Addition of steam to combustors in gas turbines and to internal-combustion engines reduces the p

step 1 In this problem, we have another combined gas steam cycle. So we have air coming into a compress

Addition of steam to combustors in gas turbines and to...

Key Concepts

Gas Turbine Cycle

This concept involves the basic thermodynamic cycle used in gas turbines, where compressed air is mixed with fuel and combusted to produce high?temperature, high?pressure gases that expand through a turbine to produce work. It encompasses the processes of compression, combustion, expansion, and exhaust, and forms the underlying principle behind many power generation systems.

Steam Injection in Combustors

Steam injection refers to the process of adding water, typically in the form of steam, into the combustor or directly into the working fluid stream before turbine entry. This technique is used to lower peak combustion temperatures, which in turn reduces the formation of nitrogen oxides (NOx) and can improve overall cycle performance by influencing the thermodynamic properties of the working mixture.

Cheng Cycle

The Cheng cycle is a modified version of a gas turbine cycle that incorporates steam injection prior to the turbine. This modification allows for a reduction in combustion temperatures through mixing water vapor with air, leading to lower NOx emissions, and it serves as an example of cycle modification to improve environmental performance and potentially enhance turbine efficiency.

Cogeneration

Cogeneration, also known as combined heat and power (CHP), refers to a system where both electricity and usable thermal energy are produced simultaneously from a single fuel source. This approach increases overall energy efficiency by utilizing the waste heat from power generation for heating or industrial processes.

Mixing Process at Constant Pressure

This concept deals with the thermodynamic process where two fluid streams—such as air and steam—are combined at the same pressure. Energy and mass balances are applied to determine the resultant properties of the mixed stream, such as temperature and enthalpy, which are critical for subsequent processes like turbine expansion.

Turbine Efficiency

Turbine efficiency is a measure of how effectively a turbine converts the energy from the high?enthalpy working fluid into mechanical work. It takes into account losses due to factors such as friction, heat transfer, and irreversibilities during the expansion process. Estimating the required inlet conditions often involves accounting for realistic turbine efficiency values to ensure that performance predictions match practical operation.

Transcript

00:01 In this problem, we have another combined gas steam cycle.

00:05 So we have air coming into a compressor, going out to a combustion chamber, going through the gas turbine, and then going into a heat exchanger before it's exhausted up to the atmosphere.

00:20 So then on the steam side of things, we have the feed water going through a pump, coming through the heat exchanger, into the turbine.

00:32 Some of that steam is let off the turbine and reheated, then back into the turbine, and then into the condenser, and then back into the pump.

00:42 So that's the flow.

00:46 So now we can, our ts diagram looks like this.

00:50 We have some efficiencies for the compressor and for the gas turbine and for the pump and the steam turbine.

01:01 Is that should be a little s there.

01:04 So they're all 80%.

01:05 So we have 80 % efficiency in all our mechanical devices here.

01:12 We have, let's see here, the high temperature here coming out of the combustion chamber is 900 degrees, 950 degrees c.

01:26 At 7 here coming in, we're at 300 kelvin.

01:34 See leaving the heat exchanger, the air is at 200 degree c.

01:43 And let's see here.

01:46 That's pretty much it, i think.

01:48 So i'll be scrolling, coming back here to this page to refer to these diagrams if i need to from the analysis.

01:54 So on the analysis side of things, again, temperature at seven, we can get enthalpy at seven.

02:01 Temperature at seven and pressure at seven, we can get the, um, entropy at 7.

02:09 I forgot to write that.

02:13 So we can get the entropy at 7.

02:16 Then we get the isentropic entropy at 8 and the pressure at 8.

02:20 So we can get the isotropic enthalpy at 8.

02:24 Using the efficiency, then we can get the actual entropy at 8.

02:29 Have the temperature at 9.

02:31 We can get the enthalpy at 9.

02:32 And with the pressure, we can also get the entropy at 9.

02:40 Now, at 10, we have the pressure, and then for the isentropic case, the entropy at 10 is the entropy at 9.

02:47 So for the isotropic case, we can get the enthalpy at 10.

02:53 And then we can get the actual specific entropy at 10 using the efficiency.

03:00 And then coming out of the heat exchanger, we can get the, why am i forgetting to write my variables in here? this would be the enthalpy at 11.

03:14 We can get the enthalpy at 11 coming out, the gas coming out of the heat exchanger.

03:19 So now we have, let's see here, turning to the steam side of things, the pump analysis, just as we have done many times in the past, pressure and temperature coming into the turbine, so we get enthalpy and entropy and entropy, in the isentropic case, it's six, we have a quality factor and an enthalpy.

03:45 And then using the efficiency, we can get the actual entropy.

03:51 And from the actual pressure and the actual entropy, we can get the actual quality factor.

03:58 And then we can figure out how much, what percentage by mass of moisture we have, and it's 1 .58 % moisture by mass exiting the turrets.

04:11 Now, you can look at the energy balance on the heat exchanger, and we were given the mass flows in both sides.

04:22 So an energy balance on the heat exchanger will tell us what h4 is.

04:27 So we know everything else in here, but we don't know h4, so we can get that.

04:33 And then we know, let's see, we have the pressure at 3 and at 4.

04:44 So this is the bleed where they're coming off for reheating.

04:49 And so at four, we know, so this is kind of a little, we got to be a little tricky here, because with the information we've given, we have to do a little bit of work here to get what we need because we don't have the temperature at three.

05:14 We don't have the temperature at 4, but we know in the isentropic case that the enthalpy at 4 is the same as the enthalpy at 3.

05:27 And we also know that the efficiency is the equation for the efficiency in the turbine, the thermal efficiency, and we know this value.

05:37 So what we don't know is we don't know what h4 is, h4s or h4.

05:46 But what we can do is we can guess a temperature here.

05:52 Get an enthalpy at 3, get an entropy at 3.

05:57 So then with that entropy at 3, at 4, in the isentropic case, with that entropy at 4 and pressure at 4, we can get the isotropic entropy at 4.

06:09 Um, enthope at 4.

06:17 And then we can, let's see here.

06:21 Um, now we have an equation.

06:25 We can get the, uh, let's see here.

06:32 We can basically plug everything in here.

06:34 And, um, well, we don't know, enthalpy at 4.