Vapor quality

In thermodynamics, vapour quality is the mass fraction in a saturated mixture that is vapour;[1] in other words, saturated vapour has a "quality" of 100%, and saturated liquid has a "quality" of 0%. Vapour quality is an intensive property which can be used in conjunction with other independent intensive properties to specify the thermodynamic state of the working fluid of a thermodynamic system. It has no meaning for substances which are not saturated mixtures (for example, compressed liquids or superheated fluids). Vapor quality is an important quantity during the adiabatic expansion step in various thermodynamic cycles (like Organic Rankine cycle, Rankine cycle, etc.). Working fluids can be classified by using the appearance of droplets in the vapour during the expansion step.

Quality ${\displaystyle \chi }$ can be calculated by dividing the mass of the vapour by the mass of the total mixture:

${\displaystyle \chi ={\frac {m_{vapour}}{m_{total}}}}$

where ${\displaystyle m}$ indicates mass.

Another definition used by chemical engineers defines quality (q) of a fluid as the fraction that is saturated liquid.[2] By this definition, a saturated vapour has q = 0. A saturated liquid has q = 1.[3]

An alternative definition is the 'equilibrium thermodynamic quality'. It can be used only for single-component mixtures (e.g. water with steam), and can take values <0 (for sub-cooled fluids) and >1 (for super-saturated vapours):

${\displaystyle \chi _{eq}={\frac {h-h_{f}}{h_{fg}}}}$; where h is the mixture specific enthalpy, defined as:

${\displaystyle h={\frac {m_{f}.h_{f}+m_{g}.h_{g}}{m_{f}+m_{g}}}}$.

Subscripts f and g refer to saturated liquid and saturated gas respectively, and fg refers to vaporisation.[4]

Calculation

The above expression for vapour quality can be expressed as:

${\displaystyle \chi ={\frac {y-y_{f}}{y_{g}-y_{f}}}}$

where ${\displaystyle y}$ is equal to either specific enthalpy, specific entropy, specific volume or specific internal energy, ${\displaystyle y_{f}}$ is the value of the specific property of saturated liquid state and ${\displaystyle y_{g}-y_{f}}$ is the value of the specific property of the substance in dome zone, which we can find both liquid ${\displaystyle y_{f}}$ and vapor ${\displaystyle y_{g}}$.

Another expression of the same concept is:

${\displaystyle \chi ={\frac {m_{v}}{m_{l}+m_{v}}}}$

where ${\displaystyle m_{v}}$ is the vapour mass and ${\displaystyle m_{l}}$ is the liquid mass.

Steam quality and work

The origin of the idea of vapour quality was derived from the origins of thermodynamics, where an important application was the steam engine. Low quality steam would contain a high moisture percentage and therefore damage components more easily. High quality steam would not corrode the steam engine. Steam engines use water vapour (steam) to push pistons or turbines, and that movement creates work. The quantitatively described steam quality (steam dryness) is the proportion of saturated steam in a saturated water/steam mixture. In other words, a steam quality of 0 indicates 100% water while a steam quality of 1 (or 100%) indicates 100% steam.

The quality of steam on which steam whistles are blown is variable and may affect frequency. Steam quality determines the velocity of sound, which declines with decreasing dryness due to the inertia of the liquid phase. Also, the specific volume of steam for a given temperature decreases with decreasing dryness.[5][6]

Steam quality is very useful in determining enthalpy of saturated water/steam mixtures since the enthalpy of steam (gaseous state) is many orders of magnitude higher than enthalpy of water (liquid state).

References

1. Cengel, Yunus A.; Boles, Michael A. (2002). Thermodynamics: an engineering approach. Boston, Massachusetts: McGraw-Hill. p. 79. ISBN 0-07-121688-X.
2. Wankat, Philip C. (1988). Equilibrium Staged Separations. Upper Saddle River, New Jersey: Prentice Hall. pp. 119–121. ISBN 0-13-500968-5.
3. Perry's Chemical Engineers' Handbook (7th Edition), p 13-29
4. Ghiaasiaan, S. Mostafa (2008). Two-phase flow, boiling and condensation in conventional and miniature systems. New York: Cambridge University Press. p. 96. ISBN 978-0-521-88276-7.
5. Soo, Shao L. (1989). Particulates and Continuum: A Multiphase Fluid Dynamics. CRC Press.
6. Menon, E. Sashi. (2005). Piping Calculations Manual. New York: McGraw-Hill.