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Point of Interest (POI) for Steam

Definition

The POI is found at an (x,y) co-ordinate.

Where it occurs

It is defined by coordinate (s,T) on the temperature-entropy curve.

Special features

On our graphs, a small red circle indicates its position.

How to draw it

(1) Locate the mouse at a point on the graph and left-click. The table will then report the corresponding pressure, temperature, specific volume, dryness fraction, specific enthalpy, specific internal energy, specific entropy and the IAPWS region.

(2) Click the "Number Input (p,T,x)" button. In reponse to prompts, input two values from the dataset pressure(p), temperature(T), and quality(x). For the third value type -1. Pressure should not exceed 300 bar.

Restrictions, limitations and innaccuracy

The simulation is provided for pedagogical purposes only. It should not be employed in formal design calculations, or for summative college assessments. No attempt is made to evaluate properties for pressures greater than 300 bar. At present I am not completely satisfied with my handling of region 3, described in IAPWS documents below. Erractic behaviour might happen at certain (s,T) values.

The theory

The phases of steam investigated are subcooled water, saturated liquid, wet steam, saturated vapour, superheated steam and supercritical steam.

Subcooled water, superheated steam and supercritical steam can be considered as "simple systems". According to the state postulate the thermodynamic state of a simple system can be specified by any two independent properties plus mass. Specifying temperature, specific entropy and mass flow rate allows us to compute all other thermodynamic properties. For saturated water or saturated steam the thermodynamic state can be specified by only one independent property plus mass.

The datum condition for enthalpy and entropy is taken at the triple point

For the purposes of power generation, steam is treated as non-ideal.

I use the IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam and see here for the revised release and in particular their Figure 1 detailing the boundaries between regions that very broadly represent subcooled water (1), superheated steam (2), the critical and supercritical regions of steam (3), and saturated steam/ water (4). For regions 1 and 2 the Gibbs Function is represented as a polynomial function of scaled pressure and temperature. Roughly 40 terms are used. For region 3 the Helmholtz Free energy is represented as a polynomical function of scaled temperature and density. Other thermodynamic properties follow by appropriate differentiation. Working with independent variables other than (p,T) or (den,T) is challenging. Rather than the IAPWS "backward equations", I have used their forward equations in conjunction with a search by golden section.

Exercises

Move the POI to different parts of the graph. Note the changes to values in the table. In particular move the POI along horizonal lines and vertical lines.

Links

IAWPS Revised release .