Engineering & Science
Žukauskas Crossflow Tube-Bank Nusselt Correlation (Shell & Economizer Bundles)
Calculate staggered tube-bundle external crossflow Nusselt number Nu_D = 0.35 * (S_T / S_L)^0.2 * Re_D,max^0.60 * Pr^0.36 * (Pr / Pr_s)^0.25 across boiler economizers and air coolers.
Why wake turbulence inside staggered tube bundles beats isolated single cylinders by 40%–70%!
Churchill-Bernstein models a SINGLE isolated cylinder in crossflow—yet inside boiler economizers, shell-side exchangers, and finless air coolers, wakes shed by upstream tubes buffet downstream rows and thin boundary layers dramatically! Algirdas Žukauskas (Advances in Heat Transfer, 1972) established the authoritative correlation for >= 20-row staggered tube banks at 1,000 <= Re_D,max <= 2 × 10^5 (with pitch ratio S_T / S_L < 2): Nu_D = 0.35 * (S_T / S_L)^0.2 * Re_D,max^0.60 * Pr^0.36 * (Pr / Pr_s)^0.25, including wall-temperature Prandtl correction (Pr / Pr_s)^0.25!
Evaluate water heating across a staggered bundle (pitch ratio S_T / S_L = 1.25, Re_D,max = 18,000, bulk Pr = 5.80, heated tube-wall Pr_s = 4.20): Žukauskas yields Nu_D = 266.99, rising to 404.68 when maximum gap Reynolds number doubles to 36,000!
| Max Gap Reynolds Re_D,max (ST/SL = 1.25, Pr = 5.8, Pr_s = 4.2) | Leading Coeff C = 0.35*(ST/SL)^0.2 | Žukauskas Nu_D | Bundle Regime |
|---|---|---|---|
| Re_D,max = 18,000 (Design Crossflow) | 0.3659 | 266.99 | Mixed Subcritical Wake Buffeting |
| Re_D,max = 36,000 (2× Velocity) | 0.3659 | 404.68 | Re^0.60 Scaling (+51.6%) |
| Re_D,max < 1,000 or ST/SL >= 2 | Out of Correlation Band | "Outside Staggered Zukauskas Regime" | Regime Guard |
Žukauskas Staggered Tube-Bank Average Nusselt Number Nu_D
Evaluates 0.35 * (S_T / S_L)^0.2 * Re_max^0.60 * Pr^0.36 * (Pr / Pr_s)^0.25 for 1,000 <= Re_max <= 200,000 (B2), bulk Pr (B3), surface Pr_s (B4), and transverse-to-longitudinal pitch ratio S_T / S_L < 2 (B5).
=IF(OR(B2 < 1000, B2 > 200000, B3 <= 0, B4 <= 0, B5 <= 0, B5 >= 2), "Outside Staggered Zukauskas Regime", ROUND((0.35 * (B5 ^ 0.2)) * (B2 ^ 0.6) * (B3 ^ 0.36) * ((B3 / B4) ^ 0.25), 2))Wall-Temperature Prandtl Correction Factor (Pr / Pr_s)^0.25
Quantifies boundary-layer viscosity thinning (> 1 during liquid heating, < 1 during liquid cooling).
=IF(OR(B3 <= 0, B4 <= 0), "Outside Staggered Zukauskas Regime", ROUND((B3 / B4) ^ 0.25, 4))Try the example
Use the original values or change them to test your understanding.