Curves and Processes (Steam)

Definition

A curve (or line) is a geometric construct. It depicts a process that transforms a system from its start state to its end state.

Where it occurs

Special processes include constant pressure, constant temperature and constant entropy. We also supply curves for irreversible expansion (in turbines).

Special features

The curve retains a handle (small circle) at the location of the original POI (see below). Clicking inside the handle highlights the curve.

How to draw it

Put the POI at its required position and then press one of the plot buttons ( isobar, isotherm, etc). There is a special option - Plot Isobar (text) - to take isobar pressure from a text box rather than the POI.

The theory

... is described separately for each curve. In general, constant pressure (isobar) approximates conditions in condensers and boilers, whereas constant entropy (isentropic) represents an idealises, reversible expansion. The irreversible, anisentropic expansion is described by means of an isentropic efficiency.

Exercises

Consider a basic Rankine cycle operating between pressures of 0.04 bar and 30 bar (this is Exercise 11.3 in Rogers and Mayhew). Plot the two isobars using the "isobar (text)" button. Define the POI at turbine inlet: saturated steam, 30 bar (I get T = 509.6 K, s = 6.188 kJ/kg K and then h = 2809 kJ/kg). Draw an isentropic.

Put the POI at boiler inlet: saturated liquid at 0.04 bar (I get T = 305K, s =0.474 kJ/kg K and then h = 137 kJ/kg). Ideally dryness is very slightly greater than zero; my selected point gave 0.1 per cent.

Put the POI at the turbine outlet - the isentropic line intersects p=0.04 bar (I get T=305 K, s = 6.204 kJ/kg K at which h = 1889 kJ/kg).

There are two results

At turbine outlet, the dryness fraction is 72.2 per cent, versus 71.6 per cent found by Rogers and Mayhew.

The approximate cycle efficiency (ignoring feedwater pump work) is $$ \eta_{cycle} = \frac{w}{q} \approx \frac{2809-1889}{2809-137} = 34.4\% $$ versus 35.0 % according to Rogers and Mayhew. Corresponding enthalpies reported by Rogers and Mayhew are 121, 1863 and 2803 kJ/kg and the feed pump work (not used here) is 3 kJ/kg.

Links

Not applicable.