Google Scholar
- Bertolotti F P. Compressible boundary layer stability analyzed with the PSE equations[R]. AIAA Paper 91-1637, 1991.Google Scholar
- Chang C L, Malik M R, Erlebacher G, Hussaini M Y. Compressible stability of growing boundary layers using parabolized stability equations[R]. AIAA Paper 91-1636, 1991.Google Scholar
- Cebeci T, Shao J P, Chen H H, Chang K C. The preferred approach for calculating transition by stability theory[C]. In: Proceeding of International Conference on Boundary and Interior Layers—Computational and Asymptotic Methods, ONERA, Toulouse, France, 2004, July.Google Scholar