Steam

Steam desuperheater sizing: spray water from the energy balance (IAPWS-IF97)

Q: How do you calculate desuperheater spray water flow?

With the adiabatic mixing energy balance: ṁ_w = ṁ_s·(h_s − h_target)/(h_target − h_w), with IAPWS-IF97 enthalpies at the steam pressure (h_s and h_target) and at the water pressure and temperature (h_w). In the example, 4,000 kg/h of steam at 10 bar(g) and 280 °C brought to 190 °C need 355.1 kg/h of water at 105 °C.

Q: Why not desuperheat down to saturation?

At or below saturation the water would not evaporate and would leave as condensate — the calculator declares it not feasible. Even above saturation, each desuperheater type has a minimum approach guaranteed by the manufacturer; below it, part of the water does not evaporate. Enter that catalogue value so the calculator checks it.

Q: What minimum approach does the calculator use if I do not enter one?

None. There is no default because the number depends on the type and manufacturer. Without it, the calculator only requires the target to be above saturation and issues the warning "Minimum approach to saturation not entered".

Q: Does the calculator check the nozzle, atomization and evaporation length?

No. Feasibility is thermodynamic only: the mass and energy balance closes and the final state exists above saturation. Minimum pressure differential for atomization, straight length for complete evaporation, desuperheater pressure drop, nozzle control range and capacity at minimum load depend on the type and manufacturer and must be confirmed before selection.

Q: What if the water is too hot or has too little pressure?

If the water pressure does not exceed the steam pressure, it neither enters nor atomizes: not feasible. If the water enthalpy is equal to or greater than the steam enthalpy at the target temperature, it does not cool the steam to the target: not feasible. And if the entered temperature is not liquid water at the entered pressure, the input is rejected.

Q: What if the steam is already below the target temperature?

Then there is no water to inject: the calculator reports that desuperheating is not needed and the steam goes to the downstream line at its inlet state.

Q: Why is the line after the desuperheater checked with a different flow?

Because the evaporated water becomes steam and adds to the flow. In the example the downstream line carries 4,355.1 kg/h, not 4,000 kg/h. The calculator uses that flow for the minimum diameter, the velocity and the line march to the consumer.

A desuperheater injects water into superheated steam to bring it to a target temperature above saturation. The water flow comes from the adiabatic mixing balance ṁ_s·h_s + ṁ_w·h_w = (ṁ_s + ṁ_w)·h_target, with complete evaporation and every enthalpy from IAPWS-IF97; the calculator checks the manufacturer minimum approach to saturation, the water pressure and temperature, and the downstream line to the consumer.

When to use

Use it when the installation has a desuperheater only, without pressure reduction: superheated steam from a boiler, turbine or header that must reach a consumer at a lower temperature, closer to saturation. The desuperheater works at the inlet pressure; the calculator requires superheated inlet steam and returns the spray water flow, the outlet steam flow, the actual approach to saturation, the minimum internal diameter of the downstream line and, if the line is entered, the pressure, temperature and velocity at the consumer. If there is also a pressure reduction, use the Pressure-reducing station, which has the same physics. The feasibility it delivers is thermodynamic only: the equipment (atomization, evaporation length, pressure drop, nozzle range, minimum load) belongs to the manufacturer.

What the calculator solves

A desuperheater removes superheat from steam by injecting water. The design question is how much water, and the answer is an energy balance: the heat the steam loses from T_inlet to T_target is what the water gains to evaporate completely at that condition.

ṁ_w = ṁ_s · (h_s − h_target) / (h_target − h_w)

LOGOS evaluates h_s and h_target at the steam pressure and h_w at the water pressure and temperature, all from IAPWS-IF97. The stand-alone desuperheater works at the inlet pressure: there is no reduction, and the pressure drop of the equipment itself is not calculated.

What is checked

Inlet. Steam must be superheated; water must be liquid at the entered pressure (below its saturation and above 0.01 °C), below the critical pressure. Product pressure up to 100 bar(a).
Target above saturation. Target at or below T_sat → not feasible.
Manufacturer minimum approach. If entered and not met → not feasible. If not entered → warning; there is no default.
Water pressure above steam pressure. Otherwise → not feasible.
Water cold enough. Water enthalpy ≥ steam enthalpy at the target → not feasible.
Desuperheating needed. If the steam is already at or below the target, there is no water to inject.
Downstream line. Minimum diameter from the velocity limit with the outlet flow (steam + water); with ID and length entered, the line is marched to the consumer — friction, fittings, elevation and heat loss — with a pressure verdict (met with margin / met without margin / not met / not evaluated) and a velocity verdict.

