ThermoFluidCalc Engineering Report

2D Lid-Driven Cavity Flow Benchmark Analysis — 2026-08-23 20:59:23
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🟦 2D Lid-Driven Cavity Flow (Ghia Benchmark)

Calculate square lid-driven cavity Reynolds number, primary vortex center coordinates (xv, yv), secondary corner eddies, and wall boundary layer thickness (Ghia benchmark).

⚡ Fortran 90 Engine Double Precision (IEEE 754) ✓ ISO / ASME Validated
📊 Solver Telemetry ● ACTIVE
👁️ Consultations 16
⚡ Calculs faits 13
💾 Téléchargements 251 📦 Code Fortran 4.4 KB
📅 Mise en service Jun 2026
⏱️ Latence < 1 ms
⚡ Outils & Rapports :
💾 Télécharger Fortran 90

🟦 2D Lid-Driven Square Cavity & Multi-Eddy Streamlines

Real-time visual simulation of top moving lid, primary central vortex & corner recirculating eddies

📝 Configuration & Presets

🔬 Benchmark Re = 100 ⭐ Classic Ghia Re = 1,000 🌪️ Multi-Eddy Re = 5,000 💧 Viscous Microcavity
📐 Cavity Geometry & Lid Velocity
💧 Fluid Physical Properties
Water: 1.0 cSt, Air: 15.0 cSt
Ghia Benchmark Formulations:
• Cavity Reynolds: Re = (Ulid · L) / ν
• Primary Vortex Core: (xv/L, yv/L) migrating toward (0.50, 0.50) as Re → ∞
• Wall Boundary Layer: δwall ≈ L / √Re [mm]
• Lid Shear Drag: Fdrag ≈ ρ ν Ulid (L / δwall) [N/m]

📊 Cavity Flow Results

📊 Output Summary
💾 Fortran Source

Cavity Reynolds Number (Re)
Re = 5,000
Regime: Complex High-Re Multi-Vortex Structure
Core: (0.515, 0.535)
Primary Vortex Center (xv, yv) (103.0 mm, 107.0 mm) Normalized: (0.515 L, 0.535 L)
Minimum Streamfunction (ψmin) -0.1210 Ghia benchmark correlation
Bottom-Right Corner Eddy Size 78.0 mm Bottom-Left: 58.0 mm
Wall Boundary Layer (δwall) 2.83 mm Top Lid Drag: 0.0018 N/m

📈 Primary Vortex Vertical Center y_v/L vs Reynolds Number

📉 Wall Boundary Layer Thickness δ (mm) vs Reynolds

=================================================================
 THERMOFLUIDCALC — 2D LID-DRIVEN CAVITY BENCHMARK REPORT
=================================================================
Case Title                 : High-Reynolds Multi-Eddy Benchmark (Re = 5,000)
Cavity Dimensions          : 200.00 mm x 200.00 mm
Top Lid Velocity           : 0.0250 m/s
Fluid Properties           : nu = 1.00 cSt, rho = 998.0 kg/m3
-----------------------------------------------------------------
REYNOLDS NUMBER (Re)       : 5,000.0
Flow Regime                : Complex High-Re Multi-Vortex Structure
Primary Vortex Core Center : (x = 0.5150 L, y = 0.5350 L) -> (103.00 mm, 107.00 mm)
Minimum Streamfunction psi : -0.1210 (dimensionless)
Secondary Corner Eddies    : BR = 78.00 mm (0.390 L), BL = 58.00 mm (0.290 L)
Wall Boundary Layer Thick  : 2.828 mm
=================================================================

📘 Calculation Methodology & Ghia Benchmark Standards

Ghia et al. Reference Benchmark

The 2D incompressible Navier-Stokes square cavity driven by a tangential moving top wall is the universal gold standard for CFD solver validation:

Re = (Ulid · L) / ν

Vortex Core Migration Dynamics

At low $Re = 100$, the primary vortex is centered high at $(0.62, 0.73)$. As inertial convection dominates at $Re \ge 1000$, the vortex core shifts downward toward the geometric center $(0.51, 0.53)$.

Key Engineering Assumptions

  • 2D planar incompressible laminar Navier-Stokes equations.
  • No-slip boundary conditions on left, right, bottom, and moving top lid.
  • Regularized corner singularities.