AeroFlow Universal Pro

Ground Effect, Shockwave & Virtual Flow Probe Simulator

Import .DAT

Active

Primary: NACA 2412

C_L: 0.52

C_D: 0.0082

L/D: 63.4

Mach: 0.15

State: Attached

Low (-C_p)

High (+C_p)

Geometry & Comparison

Primary Airfoil Designation (A):

Enable Comparison Airfoil (B)

Aircraft & Turbine Presets:

Camber: 2.0%

Pos (p): 40%

Thick (t): 12%

Flow Parameters

AoA (α): 4.0°

Velocity (V_∞): 50 m/s

Reynolds (Re): 3.4e6

Flap (δ): 0.0°

Ground (h/c): ∞ (Free Air)

Drag Composition:

• Friction: 65%

• Induced: 30%

• Pressure: 5%

Render Overlays

Particles Streamlines Pressure Vectors Force Vector Boundary Layer Flow Probe

Pressure Distribution (-C_p)

Surface Velocity Ratio (V / V_∞)

Lift Curve (C_L vs α)

Drag Polar (C_L vs C_D)

Total Lift Force (L): 0.00 N/m

Total Drag Force (D): 0.00 N/m

Center of Pressure (X_cp): 0.25 c

Pitching Moment (C_m,c/4): -0.052

Aerodynamic Governing Equations & Methodology

1. NACA Geometry Calculation Process

For a standard NACA 4-Digit Series (e.g. NACA 2412 where max camber m = 0.02, position p = 0.4, thickness t = 0.12):

y_t = 5 · t · [0.2969 · √x - 0.1260 · x - 0.3516 · x² + 0.2843 · x³ - 0.1015 · x⁴]

y_c = (m / p²) · (2px - x²) [x < p] | y_c = [m / (1-p)²] · [(1-2p) + 2px - x²] [x ≥ p]

2. Compressibility, Ground Effect & Flap Lift Slope (C_L)

Thin Airfoil Theory combined with Prandtl-Glauert compressibility correction, trailing-edge flap deflection (δ), and proximity ground effect boost (h/c):

C_{L, ideal} = [(2 · π · (α_rad + 2 · m_max + 1.15 · δ_rad)) / √(1 - Mach²)] · [1 + 0.16 / (h/c)^1.2]

Post-stall boundary layer separation reduces effective lift via parabolic decay factor:

C_L = C_{L, ideal} · max(0.15, 1.0 - ((|α| - α_stall) / 8)²)

3. Reynolds Scale Dependent Drag Coefficient (C_D)

Total drag is calculated by integrating skin friction, induced drag, flap deflection, and boundary layer thickness (δ_BL):

C_D,0 = (0.006 + 0.01 · m_max²) · (3.4 · 10⁶ / Re)^0.15 | δ_BL(x) = 0.37 · x / (Re_x)^0.2

4. Pressure Coefficient (C_p) & Force Integration

C_p(x) = (1 - (V(x) / V_∞)²) / √(1 - Mach²) | Lift = C_L · (½ · ρ · V²) · c | Drag = C_D · (½ · ρ · V²) · c

5. Wind Tunnel Wall Interference Model

Solid wind tunnel walls increase local dynamic pressure via stream tube blockage constraint:

V_tunnel = V_∞ · (1 + τ · (t / H)²) | C_{L, tunnel} = C_L · 1.08 | C_{D, tunnel} = C_D · 1.12

6. Comprehensive Reynolds Number (Re) Reference Guide

Reynolds number formula: Re = (ρ · V · c) / μ = (V · c) / ν

Flight Regime	Chord (c)	Speed (V)	Reynolds (Re)	Aerodynamic Behavior
Micro Air Vehicles / Insects	0.01–0.05 m	1–10 m/s	1e3 – 5e4	Laminar flow, separation bubbles (LSB).
RC Models / Small Drones	0.10–0.25 m	10–30 m/s	1e5 – 5e5	Transitional flow, boundary layer sensitivity.
Wind Tunnel Models (Default)	0.15–0.40 m	20–80 m/s	5e5 – 3.5e6	Mixed laminar-turbulent transition.
General Aviation (Cessna)	1.20–1.60 m	40–70 m/s	3e6 – 8e6	Fully turbulent boundary layer, max L/D.
Commercial Jet Airliners	3.00–7.00 m	200–250 m/s	2e7 – 6e7	Turbulent flow, transonic shock interactions.

Geometry & Comparison

Flow Parameters

Render Overlays

Pressure Distribution (-Cp)

Surface Velocity Ratio (V / V∞)

Lift Curve (CL vs α)

Drag Polar (CL vs CD)