Dryness fraction of saturated steam

[maserati1969]

Hi all, any thoughts on the following problem please?

When saturated steam is expanded isentropically across a turbine, the dryness fraction should decrease. However, when I calculated the answer to the following question, it actually increased slightly. Any ideas where I went wrong?

Question:
Saturated steam mixture at temperature 330°C with vapour mixture fraction of 0.5 is flowing through a turbine at a flow rate of 6 kg/s. Steam is expanded isentropically to temperature 150°C at the turbine exit. Assume that the turbine external walls are fully insulated (adiabatic turbine). Calculate enthalpy at exit.

My solution:
Using enthalpy formula at inlet (3300C) and data from table: h1 = hf +x.hfg
h1 = 2095.95 kJ/kg
Is isentropic so s1 = s2 So entropy at inlet: s1 = sf +x.sfg
s1 = 4.4969 kJ/kg.K also = s2
Therefore at 150 degrees C: entropy: 4.4969 = 1.8418 + (x.4.9953)
Therefore x = 0.53151 (This should decrease, not increase)
Now use new ‘x’ value for h2:
h2 = 632.18 + (0.53151.2113.8)
h2 = 1755.7 kJ/kg

Many thanks in advance.
Regards

 

[BvU]

Hi,

I get the same result. Perhaps the exercise composer didn't worry about reality. 100% isentropic efficiency ?
And $x_{in}=0.5$ is low: for $x_{in}>0.55$ it doesn't increase any more.

$\$

 

[maserati1969]

Thank you BvU