LES of shock wave / turbulent boundary layer interaction

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Introduction from the region of flow separation, the rearward foot from the region of flow reattachment. Further downstream, the reattached boundary layer reaches the decompression ramp and passes through the Prandtl–Meyer expansion. Even further downstream, the boundary layer relaxes again towards a developed zero-pressure-gradient boundary layer. In figure 1.2 separation and reattachment lines are indicated by S and R, respectively. Turbulence is amplified by interaction with a rapid compression within the boundary layer (item 1) and by direct interaction with the shock in the external flow, item 2. Note also that the shock foots spread out towards the wall due to reduced local Mach number and due to turbulent diffusion. Item 3 points to the damping of turbulent fluctuation by the interaction with the expansion wave at the expansion corner. After reattachment at the deflected part of the compression ramp a turbulent boundary layer is reestablished, item 4. Experimental and computational results, which are discussed in section 4, support the existence of pairs of large counterrotating streamwise vortices in the reattachment region, item 5. Within the area of flow separation the reverse mean flow has the character of a wall jet which exhibits indications of relaminarization, item 6. The shock-turbulence interaction in free and wall-bounded flows is reviewed by Andreopoulos et al. (2000). Turbulence amplification through shock wave interactions is a direct effect of the Rankine-Hugoniot relations applied in the instantaneous sense. In turn changing conditions in front of and behind the shock cause it to deform and oscillate. The mutual influence makes the interaction very complex. Three major factors in the interaction can be identified: mean flow compression across the shock, shock front curvature, and unsteady shock front motion. Kovasznay (1953) suggested to decompose small-amplitude fluctuations into three elementary modes of mutually independent fluctuations: vortical, acoustic, and entropic. Linear interaction analysis (LIA), developed by Ribner (1954), relates the turbulent fluctuations downstream of the shock wave with the orientation, amplitude, and length scale of incident elementary wave. LIA, assumed a small fluctuation, such that the Rankine-Hugoniot condition can be linearized, also valid in case of evident shock front deformation. On the other hand rapid distortion theory (RDT) was found inappropriate for the analysis of shock/turbulence interaction, since the shock front curvature and the shock front unsteadiness cannot be accounted for in the analysis (Lee et al., 1997). Anyiwo & Bushnell (1982) identify primary mechanisms of turbulence enhance-
5 Figure 1.2: Essential flow phenomena in compression ramp flows (for explanations see text on page 4) ment: amplification of the vorticity mode, generation of acoustic and entropy modes from the interaction, and turbulence pumping by shock oscillations. Near the decompression corner the flow experiences a short region of favorable pressure gradient, as well as stabilizing effects of convex curvature. It is found that the expansion wave / boundary layer interaction reduces the intensity of turbulent fluctuations (Smits & Wood, 1985; Zheltovodov & Yakovlev, 1986). The experimentally determined temperature/velocity correlation coefficient of about 0.8 supporting the validity of the strong Reynolds analogy (SRA) of Morkovin (1962) in this region. Furthermore, a rapid distortion analysis demonstrated reasonable agreement with the experimental results. Knight et al. (2003) provide a review of the compressible turbulent boundary layers in the compression/expansion corners. The unsteadiness of the shock is an important feature of separated flows. It was observed for different configurations: two-dimensional and swept corner interactions and wall-mounted blunt fins. The shock foot motion can be described by two primary components: a low frequency,
Page 1: Technische Universität München Le
Page 5 and 6: Contents Contents List of figures L
Page 7 and 8: List of Figures 1.1 Examples of can
Page 9: List of Tables 1.1 Streamwise dista
Page 12 and 13: X Nomenclature T u τ = U u,u 1 v,u
Page 15: Abstract XIII Well-resolved Large-E
Page 18 and 19: Introduction be computed explicitly
Page 22 and 23: Introduction large-scale motion and
Page 24 and 25: Introduction decompression corner n
Page 26 and 27: Introduction 1 23 4 567 8 9 10 11 1
Page 28 and 29: Introduction Reynolds numbers mainl
Page 30 and 31: Introduction Parameter value M ∞
Page 33 and 34: Chapter 2 Simulation method 2.1 Dom
Page 35 and 36: 19 2.2 Governing equations The comp
Page 37 and 38: 21 with a reference temperature T
Page 39 and 40: 23 (Stolz et al., 2001a). For simpl
Page 41: 25 2.7 2.65 T w 2.6 2.55 -20 -10 0
Page 44 and 45: Flat plate boundary layer The slow
Page 46 and 47: Flat plate boundary layer (a) (b) F
Page 48 and 49: Flat plate boundary layer δ 0 δ 1
Page 50 and 51: Flat plate boundary layer 1.5 1 x 3
Page 52 and 53: Flat plate boundary layer 1.5 1 x 3
Page 54 and 55: Flat plate boundary layer variation
Page 56 and 57: Compression corner flow parameter v
Page 58 and 59: Compression corner flow Figure 4.2:
Page 60 and 61: Figure 4.3: Three-dimensional mean
Page 62 and 63: Compression corner flow Figure 4.4:
Page 64 and 65: Compression corner flow computation
Page 66 and 67: Compression corner flow a longer de
Page 68 and 69: Compression corner flow 2 1.5 0 1 E
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Compression corner flow 1.8 1.5 1.2
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Compression corner flow (a) (b) (c)
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Compression corner flow (a) (e) (b)
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Compression corner flow forward-sho
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Compression corner flow tion events
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Compression corner flow 1 0.8 λ 0.
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Compression corner flow (a) (e) (b)
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Compression corner flow replacemen
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Compression corner flow 2 1.5 E2 (a
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Compression corner flow ure 4.21(c)
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Compression corner flow 2 2 1.5 1.5
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Compression corner flow 0.1 〈U〉
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Compression-decompression corner se
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Compression-decompression corner C
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Compression-decompression corner Th
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Compression-decompression corner 0
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Compression-decompression corner 14
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Compression-decompression corner 0.
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Chapter 6 Conclusions The numerical
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Appendix B Summary of compression r
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Hunt & Nixon (1995) Adams (1998), A
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Stolz et al. (2001a) Kannepalli et
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Computational details Table C.1: De
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Bibliography Bedarev, I. A., Zhelto
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Bibliography Floryan, J. M. 1991 On
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Bibliography Lee, S., Lele, S. K. &
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Bibliography Moin, P. & Kim, J. 198
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Bibliography Smits, A. J. & Wood, D
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Bibliography Yan, H., Knight, D. D.
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