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Research Papers: Flows in Complex Systems

# Identification of Bypass Transition Onset Markers Using Direct Numerical Simulation

[+] Author and Article Information
Shanti Bhushan, S. Muthu

Department of Mechanical Engineering,
Mississippi State University,
Starkville, MS 39762

D. Keith Walters

School of Aerospace and
Mechanical Engineering,
University of Oklahoma,
Norman, OK 73019

Crystal L. Pasiliao

Air Force Research Lab (AFRL),
Eglin Air Force Base, FL 32542

1Only key references are cited due to space limitations.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received March 16, 2017; final manuscript received May 9, 2018; published online June 13, 2018. Assoc. Editor: Elias Balaras.This work is in part a work of the U.S. Government. ASME disclaims all interest in the U.S. Government's contributions.

J. Fluids Eng 140(11), 111107 (Jun 13, 2018) (9 pages) Paper No: FE-17-1164; doi: 10.1115/1.4040299 History: Received March 16, 2017; Revised May 09, 2018

## Abstract

Efficacy of several large-scale flow parameters as transition onset markers are evaluated using direct numerical simulation (DNS) of boundary layer bypass transition. Preliminary results identify parameters $(k2D/ν)$ and $u′/U∞$ to be a potentially reliable transition onset marker, and their critical values show less than 15% variation in the range of Re and turbulence intensity (TI). These parameters can be implemented into general-purpose physics-based Reynolds-averaged Navier–Stokes (RANS) models for engineering applications.

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## References

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## Figures

Fig. 1

Initial turbulence for Reτ = 590, TI = 2% simulation is shown using: (a) isosurface of Q = 0.3, colored using streamwise velocity fluctuation (u') and (b) variation of planar-averaged TI with wall distance

Fig. 2

Temporal evolution of wall shear stress, τw, for (a) Reτ = 590, TI = 1% (case #4) with respect to nondimensional flow time, and (b) FP, TI = 3.5% (case #11) with respect to nondimensional flow time. (c) Evolution of Cf with respect to spatial coordinates, Rex for both channel flows (Re180, Re590) and FP simulations. The skin friction growth is compared with analytic profiles in laminar (Cf=0.664/Rex) and turbulent (Cf=0.131Rex−1/6) regions, and with flat-plate experimental data T3A for TI = 3% [24]. (d) Growth of momentum thickness in the transition region for Reτ = 590, TIs = 2% and 3%, and FP, TI = 2.8% simulations are compared with flat-plate boundary layer experimental data T3A corresponding to TI = 3% and case T3B corresponding to TI = 6%.

Fig. 3

Profiles of (a) mean velocity and (b) streamwise velocity fluctuations in pretransition, transition, and turbulent regions predicted for Reτ = 590, TI = 2% (C-Re590), and FP, TI = 2.8% are compared with flat-plate DNS results for TI = 3% [12] (JD), and Moser et al. [18] (Moser) plane channel DNS at Reτ = 590 results in the fully developed turbulent region. For channel flow case, Rex = 1.7 × 105 (Re1.7e5) and Rex = 1.9 × 105 (Re1.9e5) are in the pretransition region; Rex = 2.1 × 105 (Re2.1e5) to 2.4 × 105 (Re2.4e5) are in the transition region; and Rex = 2.9 × 105 (Re2.1e5) is in the fully developed turbulent region. For FP simulations and Jacob and Durbin [12] DNS, Reθ = 177 (Re177) is in the pretransition region; Reθ = 323 (Re323) to 456 (Re456) are in the transition region; and Reθ = 897 (Re897) to 980 (Re980) are in the fully developed turbulent region.

Fig. 4

Vortical structures are shown using isosurface of Q, colored using streamwise vorticity ωx for Reτ = 590, TI = 2% (case #5). Structures predicted in the pretransition region at Rex = 1.61 × 105 obtained in (a) small domain (case #5) and (b) large domain (case #8). Structures predicted on small domain (case #5) in the (b) early transition region at Rex = 2 × 105 and (c) fully developed turbulent region at Rex = 2.8 × 105.

Fig. 5

(a) Growth of peak velocity fluctuations u′2,v′2,andw′2. The vertical dotted line shows the transition onset location. The thick broken line shows that u′2 grows linearly with Rex in the transition region. Budget for (b) u′, (c) v′, and (d) w′ for Reτ =590, TI =2% (case #5). Plots on the left panel show the variation of the integral values of the budget terms against Rex. The plots on the right show the profiles of the budget terms in the boundary layer during transition (Rex = 2.3 × 105). The stresses are normalized uτ02, the integral budget terms are normalized using uτ04/ν, and the budget profiles are normalized using local uτ4/ν.

Fig. 6

Evolution of parameters k/νω, k2D/νω, and ky/ν during transition (leftmost panel) and their near-wall profiles in pretransition, transition onset, and turbulent regions. Results are presented for (a) Reτ = 590, TI = 1% (case #4); (b) Reτ = 590, TI = 2% (case #5); and (c) flat-plate boundary layer, TI = 2.8% (case #10) simulations.

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