======Flat Plate Transitional Boundary Layer======
=====LES by Yang and Voke=====

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====Description====

The case consists of a flat-plate transitional 2D boundary layer flow without pressure gradient, and
with no temperature variations.

Free-stream velocity: \(U_o=9.6\) m/s.

Upstream turbulence intensity: \(Tu_o=5.0\)%.

An LES has been performed using the geometry and boundary conditions shown schematically in <imgref cas73-geom>.

<imgcaption cas73-geom|Flow configuration>{{ figs:case073:cas73-geom.png |Flow configuration}}</imgcaption>

====Simulation Details====

An LES was carried out using a finite volume based code, with a sub-grid-scale turbulent viscosity as
described by Voke (1991) to account for low-Reynolds-number effects:
\[ \nu_s = (\Delta c_s)^2 \sqrt{2s_{ij}s_{ij}}    \qquad \nu_e = \nu_s - (2\nu/n)[ 1 - \exp(-n\nu_s/(2\nu)]  \]
with constants \(c_s=0.1\) \nd \(n=9\).

The LES was performed in a computational box extending from \(Re_x = 6620\) to \(200000\), or a total nominal length 
of 300 mm, equivalent to \(L_x^+ = 10138\) in wall units. The lateral and vertical dimensions of the 
box were \(L_z = 20\) mm (\(L_z^+ = 676\)) and \(L_y = 30\) mm (\(L_y^+ = 1014\)).
The overall meshing was \(127 \times 56 \times 48\). These dimensions 
gave a resolution \(\Delta x^+ = 80\), \(\Delta z^+ = 14\), and \(\Delta y^+\) varying from 1 at the wall 
to 80 well beyond the boundary layer. The wall units are based on the friction velocity just after 
transition is complete.

The upstream boundary of the computation represented a point 10 mm downstream of the leading edge of 
the flat plate (\(Re_x=6620\)). An appropriate Blasius profile was imposed at the inflow boundary, with the 
free-stream disturbances limited to the region above \(y=0.3\) mm. 
There was a smooth cutoff of free-stream disturbances between \(y=0.3\) mm and \(y=0.65\) mm. 
The inflowing f.s.t. was derived from separate simulations on matched meshes but without any solid 
lower surface, and with pseudorandom disturbances at their inflow superimposed on a uniform flow. 
Velocity data were extracted from these simulations at \(x=150\) mm, \(50\) mm upstream of the outflow 
boundary of the simulations.  These `precursor' simulations therefore mimicked the behaviour 
of grid turbulence, generating more realistic f.s.t. for input into the simulation of the boundary 
layer transition than a pseudorandom input would have done. The pseudorandom disturbances at 
the inflow of the precursor simulations decayed rapidly at first, but settled to a more physically 
realistic decay rate before they reached the \(x=150\) mm station at which velocity data were extracted 
for use as inflow to the boundary layer `successor' simulations.

====Available data====

The available data consists of:
  * Profiles of mean \(U\) velocity, rms velocities \(u'\), \(v'\), \(w'\) and Reynolds shear stress \(\overline{uv}\) at \(x=25\), \(45\), \(95\) and \(195\) mm.
  * Budgets of \(\overline{u^2}\), \(\overline{v^2}\), \(\overline{w^2}\) and \(\overline{uv}\) at the same four locations.

[[case073-plots|Sample plots]] of selected quantities are available.

The data can be downloaded as compressed archives from the links below, or as individual files.

  * {{cdata:case073:fptr-allfiles.zip|fptr-allfiles.zip}}
  * {{cdata:case073:fptr-allfiles.tar.gz|fptr-allfiles.tar.gz}}

^  Profiles (at the 4 \(x\) locations)  ^^
| \(U\) velocity                           |  {{cdata:case073:yv-t3b-meanu.dat|yv-t3b-meanu.dat}}  |
| Rms \(u'\)                               |  {{cdata:case073:yv-t3b-uu.dat|yv-t3b-uu.dat}}  |
| Rms \(v'\)                               |  {{cdata:case073:yv-t3b-vv.dat|yv-t3b-vv.dat}}  |
| Rms \(w'\)                               |  {{cdata:case073:yv-t3b-ww.dat|yv-t3b-ww.dat}}  |
| Reynolds shear stress \(\overline{uv}\)  |  {{cdata:case073:yv-t3b-uv.dat|yv-t3b-uv.dat}}  |
^  Reynolds Stress Budgets  ^^
| \(\overline{u^2}\) budgets  |  {{cdata:case073:yv-t3b-budguu.dat|yv-t3b-budguu.dat}}  |
| \(\overline{v^2}\) budgets  |  {{cdata:case073:yv-t3b-budgvv.dat|yv-t3b-budgvv.dat}}  |
| \(\overline{w^2}\) budgets  |  {{cdata:case073:yv-t3b-budgww.dat|yv-t3b-budgww.dat}}  |
| \(\overline{uv}\) budgets   |  {{cdata:case073:yv-t3b-budguv.dat|yv-t3b-budguv.dat}}  |


====References====

  - Yang, Z.Y., Voke, P.R. (1993). Large-Eddy Simulation studies of bypass transition. //Engineering Turbulence Modelling and Experiments 2//, (Eds. W. Rodi et al), Elsevier Science, Amsterdam, pp. 603-611.
  - Voke, P.R., Yang, Z.Y. (1993). Numerical studies of the mechanisms of bypass transition in the flat plate boundary layer. //Proc. 9th Int. Symp. on Turbulent Shear Flows//, Kyoto, Japan.
  - Yang, Z.Y., Voke, P.R. (1993). {{figs:case073:tut.pdf|Large-Eddy Simulation of transition under turbulence}}. //Report ME-FD/93.12//, Department of Mechanical Engineering, University of Surrey, U.K.
  - Yang, Z.Y., Voke, P.R. (1993). {{figs:case073:rsbmefd.pdf|Balance Equations in Finite-Volume Large-Eddy Simulations}}. //Report ME-FD/94.27//, Department of Mechanical Engineering, University of Surrey, U.K.
  - Voke, P.R. (1993). {{figs:case073:sgmmefd.pdf|Low-Reynolds-Number Subgrid-Scale Models}}. //Report ME-FD/94.26//, Department of Mechanical Engineering, University of Surrey, U.K.

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Indexed data:
<data dbcase semi_confined_flow>
case       : 073
title      : Flat plate transitional boundary layer
author*    : Yang, Voke
year       : 1995
type       : LES
flow_tag*  : 2d, transition, 2dbl
</data>