cases:case073

# Flat Plate Transitional Boundary Layer

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 figure 1.

Fig. 1: Flow configuration

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.

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.

Sample plots of selected quantities are available.

Profiles (at the 4 $x$ locations)
$U$ velocity yv-t3b-meanu.dat
Rms $u'$ yv-t3b-uu.dat
Rms $v'$ yv-t3b-vv.dat
Rms $w'$ yv-t3b-ww.dat
Reynolds shear stress $\overline{uv}$ yv-t3b-uv.dat
Reynolds Stress Budgets
$\overline{u^2}$ budgets yv-t3b-budguu.dat
$\overline{v^2}$ budgets yv-t3b-budgvv.dat
$\overline{w^2}$ budgets yv-t3b-budgww.dat
$\overline{uv}$ budgets yv-t3b-budguv.dat
1. 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.
2. 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.
3. Yang, Z.Y., Voke, P.R. (1993). Large-Eddy Simulation of transition under turbulence. Report ME-FD/93.12, Department of Mechanical Engineering, University of Surrey, U.K.
4. Yang, Z.Y., Voke, P.R. (1993). Balance Equations in Finite-Volume Large-Eddy Simulations. Report ME-FD/94.27, Department of Mechanical Engineering, University of Surrey, U.K.
5. Voke, P.R. (1993). Low-Reynolds-Number Subgrid-Scale Models. Report ME-FD/94.26, Department of Mechanical Engineering, University of Surrey, U.K.

Indexed data:

case073 (dbcase, semi_confined_flow)
case073
titleFlat plate transitional boundary layer
authorYang, Voke
year1995
typeLES
flow_tag2d, transition, 2dbl