🌊 Two-Phase Flow Patterns & Lockhart-Martinelli

Calculate two-phase liquid-gas pressure drop using Lockhart-Martinelli parameter (X) and Chisholm multiplier (phi2), void fraction, liquid holdup, and Baker flow regimes.

⚡ Fortran 90 Engine Double Precision (IEEE 754) ✓ ISO / ASME Validated

📊 Solver Telemetry ● ACTIVE

👁️ Consultations 38

⚡ Calculs faits 31

💾 Téléchargements 302 📦 Code Fortran 4.5 KB

📅 Mise en service Jun 2026

⏱️ Latence < 1 ms

🌊 Two-Phase Liquid-Gas Flow Patterns & Frictional Multiplier

Real-time visual simulation: Pipeline flow regime dynamics (Slug, Annular film, Bubbly, Stratified)

📝 Configuration & Presets

♨️ Steam-Water Boiler (x = 0.20) 🛢️ Subsea Oil-Gas Slug (500m) ❄️ R134a DX Evaporator Tube 💨 Gas-Condensate Annular Film

⚡ Flow Conditions & Vapor Quality

Total Mass Flow ṁ [kg/s]:

Vapor Mass Quality x [0 to 1]:

📏 Pipe Geometry

Pipe Inner Diameter D [mm]:

Pipe Length L [m]:

🧪 Phase Densities & Viscosities

Liquid Density ρ_L [kg/m³]:

Gas Density ρ_G [kg/m³]:

Liquid Viscosity μ_L [Pa·s]:

Gas Viscosity μ_G [Pa·s]:

Lockhart-Martinelli & Chisholm Formulation:
• Martinelli Parameter: X = √[ (dP/dL)_L / (dP/dL)_G ]
• Two-Phase Multiplier: ϕ_L² = 1 + C / X + 1 / X² (C = 20 for turbulent-turbulent)
• Two-Phase Frictional Drop: (dP/dL)_tp = ϕ_L² · (dP/dL)_L
• Void Fraction: α = 1 − ε_L (Butterworth holdup model).

📊 Two-Phase Results

📊 Output Summary
💾 Fortran Source

Total Two-Phase Frictional Pressure Drop

771.10 kPa (7.711 bar)

Gradient: 51406.6 Pa/m | Multiplier ϕ_L²: 120.11

ANNULAR (LIQUID FILM) FLOW

Lockhart-Martinelli Parameter (X) 0.208 Liquid / Gas resistance ratio

Pipe Cross-Section Void Fraction 91.1 % Liquid Holdup = 8.9 %

Two-Phase Multiplier (ϕ_L²) 120.11 (dP/dL)_tp / (dP/dL)_L

Vapor Mass Quality 45.0 % x = 0.45

📈 Two-Phase Pressure Drop ΔP (kPa) vs Vapor Quality x

📉 Void Fraction α (%) vs Vapor Quality x

=================================================================
 THERMOFLUIDCALC — TWO-PHASE FLOW & LOCKHART-MARTINELLI REPORT
=================================================================
Case Title                 : Refrigerant R134a Direct-Expansion Evaporator
Flow Parameters            : Total Mass Flow = 0.80 kg/s, Vapor Quality x = 0.450
Pipe Geometry              : ID = 22.0 mm, Length = 15.0 m
Phase Properties           : rho_L = 1260.0 kg/m3, rho_G = 18.00 kg/m3, mu_L = 0.00025 Pa.s, mu_G = 0.000012 Pa.s
-----------------------------------------------------------------
LOCKHART-MARTINELLI PARAM X: 0.2082
TWO-PHASE MULTIPLIER (phi2): 120.108
TWO-PHASE PRESSURE DROP    : 771.10 kPa (7.7110 bar)
Frictional Pressure Grad.  : 51406.56 Pa/m
Void Fraction (alpha)      : 91.05 % (Gas cross-sectional area)
Liquid Holdup (epsilon_L)  : 8.95 % (Liquid cross-sectional area)
PREDICTED FLOW REGIME      : ANNULAR (LIQUID FILM) FLOW
=================================================================

📘 Calculation Methodology & Two-Phase Flow Standards

Lockhart-Martinelli & Chisholm Correlation

Relates the two-phase frictional pressure drop to single-phase liquid flow via multiplier $\phi_L^2 = 1 + C/X + 1/X^2$. The Chisholm parameter $C$ accounts for turbulent/viscous phase interactions.

Flow Pattern Regimes (Baker / Taitel-Dukler)

Identifies slugging risks in subsea oil-gas tiebacks, dryout in steam boilers, and liquid droplet entrainment in evaporators as a function of vapor quality and superficial velocities.

Key Engineering Assumptions

Separated two-phase flow formulation with empirical liquid holdup.
Smooth or commercial pipe friction factors for liquid and gas streams.
Applicable to oil-gas pipelines, refrigeration evaporators, and nuclear steam generators.

ThermoFluidCalc Engineering Report