Duct Spray Cooling: How Many Meters to Full Evaporation

A flue gas duct cooling spray fails in two visible ways. Both are wetting failures. Give droplets too little time or distance, and they rain out on duct walls. They bind with ash and build a deposit that grows until the duct plugs. The same water reaches the baghouse downstream and blinds the media with damp dust. A wet stack and a dead filter are one sizing error seen from two ends of the duct.

The other failure runs the opposite way. Under-spray the duty and temperature excursions trip the filter inlet. Dampers warp, and the induced draft fan pushes past its rating. Duct probes respond in seconds. A control loop that lags behind evaporation physics either floods the duct or misses the setpoint. Three numbers decide a good flue gas duct cooling spray. The energy balance comes first. The droplet lifetime comes second. The wet-bulb floor comes last. This guide works all three for duct spray coolers and gas quench sections on flue gas and process air. Every figure is a published order of magnitude, not a guarantee. Your dust chemistry and duct geometry get the final vote.

The Snapshot

• Latent heat of water is about 2.26 MJ/kg at 100 C. Flue gas cp sits near 1.0-1.1 kJ/kg-K. Cooling 1 kg/s of gas by 1 C takes about 0.44-0.49 g/s of evaporated water.
• A 10,000 m3/h duct cooled 100 C carries a duty near 260 kW. It needs roughly 7 L/min of spray water. Evaporating 26-27 L/min removes close to 1 MW.
• Droplet lifetime scales with diameter squared. A 100 um drop lives 0.1-0.3 s. A 200 um drop lives 0.4-1.2 s. At 12 m/s, that is 1-4 m of duct, or 5-14 m.
• Fine droplets reach a 90-98% saturation approach in short distances. Coarse droplets need longer ducts. Keep drops under 250-300 um when the straight run is short.

Where Duct Spray Cooling Earns Its Keep

A duct spray cooler is the cheapest heat exchanger you can install. The duct is the exchanger. Evaporation is the transfer mechanism. It earns its keep where gas must cool fast and dilute particulate is acceptable. Classic spots are baghouse inlets on kilns, coolers and dryers. Induced draft fan inlets qualify, as do converter and furnace off-gas lines. Process air conditioning ahead of coating or drying stations completes the list.

Compare that with a quench tower. A tower gives long residence time, coarse drops, and a recycled water loop. It handles heavy dust loads and aggressive chemistry. A duct system is tighter and cheaper. But you get one or two seconds of flight time. There is no recovery if a droplet hits the wall.

Duct spray cooling suits duties from a few hundred kW to a few MW. The gas should be moderately clean. Wall wetting must be engineered out. When those two conditions fail, build the tower. The same logic makes evaporative cooling attractive for fast response. When kiln load swings, water on and off beats a bypass damper. Cooling starts the instant droplets enter the gas.

The trade-off is precision. Too much water is not wasteful here. It is a fouling event. That is why the flue gas duct cooling spray literature keeps returning to droplet size and distance. Pump capacity is the easy part.

One duty deserves the name gas quench in its rawest form: converter off-gas straight from the vessel. The physics is identical. What changes is the dust load and the nozzle family. A gas quench section on heavy dust behaves like a short spray tower, not a clean duct.

The Energy Balance Is Fixed Before You Pick a Nozzle

Water rate comes from the heat load. Full stop. Multiply gas mass flow by specific heat and by the temperature drop. That gives the duty. Divide the duty by latent heat. That gives the evaporation rate. Nothing about nozzle type, drop size or control scheme changes this arithmetic. Nozzles change how fast water evaporates, and where it lands. They do not change how much heat it absorbs.

Work the standard reference case. Take 10,000 m3/h of flue gas at about 120 C. Cool it by 100 C. At that temperature, density is roughly 0.9 kg/m3. Mass flow is 10,000 divided by 3,600, times 0.9. That is about 2.5 kg/s. Flue gas cp sits near 1.05 kJ/kg-K. Duty is 2.5 kg/s times 1.05 kJ/kg-K times 100 K. That equals about 262 kW.

Water absorbs that at 2.26 MJ/kg. Divide 262 by 2,260. You get 0.116 kg/s. That is close to 7 L/min of spray water.

Run the chain at the extremes of the cp band. With cp at 1.0 kJ/kg-K, duty is 250 kW. Water is 0.111 kg/s, about 6.6 L/min. With cp at 1.1, duty is 275 kW. Water is 0.122 kg/s, about 7.3 L/min. Call it 6.6-7.3 L/min per 10,000 m3/h per 100 C. Add 10-15 percent margin instead of pretending the physics is fuzzy.

