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Research Papers: Fundamental Issues and Canonical Flows

# Investigation of Turbulent Boundary Layer Flow Over 2D Bump Using Highly Resolved Large Eddy Simulation

[+] Author and Article Information
Dalibor Cavar

Department of Mechanical Engineering,  Technical University of Denmark, Kgs. Lyngby, 2800, Denmarkdaca@win.dtu.dk

Knud Erik Meyer

Department of Mechanical Engineering,  Technical University of Denmark, Kgs. Lyngby, 2800, Denmarkkem@mek.dtu.dk

$Δx+<100$, $Δz+<20$ and $Δymin+≤1$ with at least five grid points inside $y+<10$.

$FLT:$ flow-through time $tFLT=Lx/U∞=4Lc/U∞$.

Determined by integration of the mean streamwise velocity profile.

From Fig. 6 effects of the $Reθ$ -number dependence in interval $300≤Reθ≤670$ can directly be seen.

Those measurements are taken with no bump mounted.

The measurement database only includes statistical data for $U$, $V$, $urms$ and $νrms$.

J. Fluids Eng 133(11), 111204 (Nov 11, 2011) (12 pages) doi:10.1115/1.4005262 History: Received March 07, 2011; Revised October 04, 2011; Published November 11, 2011; Online November 11, 2011

## Abstract

A large eddy simulation (LES) study of turbulent non-equilibrium boundary layer flow over $2D$ Bump, at comparatively low Reynolds number $Reh=U∞h/ν=1950$, was conducted. A well-known LES issue of obtaining and sustaining turbulent flow inside the computational domain at such low Re, is addressed by conducting a precursor calculation of the spatially developing boundary layer flow. Those results were subsequently used as turbulent inflow database for the main non-equilibrium boundary layer flow computation. The Sagaut (Rech. Aero., pp. 51–63, 1996) sub grid scale (SGS) turbulence model, based on a local estimate of the subgrid scale turbulent kinetic energy $ksgs$ and implicit damping of turbulent SGS viscosity $νt(sgs)$ in the near-wall region, was selected as a suitable basis for the present LES computations due to the fact that block structured MPI parallelized CFD code used in the current computations did not provide a direct possibility for wall-damping of, e.g., the Smagorinsky constant in the near-wall region. The grid utilized in the main calculation consisted of approximately 9.4 × 106 grid points and the boundary layer flow results obtained, regarding both mean flow profiles and turbulence quantities, showed a good agreement with the available laser Doppler anemometry (LDA) measurements. Analysis of the flow was directly able to identify and confirm the existence of internal layers at positions related to the vicinity of the upstream and downstream discontinuities in the surface curvature and also partially confirm a close interdependency between generation and evolution of internal layers and the abrupt changes in the skin friction, previously reported in the literature.

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## Figures

Figure 1

Schematic description of the analyzed 2D bump flow geometry. Coordinate system origin is, as indicated, located at the bump leading edge. n refers to a coordinate direction perpendicular to the wall surface. Extension of the spanwise domain, not indicated in the Figure, is Lc. Periodic boundary conditions are applied in this direction.

Figure 2

Outline of the computational setup corresponding to the considered flow case. An instantaneous streamwise velocity is visualized on three different planes: inlet, outlet and plane corresponding to the half (of the spanwise) domain width. Most boundary conditions applied in the computations, are included in the figure. Periodical boundary conditions are applied in the spanwise direction; they are not illustrated in the figure.

Figure 3

Grid distances in the wall-adjacent cells along the bottom boundary expressed in wall-units based on locally calculated friction velocity uτ

Figure 4

(a) Estimate of the Δ/η ratio based on ksgs from eddy viscosity model of Ref. [17] and (b) Ratio of the instantaneous subgrid-scale viscosity νt and the kinematic viscosity ν

Figure 5

U/U∞ at x/Lc=0.9997. Results of four different LES computations, open circles and squares – (LDA data of Ref. [1]).

Figure 6

Boundary layer simulation results

Figure 7

U/U∞. Solid lines represent LES computations, open circles and squares (LDA data of Ref. [1]).

Figure 8

V/U∞. Solid lines represent LES computations, open circles and squares – (LDA data of Ref. [1]).

Figure 9

urms/U∞. Solid lines represent LES computations, open circles and squares – (LDA data of Ref. [1]).

Figure 10

vrms/U∞. Solid lines represent LES computations, open circles and squares – (LDA data of Ref. [1]).

Figure 11

Comparison of LES results with LDA measurements corresponding to a typical measuring position (left row x/Lc=0) and the position with the highest deviations between measurements and LDA data (right row x/Lc=0.75). Solid lines represent LES computations, open circles with errorbars (LDA data of Ref. [1]).

Figure 12

Cp, Cf Skin friction and Static Pressure Coefficients. JJS refers to Experimental data of Ref. [25]. The black solid line indicates the bottom wall surface geometry, including the bump.

Figure 13

Contour plots of (a) time averaged mean streamwise velocity U superimposed by the plot of a corresponding streamline function, (b) Turbulent kinetic energy k

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