What is not checked

“Feasible” here is thermodynamic only. The calculator does not evaluate the minimum pressure differential for atomization, the straight length for complete evaporation, the desuperheater pressure drop, the nozzle control range or the capacity at minimum load. These depend on the type and manufacturer and must be confirmed before selection — the calculator issues this warning whenever the balance is feasible and there is water to inject.

How it ties to the references

Water and steam properties follow IAPWS R7-97(2012) (IF97); viscosity and conductivity in the downstream line, IAPWS R12-08 / R15-11; heat loss of the insulated line, ISO 12241:1998. The velocity limits (40 and 70 m/s) and the 0.045 mm roughness are LOGOS default criteria, adjustable. The calculation report cites NR-13 only as a documentation reference and interface with the legally qualified professional.

Formulas and fundamentals

Spray water — adiabatic mixing balance ṁ_s·h_s + ṁ_w·h_w = (ṁ_s + ṁ_w)·h_target → ṁ_w = ṁ_s·(h_s − h_target) / (h_target − h_w)

The heat the steam loses down to the target temperature is what the water gains to evaporate completely at that condition. ṁ_s = inlet steam flow [kg/h]; ṁ_w = spray water flow [kg/h]; h_s = inlet steam enthalpy [kJ/kg]; h_target = steam enthalpy at the working pressure and target temperature [kJ/kg]; h_w = water enthalpy at its own pressure and temperature [kJ/kg]. Adiabatic balance (no heat loss in the equipment) and complete evaporation.

States from IAPWS-IF97 h_s = h(P, T_inlet) ; h_target = h(P, T_target) ; h_w = h(P_water, T_water)

All enthalpies come from the LOGOS IAPWS-IF97 engine, with absolute pressures (bar(g) + atmosphere). P = steam pressure, the same at inlet and outlet: the stand-alone desuperheater does not reduce pressure, and the pressure drop of the equipment itself is not calculated.

Outlet steam flow ṁ_out = ṁ_s + ṁ_w

Evaporated water adds flow. It is ṁ_out — not ṁ_s — that sets the minimum diameter, velocity and pressure drop of the downstream line.

Approach to saturation ΔT_ap = T_target − T_sat(P) ≥ ΔT_ap,min (manufacturer)

How far the target temperature stays above saturation at the working pressure [K]. ΔT_ap ≤ 0 is not feasible (the water would not evaporate). ΔT_ap,min is the minimum approach guaranteed by the desuperheater manufacturer; the calculator has no default — without it, it only requires being above saturation and issues a warning.

Minimum internal diameter from velocity D_min = √(4·ṁ·v / (π·V_lim))

ṁ = mass flow in the line [kg/s]; v = steam specific volume [m³/kg]; V_lim = design velocity limit [m/s]. LOGOS default (D124): 70 m/s if the steam leaves superheated, 40 m/s if it leaves saturated or wet; adjustable.

Consumer pressure verdict available margin = P_consumer − P_req → < 0: not met ; < M_P: met without margin ; ≥ M_P: met with margin

P_consumer comes from marching the downstream line (Darcy-Weisbach friction with Colebrook, fittings, elevation, acceleration and heat loss per ISO 12241). P_req = required pressure at the consumer [bar(g)]; M_P = design margin [bar].

Standards & methods

IAPWS R7-97(2012) — IAPWS-IF97, thermodynamic properties of water and steam
IAPWS R12-08 / R15-11 — viscosity and thermal conductivity of water (downstream line)
ISO 12241:1998 — heat loss of the insulated line (LOGOS implements the 1998 edition)
NR-13 (Brazil) — documentation reference and interface with the legally qualified professional; LOGOS does not perform legal classification nor replace the construction code

