Name: Turbulent Flat Plate validation
Creator: FlowDeck
License: https://creativecommons.org/licenses/by/4.0/

Validation: 2D Coupled Lattice Boltzmann and Finite Difference, Turbulent Flow, Turbulent transport

Description

Turbulent, zero pressure-gradient boundary layer flow over a 2D flat plate. A uniform free stream enters at the inlet and runs over a symmetry (slip) section before reaching the no-slip plate, where the boundary layer develops from the leading edge.

The wall is modelled with a wall function and the slip section uses a symmetry boundary. The top boundary is zero gradient and the outlet is an outlet condition. Eddy viscosity is set as 0.0 at the inlet and zero gradient on all other boundaries. The wall eddy viscosity is set using the wall function.

Figure 1: Flow domain

Simulation Inputs

Input	Value
Material Properties	Density = 1.0 kg/m³, Viscosity = 5.05 × 10⁻⁶ m²/s.
Geometry	L = 0.914m, L_slip = 0.274m, H = 0.0366m.
Boundary Conditions	Inlet uniform velocity U_∞ = 33.1 m/s. Reynolds number = L*U_∞/v = 6.0 × 10⁶.

Assumptions and Notes

Flow is steady and incompressible.

Results

Velocity magnitude over the flat plate — Figure 2: Velocity magnitude |u|/U_∞

Skin friction coefficient vs experiment

Hover or tap the chart to read the values at any point. Click a legend item to show or hide it.

Figure 3: Skin friction coefficient vs experiment

Skin friction: experiment vs FlowDeck at the measured stations

Reₓ	Experiment C_f	FlowDeck C_f
193,268	0.00534	0.00460
411,651	0.00424	0.00408
631,400	0.00386	0.00380
840,636	0.00364	0.00361
1,071,400	0.00345	0.00346
1,382,961	0.00337	0.00331
1,708,619	0.00317	0.00321
2,028,112	0.00317	0.00312
2,344,510	0.00308	0.00306
2,668,039	0.00301	0.00300
3,090,020	0.00293	0.00294
3,627,602	0.00284	0.00287
4,285,687	0.00278	0.00280
4,998,080	0.00269	0.00274
5,712,235	0.00266	0.00269

Velocity profile in wall units at Reₓ ≈ 4.85 × 10⁶

Hover or tap the chart to read the values at any point. Click a legend item to show or hide it. FlowDeck values in the table are interpolated (in log y⁺) to the measured points; the chart and CSV have the full profiles.

Figure 4: Velocity profile in wall units at Re_x ≈ 4.85 × 10⁶ vs SA analytic law of the wall and experiment (Re_x = 4.998 × 10⁶)

u⁺ at the measured points: experiment vs FlowDeck and the SA law of the wall

y⁺	Experiment u⁺	FlowDeck u⁺	SA law u⁺
40.1	14.43	–	14.12
80.1	15.57	15.58	15.79
160.3	17.32	17.49	17.45
400.7	19.63	19.97	19.67
801.4	21.84	22.05	21.35
1202	23.26	23.50	22.34
1603	24.76	24.65	–
2003	25.88	25.56	–
2404	26.81	26.27	–
3206	27.27	27.00	–

Reference Data

Skin friction is compared against the experimental data from the NASA NPARC zero-pressure-gradient flat plate case [1].

The velocity profile at Re_x = 4.85 × 10⁶ is compared against the nearest experimental profile, at Re_x = 4.998 × 10⁶ (x = 2.287 m) [1] and against the analytic Spalart–Allmaras law of the wall [2]:

u^{+} = \bar{B} + c_{1} \ln [{(y^{+} + a_{1})}^{2} + b_{1}^{2}] - c_{2} \ln [{(y^{+} + a_{2})}^{2} + b_{2}^{2}] - c_{3} \tan^{- 1} \frac{b_{1}}{y^{+} + a_{1}} - c_{4} \tan^{- 1} \frac{b_{2}}{y^{+} + a_{2}}

The coefficients are obtained by solving the SA model in the constant-stress near-wall layer with κ = 0.41 [2]. Here $u^{+} = u / u_{τ}$ , $y^{+} = y u_{τ} / ν$ and $u_{τ} = \sqrt{τ_{w} / ρ}$ .

References

NPARC Alliance Validation Archive, “Turbulent Flat Plate,” NASA Glenn Research Center: the data of Wieghardt, K. and Tillmann, W., “On the Turbulent Friction Layer for Rising Pressure,” NACA TM 1314, 1951, as included in Coles and Hirst (1969). https://www.grc.nasa.gov/www/wind/valid/fpturb/fpturb.html
Allmaras, S. R., Johnson, F. T., and Spalart, P. R., “Modifications and Clarifications for the Implementation of the Spalart–Allmaras Turbulence Model,” Seventh International Conference on Computational Fluid Dynamics (ICCFD7), Big Island, Hawaii, 9–13 July 2012, ICCFD7-1902.

Data licence. The model results on this page and in the CSV downloads are published by FlowDeck under the Creative Commons Attribution 4.0 licence (CC BY 4.0). The reference values are from the sources listed under References.