Irreversible expansion (steam)
Definition
... expansion is defined by an isentropic efficiency below 100 percent, indicated by a curve showing increasing entropy on a Ts diagram.
Where it occurs.
In turbines and nozzles. In practice, compressors are not used with steam and such an option is omitted.
Special features
Were the isentropic efficiency set to 100 percent a vertical line would follow. Heat transfer is equal to the area under the curve only for reversible processes.
For these curves we cannot get the heat transfer by integration.
How to draw it
In the appropriate text box, set the isentropic efficiency to between 0 and 1. Locate the POI and press "irreversible expansion".
The theory
Let the start condition (POI) be state 1. Further states are calculated for a set of end pressures, \( p_k , k=1,2...\). At each of these a tentative estimate of temperature is made according to isentropic expansion from the previous state .
$$ h_{k,isen} = h (s_{k-1} , T_{k-1} ) $$
The irreversible version of \( h_k \) and \(s_k \) is,
$$ h_k = h_1 + \eta_{isen,t} \times (h_{k,isen}-h_1) $$
$$ s_k = s(h_k , T_k) $$
(and similarly \(T_k \) ).
Exercises
Set an efficiency of 0.85, click on the graph to get a POI and plot an isentropic expansion through it. Click along the curve to set new POIs and note changes in pressure and enthalpy. Repeat with an efficiency of 1.00.
Links
... to follow.