DNS and LES of Laminar Separation Bubbles at Moderate

Reynolds Numbers

Francois CadieuxPhD candidate (4th-year)

Department of Aerospace & Mechanical EngineeringUniversity of Southern CaliforniaLos Angeles, California 90089

E-mail: cadieux@usc.edu

Professor Julian A. DomaradzkiDepartment of Aerospace & Mechanical Engineering

University of Southern CaliforniaLos Angeles, California 90089

Taraneh Sayadi and Sanjeeb BoseCenter for Turbulence Research

Stanford UniversityStanford, California, 94305

March 3, 2013

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DNS and LES of Laminar Separation Bubbles at Moderate Re

Flows over airfoils and blades in rotating machinery, for unmanned and micro-aerial vehicles, windturbines, and propellers consist of different flow regimes. A laminar boundary layer near the leadingedge is often followed by a laminar separation bubble (LSB) with a shear layer on top of it thatexperiences transition to turbulence. The separated turbulent flow then reattaches and evolvesdownstream from a non-equilibrium turbulent boundary layer to an equilibrium one. In order toproduce more efficient airfoil or blade designs, to create control schemes to reduce separation effects,and to better predict HCF, numerical prediction tools for LSB flows are needed. Typical Reynolds-averaged Navier-Stokes (RANS) turbulence modeling methods were shown to be inadequate forsuch LSB flows [1]. Direct numerical simulation (DNS) is the most reliable but is also the mostcomputationally expensive alternative. Large eddy simulation (LES) results obtained with thedynamic Smagorinsky model were reported to be in good agreement with experiments for boundary-layer separation and transition due to surface curvature [2, 3], but agreement required numericalresolution comparable to DNS of the same flow and high order numerical methods. Can LESproduce sufficiently accurate results for LSB flows with drastically reduced resolution, around 1%of DNS resolution, which is commonly achievable for fully turbulent flows?

This work assesses the capability of LES to significantly reduce the resolution requirements for suchflows to enable aerodynamics-in-the-loop design optimization. Flow over a flat plate with suitablevelocity boundary conditions away from the plate to produce a LSB is considered (see Fig. 1).

Figure 1: Physical domain, boundary and inlet conditions used to investigate laminar separationbubble flow

The full compressible LES equations are solved using a sixth-order compact finite volume schemewith periodic horizontal boundary conditions [4]. An implicit scheme is used near the wall whilean explicit scheme is used outside the boundary layer. Compact filtering as described in Ref. [5] isemployed at each time step to ensure overall scheme stability and zonal matching at the interfacebetween the implicit and explicit grids [6]. Three simulations were run: a benchmark DNS case(DNS) with 59106 mesh points, a wall-resolved LES with the dynamic Smagorinsky model (LES)at 4% of DNS resolution, and a highly under-resolved DNS (UDNS) at 1% of DNS resolution.Results confirm that accurate LES are possible using O(1%) of the DNS resolution.

The wall pressure coefficients shown in Fig. 2(a) are in good agreement with the DNS. The sepa-ration point is well predicted by the wall skin friction coefficients in Fig. 2(b). The UDNS predictsthe shape and maximum value of the peak negative skin friction almost exactly. LES performs

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

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(b) Wall coefficient of friction. DNS (circles), LES withdynamic Smagorinsky model (line), and UDNS (dashedline).

slightly worse than the UDNS, but still reaches within 15% of the DNS peak negative skin friction.Reattachement is predicted within 5% of DNS. UDNS recovers almost exactly the turbulent Cf inthe region downstream of the bubble whereas LES results never recover completely. The betterperformance of the UDNS is attributed to the use of explicit filtering used to ensure the numericalstability of the code. The dissipation due to the filtering operation was investigated using tech-niques developed in Ref. [7] and was found to act as an implicit sub-grid scale model which producesnumerical viscosity on the same order of magnitude as computed dynamic Smagorinsky eddy vis-cosities for this particular simulation. The addition of another source of dissipation through explicitSGS modeling as in the LES case introduces excessive dissipation. Work is ongoing to explore theeffects of specific SGS models using non-dissipative codes for the same problem.

References

[1] P. Spalart and M. Strelets, Mechanisms of transition and heat transfer in a separation bubble,J. Fluid Mech., vol. 403, pp. 329349, Jan. 2000.

[2] Z. Yang and P. Voke, Large-eddy simulation of boundary-layer separation and transition at achange of surface curvature, J. Fluid Mech., vol. 439, pp. 305333, 2001.

[3] S. Eisenbach and R. Friedrich, Large-eddy simulation of flow separation on an airfoil at ahigh angle of attack and Re = 105 using cartesian grids, Theor. Comp. Fluid Dyn., vol. 22,pp. 213225, 2008. 10.1007/s00162-007-0072-z.

[4] T. Sayadi and P. Moin, Large eddy simulation of controlled transition to turbulence, Phys.Fluids, vol. In Press, p. 114103, 2012.

[5] S. K. Lele, Compact finite difference schemes with spectral like resolution, J. Comput. Phys.,vol. 103, pp. 1642, 1992.

[6] S. Nagarajan, Leading edge effects in bypass transition. PhD thesis, Stanford University, 2004.

[7] J. A. Domaradzki, Z. Xiao, and P. K. Smolarkiewicz, Effective eddy viscosities in implicit largeeddy simulations of turbulent flows, Phys. Fluids, vol. 15, no. 12, pp. 38903893, 2003.

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