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Special Section Articles

Direct Numerical Simulation and Large Eddy Simulation of Laminar Separation Bubbles at Moderate Reynolds Numbers

[+] Author and Article Information
Francois Cadieux

Department of Aerospace &
Mechanical Engineering,
University of Southern California,
Los Angeles, CA 90089
e-mail: cadieux@usc.edu

Julian A. Domaradzki

Professor

Department of Aerospace &
Mechanical Engineering,
University of Southern California,
Los Angeles, CA 90089
e-mail: jad@usc.edu

Taraneh Sayadi

Center for Turbulence Research,
Stanford University,
Stanford, CA 94305
e-mail: talashirazi@gmail.com

Sanjeeb Bose

Center for Turbulence Research,
Stanford University,
Stanford, CA 94305
e-mail: stbose@stanford.edu

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received October 22, 2012; final manuscript received February 14, 2013; published online April 28, 2014. Assoc. Editor: Ye Zhou.

J. Fluids Eng 136(6), 060902 (Apr 28, 2014) (5 pages) Paper No: FE-12-1528; doi: 10.1115/1.4023787 History: Received October 22, 2012; Revised February 14, 2013

Flows over airfoils and blades in rotating machinery for unmanned and microaerial vehicles, wind turbines, and propellers consist of different flow regimes. A laminar boundary layer near the leading edge is often followed by a laminar separation bubble with a shear layer on top of it that experiences transition to turbulence. The separated turbulent flow then reattaches and evolves downstream from a nonequilibrium turbulent boundary layer to an equilibrium one. Typical Reynolds-averaged Navier–Stokes (RANS) turbulence modeling methods were shown to be inadequate for such laminar separation bubble flows (Spalart and Strelets, 2000, “Mechanisms of Transition and Heat Transfer in a Separation Bubble,” J. Fluid Mech., 403, pp. 329–349). Direct numerical simulation (DNS) is the most reliable but is also the most computationally expensive alternative. This work assesses the capability of large eddy simulations (LES) to reduce the resolution requirements for such flows. Flow over a flat plate with suitable velocity boundary conditions away from the plate to produce a separation bubble is considered. Benchmark DNS data for this configuration are generated with the resolution of 59 × 106 mesh points; also used is a different DNS database with 15 × 106 points (Spalart and Strelets, 2000, “Mechanisms of Transition and Heat Transfer in a Separation Bubble,” J. Fluid Mech., 403, pp. 329–349). Results confirm that accurate LES are possible using O(1%) of the DNS resolution.

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Figures

Grahic Jump Location
Fig. 1

Physical domain, boundary, and inlet conditions used to investigate laminar separation bubble flow

Grahic Jump Location
Fig. 2

Normalized wall-normal velocity top boundary condition (V/U0 at Y = 1): S & S 2000 [5] (circles) and UDNS (dashed line). Normalized mean streamwise difference from freestream velocity ((U − U0)/U0 at Y = 1): UDNS (line).

Grahic Jump Location
Fig. 3

Isosurfaces of vorticity: Kelvin–Helmholtz rolls are visible over the separated shear layer leading to transition to turbulence and subsequent turbulent flow reattachment, closing of the separation bubble

Grahic Jump Location
Fig. 4

Contour plot of normalized average streamwise velocity U/U0 from the UDNS case. Notice the laminar boundary layer growth followed by a clear separation bubble spanning from x = 2.8 to x ≈ 4.6.

Grahic Jump Location
Fig. 5

Coefficient of pressure at the wall. DNS (circles), LES with dynamic Smagorinsky model (line), and UDNS (dashed line).

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Fig. 6

Wall coefficient of friction. DNS (circles), LES with dynamic Smagorinsky model (line), and UDNS (dashed line).

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Fig. 7

Total energy decay in turbulent boundary layer following the LSB as a function of time. UDNS (squares), UDNS without filtering (line), UDNS without filtering and 18% larger molecular viscosity (dashed line), UDNS without filtering and 33% larger molecular viscosity (dash-dotted line).

Grahic Jump Location
Fig. 8

Total energy increase in turbulent boundary layer following the LSB as a function of time. UDNS (squares), UDNS without filtering (line), UDNS without filtering and 18% larger molecular viscosity (dashed line), UDNS without filtering and 33% larger molecular viscosity (dash-dotted line).

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