Formula
Mass and energy balance across the desuperheater (throttling, if any, is adiabatic):
\(\dot m_1 h_1 + \dot m_w h_w = \dot m_2 h_2 \qquad \dot m_2 = \dot m_1 + \dot m_w\)
\(\dot m_w = \dot m_1\,\frac{h_1 - h_2}{h_2 - h_w} \qquad \Delta T_{sh,2} = T_2 - T_{sat,2}\)
Variables
| Symbol | Meaning | SI unit |
|---|---|---|
| \(\dot m_1\) | inlet steam flow | kg/s |
| \(p_1\) | inlet steam absolute pressure | Pa |
| \(T_1\) | inlet steam temperature | K |
| \(p_2\) | outlet steam absolute pressure | Pa |
| \(T_2\) | outlet steam temperature (target) | K |
| \(p_w\) | spray water absolute pressure | Pa |
| \(T_w\) | spray water temperature | K |
| \(\dot m_w\) | spray water flow | kg/s |
| \(\dot m_2\) | outlet steam flow | kg/s |
| \(\dot m_w / \dot m_1\) | spray water per kg of inlet steam | – |
| \(T_{sat,2}\) | saturation temperature at the outlet pressure | K |
| \(\Delta T_{sh,2}\) | outlet superheat | K |
| \(h_1\) | inlet steam enthalpy | J/kg |
| \(h_2\) | outlet steam enthalpy | J/kg |
| \(h_w\) | spray water enthalpy | J/kg |
Method and standards
Enthalpies from FireCAD's IAPWS-IF97 implementation (region 2 for the steam, region 1 for the water). The balance is the standard first-law statement for an adiabatic mixing device with no shaft work.
Assumptions and limits
- No heat loss from the desuperheater and piping.
- All spray water evaporates; the outlet is superheated steam.
- Inlet and outlet steam must be superheated; spray water must be liquid.
References
- IAPWS R7-97(2012) IF97
Questions and answers
How much spray water does a PRDS need?
For 20 t/h of steam at 64 bar(a) and 480 °C reduced to 12 bar(a) and 250 °C with spray water at 130 °C, about 1.01 kg/s (3.6 t/h), or 18 % of the inlet steam. The outlet flow is the inlet steam plus the spray.
Can I desuperheat to saturation?
Not with this balance. Spray desuperheaters need some superheat at the outlet (commonly at least a few kelvin) to evaporate every droplet; the calculator requires a target above the saturation temperature.
Does the spray water pressure matter?
Only through the water enthalpy, which changes little with pressure. It must be above the steam pressure for the water to enter the nozzles.