In a Rankine power system, 1.5 kg / s of steam leaves the turbine as saturated vapor at 0.51 ba

step 1 So let's see here. We now have this crazy setup here. That's very interesting. It's illustrated

In a Rankine power system, 1.5 kg / s of steam leaves the...

Key Concepts

Rankine Cycle

The Rankine cycle is a thermodynamic cycle used for power generation in steam power plants. It involves the conversion of heat into mechanical work by circulating water/steam through a series of processes, including boiling, expansion in a turbine, condensation, and pumping. Understanding the Rankine cycle is fundamental to analyzing how energy is transferred and transformed in conventional steam power systems.

Phase Change and Condensation

In many thermal systems, phase change plays a critical role in energy transfer. Condensation, which is the process where vapor transforms into liquid, involves the release of latent heat. Accurately quantifying the energy removed during this phase change is crucial for determining parameters such as outlet temperatures and required heat exchanger surface areas in condensers.

Heat Exchanger Design

Heat exchanger design involves determining the suitable geometry and configuration (for example, shell-and-tube arrangements) to achieve efficient heat transfer between two fluids. Key parameters include flow rates, tube dimensions, and overall surface area, which are essential for ensuring that the required thermal duties are met while maintaining mechanical and thermal integrity.

Convection Heat Transfer

Convection heat transfer is the mechanism by which heat is transferred between a surface and a fluid moving over it. The convection heat transfer coefficient is used to characterize this process and plays an important role in designing and evaluating heat exchangers since it directly influences the rate of heat exchange between the condensing steam and the cooling water.

Fouling Factors

Fouling refers to the accumulation of unwanted deposits on heat transfer surfaces, which adds additional thermal resistance and diminishes the efficiency of a heat exchanger. The fouling factor quantifies this additional resistance and must be incorporated into design calculations to ensure the system operates effectively over its service life, accounting for reductions in heat transfer performance.

Parameter Variation and Sensitivity Analysis

Assessing how variations in parameters such as fluid flow rates and inlet temperatures affect system performance is an essential part of thermal system design. Sensitivity analysis allows engineers to identify optimal operating conditions, ensure safety margins, and improve the overall efficiency of the condenser by exploring the effects of changes within plausible ranges.

Transcript

00:01 So let's see here.

00:02 We now have this crazy setup here.

00:06 That's very interesting.

00:08 It's illustrated in the book, and i've tried to reproduce it somewhat in my schematic here.

00:15 So let's see here.

00:18 We have, let me just kind of talk through it here a little bit.

00:25 Coming out at the condenser.

00:29 So we have a, let's see here, i didn't really.

00:32 Draw that, but we have, this is a flow in and out.

00:39 Let's basically, let's actually draw it as a closed system here, so flow in and out from cooling water.

00:49 So here's our condenser.

00:51 It's being, you know, cooled with cooling water here.

00:54 We have the output from the turbine coming in, and then we also have the output from the steam traps coming into it.

01:03 Then we have it coming out to the pump.

01:07 Going through two closed feed water heaters.

01:13 And so heating up to heating it up some and then heating it up again.

01:18 And the heat exchange from those closed feed water heaters come from two, two taps in our two pressure bleeds or two bleeds in our turbine.

01:29 One at a little two different points here.

01:34 One at 1 .4 megapascals and one at 245 kilopascals.

01:42 And then they come into here, and then we have these steam traps where, again, the steam traps help, you know, if there's any steam left, you know, if this hasn't condensed fully or this hasn't condensed fully, then we will get it here.

02:04 But again, that's usually, in this problem, we're not going to really analyze this.

02:10 We're going to assume that essentially it's condensed and we got full, you know, we got full heat transfer here.

02:17 And this was all kind of condensed.

02:20 This was condensed liquid and then this winds up being condensed liquid afterwards.

02:26 As it goes from 6 to 0 .9.

02:30 Yeah, so here to here.

02:33 So if there was any steam in here, then we'd get kind of trap it into here.

02:38 So we didn't put it back into there, which i'll put it back into the, i'm not sure why you actually even need to do that.

02:48 But there's a problem.

02:49 I'm sure there's a good reason.

02:50 I'm not a power plant engineer, so i'm not exactly sure why these would come into play.

02:58 So anyway, you can see in the ts diagram, we have a pretty big mess here.

