Isentropic Expansion Within a Steam Turbine System

[Matthew Hunter]

Homework Statement

Steam is expanded from 90 bar, 412°C to 4.0 bar saturation in a high pressure turbine, after-which a certain percentage of the steam is bled off to a feed heater. The remaining steam is then expanded through a low pressure turbine to 1.0 bar and dryness fraction of 0.93. All ‘steam’ entering the feed pumps shall be a saturated fluid. Using steam tables only, calculate

a) the percentage of steam bled of to the feed heater

b) the power generated by the turbines per unit mass of steam leaving the boiler

c) the energy available for low grade heating from the condenser

2. The attempt at a solution

I have calculated the following enthalpy and entropy values for the inlet, high pressure turbine, and low pressure turbine:

Inlet - h = 3153.5 kJ/kg, s = 6.338 kJ/kgK
High Pressure - h2 = 2506.394 kJ/kg, h2s = 605 kJ/kg (25% isentropic efficiency)
Low Pressure - h2 = 2516.94 kJ/kg, h2s = 417 kJ/kg (23% isentropic efficiency)

Regarding a), I calculated the specific steam capacity of both the high pressure and low pressure turbine using SSC = 1 / h1 - h2. My assumption was that the SSC value in the low pressure turbine would be lower than the high pressure turbine, and then I would calculate the percentage difference and determine that this would be the amount to send to the feed heater to meet limitations. However, the SSC value in the low pressure turbine was larger. I want to know whether I'm barking up the completely wrong tree or not here.

For b), I realize that the power generated can be calculated from W = m(h1 - h2). I also know that the mass flow rate can be gotten from overall available power = m(h1 - h2). But without either a mass flow value or an overall power value I am struggling to progress here.

 

[BvU]

Hello Matthew,

Let's start with the high-pressure turbine. From 9 MPa (your $h_g$ = 3153 kJ/kg, $s_g$ = 6.338 kJ/kg/K) to 0.4 MPa saturated.

in table A-5 here I find $h_v$ = 2738.1 kJ/kg, $s_v$ = 6.8955 kJ/kg/K, $h_f$ = 604.66 kJ/kg, $s_f$ = 1.7765 kJ/kg/K

Your 2506.394 kJ/kg looks more like the enthalphy at saturation when T = 4 $^\circ$C ?!

Can you show how you calculate the isentropic efficiency ?