The rule of thumb behind the chain is small enough to memorize. Cooling 1 kg/s of gas by 1 C needs 1.05 kW, roughly. Against 2,260 kJ/kg of latent heat, that is 0.46 g/s of water. The band is 0.44-0.49 g/s. Every sizing in this guide reduces to that factor.

Water Rate Per Gas Flow, Worked Row by Row

Fix the drop at 80 C and cp at 1.05 kJ/kg-K. Water rate then scales linearly with gas volume. Duty in kW is mass flow times 1.05 times 80. Water in L/min is duty divided by 2.26, times 60. The table shows the chain at four flow sizes. Gas density is 0.9 kg/m3 throughout.

Gas flow at duct temperature	Gas mass flow	Duty for 80 C drop	Spray water rate
5,000 m3/h	1.25 kg/s	105 kW	2.8 L/min
10,000 m3/h	2.50 kg/s	210 kW	5.6 L/min
20,000 m3/h	5.00 kg/s	420 kW	11.2 L/min
40,000 m3/h	10.0 kg/s	840 kW	22.3 L/min

Check the last row twice. 40,000 m3/h gives 10 kg/s. Times 1.05, times 80 K, equals 840 kW. Divide by 2.26 MJ/kg for 0.372 kg/s. That is 22.3 L/min. The row is about 0.84 MW. Its water rate works out near 26.5 L/min per MW. That is the figure cooling tower people quote.

Change the temperature drop and you scale water proportionally. Halve the drop and the 10,000 m3/h row falls from 5.6 to 2.8 L/min. This is why honest vendors quote a flue gas duct cooling spray in litres per minute per megawatt first. Nozzle talk comes second.

Saturation Approach: How Close Is Realistically Close

Evaporation cools the gas and adds moisture. It continues until the gas nears its adiabatic saturation temperature. The approach percentage measures how much of the available span you capture. Define the span as inlet temperature minus the saturation limit. A 95% approach captures 95 percent of that span.

Take the 120 C duct again. Suppose the gas tops out cooling at 35 C after picking up spray moisture. The span is 85 K. A 90% approach captures 76.5 K and leaves gas near 44 C. A 95% approach captures about 81 K, leaving roughly 39 C. A 98% approach captures 83.3 K and lands near 37 C.

Saturation approach	Span captured of 85 K	Outlet gas from 120 C
90%	76.5 K	about 44 C
95%	81 K	about 39 C
98%	83.3 K	about 37 C

The last two or three points are the expensive ones. Spray saturation obeys the same transfer laws as cooling, and a spray saturation target is really an approach target in disguise. Approach climbs slowly with duct length. The driving force shrinks as the gas saturates. Fine droplets buy approach cheaply. They saturate their local air film fast and keep evaporating as the gas cools. Coarse droplets mostly add wetting risk, not approach.

One honest note for combustion gas. Fuel moisture already eats part of the span. The wet-bulb floor of real flue gas sits higher than dry-air psychrometrics suggest. Measure it or calculate it. Do not assume 35 C.

The Wet-Bulb Floor Is Not a Suggestion

Water cannot cool gas below its adiabatic saturation temperature, read as wet-bulb. This is a hard thermodynamic boundary. It is not an equipment limitation. No pressure, nozzle count or plenum length crosses it. Push more water in and the surplus survives as droplets. It wets the duct. The evaporation load is capped by the gas, not the pump.

For duct spray coolers this gives a clean commissioning rule. Compute the wet-bulb limit. Set the trip 3-5 C above it. Cap maximum water rate at whatever achieves about 95% approach. A control loop chasing setpoints below the floor responds by over-wetting. Over-wetting in a dusty duct is a maintenance event with a date stamp.

Combustion air or process air with low inlet humidity can look attractive on paper. It still fails when summer dewpoints rise. The floor rises with the air. The floor also explains two-stage systems. A quench tower or heat exchanger takes the coarse first half. The flue gas duct cooling spray polishes the last 10-30 K. That top span costs little water per kelvin and demands fine droplets.

Droplet Lifetime Scales With Diameter Squared

Once a droplet leaves the nozzle, size sets its survival time. Evaporation rate follows surface area, roughly diameter squared. The water to shed is the volume, diameter cubed. The ratio leaves lifetime proportional to diameter squared. Halve the diameter and lifetime drops to a quarter. That relation is the most useful number in duct spray design.

