A steam power plant operates on an ideal reheat regenerative Rankine cycle and has a net power o

A steam power plant operates on an ideal reheat regenerative...

Key Concepts

Mass Flow Rate Determination

The mass flow rate of steam in a power plant cycle is typically determined by relating the total net power output of the plant to the specific work done per unit mass of steam. By calculating the net work per unit mass from the cycle processes and dividing the total power output by this value, one can estimate the required mass flow rate through the cycle. This is critical for the design and operational aspects of the power plant.

Thermal Efficiency

Thermal efficiency in the context of a power cycle is the ratio of the net work output of the cycle to the heat input into the cycle. It provides a measure of how effectively a power plant converts the heat supplied, usually from fuel combustion, into useful work. Improving thermal efficiency is crucial for reducing fuel consumption and minimizing the environmental impact of power generation.

Open Feedwater Heater

An open feedwater heater is a device used in regenerative cycles where a portion of steam extracted from the turbine is directly mixed with the condensate from the condenser to raise its temperature before it enters the boiler. This direct contact heat exchange method simplifies the cycle by eliminating the need for separate heat exchangers and improves overall cycle efficiency by utilizing the enthalpy of the extracted steam.

T-s Diagram

The Temperature-Entropy (T-s) diagram is a graphical representation of a thermodynamic cycle, showing the relationship between the temperature and entropy of the working fluid. In the context of the Rankine cycle and its variations, the T-s diagram helps visualize the different processes—such as heat addition, expansion, condensation, and compression—and provides insight into the cycle’s performance by illustrating areas that correlate with the net work output.

Reheat Cycle

A reheat cycle is an extension of the basic Rankine cycle where steam that has partially expanded in a turbine is returned to the boiler to be reheated before further expansion. This process enhances the efficiency and work output of the cycle while reducing the moisture content at the later stages of turbine expansion, thereby improving turbine performance and reducing the risk of blade erosion.

Rankine Cycle

The Rankine cycle is a thermodynamic cycle used to convert heat into work, most commonly in steam power plants. It involves the phase change of water to steam by adding heat in a boiler, expansion of the high-pressure steam in a turbine to produce work, condensation of the steam back into water in a condenser, and pumping the water back to the boiler. This fundamental cycle forms the basis of thermal power generation and is widely studied due to its practical application in converting thermal energy to electrical energy.

Regenerative Feedwater Heating

Regenerative feedwater heating is a technique used to improve the efficiency of a Rankine cycle by preheating the feedwater using steam extracted from various stages of the turbine. This process recovers some of the energy from the expanding steam, which would otherwise be wasted, and reduces the required heat input in the boiler. It increases the thermal efficiency of the power cycle while also reducing fuel consumption.

Transcript

00:02 In this problem, we have a steam power plant, again, the reheat regenerative ranking cycle.

00:10 Let's see here.

00:12 So we got, it's best to probably just walk through the schematic here of it.

00:19 I drew both turbines as one.

00:21 You could either say that this is a high pressure and then there's a low pressure afterwards weather and then they're connected by the same, you know, to a shaft.

00:30 But i just drew them as one and just as a high pressure.

00:33 That we kind of had a bleed.

00:37 So what we have here, let's say we start at one, we go through, we pump it up, pump the water out of the condenser up to a pressure of, let's see here, 800 kilopascals.

00:53 It goes into this open feed water heater, and we mix it with some of the steam we took off or came out of the high pressure turbine.

01:09 And so we mix that in this open feed water chamber.

01:12 Then we take that and we pump it back up, we pump it up to the pressure, the boiler pressure, which in this case is 10 megapascals.

01:25 And we then boil it and we feed it into the turbine.

01:32 And some of the, some of the, some of the some of the steam that we take out of the high -pressure turbine, actually let me actually just put a line in here so that makes things a little bit easier to see.

01:52 Let's put it right here.

01:54 So there's like two turbines.

01:57 So we take some of this that's coming out of the high -pressure turbine, the steam, and we heat it again.

02:04 We throw it back into the boiler.

02:09 And we have, let's see here, we have it then coming back and being fed into the, into the, the low pressure turbine.

02:23 There's also, basically there's, you could see, is it, is all of it, the steam, there's some steam in that, that this pressure to feed the speed, the rest of the steam is we heat it to and is spanned it in the low pressure turbine.

02:38 Yeah, so then i guess we take it all out of here.

02:42 We take it all out of here, reheat some of it, and then help some of it here, and then feed it back into this.

02:49 There's nothing coming.

02:50 There's no direct connection here.

02:53 So these are really two separate turbines, and i guess i should have really drawn them as that.

03:00 But anyway, then it comes out, and it goes in the condenser, and you get heat out.

03:05 So we have pump, work from the pumps in, work from the turbine out, heat in and the boiler, heat out at the condenser.

03:12 And so we're told that we have 80 megawatt cycle here.

03:18 Temperature here is 550 degrees c.

03:21 Low pressure side here at the condenser is 10 kilopascals.

03:26 And we have quality factors of one at here and at here.

03:31 So we have condensed liquid here, both of these states.

03:37 So let's see here.

03:39 We can get the entropy in specific volume at one, so we can get the power that is being put into the pump one, and then we can get the entropy at two.

03:52 Entropy and specific volume at three, we can get that.

03:57 You have enough information to get that.

03:59 And then we can get the work put into the pump two, which is 10 .3 kilojoules per kilogram, and then we can get the enthalpy at at 4, which is just this plus this from energy balance on the pump here.

04:17 Now we can find the enthalpy at 5 because we know the pressure and temperature and we can get the entropy.

04:24 We know the both turbines are 100 % efficient.

04:28 So the entropy at 6 is the same as entropy at 5 and that allows us to get the enthalpy at 6.

04:38 We can get the enthalpy at 7.

04:43 Because, let's see here, we know the pressure at seven.

04:47 Is the same as the pressure at six, right? and what else do we know about seven? let's see here.

04:59 What did i, again, i didn't copy everything completely from my notes.

05:05 So let me see how i got, what i used to get that.

05:10 It's just trying to condense these problems a little bit, because really, if you, if you work them all out, like, without redoing them, there is a lot of pages of work that i'm leaving out here.

05:24 But, oh, yeah, at six, let's see here, at six, did we say it was a saturate? wait a minute.

05:37 Is this the right problem? no, that's why.

05:41 Let's see here.

05:47 This analysis is lengthy.

05:49 So six, we know, no, seven.

05:55 You know the pressure and the temperature at seven.

06:00 Did i not write that down here? that's probably why i can't find.

06:05 Yeah.

06:08 At seven, they actually told us some information there.

06:13 T7 is 500 degrees c.

06:16 That's why i couldn't find the other piece of information...