Design studyIndustrial ductwork

The elbow that starves a heat exchanger.

A short-radius bend discharging into an exchanger casing delivers 13.8% RMS non-uniformity across the tube face, against a 10% specification. Turning vanes inside the existing elbow clear it and take pressure off the fan rather than adding it. Add a distribution plate to those same vanes and the face reaches 1.9%, still cheaper to run than the duct as drawn.

The duct: gas enters, turns through a short-radius elbow, expands into the casing and passes the tube bundle — Gas enters at 12 m/s, turns through a short-radius elbow, dumps into the casing and passes the tube bundle. Uniformity is judged on the plane where the gas enters the bundle.

13.8%

RMS AS DESIGNED · SPEC IS 10%

1.9%

RMS · VANES AND PLATE

−26 PA

FAN DUTY, NOT MORE

CONFIGURATIONS

THE PROBLEM

An exchanger is bought on a duty, and the duty assumes the gas arrives evenly.

Ductwork rarely obliges. Where the plant room is tight, the last thing upstream of the casing is often a short-radius elbow and a sudden expansion, and both do the same thing: they put all the momentum on one side and leave the rest of the face to be fed by whatever recirculates back into it.

Non-uniformity here is the area-weighted RMS deviation of flow per unit area from its own mean. Flow rather than velocity, because it sums to the inlet flow exactly. Recirculation is reported separately, and measured upstream of the face: a core this resistive suppresses reverse flow at its own inlet plane, so a face-only metric would report zero recirculation for a plenum that is half filled with it. That is exactly the trap a face measurement sets.

Duct	500 mm square	12 m/s, Re 1.7 × 10⁵
Bend	R/D = 0.75	short radius, no vanes as designed
Casing	1200 mm square	1.44 m² face, 5.8:1 expansion
Core	250 mm deep, 150 Pa	face velocity 2.08 m/s
Fluid	0.746 kg/m³, 34.9 cSt	flue gas at about 200 °C
Flow	10,800 m³/h	3.00 m³/s

AS DESIGNED

The gas cannot turn a corner that tight.

It separates off the inner wall of the elbow, and the separation bubble narrows the duct's effective exit, so the gas arrives at the expansion as a jet that is both faster and narrower than the duct that made it. It then crosses the plenum as a jet instead of spreading into it, and 16% of the plenum ends up recirculating around it. At the face that lands as 13.8% RMS against a 10% specification, with a peak of 1.41× the mean. The duct fails.

Speed on the plane of the bend, as designed beside the vaned elbow — Speed on the plane of the bend. Left: as designed. The jet separates off the inner wall, crosses the elbow and drives straight through the plenum to one side of the core, with a recirculation filling the rest of the casing.

Flow per unit area where the gas enters the bundle, as a multiple of the mean. The dashed rectangle is the duct footprint projected onto the face. The defect is mostly a centre-peaked jet with a starved perimeter.

TURNING VANES

The fix that pays for itself.

A turning vane is a strip of sheet metal on a constant radius inside the elbow. It splits one impossible turn into several achievable ones: each channel is short enough and its radius ratio gentle enough that the gas stays attached. Nothing else about the duct changes.

Vanes	RMS · % settled	Plenum recirc · %	Peak / mean	Duty short · %	Δp · Pa
0	13.8 ±0.39	16	1.41	0.57	211
1	11.5 ±0.06	14	1.35	0.41	193
2	9.5 ±0.30	13	1.25	0.28	186
3	8.4 ±0.20	9	1.23	0.22	182
4	7.7 ±0.27	11	1.22	0.19	185

Uniformity and duty against vane count. Bars are the movement of the answer over the last part of the run. The first vane does most of the work: 13.8% becomes 11.5% for a single strip of steel.

Where to put them

Three vanes can be spaced evenly across the gap, or on a constant radius ratio, the classical rule, which crowds them towards the inner wall where the turning is sharpest. Both were run, at the same vane count, in the same elbow. The classical rule wins, and the margin is small enough that fabrication tolerance matters as much as the rule does.