Typical reference values

Quantity	Typical range	Note
Velocity limit — superheated steam	70 m/s	LOGOS default criterion (D124), adjustable. Applied when the steam leaves the desuperheater with at least 1 K of superheat.
Velocity limit — saturated or wet steam	40 m/s	LOGOS default criterion (D124), adjustable. The velocity judged is the maximum along the downstream line, not the one at its start.
Minimum approach to saturation	no default value	Depends on the desuperheater type and manufacturer; enter the catalogue value. Without it, the calculator only requires a target above saturation and warns.
Downstream line roughness	0.045 mm	LOGOS default for commercial steel (D123); for an existing line, use the effective roughness or calibrate with field data.
Two-phase model domain in the line	quality ≥ 0.95 declared; 0.80–0.95 indicative; < 0.80 not evaluated	A LOGOS criterion, not a normative limit — it only matters if the downstream line condenses.
Product maximum pressure	100 bar(a)	LOGOS Steam product limit (D220); above it the input is rejected.

Worked example

Desuperheater from 10 bar(g) / 280 °C to 190 °C, 4,000 kg/h

Inputs

Inlet steam pressure: 10 bar(g)
Inlet steam temperature: 280 °C
Steam flow: 4,000 kg/h
Target temperature: 190 °C
Minimum approach to saturation (manufacturer): 5 K
Spray water (temperature / pressure): 105 / 15 °C / bar(g)
Downstream line (ID × L): 128.2 × 40 mm × m
Downstream line fittings: 4 × 90° elbows + 1 open gate valve -
Insulation (thickness · λ · OD): 50 · 0.05 · 141.3 mm · W/m·K · mm
Required consumer pressure / margin: 9.5 / 0.1 bar(g) / bar

Results

Saturation at the working pressure: 184.12 °C
Inlet superheat: 95.9 K
Inlet steam / water enthalpy: 3,005.7 / 441.3 kJ/kg
Spray water: 355.1 kg/h
Outlet steam: 4,355.1 kg/h
Approach to saturation (minimum 5 K): 5.88 K
Downstream minimum ID (70 m/s limit): 63.0 mm
Maximum velocity in the downstream line: 16.97 m/s
Consumer pressure (line ΔP): 9.930 (0.07) bar(g) (bar)
Consumer temperature / local saturation: 188.7 / 183.8 °C
Pressure verdict: met with margin 0.43 bar available / 0.1 bar required

At 10 bar(g) saturation is 184.12 °C, so the steam at 280 °C enters with 95.9 K of superheat. To bring it to 190 °C the balance calls for 355.1 kg/h of water at 105 °C (enthalpy 441.3 kJ/kg, against 3,005.7 kJ/kg for the steam), and the flow going to the line rises to 4,355.1 kg/h. The target sits 5.88 K above saturation — above the 5 K minimum entered, but with little room: an even lower target would hit the manufacturer limit. The water at 15 bar(g) exceeds the steam pressure and the balance closes: the desuperheater is feasible in the thermodynamic sense, and the calculator issues the warning that the equipment was not checked. As the steam still leaves superheated, the 70 m/s limit applies; the 128.2 mm line (minimum ID 63.0 mm) runs at 16.97 m/s. Along the 40 m insulated run, the steam reaches the consumer at 9.930 bar(g) and 188.7 °C, still above local saturation (183.8 °C), with no condensate; the available margin of 0.43 bar covers the 0.1 bar required.

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Common mistakes

Setting the target temperature at or below saturation. The water would not evaporate and would leave as condensate; the calculator declares the desuperheater not feasible.
Leaving the minimum approach blank. Each desuperheater type has its own, guaranteed by the manufacturer; without it the calculator only checks that the target is above saturation, which is not enough for the equipment to evaporate all the water.
Entering water at a pressure equal to or below the steam pressure. Water must exceed the steam pressure at the injection point to enter and atomize; in that case the result is not feasible. The calculator only checks that the pressure is higher — the minimum atomizing differential belongs to the manufacturer.
Using water that is too hot. If the water enthalpy is equal to or greater than the steam enthalpy at the target temperature, injecting it does not cool the steam to the target: not feasible. Colder water needs less flow, because each kg removes more heat.
Sizing the downstream line with the inlet flow. Evaporated water adds flow: the line carries ṁ_s + ṁ_w, and the minimum diameter, velocity and pressure drop come from it.
Taking "balance feasible" as equipment selection. The calculator does not check the atomizing differential, straight length for complete evaporation, desuperheater pressure drop, nozzle control range or capacity at minimum load.

Frequently asked questions

How do you calculate desuperheater spray water flow?