two-phase-flow

name	two-phase-flow
description	Two-phase gas-liquid flow — flow regimes, void fraction, Lockhart-Martinelli pressure drop, Baker chart, two-phase multiplier, steam-water quality, drift-flux model.
metadata	{"priority":7,"promptSignals":{"phrases":["two-phase flow","two phase","void fraction","Lockhart-Martinelli","flow regime","quality","steam water"],"minScore":3}}

Two-Phase Gas-Liquid Flow — Complete Skill

Flow Regimes (Horizontal Pipe)

Depends on gas and liquid superficial velocities (j_G = Q_G/A, j_L = Q_L/A):

Stratified: low velocity, gravity separates phases (horizontal only) Wavy: stratified with waves at interface Slug: intermittent gas plugs + liquid slugs; most common in pipelines Plug (Elongated bubble): elongated gas bubbles in liquid Annular: gas core, liquid film on wall; high gas velocity Dispersed bubble (froth): gas bubbles in liquid continuum; high liquid velocity Mist: liquid droplets in gas; very high gas velocity

Baker Chart (horizontal): map of G_L [lb/hr ft²] vs. G_G [lb/hr ft²] with regime boundaries

Quality and Void Fraction

Definitions

Quality: x = ṁ_G / (ṁ_G + ṁ_L) = mass fraction vapor (x=0 saturated liquid, x=1 saturated vapor) Void fraction: α = A_G/A = fraction of flow area occupied by gas Slip ratio: S = u_G/u_L = actual velocity ratio gas/liquid (S ≥ 1)

Relation (with slip): α = x / (x + S(1-x)(ρ_G/ρ_L)) Homogeneous (S=1): α = x/(x + (1-x)ρ_G/ρ_L) = xv_G / (xv_G + (1-x)v_L)

Two-Phase Pressure Drop — Lockhart-Martinelli

Martinelli Parameter

X = (ΔP/ΔL)_L^0.5 / (ΔP/ΔL)_G^0.5

(ΔP/ΔL)_L = pressure gradient if only liquid flowed (Darcy-Weisbach with G_total as liquid) (ΔP/ΔL)_G = pressure gradient if only gas flowed

For turbulent-turbulent (both phases turbulent): X_tt = ((1-x)/x)^0.9 × (ρ_G/ρ_L)^0.5 × (μ_L/μ_G)^0.1

Two-phase multiplier: Φ_L² = 1 + C/X + 1/X² [Chisholm correlation] C = 20 (turb-turb), 12 (visc-turb), 10 (turb-visc), 5 (visc-visc)

(ΔP/ΔL)_TP = Φ_L² × (ΔP/ΔL)_L

Chisholm Correlation (Simpler)

Φ_LO² = 1 + (Γ² - 1)[B x^(2-n)/2 (1-x)^(2-n)/2 + x^(2-n)] Γ² = (ΔP/ΔL)_GO / (ΔP/ΔL)_LO (both phases as all-liquid or all-gas)

Drift Flux Model (Void Fraction)

α = j_G / (C₀ j + V_Gj) j = j_G + j_L (total superficial velocity) C₀ = profile factor (≈ 1.2 for bubbly/slug; 1.0 for annular) V_Gj = drift velocity [m/s] (gas relative to mixture): Bubbly: V_Gj = 1.53[σg(ρ_L-ρ_G)/ρ_L²]^0.25 Slug: V_Gj = 0.35√(gD) Annular: V_Gj ≈ 0

Pressure Drop Components

ΔP_total = ΔP_friction + ΔP_acceleration + ΔP_gravity ΔP_gravity = ρ_mix g L sin θ (θ = inclination angle) ρ_mix = α ρ_G + (1-α) ρ_L

Acceleration (evaporation or condensation): ΔP_acc = G²[(1-x_2)²/(ρ_L(1-α₂)) + x_2²/(ρ_G α₂) - same at inlet 1] G = total mass flux [kg/m²s]

Critical Flow (Choked Two-Phase)

Maximum mass flux at critical (sonic) conditions: G_crit = √[-(dP/d(1/ρ_mix))] at throat Homogeneous: G_crit = [P_0 ρ_mix,0 / (x_0 v_fg/v_g + 1/(γ P_0))]^0.5 (approximate)

Output

Provide: flow regime identification, void fraction α [—], quality x [—], two-phase pressure gradient (ΔP/ΔL)_TP [Pa/m], Martinelli parameter X_tt, two-phase multiplier Φ_L², total ΔP [kPa] over pipe length.