To control an isentropic steam turbine, a throttle valve is placed in the steam line leading to

To control an isentropic steam turbine, a throttle valve is...

Key Concepts

Exergy

Exergy is a measure of the maximum useful work obtainable from a system as it comes into equilibrium with its environment. It quantifies the quality or usefulness of energy, taking into account both the energy content and its potential to perform work relative to a chosen reference state. In thermal processes, exergy analysis identifies inefficiencies, irreversibilities, and helps in optimizing energy conversion systems by comparing actual performance with the ideal reversible process.

Throttling (Isenthalpic Expansion)

Throttling is a process in which a fluid undergoes an expansion to a lower pressure through a restriction, such as a valve, without performing work on the surroundings and with nearly constant enthalpy. This process is inherently irreversible, resulting in an unavoidable loss of exergy. Despite the constant enthalpy, the drop in pressure and the associated increase in entropy lead to a degradation of the fluid’s ability to do useful work.

Stream Exergy Change with Pressure Reduction

Changing the pressure at the turbine inlet alters the thermodynamic state and thus the stream exergy. When a throttle valve partially closes, reducing the pressure at the turbine inlet, the altered pressure–entropy state results in lower availability for work extraction. This is because the exergy content depends on both the energy state and how far the state is from the dead state; a reduction in pressure can mean a reduction in the potential work output even if enthalpy remains nearly constant.

Second-Law Efficiency

Second-law efficiency is a performance metric that compares the actual work output of a device, such as a turbine, to the maximum possible work output as determined by an ideal reversible (i.e., isentropic) process. It reflects the degree of irreversibility in the process. When a throttle valve is used, the process introduces additional irreversible losses, thereby reducing the second-law efficiency compared to the scenario where the valve is fully open and the system experiences less throttle-induced exergy destruction.

Transcript

00:01 In this problem, we have an isentropic steam turbine, and we have a throttle valve here to basically adjust the power we get out of this turbine.

00:11 So we can adjust the pressure coming in here.

00:18 So at one, we're back in si units.

00:23 At one, we have a pressure of six megapascals or 6 ,000 kilopascals.

00:30 And a temperature of 600 degrees c.

00:36 At three, at the exit, we have a pressure of 40 kilopascals.

00:44 And at two here, when we actually have the valve partially shut, we have a pressure of two megapascals.

00:55 So, well, and then we also have, let's see, i should probably make, quote, this is either or 600 ,000.

01:04 Okay, so if the valve is open, then we have no change here.

01:08 If the valve is partially closed, then we closed it enough so that the pressure dropped to 2 megapascals here.

01:17 So we know that the turbine is isotropic.

01:20 So we know that whatever is coming in, the entropy is of whatever is coming in is also going out.

01:26 Take the surrounding temperatures to be 25, temperature to be 25 degrees c.

01:30 Now, we have, so if the open valve case, then we have state two equals state one.

01:39 So we can just say the, so the entropy, we know this, so the entropy coming in is about 3 ,660 bt, no, not bt, kilojoules per kilogram, and then the entropy coming in.

02:01 We have that.

02:03 And we know these are, let's see here.

02:06 I think this should be a two.

02:08 Oops, not erase.

02:10 I just want to make a two there.

02:12 So we know that the entropy leaving is the entropy coming in.

02:17 So that gives us two thermodynamic properties at the exit.

02:20 And we can get a quality factor here of about 92 .5%.

02:26 And the entropy at the exit then is 2 ,460.

02:31 Kilojoules per kilogram.

02:35 We can then figure out the the exergy, the specific exergy at the at point two.

02:45 In this case, we're just going to look at this relative to the dead state, or ground state, well, i guess you really couldn't have a certain ground state.

02:57 Physics, that has a physics meaning to it.

03:00 So the dead state, and again, we can just, we have a 100 kilopascals and 25 degrees c.

03:12 So we can get the entropy of that, and we have the enthalpy at 2 and the entropy at 2, and we can get the entropy at the dead state.

03:25 So this winds up being the exorgy at the turbine inlet is then 1 ,527 kilojoules per kilogram.

03:37 Now, we can find that the second law efficiency is then, so that's, they asked us for that specifically.

03:49 They, uh, let's see here.

03:52 What is the effect of the extreme, uh, stream exergy at the inlet? okay, so, well, this is what we have, um, if we don't do anything, if we don't close the bell.

04:02 Now, we can then figure out what the second law efficiency is by looking at the actual workout, which is from energy balance, is h2 minus h3, divided by the isocentric workout or the reversible workout, which is basically the exergy destroyed or the, yeah, in there.

04:32 So again, we're putting back in this entropy loss.

04:38 So we have the, and again, this thing, but we can see here that this thing is actually we, because we had no entropy change because this was isotropic, this term is zero...

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