3 vanes at	Radii · mm	RMS · %	Duty short · %	Δp · Pa
even spacing	250, 375, 500	8.4	0.22	182
constant radius ratio	179, 286, 411	8.1	0.21	179

THE OTHER FIX

A plate is the more powerful device, and the more expensive habit.

The standard alternative is to leave the elbow alone and put a perforated distribution plate across the casing ahead of the core. It adds a resistance in series with the bundle, and a resistance in series makes the flow through it more even. It works better than the vanes do, 4.3% RMS from a K = 2 plate against 7.7% from four vanes, because it acts on the whole face at once rather than on the thing that spoiled it.

But look at what it does upstream of itself. Plenum recirculation goes up with a plate fitted, from 16% to 24%, because the plate blocks the jet and the blocked gas has to go somewhere. The vanes take the same number from 16% to 9%. The plate does not remove the recirculation; it stops the recirculation reaching the face. That is the difference between treating a symptom and removing a cause, visible in a number rather than asserted.

Plate	RMS · %	Centre peak · %	Duty short · %	Δp · Pa	vs as designed
none	13.8	28	0.57	211	+0
K = 2	4.3	9	0.06	246	+35
K = 4	3.0	6	0.03	249	+38

Uniformity against the pressure drop it costs, for vanes and for plates — Uniformity against the pressure drop it costs. The two fixes move in opposite directions. Vanes go down and to the left: more uniform and cheaper. A plate goes down and to the right: more uniform and dearer.

It also has to be paid for on every hour the plant runs. The K = 2 plate costs +35 Pa, about 160 W of shaft power at 3.0 m³/s and 65% fan efficiency. The vanes cost −26 Pa, which is to say they give 119 W back, because a vaned elbow has a lower loss coefficient than a separated one.

The two fixes at the face: a plate beside vanes — The two fixes at the face. A plate flattens the profile by resisting it everywhere; vanes flatten it by never creating the jet.

BOTH TOGETHER

Fix the cause and the symptomatic fix costs less than it does alone.

Three vanes and a K = 2 plate give 1.9% RMS at 204 Pa: seven times more uniform than the duct as designed, for 7 Pa less pressure drop than the duct as designed. The duty shortfall falls from 0.57% to 0.01%.

The arithmetic is not additive. Separately the vanes save 29 Pa and the plate costs 35 Pa, which would put the combination +6 Pa against the duct as designed. It actually comes out −7 Pa, some 13 Pa better than the parts predict: with the jet already removed the plate has less to correct, and its own loss does less harm.

If the specification is the 10% this study started from, the combination is not needed. Three vanes reach 8.4% and save 133 W. Two reach 9.5%, inside the specification but not clear of it once the 0.6-point spread across the grid study is allowed for, so three is the number to fit.

Face velocity across the casing in the plane of the bend, labelled by vane count. The as-designed profile is the one that goes negative.

LIMITATIONS

Stated rather than buried.

Single phase and isothermal. No buoyancy in the plenum, no fouling layer.

The core is a porous zone with real depth, not modelled tubes.

The plate's uniformity benefit is model-dependent. Its pressure penalty is not.

Grid convergence on uniformity is not monotone, so no GCI is quoted.

Uneven fouling and tube metal temperature are not priced.

BRING US THE DECISION

Before the casing is fabricated.

If an exchanger is not making its duty, or a purchase specification names a uniformity figure nobody has checked, send us the duct arrangement and the flow. The cheapest fixes are usually upstream of the thing that is failing.

TALK TO AN ENGINEER

OpenFOAM v2512, simpleFoam, steady, incompressible, k–ω SST with wall functions. Hexahedral mesh from blockMesh, Cartesian throughout except the bend; max non-orthogonality 0.74, max skewness 0.034. Core as a Darcy–Forchheimer zone 250 mm deep, F = 371 m⁻¹ along the flow and 3706 across it. Vanes as zero-thickness walls cut from internal faces at constant radius. 2,500 iterations. Pressure differences are inlet-to-outlet static. Basis: a representative duct, not a named client.