Steam nozzles and metastable expansion:\nIn a convergent–divergent nozzle, if the expansion is supersaturated (condensation is delayed), the effective dryness fraction of the steam within the nozzle will tend to be ________ compared with the equilibrium value at the same pressure.

Difficulty: Easy

Correct Answer: Yes

Explanation:


Introduction / Context:
When wet steam expands rapidly in a nozzle, condensation may not occur instantly even when the equilibrium saturation line is crossed. This metastable phenomenon is called supersaturation. Understanding how supersaturation affects the dryness fraction (mass fraction of vapour) is important for predicting exit velocity, heat drop, and erosion risks in steam turbines and ejectors.


Given Data / Assumptions:

  • Flow is through a nozzle with rapid pressure drop.
  • Condensation kinetics are finite; nucleation and droplet growth take time.
  • Comparison is at the same static pressure between supersaturated and equilibrium states.


Concept / Approach:
In equilibrium expansion, part of the vapour condenses as pressure and temperature fall, producing a wet mixture with lower dryness fraction. In supersaturated expansion, condensation is delayed; the steam remains vapour for longer, so at a given pressure it is effectively drier (higher dryness fraction) than the equilibrium wet mixture. Because fewer liquid droplets exist, the specific volume is slightly larger and the isentropic-like heat drop available for kinetic energy tends to increase.


Step-by-Step Solution:

Recognize that equilibrium wet expansion decreases dryness fraction as pressure falls.Account for delayed condensation: metastable vapour persists → fewer droplets.Conclude that the dryness fraction in the nozzle under supersaturation is higher than the equilibrium value at the same pressure.


Verification / Alternative check:
Classical nozzle experiments (Wilson line) show onset of condensation delayed below the saturation line, confirming higher effective dryness fraction until nucleation occurs downstream.


Why Other Options Are Wrong:

  • No: Opposite of observed metastable behaviour.
  • Depends only on inlet superheat: Kinetics and rate of pressure drop matter; it is not solely a function of initial superheat.
  • Cannot be predicted: While exact onset is complex, the qualitative trend (higher dryness fraction before nucleation) is well established.


Common Pitfalls:
Confusing supersaturated (metastable) expansion with superheated steam; supersaturation refers to delayed condensation below saturation temperature, not simply high temperature above saturation.


Final Answer:
Yes

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