Plate-Fin Cryogenic Heat Exchanger (PFHE) Sizing Calculator
Perform industrial thermal-hydraulic sizing for brazed aluminum plate-fin heat exchangers (BAHX). Calculate offset-strip fin Colburn j and Fanning f friction factors (Manglik-Bergles), fin efficiency, overall UA rating, stream pressure drops, and core block stacking dimensions.
1. Process Service & Core Specifications
2. Thermal, Hydraulic & Core Sizing
Engineering Principles & Rigorous Mathematical Derivations
Brazed Aluminum Plate-Fin Heat Exchangers (BAHX) provide the highest surface area density of any industrial heat exchanger type, handling temperatures down to 4 Kelvin (-269°C) in aerospace, LNG liquefaction, and air separation industries.
1. Offset Strip Fin (OSF) Hydraulic Geometry
The interrupted fin structure has four fundamental microscopic dimensions: fin height (h'), fin pitch (s) (where (s = 1 / ext{FPI})), fin strip length (ell), and fin metal thickness (t). The hydraulic diameter (D_h) is derived from wetted perimeter and free flow area:
The aspect ratio (alpha = s / h'), thickness ratio (delta = t / ell), and contraction ratio (gamma = t / s) parameterize the boundary layer development.
2. Manglik & Bergles Heat Transfer & Friction Correlations
Using the dimensionless Reynolds number (Re = rac{G D_h}{mu}) (where mass velocity (G = rac{dot{m}}{A_{free}})), the Colburn factor (j) and Fanning friction factor (f) are calculated via the Manglik-Bergles equations:
Convective film heat transfer coefficient (h = j cdot G cdot c_p cdot Pr^{-2/3}).
3. Fin Efficiency & Overall Surface Temperature Effectiveness
Extended surface efficiency accounts for the conduction resistance down the thin corrugated aluminum fin:
Where (k_{al} approx 180, ext{W/m}cdot ext{K}) for brazed aluminum alloys (AA 3003).
4. Core Pressure Drop Across Interrupted Passages
The frictional core pressure drop over active heat transfer length (L) is governed by Fanning friction:
5 Fatal Engineering Traps & Industrial Operating Hazards
1. Thermal Shock Cracking via Excessive Ramp Rates (>50°C/hr)
During plant startup, cool-down, or sudden tripped restarts, introducing cryogenic fluids faster than 50°C per hour creates violent transient temperature gradients across the block. The thick solid aluminum side bars respond slower thermally than the micro-thin corrugated interior fins, inducing massive internal shear stresses that rupture parting sheet brazes and destroy interlayer seals.
2. Two-Phase Maldistribution across Parallel Brazed Layers
In boiling mixed refrigerants or flashing LNG, liquid and vapor phases separate easily in inlet header manifolds. If header distributor nozzles are improperly baffled, liquid preferentially floods center layers while vapor starves outer layers. This maldistribution collapses the effective LMTD, causing severe pinch-point violations and under-performance by up to 35%.
3. Mercury Liquid Metal Embrittlement (LME) Catastrophic Rupture
Elemental mercury in untreated gas streams passes into the cold box and condenses on aluminum core surfaces above -38.8°C. Liquid mercury wets and penetrates aluminum grain boundaries, inducing catastrophic brittle cracking without prior warning. All natural gas entering aluminum PFHEs must pass through non-regenerable sulfur-impregnated carbon guard beds (<0.01 µg/Nm³ Hg).
4. Inter-Layer Pressure Reversal Parting Sheet Buckling
In multi-stream cores, high-pressure natural gas (60 to 80 bar) runs directly adjacent to low-pressure boiling refrigerant (3 to 6 bar). During emergency pressure relief or testing, sudden depressurization of one circuit without equalizing adjacent passages creates huge differential pressure across 1.5 mm parting sheets, buckling internal corrugation fins and causing internal cross-stream leakage.
5. Serrated Channel Particulate Clogging & Freeze-up
Serrated fin passages have hydraulic openings under 1.5 mm. Migrating desiccant dust from upstream molecular sieve dehydration beds, pipe scale, or frozen moisture/carbon dioxide instantly clogs fin gaps. Trapped dead zones freeze solid, creating localized pressure spikes that physically rupture fin passages during defrost cycles.