Staggered Tube Bundle Cross-Flow Pressure Drop (Zhukauskas Correlation)

Cross-flow pressure drop and mass balance across a 5-tube staggered heat exchanger bundle in a rectangular duct, verified against the classical empirical correlation of Zhukauskas.

Tolerance:

5%

Problem statement

Geometry

Rectangular duct 560 × 220 × 90 mm with 5 staggered circular tubes of diameter D = 44 mm across the full height of 90 mm (Row 1: 2 tubes at X = -20 mm, Y = ±50 mm; Row 2: 1 central tube at X = 45 mm, Y = 0 mm; Row 3: 2 tubes at X = 110 mm, Y = ±50 mm).

Material

Water at 20 °C (rho = 998.2 kg/m³, mu = 1.002e-3 Pa·s).

Boundary conditions

Inlet uniform velocity U = 2.5 m/s along +X (intensity 5%), gauge pressure 0 Pa at outlet, slip symmetry on top and bottom walls, no-slip viscous walls on duct side walls and tube cylinders.

Measured quantity

Total static pressure drop Delta_p across the tube bank (target 182.0 kPa from Zhukauskas correlation) and mass flow conservation between inlet and outlet (|massImbalance| <= 2%).

WebCAE Terminal

units mm
import path="cfd_staggered_tube_bundle.step" format=step
mesh tet size=15
cfd fluid water
cfd set mode=steady speed=2.5 turbulence=sst iterations=280 tol=1e-4 threads=8 intensity=5 multigrid=1 cfl=8
cfd inlet surface number 1 speed=2.5 intensity=0.05
cfd outlet surface number 8 pressure=0
cfd symmetry surface number 2
cfd symmetry surface number 10
cfd wall surface number 9 monitor=off
cfd wall surface number 11 monitor=off
cfd wall surface number 3 monitor=on
cfd wall surface number 4 monitor=on
cfd wall surface number 5 monitor=on
cfd wall surface number 6 monitor=on
cfd wall surface number 7 monitor=on
solve cfd

Results comparison

Updated: 2026-10-19 · WebCAE solver