At duct conditions, published orders of magnitude look like this. Hot dry gas moves past drops at 10-15 m/s. A 100 um drop survives roughly 0.1-0.3 s. A 200 um drop lives about 0.4-1.2 s, four to nine times the fine band. A 300 um drop runs about 0.9-2.7 s.

At the fine end, ultrasonic and two-fluid atomizers make 30-60 um drops. Their lifetimes fall under 0.1 s. That is why they dominate tight retrofit ducts.

The bands are wide because gas temperature, humidity and turbulence move them. Hotter, drier gas shortens every lifetime. Near-saturated gas lengthens them sharply. That gas sits downstream of a previous spray row. Serial rows without a measurement point between them are a design smell. A duct spray cooler sized on cold-air tables will overfeed a hot, dry kiln duct and underfeed a cool, damp one. Always re-check lifetimes at the actual gas condition, not the nameplate.

Treat the numbers as a starting map. Validate with a simple test. Spray on for 60 seconds. Watch the outlet probe. Then watch the wall thermocouples. A wall dip means rainout.

Evaporation Distance: Velocity Multiplies Everything

Distance is lifetime times duct velocity. That is the whole conversion. It makes velocity a double-edged blade. Faster gas delivers more heat per second. It also carries surviving droplets farther before they die.

SMD of spray	Droplet lifetime band	Distance at 12 m/s	Design comment
80 um	0.06-0.19 s	0.7-2.3 m	fine mist, shortest ducts
100 um	0.1-0.3 s	1.2-3.6 m	workhorse band for short ducts
150 um	0.23-0.67 s	2.7-8.1 m	needs a generous 8 m class
200 um	0.4-1.2 s	4.8-14.4 m	medium duct or taller quench
300 um	0.9-2.7 s	10.8-32.4 m	duct territory ends; use a tower

Read each row as required straight duct. Measure from the spray plane to anything you care about. Walls, probes, filter inlets and fan rotors all count. Then add honest losses. Spray plumes are not uniform. Droplets travel along the injection axis. Air entrainment bends them. Every hydraulic spray carries a coarse tail beyond its SMD.

Design the free distance at the top of the band, not the middle. Keep droplets under 250-300 um in short ducts. When the duct cannot give 5-10 m, change the nozzle, not the ductwork. A finer pattern with more nozzles is cheaper than a longer duct with an expansion joint.

Sizing Exercise: 10,000 m3/h From 120 C to 40 C

Set a concrete target for the reference flow. Gas in at 120 C. Out at 40 C. Duct velocity of 12 m/s. Step one is duty. 2.5 kg/s times 1.05 kJ/kg-K times 80 K gives 210 kW. Step two is water. Divide 210 by 2,260 for 0.093 kg/s. That is 5.6 L/min, matching the table row. Add 10 percent and you spray about 6 L/min.

Step three is approach. Suppose the wet-bulb limit sits near 35 C. The span is 85 K. A 40 C outlet captures 80 K of it. That is 80 divided by 85, roughly 94 percent approach. A realistic target, not a fantasy.

Step four is distance. Choose a spray in the 100 um class. The table gives 1.2-3.6 m at 12 m/s. Design the free straight run at the top, about 4 m. Add plume penetration and probe standoff.

The deliverable is four numbers. About 6 L/min at moderate pressure. Hollow cone or fine mist nozzles near 100 um SMD. Four meters of clean duct ahead of the filter inlet. A control cap that stops water chasing setpoints below 35 C. That is a complete flue gas duct cooling spray spec.

Fouling, Deposits and the Wet Stack

Every drop that survives to the wall becomes a deposit event. Duct gas carries ash. Wet ash is cement in its first hour and a brick once dry. Fouling rate depends on dust chemistry and wetting frequency. It also depends on whether anyone drains and washes the section. Sticky dusts from kilns, biomass and certain minerals are the worst. One over-wetting event becomes weeks of gradual duct narrowing.

The narrowing feeds itself. A plugged-down duct raises velocity. Higher velocity raises rainout elsewhere in the system.

Water source drives the other half of fouling. Potable water leaves dissolved solids wherever a droplet dies. Recycled quench water and process condensate carry solids, fines, sometimes chlorides or sulfates. The nozzle choice then changes. Spiral nozzles have a large free passage. They resist blockage, so they are the standard answer on recycle water. Their coarse droplets belong in a tower or long duct, not a 4 m spray section.

