cfd-postprocessing

name	cfd-postprocessing
description	CFD post-processing — drag/lift coefficient extraction, force/moment integration, wake analysis, flow visualization techniques, pressure coefficient, boundary layer quantities, turbulence statistics.
metadata	{"priority":7,"promptSignals":{"phrases":["CFD post","drag coefficient","lift coefficient","force integration","pressure coefficient","wake analysis","flow visualization","CFD results","boundary layer analysis","y plus"],"minScore":3}}

CFD Post-Processing — Complete Skill

Force and Moment Integration

Pressure and Viscous Forces

Total force on body: F = Σ (p_i × n̂_i + τ_i) × A_i (over all surface faces) n̂_i = face outward normal [unit vector] τ_i = wall shear stress vector [Pa] A_i = face area [m²]

Decompose into pressure + friction: F_pressure = Σ p_i × n̂_i × A_i F_friction = Σ τ_w,i × t̂_i × A_i (t̂ = tangential direction along flow)

In most CFD solvers: wall shear stress τ_w = μ × ∂u/∂n|_wall (computed from velocity gradient at wall)

Aerodynamic Coefficients

Reference quantities: ρ_∞, V_∞ (freestream density and velocity), A_ref (reference area)

Drag coefficient: C_D = F_D / (½ ρ_∞ V_∞² A_ref) F_D = force component in freestream direction

Lift coefficient: C_L = F_L / (½ ρ_∞ V_∞² A_ref) F_L = force component perpendicular to freestream (in lift direction)

Reference areas: Airfoil/wing: A_ref = planform area (span × chord) or chord × unit span Bluff body (vehicle): A_ref = frontal area (projected area ⊥ to flow) Sphere: A_ref = πD²/4

Moment coefficient: C_M = M / (½ ρ_∞ V_∞² A_ref × L_ref) L_ref = reference length (chord, diameter) M = pitching/rolling/yawing moment about specified point

Pressure Coefficient

C_p = (p - p_∞) / (½ ρ_∞ V_∞²) C_p = 1.0: stagnation point (all kinetic → static pressure) C_p = 0: freestream conditions C_p < 0: suction (velocity > V_∞) C_p = 1 - (V/V_∞)²: Bernoulli relationship (incompressible)

Suction peak: large negative C_p near leading edge suction surface → indicates attached flow and high lift Separation indicator: C_p plateau followed by recovery region → indicates flow separation

Boundary Layer Analysis

Wall y+ and Resolution

y⁺ = u_τ y₁ / ν u_τ = √(τ_w/ρ) (friction velocity) y₁ = distance from wall to first cell center [m]

y+ targets: Low-Re treatment: y⁺ < 1 (resolve viscous sublayer) Wall function: 30 < y⁺ < 300 (log-law region; first cell in log layer) Transition between: y⁺ = 5-30 (buffer layer, avoid this region)

Checking after simulation: Plot y⁺ contour on all walls; identify regions with y⁺ outside target Regions with excessive y⁺ → local refinement needed

Integral Boundary Layer Quantities

Displacement thickness: δ* = ∫₀^∞ (1 - u/U_e) dy [m] Indicates outward displacement of streamlines

Momentum thickness: θ = ∫₀^∞ (u/U_e)(1 - u/U_e) dy [m]

Shape factor: H = δ*/θ H = 1.3: fully turbulent attached H = 1.5-2.5: transitional to separated H > 3.5: separated/reversed flow

Skin friction coefficient: C_f = τ_w / (½ρU_e²) Integrate over surface: friction drag = ∫ τ_w dA

Boundary Layer Separation Detection

Methods:

1. C_f < 0: reversed flow (wall shear opposite to freestream)
2. Vortex core lines or isosurfaces of Q-criterion (Q > 0)
3. Oil flow patterns / particle traces on surface

