flow-boiling

name	flow-boiling
description	Flow boiling heat transfer — flow regimes (bubbly/slug/annular), Chen correlation, Shah chart, critical heat flux (CHF), flow patterns, boiling crisis, microchannel boiling, two-phase multiplier.
metadata	{"priority":7,"promptSignals":{"phrases":["flow boiling","two phase flow heat transfer","boiling heat transfer","critical heat flux","CHF","Chen correlation","flow pattern boiling"],"minScore":3}}

Flow Boiling Heat Transfer — Complete Skill

Flow Regimes in Upward Vertical Two-Phase Flow

Flow Pattern Progression (low → high quality x)

1. Bubbly flow (x ≈ 0–0.05): discrete bubbles in continuous liquid; high h
2. Slug flow (x ≈ 0.05–0.25): Taylor bubbles; slugs of liquid; pulsating; high h
3. Churn flow (x ≈ 0.25–0.40): chaotic; transition; oscillating liquid
4. Annular flow (x ≈ 0.40–0.85): liquid film on wall; vapor core; highest h
5. Mist/droplet flow (x > 0.85–0.95): droplets in vapor; h drops sharply → DNB risk

Flow pattern map (Baker chart or Hewitt-Roberts): G vs. x (or G vs. gas/liquid superficial velocities) — identifies regime for design

Boiling Heat Transfer Mechanisms

Nucleate Boiling Contribution

From bubble nucleation on heated wall surface Chen correlation (nucleate boiling part): h_nb = S × h_pool [S = suppression factor] h_pool = Forster-Zuber pool boiling coefficient

Forster-Zuber correlation: h_pool = 0.00122 × (k_L^0.79 × C_pL^0.45 × ρ_L^0.49) / (σ^0.5 × μ_L^0.29 × h_fg^0.24 × ρ_v^0.24) × ΔT_sat^0.24 × ΔP_sat^0.75

Suppression factor S (Chen): S = 1/(1 + 2.53 × 10⁻⁶ × Re_TP^1.17) [Re_TP = G(1-x)D/μ_L]

Convective Boiling Contribution

Convection through liquid phase (single-phase-like, enhanced): h_cb = F × h_lo [F = enhancement factor; h_lo = Dittus-Boelter for all-liquid flow]

Enhancement factor F (Chen 1966): F = f(1/X_tt) where X_tt = Martinelli parameter For X_tt < 0.1: F = 2.35 × (1/X_tt + 0.213)^0.736 For X_tt > 0.1: F = 1.0

Martinelli parameter: X_tt = [(1-x)/x]^0.9 × (ρ_v/ρ_L)^0.5 × (μ_L/μ_v)^0.1

Chen Correlation (Complete)

h_tp = h_cb + h_nb = F × h_lo + S × h_pool

Valid range: upward flow, low-to-moderate heat flux, subcooled to bulk boiling Used for: refrigerants, water, light hydrocarbons

Shah Correlation (1988)

Co number (Convection number): Co = [(1-x)/x]^0.8 × (ρ_v/ρ_L)^0.5

Boiling number: Bo = q'' / (G h_fg)

Fr number: Fr_lo = G² / (ρ_L² g D)

h_tp = h_lo × f(Co, Bo, Fr_lo): Four regions (nucleate dominant, convective dominant, suppressed nucleate) based on Co and Bo → simplified and widely used; accuracy ±30%

Horizontal Flow Boiling

Gravity effects: liquid pools at bottom; vapor at top Regime map (Taitel-Dukler): different from vertical Different correlations required: Gungor-Winterton, Kattan-Thome for horizontal

Critical Heat Flux (CHF) — Boiling Crisis

Two types: DNB (Departure from Nucleate Boiling): at high heat flux, low quality; bubble blanketing; steep temperature rise; Type I CHF Dryout: at high quality (x > 0.7); liquid film depletes; h drops; Type II CHF

Lookup Tables (standard method for water)

Groeneveld correlation tables: q''_CHF as function of (G, x, D, P) Most accurate for water in tubes: AECL CHF Tables (1996, 2006) Available in IAEA-TECDOC-1203

Simplified correlation (Bowring): q''_CHF = (A - B × x) / (C + D × x) A, B, C, D = functions of G, P, D from Bowring tables

Katto-Ohno Correlation (general fluids)

q''_CHF / (G h_fg) = function of (L/D, G²L/(ρ_L σ), ρ_v/ρ_L) Valid for many fluids; ±20–30% accuracy

CHF reduction factors: Non-uniform heat flux: F_q = non-uniform/uniform CHF ratio Subcooling: higher subcooling → higher CHF Mass flux: q''_CHF ∝ G^0.3 (roughly) Pressure: CHF peaks at 30–50% of P_c; drops near critical point

Minimum DNB Ratio (MDNBR)

MDNBR = min(q''_CHF / q''_local) along heated length Design requirement: MDNBR ≥ 1.3 (nuclear); ≥ 1.5 (conservative); ≥ 1.2 (electronics cooling)

Microchannel Flow Boiling (D < 1 mm)

Confinement number: Co_new = √(σ/(g(ρ_L - ρ_v) D²)) > 0.5 → confined (microchannel regime)

Differences from macroscale:

• Nucleation suppressed (high confinement pressure)
• Two-phase pressure drop much higher
• Slug/annular flow dominates; no stratification
• Higher heat transfer than macro for same pumping power

Correlations (microchannel): Kandlikar (2004): h = max(h_nucleate, h_convective) h_nucleate = 0.6683 Co^(-0.2) (1-x)^0.8 h_lo + 1058.0 Bo^0.7 (1-x)^0.8 F_fl h_lo F_fl = fluid-surface parameter (1.0 for water-copper; 1.63 for R-134a-copper)

Flow instability in microchannels: Upstream compressibility → pressure-drop oscillations → intermittent dryout Prevention: inlet restriction; multiple parallel channels; outlet constraint

Two-Phase Pressure Drop

Lockhart-Martinelli method: ΔP_tp = Φ_L² × ΔP_L [two-phase multiplier] ΔP_L = single-phase liquid pressure drop (at same mass flow rate)

Chisholm correlation for two-phase multiplier: Φ_L² = 1 + C/X_tt + 1/X_tt² C = 20 (turbulent-turbulent); 12 (turbulent-viscous); 10 (viscous-turbulent); 5 (viscous-viscous)

Void fraction (Zivi): α = 1 / [1 + (1-x)/x × (ρ_v/ρ_L)^(2/3)]

Average mixture density: ρ_m = α × ρ_v + (1-α) × ρ_L

Condensation Flow Regimes (for reference — complement to flow boiling)

Opposite process: x decreasing; annular mist → slug → bubbly Nusselt condensation (film on wall) + convective condensation Shah condensation correlation: h_tp = h_lo × [1 + 3.8/Z^0.95] (Z = similar to Shah boiling)

Output

Provide: flow regime identification at inlet and outlet conditions, Chen or Shah h_tp [W/m²K] at each quality increment, h_pool and h_conv components, CHF limit (q''_CHF [W/m²]) and MDNBR, two-phase pressure drop ΔP_tp [kPa], void fraction α at exit, DNB or dryout risk assessment, and recommended design safety factor on CHF (≥ 1.3 for engineering applications).