Supersaturation (Supercooling) in Steam Nozzles – Net Effect on Discharge and Properties When condensation is delayed and the steam remains metastable (supersaturated) while expanding through a nozzle, what is the predominant effect?

Introduction / Context:
During rapid nozzle expansions, steam can remain in a metastable, supersaturated state below the saturation temperature corresponding to local pressure. This delays droplet formation and shifts thermodynamic properties away from equilibrium values. Designers must understand whether this increases or decreases discharge and how it affects quality and velocity.

Given Data / Assumptions:

• Fast expansion with delayed nucleation (Wilson line behavior).
• One-dimensional nozzle flow reaching or exceeding sonic conditions.
• Comparison with an equilibrium (fully condensed) expansion at the same upstream conditions.

Concept / Approach:

Supersaturation implies the steam remains drier than equilibrium at the same pressure—droplet formation is postponed. The metastable vapor has lower specific volume than the equilibrium wet mixture at that pressure, and the entropy rise due to phase change is delayed. Consequently, for the same pressure ratio, the nozzle can achieve a slightly higher mass flux and higher exit velocity than predicted by equilibrium wet-steam tables. This manifests as an apparent discharge coefficient greater than unity relative to equilibrium calculations.

Step-by-Step Solution:

Verification / Alternative check:

Classic Wilson line experiments show higher-than-equilibrium mass flows, requiring correction factors in nozzle testing. The metastable path features lower entropy than the equilibrium wet path at the same pressure, contradicting the notion that entropy increases in the supersaturated state.

Why Other Options Are Wrong:

(b) is incorrect because, at a given pressure, the supersaturated vapor typically exhibits lower entropy and smaller specific volume than the equilibrium wet mixture. (c) is wrong since exit velocity generally increases slightly. (d) cannot be true if (b) and (c) are false.

Common Pitfalls:

Assuming any condensation automatically reduces discharge; in metastable flow, the opposite trend is observed until nucleation occurs abruptly downstream.

Final Answer:

mass of the steam discharged increases