03:02 So anyway, we get this coming out, heating up, heating up some more, going into the boiler, getting, you know, heating up some more into a saturated vapor turbine, and then some of it, some of it bleeds off here, some of it pleads off here, and the rest of it goes back to condenser.

03:19 And then the bleed stuff comes in.

03:23 He's all wind up nine, eight, nine, and eleven are saturated vapor or saturated liquid.

03:33 And so then we come back here and then we mix that back in with this and then we go.

03:41 So how does this look on here? so we go from one to two to three heating up some more to four heating up some more and then we boil it or then we keep heating it into the boiler and then we boil it and then we superheat it.

04:02 Comes into the turbine, some comes off here, so the fraction y comes off here, and we have 1 minus y continuing through the turbine.

04:14 Then we have another fraction z coming off at 7, and we have 1 minus y minus z continuing through the turbine.

04:22 Then we have 1 minus y minus z going into the contensor.

04:27 So then at this 6 point we have 6 going to 9.

04:33 So it gets basically it cools down and then it condenses while it's giving up heat.

04:45 And you can see that we have these temperatures here are the same, which is where kind of inefficiencies would happen because you wouldn't really have the same temperature coming out here because you wouldn't get a perfect transfer of energy here, thermal energy.

05:00 Now, so then from cit 9, we go to 10, which is basically just is cooling things down a bit.

05:11 So the steam trap, we basically cool things down a little bit in there.

05:17 And we increase some entropy.

05:20 Now, it's odd.

05:25 Yeah, i mean, is there, i think, i think, let's see here.

05:29 Did i try to remember the whole analysis here.

05:33 Oh, we never had to calculate.

05:37 The heat transfer out.

05:41 That is why i didn't do that.

05:45 Because the heat transfer out, you probably have some heat transfer out here and here too.

05:51 So you're, you know, you're dumping heat here and here and here.

05:57 Because again, as we go from here to here.

06:05 So then it comes down to 10 and then it comes to 11 where it mixes in here.

06:12 With stuff coming off from seven.

06:15 So seven and ten it's coming here and here mix and then we go to 11 and then we come down here to 12 through this steam trap and then these this mixes with this in the condenser so we have the point 176 over the last 15 then we have we have everything we need so hopefully i've described this system in enough detail that you can follow what is going on here.

06:48 We're also told what y is.

06:51 So whatever, it's 14 .5 % basically.

06:54 So about 14 .5 % is coming out of here.

06:58 We don't know what z is yet, but i'll figure that out.

07:01 Okay, so let's start with the pump.

07:04 So we can get the power into the pump as usual.

07:06 And we can get the anthropia 2 as usual.

07:09 The anthopy at 3 and at 11 are the same, again, because we're assuming perfect, you know, transfer energy here.

07:21 And it's also the same as the anthope at 12, we're going to assume.

07:29 Let's see here.

07:31 And that all winds up being this plus this.

07:34 No.

07:36 Enthope at 3 we can get because, what are we? using it three here i didn't write a lot of the probably i should have written more of this stuff down um oh yeah because it's it's basically at 11 it is a it is a condensed uh it's a saturated fluid at 11 and we know the enthalpyate 11 and 3 and 12 are going to be the same or going to assume that they're same.

08:18 So let's see here.

08:20 Then we get the entropy at four eight, four, nine, and ten.

08:24 Okay, so then four, nine, and ten.

08:30 Because we know, let's see, four, again, it's now again at four, not nine, we have a saturated, saturated, saturated liquid.

08:46 So, and then at ten, again, again, again, again, again.

08:49 We're assuming that we're not having any changes there.

08:52 You know, this is kind of a enthalpy, constant end -of -constant, and then at four, it's also the same.

09:01 Okay, so again, these are a lot of assumptions that we're not necessarily told to us, but we're kind of, you know, making them anyway, because again, there's, you can, they're, we're assuming that there's no heat transfer here, which is kind of weird by assuming that these are the same because there's a drop in temperature, of course.

09:31 But if you did an energy balance on this and there's no work, no external work and no heat transfer, then these entopies would be the same.

09:40 So it's kind of, i'm not exactly sure how our steam trap works, but anyway, we're basically assuming there's no heat energy flowing, no heat flowing in or out here or here.

09:54 Okay, and then we have perfect heat transfer through there...

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