Full cone nozzles on clean water give even distribution. That is what a short flue gas duct cooling spray section needs. Gas cooling nozzles in the hollow cone family deliver the 100-400 um band. Match drop size to available distance first. Then pick the family that survives your water.

Design the wet-stack margin as a physical feature. Slope the duct floor away from the spray plane. Provide drain taps and wash lance connections at low points. Keep wall temperature above the acid dewpoint wherever spray water runs down. Put inspection ports where plume impingement is expected. Deposit growth is slow and invisible. It is found at shutdown, when the duct is already half gone.

Water chemistry belongs in the spray line, not the nozzle datasheet. Feedwater temperature moves the duty by a few percent, since warm water arrives pre-charged with sensible heat. Dissolved solids decide what the wall sees when a droplet dies. A cheap conductivity meter on the spray header tells you more about next month’s fouling than any brochure. On closed-loop spray water, blowdown sets the solids ceiling; on once-through potable water, the ceiling is the supply itself. Check both before choosing an evaporative cooling pattern, because finer drops spread the same solids over a wider wall area.

Controls, Turndown and Measurement

The control loop keeps water rate just under evaporation capacity. That must hold during transients too. The practical scheme is feedforward from gas flow and inlet temperature. Outlet temperature feedback corrects it, with a slow rate limit. Cap the loop hard at the 95 percent approach water rate. Cheap relative probe hygrometers earn their price in saved filter bags.

Turndown discipline matters more here than in most spray duties. A flue gas duct cooling spray at 20 percent flow with five nozzles is not a scaled-down system. Pressure can collapse below the nozzle curve. SMD rises. The coarse tail then survives the duct. If the process swings widely, stage the nozzles. Keep the active set near design pressure. Put at least one nozzle per duct corner so the plume stays symmetric.

Two control details pay for themselves. Place the outlet probe in the gas centerline, downstream of full evaporation distance. A probe inside a wet plume reads droplet strikes as noise. The loop will choke flow to quiet it. Second, interlock on low spray water pressure. A plugged strainer feeds a coarse, sagging plume. That does more damage than no spray at all. For tight, high-response duties, an evaporation cooling nozzle holding 30-80 um across wide turndown buys approach without length.

Selection Checklist Before You Order

Run this list on paper before the purchase order. Each line is a failure mode with a cost attached.

• Gas flow, inlet temperature, target outlet temperature, and the wet-bulb limit for your gas chemistry.
• Duty in kW from mass flow, cp near 1.0-1.1, and the temperature drop.
• Water rate as duty divided by 2.26 MJ/kg, plus a 10-15 percent margin.
• Duct velocity, and straight distance from spray plane to the first obstruction.
• SMD class the distance table demands: 80-100 um under 4 m, 150-200 um for 5-14 m.
• Nozzle family against water quality: fine patterns need clean water, spiral hardware takes recycle duty.
• Drain, wash and inspection provisions at every expected impingement point.
• A control cap near 95 percent approach, staged nozzle groups, and probes outside the wet plume.

If any line reads unknown, the design is not done. The energy balance is arithmetic. The distance rules are published orders of magnitude. A missing line is an unasked question, not a science gap. For pattern, drop size and pressure curves, use the cooling nozzle selection guide. For the finest-drop end of the market, see the ultrasonic evaporative cooling page.

The Bottom Line

Duct spray cooling is honest physics with a sharp edge. Water rate is duty divided by latent heat. For 10,000 m3/h per 100 C that is 6.6-7.3 L/min, and no nozzle changes it. The nozzle changes the next two numbers. Droplet lifetime scales with diameter squared. Evaporation distance is lifetime times duct velocity. Fine drops near 100 um clear a 12 m/s duct in 1-4 m. 200 um drops claim 5-14 m. 300 um drops belong in a tower. Approach stops at the wet-bulb floor, so target 95 percent with a hard water cap.

A well-designed flue gas duct cooling spray section runs dry on the walls. It keeps the baghouse and stack clean. It never trips the plant downstream. Where recycle water and blockage-prone manifolds rule the site, the clog-resistant spiral nozzles hold the pattern. Where clean water sets the spec, full cone families carry the load. Want your own flows and duct length run through these chains? Send them to the contact page and we will work the rows with you.