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Research Papers: Fundamental Issues and Canonical Flows

An Assessment of the Two-Layer Quasi-Laminar Theory of Relaminarization Through Recent High-Re Accelerated Turbulent Boundary Layer Experiments

[+] Author and Article Information
Rajesh Ranjan

Mem. ASME
Jawaharlal Nehru Centre for
Advanced Scientific Research,
Bangalore 560064, India
e-mail: rajesh@jncasr.ac.in

Roddam Narasimha

Jawaharlal Nehru Centre for
Advanced Scientific Research,
Bangalore 560064, India
e-mail: roddam@jncasr.ac.in

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received January 27, 2017; final manuscript received June 6, 2017; published online August 25, 2017. Assoc. Editor: Pierre E. Sullivan.

J. Fluids Eng 139(11), 111205 (Aug 25, 2017) (10 pages) Paper No: FE-17-1058; doi: 10.1115/1.4037059 History: Received January 27, 2017; Revised June 06, 2017

The phenomenon of relaminarization is observed in many flow situations, including that of an initially turbulent boundary layer (TBL) subjected to strong favorable pressure gradients (FPG). As several experiments on relaminarizing flows have indicated, TBLs subjected to high pressure gradients do not follow the universal log-law, and (for this and other reasons) the prediction of boundary layer (BL) parameters using current turbulence models has not been successful. However, a quasi-laminar theory (QLT; proposed in 1973), based on a two-layer model to explain the later stages of relaminarization, showed good agreement with the experimental data available at that time. These data were mostly at relatively low Re and hence left the precise role of viscosity undefined. QLT, therefore, could not be assessed at high-Re. Recent experiments, however, have provided more comprehensive data and extended the Reynolds number range to nearly 5 × 103 in momentum thickness. These data provide a basis for a reassessment of QLT, which is revisited here with an improved predictive code. It is demonstrated that even for these high-Re flows subjected to high acceleration, QLT provides good agreement with experimental results, and therefore, has the potential to substitute for Reynolds-averaged Navier–Stokes (RANS) simulations in high FPG regions.

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References

Figures

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Fig. 1

“Soft” relaminarization due to strong FPG. Note that the Reynolds stress does not go down in absolute magnitude in the “laminarized” region but becomes negligible compared to imposed dynamic pressure.

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Fig. 2

Velocity distribution in the relaminarizing region for various flows

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Fig. 3

Prediction using TBL code for BT-flow

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Fig. 4

Reynolds shear stress along streamlines for BT and WF2, exhibiting stress freezing in the outer parts of the BL (high values of ψ/ν)

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Fig. 5

The two-layer model. Matched asymptotic solution.

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Fig. 6

Different pressure gradient parameters proposed for the prediction of onset of relaminarization. Triangle: K = 3 × 10−6, Circle: Δp = −0.025, Square: Λ = 50 (see Table 1).

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Fig. 7

Edge velocities for outer (Ue) and inner (Us) layer calculations for BT flow. Downstream of the relaminarizing region, (Ue − Us) decreases rapidly.

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Fig. 8

Velocity gradients for BT flow. (dUe/dx)0 indicates streamwise velocity gradient at x = x0.

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Fig. 9

Uniformly valid solution using the two-layer model

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Fig. 10

Predictions for BT and WF flows using TBL and QLT. Dashed and solid thick lines represent predictions with TBL and QLT, respectively. Markers are experimental values. The shaded portion shows the laminarized region (x1 to xrt), where QLT is expected to be valid.

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Fig. 11

Comparison of velocity profiles from QLT with experiment: (a) BT at x − x0 = 0.22 m and (b) WF4 at x − x0 = 0.245 m

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Fig. 12

BL Reynolds numbers in the BT-flow

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Fig. 13

BL Reynolds numbers in the laminarized region in other studies

Tables

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