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.

## References

1.
Jensen
,
T. B.
, 1992, “
Eksperimental Og Numerisk Studium af Turbulent Grænselæg hen over en Cylindersektion
,” Master’s thesis, (In Danish), Department of Mechanical Engineering, MEK - DTU.
2.
,
P.
, and
Ahmed
,
A.
, 1993, “
Turbulent Boundary Layers Subjected to Multiple Curvatures and Pressure Gradients
,”
J. Fluid Mech.
,
246
, pp.
503
527
.
3.
Patel
,
V. C.
, and
Sotiropoulos
,
F.
, 1997, “
Longitudinal Curvature Effects in Turbulent Boundary Layers
,”
Prog. Aerosp. Sci.
,
33
(
1–2
), pp.
1
70
.
4.
Spalart
,
P.
and
Watmuff
,
J.
, 1993, “
Experimental and Numerical Study of a Turbulent Boundary Layer With Pressure Gradients
,”
J. Fluid Mech.
,
249
, pp.
337
371
.
5.
Fernholz
,
H.
, and
Warnack
,
D.
, 1998, “
Effects of a Favourable Pressure Gradient and of the Reynolds Number on an Incompressible Axisymmetric Turbulent Boundary Layer. Part 1. The Turbulent Boundary Layer
,”
J. Fluid Mech.
,
359
, pp.
329
356
.
6.
Warnack
,
D.
, and
Fernholz
,
H.
, 1998, “
Effects of a Favourable Pressure Gradient and of the Reynolds Number on an Incompressible Axisymmetric Turbulent Boundary Layer. Part 2. The Boundary Layer With Relaminarization
,”
J. Fluid Mech.
,
359
, pp.
357
381
.
7.
Webster
,
D.
,
DeGraaff
,
D.
, and
Eaton
,
J.
, 1996, “
Turbulence Characteristics of a Boundary Layer Over a Two-Dimensional Bump
,”
J. Fluid Mech.
,
320
, pp.
53
69
.
8.
,
V.
,
Smits
,
A. J.
, and
Joubert
,
P. N.
, 1987, “
Turbulent Flow Over a Curved Hill: Part 1. Growth of an Internal Boundary Layer
,”
J. Fluid Mech.
,
182
, pp.
47
83
.
9.
,
V.
,
Smits
,
A.
, and
Joubert
,
P.
, 1991, “
Turbulent Flow Over a Curved Hill. Part 2. Effects of Streamline Curvature and Streamwise Pressure Gradient
,”
J. Fluid Mech.
,
232
, pp.
377
402
.
10.
Wu
,
X.
, and
Squires
,
K. D.
, 1998, “
Numerical Investigation of the Turbulent Boundary Layer Over a Bump
,”
J. Fluid Mech.
,
362
, pp.
229
271
.
11.
Kim
,
J.
, and
Sung
,
H. J.
, 2006, “
Wall Pressure Fluctuations and Flow-Induced Noise in a Turbulent Boundary Layer Over a Bump
,”
J. Fluid Mech.
,
558
, pp.
79
102
.
12.
Reck
,
M.
, 2005, “
Computational Fluid Dynamics, With Detached Eddy Simulation and the Immersed Boundary Technique, Applied to Oscillating Airfoils and Vortex Generators
,” Ph.D. thesis, Department of Mechanical Engineering, MEK - DTU.
13.
Gullbrand
,
J.
, and
Chow
,
F.
, 2003, “
The Effect of Numerical Errors and Turbulence Models in Large Eddy Simulations of Channel Flow, With and Without Explicit Filtering
,”
J. Fluid Mech.
,
495
, pp.
323
341
.
14.
Piomelli
,
U.
, and
Balaras
,
E.
, 2002, “
Wall-Layer Models for Large-Eddy Simulations
,”
Annu. Rev. Fluid Mech.
,
34
, pp.
349
374
.
15.
Frohlich
,
J.
,
Mellen
,
C. P.
,
Rodi
,
W.
,
Temmerman
,
L.
, and
Leschziner
,
M. A.
, 2005, “
Highly Resolved Large-Eddy Simulation of Separated Flow in a Channel With Streamwise Periodic Constrictions
,”
J. Fluid Mech.
,
526
, pp.
19
66
.
16.
Pope
,
S. B.
, 2000,
Turbulent Flows
,
Cambridge University Press
,
Cambridge, UK
.
17.
Sagaut
,
P.
, 1996, “
Simulations of Separated Flows With Subgrid Models
,”
Rech. Aerosp.
, 1996-1, pp.
51
63
.
18.
Michelsen
,
J. A.
, 1994, “
Block Structured Multigrid Solution of 2D and 3D Elliptic PDE’s
,” Technical Report No. AFM 94-06, Technical University of Denmark.
19.
Sørensen
,
N. N.
, 1995, “
General Purpose Flow Solver Applied to Flow Over Hills
,” Ph.D. thesis, Risø National Laboratory, Roskilde, Denmark.
20.
Cavar
,
D.
, 2006, “
Large Eddy Simulation of Industrially Relevant Flows
,” Ph.D. thesis, Department of Mechanical Engineering, MEK - DTU.
21.
Lund
,
T.
,
Wu
,
X.
, and
Squires
,
K.
, 1998, “
Generation of Turbulent Inflow Data for Spatially Developing Boundary Layer Simulations
,”
J. Comput. Phys.
,
140
(
2
), pp.
233
258
.
22.
Spalart
,
P. R.
, 1988, “
Direct Simulation of a Turbulent Boundary Layer up to ReΘ = 1410
,”
J. Fluid Mech.
,
187
, pp.
61
98
.
23.
Benedict
,
L. H.
, and
Gould
,
R. D.
, 1996, “
Towards Better Uncertainty Estimates for Turbulence Statistics
,”
Exp. Fluids
,
22
(
2
), pp.
129
136
.
24.
Simpson
,
R. L.
, 1989, “
Turbulent Boundary-Layer Separation
,”
Annu. Rev. Fluid Mech.
,
21
, pp.
205
234
.
25.
Schmidt
,
J. J.
, 1997, “
Experimental and Numerical Investigation of Separated Flows
,” Ph.D. thesis, Department of Mechanical Engineering, MEK - DTU.
26.
Velte
,
C. M.
,
Hansen
,
M. O. L.
, and
Cavar
,
D.
, 2008, “
Flow Analysis of Vortex Generators on Wing Sections by Stereoscopic Particle Image Velocimetry Measurements
,”
Environ. Res. Lett.
,
3
(
1
), pp.
1
11
.