2 results
Numerical investigation of the nonlinear transition regime in a Mach 2 boundary layer
- CHRISTIAN S. J. MAYER, STEFAN WERNZ, HERMANN F. FASEL
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- Journal:
- Journal of Fluid Mechanics / Volume 668 / 10 February 2011
- Published online by Cambridge University Press:
- 26 November 2010, pp. 113-149
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The transition process in a supersonic flat-plate boundary layer at Mach 2 is investigated numerically using linear stability theory (LST) and direct numerical simulations (DNS). The experimental investigations by Kosinov and his co-workers serve as a reference and provide the physical conditions for the numerical set-up. In these experiments, the weakly nonlinear regime of transition was studied. This led to the discovery of asymmetric subharmonic resonance triads, which appear to be relevant for transition in a Mach 2 boundary layer. These triads were composed of one primary oblique wave of frequency 20kHz and two oblique subharmonic waves of frequency 10kHz. While the experimentalists have focused on this new breakdown mechanism, we have found that the experimental data also indicate the presence of another mechanism related to oblique breakdown. This might be the first experimental evidence of the oblique breakdown mechanism in a supersonic boundary layer. With the simulations presented here, the possible presence of oblique breakdown mechanisms in the experiments is explored by deliberately suppressing subharmonic resonances in the DNS and by comparing the numerical results with the experimental data. The DNS results show excellent agreement with the experimental measurements for both linear and nonlinear transition stages. Most importantly, the results clearly show the characteristic features of oblique breakdown. In addition, we also investigated the subharmonic transition route using LST and DNS. When forcing both the subharmonic and the fundamental frequencies in the DNS, a subharmonic resonance mechanism similar to that in the experiments can be observed.
1 - Jets and mixing layers
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- By M. M. Koochesfahani, P. E. Dimotakis, M. Gharib, P. Derango, E. Villermaux, H. Rehab, E. J. Hopfinger, D. E. Parekh, W. C. Reynolds, M. G. Mungal, T. Loiseleux, J.-M. Chomaz, T. F. Fric, A. Roshko, S. P. Gogineni, M. M. Whitaker, L. P. Goss, W. M. Roquemore, S. Wernz, H. F. Fasel, S. Gogineni, C. Shih, A. Krothapalli
- M. Samimy, Ohio State University, K. S. Breuer, Brown University, Rhode Island, L. G. Leal, University of California, Santa Barbara, P. H. Steen, Cornell University, New York
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- Book:
- A Gallery of Fluid Motion
- Published online:
- 25 January 2010
- Print publication:
- 12 January 2004, pp 1-10
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Summary
Laser-induced fluorescence (LIF) diagnostics and highspeed, real-time digital image acquisition techniques are combined to map the composition field in a water mixing layer. A fluorescent dye, which is premixed with the lowspeed freestream fluid and dilutes by mixing with the highspeed fluid, is used to monitor the relative concentration of high-speed to low-speed fluid in the layer.
The three digital LIF pictures shown here were obtained by imaging the laser-induced fluorescence originating from a collimated argon ion laser beam, extending across the transverse dimension of the shear layer, onto a 512–element linear photodiode array. Each picture represents 384 contiguous scans, each at 400 points across the layer, for a total of 153 600 point measurements of concentration. The vertical axis maps onto 40 mm of the transverse coordinate of the shear layer, and the horizontal axis is time increasing from right to left for a total flow real time of 307 msec. The pseudocolor assignment is linear in the mixture fraction (ξ) and is arranged as follows: red-unmixed fluid from the low-speed stream (ξ=0); blue-unmixed fluid from the high-speed stream (ξ=1); and the rest of the spectrum corresponds to intermediate compositions.
Figures 1 and 2, a single vortex and pairing vortices, respectively, show the composition field before the mixing transition. The Reynolds number based on the local visual thickness of the layer and the velocity difference across the layer is Re=1750 with U2/U1=0.46 and U1=13 cm/sec. Note the large excess of high-speed stream fluid in the cores of the structures.