Reattachment: C_f recovers positive after separation bubble

Wake Analysis

Velocity Deficit

U_deficit = (U_∞ - U(y,z)) / U_∞ at downstream plane Integrate for drag: D = ρ ∫∫ U(U_∞-U) dA + ∫∫(p-p_∞) dA (far-wake, negligible pressure term)

Trefftz plane analysis (far-field drag): Decompose: D = D_friction + D_pressure = D_profile + D_induced Induced drag: from vorticity in wake plane (trailing vortices of wing)

Turbulence intensity in wake: TI = u'/U_local × 100% u' = RMS of velocity fluctuations (from time-averaging or from k: u' = √(2k/3)) Wake recovery length: U_deficit < 5% requires 10-20 diameters downstream (bluff body)

Vortex Identification

Q-criterion: Q = ½(||Ω||² - ||S||²) > 0 (vortex where rotation > strain) Ω = antisymmetric part of velocity gradient (rotation rate tensor) S = symmetric part (strain rate tensor) Isosurface Q = const: visualizes vortex tubes

λ₂-criterion: second eigenvalue of (S² + Ω²) < 0 in vortex core Preferred over Q for accuracy; less sensitive to freestream

Δ-criterion: discriminant of velocity gradient tensor > 0 (complex eigenvalues → swirling)

Flow Visualization

Streamlines, Pathlines, Streaklines

Streamlines: tangent to instantaneous velocity field; defined by dx/u = dy/v = dz/w In steady flow: streamline = pathline = streakline (all equivalent) In unsteady flow: they differ — use appropriate one for physical meaning

Particle traces: integrate dx/dt = u(x,t) forward in time → pathline of tracer LIC (Line Integral Convolution): dense texture-based streamline visualization on surface

Surface streamlines / limiting streamlines: u_wall = 0 (no-slip), so trace wall shear stress vectors τ_w Saddle points: flow reattachment/separation lines Nodal points: spiral sources/sinks (recirculation zones)

Volume Visualization

Iso-surfaces: surfaces where scalar = constant (pressure, temperature, y+, Q-criterion) Volume rendering: semi-transparent 3D view of scalar (turbulence kinetic energy, temperature) Cutting planes: 2D slices of any field quantity at selected positions

Turbulence Statistics

Time-averaged quantities (RANS): Ū, k = ½ u_i'u_i', ε or ω Turbulence intensity: TI = √(2k/3) / U_ref × 100% Reynolds stress tensor: τᵢⱼ = -ρ<u_i'u_j'> (anisotropy from non-diagonal terms → secondary flows)

Spectral analysis (LES/DNS): Power Spectral Density of u': E(k) ∝ k^(-5/3) in inertial subrange (Kolmogorov) Deviation from -5/3: indicates insufficient spatial resolution (LES) or wall-bounded effects

Common Post-Processing Workflow

CFD Report Checklist

1. Residuals: converged to 10⁻⁴ (10⁻⁶ for sensitive quantities)
2. y+ distribution: on all walls; within target range
3. Grid independence: compare coarse/medium/fine solutions (GCI < 5%)
4. Global quantities: C_D, C_L, Nusselt number vs. experiment/correlation
5. Local fields: C_p distribution, velocity profiles at key sections
6. Separation/attachment: C_f map, flow topology (saddle/node points)
7. Uncertainty: discretization error (GCI), turbulence model sensitivity
8. Comparison: simulation vs. experiment/analytical with percent deviation

Reporting Aerodynamic Coefficients

Always specify:

• Reference area A_ref [m²]
• Reference length L_ref [m]
• Moment reference point [m]
• Freestream conditions (ρ, V, T, Re)
• Angle of attack α [°]
• Decomposition (pressure vs. friction contributions)

Output

Provide: C_D and C_L [—] with pressure/friction breakdown, C_p distribution at key stations, y+ check (max, min, mean), separation detection (C_f < 0 location), wake velocity deficit [%] at downstream plane, GCI-based discretization uncertainty [%], comparison to experimental data or analytical correlation.