Flat Plate Boundary Layer: Primary Validation
The PRIMARY validation case for the AK-Vortex solver. Laminar boundary layer over a flat plate, compared against the Blasius similarity solution. AoA sweep (0 to 15 deg) and Re sweep (500--2000) for drag polar and boundary layer profiles. This case directly validates the viscous stress formulation and wall treatment in the MRT collision operator.
Setup
| Parameter | Value |
|---|---|
| Grid | 1200 × 800 |
| Chord length | 200 cells |
| Reynolds number (AoA sweep) | 1000 |
| Reynolds number (Re sweep) | 500, 1000, 2000 |
| Angle of attack sweep | -10, -5, 0, 5, 10, 15 deg |
| Inlet velocity | uinflow = 0.1 lu/ts |
| Tau (relaxation parameter) | Re=500: 0.59, Re=1000: 0.55, Re=2000: 0.52 |
| Number of steps | 80,000 |
| Reference length | Chord = 200 cells |
| Collision | MRT (d'Humieres 2002) |
| Boundary condition | Bouzidi interpolated bounce-back |
| Lattice spacing / time step | Δx = 1, Δt = 1 |
Flow Field
Use the tabs below to select the angle of attack (AoA), the inclination of the plate relative to the free stream, at a fixed Re = 1000. Top left: steady-state velocity contour with streamlines. Top right: flow evolution from rest to steady state. Bottom: pressure and vorticity fields at steady state.
Velocity (Contour | Streamlines)
Drag the handle to wipe between the velocity-magnitude contour and the streamline plot.
Flow Evolution
Pressure Coefficient Cp
Pressure Coefficient Cp
Vorticity
Vorticity
AoA Sweep: Validation (Re=1000)
| AoA (deg) | Regime | Computed Cd | Computed Cl | Blasius Cd (AoA=0) |
|---|---|---|---|---|
| 0 | Blasius boundary layer | 0.070 | 0.000 | 1.328/√ReL |
| 5 | Small incidence | 0.074 | 0.333 | -- |
| 10 | Incidence, suction side | 0.130 | 0.604 | -- |
| 15 | Strong incidence, possible separation | 0.211 | 0.689 | -- |
Re Sweep: Boundary Layer at AoA=0
Boundary layer development at zero angle of attack for Reynolds numbers 500, 1000, and 2000. The displacement thickness and momentum thickness are compared against the Blasius similarity solution. The laminar boundary layer thickness grows as δ ~ x1/2.
| Re | Regime | Computed Cd | Blasius Cd | BL Thickness Trend |
|---|---|---|---|---|
| 500 | Low Re laminar | 0.103 | 0.119 | Thicker BL, higher skin friction |
| 1000 | Reference Re | 0.070 | 0.084 | Baseline for comparison |
| 2000 | Higher Re laminar | 0.049 | 0.059 | Thinner BL, lower skin friction |
Discussion
The flat plate boundary layer is the most fundamental viscous flow validation case. It exercises the solver's core capabilities: accurate viscous stress computation, proper wall boundary conditions, and correct momentum transport in the boundary layer. The Blasius similarity solution provides an exact reference for the laminar case.
At AoA=0, the boundary layer grows from the leading edge as δ(x) ~ √(νx/U∞), producing the characteristic parabolic profile. The drag coefficient decreases with increasing Re as Cd ~ 1/√Re. At non-zero AoA, the pressure gradient modifies the boundary layer development, with favorable gradients on the suction side (positive AoA) and adverse gradients that can lead to separation at large incidence angles.
The AoA sweep generates a drag polar (Cd vs AoA) that can be compared against thin airfoil theory predictions for small angles. This validates both the viscous and inviscid aspects of the LBM formulation. The Re sweep confirms that the solver correctly captures the Reynolds number scaling of boundary layer properties.