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Research Papers: Fundamental Issues and Canonical Flows

Toward Cost-Effective Boundary Layer Transition Computations With Large-Eddy Simulation

[+] Author and Article Information
Solkeun Jee

School of Mechanical Engineering,
Gwangju Institute of Science
and Technology (GIST),
123 Cheomdan-gwagi-ro, Buk-gu,
Gwangju 61005, South Korea
e-mail: sjee@gist.ac.kr

Jongwook Joo

United Technologies Research Center (UTRC),
411 Silver Lane,
East Hartford, CT 06108
e-mails: jooj@utrc.utc.com;
jw.joo@samsung.com

Ray-Sing Lin

United Technologies Research Center (UTRC),
411 Silver Lane,
East Hartford, CT 06108
e-mails: linr@utrc.utc.com;
ray_sing@hotmail.com

1Corresponding author.

2Present address: Samsung Electronics, 129 Samsung-ro, Yeongtong-gu, Suwon-si 16677, Gyeonggi-do, South Korea.

3Present address: Reliable Solutions Corporation, 49 Bayberry Road, Glastonbury, CT 06033.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received November 26, 2017; final manuscript received March 6, 2018; published online May 18, 2018. Assoc. Editor: Praveen Ramaprabhu.

J. Fluids Eng 140(11), 111201 (May 18, 2018) (12 pages) Paper No: FE-17-1757; doi: 10.1115/1.4039865 History: Received November 26, 2017; Revised March 06, 2018

An efficient large-eddy simulation (LES) approach is investigated for laminar-to-turbulent transition in boundary layers. This approach incorporates the boundary-layer stability theory. Primary instability and subharmonic perturbations determined by the boundary-layer stability theory are assigned as forcing at the inlet of the LES computational domain. This LES approach reproduces the spatial development of instabilities in the boundary layer, as observed in wind tunnel experiments. Detailed linear growth and nonlinear interactions that lead to the H-type breakdown are well captured and compared well to previous direct numerical simulation (DNS). Requirements in the spatial resolution in the transition region are investigated with connections to the resolution in turbulent boundary layers. It is shown that the subgrid model used in this study is apparently dormant in the overall transitional region, allowing the right level of the growth of small-amplitude instabilities and their nonlinear interactions. The subgrid model becomes active near the end of the transition where the length scales of high-order instabilities become smaller in size compared to the given grid resolution. Current results demonstrate the benefit of the boundary-layer forcing method for the computational cost reduction.

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Figures

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Fig. 1

Schematic diagram of a transition mechanism and the current boundary-layer forcing method based on the linear stability theory. The region of interest in this paper is depicted with the enclosed box.

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Fig. 3

Grid resolution on the flat plate for current LES computations on the fine ((a) and (b)) and the medium grids ((c) and (d))

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Fig. 2

Schematic diagram of computational domain for the flat plate case with LES with the BL forcing method. The grid resolution associated with the fine grid is used in this diagram.

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Fig. 4

Tollmien–Schlichting wave at inlet: (a) streamwise u1,0o(y,t) and (b) wall-normal v1,0o(y,t) components normalized by the amplitude A1,0

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Fig. 5

Profiles of amplitudes (a) and phases (b) of the shape function u_̂1,0o(y) for the fundamental wave at the inlet

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Fig. 6

Subharmonic oblique wave on the inlet yz plane. Streamwise u1/2,0o(y,z,t) and spanwise w1/2,0o(y,z,t) components are normalized by the amplitudeA1/2,0.

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Fig. 7

Profiles of amplitudes (a) and phases (b) of the shape function u_̂1/2,1o(y) for the subharmonic wave at the inlet

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Fig. 8

Instantaneous flow structures in the laminar-to-turbulent boundary layer, visualized by isosurfaces of the second invariant of the velocity gradient tensor, Q, colored by the streamwise velocity ũ: (a) 3D view on the boundary layer and (b) top view to the transitional region showing Λ vortices staggered in the streamwise direction

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Fig. 14

Wall-normal distribution of amplitude ((a) and (b)) and phase ((c) and (d)) of the fundamental u¯̂1,0(y) and subharmonic wave u¯̂1/2,1(y) at Rex=610 and the midspan z = 0. The fine grid is used for the current LES case.

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Fig. 15

Spatial development of instability modes at y/δ=0.26 in the current LES computation with the fine grid and the experiment [16]

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Fig. 16

Growth of instability modes from the current LES computation with the fine grid

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Fig. 13

Evolution of the velocity profiles in the transitional boundary layer. The reference velocity is the freestream velocity in (a) and the local friction velocity in (b).

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Fig. 9

(a) Skin friction compared to the DNS data [26] and theoretical value for laminar and turbulent boundary layers. (b) Skin friction predicted from current LES computations with the BL forcing on the fine, medium and coarse grids.

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Fig. 10

Relative computational cost based on grid counts in current LES computations and the DNS study of Sayadi et al. [26]

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Fig. 11

Top view for the instantaneous wall-normal velocity ṽ on the y=0.76δo plane from the three grids

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Fig. 12

Top view for the instantaneous eddy viscosity νt on the y=0.76δo plane from the three grids

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Fig. 17

One-dimensional frequency spectra of streamwise velocity Euu at y/δo=0.78 (y/δ∼0.25 for Rex=700–750; y+∼80 for Rex=800–850)

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Fig. 18

Growth of instability modes on three grids: fine (solid curves), medium (dashed curves), and coarse (dotted curves)

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