Steam enters a two-stage adiabatic turbine at 8 MPa and 500^∘ C. It expands in the first stage t

step 1 Here we have another two -stage turbine. So coming in, then coming out, and the stuff coming out

Steam enters a two-stage adiabatic turbine at 8 MPa and...

Steam enters a two-stage adiabatic turbine at $8 \mathrm{MPa}$ and $500^{\circ} \mathrm{C}$. It expands in the first stage to a state of $2 \mathrm{MPa}$ and $350^{\circ} \mathrm{C}$. Steam is then reheated at constant pressure to a temperature of $500^{\circ} \mathrm{C}$ before it is routed to the second stage, where it exits at $30 \mathrm{kPa}$ and a quality of 97 percent. The work output of the turbine is $5 \mathrm{MW}$. Assuming the surroundings to be at $25^{\circ} \mathrm{C}$, determine the reversible power output and the rate of exergy destruction within this turbine.

Key Concepts

Adiabatic Process

An adiabatic process is one in which no heat is transferred to or from the working fluid. In turbomachinery, this assumption simplifies energy analysis by implying that all changes in the energy of the system are due to work interactions and changes in internal energy, not heat transfer.

Reheat Cycle

A reheat cycle in turbines involves expanding the steam in one stage, then reheating it before further expansion in a subsequent stage. This process helps increase the overall thermal efficiency of the turbine and alleviates issues like moisture formation at later stages, improving the performance and longevity of the turbine.

Exergy Analysis

Exergy analysis is a thermodynamic tool used to quantify the maximum useful work obtainable from a system relative to its environment. It takes into account both the first and second laws of thermodynamics, thereby highlighting the quality or utility of energy and helping identify where and how efficiency losses occur.

Irreversibility and Exergy Destruction

Irreversibilities in real processes, such as friction, turbulence, and heat transfer across finite temperature differences, lead to exergy destruction. Exergy destruction quantifies the loss of potential work due to these irreversibilities, and its evaluation is essential for improving system performance by identifying and minimizing sources of inefficiency.

Reversible Process and Reversible Power Output

A reversible process is an idealized thermodynamic process that occurs without any irreversibilities, meaning it can be reversed without leaving any net change in the system and its surroundings. The reversible power output represents the maximum possible work that can be extracted from the system under these ideal conditions, serving as a benchmark for evaluating the efficiency of real processes.

Transcript

00:01 Here we have another two -stage turbine.

00:05 So coming in, then coming out, and the stuff coming out of the first stage goes to the heater.

00:13 So we have heat coming in, heat transfer going in, comes out and goes into the second stage, and then comes out to the atmosphere again, or comes out of the turbine.

00:22 Again, we have some power output, and we're assuming that this is all running in a steady state.

00:29 Now, what we can do in this case is basically it's easiest to basically take a control volume that just consists of, it gets rid of the heater.

00:45 So we take a control volume and then, you know, basically cut through here.

00:50 So we have one in, three in, two out, four out, and work out.

00:57 Now we're given properties, 8 megapascals and 500 degrees c at the inlet here.

01:04 At the exit here we have 2 megapascals and 350 degrees c.

01:09 At 3 after we heat, we have 200 megapascals and 2 megapascals and 500 degrees c.

01:19 So we heated it up a little bit here.

01:23 Maybe we got some, took some heat from, you know, that was being dumped out by the turbine or something and used it to warm up the gas, the steam.

01:33 And then we know the quality factor coming out here and the pressure coming out after the second stage of the turbine.

01:42 So we can, now we have two thermodynamic properties at all four stages.

01:47 So we can just write the entopies and the entropies at every stage by just looking, the steam tables.

01:54 So we have all of this information.

01:58 And so what we want, we're told that we have, what, five megawatts coming out, so 500 kilowatts of power coming out.

02:06 But we're not told what the mass flow rate is.

02:10 So we can use conservation of energy, so the energy flowing in is the energy flowing out.

02:14 And again, a control volume cut here, cutting the heater out, because we don't know anything about this heat transfer.

02:20 We know that, you know, the temperature went up, but they didn't ask us anything about how much heat was transferred into here...

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